Time Series Analysis of Influence of Water Cycle on Nitrate Contamination in Miyako Island Ryukyu Limestone Aquifer

Abstract

This study investigates the complex factors influencing groundwater NO₃-N concentrations on Miyako Island, which has a geological structure of highly permeable Ryukyu Limestone over less permeable mudstone. The groundwater NO₃-N levels peaked at nearly 10 mg/L in 1989 and have since declined. Our analysis used agricultural statistics, machine learning, and time-series correlation to elucidate the causes of these changes. We found that the decline in concentrations since 1989 was directly linked to a reduction in sugarcane cultivation. However, the mechanism of increase is more complex. A cross-correlation analysis over 60 years revealed two distinct infiltration mechanisms: a rapid one with zero-time lag, responsible for approximately 70% of the NO₃-N concentration, and a slow one with a 15-year lag, accounting for the remaining 30%. The slow infiltration is likely due to temporary nitrogen storage in the clay layer. These findings have significant implications for water quality management. The recent shift from summer planting to ratoon cultivation has increased fertilizer use, and this, combined with the 15-year lag effect, suggests that NO₃-N concentrations may begin to rise again in about a decade, possibly exceeding the environmental standard. Therefore, continuous monitoring is crucial to prevent future pollution. The methodology developed in this study is also applicable to other islands with similar environments.

1. Introduction

Miyako Island is a subtropical island located approximately 2000 km southwest of Tokyo, with an area of 158 km² (Figure 1). The average annual temperature is 23 °C, and the average annual precipitation is 2200 mm. The Miyako Islands consist of Miyako Island and its surrounding islands, including Irabu Island, Ikema Island, and Kurima Island (Figure 1b). Miyako Island is characterized by a relatively flat plateau topography, with its highest point being 113 m above mean sea level (EL). Approximately 57% of the total area is farmland, and 14% is forest. Sugarcane and tobacco production collectively account for 82% of agricultural production on the island [1].

Miyako Island has been central to two key themes in Japanese groundwater research: first, the challenges of nitrate contamination in groundwater, and second, the construction of the world’s first large-scale subsurface dam.

The geology of Miyako Island is characterized by permeable Quaternary Ryukyu Limestone overlying mudstone of the Tertiary Shimajiri Group. Due to this characteristic, Miyako Island has no surface water system, which makes groundwater the sole source of drinking water for its inhabitants. In 1967, the Miyako Island local government launched a project to supply tap water to the entire island using three groundwater sources: Shirakawada, Kajido, and Sodeyama (Figure 1b). With an annual water supply of 7.98 million cubic meters, the system provides water to approximately 50,000 people [2]. However, because the groundwater from this project could not be used for field irrigation, a plan was developed in 1979 to build a subsurface dam as an alternative water source [3].

A subsurface dam Is a facility designed to increase an aquifer’s storage capacity by inserting a cutoff wall into the aquifer within an underground valley, which obstructs the flow of groundwater or prevents seawater intrusion.. Miyako Island’s geological structure, with numerous faults along a northwest–southeast trend forming underground valleys, is well-suited for subsurface dam construction. On Miyako Island, Japan’s first irrigation project, which utilized two large subsurface dams to extract water from two underground valleys, began in 1987. Sunagawa Dam (total water storage capacity: 9.7 million m³) was completed in 1993, followed by Fukusato Dam (11 million m³) in 1996. Currently, groundwater from these two subsurface dams irrigates agricultural land throughout the island via a pipeline system [4]. Based on the success of the Miyako Island subsurface dam project, 10 subsurface dams have already been completed on islands in the Ryukyu Arc [3].

Figure 1. Location map and topography of Miyako Island. (a) Location of Miyako Island in East Asia, (b) Location of Miyako and Yoron Islands in the Ryukyu Arc, and (c) Topography of Miyako Island. Figure (b) is a simplified version of a figure from [5], and figure (c) is a modified version of a figure from [3].

Figure 1. Location map and topography of Miyako Island. (a) Location of Miyako Island in East Asia, (b) Location of Miyako and Yoron Islands in the Ryukyu Arc, and (c) Topography of Miyako Island. Figure (b) is a simplified version of a figure from [5], and figure (c) is a modified version of a figure from [3].

In the early 1990s, as Sunagawa Dam construction began, groundwater NO₃-N concentrations were steadily rising in parts of Miyako Island, with predictions that certain areas would soon exceed the environmental standard of 10 mg/L. NO₃-N pollution stems from anthropogenic sources such as excess fertilizer and improper treatment of livestock waste and domestic wastewater. According to Japan’s Ministry of the Environment (ME)’s first nationwide groundwater quality survey in 1982, NO₃-N had the highest detection ratio: approximately 80% of sampled groundwater contained NO₃-N, and 10% exceeded the tap water quality standard of 10 mg/L [6]. In 1993, the ME designated NO₃-N as a monitoring item and initiated annual monitoring. By 1999, a limit of 10 mg/L was established for NO₃-N in groundwater.

The earliest groundwater quality survey on Miyako Island, conducted by the local government in 1966 at 21 locations, showed NO₃-N concentrations ranging from 0.23 mg/L to 3.74 mg/L, with an average of 1.95 mg/L. However, a 1989 groundwater NO₃-N survey revealed the highest NO₃-N value to be 22.7 mg/L, with 20.8% of samples being between 8.00 and 9.99 mg/L and 5.1% exceeding the drinking water standard of 10 mg/L. Over approximately 20 years, following 1966, the groundwater NO₃-N concentration increased about fourfold [2] (Figure 2).

The local government of Miyako Island established the “Miyako Islands Groundwater Quality Conservation Measures Council” (hereafter, the “Council”) in 1988. The Council’s primary activity was investigating the causes of contamination. It initiated regular monthly groundwater quality monitoring at 52 locations throughout the Miyako Islands and conducted statistical surveys of contamination sources. Specifically, for fertilizers, it performed detailed surveys of fertilizer types, application timing, and application amounts. Notably, these survey results were published annually and were accessible online to both residents and non-residents. Although the Council was dissolved in 2005, Miyakojima City continues to conduct surveys and provide reports [7,8]. In 2021, Miyakojima City published a report titled “Consideration of the Proportion of Nitrate Nitrogen by Origin in Groundwater,” summarizing the survey results to date [9].

The groundwater NO₃-N concentrations at regular monitoring points peaked in 1988–1989 and then gradually decreased. Recent fluctuations have been around 4–5 mg/L, but by 2023, it had dropped to an average of 3.4 mg/L [8]. The ME summarized the reasons for this decrease in the Miyako Islands as follows [2]:

• Improved fertilization methods for sugarcane cultivation (adjustment of fertilization timing and switching to slow-release fertilizers);
• Livestock waste management measures (prohibition of inappropriate livestock waste management such as open piles and dumping in open pits, and promotion of composting of livestock waste);
• Domestic wastewater treatment measures (promotion of switching from underground infiltration treatment to sewerage treatment).

However, the 2014 report [7] revealed that expensive slow-release fertilizers are hardly used. It will take a long time for the Council’s recommendations to be fully implemented. Therefore, the decrease in NO₃-N concentrations since 1989 cannot be solely attributed to these recommendations.

This paper aims to scientifically analyze the causes of the decline in groundwater NO₃-N concentration and examine remaining issues regarding the contamination mechanisms to maintain this declining trend. There are four remaining issues:

• Validity of obtaining the leaching ratio from the nitrogen load using a multiple regression model, especially the leaching ratio for fertilizer;
• Presence of seasonal variation in groundwater NO₃-N concentration fluctuations;
• The influence of fast and slow infiltration rates on the recharge mechanism, especially the possibility of a slow infiltration recharge;
• Impact of precipitation on the increase or decrease in the groundwater NO₃-N concentration.

Nakanishi et al. [10] calculated the leaching rate on Miyako Island as the three partial regression coefficients of a multiple regression analysis. In this analysis, the nitrogen loads from fertilizer, livestock waste, and domestic wastewater were used as the three explanatory variables, and the nitrogen load calculated from NO₃-N concentrations in groundwater was used as the dependent variable. However, estimating leaching rates with multiple regression analysis has two important weaknesses. First, it is not applicable when the relationship between the nitrogen load sources (explanatory variables) and the dependent variable is nonlinear. Second, although Nakanishi et al. [10] calculated three partial regression coefficients using 16 data points from two years’ worth of data, multiple regression calculations typically require 15 or more data points per explanatory variable (e.g., [11]). Therefore, if the data are insufficient, the partial regression coefficients may be calculated by overfitting.

To overcome these limitations, we conducted multiple regression analysis using 207 observations collected across multiple sites over a 30-year period (Miyakojima City Report [9]). In addition, to account for potential nonlinear relationships, we applied machine learning (ML) regression models, including decision tree regression (CART), random forest (RF), XGBoost, and LightGBM [12,13]. In this study, we specifically estimated the leaching rate using decision tree and random forest regressions.

The monthly variation in groundwater NO₃-N concentrations on Miyako Island shows little seasonal cycle patterns (Tashiro and Takahira [14]). However, the weekly variation at Noshiro Spring, located below the Higa Plateau cliffs (Figure 2), does show seasonality [15]. To resolve this discrepancy, this study analyzes why monthly variations lack seasonality by decomposing NO₃-N time series.

On Miyako Island, two contrasting theories describe the travel time of fertilizer-derived NO₃-N moving through the Ryukyu Limestone unsaturated zone. Nakanishi [15] proposed rapid infiltration, whereas Tashiro and Takahira [14] suggested slow infiltration. A delayed peak in groundwater NO₃-N relative to nitrogen inputs is known as the “legacy effect” (e.g., [16]). The rapid infiltration hypothesis has become mainstream because annual nitrogen loads from fertilizers, livestock wastewater, domestic wastewater, and natural soils, divided by recharge (annual precipitation × infiltration rate of 0.4 [17]), closely match average groundwater NO₃-N concentrations and tap water values for the same period. If this hypothesis were correct, NO₃-N concentrations would correlate with precipitation. In reality, however, the annual NO₃-N shows little correlation with precipitation (e.g., [14]).

The slow infiltration rate theory is based on the observation that the time-dependent flux of nitrogen loads, based on fluctuations in fertilizer sales, livestock numbers, and the population from 1976 to 1998, peaked in 1980 [14]. In contrast, the average groundwater NO₃-N concentration at 13 observation points peaked in 1987 (subsequent data showed the peaks for three water sources were in 1988–1989; Figure 2). If these two peaks correspond to one another, the nitrogen load propagated to the groundwater with a time lag of about 7 years. Assuming an average unsaturated zone depth of approximately 22 m, the average infiltration rate of NO₃-N would be approximately 3 m/year [14] (assuming the peak occurred in 1989, the time lag would be 9 years, with an average rainfall infiltration rate of about 2.5 m/year). Although no additional evidence for slow recharge was presented previously, Kim et al. (2020) [18] recently used cross-correlation analysis and SF₆ dating to show that limestone aquifers in France also have lag times of 8–24 years due to matrix storage.

Physical modeling studies have struggled to quantify the time lag between surface nitrogen inputs and groundwater NO₃-N concentrations, often relying on simplifications such as assuming saturated soil conditions [19] However, a realistic approach requires modeling the water flow in the unsaturated zone using Richards’ equation (e.g., Hydrous 1D [20]) and site-specific parameters such as the precipitation, groundwater level, runoff, soil type, land use, slope, elevation, lithology, and aquifer characteristics. These models demand extensive data and computation, which makes them difficult to apply on Miyako Island.

Statistical models have also been used to investigate time lags between nitrogen sources, precipitation recharge, and NO₃-N concentrations. Methods include time-series analysis, linear regression, Mann–Kendall tests, and auto- and cross-correlation analyses. Among these, the cross-correlation function (CCF) is particularly useful for estimating mean delay times [18]. Here, we apply CCF analysis to nitrogen load and NO₃-N time-series data, relating the results to the recently described hydrogeological structure of Miyako Island (Mori et al. [21]; Yoshimoto et al. [22]) to clarify unresolved aspects of the pollution mechanism.

Although the annual NO₃-N concentrations on Miyako Island are generally not correlated with the annual precipitation (e.g., [14]), Nakanishi [15] found a negative correlation between the precipitation and NO₃-N concentrations when weekly data were converted to monthly data. Common methods for assessing the groundwater response to changes in precipitation include physical and statistical models (e.g., [23]). Again, physical models are difficult to apply to Miyako Island due to the extensive computational time and numerous input parameters required. Therefore, we applied cross-correlation analysis as a simple and cost-effective method to correlate annual NO₃-N concentrations with annual precipitation.

However, cross-correlation analysis has the following drawbacks [23]:

• It can only be applied to stationary and ergodic sequences;
• It cannot reveal cross-correlations across different time scales.

Recognizing these issues, we thoroughly investigated the cross-correlation between accumulated precipitation and NO₃-N concentrations at different time scales. Since cross-correlation analysis may not be applicable to non-stationary time series where the signal frequency changes with time, we also used wavelet transform analysis. This is the first time that wavelet analysis has been applied to cross-correlation between precipitation and NO₃-N concentrations in this context.

This paper is structured as follows: Section 2 provides an overview of Miyako Island’s topography and geology. Section 3 summarizes changes in the island’s agricultural structure based on agricultural statistical data. Section 4 describes the data sources and analysis methodology. Section 5 presents the results of our analyses, including the leaching ratio calculated by multiple regression analysis and a machine learning model, the seasonal cycle derived from the NO₃-N concentration time series, and the cross-correlation between time series data on agricultural statistics and NO₃-N concentrations, as well as between NO₃-N concentrations and cumulative precipitation. Section 6 discusses the relationship between our findings and the existing literature, hydraulic issues, the application of wavelet transforms, geological structures that cause slow infiltration, the general validation of the cross-correlation method using Yoron Island as an example, and the mechanisms by which NO₃-N concentrations are increased and decreased. Finally, Section 7 summarizes the findings.

2. Overview of Miyako Island’s Geography and Geology

2.1. Topographical Characteristics of Miyako Island

The Ryukyu Arc is an island arc that stretches about 1200 km from Kyushu to Taiwan (Figure 1). It is divided into three regions—North Ryukyu, Central Ryukyu, and South Ryukyu—by two deep submarine canyons, the Tokara Strait and the Kerama Gap, which were formed by left-lateral strike-slip faults [24]. Miyako Island is located in Central Ryukyu.

According to Yazaki’s classification of Miyako Island’s topography by altitude, elevations of 0–20 m comprise 17% of the total area, 20–40 m 19%, 40–60 m 42%, 60–80 m 20%, and 80–100 m 1.7%. Areas above 100 m constitute only 0.3% [25]. The area between 20 and 100 m above sea level consists of several plateaus. These plateaus are characterized by a sloping topography (cuesta terrain) from east to west, which was formed by topographic tilting caused by fault movement [25]. However, not all plateaus are tilted. The highest, Higa Plateau, in the southeast of the island (80–110 m above sea level), is not tilted, while the Nohara Plateau to its west is.

In the Nohara Plateau, three limestone walls—the North Mountain Range (7 km long), the Middle Mountain Range (15 km long), and the South Mountain Range (15 km long)—have developed parallel to the island’s northwest–southeast extension. These limestone walls are hardened outcrops along faults, forming limestone dikes with a convex topography that have resisted dissolution [26]. The width of these ranges varies from 500 m to 400 m or less. The Nohara Plateau, excluding these limestone walls, presents a flat topography with an elevation of 50–70 m. It is divided by these faults and limestone walls into the following narrow, strip-shaped basins from west to east: the Sunagawa basin, the Nakahara basin, the Fukusato basin, and the Bora basin (Figure 3). To the west of the Nohara Plateau, the Shimoji Plateau maintains a flat topography with an elevation of 15–20 m and is not tilted. Kurima Island, west of the Shimoji Plateau, exhibits a tilted topography.

The karst topography of Miyako Island is characterized by the presence of limestone walls and limestone mounds that have convex topographies and numerous caves [26]. Most caves are short and horizontal because the Ryukyu Limestone layer is thin (30–50 m). According to an academic survey by Ehime University, 68 caves have been confirmed on Miyako Island. However, based on interviews with local residents conducted by Ehime University, there may be over 500 caves [27].

The Okinawa Quaternary Research Group [28] found that the floor levels of horizontal caves could be divided into three distinct levels, based on their survey of nine caves on Miyako Island. Imaizumi et al. [29] similarly demonstrated that the caves were distributed at three levels—EL. 40 m, EL. 30 m, and EL. 20 m—based on electrical exploration in the Sunagawa and Nakahara Basins. Mori et al. [21] found that the caves were concentrated at EL. 15–20 m and EL. 35–45 m, based on their analysis of drilling cores in the Sunagawa Basin. The EL. 20 m elevation corresponds to the groundwater level before the completion of the subsurface dam. Caves at EL. 40 m and EL. 30 m are considered to be distributed within the unsaturated zone.

2.2. Characteristics of Precipitation on Miyako Island

The average annual precipitation from 1989 to 2019 was 2003 mm at the Japan Meteorological Agency’s Gusukube Observatory (Figure 1), and data from this observatory are primarily used for time series analysis. The fluctuation pattern of annual precipitation shows no discernible regularity. The precipitation in the wet year of 2016 reached 2752 mm, while, in the drought year of 2003, it was 1338 mm. The fluctuation pattern of the average monthly precipitation exhibits two distinct peaks, in May and August–September.

According to 87 years’ (1938–2024) worth of data from the Japan Meteorological Agency’s Miyakojima Observatory (Figure 1), the average daily precipitation is 172 mm, and the maximum daily precipitation was 452 mm (2017). Daily precipitation of 200 mm or more occurred 28% of the time. Precipitation of 100 mm or more occurred 86% of the time. There have been four major drought years with annual precipitation less than 1400 mm: 1946 (1238 mm), 1971 (1321 mm), 1976 (1303 mm), and 1991 (1362 mm). The 1971 drought was particularly severe, with 186 consecutive dry days recorded from 15 March to 16 September. The drought notably impacted the islands of Miyako and Ishigaki [30]. The impact of this drought is also clearly evident in the fluctuation in sugarcane area, as will be described in Section 3.

2.3. Geological Characteristics of Miyako Island

The geology of Miyako Island primarily consists of the highly permeable Pleistocene Ryukyu Limestone, which overlays the impermeable Pliocene to Pleistocene Shimajiri Mudstone [31]. Within depressions in the Ryukyu Limestone topography, the Ohnokoshi Clay Layer, estimated to date from the Pleistocene to Holocene era, is distributed (Figure 3).

The Shimajiri Group is mainly composed of mudstone layers, reaching a thickness of 2000 m. This geological formation resulted from the deposition of a large amount of sand and mud from the Chinese mainland onto the semi-deep-sea floor during the late Miocene to Pliocene. The mudstone of the Shimajiri Group exhibits a nearly constant permeability of less than 1.0 × 10⁻⁷ m/s [1].

The contour lines on the geological map indicate the top elevation of the mudstone layer below the Ryukyu Limestone. The subsurface dam axis indicates the location of the cut-off walls of the Sunagawa and Fukusato subsurface dams. The circular dots indicate the location of the water supply source and the recharge test site.

Figure 3. Geological map and cross-section of Miyako Island (modified from [31]). Contour lines on the geological map represent the top elevation of the mudstone layer underlying the Ryukyu Limestone. The sub-surface dam axis indicates the location of the cut-off walls of the Sunagawa and Fukusato subsurface dams. Dots mark the locations of the water supply sources, the Noshiro spring [15], and the recharge test site [22].

Figure 3. Geological map and cross-section of Miyako Island (modified from [31]). Contour lines on the geological map represent the top elevation of the mudstone layer underlying the Ryukyu Limestone. The sub-surface dam axis indicates the location of the cut-off walls of the Sunagawa and Fukusato subsurface dams. Dots mark the locations of the water supply sources, the Noshiro spring [15], and the recharge test site [22].

The Ryukyu Group, which overlies the Shimajiri Group, is distributed as terrace deposits [23]. The Ryukyu Limestone ranges in thickness from 20 to over 50 m, though it reaches 100 m on Irabu Island. This porous Ryukyu Limestone exhibits characteristics typical of a coral reef complex. It consists of boulder-shaped algal limestone, sandy limestone, muddy limestone, and coral limestone [21]. The sandy and muddy limestone contains diverse granular fossil fragments, such as coral fragments and foraminifera.

The Ryukyu Limestone was primarily formed approximately 1 million to 500,000 years ago. During its final depositional stage, the main part of the limestone was divided into blocks by fault movement, a process known as the Uruma Crustal Deformation [24]. This movement caused crustal uplift and subsidence. Notably, several faults trending northwest–southeast were formed on Miyako Island [32]. Karst topography subsequently developed in the uplifted Ryukyu Limestone due to groundwater circulation.

The Ohnokoshi Clay Layer is a reddish-brown to dark-brown unconsolidated clay deposited in depressions within the Ryukyu Limestone topography. Its typical thickness ranges from a few meters to 10 m, and it has a maximum thickness of 20 m [21]. The Kunigami Mahji soil, which originates from the Ohnokoshi Clay Layer, characteristically easily develops shrinkage cracks. Consequently, its saturated hydraulic conductivity (0.011 cm/s) is an order of magnitude higher than that of the Shimajiri–Mahji soil, as described below [33]. While the saturated hydraulic conductivity of the Ohnokoshi Clay Layer at the sample level is less than 1 × 10⁻⁵ cm/s [21], its field permeability is thought to be high. Additionally, the Kunigami Mahji distribution area constitutes only 7.3% (664 ha) of the Miyako Islands’ total area [26], which suggests that its impact on the recharge of the Ohnokoshi clay is minor. However, as will be discussed in the next section, this clay, which flows into the limestone’s unsaturated zone, controls limestone permeability [21] and affects infiltration in the Ryukyu Limestone’s unsaturated zone [22]. The origin of this clay layer was traditionally thought to be a weathered layer of limestone [25], but recent research has proposed the theory that it originates from eolian dust (LOESS) from the continent [34].

Miyako Island’s main soil type is Shimajiri–Mahji soil. Other soil types include Kunigami–Mahji soil, Jahgaru soil (hereafter, the word “soil” will be omitted from these soil names), and alluvial soil. Shimajiri–Mahji, which overlies the Ryukyu Limestone, is a dark red soil of limestone origin. Kunigami–Mahji is also a dark red soil, but the two are distinguished by their soil pH. Shimajiri–Mahji is weakly acidic to alkaline, while Kunigami–Mahji is strongly acidic. Jahgaru is a grayish-brown to gray soil distributed in areas where Shimajiri Group mudstone is directly exposed on the ground surface [26]. Alluvial soil is a sandy soil scattered in the coastal lowlands. Shimajiri–Mahji accounts for 90.8% (8254 ha) of the Miyako Islands’ total area of 9093 ha. The proportions of other soils are: Kunigami–Mahji, 7.3%; Jahgaru, 1.3%; and alluvial soil, 0.6% [26]. Therefore, given the overwhelming prevalence of Shimajiri–Mahji, we will describe only its hydraulic properties in the following sections.

This soil is a heavy clay with a clay content exceeding 50% [35]. Consequently, it exhibits strong adhesion when wet, but upon drying, it hardens, develops cracks, and has low water retention [36]. In the topsoil, the saturated hydraulic conductivity exceeds 10⁻³ cm/s. Asada et al. [36] clarified this characteristic by measuring its soil matrix potential. When the surface layer’s matrix potential is between 0 kPa (saturated) and −0.3 kPa, the unsaturated hydraulic conductivity increases to approximately 10⁻³ cm/s. At a matrix potential of −0.3 kPa or less, the unsaturated hydraulic conductivity is 10⁻⁴ cm/s [36]. This observation indicates that, when the matrix potential is in a negative pressure state from saturated to −0.3 kPa, numerous coarse pores and cracks contribute to infiltration, leading to preferential flow. The Shimajiri–Mahji layer is very thin, about 0.5 to 1 m thick [21], so precipitation immediately seeps through the soil into the unsaturated limestone.

2.4. Relationship Between Permeability of Ryukyu Limestone and Degree of Clogging of Limestone Cavities by Inflowing Clay

Research on Ryukyu Limestone conducted up to the early 1980s indicated that its permeability ranged from 10⁻² cm/s to 10⁰ cm/s, with an average value of 3.54 × 10⁻¹ cm/s [37]. It was then believed that the permeability of Ryukyu Limestone was largely determined by the distribution of cracks and pores. Mori et al. [21] reviewed approximately 500 geological drilling cores (totaling over 20,000 m) and the results of more than 200 pumping tests in the Sunagawa Basin, conducted for the design of intake facilities for a subsurface dam. Their findings led them to conclude that “the relationship between the distribution of cracks and pores and the permeability of Ryukyu Limestone is negligible, and the permeability of Ryukyu Limestone can be predicted with sufficient accuracy by considering only the presence or absence of allochthonous inflowing clay.” Here, inflow clay refers to an allochthonous reddish-brown unconsolidated clay that secondarily flowed into the gaps and cracks of the Ryukyu Limestone, originating from the Ohnokoshi Clay Layer (Figure 4). These clays are termed “inflow clays” to distinguish them from clays deposited concurrently with the limestone formation [21].

Clays similar to the inflow clays of Miyako Island are also distributed in cracks and cavities within the Ryukyu Limestone in southern Okinawa Island [38] and within the Chalk aquifer in Europe [39]. Mori et al. [21] classified boring cores into four types based on their observations of the degree of clay filling (density) within cavities:

• Type-a layer: a clay core where the entire large cavity of the Ryukyu Limestone is filled solely with clay;
• Type-b₁ layer: a layer where gaps, cracks, and the matrix are completely filled with clay;
• Type-b₂ layer: a layer where clay adheres to gaps, cracks, and the matrix in a film-like form;
• Type-c layer: a layer where the gaps in the Ryukyu Limestone contain no clay at all.

Based on a regression analysis of permeability coefficients from 225 locations in the inflow clay layers of a borehole and the specific yield, the permeability coefficients for each layer type are as follows [21]: Type-a layer: 1.69 × 10⁻⁴ cm/s; Type-b₁ layer: 1.04 × 10⁻³ cm/s; Type-b₂ layer: 1.29 × 10⁻² cm/s; and Type-c layer: 7.06 × 10⁻¹ cm/s. This indicates that permeability coefficients decrease with an increasing clay content density.

Figure 5 presents a plan view and a geological cross-section in the north–south direction of the Ohnokoshi clay distribution area within the Sunagawa Dam basin [1]. The cross-section also depicts the groundwater level before the cut-off wall’s completion and the full water level after the dam’s completion. The Ohnokoshi Clay Layer in the Sunagawa Basin is distributed beneath the fault scarp on the basin’s west side. In the center of the surface clay distribution (around well D), the Ohnokoshi Clay Layer is deposited to a thickness of over 12 m (Figure 5a). In the upstream portion (north of well D) of the geological cross-section (Figure 5b), a Type-a layer is distributed in a lens shape with a maximum thickness of approximately 20 m. The Type-b₁ layer occurs as four distinct layers derived from the Type-a layer. In the midstream portion (near well L) and close to the dam cut-off wall, a Type-c layer is distributed. Near well W, even though the Ohnokoshi Clay Layer on the surface is thin, a Type-b₁ layer exceeding 10 m in thickness is distributed underground.

Mori et al. [21] proposed the following mechanism for the formation of the inflow clay: Turbid water from heavy rainfall, containing clay from the Ohnokoshi Clay Layer, moved to the groundwater level through drains and vertical holes. The clay then dispersed laterally with the groundwater flow through lateral cavities in the saturated zone. Most of these cavities are now filled with clay. According to their hypothesis, the inflow clay layers, which comprise three or more distinct layers between EL. 0 m and EL. 40 m, formed at past groundwater levels.

Figure 5 presents the thickness contour map (a) of the Ohnokoshi Clay and geological cross-section (b) [1]. Panel (a) also indicates the locations of six groundwater-level observation stations and the SF₆ dating observation wells (D, L, W) used by Ishida et al. [40]. Panel (b) additionally displays groundwater levels and dating results from both before and after the subsurface dam’s completion. In 2012, 18 years after the Sunagawa Dam’s completion, Ishida et al. [40] performed inert gas sulfur hexafluoride (SF₆) dating on five groundwater samples from the following wells: Well D (5 m below the water table), Well L (5 m and 20 m below the water table), and Well W (5 m and 20 m below the water table) (Figure 5a). The results are presented in Figure 5b. Note that the well positions on the cross-section are projected from their locations in Figure 5a. The groundwater residence times were very recent for Well D (5 m below the water table), 1 year for Well L (5 m and 20 m below the water table), and 5 and 7 years for Well W (5 m and 20 m below the water table), respectively.

The 1-year residence time in Well L suggests the residence time of groundwater through the Type-c layer. The very recent residence time at −5 m in Well D, considering the projection, probably indicates the residence time of groundwater through the Type-b₂ layer. The 5-year residence time at −5 m in Well W represents the residence time of groundwater through the Type-b₁ layer. The 7-year residence time at −20 m in Well W, considering the projection, is likely to be the residence time of the Type-b₁ layer. In the geological section (Figure 5b), groundwater flows selectively through the Type-c layer (7.06 × 10⁻¹ cm/s) and the Type-b₂ layer (1.29 × 10⁻² cm/s), which have high permeability. Therefore, it is reasonable to assume that relatively young water is distributed in these layers. The SF₆ age results are consistent with this idea.

2.5. Vertical Permeability Characteristics of Ryukyu Limestone

To evaluate the results of the cross-correlation analysis between the NO₃-N concentration time series, the nitrogen load index, and precipitation time series, it is necessary to understand the infiltration phenomenon in the unsaturated zone of the Ryukyu Limestone. Yoshimoto et al. [22] conducted a tracer recharge test on the Ryukyu Limestone in farmland in the Fukusato Basin, Miyako Island. Here, we explain the results of this test, including some new figures.

The characteristics of this test are as follows:

• The geological structure of the unsaturated Ryukyu Limestone at the recharge test site consists of two layers: muddy limestone and calcareous algal limestone, which have different permeabilities. Three layers of inflow clay are embedded within them;
• A borehole simulating a karst shaft was placed in the center of the recharge pit, which resulted in a triple porosity of the Ryukyu Limestone consisting of matrix, cracks, and a simulated shaft;
• During the 5.58 h recharge period, the recharge intensity was changed in two stages: high intensity simulating heavy rain and low intensity simulating normal rain. As a result, shaft flow occurred during heavy rain and fissure flow occurred during normal rain. After the recharge was stopped, the recharged water in the unsaturated zone slowly descended as matrix flow;
• The recharge water’s descent was visualized by the volumetric water content change obtained by neutron moisture logging and breakthrough curves based on monitoring of the pyranine dye concentration and seawater electrical conductivity values. Analysis of the breakthrough curves revealed the ratios of shaft flow, fracture flow, and matrix flow.

Figure 6b shows the geology of the test site. Ryukyu Limestone is distributed from GL. −0.65 m to GL. −31.50 m, while Shimajiri Group mudstone is distributed below GL. −31.50 m. The groundwater level before recharge is at GL. −14.4 m. The unsaturated limestone is divided into three layers: the upper calcareous algal ball limestone layer (hereafter referred to as algal limestone), the muddy limestone layer, and the lower algal limestone. According to the core sketch, vertical cracks are rare. The frequency of major horizontal cracks is 5–20 fractures/m (Figure 6a). Cracks tend to be more abundant in the algal limestone layer and less frequent in the muddy limestone layer. Vertical cracks are short cracks connecting horizontal cracks.

According to the classification of inflow clay by Mori et al. [21] (Figure 6c), the algal ball limestone layer is mainly classified as a Type-c layer, and the muddy limestone layer is classified as a Type-b₂ layer. Therefore, due to the difference in permeability between Type-c and Type-b₂, some of the recharged water may stagnate in the upper algal ball limestone layer. The inflow clay layers can be identified by depressions in the resistivity logging curve (colored blue on the outside of the curve) (Figure 6d). These Type-b₁ inflow clay layers were named, from top to bottom, A-clay, B-clay, and C-clay layers.

The recharge water consisted of 0.5 m³ of a solution containing 500 g of the dye pyranine dissolved in water, along with 4.5 m³ of seawater transported from the nearby sea. The recharge test started at 12:00 on 6 December 2005. After the pyranine solution was initially introduced, seawater was recharged for 5.58 h to push the pyranine solution downward. Recharge was performed at a high intensity of 6.10 m³/h from the start of the test until the 1 h mark. Subsequently, recharge was performed at a low intensity of 0.67 m³/h from 1 h to 5.58 h. The infiltration of the recharge water was very fast, and no standing water formed in the recharge pit.

2.5.1. Neutron Moisture Logging

Measurements of neutron moisture logging were taken hourly for the first 24 h after the test began. From 24 to 48 h, measurements were taken every 2 h. For details on the neutron moisture logging method, see Appendix A.1.

Figure 6e shows the background (BG) volumetric water content (VWC) profile (brown curve) measured 1 h before the start of recharge. The BG profile is 20–30% except for the top 50% of the upper algal limestone layer. It is 10–15% in the muddy limestone layer. The VWC of the lower algal limestone layer is 20–30%. However, the VWC of the Type-B1 clay layer at GL −7 m and GL −9 m is high, ranging from 35–40%. The area between GL −14.2 m and GL −14.4 m is the capillary zone.

The change in volumetric water content (VWC) during the recharge test was only 1–2%. Simply displaying the VWC profiles side by side would not make this subtle difference visible. To better visualize this change, two display methods were applied. For details on the display method, see Appendix A.2. One method displays the residual VWC profile by subtracting the profile measured before the recharge test (the background profile, or BG) from the profile at each time after the start of recharge. This display method is called “BG-corrected VWC.” In Figure 6e, the green and pink curves show the BG-corrected profiles at 0 h and 1 h, respectively. This method effectively highlights the VWC changes in the Type-B1 clay layer. A time–space distribution map of the BG-corrected VWC (BG-corrected VWC map) allows for visualization of areas where artificially recharged water is trapped or temporarily stored in the unsaturated zone. The other display method, called “differential VWC,” displays the difference profile between two consecutive measurements [41,42]. This differential VWC map allows for the visualization of artificial recharge water movement by observing the displacement of the moisture increase area (excess moisture zone) between two measurements.

Figure 7a,b present the BG-corrected VWC map and the differential VWC map, respectively. Figure 7a clearly shows where the recharged water was temporarily stored within the unsaturated aquifer, which is indicated by reddish-brown areas that represent a volumetric water content that is 0.5% higher than the background VWC.

During the recharge water injection, several high-VWC zones formed (Figure 7a). The high-VWC zone in the upper algal limestone layer developed due to temporary storage of recharged water by the relatively impermeable muddy limestone beneath it. However, this zone faded within a few hours (after 5.5 h) following the cessation of recharge. The A-clay layer exhibited similar behavior.

Zones that maintained a high VWC after 5.5 h included the B-clay layer, the C-clay layer, and the capillary zone. The high-VWC zone in the capillary zone persisted for up to 32 h. The B- and C-clay layers maintained a high-VWC zone of 0.5% for up to 50 h. While subsequent patterns showed alternating 0.5% and 0.3% VWC zones, this was an artifact of imperfect interpolation caused by a change in logging frequency from every 2 h to every 4 h. Thus, the high-VWC state in the B- and C-clay layers continued for over 69 h, which indicates significant water storage.

Figure 7b reveals that the most prominent movement of recharged water occurred between 0 and 1 h. At 0 h (specifically, 30–40 min after recharge), the differential VWC increased by approximately 0.15% (brown area) between GL −1.5 m and GL −5.5 m. This increased VWC area was temporarily stored in the B-clay layer, reaching the capillary zone at GL −14.4 m after 1 h.

In Figure 7b, the high differential VWC area (orange) hangs down from the capillary zone (brown), which shows that water drained from the capillary zone toward the groundwater table. The differential VWC diagram indicates that the recharged water descended to GL −14.4 m in about 2 h (7.2 m/h). Such rapid movement was likely caused by recharge through the karst shaft (in this case, the borehole). Gunn [43] referred to this type of flow as shaft flow, a film-like flow occurring along the walls of vertical shafts.

Figure 7b indicates that this shaft flow recharge occurred only once. This phenomenon can be attributed to the difference in recharge intensity. Approximately one hour after the start of recharge, 2 m³ of water was injected at a high intensity of 6.10 m³/h, which completely saturated the fracture and consequently ceased fracture flow. As a result, the recharge water likely concentrated in the shaft and flowed downward as shaft flow. Subsequently, shaft flow did not recur because the recharge intensity decreased to 1/10 (0.67 m³/h), allowing the recharge water to descend solely through the fractures.

Two other recharge paths can also be inferred. One is the vertical path of fracture flow, occurring from 2 to 14 h after recharge (vertical arrow) with a flow velocity of 7.2 m/h. The other is the descending path indicated by the diagonal white arrow in the figure, which began 15 h after the start of recharge. This path represents a flow that connects high differential VWC points occurring in a pulsed manner. The descent speed, for example, follows the diagonal direction shown in the square frame in the figure (5 m descent × 35 h). This corresponds to a descent rate of 5 m/35 h = 0.14 m/h = 0.004 cm/s. This speed is on the same order as the saturated hydraulic conductivity of the b1 layer, 0.001 cm/s [20]. This flow is a matrix flow. Gunn [43] referred to this flow as unsaturated zone seepage.

The differential VWC data show that the occurrence and movement of an increased number of differential VWC points were observed even after 52 h, suggesting continued recharge. From the viewpoint of recharge, a significant finding presented in Figure 7 is that the increased moisture points temporarily stored in the B- and C-clay layers descended from these layers (indicated by the white dotted arrows in the figure). This descent rate is also estimated to be 0.14 m/h. In other words, it became clear that the B- and C-clay layers have a buffering capacity that stores some of the recharge water and delays its movement.

2.5.2. Tracer Breakthrough Curves

Groundwater for tracer analysis was collected 48 times at the same frequency as the neutron moisture logging. Pyranine analysis was performed using a spectrofluorometer. The analytical lower limit was approximately 1 ppb. The electrical conductivity (EC) of the sampled surface water and groundwater was measured by using a portable EC sensor immediately after the sampling. The electrical conductivity (EC) of the recharged seawater was approximately 50 mS/cm. The measurement frequency was the same as that for pyranine, but was increased to once a day from 10 December 2005 to 16 December 2005. As a result, the fluctuation of the EC was tracked over a period of 240 h.

Figure 8 shows the semi-logarithmic breakthrough curves of the pyranine concentration and seawater EC from the start of recharge to 240 h. The pyranine reached a maximum concentration of 73 mg/L after 0.7 h, which indicates that the initial pyranine concentration (1000 mg/L) was diluted to about 7% through mixing with groundwater. After 1.7 h, it dropped sharply to 13 mg/L. It then decreased to 3.2 mg/L after 5.7 h, and 1.0 mg/L after 7 h. Subsequently, it showed a gradual tailing decrease until 63.7 h (0.0006 mg/L). After 68.9 h, the concentration sharply dropped to 0.0002 mg/L. Although the detection limit for pyranine is 1 ppb, the smooth and continuous concentration decrease until 63.7 h suggests that all pyranine had eluted by this time.

Based on the area ratio calculation of the pyranine breakthrough curve up to 60 h, the recharge ratio is 69.3% in the 0–1.7 h period; 22.6% in the 1.7–6 h period; 3.0% in the 6–10 h period; 2.0% in the 10–30 h period; and 3.1% in the 30–60 h period.

These ratios correspond to the flow classifications estimated from the volumetric moisture content change obtained by neutron moisture logging: 69.37% in the 0–1.7 h period corresponds to shaft flow, 25.6% in the 1.7–10 h period corresponds to fracture or macropore flow, and 5.1% in the 10–60 h period corresponds to matrix flow. The 5.1% matrix flow is almost identical to Gunn’s [43] estimate.

The average EC value in the groundwater before the test was 0.635 mS/cm, and this served as the background value. The EC breakthrough curve (Figure 8) plots the measured values minus this background. The EC reached a maximum conductivity of 5.4 mS/cm after 0.7 h. Since the EC of seawater is approximately 50 mS/cm, this indicates that the seawater reaching the groundwater table was diluted to about 11% through mixing with groundwater. It then sharply decreased to 3.44 mS/cm after 1.7 h. The EC remained around 3.5–3.9 mS/cm until 5.7 h but decreased afterwards, as seawater recharge ceased at 5.6 h. After 10 h, the EC suddenly dropped to 0.93 mS/cm (Figure 8). Subsequently, the EC gradually decreased with a tailing effect until 63.7 h (0.20 mS/cm). Notably, at 68.8 h, the EC rose again to 0.41 mS/cm, which roughly coincides with the time all pyranine had reached the groundwater table. This increase in EC after pyranine depletion suggests that the initial 2 m³ of seawater that was recharged at a high intensity for the first 0.33 h was diluted by 0.5 m³ of pyranine solution, but the recharge seawater solution after 0.33 h was not diluted by the pyranine solution. If correct, this implies that all of the initial 2 m³ of recharged water reached the groundwater table in approximately 64 h.

Subsequent EC readings show the influence of weakly recharged seawater. It fluctuated but consistently remained higher than the background value (more than 0.01 mS/cm) for over 240 h. The EC fluctuations in the breakthrough curve include a tenfold decrease from 0.04 mS/cm at 68.8 h to 0.005 mS/cm at 119.5 h, followed by a tenfold increase to 0.05 mS/cm at 191.5 h (Figure 8). This fluctuation indicates that some recharged seawater was stored in the unsaturated zone and was released in a pulsating manner for over 240 h.

Based on the area ratio calculation of the EC breakthrough curve up to 240 h, the recharge ratios were 19.7% for 0–1.7 h; 43.4% for 1.7–6 h; 19.6% for 6–10 h; 13.5% for 10–30 h; and 3.8% for 30–60 h. It is estimated that 17.6% of the 0–1.7 h flow was shaft flow, 56.1% of the 1.7–10 h flow was fracture or macropore flow, and 26.3% of the 10–240 h flow was matrix flow. This matrix flow ratio is considerably higher than estimates from the pyranine breakthrough curve and Gunn’s [43] estimate of less than 5 percent.

2.6. Relationship Between Spring Discharge, Groundwater Level, and Precipitation in Springs and Wells of the Ryukyu Limestone Aquifer

The monthly discharge of the Shirakawada spring shows a strong correlation with the four-month cumulative precipitation (R² = 0.49), with a slightly lower correlation for the three-month cumulative monthly precipitation (R² = 0.45) [44]. The relationship between the groundwater level and precipitation at the Nishi-Sokobaru, Takano, and Kajido wells (Figure 3) varies by well location. Specifically, the Nishi-Sokobaru well’s groundwater level correlates most strongly with the three-month cumulative precipitation (R² = 0.22). For the Takano well, the highest correlation is with the 4-month cumulative precipitation (R² = 0.27), while the Kajido well shows the strongest correlation with the 15-month cumulative precipitation (R² = 0.66) [44]. The correlation between spring the water amount and groundwater level and the cumulative precipitation over a certain period was also examined in the following time series analysis.

3. Historical Changes in Agricultural Structure on Miyako Island

3.1. Agriculture on Miyako Island

Agriculture is the primary industry on Miyako Island. The island’s agricultural system primarily revolves around sugarcane cultivation, which is complemented by a mixed farming approach that includes raising beef cattle, cultivating tobacco leaves, and growing vegetables. Sugarcane fields constitute the majority of cultivated land. Consequently, historical changes in fertilizer application are linked to the evolution of sugarcane cultivation methods. These methods include the following:

• Summer planting: Cuttings are planted in summer (July to September), with harvesting from January to March of the following year. This method’s cultivation period is approximately 1.5 years and occupies farmland for two years;
• Spring planting: Cuttings are planted from February to April, with harvesting from January to March of the following year. While the yield per area is lower than summer planting, this method allows for annual harvesting;
• Ratoon cultivation: New sugarcane grows from buds on harvested sugarcane stumps. Ratooning occurs in spring (March to April), with harvesting from January to March of the following year. This method can be repeated three to four times for harvesting.

Compared to summer planting, ratoon cultivation offers a lower yield but has the advantage of reduced production costs and energy input as it eliminates the need for replanting. Since ratoon cultivation allows for annual harvesting, its total yield over multiple years surpasses that of summer planting. For these reasons, farmers typically prefer ratoon cultivation.

3.2. Timing and Amount of Fertilizer Application on Miyako Island

The most important information to refer to when applying fertilizers appropriately while also taking the environment into consideration is the prefectural fertilization standard. This standard indicates the amount of fertilizer needed to ensure that the target yield and quality are reached in fields with good chemical and physical soil properties. The Okinawa Prefecture fertilization standard for sugarcane was first established in 1963. In 1988, the standard values were revised to allow for a reduction in the amount of fertilizer applied, based on the accumulation of field data for the sugarcane variety NCo310 [45] (

Table 1. Changes in the standard amount of nitrogen fertilizer for sugarcane planted in Shimajiri–Mahji in Okinawa Prefecture [45,46].

Standard	Period	Summer Planting Cultivation	Spring Planting Cultivation	Ratooning Cultivation	Target Sugarcane Species
		(for 2 Years)	(for 1 Year)	(for 1 Year)
Old standard	1963~1985	310	220	250	NCo310
New standard	1986~1992	240	180	200	NCo310
Revised standard	1993~	240	200	220	F172

). Phosphate and potassium fertilizers are not covered in this paper.

The 1988 revision reduced the nitrogen standard for summer planting in Shimajiri–Mahji soil from 310 kg/ha/2 years to 240 kg/ha/2 years. For spring planting, it decreased from 220 kg/ha/year to 180 kg/ha/year, and for ratooning, from 250 kg/ha/year to 200 kg/ha/year. In 1992, minor adjustments were made to the standard values following tests where the target variety was changed to F172 [46,47]. From a nitrogen leaching perspective, it is important to note that the annual fertilizer amount for summer planting is half the standard value due to its longer 1.5-year cultivation period before harvest. Therefore, farmers switching from spring planting and ratooning to summer planting can achieve fertilizer reduction. While farmers tended to choose ratoon cultivation, the pesticide ban in the early 1970s (see Section 3.4) prompted Miyako Island farmers to switch from ratoon cultivation to summer planting.

The standard amount of fertilizer for sugarcane is applied in several separate applications. Fertilizer mixed into the soil before or at planting is referred to as basal fertilizer. Fertilizer applied after seeds sprout is top dressing. Figure 9 illustrates the application time and amount of fertilizer for each crop, based on a 2006 questionnaire survey of farmers in the Sunagawa basin conducted by Fujiie et al. [48]. On Miyako Island, basal fertilization of 72 kgN/ha is common in July. The first top dressing of 48 kgN/ha is applied in mid-October, and the second, 120 kgN/ha, in early February. In many cases, the third top dressing is not applied [15,33].

According to a cultivation experiment of summer-planted sugarcane [45], applying a third top dressing in July that exceeded the standard amount increased the sugarcane yield but decreased the sugar content by 1%. In 1995, sugar companies changed their purchase standard for sugarcane from stalk weight to sugar content [15]. According to a questionnaire survey, farmers have tended to reduce their nitrogen fertilizer use since 1995 because excessive nitrogen application hinders increases in sugar content [15].

The fertilization periods for spring planting and ratooning are almost identical. On Miyako Island, in 1977, basal fertilization (75 kg/ha) was applied in mid-February, followed by a first top dressing (75 kg/ha) in mid-April and a second (100 kg/ha) in mid-July [33]. Additionally, 50 kg/ha of compost was added to the basal fertilization, bringing the total to 300 kg/ha [33].

The nitrogen fertilization standard for pasture in Okinawa is 350 kg/ha/year [48]. A questionnaire survey [33] revealed that 72% of farmers cultivate Rhodes grass. For Rhodes grass, chemical fertilizer (50 kg/ha) is applied as a basal fertilizer in March, with additional fertilizer (100 kg/ha) being applied after each pasture harvest [48]. If pasture is harvested three times annually (May, July, and September), top dressing will be applied three times. Figure 9 also illustrates the fertilization timing and amount for tobacco leaves. The nitrogen fertilization standards for vegetables and tobacco leaves are 295 kg/ha/year and 120 kg/ha/year, respectively [9].

3.3. Changes in the Agricultural Structure of Miyako Island

3.3.1. Cultivated Land Area

Figure 10a shows the trends in cultivated land area and planted area for each crop in the Miyako Islands [49,50]. The oldest record is from 1955 [50], when the cultivated land ratio was about 52% (11.7 × 10³ ha), but it decreased to a minimum of 46% (10.4 × 10³ ha) in 1976. This decrease may be related to the abandonment of cultivation due to the severe droughts in 1971 and 1976. The cultivated land ratio then increased, reaching a maximum of 53.9% from 1996 to 2001 (12.2 × 10³ ha). It has decreased since then. The cultivated land ratio in 2023 is 51.3% (11.6 × 10³ ha). The rate of decrease from 2001 to 2023 is about −27 ha/year.

3.3.2. Trends in Sugarcane Cultivation Area

In the 1950s, the agricultural landscape of the Miyako Islands was primarily characterized by self-sufficient sweet potato cultivation. By 1955, sweet potatoes occupied 54% of the cultivated land (Figure 10a). However, the early 1960s saw a significant shift. Driven by the Vietnam War’s economic boom and a surge in international sugar prices due to the 1962 Cuban Missile Crisis, farmers increasingly adopted ratoon-type sugarcane cultivation. This choice facilitated part-time farming due to its ease of cultivation, leading to a monoculture-based agricultural structure (the first sugarcane boom) [51]. In 1964, the Japanese government further supported this transition with the “Special Measures Act Concerning Sweetening Resources Crop,” a national law for bulk sugarcane purchases. Consequently, sweet potato cultivation plummeted to less than 1% by 1975, while sugarcane cultivation expanded to 9583 ha in 1969 (Figure 10a).

The initial sugarcane boom was short-lived. The liberalization of sugar trade, a sudden drop in international sugar prices, and the unprecedented 1971 drought caused many farmers to abandon farming. This led to a sharp decline in sugarcane cultivation, which fell to 5917 ha in 1971. In 1972, Okinawa was returned to Japan, and to bolster Okinawan agriculture, the Japanese government doubled the sugarcane purchase price in 1974. This spurred farmer interest, triggering a second sugarcane boom that surpassed the first [51]. Sugarcane cultivation gradually increased, reaching 10,325 ha in 1985. However, this boom also ended within a decade.

By the 1990s, farmers’ net income from sugarcane decreased, and the engagement of the next generation in farming stagnated. The area under sugarcane sharply declined by 16% (1415 ha) from 9936 ha in 1989 to 8521 ha in 1992 (−35.4 ha/y). This notable decline was observed across all remote islands of Okinawa Prefecture, not just the Miyako Islands [52]. The significant reduction in cultivated land may be partly attributed to some second-generation farmers shifting to the construction industry. The area under sugarcane has continued to decline since, decreasing at a rate of −29 ha/y until 2023 (7628 ha). This rate is slightly higher than the overall decline in cultivated land (−27 ha/y), indicating a shift from sugarcane to pasture and tobacco.

Figure 10b illustrates the trends in different sugarcane cultivation types. Ratooning cultivation rapidly increased from 100 ha in 1960 to 4500 ha in 1965, coinciding with the first sugarcane boom. However, the area of ratooning cultivation peaked at 5000 ha in 1970 and then rapidly decreased. This decline was due to the discontinuation of organochlorine insecticides after 1971 [50], which were highly effective for pest control.

Pests, such as the larvae of the sugarcane beetle and wireworm beetle, pose a significant obstacle to sugarcane cultivation by feeding on roots and shoots [53]. This can stunt plant growth or even kill the plants. Organochlorine insecticides, though effective, were discontinued in 1971 due to concerns about their environmental persistence.

On Miyako Island, the timing of ratooning cultivation’s germination coincided with these pests’ active period, which led to a sharp increase in pest density and an outbreak after insecticide cessation [54]. Conversely, the germination timing for summer planting did not overlap with the pests’ active period, minimizing its impact. Consequently, farmers transitioned from ratooning to summer planting [54]. Ratooning areas, which constituted 60–70% of the total agricultural area in the early 1970s, rapidly decreased to only a few percent by the 1980s, with most sugarcane then being cultivated in the summer. The impact of pests varies across the Ryukyu Arc; notably, the impact was less severe in the Northern Ryukyu Islands than on Miyako Island, so that the area of transplanted cultivation did not tend to fell below 50% (see the example of Yoron Island in Section 6.7). The area of summer planting cultivation peaked in 1985 and has since gradually declined, primarily due to a shift towards pasture and tobacco leaves [55].

Due to the lack of effective pest control measures, summer planting remained the norm on Miyako Island until 2010 (Figure 10b) [54]. In the late 2000s, the development of fipronil bait and light traps provided effective pest control. As these measures became more widespread, the proportion of ratooning cultivation area increased from 2.9% in 2009 to 8.8% in 2011, and further to 50% in 2017 [56]. Given government encouragement for ratooning cultivation, which allows annual harvests, this shift from summer planting is projected to continue. Conversely, the area cultivated in spring has remained around 10% of the total for the past 30 years, which suggests continued cultivation in parts of the Miyako Islands [57].

The sugarcane harvest exhibits a similar trend to that of the sugarcane cultivation area but shows three clear peaks: in 1970 (453 × 10³ t), 1978 (448 × 10³ t), and 1989 (507 × 10³ t). In 1971, the harvest dropped sharply to 58 × 10³ t due to a poor harvest caused by a severe drought. After reaching its peak in 1989, the harvest began to decline until 2004 (218 × 10³ t). Since then, the harvest has increased despite the decrease in the cultivated area. This is thought to be due to the expansion of ratoon cultivation. The harvest in the Gusukube district, where the Kajido Water Source is located, is one-third that of Miyako Island, and shows a similar trend.

3.3.3. Expansion of Pasture Areas

Okinawa Prefecture, with its subtropical climate, had a pasture yield of 10,600 kg/10a in 2018, three times higher than the national average of 3390 kg/10a [58]. This high yield spurred the growth of livestock farming in the early 1980s [59]. The number of beef calves in Okinawa Prefecture grew from approximately 7000 in 1987 to over 25,000 in 2012 [49].

On Miyako Island, farmers also converted sugarcane fields into pastures in the early 1980s to diversify from sugarcane monoculture to a combination of sugarcane and livestock farming. The pasture area nearly doubled, increasing from 202 ha in 1982 to 445.6 ha in 1989. Furthermore, during the period of rapid decline in sugarcane fields (1989–1992), the pasture area increased to 900 ha.

The trend of sugarcane field growth on Miyako Island peaked around 1980–1990 and then began to decline. Meanwhile, the area of pasture increased to 1118 ha in 2005. While it decreased slightly to 878.3 ha in 2010, the trend has been relatively consistent since 2011 (Figure 10a).

Figure 11 illustrates the relationship between the sugarcane area and pasture grassland area from 1991 to 2021. The relationship between the pasture area and sugarcane area from 1978 (8865 ha) to 1990 (9457 ha) showed a positive correlation (y = 0.23x − 1754, R² = 0.74). However, from 1991 to 2021, this relationship changed to a negative correlation (y= −0.29x + 3291, R² = 0.57). The figure shows that, as the sugarcane field area decreased by −42 ha/y, the pasture area increased by 15 ha/y, indicating that one-third of the decrease in sugarcane area was due to conversion to pasture.

3.3.4. Tobacco and Vegetable Area

Records of the vegetable area began in 1960 [49]. This area increased until 1981 but has been slowly decreasing since then. The area cultivated with tobacco gradually increased until 1998 but has remained stable since. In 2018, the area cultivated with tobacco was 467 hectares. Figure 11 illustrates that some of the decrease in sugarcane area was due to it being converted to tobacco area. A negative correlation (y = −0.15x + 1804, R² = 0.66) was observed between sugarcane and tobacco cultivation areas from 1991 (411 ha) to 2011 (633 ha). As the sugarcane area decreased, the tobacco area increased at a rate of 11.1 ha/y.

3.4. Leaching Ratio for Livestock Manure Compost

The standard fertilizer application for pastures is 350 kg/ha/year, while, for tobacco leaves, it is 120 kg/ha/year, the same as for summer-planted sugarcane. Consequently, it is unclear from a fertilizer application perspective how converting a sugarcane field to a pasture or tobacco field would affect NO₃-N concentrations.

Nitrogen in organic fertilizers, such as livestock manure compost, decomposes more slowly than nitrogen in chemical fertilizers. Therefore, nitrogen from livestock manure compost is known to have a smaller impact on groundwater NO₃-N concentrations than nitrogen from chemical fertilizers [60]. Unless applied excessively over prolonged periods, the NO₃-N leaching from farmlands treated with livestock manure compost is generally lower than that from those treated with chemical fertilizers [61]. The Kumamoto Prefectural Agriculture Center [62] revealed that the nitrogen leaching from areas treated with livestock manure compost was 70% lower than that from areas treated with chemical fertilizers. Based on these data, the leaching ratio of livestock manure compost on Miyako Island is 12.0% (chemical fertilizer 40% × 30%) [9].

A questionnaire survey on compost use among farmers on Miyako Island [33] revealed that 74% of farmers use compost in fields cultivating both pasture and sugarcane. Livestock manure compost application has permissible limits: 75 t/ha for pastures [60] and 45.3 t/ha for sugarcane fields [46]. Notably, 50 to 60 t/ha of cow manure slurry is equivalent to 160 to 200 kg/ha of nitrogen [63]. These limits are based on maintaining the nitrate nitrogen concentration in soil seepage water below 10 mg/L even when cow manure slurry is applied within the range of 60 to 80 t/ha [63]. Replacing a portion of the fertilization applied to sugarcane fields and pastures with permissible amounts of livestock manure slurry can reduce the fertilizer’s leaching ratio below that of solely chemical fertilizers.

Fujiie et al. [33] calculated the reduction effect of livestock manure compost on the leaching ratio using the DNDC model (Denitrification and Decomposition model) [64]. The DNDC model is a process-based model that addresses carbon and nitrogen dynamics in soil. This model can compute nitrogen dynamics for chemical fertilizers and can also simulate the dynamics of nitrogen from livestock manure compost by inputting the C/N ratio. Fujiie et al. [33] calculated the amount of NO₃-N leaching from sugarcane fields and pastures where livestock manure compost was applied in 1977 (old standard), 1994 (new standard), and 2005 (revised new standard). These calculations utilized cultivation data from fields in the Sunagawa watershed. Here, we will present only the calculation results for pastures.

The nitrogen fertilization standard for pasture [48] is 350 kg/ha/year, while the annual fertilizer application in the model case is 383 kg/ha/year. According to the calculation results, the leaching load from pastures using livestock manure compost in 1977, 1994, and 2005 was 7 kg/ha, 9 kg/ha, and 18 kg/ha, respectively. Compost use was revealed to reduce the leaching load by 5% to 12% compared to chemical fertilizer alone (383 × 40% = 153.2 kg/ha). This result aligned with the 12.0% leaching ratio of livestock manure compost [9] based on data from the Agricultural Research Center of Kumamoto Prefecture [62]. Therefore, converting sugarcane fields to pasture and utilizing livestock manure compost up to the permissible input limit would reduce the leaching ratio by approximately 63% to 85% compared to the leaching load from solely chemical fertilizers (120 × 0.4 = 48 kg/ha).

3.5. Estimating Long-Term Nitrogen Loads from Fertilizers

Fertilizers are classified into chemical, organic, and others. Chemical fertilizers are further categorized as “high-analysis compound fertilizers,” containing ≥30% nitrogen, phosphorus, and potassium, and slow-release fertilizers with nitrification inhibitors. Records of high-analysis compound fertilizer sales began in 1986, with all types being recorded since 1988 [44]. The nitrogen load from chemical fertilizers can be calculated as approximately 14% of their sales volume, and that from organic fertilizers as about 3% [44].

Figure 12 shows the trends in fertilizer sales and the nitrogen supply from various fertilizers on Miyako Island [44]. The total amount of nitrogen applied to farmland decreased from the start of the survey in 1989 until 1998. However, it started to increase slightly in 1999. Since 2000, it has been maintained at around 1000 tons. The amount of nitrogen applied in 2013 was about 1290 tons. The breakdown of nitrogen sources from fertilizers is as follows: Nitrogen from chemical fertilizers, including slow-release fertilizers (orange line), accounted for 871.4 tons, or about 68% of the total. Most of this was from high-analysis compound fertilizers (blue line). The difference between the total chemical fertilizers and high-analysis compound fertilizers shown in the figure represents slow-release fertilizers. Slow-release fertilizers are rarely applied because they are relatively expensive [65]. On the other hand, the proportion of organic fertilizer sales was about 44%, but due to the low nitrogen content in organic fertilizers, the nitrogen from these fertilizers accounted for only about 13% of the total (excluding livestock manure compost) [65].

Tashiro and Takahira [14] estimated the nitrogen amount (green circles in Figure 12) from 1976 to 1986, a period lacking fertilizer sales volume records, using the monetary sales amount of fertilizer (black circles in Figure 12). This estimation method is flawed as it is influenced by fertilizer market prices; for instance, the oil shock between 1980 and 1985 caused fertilizer unit prices to soar, leading to significant fluctuations in monetary sales [45].

To examine the cross-correlation between the historical time series of fertilizer amounts for sugarcane fields and NO₃-N concentrations, data on fertilizer amounts from the 1960s (when the first sugarcane boom occurred) to the present are necessary. However, records of fertilizer monetary sales and the sales volume only extend back to 1976. Since Miyako Island farmers generally follow established fertilization standards [15], nitrogen amount trends can be estimated from sugarcane area trends and the fertilization standard for each cultivation method. If only one type of sugarcane cultivation method exists, the fertilizer amount should correspond one-to-one. Figure 13a shows the change in synthetic fertilizer amount, estimated by multiplying the time-varying area of each cultivation method by its corresponding fertilizer standard (Table 1).

Figure 13a also shows the change in nitrogen amount estimated from the fertilizer sales volume by Tashiro and Takahira [14] (Figure 12). The fertilizer application amount estimated from the sales volume after 1989 roughly correlates with the change in total fertilizer application. However, the fertilizer application amount estimated from monetary sales from 1976 to 1988 is plotted on the line of change in synthetic fertilizer application. The significant fluctuation in the fertilizer unit price during 1976–1988 due to the oil shock [44] suggests that the fertilizer application amount estimated from monetary sales for this period may be overestimated. The peak in 1980 is thought to correlate with the false local maximum value of synthetic fertilizer application in 1978.

Figure 13b shows the trend of the synthetic fertilizer ratio, which is the amount of fertilizer applied divided by the area of the sugarcane field. The synthetic fertilization ratio began to increase in 1960, reaching a peak in 1965 (207 kg/ha). At that time, the area ratios of ratooning and summer planting were 51.7% and 43.3%, respectively. It then remained at 195 kg/ha until 1971, after which it remained at185 kg/ha until 1979. These values correspond to 58.1% and 42.6% of the ratooning area, respectively (Figure 10b). The synthetic fertilization ratio gradually decreased starting in 1979, reaching 125 kg/ha in 1990. At that time, the area ratios of ratooning and summer planting were 3.7% and 93.1%, respectively, which indicates that almost all cultivation had shifted to summer planting. Subsequently, the synthetic fertilization ratio remained largely constant until 2010, then increased after 2010 due to an expansion in the ratooning area. In 2023, it reached 172.5 kg/ha, with ratoons comprising 48.8% of the area.

The orange line in Figure 13b shows the trend of the actual fertilization ratio, calculated by dividing the amount of fertilizer sold (Figure 12) by the area of the sugarcane field. The actual fertilizer ratios, until 1995, closely tracked the synthetic fertilizer ratio, fluctuating around 120 kg/ha—the standard annual fertilization value for summer-planted sugarcane. However, since 1996, the actual fertilizer ratios have been lower than the synthetic fertilizer ratio, ranging from 100 kg/ha to 110 kg/ha. This change is presumably due to the 1995 shift in sugarcane purchasing standards from weight to sugar content, which prompted farmers to apply less fertilizer to increase the sugar content of their plants [15]. Nevertheless, the synthetic fertilizer ratio trend can be considered an approximate estimate of the actual fertilizer ratio, suggesting what the peak of the actual fertilizer ratio was in 1965.

It is crucial to note when analyzing this figure that the synthetic fertilizer ratio had already declined from 185 kg/ha in 1979 to 127 kg/ha by 1986, when fertilizer standards were revised. This indicates that the decline in the synthetic fertilizer ratio is not related to the 1986 fertilizer standard revision, but rather to the shift in sugarcane cultivation methods from ratooning to summer planting.

4. Materials and Methods

4.1. Data

In this paper, we examine the relationship between groundwater NO₃-N concentrations, agricultural statistics, and precipitation time series using cross-correlation analysis. Because cross-correlation captures relationships only within specific time scales, we analyzed data at weekly, monthly, and annual resolutions.

Figure 14 presents the analyzed data periods. Continuous colored bands indicate continuous data, while separated bands indicate missing data. Annual NO₃-N concentrations from 1976 to 2023 and monthly NO₃-N concentrations from 1976 to 2013 from the Kajido water sources were obtained from Miyakojima City [7,8,9]. The numbers in the monthly NO₃-N concentration data for the Kajido water sources indicate the number of measurements per year. Annual agricultural statistics were obtained from Miyakojima City publications and Okinawa Prefecture Agriculture and Forestry Statistics [49]. Mukai (1979) [50] only provides biennial data for the area of sugarcane grown using each cultivation method from 1955 to 1970. Okinawa Prefecture Agriculture and Forestry Statistics has not included area data by cultivation method since 2007. Nitrogen load time series data, limited to the northern Fukusato area where the Kajido Water Source is located, were obtained from Miyakojima City [9], but these data are available only every five years. Precipitation time series data from 1978 onward were obtained from the Gusukube Observatory of the Japan Meteorological Agency [66], located near northern Fukusato. Precipitation data prior to 1978 were obtained from the Miyakojima Observatory, located approximately 10 km northwest of the Gusukube Observatory. The lack of a match between the data from the Miyakojima Observatory and the Gusukube Observatory may be a source of error when using the Miyakojima Observatory data.

The only available weekly NO₃-N dataset comes from the Noshiro spring in southeastern Miyako Island, collected by [15] from July 1994 to September 1999. The original graphical data were digitized, yielding a regression equation (y = −0.0014x + 53.3) consistent with Nakanishi’s reported equation (y = −0.0014x + 52.1), which confirmed their suitability for use as weekly data. Similarly, annual NO₃-N concentrations and nitrogen loads on Yoron Island (Section 6) were digitized from [55,67].

4.2. Methods

4.2.1. Calculation of Leaching Ratio Using Multiple Regression Analysis

Multiple regression analysis utilizes an equation in the following form:

$$y=w_1{x}_1+w_2{x}_2+\dots +w_n{x}_n+\epsilon$$

(1)

where y is the objective variable; x₁, x₂, …, x_n are explanatory variables; n is the number of explanatory variables; and ε represents the error. The coefficients w₁, w₂, …, w_n are the partial regression coefficients of the explanatory variables.

Nakanishi et al. [10] defined the following multiple regression Equation (2).

$$y=G{W}_n-N_n=w_1{F}_n+w_2{L}_n+w_3{D}_n$$

(2)

Here, y is the annual nitrogen load, calculated by subtracting the naturally occurring nitrogen (N_n) from the total annual nitrogen (GW_n). The explanatory variables F_n, L_n, and D_n represent annual loads from fertilizer, livestock wastewater, and domestic wastewater, respectively. The partial regression coefficients w₁, w₂, … represent the ratios of the leaching from each source to the groundwater. N_n was calculated by multiplying the annual precipitation for each catchment area by the rainwater nitrogen concentration (1.4 mg/L) [10]. GW_n was calculated by multiplying the groundwater infiltration from precipitation (R_p) by the measured groundwater NO₃-N concentration (GW_nc), as shown in Equation (3):

$$G{W}_n=R_p\times G{W}_{nc}$$

(3)

Here, R_p was derived by multiplying the annual precipitation in the selected catchment area (1989 and 1992) by the groundwater infiltration ratio of 0.4 [17]. They calculated the leaching ratio of each nitrogen load source using multiple regression analysis on 16 equations for 1989 and 1992.

Since Nakanishi’s [10] multiple regression equation was incomplete (lacking the error term ε), Tashiro and Taniyama [69] employed the complete multiple regression Equation (4) for Okinoerabu Island (Figure 1), which shares the same Ryukyu Limestone aquifer as Miyako Island:

$$y=G{W}_n=w_1{F}_n+w_2{F}_f+w_3{L}_n+w_4{D}_n+\epsilon$$

(4)

Here, F_f represents fertilizer for flower fields. They performed their analysis using 11 multiple regression equations. They considered ε to be nitrogen loaded from natural sources.

As a rule of thumb, multiple regression analysis generally requires 10–15 data points per explanatory variable (e.g., [11]). Therefore, we performed multiple regression analysis by creating 207 sets of multiple regression equations based on annual NO₃-N concentrations from 1989 to 2019 in seven Miyako Island groundwater basins for three explanatory variables (

Table 2. Data for creating multiple regression equation for Miyako Island.

Basin Name	Groundwater	Survey Year	Number of Data
Sirakawada	Spring	1989–2019	31
Sunagawa	Taragawa well	1989–2013	28
Nakahara	Mui-ga spring	1989–2012	24
Minfuku	Subsurface dam well	1989–2019	31
Fukusato	Kajido well	1989–2019	31
Bora	Bora-ga spring	1989–2019	31
East Soedou	Sodeyama well	1989–2019	31
Total number of data			207

). In this paper, we used Excel’s functions (Microsoft Office Home and Business 2019) to conduct multiple regression analysis on the complete multiple regression equation, using Nakanishi’s data and data from the entire Miyako region (Miyako data).

4.2.2. Regression Analysis Using Machine Learning Models

When the relationship between the leaching ratio and the load source is nonlinear, a multiple regression model may be unsuitable for calculating the leaching ratio. To address this, we applied machine learning (ML) regression methods, specifically classification and regression trees (CART) and random forests (RF).

CART (classification and regression trees) splits a target variable using a threshold of an explanatory variable, employing simple IF-THEN rules. This recursive splitting continues, with each split selected to maximize impurity reduction (e.g., Gini impurity). Gini impurity is 0 for a perfectly classifiable branch and 1 if it is not. Splitting ceases when a termination criterion, such as a complexity parameter (cp), is met. For example, a split may terminate if the impurity is less than 0.5% when a cp of 0.005 is used. CART analysis was implemented in R using the rpart package [70], which also calculates the importance of explanatory variables.

We first performed a regression analysis using the parameters minsplit = 2 and cp = 0.005. This resulted in 7 splits for the 16 datasets from Nakanishi [10] and 19 splits for the 207 datasets covering the entire Miyako region. Next, we used the m.lzn.rp function to determine the complexity parameter values that minimize cross-validation error, which were 0.538 and 0.295, respectively. These values were then used to prune the decision tree. The final decision tree structure had 4 and 19 splits. For the Miyako region, the number of splits and leaves remained unchanged after pruning. See [71] for details on CART analysis. The R code for CART analysis published by [72,73] is useful for parameter determination.

Random forest (RF) extends CART to overcome its unstable predictive performance, which is a result of small changes in the sample set that can fundamentally alter the tree structure. RF employs an ensemble learning approach by creating multiple CART models to reduce overfitting and variance, thereby achieving more stable and accurate predictions than single regression trees [74].

Each RF tree is trained on bootstrap samples drawn from the original dataset, and out-of-bag (OOB) samples—those not included in the bootstrap—are used to evaluate its performance. RF regression reduces variance by averaging predictions from multiple trees and assesses the importance of each predictor variable. For further details, see [75].

Random forest analysis was implemented in R (version 4.2.1) using the randomForest package [76]. We built the forest using the randomForest function with the hyperparameter mtry = 1. The default mtry value is p/3 (where p is the number of predictors); therefore, mtry was set to 1 in this study (3/3 = 1). For specific R code regarding hyperparameter selection, cross-validation, and model performance metrics, see [73,77].

The goodness of fit for the CART and random forest regression models was evaluated using the root mean squared error (RMSE) and the coefficient of determination (R²).

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=0}^{n-1}{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(5)

Here, y_i represents the actual value, ${\widehat{y}}_i$ is the predicted value, and n is the total number of data points. Although RMSE is a common metric for evaluating machine learning models, its value is highly dependent on the magnitude of the data, which makes intuitive interpretation difficult. Therefore, RMSE values must be interpreted in the context of the data’s scale when comparing models.

The concept of explanatory variable importance in machine learning models is not as formalized as partial regression coefficients in multiple regression. For instance, CART calculates importance based on how much splitting at a variable’s threshold reduces the Gini impurity. RF feature importances are the average of many CART feature importances. Therefore, machine learning explanatory variable importance cannot be directly correlated with multiple regression partial regression coefficients.

Partial dependence plots (PDPs) in machine learning models approximate multiple regression partial regression coefficients. PDPs describe the relationship between a target variable and specific explanatory variables while holding other explanatory variables constant [78]. However, this functionality is available only in random forest regression. PDPs were created using the pdp package in R [79].

4.2.3. Time Series Analysis

Time series analysis is a valuable technique in water quality modeling and forecasting (e.g., [80]). Our water quality time series analysis aims to decompose the data to clarify trends and seasonal variations. We analyzed weekly and monthly NO₃-N concentration time series, focusing on weekly data from the Noshiro spring [15] (Figure 3) and monthly/annual data from the Kajido water source. For this analysis, we used the decompose function from the “Forecast” (8.24.0.tar.gz) package in R (version 4.2.1) [81].

4.2.4. Cross-Correlation Analysis

Cross-correlation analysis evaluates the statistical correlation between two datasets, x and y, at a given time lag. The cross-correlation function (CCF) quantifies the similarity between two time series when one is shifted relative to the other. Typically, results from a single analysis are presented as a bar graph of CCF values for each time lag. To compare multiple analyses, several CCF curves are plotted with time lag on the x-axis and CCF values on the y-axis. A causal relationship between two time series exists if CCF values are statistically significant and the CCF curves are not symmetrically distributed at the maximum CCF [82].

Cross-correlation analysis has been used to clarify the relationship between matrix flow and fissure flow related to chalk recharge [83,84,85,86,87]. It has also been applied to analyze the relationship between groundwater NO₃-N concentration time series and loading sources or precipitation to understand NO₃-N generation mechanisms in groundwater (e.g., [16,18]).

In this paper, we calculate the strength and response-time offset of cross-correlations between NO₃-N concentrations and agricultural statistics (cultivated area and fertilizer input), and between NO₃-N concentrations and precipitation. Cross-correlation strength is evaluated by the CCF coefficient (ranging from −1.0 to 1.0). For instance, with precipitation and NO₃-N concentration, a time offset indicates a delayed increase (+CCF) or decrease (−CCF) in NO₃-N concentration after rainfall.

When the direction of influence is assumed or known, the influencing time series is termed “input,” and the affected time series is “output.” In this paper, cultivated area, fertilizer input, and precipitation are input time series, while groundwater NO₃-N concentration is the output time series.

The cross-correlation was calculated using the following relationship [85]:

$${\rho }_y\left(k\right)={\displaystyle \frac{E\left[\left(x_t - {\mu }_x\right)\left(y_{t+k} - {\mu }_y\right)\right]}{{\sigma }_x{\sigma }_y}}$$

(6)

where ρ_y(k) is the cross-correlation at time lag k (days, months, or years, for k = 0, ±1, ±2, …, ±n). x_t is the output time series at time t, and y_t is the input time series at time t. μ_x and μ_y are the means of the output and input time series, respectively. σ_x and σ_y are their standard deviations. A significant CCF coefficient at the 95% confidence level is considered larger than the standard error $2/\sqrt{N}$, where N is the number of values in the dataset.

Four types of time-lagged cross-correlation can be defined [88]: (1) a positive CCF with a negative time lag, (2) a positive CCF with a positive time lag, (3) a negative CCF with a negative time lag, and (4) a negative CCF with a positive time lag. When groundwater levels rise after precipitation [85] or when groundwater NO₃-N concentrations increase after surface nitrogen loading [18], a positive CCF with a negative time lag results. This is represented by a significant CCF in the upper-left quadrant (negative time lag and positive CCF). Conversely, when groundwater NO₃-N concentrations decrease due to dilution after precipitation, a negative CCF with a negative time lag results. This is represented by a significant CCF in the lower-left quadrant (negative time lag and negative CCF).

Normally, the lag time of a cross-correlation is determined by the lag corresponding to the maximum CCF value at or above the 95% confidence level [18,85]. However, when the 95% confidence interval is wide, identifying this maximum value can be difficult. For example, the cross-correlation between groundwater levels and rainfall events in the East Anglian Chalk aquifer showed a CCF distribution that maintained a 95% confidence level or higher for 24 months. This was interpreted to mean that it took 24 months for groundwater levels to fully respond to monthly rainfall events [87].

Tashiro and Takahira [14] exclusively used fertilizer trends estimated from sales data as the nitrogen load from farmland. However, this paper also considers agricultural statistical data, such as sugarcane cultivation area and harvest volume, as proxies for nitrogen load. We investigated the time lag of weekly, monthly, and annual agricultural statistics and precipitation, as well as NO₃-N concentration time series for different periods. Cross-correlation analysis was performed using the “Forecast” package in R.

The R cross-correlation analysis package does not handle missing data. Therefore, missing data between known data points (Figure 14) were linearly interpolated. While the cross-correlation error depends only on the number of data points (N), a longer interpolation interval can degrade the data, thereby increasing analysis error. We did not consider errors from data imputation in this study, given that the interpolation period varied, the interpolation period only comprised a portion of the total data, and other error sources existed (e.g., differences between meteorological stations and chart reading errors). Instead, we comprehensively evaluated the validity of the cross-correlation analysis results by examining their consistency with other cross-correlation and machine learning regression analysis results, as well as the flow mechanism in the Ryukyu Limestone unsaturated zone.

4.2.5. Mann–Kendall Trend Analysis

The Mann–Kendall test is a widely used non-parametric method for identifying linear or nonlinear trends in hydrology and water-quality time series [88]. This test uses the rank correlation coefficient, τ, to determine trends based on relative magnitudes rather than original ranks. The Mann–Kendall test was implemented using the Kendall package in R [89], which returns a τ value and a p-value. A positive τ indicates an increasing trend, while a negative value indicates a decreasing trend. A p-value less than 0.05 signifies a statistically significant trend in the two time series with 95% confidence.

4.2.6. Wavelet Transform and Cross-Wavelet Transform for Time Series Analysis

While correlation analysis is widely used in hydrology and hydrogeology, it may not be applicable when time series data are nonlinear and the signal frequency changes over time. The wavelet transform (WT) effectively detects periodicities in nonlinear systems and can reveal locally intermittent periodicities [23].

The wavelet transform decomposes a signal into a mother wavelet, which is shifted in time and scaled to identify the exact period of every frequency window in the signal [90]. In this paper, we used the Morlet wavelet (Equation (7)) as the mother wavelet due to its good balance between time and frequency localization [90].

$${\phi }_0\left(\eta \right)={\pi }^{-1/4}{e}^{-i\omega 0\eta }{e}^{-{\displaystyle \frac{1}{2}}{\eta }^2}$$

(7)

Here, ω₀ and η represent dimensionless frequency and time, respectively.

To identify similarities between two signals, superimposition is crucial. The cross-wavelet transform (CWT) is suitable for identifying similar periods between two signals. Considering a time series (x_n, n = 1, …, N) with a uniform time step δ_t, the CWT is defined as the convolution of xn with a scaled and transformed mother wavelet, ψ₀(η), as follows [91,92,93]:

$$W_n^X\left(s\right)=\sqrt{{\displaystyle \frac{\delta t}{s}} }{\sum }_{n^{\prime }=1}^N{x}_{n^{\prime }}{\Psi }_0^{*}\left[\left(n^{\prime } - n\right){\displaystyle \frac{\delta t}{s}}\right]$$

(8)

Here, $\sqrt{\delta t/s}$ is a normalization factor, and the asterisk denotes the complex conjugate. The complex part of $W_n^X\left(s\right)$ represents the local phase. ${\left|W_n^X\left(s\right)\right|}^2$ is the wavelet power, which is the time-frequency (or time-period) wavelet energy density. The image plot function allows us to visualize the wavelet power spectrum and depict regions of interest [94].

Wavelets are not perfectly localized in time, so both WT and CWT can introduce edge artifacts. These artifacts arise from finite time series lengths, which leads to errors at the beginning and end of the wavelet power spectrum [93]. This limitation results in truncated coefficients on the scalogram’s periphery, visually represented by a black line separating the cone of influence (COI). Values outside the COI are excluded from average spectrum calculations due to their unreliability. WT and CWT analyses were implemented using the WaveletComp R package [94].

5. Results

5.1. Calculation of Leaching Ratio by Multiple Regression Analysis

Table 3. Results of calculation of leaching ratio by multiple regression analysis.

Data		Nakanishi et al. [10]			Recalculation			Miyako			Tashiro & Taniyama [69]
Number of observed data		16			16			207			11
Multiple correlation coefficient R		0.872			0.912			0.844			0.989
Significance F					6 × 10−5			9 × 10−55			3 × 10−5
			t	p		t	p		t	p		t	p
Partial Regression Coefficent	Fertilizers1	0.4	3.607	0.003	0.29	1.733	0.109	0.58	13.01	1.5 × 10−28	0.212	2.2	0.07
	Fertilizers2										0.714	6.892	0.0005
	Livestock Waste	0.44	1.878	0.083	0.57	2.355	0.04	0.007	0.13	0.89	0.239	2.187	0.071
	Domestic Wastes	0.69	0.591	0.565	1.04	0.846	0.414	0.17	0.887	0.376	1.1	2.105	0.08

presents the results of multiple regression analysis. “Recalculation” in the table refers to the results derived from applying the full multiple regression equation to the data from Nakanishi et al. [10]. “Miyako” denotes the results obtained by applying the full multiple regression equation to the 207 datasets. For comparison, the table also includes results from Nakanishi et al. [10] and Tashiro and Taniyama [69].

All multiple regression analyses predict the target variable with a high correlation (R ≥ 0.8). However, the regression equations and explanatory variables exhibit the following statistical problems. Nakanishi et al. [10] does not report an F-value, but the F-values of the other multiple regression equations are less than 0.05, which indicates that the explanatory variables have a significant effect on the target variable. The evaluation criteria for each explanatory variable are a t-value > 2 and a p-value < 0.05. Based on these criteria, explanatory variables other than fertilizer in Nakanishi et al. [10] are not statistically supported. Similarly, explanatory variables other than fertilizer in Tashiro and Taniyama [69] are not statistically supported. Only livestock waste is statistically supported in the recalculation. For the entire Miyako region, only fertilizer is statistically supported.

When Nakanishi’s data [10] were calculated using Equation (4), the multiple regression coefficient increased from 0.872 to 0.912. The partial regression coefficient for fertilizer changed from 0.4 to 0.29, that for livestock waste from 0.441 to 0.570, and that for domestic wastewater from 0.689 to 1.04. On the other hand, in the multiple regression analysis based on 207 observations, the multiple regression coefficient was 0.844, while the partial regression coefficient for fertilizer was 0.580, that for livestock waste was 0.007, and that for domestic wastewater was 0.170. The t-value for the partial regression coefficient for fertilizer was 12, and the p-value was also very low, which indicates that 0.58 is statistically significant. However, it became clear that the method of calculating the leaching ratio from the partial regression coefficient of multiple regression analysis is not stable, as it changes depending on the formula and the amount of data.

Table 4. Verification results obtained using decision trees and random forests.

Data	Nakanishi et al. [10]			Miyako
Model	Decision tree	Random Forest		Decision tree	Random Forest
Number of observed data	16			207
	Model validation		Out-of-bag validation	Model validation		Out-of-bag validation
RMSE	6.784	6.858	12.766	4.996	3.586	6.96
Pearson Correlation Coefficient R	0.960	0.964	0.855	0.942	0.973	0.884
Variable importance	%IncMSE	%IncMSE	PDP slope of the regression line	%IncMSE	%IncMSE	PDP slope of the regression line
Fertilizers	30.2	25.6	0.284	48.2	47.0	0.293
Livestock Waste	31.6	34.2	0.486	22.3	24.2	0.201
Domestic Wastes	30.2	40.2	1.800	29.5	28.8	0.450

shows the results of regression analysis using the CART model and the RF model on the 16 datasets from Nakanishi et al. [10] and the 207 datasets for the entire Miyako region. The RMSEs for the two datasets for the CART model were 6.784 and 4.996, respectively. The RMSEs for the two datasets for the random forest regression were 6.858 and 3.586, respectively.

The average input values for both datasets were 54.2 and 31.7 ton/year. The RMSEs for both models were approximately 10% of the average input values, so the RMSEs can be evaluated as reasonable. The coefficients of determination between the actual input values and the predicted values were both high, above 0.94, for both models, which confirms that the model has sufficient prediction accuracy (Figure 15). It is particularly noteworthy that the RF model showed a high correlation of R² = 0.85 or higher between the values of out-of-bag data (data not used in model creation) and the predicted values. This shows that random forest regression can predict the target variable with sufficient accuracy even for unknown values (Figure 15).

Figure 16 presents the PDPs for examining leaching ratios using a random forest model and the results of locally smoothing them using LOESS (locally estimated scatterplot smoothing) [95]. Figure 16 reveals that the relationships between groundwater NO₃-N concentrations and the fertilizer, livestock waste, and domestic wastewater variables are nonlinear. Therefore, it is difficult to accurately predict leaching ratios from the partial regression coefficients of a multiple regression model. However, since studies on load sources that are based on leaching ratios from a multiple regression model are used for NO₃-N pollution on Miyako Island [2,9], it is meaningful to extract the linear portion from the PDP and calculate the leaching ratio.

For the fertilizer variables obtained using data from Nishiyama et al. [10] (Figure 16a), the leaching ratio in the 25–100 range may exhibit a linear relationship, as indicated by the red arrow. Similarly, a linear relationship may be observed for livestock waste variables from 0 to 40 (Figure 16b) and for domestic wastewater variables across the entire range (Figure 16c). Regarding the Miyako data’s PDP, a linear relationship exists for fertilizer variables across the entire range (Figure 16d) and for livestock waste variables from 10 to 60 (Figure 16e), suggesting that leaching ratios can be defined for these ranges. However, the domestic wastewater variables show an S-shaped curve (Figure 16f) and cannot be expressed linearly. To compare this approach with the multiple regression model, the leaching ratio was calculated using the arrow line in Figure 16. The calculation results are shown in the “PDP Slope of Regression Line” column in Table 4.

The leaching ratios of fertilizer estimated from the linear range of the PDP curves of the Nakanishi et al. [10] and Miyako data were 0.284 and 0.293, respectively, which were nearly identical. These values are also almost the same as the 0.29 recalculated using the multiple regression method. The 0.212 value from the multiple regression method for Okinoerabu Island conducted by Tashiro and Taniyama [69] is also close to this value.

5.2. Weekly Precipitation and Weekly NO₃-N Concentration of Noshiro Spring

Figure 17 shows the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the weekly NO₃-N concentration time series data from Noshiro spring. The ACF has a maximum value at lag 0. Its slow decrease with an increasing lag indicates a trend in the time series data. The ACF increases to a local maximum at 40 weeks and then decreases again. At 60 weeks (almost a year), it falls below the confidence line. The formation of the local maximum at 40 weeks is due to seasonality in the time series data. The PACF is above the confidence line for only 12 weeks (3 months), suggesting periodicity within this duration.

Figure 18a displays the decomposition of weekly NO₃-N concentration time series data into trend, seasonal, and noise components using the decompose function. Figure 18b shows the decomposition of one-week cumulative precipitation time series data at the Gusukube observation station. Each graph in the figure presents, from top to bottom, the original data, trend, seasonal cycle, and residual.

The trend of the NO₃-N concentration (y_N) shows a decreasing pattern over time (x), expressed as y_N = −0.0014x + 53.3 (R² = 0.94). Conversely, the trend of the weekly cumulative precipitation (y_R) exhibits an upward trend with time (x), represented by y_R = 0.0104x − 332.76 (R² = 0.53).

A low negative correlation exists between the NO₃-N concentration time series and the weekly cumulative precipitation time series, depicted by Y = −14.123x + 92.961 (R² = 0.077). This correlation was further confirmed by the Mann–Kendall test, which yielded a negative correlation of τ = −0.172 (p < 0.05) (

Table 5. Relationship between weekly NO₃-N concentration and various cumulative precipitation amounts.

Cumulative Precipitation	Correlation Equation		Kendall (x,y)
	Equation	R2	τ	p-Value
7 days	y = −14.123x + 92.961	0.0772	−0.172	2.88 × 10−5
30 days	y = 9.152x + 94.834	0.0112	0.0312	0.446
90 days	y = 42.344x + 238.1	0.1231	0.286	2.22 × 10−16
150 days	y = 23.385x + 536.76	0.0322	0.117	0.004

). The relationship between these trends is y_T = −7.91336x + 66.733 (R² = 0.66), which indicates a clear negative relationship between NO₃-N concentration and precipitation. The very small negative correlation observed occurs because the correlation between trends is masked by seasonal variation and residuals.

Figure 19 illustrates five seasonal cycles of NO₃-N concentration and weekly cumulative precipitation. The seasonal cycle of the NO₃-N concentration exhibits an annual cycle with a local minimum around 19–23 October and a local maximum around 22–27 February of the following year, rather than the clear 12-week (3-month) periodicity estimated by the PACF correlogram. This annual cycle confirms the yearly cycle of a local minimum from September to October, as pointed out by Nakanishi et al. [15].

Conversely, the seasonal cycle of weekly precipitation shows an annual cycle with a sharp peak from 6 to 12 June each year. This peak reduces the NO₃-N concentration, but its effect is minimal. Comparing the two figures reveals no correlation between the precipitation cycle and the NO₃-N concentration cycle. Therefore, it is reasonable to conclude that the seasonal cycle of the weekly NO₃-N concentration time series is formed by factors other than the weekly precipitation.

5.3. Monthly NO₃-N Concentration Time Series for the Kajidou Water Source in the Fukusato Basin

5.3.1. Decomposition of NO₃-N Concentration Time Series for the Kajidou Water Source

Figure 20 displays the decomposition results of the monthly NO₃-N concentration time series (a) from the Kajidou water source and the monthly precipitation time series; (b) from the Gusukube meteorological station, spanning from 1989 to 2013. The trend of the monthly NO₃-N concentration has been consistently decreasing, but two significant decreases and subsequent recoveries were observed between 1985 and 1995. Conversely, the trend of the monthly precipitation time series does not exhibit clear characteristics. The seasonal component of the NO₃-N concentration time series shows three peaks per year, occurring in early January, early May, and from early September to early October. In contrast, the seasonal component of the monthly precipitation time series has two annual peaks, in early May and mid-August. We will now extract the trend and seasonal cycle data from the decomposed data for detailed examination.

Figure 21 illustrates the trends in monthly NO₃-N concentrations and annual precipitation fluctuations. The long-term decreasing trend of the NO₃-N concentration (y) over time (x) can be regressed with y = −0.0003x + 19.13 (R² = 0.86). Conversely, the long-term annual precipitation fluctuations occur randomly and are unrelated to the decreasing trend of NO₃-N concentrations. The two significant decreases observed in the NO₃-N concentration may be related to periods of decreasing annual precipitation; however, the exact reasons remain unclear. The short-term rapidly decreasing trend from January 1989 to December 1991 (orange dots) can be regressed with y = −0.0013x + 52.624 (R² = 0.96). This rapidly decreasing trend is four times faster than the long-term decreasing trend in NO₃-N concentrations. This period of abrupt decline in NO₃-N concentration may correspond to the period of sharp reduction in the sugarcane field area (Figure 10).

Figure 22 shows the seasonal cycles of the NO₃-N concentration time series (blue line), monthly precipitation time series (orange line), and five-month cumulative precipitation time series (gray line) for a representative year, 1986. The five-month cumulative precipitation was selected by trial and error because the groundwater level change at the Kajido water source well is highly correlated with the 15-month cumulative precipitation [44].

The annual cycle of the NO₃-N concentration has three peaks: from late January to early February, early July, and early October. There is also a small peak in early April. The seasonal cycle of monthly precipitation has only two peaks: in early May and mid-August. The peak times of the seasonal NO₃-N concentration cycle and the seasonal precipitation cycle do not coincide. Conversely, the seasonal cycle of the five-month cumulative precipitation has a large peak in July and small peaks in April and October. These coincide with three peaks in the seasonal cycle of the NO₃-N concentration. However, there is no peak that corresponds to the NO₃-N concentration peak in early February. Therefore, all peaks in the seasonal NO₃-N concentration cycle cannot be explained by the seasonal precipitation cycle. A possible explanation for the three peaks in the seasonal cycle of the NO₃-N concentration is the fertilization periods in February, July, and October (Figure 9). If this explanation is valid, the April peak may be related to the fertilization period for ratoon cultivation (Figure 9).

5.3.2. Annual and Monthly Cross-Correlation Analysis Between the Time Series of Three Load Sources (Fertilizer, Livestock Waste, and Domestic Wastewater) and the Time Series of NO₃-N Concentration

Figure 23a presents the cross-correlation function (CCF) curves between the time series of annual nitrogen load sources in the northern Fukusato Basin and the NO₃-N concentration in the Kajido water source over 29 years, from 1989 to 2018. Here, the nitrogen load sources include: (1) fertilizer, (2) livestock wastewater, (3) domestic wastewater, and (4) total nitrogen load. Additionally, the sugarcane cultivation area [9] was considered as a separate factor. The total sugarcane area of Miyako Island is used as the annual data for the sugarcane area in the northern Fukusato Basin. Each variable has 29 data points.

The total nitrogen load time series exhibited the highest CCF with the NO₃-N concentration time series (CCF = 0.880), followed by fertilizer (CCF = 0.865) and sugarcane cultivation area (CCF = 0.854). The time lag for these variables is 0 years. The similar pattern observed in the CCF curves for the fertilizer and sugarcane cultivation area indicates similar causal relationships. Conversely, the distinct pattern of the CCF curve for the total nitrogen load from the aforementioned two curves suggests a different causal relationship for this index.

The CCF values for livestock waste and domestic wastewater did not exceed the 95% confidence line (CCF = ±0.37), indicating that these indices did not have a statistically significant impact on the 29-year annual NO₃-N concentration time series. However, the CCF of the total nitrogen load was 0.015 greater than the CCF of fertilizer, which suggests that livestock waste and domestic wastewater may have some impact on NO₃-N concentrations, though their contribution is small.

Figure 23b presents the cross-correlation function (CCF) curves between the monthly time series of each nitrogen load source and the NO₃-N concentration data in the Kajido water source from January 1989 to March 2013. The NO₃-N concentration data comprise 291 points. The data for each nitrogen load source time series were linearly interpolated from annual data. Notably, the sufficient number of data points reduces the confidence interval to CCF = ±0.116.

The time series exhibiting the highest CCF is the sugarcane area (CCF = 0.869), followed by the fertilizer time series (CCF = 0.744) and the total nitrogen load (CCF = 0.73). The time lag for these variables is 0. The CCF curves for the fertilizer and sugarcane area show the same shape. Conversely, the CCF curve for the total nitrogen load differs from the patterns of the two aforementioned variables because its slope is gentler on the positive time lag side. This difference in patterns indicates a different causal relationship.

The CCF of livestock waste is 0.285 at a time lag of 0, which suggests that it contributes to an increase in the NO₃-N concentration. In contrast, the CCF of domestic wastewater shows a dilution effect, with a value of −0.251 at a time lag of 0. The CCF of the total nitrogen load is slightly lower than that of fertilizer because it incorporates not only fertilizer but also the combined positive and negative effects of livestock wastewater and domestic wastewater.

5.4. Annual Cross-Correlation Between Agricultural Nitrogen Load Sources and NO₃-N Concentration (1977–2013)

This section analyzes the cross-correlation between the nitrogen load generation time series (1977–2013), which includes the 1980 peak in nitrogen load sources estimated by Tashiro and Takahira [14], and the NO₃-N concentration time series. We considered the following time series as indicators of nitrogen load sources: sugarcane cultivation area, summer planting cultivation area, sugarcane harvested area, sugarcane harvest volume in the Gusukube area, and sales volume of high-analysis compound fertilizer.

Tashiro and Takahira [14] used the average NO₃-N concentration of 13 wells for their NO₃-N concentration time series data. However, we use the NO₃-N concentration of the Kajido water source here. Although the NO₃-N concentration time series of the Shirakawada and Kajido water sources, which have long-term NO₃-N concentration data, differ in concentration, their peak times and decreasing trends are the same (Figure 2). Therefore, they likely represent the general trend of NO₃-N concentration on Miyako Island. The peak of NO₃-N concentration was in 1989, two years later than the 1987 peak estimated by Tashiro and Takahira [14]. Since NO₃-N concentration measurements before 1989 were limited to data taken once or twice a year (1997–1989 in the figure), they were converted to monthly NO₃-N concentration data by linear interpolation. Annual agricultural statistics data were also linearly interpolated to monthly data.

Figure 24 shows the cross-correlation function (CCF) curves between agricultural statistics time series and NO₃-N concentration time series from 1977 to 2013. The cross-correlation indicates a positive relationship with a negative time lag. The confidence intervals vary depending on the number of data points; the CCF = ±3.3 to ±3.7 lines indicate the 95% confidence interval.

The time series for the summer planting cultivation area, summer planting harvested area, and high-analysis compound fertilizer show high correlations with CCF values of 0.81, 0.73, and 0.82, respectively, at a time lag of 0. The total sugarcane area and sugarcane harvest volume in the Gusukube area have CCF values of 0.83 and 0.67, respectively, at a time lag of −2 years. This −2-year time lag may be attributed to the approximately two years required for harvesting with summer planting.

The CCF curve for the nitrogen load time series, estimated from the monetary sales amount and sales volume of fertilizer, had a CCF of 0.71 with a time lag of −5 years. On the other hand, for the time series of sales, the CCF was 0.69. Its shorter record period compared to the nitrogen load increased the time lag by one year to −6 years.

5.5. Annual Cross-Correlation Between Sugarcane Field Area, Fertilizer Amount, and Fertilizer Application Ratio and NO₃-N Concentration (1960–2023)

This section presents an annual cross-correlation analysis between the time series of the sugarcane field area (Figure 10), the fertilizer amount (Figure 13a), the fertilizer ratio (Figure 13b), and the annual NO₃-N concentration in the Kajido water source for the 63-year period from 1960 to 2023.

Figure 25 shows the results of a cross-correlation analysis between the time series of the sugarcane cultivation area, the fertilizer amount and ratio, and the NO₃-N time series of the Kajido water source. These cross-correlations exhibit a positive relationship with a negative time lag.

The sugarcane cultivation area and NO₃-N concentration time series show a CCF of 0.378 with a time lag of −3 years (Figure 25a). While the time lag of the monthly data for 38 years (1975–2013) was −2 years (Figure 24), the time lag for both the monthly and annual CCF of the sugarcane cultivation area was almost the same. However, because the primary cultivation method for sugarcane has changed significantly over 60 years, the CCF of the annual data was lower at 0.378 compared to the 0.8 obtained for the monoculture method. The nitrogen loading time series over 38 years had a CCF of 0.71 with a time lag of −5 years (Figure 24). In contrast, the cross-correlations of the annual fertilizer amount (Figure 25b) and fertilizer ratio (Figure 25c) over 60 years decreased to CCF values of 0.33 and 0.322, respectively, with a time lag of −15 years.

5.6. Cross-Correlation Analysis Between Cumulative Precipitation Time Series and NO₃-N Concentration Time Series

5.6.1. Cross-Correlation Between Daily Cumulative Precipitation and Weekly NO₃-N Concentration

Figure 26 displays the cross-correlation analysis results between the cumulative precipitation for various durations and weekly NO₃-N concentrations in the Noshiro spring. The 1-week (7-day) cumulative precipitation time series shows a correlation of CCF = −0.28 at a time lag of 0. This low correlation indicates that the 1-week (7-day) cumulative precipitation only partially explains the NO₃-N concentrations.

When the cumulative precipitation period is extended to 30 days, the CCF changes from negative to positive, reaching 0.163 at a time lag of −21 weeks. Further extending the period to 90 and 150 days yields CCF values of 0.442 at a lag of −14 weeks and 0.324 at a lag of −13 weeks, respectively. The CCF curves for the 90-day and 150-day cumulative precipitation show more than 95% confidence intervals for the CCF over a wide range of lag times (0 to −20 weeks). This suggests that these precipitation amounts have a prolonged effect on NO₃-N concentrations for up to 20 weeks, similar to the cross-correlation observed between groundwater levels and rainfall events in the East Anglian Chalk aquifer [88].

Table 5 also presents the results of the Mann–Kendall test for the NO₃-N concentration time series and the 30-day, 90-day, and 150-day cumulative precipitation time series. There is a negative correlation between the NO₃-N concentration and the one-week cumulative precipitation, but, although the 30-day cumulative precipitation is positively correlated, its p-value of 0.445 indicates no statistical significance.

However, the p-value for the 90-day cumulative precipitation is a very small value of 10⁻¹⁶, which indicates statistical significance. In addition to the Mann–Kendall test result, the coefficient of determination is also the largest, clearly indicating that the 90-day cumulative period (about three months) has the most positive effect on weekly NO₃-N concentration formation. In other words, it can be inferred that the weekly NO₃-N from chemical fertilizers leached from the soil is transported to groundwater along with the cumulative precipitation for more than 90 days.

5.6.2. Monthly and Annual Cross-Correlation Between Cumulative Precipitation and NO₃-N Concentration

Figure 27a displays the results of a cross-correlation analysis between precipitation time series with various accumulation periods and monthly NO₃-N concentration time series. The accumulation periods range from 1 to 12 months. The main CCF curve, plotted in the lower-left quadrant, indicates a negative relationship with a negative time lag between the monthly accumulated precipitation series and NO₃-N concentration time series, suggesting a dilution effect of precipitation.

The correlation between the one-month accumulated precipitation and NO₃-N concentration does not exceed the 95% confidence interval (thick blue dashed line), which differs from previous findings [15]. A statistically significant CCF is observed starting from the 2-month accumulated precipitation (orange thick dashed line), exhibiting a CCF of −0.396 with a time lag of −3 months. For the 4-month accumulated precipitation, the maximum CCF is plotted at the edge of the lower right quadrant, with a time lag of one month and a CCF of −0.576. The highest correlation is for the six-month accumulated precipitation, with a time lag of one month and a CCF of −0.690. While the rainfall time series for the six-month accumulated precipitation appears to lag behind the NO₃-N concentration time series. It is important to note that the precipitation actually leads by five months, as the precipitation time series represents the cumulative precipitation over six months.

Figure 27b illustrates the CCF distribution chart between the annual cumulative precipitation and annual NO₃-N concentration for different periods. The main CCF curve is plotted positively, indicating a “positive relationship with a negative time lag” pattern. This pattern suggests that precipitation transports NO₃-N.

As previously pointed out by [14], the CCF for 1-year precipitation (thick blue dashed line) does not show a significant correlation beyond the 95% confidence interval. The CCF for the 2-year cumulative precipitation time series (orange thick dashed line) has a statistically significant CCF of 0.45, but only at a time lag of 0 years. The maximum CCF for the 3-year cumulative precipitation time series is also 0.42 at a time lag of 0 years. The maximum CCF from the 4-year cumulative precipitation time series is plotted on the positive time-lag side. The maximum CCF for the 5-year cumulative precipitation time series is 0.52 at a 2-year time lag. The 11- to 18-year time series show significant correlations from a lag of 0 to a lag of 7 years, but the maximum CCF is observed with the 10-year cumulative precipitation time series (thick brown line), with a CCF of 0.771 and a time lag of 3 years. Although the NO₃-N concentration time series appears to lead the 10-year precipitation time series by 3 years, it should be noted that the precipitation, in reality, leads by several years. A correlation analysis between the annual cumulative precipitation and annual NO₃-N concentrations revealed that NO₃-N in field soils, which contributes to the increase in NO₃-N concentrations in groundwater, infiltrates with long-term precipitation for more than 10 years.

6. Discussion

6.1. Leaching Ratio by Multiple Regression and Machine Learning Regression Model

In the multiple regression analysis, where the three nitrogen load sources of Miyako Island served as explanatory variables and the groundwater nitrogen amount as the target variable, the partial regression coefficients varied depending on the regression equation and data period, even within the same region. This suggests a nonlinear relationship between the three nitrogen load sources and the groundwater nitrogen amount. Indeed, the partial dependence plots (PDPs) of the random forest model, which can handle nonlinearity, confirmed this nonlinear relationship between each nitrogen load source and groundwater nitrogen amount.

The fertilizer leaching ratio, estimated solely from the linear part of the PDPs for comparison with partial regression coefficients, was 0.284 based on Nakanishi’s [10] two-year data and 0.293 based on 30 years of the Miyako data. Furthermore, these values closely matched the fertilizer’s partial regression coefficient of 0.29, which was recalculated from Nakanishi’s [10] data. It is noteworthy that the fertilizer leaching ratios from different data and methods consistently fall between 0.28 and 0.30, potentially holding physicochemical significance.

Kunimatsu [96] found a leaching ratio of 0.31 based on cultivation trials of non-sugarcane crops in Japan. Zhou and Butterbach-Bahl [97] reported average leaching ratios for wheat and corn of 0.22 and 0.15, respectively, from 32 global cultivation trials. Reviewing recent cultivation trial studies, Bijay and Craswell [61] found that the percentage of applied fertilizer nitrogen infiltrating below the root zone was below 0.30.

Focusing on sugarcane cultivation trials in lysimeters filled with limestone-derived soils (including Shimajiri–Mahji), the reported leaching ratios are as follows: 0.265 for summer planting on Miyako Island [98]; 0.33 for spring planting and 0.067 for ratooning on Tokuno Island [99]; and 0.293 for ratooning and 0.444 for spring planting on Amami Island [100]. Based on these results, an appropriate fertilizer leaching ratio appears to be between 0.2 and 0.3. While the Ministry of the Environment [2] attributed the NO3-N pollution of Miyako Island to a high leaching rate of 0.4, this claim is not supported by our findings.

It should be noted that these lysimeter values are from single-cycle cultivation tests. The leaching ratio for summer planting, according to Nakagawa et al. [98], represents the leaching ratio over two years. The leaching ratio converted to one year is 0.134. On Miyako Island, most sugarcane cultivation from 1980 to 2000 was summer planting, which makes the leaching ratio 0.134. If the leaching ratio contributing to the groundwater NO₃-N concentration is 0.3, approximately 0.15 (obtained by subtracting 0.134 from 0.3) may represent NO₃-N released from the limestone unsaturated zone below the soil layer. This will be discussed further in Section 6.6.

6.2. Trends and Seasonal Components in NO₃-N Concentration Time Seriess

Despite the limited timing of farmland fertilizer application, groundwater NO₃-N concentrations are often reported to show little discernible seasonal fluctuation (e.g., [14,101,102]). However, a review of 51,000 groundwater datasets from all UK aquifers by Stuart et al. [103] found that approximately one-third had significant seasonal cycles in their NO₃-N concentrations. When limited to the Chalk aquifer dataset, almost 50% exhibited statistically discernible seasonal cycles [104]. Seasonal cycles in NO₃-N concentrations usually show a maximum during the wet winter, coinciding with wheat fertilization [104].

Stuart et al. [103] and Ascott et al. [16] revealed that seasonal cycles are unique to fractured chalk layers. To clarify areas with seasonal cycles in their NO₃-N concentrations, Ascott et al. [16] classified groundwater NO₃-N concentration time series data from 96 sites in southeast England (1995–2022) into four clusters using cluster analysis. They found that the seasonal cycle of Cluster 3 is formed by fracture flow (or bypass flow) through fault cracks. Interestingly, Cluster 4, which lacks a seasonal cycle, is located close to Cluster 3, and Cluster 3 tends to be in areas of intense fracturing within chalk fault zones. Therefore, even within the same area, seasonal cycles in NO₃-N concentration fluctuations may or may not appear depending on the extent of crack development [16].

Even in Ryukyu Limestone aquifers, the monthly NO₃-N concentration time series sometimes lack a seasonal cycle. While the seasonal cycle is unclear in the monthly NO₃-N concentration time series for Miyako Island in the Central Ryukyu Arc [14], it is clear in the Amami Islands in the Northern Ryukyu Arc [105,106]. The time series decomposition technique in this study not only reaffirmed the seasonal component’s presence in weekly NO₃-N concentration time series but also revealed a clear seasonal cycle in the monthly NO₃-N concentration time series. The seasonal cycle of the weekly NO₃-N concentration time series showed no correlation with the seasonal cycle of the precipitation time series. This suggests, as Nakanishi [15] pointed out, that the seasonal cycle of NO₃-N concentrations is highly likely to be influenced solely by fertilization periods. The three peaks in the seasonal cycle of the monthly NO₃-N concentration time series coincided with the three fertilization periods of summer-planted sugarcane cultivation. This finding confirms that monthly NO₃-N concentration fluctuations in groundwater exhibit seasonal cycles across all regions of the Ryukyu Limestone area. The unobserved seasonal cycles on Miyako Island are likely due to the significant influence of trend and residual components, which masks the seasonal cycle. These results are important for water quality management. Since the timing of sugarcane fertilization varies depending on the cultivation method, understanding the changes in the seasonal cycle may be useful in understanding the impact of an expected increase in the ratoon cultivation area on NO₃-N concentrations.

Both Miyako Island, where seasonal cycles are obscured in the NO₃-N concentration time series, and Amami Island, where seasonal cycles are evident, have aquifers composed of Ryukyu Limestone. In the chert aquifer, seasonal cycles tended to occur in areas where fracture flow was dominant [16,103]. However, there is no significant difference in hydraulic structure between the Ryukyu Limestone aquifers in both regions. Conversely, sugarcane cultivation methods differ. As of 2015, over 50% of sugarcane on Amami Island was cultivated by ratooning [107], while over 90% on Miyako Island was summer-planted (Figure 10). It is possible that the strength of seasonal changes in the monthly NO₃-N concentration time series may differ depending on the sugarcane cultivation method (fertilization pattern); however, further investigation is needed.

6.3. Cross-Correlation Analysis of Nitrogen Load Indicators and Groundwater NO₃-N Concentration

6.3.1. Potential for Domestic Wastewater to Produce Negative CCF

The time series CCF for each monthly nitrogen load source was 0.774 for fertilizer, 0.285 for livestock wastewater, and −0.251 for domestic wastewater (Figure 23b). The CCFs for fertilizer and livestock wastewater are thought to roughly reflect the proportions of surface load sources. However, a negative CCF for domestic wastewater has not been previously reported. This section explores the possibility of such a CCF occurring for domestic wastewater.

In Japan, a system of returning human waste from septic tanks to farmland was established over more than 800 years, spanning from approximately the 12th century to the 20th century [108]. However, this practice was banned in 1950 by instructions from the General Headquarters of the Supreme Commander for the Allied Powers (GHQ), which occupied Japan after World War II. As a result, human waste is now either collected from dedicated collection tanks for centrally managed systems (night soil collection system) or treated in septic tanks.

A combined-treatment septic tank processes both toilet wastewater (sewage) and household wastewater from kitchens and bathrooms. From 1990 to 2010, the adoption rate of flush toilets on Miyako Island increased to 45.6% [9]. Consequently, in rural areas, about half of the residents’ human waste is diluted with 13 to 20 L of water in the toilet. This wastewater then mixes with other household wastewater in the septic tank and is further diluted. In an advanced-treatment septic tank, nitrogen is removed through biochemical processes. A nitrogen-removal combined-treatment septic tank [109] can reduce the NO₃-N concentration of wastewater to an average of 6.2 mg/L [110].

On Miyako Island, while sewerage systems are installed in some densely populated areas, such as the Hirara district, public sewerage systems are not available across the entire island. In other areas, domestic wastewater was primarily treated using either the human waste collection tank method (load unit: 4.1 kg/person/year) or a septic tank for combined wastewater (load unit: 2.4 kg/person/year) [9]. According to a 2018 survey [9], 432 people (7.4%) of the 5808 residents in Gusukube district were connected to public sewerage (agricultural and fishing village wastewater). The remaining domestic wastewater was mainly treated using the combined-treatment septic tank method.

Ishida et al. [111] conducted a survey of NO₃-N concentrations in the Sunagawa Basin in 2000 and 2003, revealing that the NO₃-N concentrations near settlements of several dozen houses ranged from 2.69 to 6.11 mg/L (average 4.76 mg/L), which was lower than the surrounding farmland areas (8–10 mg/L). Therefore, if sufficiently diluted septic tank-treated water seeps into the ground, the NO₃-N load on groundwater is expected to be smaller than that predicted by the basic unit method. As the domestic wastewater CCF of −0.251 is statistically significant, its cause requires clarification in future research.

6.3.2. Monthly Cross-Correlation Between Nitrogen Load Sources and NO₃-N Concentrations in Kajido Water Sources

In the cross-correlation analysis between monthly nitrogen load source indicators and NO₃-N concentrations in the Kajido water headwaters over 37 years (1977–2013), the CCF for indicators other than the nitrogen supply indicator ranged from 0.67 to 0.83, with a time lag of 0 to −2 years. The CCF for the nitrogen supply indicator was 0.71, with a time lag of −5 years.

It is noteworthy that, while the time lag between the peak nitrogen supply event in 1980 and the peak NO₃-N concentration event in 1989 was −9 years, the cross-correlation showed a time lag of −5 years. This 4-year shortening of the time lag occurred because time series cross-correlation analysis calculates the overall balance between two time series, rather than the time lag between individual peak events. This finding is consistent with the fact that the 1980 peak event, estimated from fertilizer monetary sales amount, was not an anchoring peak event in the 37-year long-term time series.

6.3.3. Annual Cross-Correlation: Nitrogen Load Indicators and NO₃-N Concentration (1960–2023)

The CCF between Miyako Island’s 63-year time series of the fertilizer application amount (Figure 13a) and fertilizer application ratio (Figure 13b) and the NO₃-N concentration time series was 0.33 and 0.322, respectively. The time lag for both indicators was also −15 years. This indicates that the 1964 peak event for both the fertilizer application amount and ratio indicators influenced the 1989 peak event of NO₃-N concentration.

Kim et al. [18] analyzed the lag time between the soil surface N surplus (kg/ha/year) and groundwater NO₃-N concentrations in France’s La Voulzie limestone aquifer using cross-correlation analysis and SF₆ dating. All three springs in the La Voulzie limestone aquifer showed strong correlations (CCF = 0.70 − 0.83), with lag times of 8, 15, and 24 years, respectively. Based on the relationship between the sample collection depth, delay time, and groundwater age, Kim et al. [18] estimated that matrix flow was the dominant pathway for nitrate flux in the La Voulzie limestone aquifer.

The CCFs for Miyako Island are lower than those reported by Kim et al. [18], and the SF₆ ages tend to be younger than Kim’s time lags. From 2001 to 2005, an average of 5.05 million m³ of groundwater was pumped from the Sunagawa Dam and 2.46 million m³ from the Fukusato Dam [112]. The effective storage volumes of the Sunagawa Dam and Fukusato Dam are 6.8 million m³ and 7.6 million m³, respectively. Records show that 74% of the water volume at Sunagawa Dam and 32% at Fukusato Dam was replaced with new groundwater annually. Consequently, the analyzed groundwater characteristics of Miyako Island were strongly influenced by new groundwater, which likely resulted in lower CCF values and younger SF₆ ages compared to those of Kim et al. [18].

6.4. Periodicity Analysis of NO₃-N Concentration Time Series Using Wavelet Transformation

A 30-year hydrological sample size is generally considered sufficient for hydrological frequency analysis in water resource management [113]. However, in this study, the cross-correlations between weekly, monthly, and yearly NO₃-N concentration time series and precipitation time series within this 30-year sample were inconsistent. Specifically, the CCF of the weekly NO₃-N concentration time series and 90-day (3-month) cumulative precipitation was 0.442, indicating a transport effect of NO₃-N. Conversely, the CCF of the monthly NO₃-N concentration time series and 3-month cumulative precipitation was negative, suggesting a dilution effect on NO₃-N concentrations. This inconsistency likely stems from the assumption that weekly and monthly NO₃-N concentrations are correlated with precipitation for the same period with the same weight (stationary).

Assuming that fluctuations in weekly, monthly, and yearly NO₃-N concentration time series can be expressed by trigonometric functions, these time series can be considered as a hierarchical structure simulated by high-frequency (Sin 1), medium-frequency (Sin 2), and low-frequency (Sin 3) trigonometric functions, as illustrated in Figure 28. In the field, these time series sum to form a composite time series (Sin 1 + Sin 2 + Sin 3). The figure shows that the weight of the NO₃-N concentration at a certain time in the summed time series differs depending on which component time series it is incorporated into. However, because actual NO₃-N concentration time series fluctuate non-stationarily, the summed time series become more complex and cannot be decomposed into individual time scales.

Recently, applying wavelet transforms to cross-correlation analysis between non-stationary groundwater level time series and precipitation time series has revealed various correlation periods [113,114,115]. Li et al. [113] combined the wavelet analysis method with long-series sunspot number data and representative station annual precipitation data to show that solar activity has a 10-year cycle, that the annual wet–dry cycle of representative precipitation observation stations has a 10–12 year cycle, and that sunspot and precipitation data are consistently aligned. Schuler et al. [115] applied wavelet coherence analysis to the correlation between spring discharge and river runoff in a karst aquifer. The results revealed short-term periods ranging from 0.1 days (2 h) to less than 10.7 days (256 h), medium-term periods ranging from 35 to 72 days, and long-term periods ranging from 333 days to 2 years. In short-term rainfall events, spring discharge responded quickly to peak river runoff. In the medium-term period, spring discharge was related to the seasonal precipitation pattern, with a time lag between spring discharge and surface water runoff. In the long-term period, spring discharge and river runoff were in phase and had no time lag.

Figure 28. Conceptual diagram of the hierarchical structure of weekly, monthly, and annual NO₃-N concentration time series (modified from [116]). The weekly time series is modeled using a high-frequency trigonometric function (Sin 1), the monthly time series using a medium-frequency function (Sin 2), and the annual time series using a low-frequency function (Sin 3). Their summed time series is modeled using (Sin 1 + Sin 2 + Sin 3).

Figure 28. Conceptual diagram of the hierarchical structure of weekly, monthly, and annual NO₃-N concentration time series (modified from [116]). The weekly time series is modeled using a high-frequency trigonometric function (Sin 1), the monthly time series using a medium-frequency function (Sin 2), and the annual time series using a low-frequency function (Sin 3). Their summed time series is modeled using (Sin 1 + Sin 2 + Sin 3).

Figure 29a,b show the wavelet power spectra for the weekly NO₃-N concentration time series in spring water and the precipitation time series, respectively. Figure 29c,d show the wavelet power spectra for the monthly NO₃-N concentration time series in the Kajido water source and the precipitation time series, respectively. The semicircle behind the wavelet power spectrum indicates the cone of influence (COI). The white lines represent regions where the p-value is less than 0.1 for the null hypothesis that the series at time t has no periodicity, indicating statistically significant periods. The black lines are the ridges of wavelet power, which denote significant periodicity.

In the power spectrum of the weekly NO₃-N time series, the 1-year (52-week) cycle is significant with a power level of 0.1 or higher (Figure 29a). Its significance is indicated by a white line and a central black power ridge. The 2.5-year (128-week) cycle is statistically significant but lacks a black power ridge. The approximately 4-month (12–20-week) cycle is also significant, being surrounded by a white line and with a central black power ridge, although it is interrupted for part of the study period (7 years). This cycle is likely related to the 3-month (12-week) cycle predicted by the partial autocorrelation function (PACF) (Figure 17). The power spectrum of the precipitation time series has 1-year (52-week), 4-month (16-week), and 2-month (8-week) cycles. However, the white line area is island-like and discontinuous (Figure 29b). Comparison of the power spectra of the NO₃-N and precipitation time series indicates that the annual and four-month cycles may be correlated.

The wavelet power spectrum of the monthly NO₃-N concentration time series shows a long-term 9–10-year (107–128 months) cycle, indicated by a prominent white line encompassing a central black line. The power spectrum of the monthly precipitation shows long-term 10-year, medium-term 2-year, and short-term 1-year cycles. However, these high spectral areas occur in pulses and have low power levels (Figure 29d). A comparison of the power spectra of both time series indicates that the 10-year cycles of NO₃-N concentration and precipitation may be correlated. This result is consistent with the CCF values for the annual fertilizer application over a 60-year period, which have a time lag of −15 years (Figure 25), and the CCF for the 10-year cumulative precipitation and NO₃-N concentration, which is 0.771 (Figure 27b).

The spectral area of the medium-term 2–3-year (23–37 months) cycle in the NO₃-N concentration time series is interrupted around April 1997. This observation is likely due to a change in the precipitation cycle from 2.2 years (26 months) to 1.3 years (16 months). Given that NO₃-N concentrations are correlated with the time of fertilization and the amount of precipitation, the discontinuity in the spectral area is likely caused by the change in precipitation timing while the fertilization timing remains constant. The power spectrum of precipitation shows high power spectral pulses at 8 months, 5 months, 3 months, and 2 months. Some of these pulses may correlate with short-term pulses in NO₃-N concentrations.

Figure 30 shows the cross-wavelet transform results of the monthly NO₃-N and precipitation for the Kajido water source. The arrows in the figure indicate the phase difference between the NO₃-N concentration time series and the precipitation time series. An upward arrow indicates that the NO₃-N concentration time series and the precipitation time series are in phase. An arrow pointing downwards to the right indicates that the NO₃-N concentration time series lags behind the precipitation time series by a period of 4/π (3 months) [95]. The results show a 12-month (1-year) correlation period between the NO₃-N concentration time series and the precipitation time series, with a 3-month lag. The 3-month correlation period of the strong power spectrum has no phase difference, but it only lasted until April 1997 due to a change in the precipitation period. The 24-month (2-year) and 48-month (4-year) correlation periods are outside the cone of influence (COI) and are therefore not statistically significant.

6.5. Hydrogeological Structure of the Ryukyu Limestone Unsaturated Zone Related to a Time Lag Exceeding 10 Years

In chalk aquifers, the “legacy effect,” where the peak of the surface nitrogen load lags several years behind the peak of the NO₃-N concentration in groundwater, is thought to be caused by the matrix’s storage function. The “Nitrate Time Bomb” (NTB) model estimates the recharge water descent rate in the chalk unsaturated zone to be 0.76–1.11 m/year and uses it to calculate the “legacy effect” [87]. Calculations across the UK revealed nitrate transport times ranging from 1 year to over 400 years. In approximately 27% of the country, the input NO₃-N was predicted to reach the groundwater level within 1 year, while, in about 88% of the country, it was predicted to reach the groundwater within 20 years [87].

The legacy effect in limestone aquifers is thought to occur when infiltrating NO₃-N solution is temporarily stored as perched water due to a relatively impermeable layer in the unsaturated zone, then gradually seeps out [117]. The most likely locations for this effect are the epikarst reservoir and the unsaturated zone matrix reservoir. Husic et al. [118] found in a reservoir model that the delay in the epikarst reservoir is several weeks to several months, and the delay in the unsaturated zone reservoir is usually several months. Gunn [43] reported that tracer tests in limestone unsaturated zones showed times to reach groundwater ranging from 0 to 19 weeks. The initial flow is interpreted as rapid movement through small fractures (macropore flow), while long-term flow is associated with slow movement down the porous material (matrix flow). Based on the storage model formulated by Husic et al. [118] and observational data from Gunn [43], it is not possible to predict legacy effects for several years in the limestone unsaturated zone. However, Kim et al. [18] demonstrated that the time lag between the soil surface nitrogen surplus and groundwater NO₃-N concentrations ranged from 8 to 24 years in three springs within France’s Cretaceous La Voulsy massive limestone aquifer, attributing this slow flow to matrix flux.

Archie [119] categorized Paleozoic limestone samples from west Texas into three types: (1) oolitic, (2) compact crystal, and (3) chalky. He plotted their matrix porosity against the logarithm of hydraulic conductivity, considering this classification and plot generally applicable to all limestones. Kodai [120] reviewed the porosity–permeability relationships of various limestones, chalks, and salts worldwide and improved Archie’s diagram (Figure 31). Since Kodai [120] did not collect data on Quaternary limestones, data on Ryukyu Limestones [3,37] and South Australian limestones [121] were added. Figure 31 shows that Paleozoic to Mesozoic limestones are more permeable than chalks but less permeable than Quaternary limestones. Quaternary limestone data are derived from pumping tests, so the permeability includes information beyond the matrix. However, it is clear that the matrix permeability of Quaternary limestones is two to three orders of magnitude higher than that of older limestones. Therefore, while the low matrix permeability of chalk aquifers can explain the legacy effect, the high matrix permeability of Quaternary limestones makes it difficult to explain legacy effects exceeding 10 years.

If horizontal cavities in the unsaturated zone are filled with allochthonous inflowing clay layers, recharge water seeping through matrix flow may be stored in these layers. In this case, the descent speed is expected to be slower than with matrix flow alone. Several such inflowing clay layers have been confirmed on Miyako Island (Figure 5). Three layers of inflowing clay were identified at the recharge test site by Yoshimoto et al. [22] (Figure 6).

Yoshimoto et al. [22] conducted a recharge test of an unsaturated aquifer in Ryukyu Limestone, revealing the storage function of the inflowing clay layer in the unsaturated zone. The EC breakthrough curve showed that the EC reached a minimum of 0.20 mS/cm 63.7 h after the test’s start, then increased to 0.41 mS/cm. The EC then continued to fluctuate, increasing and decreasing by more than 10 times, and remained above background values (>0.01 mS/cm) for over 240 h. This change in the breakthrough curve is interpreted as a small amount of seawater being stored in the allochthonous clay layer and recharged from there in a pulsatile manner for more than 240 h. This was also confirmed by neutron moisture logging results. In this test, we were unable to confirm the final time of matrix recharge. However, in tracer tests on landslide areas with fractured rock, for example, it has been reported that the tracer breakthrough curve tails for more than two years [123]. If the matrix flow in the recharge test continues for, say, one year, the ratio of matrix flow could be 30% or more.

The behavior of seawater (EC) in recharge tests can be used to infer the behavior of NO₃-N. NO₃-N leached from the field is temporarily stored in the allochthonous clay layer during the recharge process with precipitation, then it slowly descends. This phenomenon may account for influences on the groundwater from more than 10 years ago. The CCF values for the annual fertilizer application over a 60-year period, with a time lag of −15 years, as well as the CCF for the 10-year cumulative precipitation and NO₃-N concentration (0.771) and the 10-year cycle from the wavelet transform for both annual precipitation and NO₃-N concentration, all may indicate the influence of such long-term groundwater.

6.6. Relationship Between Nitrogen Load Sources and Groundwater NO3-N Concentrations on Yoron Island in the Northern Ryukyu Arc

Cross-correlation analysis of time series of fertilizer nitrogen application (as an indicator of sugarcane field area) and the groundwater NO₃-N concentration on Miyako Island revealed a time lag between increases in fertilizer nitrogen and increases in NO₃-N concentration. If cross-correlation analysis is effective in detecting the time lag between increases in fertilizer nitrogen and increases in the NO₃-N concentration, this method may be generally applicable to areas of the Ryukyu Arc where sugarcane is grown in the Ryukyu Limestone region. In this section, we applied cross-correlation analysis to a time-series analysis of groundwater NO₃-N concentrations, nitrogen load sources, and the sugarcane field area on Yoron Island in the Amami Islands in the Northern Ryukyu Arc (Figure 1), which has similar geological and agricultural conditions to Miyako Island, to verify its versatility.

Nakano et al. [67] examined trends in NO₃-N concentrations over a 74-year period (1945–2019) on Yoron Island, as well as the time series of nitrogen loading sources over a 33-year period (1984–2017). The groundwater NO₃-N concentrations were approximately 0.1 mg/L in 1945, increased to 2.5–3.7 mg/L between 1967 and 1969, peaked at 9.5 mg/L in 1995, and then declined to 4.4 mg/L in 2019 (Figure 32a). The time series of nitrogen loading sources showed that fertilizer use peaked at 501 t/year in 1987 and then declined, reaching 183 t/year in 2017. Livestock waste increased from 71 t/year in 1984 to 233 t/year in 2004, then decreased to 83 t/year in 2017. Domestic wastewater remained at approximately 10 t/year, with little change. The total nitrogen load, combining these sources, was 546 t/year in 1984, peaked at 627 t/year in 1996, and then decreased to 276 t/year in 2017 (Figure 32b).

A comparison of the trends in nitrogen load sources and NO₃-N concentrations over the 33-year period suggests that nitrogen load sources have an impact with a time lag of −1 year (Figure 32a). Indeed, cross-correlation analysis of the 33-year nitrogen load source and NO₃-N concentration time series revealed that the CCF of the fertilizer and NO₃-N concentration time series reached a maximum of 0.867 at a time lag of −1 year. The CCF of the total nitrogen and NO₃-N concentration time series reached a maximum of 0.810 at a time lag of 0 year (Figure 32b). Interestingly, the relationship between the CCF of fertilizer and the CCF of total nitrogen is similar to the Miyako Island example (Figure 23b), with the CCF of fertilizer being higher than the CCF of total nitrogen. This is likely due to the negative CCF of domestic wastewater The distribution patterns are also similar: the CCF pattern for fertilizer forms a symmetrical triangle on the positive and negative time-lag axis, while the CCF pattern for the total nitrogen on the positive side of the time lag exhibits a more gradual slope than on the negative side. However, it is important to note that the 33-year cross-correlation analysis does not include the changes from 1964 to 1993, when NO₃-N concentrations increased sharply.

On Yoron Island, approximately 200 hectares of paddy fields were present between 1945 and 1966. This indicates that the vertical permeability of the Ryukyu Limestone on Yoron Island is lower than that on Miyako Island [124]. However, due to the economic prioritization of sugarcane over rice, the paddy field area declined to less than 6 hectares after 1975. Meanwhile, the sugarcane cultivation area increased sharply from 120 hectares in 1960 to 716 hectares in 1970 [55] (Figure 31). Thereafter, the sugarcane area increased gradually, peaking at 886 hectares in 1985, and then decreasing to 863 hectares in 1990. After 1990, however, it declined at a rate of approximately 14 hectares per year, reaching 405 hectares in 2023.

For example, in 2018, the sugarcane cultivation on Yoron Island consisted of 80.5% ratoon crops, 13.1% spring plantings, and 6.4% summer plantings, which made it the region with the highest proportion of ratoon cropping in the prefecture (72.0% for the prefecture as a whole) [55]. Because Yoron Island was less affected by pests and diseases than Miyako Island, there has been little change in cultivation methods over the past 60 years. Therefore, changes in sugarcane cultivation area are considered to be correlated with changes in fertilizer use.

Figure 33a shows that temporal variations in groundwater NO₃-N concentrations generally correspond to trends in sugarcane-derived nitrogen loading. The estimated time lag between the rapid increase in sugarcane area and the rise in NO₃-N concentrations is −10 years for the difference between the sugarcane area growth curve and the NO₃-N concentration growth curve, −12 years for the transition point from rapid to slow increase (1971 vs. 1983), −12 years for the difference between peaks (1985 vs. 1997), and −7 years for the transition point of the rapid decline (1990 vs. 1997). The CCF distribution in Figure 33b shows the results of a cross-correlation analysis of sugarcane area and NO₃-N concentration time series over the 59-year period from 1960 to 2019. The maximum CCF value is 0.631 at lags of −10 and −11 years. However, from lags of −14 to 0 years, the CCF remains statistically significant at ≥0.5, which indicates that the influence of the sugarcane cultivation area persists over this range of lags.

On Yoron Island, as on Miyako Island, the 30-year time series of nitrogen loading sources and the sugarcane area showed short-term effects on NO₃-N concentrations with lags of −1 to 0 years, whereas the 60-year-or-longer time series showed lags of −10 to −15 years. The similarity of the results obtained in the two regions demonstrates that the cross-correlation analysis method applied in this study is effective for analyzing the formation of NO₃-N concentrations in the Ryukyu Limestone-covered Nansei Islands.

6.7. Implications for Water Quality Management: The Formation Mechanism of Groundwater NO₃-N Concentrations on Miyako Island

Based on our findings, the mechanism underlying the formation of groundwater NO₃-N concentrations on Miyako Island is interpreted as follows:

The decline in NO₃-N concentrations from their 1988–1989 peak was due to a decline in fertilizer application to sugarcane cultivation areas, not a decrease in cultivated land area. This decline occurred with no time lag (Figure 34). The subsequent decline in concentrations may be related to the conversion of some sugarcane fields to pasture, for which compost that has a lower leaching rate than chemical fertilizer is used.

Conversely, the mechanism underlying the increase in NO₃-N concentrations is complex. This complexity may be due to historical changes in the area under sugarcane cultivation and the amount of fertilizer applied. The area under sugarcane cultivation experienced two peaks, in 1964 and 1989 (Figure 34). The first peak was caused by the expansion of ratoon cultivation, which later collapsed after pesticide withdrawal in 1971, leading to conversion to summer planting. By 1987, summer planting accounted for over 90% of the total area. Because the fertilizer application is 250 kg/ha/year for ratoon and 155 kg/ha/year for summer planting, fertilizer use peaked only once, in 1964, despite the two cultivation peaks. Consequently, during the rise in NO₃-N concentration, 70% of the NO₃-N concentration (Figure 23) was due to fertilization from current sugarcane cultivation areas, with no time lag, while the remaining 30% was due to fertilization 15 years prior (Figure 25). Therefore, the change in NO₃-N concentration may have exhibited different hysteresis patterns between its increase and decrease phases.

The hysteresis in NO₃-N concentrations in the Ryukyu Limestone Aquifer is important for water quality management. Although NO₃-N concentrations in Miyako Island’s groundwater are currently declining, the reduction in sugarcane area, which influences this decline, is approaching a steady state (Figure 34). Meanwhile, the trend in fertilizer amounts, which had been decreasing with the reduction in summer-planted sugarcane area, has recently shifted to an upward trend due to the increase in ratoon-cultivated area (Figure 34). This effect may become apparent in a decade. If the sugarcane area is not reduced at that time, NO₃-N concentrations may rise again to reach the environmental standard of 10 mg/L. Therefore, continued monitoring and careful observation of fluctuations in NO₃-N concentrations are necessary.

7. Conclusions

This study investigated the historical changes in groundwater NO₃-N concentrations on Miyako Island, which averaged 1.95 mg/L in 1966, rose to nearly 10 mg/L by 1989, and then declined to 3.4 mg/L by 2023. We used agricultural statistics, machine learning regression analysis, and time-series correlation analysis to determine the causes of these fluctuations.

Key findings:

• Agricultural statistics and random forest analysis: We identified two peaks in sugarcane cultivation area (1964 and 1989) but only one peak in fertilizer use (1964), because ratoon cultivation, which has a higher fertilizer application rate (250 kg/ha/year vs. 155 kg/ha/year for summer planting), dominated during the first peak. Our random forest model revealed a leaching rate of 0.2–0.3, which is consistent with lysimeter tests and contradicts the Ministry of the Environment’s claim of a high leaching rate of 0.4;
• Time-series analysis: Our cross-correlation analysis of annual and monthly fertilizer data with NO₃-N concentrations revealed a dual infiltration mechanism. Approximately 70% of the NO₃-N originates from rapid infiltration (zero-lag correlation of 0.744), while the remaining 30% is attributed to slow infiltration over a 15-year period (15-year lag correlation of 0.330). This slow infiltration is likely due to the temporary storage of nitrogen in the clay layer.

Implications for water quality management:

The hysteresis in NO₃-N concentrations is a critical factor for water quality management. While concentrations are currently declining, the recent shift from summer planting to ratoon cultivation has increased fertilizer application, raising concerns about future pollution. Given the 15-year time lag for slow infiltration, we predict that NO₃-N concentrations may begin to rise again in approximately 10 years, potentially exceeding the environmental standard of 10 mg/L. Therefore, continued monitoring is essential.

This study provides a predictive framework for water quality management in similar geological and agricultural environments, as demonstrated by a comparative analysis with Yoron Island, which showed similar dual infiltration mechanisms. Our findings offer a comprehensive understanding of the complex factors influencing groundwater quality on Miyako Island and establish a robust approach for managing water resources in the Ryukyu Arc.