Addressing the Advance and Delay in the Onset of the Rainy Seasons in the Tropical Andes Using Harmonic Analysis and Climate Change Indices

Abstract

The advance and delay of the rainy season is among the most frequently cited effects of climate change in the central Ecuadorian Andes. However, its assessment is not feasible using the indicators recommended by the standardized indices of the Expert Team on Climate Change Detection and Indices (ETCCDI), designed to detect changes in intensity, frequency, or duration of intense events. This study aims to analyze such advances and delays through harmonic analysis in Tungurahua, a predominantly agricultural province in the Tropical Central Andes, where in situ data are scarce. Daily in situ data from five meteorological stations were used, including precipitation, maximum, and minimum temperature records spanning 39 to 68 years. The study involved an analysis of the region’s climatology, climate change indices, and harmonic analysis using Cross-Wavelet Transform (XWT) and Wavelet Coherence Transform (WCT) to identify seasonal patterns and their variability (advance or delay) by comparing historical and recent time series, and Krigging for regionalization. The year 2000 was used as a study point for comparing past and present trends. Results show a generalized increase in both minimum and maximum temperatures. In the case of extreme rainfall events, no significant changes were detected. Harmonic analysis was found to be fruitful despite of the missing data. Furthermore, the observed advances and delays in seasonality were not statistically significant and appeared to be more closely related to the geographic location of the stations than to temporal shifts.

1. Introduction

In many regions around the world, climate change is significantly altering seasonal patterns, directly affecting the timing and duration of rainy and dry periods. These changes not only impact local ecosystems and biodiversity but also have profound implications for agriculture, a critical pillar of developing economies [1]. Previous research, such as that conducted by [2] in Central and South America, has demonstrated that variability in the rainy season is a decisive factor influencing agricultural productivity and food security, primarily due to the resulting droughts and floods. At the global level, studies such as [3] in China have documented a decline in precipitation and shifts in seasonal patterns attributable to climate change.

The evaluation of climate change impacts is commonly conducted using the climate extreme indices developed by the Expert Team on Climate Change Detection and Indices (ETCCDI) [4,5]. This framework comprises 25 internationally accepted indices that are widely recognized as standard tools for characterizing climate extremes. The ETCCDI is designed to describe the temporal behavior of extreme events associated with minimum and maximum temperatures and precipitation, providing a consistent and comparable methodological basis for climate change detection and analysis across different regions worldwide [6]. In Ecuadorian Tropical Andes, two general characteristics of anthropogenic climate change were identified [7]: a global increase in temperature from 0.6–1.4 °C during 2011–2040 [8] and a rise in the frequency and intensity of extreme weather events: precipitation increases reach up to approximately 32 mm/year, with heavy rainfall days (>10 mm and >20 mm) projected to rise to about 148 and 76 days per year, respectively, especially in the Amazon and northern coastal areas, under the RCP 8.5 (pessimistic) scenario [9].

Also, Tropical Andes is considered highly vulnerable to El Niño-Southern Oscillation (ENSO). Intensification of El Niño episodes in the Ecuadorian coastal and central Andes region, with recurrence intervals of 2, 4, and 7 years [10], has led to increased precipitation, causing significant human and material losses [11,12]. On the other hand, La Niña events result in extreme droughts, negatively impacting the socioeconomic landscape [13]. This climatic variability poses serious challenges to the agricultural sector, primarily due to increased hydrological stress [14,15]. Furthermore, anthropogenic activities such as deforestation, water pollution, and land-use change exacerbate the impacts of climate change [16]. These challenges are particularly acute in rural areas that lack adequate infrastructure, technology, and investment for climate adaptation [17,18].

In Ecuador, in addition to the climatic challenges, the analysis of precipitation is further constrained by an insufficient meteorological observation network that is not optimally distributed across the territory. The limited number of available in situ stations, particularly in mountainous regions, results in sparse spatial coverage and restricts the representativeness of local climate conditions. Moreover, existing stations frequently exhibit discontinuous records, and their sensors are prone to calibration drift due to harsh environmental conditions and limited maintenance. Consequently, the process of data quality control and homogenization becomes particularly demanding and time-consuming. These limitations are largely attributable to insufficient public investment, both in the expansion and modernization of meteorological monitoring infrastructure and in sustained research efforts in weather and climate sciences [19].

On the other hand, Tungurahua is one of the most important agricultural provinces in Ecuador and plays a strategic role in national food sovereignty [20]. Beyond the relevance of agriculture as a key economic activity, the province is highly sensitive to climatic variability, which directly affects farming systems and the livelihoods of rural households. According to [21], while both minimum and maximum temperatures will increase to 1.7 °C and 1.4 °C, respectively, they have not yet reached thresholds that cause significant physiological stress in plants and animals [22]. However, projections indicate that by 2070, temperature increases may exceed 2 °C [23]. Regarding precipitation, the analysis of climate indices in the study area shows that almost none of the precipitation-related indices exhibit statistically significant trends, indicating no robust increases in extreme rainfall in terms of intensity, frequency, or duration. However, local farmers consistently express a negative perception of rainfall variability [17]. This perception is not driven by the mere occurrence of extreme events, but rather by their timing relative to the expected seasonal cycle. Farmers report that both excessive and insufficient rainfall can cause substantial crop damage when these events occur outside the typical rainy or dry seasons. Specifically, an extension of the rainy season is associated with an increased incidence of crop diseases, particularly fungal infestations, whereas a prolonged dry season tends to favor the proliferation of insect pests [21].

Several studies have shown that identifying the onset and cessation of the rainy season constitutes a substantial methodological challenge due to strong interannual climate variability, particularly in regions with complex topography such as the tropical Andes. In this context, the analyses presented in [24,25] demonstrate that, even when advanced approaches based on precipitation thresholds, cumulative anomalies, or standardized climate indices are employed, deriving robust trends in the timing of the rainy season remains difficult. This challenge is further compounded by the widespread reliance on climate model outputs in previous studies, which, although valuable at regional scales, are often difficult to validate under local conditions where in situ observations are sparse or discontinuous. As a result, signals of advances or delays in seasonal onset may be obscured by the combined effects of high natural variability, model uncertainty, and large-scale forcings that are not yet fully understood.

In parallel, modeling-based studies such as [26] have documented statistically significant delays in the onset of the rainy season and reductions in its duration associated with deforestation, increased atmospheric stability, and diminished moisture transport from the Amazon. These findings underscore the importance of land–atmosphere interactions and vegetation physiology in regulating the regional hydrological cycle. However, adequately capturing these processes requires ecohydrological frameworks and coupled land–atmosphere models, whose outputs remain challenging to constrain and evaluate in data-scarce regions. Consequently, while such studies provide critical physical insights, their applicability at local scales is limited in areas where observational records are insufficient to support robust validation.

Within this context, there remains a lack of robust methodological approaches capable of detecting changes in the timing of rainy and dry seasons using incomplete and non-homogeneous in situ precipitation records, particularly in data-scarce regions of the tropical Andes. The present study seeks to assess the feasibility of applying harmonic analysis to in situ precipitation records in Tungurahua, which are characterized by limited availability, substantial data gaps, and non-homogeneous observation periods. Rather than relying on modeled precipitation fields, this research evaluates whether harmonic and wavelet-based techniques—combined cross-correlation, wavelet coherence, and standardized climate change indices—can reliably detect shifts in the timing of seasonal precipitation under realistic observational constraints. By explicitly testing the performance of these methods, this study aims to improve the understanding of seasonal precipitation variability in a predominantly agricultural region and to provide a methodological foundation for climate analysis and decision-making in environments where long, homogeneous in situ records are not available.

2. Study Area and Methods

The province of Tungurahua covers an area of 3386 km² and has a population of 563,532 inhabitants, of which 39.97% reside in rural areas where more than half of the local economy relies on agricultural activities [27,28]. It is located in a mountainous region of the Tropical Andes, in the central part of Ecuador. Although the prevailing climate is predominantly arid and temperate, the province encompasses a diversity of unique microclimates. On average, the mean annual temperature remains around 14 °C; however, at higher elevations—such as the Carihuairazo and Chimborazo mountains—colder conditions prevail, with snow present for most of the year [20], although Carihuairazo is practically thawed [29].

2.1. Meteorological Data

In general, in situ meteorological observations in Ecuador are limited and often discontinuous. For this study, precipitation data were collected from six meteorological stations located within the province of Tungurahua (Figure 1), with detailed information on each station provided in

Table 1. Description of the in situ data used in this study.

Code	Station	Latitude	Longitude	Altitude m.a.s.l	Temporal Range	From	To	Data Availability
M0029	Baños	−1.260	−78.405	1820	68	1950	2018	79.34%
M0126	Patate	−1.300	−78.500	2442	50	1948	2015	65.12%
M0127	Pillaro	−1.169	−78.553	2781	50	1964	2014	84.22%
M0128	Pedro Fermín	−1.352	−78.615	2897	37	1978	2015	93.52%
M0258	Querochaca	−1.367	−78.606	2863	39	1979	2018	83.07%
M1069	Calamaca	−1.281	−78.821	3417	27	1988	2015	73.41%

. All datasets were supplied by the National Institute of Meteorology and Hydrology (INAMHI).

2.2. Methods

The methodological framework adopted in this study is structured in two complementary phases. The first phase focuses on climate change assessment, involving a climatological analysis of precipitation and the computation of standardized climate change indices recommended by the ETCCDI [4,5]. This step provides a conventional characterization of rainfall variability and long-term trends. The second phase applies a harmonic analysis approach to examine the advance and delay of the onset of the rainy season. This is achieved through bivariate wavelet techniques, namely the Cross-Wavelet Transform (XWT) and Wavelet Coherence (WTC), which allow the identification of shared temporal–frequency patterns and phase relationships between past and present rainfall signals. The flowchart of this methodology is in Figure 2.

Quality Control

The air temperature and precipitation series were revised to eliminate errors that could affect the analysis, primarily through the identification of outliers, as described in [30,31]. Maximum and minimum temperatures exceeding three standard deviations or falling outside the diurnal range were zero-padded. Negative precipitation values were removed, and positive outliers were carefully examined, since they often correspond to extreme rainfall events, which are the main focus of this study. In this case, extreme rainfall events were retained, as they were consistent with the climatology of the region. Additionally, highly discontinuous periods or periods with missing data were identified and removed, as illustrated in Figure 3. The quality control was performed through the Plotly package in RStudio (Version 2024.12.1+563). Furthermore, a statistical analysis was carried out for each station, identifying, in addition to maximum and minimum values, quartiles (Q1, Q2, Q3) and percentiles (90, 99) [22,30]. Despite this data conditioning, the time series available for each station differed in their number of samples and contained numerous missing observations (Figure 4) [28].

2.3. Climate Change Analysis

The ClimDex package in R (v. 1.1-11) was used to calculate climate change indices recommended by the ETCCDI [4]. This tool allows the assessment of how climate change affects precipitation and temperature patterns [5]. Based on [21], only climate change indices exhibiting statistical significance greater than 80% are presented in this study. However, under a more stringent significance criterion, the results indicate that only temperature-related indices reach significance levels exceeding 90%, whereas precipitation indices generally do not meet this threshold. These, including their definitions and corresponding equations, are presented in

Table 2. Climate change indices used in this study are due to their statistical significance exceeding 80% since [21].

Index	Unit	Definition	Equation
PRCPTOT	mm/year	Total precipitation. Annual total precipitation on wet days (days with ≥1 mm of rainfall).	$PRCPTOT={\displaystyle \sum _{i=1}^N}Pi (Where Pi\ge 1 mm)$ $\mathrm{Where} P_i$ is daily precipitation, and N is the total number of wet days in the period of interest.
SDII	mm/day	Simple daily intensity index. Average daily precipitation on wet days.	$\mathrm{S}\mathrm{D}\mathrm{I}\mathrm{I}={\displaystyle \frac{{\sum }_{i=1}^N Pi}{N}}(\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} Pi\ge 1 \mathrm{m}\mathrm{m})$
R95p	mm	Very wet days. Annual total precipitation (in millimeters) exceeding the 95th percentile.	$R95p= \sum _{i=1}^M P_i (\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} \mathrm{P}\mathrm{i}>95\mathrm{t}\mathrm{h} \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}$) $\mathrm{Where} P_i$is daily precipitation, and M is the number of days exceeding the 95th percentile.
TXx	°C	Monthly maximum value of daily maximum temperature.	${TX}_{Xkj}=max\left({Tx}_{kj}\right)$ $\mathrm{Let} {Tx}_{kj}$ be the daily maximum temperature in month k, and period j.
TNx	°C	Monthly maximum value of daily minimum temperature.	${TN}_{Xkj}=max\left({Tn}_{kj}\right)$ $\mathrm{Let} {Tn}_{kj}$ be the daily minimum temperature in month k, and period j.

.

2.4. Comparison Between Present and Past

It is important to note that climate change is a gradual and sustained process over time [28]; therefore, there is no distinct point that separates past from present climate conditions. Using the R ClimDex package, the evolution of climate change indices (PRCPTOT, R95p, SDII, TXx, TNx) was analyzed over time to identify the effects of climate change in the study area. For this purpose, comparable time periods with the fewest possible missing data were selected.

Given the gradual and continuous nature of climate change, a clear and statistically distinct inflection point between past and present climate conditions may not always be evident, particularly in regions characterized by strong interannual variability and incomplete observational records.

In this study, the year 2000 was not selected based on a specific climatological or statistical threshold, but rather as a pragmatic choice to ensure comparable sample sizes before and after the study point across the analyzed stations. This selection allowed for a balanced comparison between two periods with similar data availability, despite the heterogeneous and discontinuous nature of the in situ precipitation records.

2.5. Normalization and Gap-Filling

Based on the requirements for harmonic analysis of the series, the data were normalized and gap-filled [31,32]. Normalization was performed by dividing the precipitation data by the maximum recorded value in each series, while missing values were replaced with zero, representing no rainfall which is the distribution’s most frequent value [8,33].

2.6. Monthly Aggregation of Data

To achieve a more precise seasonal analysis, daily precipitation data were aggregated into monthly totals. This procedure enabled the harmonic analysis to be reproduced using monthly aggregated values. Figure 5 presents the time series on a monthly basis for the stations, providing a clear view of seasonal trends and variations.

2.7. Wavelet Harmonic Analysis

The methodology applied in this study employs wavelet harmonic analysis, a mathematical tool that has enabled new applications in various scientific fields, including those related to the study of natural phenomena [34]. The interaction between time and frequency allows the extraction of valuable information from precipitation data and other relevant indicators, highlighting their significant concentration in both domains [35].

First, the Continuous Wavelet Transform (CWT) was employed to characterize the temporal and harmonic structure of the precipitation time series, which allows us to characterize the relationship between the rainfall series selected before and after the climate study-point. The applied techniques used to analyze these two sets of wavelet data, or bivariate wavelet, are the Cross-Wavelet Transform (XWT) and Wavelet Coherence (WTC), which quantify the common power and the degree of time–frequency correlation between these two rainfall signals. These methods enable the identification of coherent oscillations and phase relationships, thereby providing a robust assessment of temporal dependencies and shifts in rainfall dynamics across multiple time scales [33,36].

All stages of the bivariate wavelet analysis—including numerical computations and graphical representation of the results—were carried out using the Wavelets Toolbox, Signal Processing Toolbox, and Descriptive Statistics Toolbox [37]. In addition to the Cross-Wavelet and Wavelet Coherence toolbox developed by [38,39].

2.7.1. Continuous Wavelet Transform

The Continuous Wavelet Transform (CWT) is defined as a function $\psi \left(t\right)$ with zero mean, ensuring that it captures localized oscillatory behavior without introducing a net temporal bias.

The wavelet function $\psi \left(t\right)$ is modified through scaling and translation, governed by the scale parameter (s) and the temporal localization parameter (u), respectively (Equation (1)):

$${\mathsf{\psi }}_{u,s}\left(t\right)={\displaystyle \frac{1}{\sqrt{s}}}\mathsf{\psi }\left({\displaystyle \frac{t-u}{s}}\right)$$

(1)

The wavelet transform W of a function f(u,s), on scale s and time u, is calculated by correlating f in the wavelet function:

$$Wf\left(u,s\right)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f\left(t\right){\displaystyle \frac{1}{\sqrt{s}}}{\mathsf{\psi }}^{\ast }\left({\displaystyle \frac{t-u}{s}}\right)dt$$

(2)

where * represents the is the complex conjugate. Then, the wavelet transform of a signal f(t) at a given scale and time position is computed by correlating the signal with the scaled and shifted version of the wavelet function. The resulting wavelet coefficients represent localized spectral variations in the time–frequency domain.

Because the complex conjugate of the wavelet function is used, the CWT provides a detailed representation of the signal’s spectral content, comparable to windowed Fourier or spectrogram approaches, but with improved time–frequency localization. This advantage allows the identification of transient and non-stationary features, while remaining subject to the constraints imposed by the Heisenberg uncertainty principle [40].

2.7.2. Bivariate Analysis: Cross-Wavelet Transform (XWT) and Wavelet Coherence (WTC)

When the CWT is applied to two time series as explained in [38], the resulting wavelet coefficients can be used to perform a covariance analysis. This method enables the identification of shared frequency components, their temporal localization, and the magnitude of common spectral energy between the two signals. These relationships are typically represented in two-dimensional visualizations referred to as cross-wavelet spectra.

Unlike correlation coefficients, which are bounded between −1 and +1, covariance-based measures are unbounded and may assume any real value. The Cross-Wavelet Transform (XWT) is obtained by first applying the wavelet transform independently to each time series, denoted as $x_t$ and $y_t$, yielding the corresponding wavelet coefficients $W_x(u,s)$ and $W_y(u,s)$. Here, $u$ represents the temporal position and $s$ denotes the scale parameter, consistent with the formulation introduced in Equation (3). Based on these components, the bivariate wavelet representation is defined as

$$W_{xy}\left(u,s\right)=S\left(W_x^{\ast }\left(u,s\right)\cdot W_y\left(u,s\right)\right)$$

(3)

Coherence and correlation between two wave functions, commonly used in wavelet analysis, share notable similarities with conventional correlation coefficients; however, they differ in that they are defined within the time–frequency space. These relationships are visualized using a scalogram, which employs a color map to represent the coherence between two sinusoidal signals, offering a graphical depiction of the relationship between the signals over time and across frequency scales [35]. In the scalogram, the horizontal axis represents the temporal domain, while the vertical axis indicates the periods (or frequencies). This graphical representation facilitates the interpretation of how the frequencies common to both signals vary over time.

These frequencies are validated for events of interest, allowing the delineation of contours that reflect a statistical significance level of 5% [40]. The process of establishing this significance involves generating a background spectrum using white or red noise, against which the actual wavelet coherence spectrum is compared. This procedure enables the distinction between statistically significant coherences and those that may arise from random signals [38].

Where asterisk represents the complex conjugate, and “S” is a smoothing operator. Then, the XWT of two functions is [40]

$$XWT\left(u,s\right)=\left|W_{xy}\left(u,s\right)\right|$$

(4)

The instantaneous phase relationship, also referred to as the relative phase angle between $x_t$ and $y_t$ in the time–frequency domain, is obtained by evaluating the complex argument of the bivariate wavelet transform [37]. This phase angle, denoted as $\varphi (u,s)$, is expressed as [31]

$$\theta \left(u,s\right)=\mathrm{a}\mathrm{r}\mathrm{g}\left(W_{xy}\right(u,s\left)\right)$$

(5)

In practical applications, this phase information is visualized in cross-wavelet spectra using directional arrows, which indicate values confined to the interval $\left[-\pi ,\pi \right]$. Arrows pointing right indicate that the wavelet series are in-phase, while arrows pointing left indicate an out-of-phase behavior. When the absolute value of the phase angle is smaller than $\pi /2$, the first wavelet series lags in relation to the second series. Hence, arrows in this direction would indicate a “late onset” of the rainfall series from the year 2000. Conversely, absolute values of the phase angle exceeding $\pi /2$ indicate that the first series leads the second, indicating that exist an “early onset of rainfall” from the year 2000.

On the other hand, the continuous wavelet coherence (WTC) is derived by normalizing the XWT and is therefore commonly referred to as the magnitude-squared coherence. It can be expressed as follows:

$$WT{C}_{xy}\left(u,s\right)={\displaystyle \frac{{\left|S\left(W_x^{\ast }\left(u,s\right)\cdot W_y\left(u,s\right)\right)\right|}^2}{S\left({\left|W_x\left(u,s\right)\right|}^2\right)\cdot S\left({\left|W_y\left(u,s\right)\right|}^2\right)}}$$

(6)

The Cross-Wavelet Transform (XWT) has a meaning similar to that of correlation between signals, and it is sensitive not only to the common frequencies in the data but also to the magnitude of the variables under study (in this case, precipitation intensity). In this manner, the XWT and the WCT are complementary techniques that enable the analysis of the interaction and joint dynamics of the signals, integrating their results to obtain a deeper understanding of their temporal and frequency-domain relationships [40], and both the XWT and the WCT provide information on phase, which is essential for estimating leads or lags in precipitation events.

3. Results

3.1. Meteorological Description of the Stations

After performing the quality control in daily data and considering the non-parametric nature of precipitation, the maximum rainfall values recorded at each station are as follows: Baños (198.9 mm in May 1976, 160.4 mm in November 1982, 156.5 mm in August 1989, and 187 mm in March 2001). For Patate, the maximum values were 260 mm in September 1930 and 199.8 mm in January 1981.

An analysis of the climatology of the studied stations indicates that the rainiest area corresponds to Baños, which exhibits maximum daily precipitation values of up to 955.1 mm, being the lowest-altitude station. In contrast, the highest-elevation station in each record shows the lowest precipitation values, with a maximum of 320.20 mm per day.

Table 3. Main statistical descriptors of daily precipitation for each station.

mm	Baños	Patate	Píllaro	Pedro Fermín	Querochaca
Min	0.1	0.1	0.1	0.1	0.1
Max	198.9	260	49.9	42.2	41.7
Q1	1.1	0.7	0.6	1	0.5
Q2	3.1	2.2	1.7	2	1.3
Q3	7.5	5.4	4.2	4.4	3.5
P90	14	10.3	8.7	8.6	7.4
P99	37.5	26.8	21.2	22.90	20.9

presents the minimum, maximum, and quartile values, including the 90th and 99th percentiles.

The minimum values correspond to the precision limits of the rain gauges in the INAMHI network. Likewise, it should be noted that the rainiest stations are those located farther to the west, apparently due to the influence of Amazonian climatology, which contains higher moisture levels. The data from Calamaca station were excluded due to the limited amount of available information.

3.2. Climate Change Indices Analysis

The precipitation-related indices listed in Table 2 were analyzed, and the results are presented in

Table 4. Selected climate indices for precipitation and temperature recommended by the ETCCDI, applied to in situ data, ** means a confidence level above 95%, and * over 90%, bold indices means confidence level above 80%.

Station	Baños	Patate	Píllaro	Pedro Fermín	Querochaca
(SDII) [mm/day/year]	−0.005	−0.005	−0.006	0.013	0.008
p-value	0.719	0.719	0.504	0.175	0.352
(PRCPTOT) [mm/year]	−0.916	−0.916	−3.012	3.038	1.681
p-value	0.675	0.675	0.152	0.114	0.38
(R95p) [mm/day/year]	−0.402	−0.366	−1.099	1.182	0.788
p-value	0.839	0.852	0.215	0.222	0.464
(TXx) [°C/year]	0.028 **	0.018 *	0.041	0.048 *	0.018 *
p-value	0.004	0.067	0.227	0.049	0.067
(TNx) [°C/year]	0.028 **	0.038 **	0.011	0.003	0.042 **
p-value	0.019	0.006	0.639	0.764	0

. For the calculation of each index, a least-squares interpolation was performed using a linear function (solid line in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10). Each index exhibits either a positive slope—indicating an increase—or a negative slope—indicating a decrease. To determine whether this increase or decrease is statistically significant, the p-value is used; a value below 0.05 indicates a confidence level above 95%, in which case the result is marked with **. When the p-value is less than or equal to 0.1, the result is marked with *, corresponding to a 90% confidence level. Likewise, in the following figures, the moving average is shown with a dashed line.

As can be observed, the precipitation indices are not statistically significant, whereas the temperature indices are. These results support the conclusion that climate change is occurring in the study area, evidenced by a sustained increase in both maximum and minimum temperatures. However, no statistically significant change is detected for precipitation indices.

In Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10, in order to assess potential changes in precipitation patterns, past and present precipitation values are compared. The year 2000 was empirically selected as the dividing point. As the figures point out, this choice was necessary to identify a common reference point for all stations and indices while also balancing the amount of data available before and after that year.

The PRCPTOT index shown in Figure 6 measures the total annual accumulated precipitation. Although it does not exhibit strong statistical significance, an increase in precipitation after the year 2000 can be observed in the Pedro Fermín and Querochaca stations, as well as a rise in extreme precipitation events. For the Baños and Patate stations, no relevant change is evident between the periods before and after 2000. In the case of the Calamaca station, the absence of data prevents the analysis of this index. At the Píllaro station, a decrease in total precipitation is observed after the year 2000.

In Figure 7, the R95p index indicates a significant increase in the occurrence of extreme rainfall events, with the exception of the Píllaro station. For the Pedro Fermín and Querochaca stations, a marked increase after the year 2000 is evident, consistent with the previously noted rise in extreme precipitation.

Figure 8 presents the results for the SDII, which reflects the amount of rainfall precipitated per wet day. For the Pedro Fermín and Querochaca stations, the year 2000—indicated by the vertical red line—coincides with a change in the behavior of the SDII. This change may reflect variations in precipitation patterns driven by regional or global climatic factors such as El Niño, La Niña, or broader climate change trends [33]. For the remaining stations, the index exhibits a negative slope, indicating a decrease in daily precipitation intensity after the year 2000.

The temperature indices exhibit markedly different patterns, showing a consistent increase across all stations (Figure 9), despite the large number of missing data points. The Baños, Patate, and Píllaro stations display significant and steady warming trends, with clear positive slopes that reflect a continuous rise in temperature after the year 2000. In contrast, although the Pedro Fermín and Querochaca stations also show an upward trend, it does not reach statistical significance, possibly due to the high interannual variability observed at these locations (Table 4).

The TNx index, shown in Figure 10, measures the maximum monthly values of daily minimum temperature. All stations exhibit an increasing trend, with the exception of the Pedro Fermín station, where the moving average changes during the most recent years.

3.3. Past and Present Seasonal Analysis

To determine the climatology of the area, seasonality was analyzed using monthly accumulated precipitation, which allowed the identification of precipitation influences from both the Andes (characterized by a bimodal rainfall pattern) and the Amazon region (characterized by a unimodal pattern). Once the inflection point was established, the seasonal patterns before and after the year 2000 were examined (Figure 10).

Figure 11 presents the general behavior of monthly accumulated precipitation before and after the year 2000. The Baños station shows a unimodal pattern typical of the Amazon region (despite being located at 1820 m.a.s.l.), with the highest values of monthly accumulated precipitation occurring in June, July, and August. This is associated with the northward displacement of the Intertropical Convergence Zone (ITCZ). At the Patate station, located at 2442 m.a.s.l., the precipitation pattern reflects an Amazonian influence in June and July, and an Andean influence from February to May.

Despite the proximity between the Patate and Píllaro stations, the Píllaro station (2781 m a.s.l.) exhibits a bimodal pattern characteristic of the Andean region, with a dry season occurring in June, July, and August in the period prior to the year 2000. Likewise, although the Pedro Fermín and Querochaca stations are relatively close to one another, both show a bimodal pattern, with Pedro Fermín presenting higher precipitation values before the year 2000, particularly in September. For the Querochaca station, the most notable changes after 2000 occur in July, September, and December. The remaining behavior was very similar both before and after the year 2000.

To analyze the rainfall patterns more effectively for the periods before and after 2000, the monthly accumulated values were examined, as presented in

Table 5. Statistical summary of the stations based on monthly precipitation before and after 2000 (in bold).

Variable	Baños 15 Years	Patate 15 Years	Píllaro 14 Years	Pedro Fermín 16 Years	Querochaca 14 Years
Min [mm]	3.10 2.11	2.60 1.10	2 1.60	3.60 4.60	3.20 1.5
Max [mm]	414.20 474.9	191.60 336	142.70 164.50	144.70 199.50	154.80 215.60
Q1 [mm]	63.02 72	24.9 19.85	27.87 23.17	24.80 26.36	31.40 33.50
Q2 [mm]	105.30 100.9	43.80 40.85	43.80 35.80	37.90 37.40	44.60 44.50
Q3 [mm]	153.72 138.82	66.30 64.25	64.57 57.27	58.10 60.77	62.30 70.35
P90 [mm]	199.45 187.27	93.72 94.66	82.43 100.30	75.32 80.07	82.30 83.64
P99 [mm]	272.69 290.35	185.616 176.44	133.71 136.74	113.06 158.34	110.51 127.24
Total annual precipitation [mm]	1287.13 1198.65	469.52 456.77	553.02 417.59	513.33 504.08	578.36 616.05

. The table also indicates the number of years used for the comparison in each period.

These preliminary analyses already reveal much more pronounced changes in seasonality after the study point (year 2000) at the Andean stations—Patate, Píllaro, Pedro Fermín, and Querococha.

The analysis of the precipitation data in Table 4 and Table 5 reveals that, overall, there has been an increase in both maximum precipitation and the frequency of extreme events in most stations after the year 2000. The Baños and Querochaca stations show the most notable increases in maximum precipitation and in the percentile values, indicating greater variability and more frequent extreme events. In contrast, stations such as Patate exhibit a decrease in both minimum and maximum precipitation, suggesting a reduction in variability. For a clearer understanding of precipitation behavior before and after 2000, Figure 12 provides a visual comparison.

3.4. Harmonic Analysis

The following section presents the harmonic analysis of the monthly precipitation data for each station, comparing at least 14 years before and after the year 2000. In the figures, the horizontal axis represents the years, while the vertical axis indicates the wavelet scale periods for both Wavelet Coherence (WTC) and Cross-Wavelet Transform (XWT). The color scale ranges from blue to yellow, where yellow denotes high coherence or correlation values, and blue denotes low values. The black contour line indicates statistical significance at the 95% confidence level, relative to two completely random signals. In all figures, the x-variable corresponds to the series before the year 2000, and the y-variable to the series after.

The wavelet analysis conducted using daily data is presented in Annex 1 and is consistent with the results shown in the monthly scale analysis.

In the case of Baños (Figure 13), significant areas of high coherence are observed near the 12-month principal period, confirming the strong unimodal seasonality of the series. The black arrows indicate the relative phase between the two series: arrows pointing to the right denote in-phase synchronization. In this case, the arrows predominantly point to the right within regions of high coherence, indicating similar climates before and after the study point 2000. However, the late onset of the rainy season, around 2–3 months, is observed during the first four years (left side of the plot), and the early onset of the rainy season, of 2–3 months, occurs in the most recent years (right side), for both WTC and XWT.

Additionally, secondary periodicities besides the 12-month cycle were identified, ranging from 2 to 6 months and occurring sporadically. The behavior observed in 2001–2002 is particularly notable, as it closely resembles that of 1987–1988 and is characterized by short sub-periods of 2 to 6 months. It is worth noting the robustness of the method despite the presence of missing data.

The Patate station (Figure 14) contains the highest proportion of missing data, and its results should therefore be interpreted with caution. Nevertheless, its behavior is consistent with that observed at the other highland stations located at progressively higher elevations—Píllaro, Pedro Fermín, and Querochaca—where a clear disruption of the dominant 12-month period is observed, accompanied by the emergence of shorter periodicities.

The Píllaro station (Figure 15) exhibits the largest discrepancy in precipitation behavior after the selected study point. From approximately 2001 onward, the expected 12-month mode weakens and effectively disappears, while new dominant modes emerge at shorter periods, ranging from 0–4 and 4–8 months. These changes indicate that, from 2001 onward, the precipitation regime has been altered markedly relative to the patterns observed in the 1989–2000 period.

Pedro Fermín (Figure 16) is a station with a much more complete dataset than Patate and initially exhibits a dominant 12-month periodicity. However, this cycle shows a sustained delay, reaching up to a 6-month lag, as indicated by the vertical arrows between 2004 and 2006. During this interval, the annual cycle progressively weakens until the 12-month period disappears and a 6-month periodicity becomes established from 2007 onward. Another secondary periods 2–3 months, appears at the other stations. This shift in dominant periods indicates clear changes relative to the pre-2000 climatic regime, consistent with local perceptions of altered rainfall seasonality [21].

The Querochaca (Figure 17) time series, which contains the most complete dataset, shows behavior similar to that observed at the other Andean stations. From approximately 2003 onward, a weakening of the expected 12-month mode is evident, accompanied by the emergence of new modes at shorter periods. The 2003–2004 interval is particularly notable, as the meteorological conditions closely resemble those observed during 1989–1990, but with a shortened dominant period of 0–6 months and a slight advance of a few weeks. After 2007, the expected 12-month periodicity reappears; however, it does not occur as a single dominant mode, since shorter periodicities of approximately 2, 3, and 6 months remain evident.

In this way, the analysis of the Andean stations clearly indicates that climate seasonality after the year 2000 has been disrupted, regardless of the emergence of shorter secondary periods. This behavior contrasts with that observed at stations more strongly influenced by Amazonian climate, such as Baños, where the dominant annual cycle is preserved despite the presence of advances or delays in precipitation timing.

4. Discussion

The findings of this study provide evidence of the presence of climate change in the region, primarily reflected in the consistent and statistically significant increase in both maximum and minimum temperatures across the stations (Table 4, Figure 9 and Figure 10, Appendix C). However, this climatic signal is not mirrored in extreme rainfall behavior, for which no statistically significant trends were detected (Table 4, Figure 6, Figure 7 and Figure 8, Appendix B). Nonetheless, the harmonic analysis reveals both advances and delays in the onset of the rainy season, indicating modifications in seasonal timing even in the absence of a detectable intensification in extreme precipitation, and missing data.

When comparing the present results with methodologies used globally to detect shifts in rainy-season onset and cessation, a clear contrast emerges between locally calibrated threshold-based definitions and more advanced regional or frequency-domain approaches. Threshold methods—commonly used in Africa and tropical regions—provide intuitive and agriculturally relevant indicators but are highly sensitive to arbitrary cutoff values and to data gaps [41,42]. More recent frameworks, such as the flexible driest-period method, demonstrate that part of the apparent shifts in rainy-season timing may arise from methodological choices rather than true climatic changes, especially in transitional climates [43]. Regional-scale approaches based on multivariate analysis, such as PCA, reduce noise and yield robust signals of onset and cessation but require dense and continuous datasets, which remain a limitation in our study area [44]. Large-scale gridded diagnostics, such as the RADS dataset, offer globally consistent seasonality metrics; however, they smooth local features and inherit biases from gridded precipitation products [45]. Within this landscape of methodologies, harmonic and wavelet-based analyses—as applied in the present study—offer a complementary advantage by directly examining changes in phase and periodicity of the annual rainfall cycle, which helps detect advances and delays even under high data variability and missing data.

The results highlight the usefulness of harmonic analysis for identifying shifts in seasonal timing. In the study area, farmers’ perceptions [21] are consistent with the detected advances and delays in the rainy season. These findings are also in line with IPCC reports [28], which indicate that climate change can lead to shifts in the timing of rainy seasons. However, unlike the well-established frameworks used to assess extreme events and temperature increases, there is a need for a standardized methodology comparable to CLIMDEX that is specifically designed to detect advances and delays in the onset of the rainy season and remains robust under regional constraints such as limited in situ data availability.

Despite the results obtained in this study in concordance with [24,44], other limitations associated with the application of harmonic analysis should be acknowledged. The robustness of harmonic methods may be reduced when applied to relatively short (<40 years) records, as limited record length can affect the stability of phase estimates and increase sensitivity to noise. In addition, the interpretation of harmonic components depends on the underlying precipitation regime. In the study area, stations located in the eastern sector exhibit predominantly unimodal rainfall patterns, whereas stations influenced by highland climatic conditions tend to display bimodal precipitation regimes. In such cases, close attention to other harmonic components is required to adequately represent multiple seasonal peaks, and the identification of onset and cessation timing may involve greater uncertainty. Recognizing these differences is essential for a rigorous interpretation of the results and for assessing the applicability of the proposed methodology across distinct climatic settings.

Finally, the selection of the year 2000 as a temporal study point between past and present conditions represents a pragmatic methodological decision and constitutes one of the limitations of this study. Ideally, an objective breakpoint could be identified using formal statistical techniques, such as breakpoint detection or bootstrapping methods [31,36]. However, given the gradual and non-linear nature of climate change, particularly in regions characterized by strong interannual variability, a distinct and statistically robust inflection point between past and present climate conditions may not be evident. In this context, the year 2000 was chosen to ensure comparable lengths of observational records before and after the study point across the analyzed stations, thereby allowing a balanced comparison despite the heterogeneous, incomplete, and non-homogeneous nature of the in situ precipitation data. Although this choice is not based on a specific climatological threshold, the consistency of the results with findings reported in previous studies using more complex methodologies [24,26] supports the validity of the observed patterns. Acknowledging this limitation highlights the need for future research to explore objective study-point detection approaches as longer and more homogeneous observational records become available.

5. Conclusions

Based on the analyses presented in this study, several key conclusions can be drawn. Firstly, temperature-related climate indices exhibit a clear and statistically consistent warming signal in the province of Tungurahua, whereas most precipitation extreme indices show weak or non-significant trends. Despite this, harmonic and wavelet analyses reveal marked changes in precipitation seasonality after the year 2000, particularly at Andean stations, where the dominant 12-month cycle weakens or fragments into shorter periodicities. These results indicate the presence of advances and delays in the onset of the rainy season, consistent with local perceptions and with international assessments recognizing that climate change also affects the timing of seasonal processes, beyond changes in extremes.

From a methodological perspective, the results demonstrate that harmonic analysis is a viable and robust approach for identifying shifts in seasonal timing using in situ precipitation data comparing with other methodologies [24,44], even when records are scarce, incomplete, and non-homogeneous. Nevertheless, future research would benefit from incorporating additional statistical techniques, such as bootstrapping [31,36], to more objectively identify potential inflection points in climatic time series, particularly given the gradual nature of climate change and the absence of clearly defined breakpoints.

In terms of practical implications, climate change indices indicate that a sustained increase in temperature is already occurring in the study region. Although current temperature levels are not yet sufficient to induce widespread thermal stress in most crops cultivated in Tungurahua [21], projections suggest that critical thresholds may be reached within the coming decade. A similar situation applies to extreme rainfall events, which do not yet show clear or statistically robust increases in frequency, intensity, or duration, but may become more pronounced in the near future. What is already evident, however, is the occurrence of both earlier and later onsets of the rainy season. These shifts imply that rainfall may occur outside the traditionally expected periods or be absent when it is normally anticipated.

For decision-makers and the agricultural sector, these findings highlight the need to strengthen adaptation strategies. Farmers must be prepared to manage both excessive rainfall, which is commonly associated with fungal diseases, and prolonged dry conditions, which favor insect pest outbreaks. Consequently, improved pest management, the availability of irrigation systems to cope with rainfall deficits, and stronger institutional support are essential. Public investment in adaptation measures and the implementation of agricultural insurance schemes would contribute significantly to enhancing the resilience of this highly vulnerable sector under ongoing and future climate change.