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Article

Season-Long Time-Series Analysis of Soil Respiration in Furrow-Irrigated Corn with and Without Cover Crop in the Lower Mississippi River Basin

by
Diego Della Lunga
1,*,
Kristofor Brye
1,
Michael J. Mulvaney
2,
Mike Daniels
1,
Tabata de Oliveira
3,
Beth Baker
4,
Timothy Bradford, Jr.
3 and
Chandler Arel
1
1
Department of Crop, Soil, and Environmental Sciences, University of Arkansas, Fayetteville, AR 72701, USA
2
Department of Plant and Soil Science, Mississippi State University, Starkville, MS 39579, USA
3
Vayda Regenerative Farm, Clarksdale, MS 38614, USA
4
Department of Wildlife, Fisheries and Aquaculture, Mississippi State University, Starkville, MS 39579, USA
*
Author to whom correspondence should be addressed.
Climate 2025, 13(11), 232; https://doi.org/10.3390/cli13110232
Submission received: 2 October 2025 / Revised: 5 November 2025 / Accepted: 12 November 2025 / Published: 14 November 2025
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Abstract

Temporal resolution of carbon dioxide (CO2) release from the soil at the field scale is not completely understood. The objectives of this study were to identify trends, repetitive cycles, and residual patterns and structures with a time-series analysis from a furrow-irrigated corn (Zea mays L.) field with and without cover crops (i.e., CC and No-CC, respectively) over the course of one growing season in the Lower Mississippi River Basin. Carbon dioxide fluxes were measured from 5 May to 18 August 2024, four times a day (i.e., 0300, 0900, 1500, and 2100 h) from each of the two CC treatments. Linear trends were significant, but they were only able to explain 3 and 10% of the CO2-flux variability for CC and No-CC, respectively. Spectral density analyses indicated the significant presence of repetitive patterns every four lags, the amplitude of which was numerically 25% greater for CC than for No-CC. The structure of the residual was best described by separate autoregressive-moving-average (ARMA) models for the CC and No-CC treatments. The current study provides preliminary yet fundamental information to improve the understanding of the dynamics of soil respiration processes from a row-crop production system.

1. Introduction

The number of scientific assessments evaluating greenhouse gases (GHGs) under greenhouse and/or field conditions has steeply increased in recent decades, leading to an empirically well-established relationship between anthropogenic GHGs and climate-change implications [1]. From 1970 to 2020, carbon dioxide (CO2) accounted for 76% of total global GHG emissions, while methane (CH4) and nitrous oxide (N2O) emissions accounted for 18 and 6%, respectively [1]. Of the total global GHG emissions in 2020, the industrial sector produced the greatest portion at 25%, followed closely by the agricultural, forest, and other land-use (AFOLU) sector at 24% [1]. Assessment of GHGs involves several protocols, as well as analytical and statistical tools that encompass top-down and bottom-up approaches, life cycle assessments, ground-truth observations, modeling analyses, and machine-learning techniques [2].
Greenhouse gases are produced within all of Earth’s spheres (i.e., atmosphere, hydrosphere, pedosphere, and biosphere); therefore, analytical methodologies to assess GHGs require a multi-disciplinary approach that encompasses atmospheric, soil, and hydrologic sciences along with biogeochemistry [3]. In each sphere, the analysis of GHGs is based on assumptions that can be shared across disciplines or that can be correlated to the primary characteristics of a specific sphere. For example, GHG analysis in the atmosphere assumes the trace gases to be well mixed, especially over large areas and long-time scales (i.e., years) and that the gases are directed mainly by wind and advection processes [4]. In the pedosphere, GHGs mainly move by diffusion through air-filled pores and concentration gradients, making the assumption of well-mixed gases less applicable [5].
Greenhouse gas assessments from the pedosphere have been directed not only toward national and international sustainability goals, but also toward the acquisition of essential information used to validate agricultural and restoration management practices in terms of soil fertility, soil health, and carbon (C) sequestration [6]. Soil health has been listed among the goals of conservation practices in agricultural systems, where the outcome is to incentivize producers to adopt conservation management practices that can lead to GHG mitigation and soil C accumulation [7]. Field research has documented that conventionally cultivated land generally experiences a decline in organic C and nitrogen (N), mainly due to the temporary increase in soil respiration [1]. The value of assessing CO2 emissions from the soil to the atmosphere relies on the premise that variations in CO2 fluxes can be considered indicators of the soil ecosystem’s productivity status because CO2 fluxes are correlated to microbial turnover and organic matter accessibility [8]. Consequently, soil biogeochemical characteristics in natural and agronomic settings can be assessed through direct GHG measurement, particularly CO2 [9].
Among the three main GHGs (i.e., CO2, CH4, and N2O) produced and emitted from agricultural production systems, CO2 has the greatest magnitude and shows relatively more stable and predictable temporal patterns compared to the more sporadic nature of CH4 and N2O [10,11,12]. Production and release of CO2 from the pedosphere is often described as soil respiration. Soil respiration is considered the additive product of root and microbial metabolic processes [13]. The magnitude and variability of soil respiration across ecosystems and over time often render the assessment of soil CO2 fluxes difficult to analyze and challenging to explain through canonical analyses (i.e., parametric approaches) [14]. The degree of spatiotemporal variability in soil respiration in any ecosystem is determined by dynamic environmental factors, such as soil moisture and temperature, along with biological and physical characteristics of the system, including, but not limited to, nutrient substrates, soil organic matter, soil texture, and soil bulk density [15,16].
The temporal resolution of soil respiration processes at the field scale is generally less well understood than the spatial variability of CO2 production and release from the soil [2,17]. The temporal variability of soil surface CO2 fluxes at the field scale requires the assessment of the degree to which successive measurements and observations are correlated over time, which is information that has been rarely investigated or reported, particularly in agricultural studies [17,18]. The frequency at which soil CO2 fluxes are measured in the field also contributes to the power of analysis and the ability to capture and characterize how soil respiration changes over time [19]. Soil respiration is commonly assessed on a weekly basis, where hourly fluxes, generally measured during the mid-morning, are then converted to daily fluxes and subsequently interpolated between consecutive weekly measurements to estimate emissions over some specified time period [20,21,22].
Biases and uncertainties in global GHG budgets have been evaluated at the local level, specifically in sampling protocols and temporal variations in GHG fluxes [23]. Intervals between measurements and the time of day when measurements occur represent the two main issues affecting the accuracy of GHG emissions estimates [24,25]. Long intervals between measurements can misrepresent or altogether miss short-term variations or episodic events, increasing the potential impact of outliers [26]. Within the pedosphere, GHG fluxes have been described by non-systematic behavior, and scientific studies reported datasets with a large degree of variation and large data dispersion [1].
The attempt to categorize GHG trends and behavior led to the development of mathematical models for budget and forecasting analysis [27]. Mechanistic approaches, such as the Denitrification-Decomposition (DNDC) model, rely on several assumptions of linear or curvilinear behavior of soil gas emissions to the atmosphere [28,29]. With agricultural fields characterized by generally large heterogeneity across the soil surface and with depth in the soil profile, mechanistic assumptions do not always hold true and should be adjusted with the changing contributions of the pedosphere, atmosphere, and biosphere to the rates of specific biogeochemical cycles [14]. Studies addressing C cycles in agricultural settings reported that the dynamics of GHG fluxes are among the most statistically challenging biogeochemical processes to categorize and that protocol and frequency of sampling can highly impact the statistical power to detect differences among experimental treatments [18]. To enhance the accuracy of mathematical models to predict and explain the behavior of GHGs from the pedosphere, it is necessary to evaluate the structure of the raw data collected from the field [30]. An underused approach to determine the variability of GHG data over time and help address the underlying structure of GHG data is time-series analysis.
Time-series analysis can provide information regarding repetitions and periodic statistics in the data series that can be subsequently related to underlying physical and chemical processes responsible for all, or part, of the statistically identified recurrences of patterns [31]. Time-series analysis can also assess how a response variable, or entry, varies or covaries with past entries in a feature known as “serial correlation” [31]. In a stationary time series, the mean and variance of a response variable are independent of time. A non-stationary time series is characterized by a mean and a variance of the response variable that changes over time and can be described by three distinct elements: trend, seasonality, and irregular fluctuations, often referred to as noise [27]. The trend of a time series refers to the relatively long-term, overall increase or decrease in the response variable, while seasonality indicates the relatively short-term cycles or periodic fluctuations observed in the data series [27]. After accounting for trends and seasonality, the unexplained variation in the response variable in a time series is the noise, otherwise referred to as the residual [27]. The structure of the residual in a non-stationary and/or stationary time series can help categorize how the structure of the data can be related to physical processes in the pedosphere [32,33].
Although limited, soil surface CO2 flux studies in the Lower Mississippi River Basin (LMRB) have been conducted in a variety of ecosystems and under different management practices to assess how the pedosphere, biosphere, and atmosphere interact with respect to CO2 emissions from the soil to the atmosphere [34,35,36,37,38,39,40,41]. However, to date, no agroecosystem study in the LMRB has assessed GHGs through time-series analysis of high-density CO2 flux data. Therefore, the objectives of this study were to use time-series analysis to (i) mathematically describe the presence of a linear trend, repetitive cycles, and residual patterns in soil surface CO2 fluxes from a furrow-irrigated, corn (Zea mays L.) production system with and without a cover crop (i.e., CC and No-CC, respectively) over the course of one complete growing season in the LMRB, and (ii) evaluate the structure of the random patterns or residuals after trends and cycles were removed from the structure of the data in the two CC treatments. The addition of cover crops as treatment in the current study allowed to determine if organic amendments can have an impact on the temporal variability of soil respiration processes. It was hypothesized that (i) the time series of both CC treatments would be defined as non-stationary due to environmental field conditions that can change over time, (ii) an increasing linear trend would be present throughout the entire dataset in both CC treatments due to increased temperatures over the course of the growing season that enhance microbial and root respiration, (iii) multiple, repetitive patterns (i.e., cycles) would be statistically identified during the growing season in both CC treatments due to fluctuation of diurnal and nocturnal environmental field conditions, (iv) the CC treatment would be characterized by repetitive patterns with greater amplitude than the No-CC treatment due to the greater nutrient availability under CC, which can stimulate microbial processes, and (v) the structure of the residuals of the de-trended and de-cycled time series would be best defined by autoregressive models in both CC treatments due to time-dependent nature of GHGs and to the expected high individual plot variability. This study represents a novel extension to statistically describe temporal patterns in GHG fluxes under field conditions.

2. Materials and Methods

2.1. Site Description and Field Management

Field research was conducted at the Vayda Regenerative Farm on a Dubbs silt loam (fine-silty, mixed, active, thermic Typic Hapludalfs)) formed on alluvium, near Clarksdale, MS (34.216950 °N, 90.658806 °W, ~70 m above sea level) during the 2024 growing season [24]. The area is characterized by a humid subtropical climate with long hot summers, or Cfa according to the Koppen Climate classification [42]. A 64-ha field was divided into strips parallel with the predominant 0.2% slope and included several raised beds. Strips were randomized based on a completely randomized design (CRD) within the entire field. Each strip was characterized by a specific CC treatment. Two adjacent strips were selected within the field for the current study. The current study’s area comprised four plots, each composed of two raised beds, in two different, adjacent CC treatments, [i.e., a mix of cover crops, composed of 69% cereal rye (Secale cereale), 16% crimson clover (Trifolium incarnatum), 7% balansa clover (Trifolium michelianum), and 8% radish (Raphanus sativus)] and No-CC treatment, resulting in two replicates per CC treatment. Fertilizer, pesticide and herbicide application rates and timings were the same under both CC treatments. The management history of the study area, along with field operations, irrigation, fertilizer, herbicide, and pesticide applications were previously described by [24], who assessed CC effects on season-long GHG emissions, emissions intensity, global warming potential (GWP), and GWP emissions intensity during the 2024 growing season in the same study area under the same treatments as used for the current study. The study area received a total of 30.1 cm of rainfall from the beginning of May to the end of August, with a monthly average air temperature that fluctuated between 24.5 °C in May to 27.9 °C in July [24].
As detailed in [24], initial soil properties indicated high level of potassium (K, 259–455 kg ha−1) and phosphorus (P, 65–128 kg ha−1) in the top 15 cm, suggesting that a plant response to fertilizer addition other than N was not expected [43]. The C:N ratio indicated rapid soil organic matter (SOM) mineralization would be expected upon N-fertilizer addition, which totaled 276.5 kg N ha−1 as urea divided in three split applications [24]. A complete and detailed description of the initial soil properties was provided by [24]. Soil CO2 flux data used in [24] were used in the current study but were analyzed with different analytical tools and for different objectives.

2.2. Gas Sampling and Analyses

Greenhouse gas concentrations were measured from 5 May to 18 August 2024 four times a day at regular and equally spaced intervals (i.e., 6 h intervals) at 0300 (3 a.m.), 0900 (9 a.m.), 1500 (3 p.m.), and 2100 (9 p.m.) hours from each of the four plots, for a total of 420 observation per plot over the course of the complete corn growing season. Long-term automatic chambers (LI-8200-104; LI-COR Environmental, Inc., Lincon, NE, USA) for GHG measurement were placed on top of 21 cm inner diameter, 12 cm tall polyvinyl chloride (PVC) base collars located ~15 m in the downslope direction from the up-slope edge of the field and installed on top of raised beds. Greenhouse gas measurements were conducted with a long-term-deployment, multiplex system developed by LI-COR (LI-8250, LI-7810 and LI-7820). Chambers were programmed to operate in a sequential order and measure gas concentrations for 320 s (i.e., observation length). Once a chamber was closed, gas flow was pumped and directed toward the multiplex systems and GHG analyzers, a combined analyzer for CO2 and CH4 and a single analyzer for N2O, measured gas concentrations every second through optical-feedback, cavity-enhanced, absorption spectroscopy (OF-CEAS).
Each LI-COR automatic chamber, with a volume of 4244 cm3 and a surface area of 318 cm2, was equipped with internal sensors to track changes in air temperature and atmospheric pressure inside the collar-chamber sealed system that were subsequently used by the SoilFlux Pro software (version 5.3, LI-COR Inc., Lincoln, NE) to calculate fluxes according to the principles of the ideal gas law [44,45]. An instantaneous correction on concentration data was applied based on the initial water vapor content at the moment the chamber was sealed on the collar. Calibration curves were developed by LI-COR within a range of 0 to 10,000 parts per million (ppm) and with a precision of 0.6 parts per billion (ppb) [44,45]. The complete configuration, assembly, and settings for gas measurement, analysis, and flux calculations were previously described by [24].

2.3. Statistical Analyses

The current study represents a novel extension to statistically describe temporal patterns in GHG fluxes under field conditions. The innovative approach used in the current study allows for further investigation of the intrinsic structure of GHG flux data, providing new foundations that can facilitate modeling analysis of GHG fluxes, along with delivering new information on the appropriate statistical approaches to describe and analyze GHG fluxes using parametric tools [i.e., analysis of variance (ANOVA)]. Carbon dioxide flux data collected at each measurement time were averaged across the two replicates in order to conduct the time-series analysis. Averaging among replicates per treatment was considered a more reliable protocol than analyzing the four plots individually. Averaged values among replicates avoided the potential issue of pseudoreplication, reduced the inflation of degrees of freedom and the probability of false positives, while maintaining the underlying structure of the data as outlined in [46,47].
Time-series analysis was conducted in JMP (version 17.1.0, SAS Institute, Inc., Cary, NC, USA) using hourly CO2 fluxes over time under the CC and No-CC treatments, which were analyzed separately. Visual inspection of the data structure and the assessment of the lag average error determined the number of lags to include in the statistical analysis. Twenty-five lags were considered appropriate to capture all the elements of the time series under both CC treatments. Lags beyond 25 spikes within the 95% confidence intervals, suggesting a lack of dependency among data points. Augmented Dickey–Fuller (ADF) tests were used to determine if the time series were stationary or non-stationary. The tau statistic generated from the ADF tests was compared to the critical values and associated p-values reported by [48]. Autocorrelation and partial autocorrelation functions (ACF and PACF, respectively) were used to evaluate the degree of dependence within the data and to determine the units (i.e., lags) to be included when assessing possible repetitive patterns. Variograms and white-noise tests were then conducted to assess the serial correlation of the data variability over time. The white-noise test included Fisher’s Kappa and Bartlett’s Kolmogorov–Smirnov tests, where the statistic term for Bartlett’s Kolmogorov–Smirnov was compared against the critical value obtained from the Equation:
a/(√q)
where a was set at 1.36 and corresponded to the 5% significance level and q represented half of the sample size of the data points (i.e., 210) [49,50].
A decomposition process was then used to determine whether a significant linear trend existed in both CC treatments. Based on spectral-density analysis and white-noise tests, a decomposition process to remove a repetitive cycle composed of a specific number of units (i.e., lags) was used on the de-trended time series for both CC treatments. The de-trended and de-cycled time series, assumed to be composed exclusively by residuals, were then analyzed using autoregressive (AR) and autoregressive moving average (ARMA) models, where values between one and four were assigned to the autoregressive order coefficient (p) and the moving average order coefficient (q). The range of values assigned to the p and q parameters was based on the assessment of the ACF and PACF functions. The differencing coefficient (d) for the ARMA models was kept at zero in all instances, as the current analysis aimed to maintain the potential structure of the residual and was not directed toward forecasting processes [51]. Lung-Box Q tests were used to assess if a different (d) coefficient other than zero was necessary. The best model was initially determined based on the Akaike information criteria (AIC) and mean absolute error (MAE), followed by the evaluation of significance for the parameter estimates of the selected models. Lung-Box Q tests were used on the best model to determine if autocorrelations between residuals at different lags were significantly different than zero. Significance in all analyses was set at the 0.05 level.

3. Results

3.1. Time Series Analysis

3.1.1. CO2 Ranges and Visual Trends

The dataset collected in the current study allowed for the assessment of potential GHG patterns and trends over repeated diurnal cycles in an agricultural setting (Table 1). The analysis of minimum and maximum GHG fluxes in the two CC treatments (i.e., CC and No-CC) and across the four daily measurement times (i.e., 0300, 0900, 1500, and 2100 h) provided preliminary indications of the rapid response of the microbial community to the dynamic environmental conditions characteristic of a furrow-irrigated row crop [52,53]. Greenhouse gas flux ranges across measurement times can additionally highlight the relevance of appropriate measurement protocols that need to be defined and calibrated to capture average daily environmental conditions, specifically in relation to air temperature, to avoid substantial under- and/or over-estimations of GHG fluxes (Table 1).
Carbon dioxide flux minima and maxima from both CC treatments followed a similar daily temporal pattern, with an increasing range (i.e., maximum-minimum) from 0300 to 1500 h, followed by a decreasing trend from 1500 to 0300 h (Table 1). From both CC treatments, CO2-flux ranges were numerically greatest at 1500 and numerically lowest at 0300 h, likely due to the diurnal fluctuations of air and soil temperatures that impact microbial respiration (Table 1) [54]. The maximum CO2 fluxes measured from the CC treatment were numerically greater than from the No-CC treatment at all measurement hours, except at 2100 h, suggesting that cover crops, once terminated and potentially incorporated into the soil, can increase soil respiration (Table 2).
Carbon dioxide fluxes over the course of the growing season showed nearly identical temporal trends from the two CC treatments, although visually, sporadic and wider fluctuations occurred from the CC treatment compared to the No-CC treatment (Figure 1).
Carbon dioxide fluxes appeared to follow distinct diurnal cycles (Figure 1). As reported by [24], CO2 fluxes differed significantly between CC treatments across daily measurement times, although the only significant difference between CC and No-CC occurred for CO2 fluxes measured at 1500 h. The CO2 fluxes over time in both CC treatments clearly depicted the often-described sawtooth pattern associated with plant growth and decomposition [55], although data in the current study were collected mainly from the portion of the year when the plant experienced vegetative and reproductive growth (Figure 1). However, CO2 fluxes from both CC treatments also showed a complex structure, making the dataset an ideal candidate for further exploration using time-series analysis.

3.1.2. Stationarity

A time series that can be described as, or assumed to be, stationary is characterized by a constant mean, a constant variance, and a relationship between data points at different lags that can be measured with auto-covariance functions [27]. The time series of CO2 fluxes from CC and No-CC averaged 0.54 and 0.48 g m−2 h−1, respectively, suggesting that soil respiration processes can be increased when plant residues are added to the soil surface via CC use [24]. The ADF tests conducted on the time series for both CC treatments aimed to statistically determine the presence of a unit root that validated the null hypothesis of non-stationarity [56]. The zero-mean ADF tests if a time series is stationary when the mean is assumed to be zero [48]. The tau statistic for the zero-mean ADF for both CC treatments was lower than the critical value (−1.942) at the 0.05 level for sample size (n) composed of no more than 500 data points, indicating a significant p-value and, contrary to that hypothesized, the rejection of the null hypothesis of non-stationarity (Table 2).
Similarly, the single-mean ADF test, which assumes a non-zero mean, and the trend ADF test, which assumes a trend component within the time series, had a tau statistic lower than the critical values of −2.87 for the single-mean ADF and −3.42 for the trend ADF at the 0.05 level and n~500, indicating strong evidence to reject the null hypothesis [48] (Table 2). Overall, contrary to what was hypothesized, the ADF tests indicated that the CO2 time series fluxes from both CC treatments could be assumed stationary, trend-stationary, or weak non-stationary, which are conditions that are essential in forecast studies to enhance the reliability of the possible predictive outcomes [56]. Although not formally assessed, the ADF test in econometric studies showed general limitations when data were characterized by non-linearity and strongly correlated residuals [57]. The non-linearity aspect of GHGs from agricultural fields in Arkansas has been recently addressed in cotton [58] and soybean [59] systems, while the correlation between residuals represents one of the topics the current study attempted to address. Visual assessment of CO2 fluxes from both CC treatments suggested the lack of a clear trend but strongly indicated the possible presence of repetitive patterns along with random noise (Figure 1).

3.1.3. Serial Correlation

The autocorrelation and partial correlation functions (i.e., ACF and PACF, respectively) were evaluated on the time series before any transformation or decomposition was conducted to determine the underlying structure of the CO2 flux data (Figure 2, Figure 3 and Figure 4). While the ACF represents the correlation between a datapoint and all the preceding lagged values, the PACF represents the correlation coefficients between two values after removing the intervening lags (Figure 2) [60]. Spikes at regular intervals of four lags were visible for both CC treatments in the ACF and PACF results, suggesting seasonality in the data (Figure 2) [61]. The ACF coefficients from CC differed (p < 0.05) from zero at every lag multiple of 4, up to lag 24 (Figure 2). In contrast, the PACF coefficients from CC differed (p < 0.05) from zero only at lag 4, 12, 16, and 24 (Figure 2). From the No-CC treatment, ACF coefficients differed from zero for lag 1 to 4 and at every lag multiple of 4, up to lag 24, while PACF coefficients differed (p < 0.05) from zero at lags 1, 3, 4, 8, 12, 16, and 20 (Figure 2).
The majority of positive correlation coefficients in the time series from No-CC indicated that when the value at one time point was greater than the mean, the next time point had a large probability to also be greater than the overall mean (Figure 2) [62]. None of the negative correlation coefficients from CC and No-CC for ACF and PACF differed (p < 0.05) from zero (Figure 2). The ACF and PACF spikes at every lag multiple of 4 from both CC treatments showed a general gradual decline in magnitude, suggesting, somewhat similar to that hypothesized, a long-term dependency in the data, along with evidence of weak non-stationarity (Figure 2) [60]. The contradictory ADF tests and ACF and PACF results highlighted the complexity of the CO2 flux dataset (Table 1; Figure 2).
The variogram from both CC treatments showed a similar structure, periodicity, and trend (Figure 3). The variogram coefficients from both CC treatments indicated that the degree to which the semi-variance of CO2 fluxes changed was not constant with the progression of the lags (Figure 3). From both CC treatments, coefficients at lag multiples of 4 corresponded to the troughs of the variogram, while peaks occurred at lag 2 and at every 4 lags thereafter (Figure 3). Therefore, greater variability (i.e., semi-variance) was identified within the 4-unit, repetitive pattern, while lower variability was identified at the end of each repetitive cycle (Figure 3). The low coefficients that occurred in a repetitive pattern of 4 units from both CC treatments indicated strong temporal correlation between CO2 fluxes separated by four 6 h intervals. The range of the variogram coefficients fluctuated in a repetitive pattern with a maximum and minimum coefficient of 1.21 and 0.53 from CC, respectively, and with a maximum and minimum coefficient of 1.31 and 0.62 from No-CC, respectively (Figure 3). The peak and trough coefficients of the variogram from both CC treatments showed a slight increase as the number of lags increased (Figure 3). No apparent sill, or leveling off, was observable in the variogram from either CC treatment (Figure 3).
Autoregressive analysis from both CC treatments showed coefficients slightly numerically greater at every lag multiple of four, while the remaining coefficients were negative or close to zero (Figure 3). The AR coefficients indicated a stronger relationship between CO2 fluxes at the end of each 4-unit repetitive cycle, which were separated by weak AR coefficients, likely characterized by noise in the data (Figure 3). Furthermore, spectral density analysis determined relevant periodicities at periods characterized by 2 and 4 units, with the latter having a stronger signal (Figure 4). The white-noise test determined that the time series from both CC treatments had significant periodicities that needed to be considered to properly capture the data structure (Figure 4). Fisher’s Kappa p-values for both CC and No-CC time series were less than 0.05, and Bartlett’s Kolmogorov–Smirnov statistic exceeded the critical value calculated as 0.1, rejecting the hypothesis that both time series originated from a normal distribution and further implying the presence of periodicities separated by intervals of random variation (Figure 4) [63]. Serial correlation analyses demonstrated that high-frequency GHG flux data are characterized by structures, such as periods and/or cycles, that need to be considered to properly design analytical approaches aimed to determine the variance attributable to an imposed treatment and/or fixed factors included in the experimental design of field studies [18].

3.1.4. Decomposition

A decomposition process was conducted to determine if a trend and/or repetitive cycle were present in the time series from both CC treatments. While the ADF tests suggested that a long-term trend was not going to be present due to the stationary characteristic of the two datasets, the ACF and PACF functions contradicted the ADF tests, while, in addition, strongly suggested the presence of repetitive patterns (Table 1; Figure 2, Figure 3 and Figure 4). The decomposition process demonstrated that a significant (p < 0.05) trend was part of the CO2 flux time series in both CC treatments (Table 3). Contrary to the hypothesis, the slope of the linear trend of the time series for both CC treatment was negative, suggesting a linearly decreasing soil respiration rate during the growing season (Table 3). However, the magnitude of the slope of both time series was quite low, indicating that each CO2 measurement had a flux 0.002 units and 0.003 units lower than the previous measurement for CC and No-CC, respectively (Table 3).
Although the overall model p-value for the two linear trends was significant, linear models were only able to explain 3 and 10% of the CO2-flux variability for CC and No-CC, respectively, due to the relatively low R2 values (Table 3). While no other studies have reported CO2 fluxes at such high frequency as in the current study, previous studies reporting weekly measured CO2 fluxes in agricultural settings often described an increasing CO2-flux trend with the progression of the vegetative stages of a cash crop, followed by a plateau when plant maturity was reached [34,39,52]. The root mean square error (RMSE) for the time series from both CC treatments was slightly lower than the standard deviation of the raw data (Table 1), suggesting the linear models should be considered as tool to characterize the spread of CO2 data, at least as preliminary steps toward the modeling of the potential trends (Table 3).
An additional decomposition process was conducted on the time series of both CC treatments after the linear trend was removed. The ACF, PACF, and spectral density analyses significantly indicated the presence of repetitive patterns every 4 lags (Figure 2, Figure 3 and Figure 4). Therefore, the de-cycling step was analyzed with 4 units in each cycle for both CC time series (Table 4). No constant value was selected for the de-cycling process due to the contradictory evidence for stationarity for the time series from both CC treatments (Table 4). The amplitude of the cycle from CC was 25% numerically greater than from No-CC, while the phase of the cycles from both CC treatments was similar, suggesting stronger repetitive fluctuations of CO2 fluxes from CC than from No-CC (Table 4) [64]. The phase of the repetitive patterns in the two time series indicated that the beginning of the waves in both time series did not start with the first measurement but was shifted 0.49 units earlier in time (Table 4) [65].

3.1.5. AR and ARMA Models

The autoregressive and autoregressive-moving average models were fit to the time series for both CC treatments after trend and repetitive patterns were removed, leaving what was assumed to be just the residual structure of the data. The autoregressive factor (p) and the moving average factor (q) were assigned values between 1 and ≤4 based on the ACF and PACF results and spectral density analysis (Figure 2, Figure 3 and Figure 4). Models with a higher order (i.e., p and q values) than 4 were considered at high risk of over-fitting and were therefore not evaluated. Within the AR models, a clear decreasing trend occurred for the AIC parameter, as the p factors increased from 1 to 4, with a substantial decrease in the AIC value for the AR(4) model compared to the AR(1), AR(2), and AR(3) models for both CC treatments, which reinforced the ACF and PACF results of significant spikes every 4 lags (Table 5). A similar decreasing trend in the AIC parameter occurred for the ARMA models when p and q factors were greater than 1 (Table 1). The numerically lower and more negative AIC values for the AR and ARMA models from the No-CC treatment compared to the CC treatment suggested how the presence of cover crop residues made model fitting of the residuals more difficult (Table 5).
The best-fit models were represented by the ARMA(4, 0, 3) and ARMA(4, 0, 4) for the CC and No-CC treatments, respectively (Table 5). Both ARMA(4, 0, 3) and ARMA(4, 0, 4) models were characterized by the numerically lowest AIC parameters, the numerically second to largest and the largest coefficients of determination (R2), respectively, and the second lowest MAE factors (Table 5). The parameters estimated for both selected models were significantly (p < 0.05) different than zero. The R2 values indicated that the ARMA models explained 14 and 19% of the residual variability for the de-trended and de-cycled time series from CC and No-CC, respectively, suggesting the presence of a high level of noise within the structure of the data (Table 5). The MEA represents the average of the absolute difference between the forecasted and corresponding actual response variable value over time [66]. All models considered in the current study reported MAE between 0.16 and 0.12 g CO2 m−2 h−1, indicating a similar level of accuracy and prediction across the various models analyzed (Table 5). Due to the high frequency of CO2 flux measurements (i.e., four measurement times per day), the use of four preceding values (p = 4) to predict a current CO2 flux likely resulted in the numerically lowest AIC (Table 5). Similarly, the use of three or four past errors by the moving average (MA) component (q = 3 or 4) of the models resulted in an improved ability to predict the next CO2 flux, likely due to a changing, but repetitive, correlation between sequential CO2 fluxes at 6 h intervals, as observed from the variograms and autoregressive graphs (i.e., Table 5, Figure 3).
The Ljung–Box Q test assessed if the autocorrelations between data points within a model framework (i.e., ARM) differed (p < 0.05) from zero across a predetermined number of lags [67,68]. The presence of significant autocorrelations often indicates a remaining data structure that has not been well-characterized by the model [67,68]. In the current study, for the first 25 lags of the time series of the residuals for both CC treatments, the results of the Ljung–Box Q tests were non-significant (p > 0.05) in all instances, with an increasing trend of non-significance with the progression of the lags (Table 6). The lack of significant lags indicated that no remaining structure or pattern was present in the de-trended, de-cycled time series from either CC treatment, thus strongly suggesting that the residual portions of the time series for both CC treatments were well-characterized by the ARMA models, as hypothesized, with autoregressive components (Table 6).

4. Discussion

Time series studies published on GHGs are limited in number in US, and there is still a scientific gap of knowledge for what concerns temporal variation in GHGs at the field scale level, making the comparison of the results from the current study with previous published work difficult. The high frequency in GHG sampling performed in the current study represents a substantial improvement to the common weekly sampling protocol, resulting in novel elements that weekly GHG data could not capture. The assessment of soil respiration at a relatively high sampling frequency or at highly defined temporal scales is essential to properly assess C dynamics in agroecosystems. Time-series analysis of soil-surface CO2 fluxes can also establish land management insights in relation to crop phenological changes over time [69]. The current study conducted an analysis of the structure of CO2 flux data from furrow-irrigated corn in the LMRB that can help to contextualize experimental designs that properly monitor the complex relationship between soil respiration and agricultural management practices. The current study limited the analysis of CO2 flux data to one growing season to identify the necessary steps involved and show proof of concept; thus, results should be considered preliminary and not conclusive. Long-term data studies are necessary to improve the evaluation of trends and patterns of CO2 efflux from the pedosphere. The limited number of replicates (i.e., plots) in the current study substantially limited the power analysis of the statistical approaches, rendering results more site-specific and limited generalization to other field settings.
Carbon dioxide flux maxima and minima in both CC treatments were numerically similar to long-term studies conducted in corn production systems in the North China Plain on sandy-loam soils [70], corroborating the results from the current study. The large temporal variability and rapid change in CO2 fluxes across measurement times of day highlighted the potentially quick response of the microbial community to changing environmental conditions in the field, specifically soil temperature and soil volumetric water content [14,24]. Due to the dynamic environmental conditions expected in a furrow-irrigated, row-crop production system, CO2 flux data over time can potentially be described by different patterns and trends according to the frequency that the concentration change-over-time data are collected [14,24]. Soil respiration characteristics, including the variability across successive observations, have been described in previous studies as variable, depending on the time intervals between measurements [14,71,72].
The stationarity element of time series assessed by the ADF tests specifically referred to the stochastic trend and did not provide reliable information about deterministic trends and cyclical patterns that may still be present within the parameters of a time series [27]. A stochastic trend indicates that, under the pressure of an external disturbance (i.e., land-use change), the mean of the series drifts away from the original mean and does not revert to a long-run mean [73]. While over a timeframe of years, a stochastic approach appears to be applicable to the soil respiration processes, time scales of less than one year might not be able to be properly described by the stochastic trend [73]. The ADF test results exclusively referred to the stationarity of the overall mean of the time series from both CC treatments, while the variance of the data could still be described as non-stationary to some degree [56]. The relatively small sample size of this dataset may have influenced the results of the ADF tests, indicating that, for a short-term time series, additional analyses are required to assess the various elements within the structure of the raw data [56] (Table 1).
The regular spikes in the ACF and PACF results indicated that past CO2 fluxes had a strong predictive power for the subsequent CO2 fluxes (Figure 2) [68]. When CO2 data, specifically emissions, were analyzed on a yearly basis and/or over large geographic scale (i.e., country level), a decrease in ACF and PACF spikes has been reported shortly after the first few lags, suggesting the lack of a strong correlation between past, current, and future CO2 fluxes ([74]. However, significant autocorrelation between GHG emissions datasets, identified through ACF and PACF analyses, was reported in a meta-analysis of GHGs across European countries using data from 1990 to 2022 [74]. Correcting a time-series analysis, especially when the sample size is relatively small, for autocorrelation, has been shown to limit type I error inflation and reduce under- and/or overestimation of the models’ errors [75].
The negative trend (i.e., decreasing CO2 flux over time) identified in the time series from both CC treatments was likely driven by lower root respiration rates after plant maturity was reached (Figure 1; Table 3). Numerically lower troughs occurred toward the end of the growing season, which likely affected the slope of linear regression models (Figure 1; Table 3). Similar results were reported in previous studies in irrigated corn trials, where soil respiration rate decreased during the grain-filling stage when irrigation was terminated to prepare the field for harvest [35,70]. While the assessment of a trend in a time series is essential to determine the overall structure of the data, the practical relevance of the time-series trend relies on the length of the dataset. Short-term time series can be more susceptible to noise and random fluctuations, making the extrapolation of generalized trend assessments difficult [76]. Non-linear trends (i.e., exponential) should be considered when modeling the dynamics of soil respiration processes in order to assess if the CO2 change over time remains constant of varies by a fixed amount.
The consistently repetitive, 4-unit cycles observed in the time series from both CC treatments were likely related to diurnal and nocturnal variations in soil and air temperatures that controlled CO2 fluxes (Table 4). The evaluation of repetitive patterns in the time series for both CC treatments indicated that similar physical, chemical, or biological processes were acting on both CC treatments during the entire growing season, consequently impacting soil respiration similarly under CC and No-CC. The repetitive cycles only differed by the magnitude of the cycles, which had a numerically greater amplitude than CC compared to No-CC (Table 4). The C (20.1 Mg ha−1) and N (5.8 Mg ha−1) contents at the beginning of the growing season did not differ (p > 0.05) between CC and No-CC, but, on average, the CC portion of the study area had 10% numerically greater C and N likely enhancing microbial metabolic rates and the amplitude of the cyclic patterns [24] (Table 4). Considering that repetitive patterns started and finished on a 4-unit cycle and considering that each unit was separated by a 6 h interval, a complete cycle occurred every 24 h (Table 4). The fluctuations in soil respiration, therefore, appeared to correspond with the air-temperature fluctuations in a 24 h period as a driving force for the cycled component of the time series under both CC treatments (Table 4). The predominant role of air and soil temperature on microbial and plant respiration rate has been well-established, although the potential effect of temperature on CO2 fluxes from the pedosphere on a short-term time scale has not been fully assessed [77]. Results of the current study indicated that the time of the day when CO2 concentration changes over time are measured can impact the magnitude of the CO2 flux (Table 4). Air-temperature corrections on gas flux calculations have been suggested in situations where GHG measurements occurred outside the temporal window when the air temperature was greater or lower than the daily temperature average [1]. Results of the current study suggest that flux corrections should be tailored to specific treatments, as management practices like CC might impact the magnitude of the microbial response, altering C-cycle dynamics. Sampling protocols have been developed and evaluated for GHG analysis using various closed chamber methods by agencies and organizations, such as the Food and Agriculture Organization of the United Nations (FAO) and the International Atomic Energy Agency (IAEA), although budgetary and/or logistic considerations can dictate how frequent and during what window of time GHG sampling can occur in a study area [78]. Knowledge of the circadian cycles of soil respiration can represent an accurate alternative way to contextualize CO2 fluxes measured at different daily times during the period of study (Table 4). The assessment of repetitive, diurnal GHG cycles can allow the positioning of a GHG flux measured at a specific point in time during the day to the extrapolated appropriate temporal position along the sinusoidal curve approximated by the repetitive pattern.
The structure of the time series residuals under both CC treatments was clearly best described by autoregressive functions after trend and repetitive patterns were removed, although a large portion of the residuals remained unexplained (Table 5). The correlation and autoregressive relationship (i.e., first order, second order, etc.) between the residuals of the de-trended and de-cycled time series from both CC treatments suggested that parametric approaches applied to GHG datasets should consider the residual intrinsic structure in order to extrapolate a reliable conclusion about potential fixed factors (Table 5). The assumptions of sample independence and homogeneity of variance among treatments required to conduct parametric analysis of variance (ANOVA) are often unmet in GHG studies and analyses [18]. Incorporating the temporal relationship between GHGs measured in the same experimental units represents a necessary step, as presented in the results of the current study, to properly capture statistical comparisons. Results of the current study indicated that linear trends, repetitive patterns and autocorrelated residuals are components of the CO2 dataset in row crop cultivations. Although the dataset was restricted to one growing season, the high frequency of gas sampling allowed us to evaluate a number of data points appropriate for time-series analysis. The current study can be considered a preliminary proof of concept of the complexity of GHG data that require appropriate tools to be analyzed and contextualized in the scientific research.
Although uncommon in GHG studies, a repeated-measures analysis may be a more appropriate statistical approach to assess treatment pairwise comparisons while accounting for the autocorrelation and autoregressive aspects of GHG data [18,79]. Results of the current study demonstrate that the within-subject variability can be best described with dependent relationships between consecutive measurements, rendering the repeated-measures approach the best suited for GHG analyses. The inclusion of temporal relationships among the residuals of GHG data into statistical models can result in lower standard errors for analyses and, therefore, greater analytical power to identify treatment differences [18,80]. The inclusion of a time-series approach in GHG studies represents an additional tool to assess and evaluate management practices that can provide essential information to enhance the sustainability of the agricultural sector in the US and beyond.

5. Conclusions

Studies on GHG fluxes in agricultural settings require an understanding of intrinsic data structures to properly conduct statistical analyses. Time-series analyses can provide essential information to identify various structural components of GHG data. The objective of the current study was to apply a time-series analytical approach to assess trends, repetitive patterns, and white noise elements of CO2 fluxes measured at high temporal frequency (four times a day, each day) during a full growing season from furrow-irrigated corn under CC and No-CC in the LMRB. According to ADF tests, results did not support the hypothesis of non-stationarity, but ACF and PACF assessments supported the hypothesis of non-stationary parameters and the presence of repetitive cycles under both CC treatments. Results supported the hypothesis that a significant linear trend was present in the time series from both CC treatments, but contrary to the hypothesis, the slope of both CC treatments’ linear trends was negative, although the magnitude of the slopes was numerically low. Results supported the hypothesis that identifiable, repetitive patterns were present in the time series from both CC treatments. Results supported the hypothesis that the magnitude or amplitude of the repetitive patterns under CC would be numerically greater than under No-CC. Results also supported the hypothesis that the residual structure of the time series from both CC treatments, after trend and repetitive patterns were removed, would be characterized by autoregressive functions.
Time-series analyses of CO2 fluxes from agricultural fields provide useful information to guide research toward the most appropriate measurement protocols and statistical tools to reliably assess treatment differences and modeling approaches. Time-series analyses can also provide essential information to determine soil C dynamics in agroecosystems. Future studies should evaluate the structure of long-term time series of additional GHGs, such as CH4 and N2O, from corn and other upland row crop systems to develop guiding protocols that allow for improved understanding of the complex nature of GHG production and release from the pedosphere to the atmosphere.

Author Contributions

Conceptualization, D.D.L., K.B., M.J.M.; Methodology, D.D.L., K.B., M.J.M.; Formal Analysis, D.D.L., K.B.; Investigation, D.D.L., K.B., T.d.O.; Resources, K.B., M.D., M.J.M., B.B., T.B.J.; Data Curation, D.D.L., K.B.; Writing—Original Draft Preparation, D.D.L.; Writing—Review and Editing, K.B., M.D., M.J.M., B.B., T.d.O., T.B.J., C.A.; Supervision, K.B., M.D., M.J.M., B.B., T.B.J.; Project Administration, B.B., M.J.M., M.D., K.B.; Funding Acquisition, B.B., M.J.M., M.D., K.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by USDA Partnerships for Climate-Smart Commodities, award number NR233A750004G041.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Acknowledgments

The authors gratefully acknowledge Vayda Regenerative Farm personnel for their assistance in the field.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
ACFAutocorrelation function
ADFAugmented Dickey–Fuller
AFOLUAgriculture, Forestry, and Other Land Use
AICAkaike information criteria
ANOVAAnalysis of variance
ARMAAutoregressive-moving-average
CCarbon
CCCover crop
DNDCDenitrification-Decomposition
FAOFood and Agriculture Organization
GHGGreenhouse gases
IAEAInternational Atomic Energy Agency
LMRBLower Mississippi River Basin
MAEMean absolute error
NNitrogen
No-CCNo-cover crop
OF-CEASOptical feedback cavity enhanced absorption spectroscopy
PACFPartial autocorrelation function
RMSERoot mean square error

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Climate 13 00232 g001
Figure 1. Carbon dioxide (CO2) fluxes measured at four specific hours (i.e., 0300, 0900, 1500, and 2100 h) each day (i.e., day of the year, DOY) from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Figure 1. Carbon dioxide (CO2) fluxes measured at four specific hours (i.e., 0300, 0900, 1500, and 2100 h) each day (i.e., day of the year, DOY) from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
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Figure 2. Graphical representation of the autocorrelation and partial autocorrelation functions (ACF and PACF, respectively) for time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Figure 2. Graphical representation of the autocorrelation and partial autocorrelation functions (ACF and PACF, respectively) for time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
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Figure 3. Graphical representation of variogram and autoregression (AR) coefficients for the time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Figure 3. Graphical representation of variogram and autoregression (AR) coefficients for the time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
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Figure 4. Graphical representation of spectral-density analysis and summary of white-noise test for the time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Figure 4. Graphical representation of spectral-density analysis and summary of white-noise test for the time series of carbon dioxide (CO2) fluxes over time in the first 25 lags from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
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Table 1. Summary of minimum and maximum carbon dioxide (CO2) fluxes by measurement hour. (i.e., 0300, 0900, 1500, and 2100 h) treatment [TRT; cover crop (CC) and no-cover crop (No-CC)] combination during the 2024 furrow irrigated corn growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 1. Summary of minimum and maximum carbon dioxide (CO2) fluxes by measurement hour. (i.e., 0300, 0900, 1500, and 2100 h) treatment [TRT; cover crop (CC) and no-cover crop (No-CC)] combination during the 2024 furrow irrigated corn growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Measurement HourField TreatmentCO2
(g m−2 h−1)
MinMax
0300CC0.060.87
0900CC0.081.72
1500CC0.012.82
2100CC0.031.01
0300No-CC0.010.70
0900No-CC0.011.09
1500No-CC0.012.40
2100No-CC0.011.17
Table 2. Summary of Augmented Dickey–Fuller (ADF) tests in the time-series analysis for carbon dioxide (CO2) fluxes from furrow-irrigated corn field with cover crop (CC) and without cover crop (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 2. Summary of Augmented Dickey–Fuller (ADF) tests in the time-series analysis for carbon dioxide (CO2) fluxes from furrow-irrigated corn field with cover crop (CC) and without cover crop (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
StatisticField Treatment
No-CCCC
Mean (g m−2 h−1)0.4780.541
Standard deviation0.2860.305
Sample size420420
Zero Mean ADF−6.876−7.352
Single Mean ADF−16.081−19.280
Trend ADF−17.549−19.886
Table 3. Summary of simple linear regression analyses to predict carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) for the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 3. Summary of simple linear regression analyses to predict carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) from furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) for the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Response VariableTreatmentModel ParameterCoefficient (Standard Error)Overall Model
p-Value		Overall Model R2RMSE †
CO2CCTime−0.002 (0.0005)<0.0010.030.301
No-CCTime−0.003 (0.0004)<0.0010.100.271
† RMSE, root mean square error.
Table 4. Summary of cycle patterns determined for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) after trend removal from the time series for furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) for the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 4. Summary of cycle patterns determined for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) after trend removal from the time series for furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) for the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
ParameterCCNo-CC
Amplitude0.200.16
Units per cycle44
Phase0.490.49
Constant00
Formula0.20 x cos † (2 x π † x ((1/4) x t † + 0.49))0.16 x cos(2 x π x ((1/4) ∗ t + 0.49))
† cos, cosine; π, pi; t, time in hours.
Table 5. Summary of the statistical comparison of the autoregressive [AR(p)] and autoregressive-moving average [ARMA(p, d, q)] models where the autoregressive factor (p) and the moving average factor (q) were set between 1 and 4 and the differencing factor (d) was kept as 0 for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) over time, after trend and cycle (n = 4) removal, in furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 5. Summary of the statistical comparison of the autoregressive [AR(p)] and autoregressive-moving average [ARMA(p, d, q)] models where the autoregressive factor (p) and the moving average factor (q) were set between 1 and 4 and the differencing factor (d) was kept as 0 for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) over time, after trend and cycle (n = 4) removal, in furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Model/Parameter †CCNo-CC
AICR2MAEAICR2MAE
AR(1 ‡)77.55<0.010.163.870.030.16
AR(2)65.090.030.16−14.20.080.15
AR(3)67.060.030.16−12.90.080.15
AR(4)30.190.120.14−53.40.170.13
ARMA(1, 0, 1 §)67.560.030.16−22.60.090.15
ARMA(2, 0, 1)41.690.090.14−23.70.100.15
ARMA(2, 0, 2)32.140.120.14−50.20.160.14
ARMA(3, 0, 1)40.440.100.14−21.70.100.15
ARMA(3, 0, 2)33.570.120.14−48.30.160.14
ARMA(3, 0, 3)29.900.130.14−48.20.170.14
ARMA(4, 0, 1)29.790.130.14−53.70.170.13
ARMA(4, 0, 2)31.590.130.14−51.90.170.12
ARMA(4, 0, 3)28.650.140.14−53.80.180.14
ARMA(4, 0, 4)29.970.140.14−55.70.190.13
† AIC, Akaike Information Criterion; R2, R square; MAE, mean absolute error. ‡ The AR models’ coefficient in parentheses represents the autoregressive factor p. § The ARMA models’ coefficients in parentheses represent, in order from left to right, the autoregressive factor p, the differencing factor d, and the moving-average factor q.
Table 6. Summary of Ljung–Box Q test and associated P-value for the first 25 lags on the residuals of the best-fit autoregressive moving average [ARMA(p, d, q)] models used in the time series after trend and cycle (n = 4) removal for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) in furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
Table 6. Summary of Ljung–Box Q test and associated P-value for the first 25 lags on the residuals of the best-fit autoregressive moving average [ARMA(p, d, q)] models used in the time series after trend and cycle (n = 4) removal for carbon dioxide (CO2; n = 420) fluxes (g m−2 h−1) in furrow-irrigated corn with cover crops (CC) and without cover crops (No-CC) during the 2024 growing season at the Vayda Regenerative Farm near Clarksdale, MS.
LagCC
[ARMA (4, 0, 3 §)]		No-CC
[ARMA (4, 0, 4 §)]
Ljung–Box Qp-ValueLjung–Box Qp-Value
10.010.950.120.73
20.360.830.690.71
32.590.461.200.75
46.840.143.060.55
58.470.133.140.68
68.470.213.160.79
79.030.253.160.87
89.290.323.980.86
99.320.414.200.89
109.320.504.300.93
119.340.594.370.96
1210.490.574.370.98
1310.520.654.520.98
1411.370.664.720.98
1511.400.724.820.99
1612.120.734.890.99
1712.230.794.900.99
1812.430.825.290.99
1912.450.875.5090.99
2013.730.845.5150.99
2113.950.875.990.99
2214.130.906.120.99
2314.140.926.260.99
2414.550.937.600.99
2514.550.957.660.99
§ The ARMA models’ coefficients in parentheses represent, in order from left to right, the autoregressive factor p, the differencing factor d, and the moving-average factor q.
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Della Lunga, D.; Brye, K.; Mulvaney, M.J.; Daniels, M.; de Oliveira, T.; Baker, B.; Bradford, T., Jr.; Arel, C. Season-Long Time-Series Analysis of Soil Respiration in Furrow-Irrigated Corn with and Without Cover Crop in the Lower Mississippi River Basin. Climate 2025, 13, 232. https://doi.org/10.3390/cli13110232

AMA Style

Della Lunga D, Brye K, Mulvaney MJ, Daniels M, de Oliveira T, Baker B, Bradford T Jr., Arel C. Season-Long Time-Series Analysis of Soil Respiration in Furrow-Irrigated Corn with and Without Cover Crop in the Lower Mississippi River Basin. Climate. 2025; 13(11):232. https://doi.org/10.3390/cli13110232

Chicago/Turabian Style

Della Lunga, Diego, Kristofor Brye, Michael J. Mulvaney, Mike Daniels, Tabata de Oliveira, Beth Baker, Timothy Bradford, Jr., and Chandler Arel. 2025. "Season-Long Time-Series Analysis of Soil Respiration in Furrow-Irrigated Corn with and Without Cover Crop in the Lower Mississippi River Basin" Climate 13, no. 11: 232. https://doi.org/10.3390/cli13110232

APA Style

Della Lunga, D., Brye, K., Mulvaney, M. J., Daniels, M., de Oliveira, T., Baker, B., Bradford, T., Jr., & Arel, C. (2025). Season-Long Time-Series Analysis of Soil Respiration in Furrow-Irrigated Corn with and Without Cover Crop in the Lower Mississippi River Basin. Climate, 13(11), 232. https://doi.org/10.3390/cli13110232

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