Seasonal and annual variability of reference evapotranspiration at Rahuri in Semi-Arid Region of Western Maharashtra

Introduction

Evapotranspiration (ET), as defined by the Food and Agriculture Organization (FAO), is the combined process of water loss to the atmosphere through evaporation from soil and plant surfaces and transpiration via plant leaves. To ensure consistency in estimating evapotranspiration across diverse climatic regions, FAO introduced the concept of reference evapotranspiration (ET₀)-the rate of evapotranspiration from a hypothetical reference crop characterized by a height of 0.12 m, surface resistance of 70 s/m, and an albedo of 0.23, resembling a well-watered grass surface (Allen et al., 1998) [1] . ET₀ serves as a critical baseline for estimating actual crop water requirements under varying agroclimatic conditions and plays a vital role in irrigation scheduling, drought monitoring, regional water allocation, and long-term water resource planning. As ET₀ is primarily governed by meteorological factors such as temperature, solar radiation, wind speed, and humidity, any long-term variation in these parameters due to climate change is expected to alter the atmospheric water demand. A standardized approach for estimating reference evapotranspiration (ET₀) is the FAO Penman-Monteith method, which integrates key climatic variables such as temperature, solar radiation, wind speed, and humidity (Allen et al., 1998) [1] . It provides a consistent and reliable measure of the atmospheric water demand from a well-watered reference grass surface. Therefore, analyzing trends in ET₀ provides valuable insights into shifts in regional hydrometeorological behavior and is essential for formulating adaptive strategies in agriculture and water management under changing climatic conditions. Recent studies across varied geographical settings have reported diverse trends in ET₀ and actual evapotranspiration (ET), highlighting the influence of local climatic variables. For instance, in Piazza Armerina, Sicily, a Mediterranean climate region, a significant decline in ET₀ was observed in November, with specific humidity and wind speed identified as the most and least influential drivers, respectively (Aschale et al., 2023) [2] . In India, several regional investigations have revealed a general decline in ET₀. The Tons River Basin in Central India showed a statistically significant downward trend, especially during the pre-monsoon and monsoon seasons, mainly attributed to declining wind speeds and rising temperatures. A 32-year nationwide study further confirmed decreasing ET₀ patterns, primarily linked to increased relative humidity and reduced wind velocity (Bandyopadhyay et al., 2009) [3] . Similarly, Goroshi et al., (2017) [8] reported declining ET during the southwest monsoon in forested regions, whereas arid zones exhibited increasing ET due to enhanced rainfall and soil moisture availability. Contrastingly, a 45-year study over Iran indicated an increasing trend in ET₀, particularly during spring, pointing to a rising evaporative demand under warming conditions (Ghalami et al., 2020) [7] . A recent analysis in the Raipur region of Chhattisgarh also recorded decreasing ET₀ during peak pre-monsoon months (Kumar et al., 2023) [13] . These findings underscore the complex and region-specific interactions between ET₀ and climatic parameters, emphasizing the need for localized long-term assessments. To investigate the temporal dynamics of ET₀ over the last five decades at Rahuri, Maharashtra-a semi-arid region of Western India-this study employed the Mann-Kendall (MK) test, a widely recognized non-parametric method for detecting trends in climatic time series. Originally developed by Mann (1945) [14] and refined by Kendall (1945) [12] , the MK test is particularly suited for hydrological and meteorological data due to its robustness against non-normality and outliers. The Sen's slope estimator (Sen, 1968) [17] was used to quantify the magnitude of change per unit time. As recommended by the World Meteorological Organization (WMO), the MK test is valued for its simplicity, reliability, and suitability in long-term climate trend analysis (Bandyopadhyay et al., 2009) [3] . It is therefore undertaken to explore the trends in reference evapotranspiration (ET₀) at Rahuri, Maharashtra over the past 50 years, considering different time scales-weekly, monthly, seasonal, and annual-given the critical role of ET₀ in agricultural planning, irrigation scheduling, and effective water resource management.

Material and Methods

Study area and Data Collected

Mahatma Phule Krishi Vidyapeeth (MPKV), Rahuri, is situated at 19.3492º N latitude and 74.6461º E longitude, with an elevation of approximately 559 meters above mean sea level (Figure 1). The daily weather data for the Rahuri region, encompassing parameters such as maximum and minimum temperature, maximum and minimum humidity, sunshine hours, and wind speed, have been recorded over a 50-year period from 1975 to 2024. The meteorological observatory is located in the Ahilyanagar district of Maharashtra, positioned on the Deccan Plateau within the rain shadow zone of the Western Ghats. Rahuri experiences a semi-arid tropical climate characterized by hot summers, moderate monsoon rainfall, and mild winters. The region receives an average annual rainfall of approximately 592 mm, predominantly during the southwest monsoon season from June to September. Temperatures range with average maximums between 30°C and 42°C, peaking in May, while minimum temperatures during December and January may fall to 8°C-10°C.

Estimation of reference evapotranspiration (ETo)

Reference crop evapotranspiration is defined as it is the rate of evapotranspiration from a reference surface. According to FAO the reference surface is a hypothetic reference crop with an assumed crop height of 0.12m, a fixed surface resistance of 70s per m -1 and albedo of 0.23. Various methods to compute reference crop evapotranspiration (ETo) are available in literature. The selection of particular method depends on availability of data, accuracy of data, accuracy needed in estimation and suitability of data to climatic condition. The various methods are available to estimate the reference crop evapotranspiration in the Phule Jal app developed by RKVY-IWRAS, MPKV, Rahuri. Penman-Monteith (equation 1) method as given in FAO-56 (Allen et al. 1998) [1] was used for computation of reference evapotranspiration (ETo) in Phule Jal app.

Where, ETo is reference evapotranspiration (mm day -1 ), Rn is net radiation at the crop surface (MJ m -2 day -1 ), G issoil heat flux density (MJ m -2 day -1 ), Ta is mean daily air temperature (°C), u2 is wind speed at 2 m height (m s -1 ), es is saturation vapour pressure (kPa), ea is actual vapour pressure (kPa), es -ea is saturation vapor pressure deficit (kPa),  is slope of saturation vapour pressure curve (kPaºC -1 ) and γ is psychrometric constant (kPaºC -1 ). Mean value of all six weather parameters (Tmax, Tmin, RHmax, RHmin, n and u2), altitudes and latitudes were used to compute each parameter required for Penman-Monteith model.

Methodology

Statistical Characteristics

The universal method was used to calculate the mean, standard deviation, and coefficient of variation of reference evapotranspiration (ETo).

Linear Approach in Trend Analysis

Linear trend analysis in MS Excel involves using the TREND function, which fits a straight line to the data by applying the least squares method. To perform this, first data is organized with independent variables (years) in one column and dependent variables (ETo values) in another for considered time series. Then, apply the formula =TREND (known_y's, known_x's, new_x's, const), where known_y's are the observed data, known_x's are the corresponding time points, and new_x's represent time points for which you want predicted values. The constant (const) determines whether the intercept is forced to zero or calculated normally. After entering the formula, Excel returns predicted values along the trendline, which can be visualized alongside original data in a chart to observe increasing or decreasing trends. This method provides a straightforward approach to quantify and forecast linear trends within datasets.

Mann -Kendall non parametric test

This is a statistical method primarily used to test the null hypothesis of no trend against the alternative hypothesis of a monotonic increasing or decreasing trend in hydro-climatic time series data. For time series with fewer than 10 data points, the Stest is applied, while for more than 10 points, the normal approximation or Z-test is utilized (Gilbert, 1987). Annual, seasonal, monthly, and weekly rainfall data are evaluated as ordered time series. The Mann-Kendall Statistic (S) is calculated considering the number of tied groups (q), the number of data values in each tied group (tp), and the total number of years (n) for which data is available. The standardized test statistic Z is then computed to determine the significance of the trend. A positive or negative Z value indicates a rising or declining trend, respectively. The significance of these trends is evaluated at confidence levels of 99%, 95%, and 90%, where the null hypothesis of no trend is rejected if |Z| > 2.575, |Z| > 1.96, and |Z| > 1.645, respectively. Following the equations involved in evaluation of trend using Mann-Kendall method.

The following equations (2, 3, 4 and 5) are used in the evaluation of trends using the Mann-Kendall method:

The Mann-Kendall statistic S is calculated as:

Where n is the number of data points, xi and xj are individual data values with j>i, and the sign function sign is defined as:

The variance of VAR(S), accounting for tied groups, is given by

Where q is the number of tied groups and tp is the number of data points in the p th tied group. The standardized test statistic Z is computed as:

This Z-value follows a standard normal distribution and is used to evaluate the presence of a statistically significant monotonic trend in the data.

Sen's Slope Estimation

To estimate the true slope of an existing linear trend, Sen's nonparametric method (Equation 6 and 7) is used. This method calculates the slope Qi for all pairs of observations in a time series as:

Results and Discussion Statistical Characteristics and Interannual Variability

The reference evapotranspiration (ETo) data spanning 50 years from 1975 to 2024 at Rahuri exhibits clear seasonal and monthly variations, with its statistical characteristics summarized in Table 1. On an annual scale, the mean ETo was 1683.41 mm, accompanied by a standard deviation of 194.44 mm and a coefficient of variation (CV) of 11.55%, indicating moderate variability in atmospheric water demand. Seasonal analysis shows that the summer season recorded the highest average ETo at 634.85 mm, with the greatest variability (CV = 17.80%), reflecting the high evaporative demand and climatic fluctuations typical of this period. In contrast, the monsoon season exhibited the lowest variability (CV = 7.33%), suggesting more stable evapotranspiration under relatively uniform weather conditions. At the monthly scale, May recorded the highest mean ETo (241.67 mm), followed by April and March, while December had the lowest (91.26 mm). Notably, March and April exhibited the highest monthly variability with CVs of 21.47% and 20.81%, respectively, highlighting significant interannual fluctuations in evapotranspiration during the pre-monsoon months. The average seasonal contribution to average annual ETo, as illustrated in Figure 2, further emphasizes the dominance of the summer and monsoon periods. Summer accounts for the largest share at 37.71%, followed by the monsoon season at 30.59%.

Winter and post-monsoon seasons contribute 18.40% and 13.30%, respectively. This distribution reflects higher atmospheric water demand during the warmer parts of the year. Figure 3, showing average monthly contributions to average annual ETo, aligns with this trend. May contributes the most at 14.36%, followed by April (12.90%) and March (10.46%), underscoring peak evapotranspiration in the pre-monsoon summer months. Moderate contributions from June (9.51%), July (7.21%), and August (7.31%) correspond to the monsoon period, while the lowest contributions are observed in January (5.42%) and December (5.90%), aligning with the cooler winter months. These patterns collectively highlight a strong seasonal variation in ETo, with higher values during hot months and significantly lower values during cooler periods, emphasizing the need for season-specific water management strategies.

Analysis of trends through a linear trendline approach

Figure 4 displays the annual reference evapotranspiration (ETo) trends using a linear trendline approach for the overall period (1975-2024) and each individual decade. The overall trend (Figure 4a) shows a significant decline in annual ETo, indicating a long-term reduction in atmospheric evaporative demand. Decadal trends (Figures 4b-f) reveal variations-while 1985-1994 and 2015-2024 show a clear decreasing trend, the period 2005-2014 reflects a slight upward trend, and the other decades remain relatively stable. These patterns suggest both short-term fluctuations and a broader declining trend likely influenced by climatic shifts. Figure 5 presents seasonal ETo trends over the 50-year period for Summer, Monsoon, Post-Monsoon, and Winter seasons. The Summer and Winter seasons exhibit distinct declining trends, pointing to a consistent reduction in evaporative demand during temperature extremes. The Monsoon season shows a slightly negative trend, likely due to high humidity and cloud cover, while the Post-Monsoon period remains largely stable. These seasonal trends emphasize the need to reassess water resource planning and crop irrigation strategies under changing climatic conditions.

Results of Trend analysis using Mann -Kendall and Sens slope estimator method

The trend analysis results of reference evapotranspiration (ETo) for the period 1975 to 2024, including sub-decadal intervals, were evaluated using the Mann-Kendall Test (Z) and Sen's Slope (Q, in mm/year). Table 2 presents the trends observed in the annual and seasonal time series (summer, monsoon, postmonsoon, and winter), while Table 3 shows the trends in the monthly time series over the same period.

During the 50-year period (1975-2024), a highly significant decreasing trend (99% level) was observed in annual, summer, post-monsoon, and winter ETo, with Z-values ranging from -6.71 to -7.73 and Sen's slopes indicating substantial reductions, especially in annual (-12.37 mm/year) and summer (-6.96 mm/year) series. The monsoon season showed a moderately significant decreasing trend (at 95% level) with a Z-value of - During 2005 and 2014 significant increasing trend was observed in the Monsoon ETo time series (90% confidence). All other time series remained non-significant. This suggests a rise in evaporative demand during the monsoon, likely linked to higher temperatures or reduced relative humidity during this period. The post-monsoon period during 2015 and 2024 showed a significantly decreasing trend (90% confidence), while all other time series did not exhibit statistically significant changes. This suggests a renewed decline in ETo, particularly after the rainy season, reflecting potential shifts in weather patterns or reduced solar inputs.

During the overall 50-year period, a strong and consistent decreasing trend in ETo is observed in most months. January through May and September through December exhibit highly significant (99%) declines, with the steepest drop seen in March (Z = -7.14). July also shows a significant decline at the 95% level, while June and August are non-significant. This suggests a widespread, long-term reduction in evaporative demand across nearly the entire year. In this initial decade (1975-1984), no significant trends were observed across any of the months.

Monthly Z-values remain within the non-significant range, indicating stability in ETo patterns during this period. This phase can be considered a baseline against which subsequent climatic shifts may be compared, with no major alterations in atmospheric evaporative demand during this time. The decade from 1985 to 1994 marks the beginning of statistically significant declines in ETo. February and November show moderate (95%) decreasing trends, while April and August show weakly significant (90%) decreases. The rest of the months remain non-significant. This indicates that ETo decline began to emerge, especially in late winter, summer, and post-monsoon months, reflecting possible impacts of early climate change signals or shifts in regional weather patterns. The decade from 1095 to 2004 shows limited and isolated increasing trends. Only January recorded a significant increasing trend at the 90% level, while all other months were non-significant. The increase in ETo during January could be due to rising minimum temperatures or clearer skies in winter. Overall, this period appears to represent a temporary pause or reversal in the declining trend observed in the previous decade. In this period 2005 to 2014, only September showed a significant increasing trend at the 95% level, with all other months being nonsignificant. The increase in September may reflect a localized climatic anomaly or short-term variability during the late monsoon season. The rest of the months exhibited no statistically relevant change, indicating a relatively stable ETo pattern throughout the year during this decade. The most recent decade from 2015 to 2024 shows mixed and weakly significant monthly trends. January exhibited a slight increasing trend (90% level), possibly linked to winter warming, whereas August showed a weakly significant decrease. All other months remained statistically non-significant. This indicates that recent changes in ETo are not uniformly directional and are likely influenced by short-term variability rather than long-term climatic trends.

Discussion

The observed and statistically validated decline in ETo at Rahuri parallels findings from multiple regions across India, where significant downward trends have been consistently detected via robust non-parametric tests, such as Mann-Kendall and Sen's slope. This decreasing trend in reference evapotranspiration aligns with the literature, which reports similar patterns in diverse agro-ecological zones, including the humid northeast (Jhajharia et al., 2011) [10] , arid and semi-arid northwest India (Saxena et al., 2020) [16] , and districts like Ludhiana in Punjab (Kaur & Kaur, 2022) [11] . Notably, exceptions exist, such as the Narmada River basin (Pandey & Khare, 2018) [15] , which featured a positive annual trend, emphasizing regional heterogeneity and the influence of localized hydro-climatic factors The primary meteorological drivers responsible for this decline are reductions in net radiation, decreased wind speed, and fewer sunshine hours, all of which counterbalance the effect of rising temperatures-an outcome corroborated by studies in Udaipur (Jalgaonkar et al., 2017) [9] and other regions. Increasing humidity further enhances the downward trend in ETo, while changes in rainfall patterns contribute regionally specific responses From an agricultural perspective, declining ETo suggests reduced irrigation requirements, potentially enabling improved water management and crop system intensification, particularly in water-limited environments. However, decadal and monthly analyses reveal episodes of variability, with some decades (e.g., 2005-2014) and months (e.g., September, January in some sub-periods) showing shortterm reversals or non-significant changes, likely reflecting transient climatic fluctuations or anomalies. Moreover, while current ETo trends indicate a reduction in crop water demand, climate projections caution that potential evapotranspiration may rise under future warming scenarios, with impacts varying spatially and seasonally (Chattopadhyay & Hulme, 1997) [4] . This possibility necessitates continued monitoring of ETo alongside temperature and rainfall trends, as water management and agricultural productivity could be challenged if rainfall increases do not offset heightened evaporative losses. In summary, the analysis of Rahuri ETo trends demonstrates a statistically significant, seasonally widespread decline over the last five decades, echoing national patterns and suggesting that ongoing climatic changes are actively reshaping atmospheric water demand. These insights underscore the importance of adaptive water resource management strategies attuned to both long-term climate signals and short-term variability.

Conclusion

The observed results show that reference evapotranspiration (ETo) at Rahuri over the 50-year period exhibits clear seasonal and monthly variations, with an overall significant declining trend in annual and seasonal ETo, particularly in summer and winter periods. High water demand during summer months is evident from the higher ETo values and greater variability, while the monsoon season shows lower and more stable evapotranspiration. The dominant contribution of summer and monsoon to the annual ETo aligns with expected climatic patterns of high temperatures and rainfall cycles. Trend analyses using Mann-Kendall and Sen's slope estimators confirm a highly significant decrease in ETo at annual and seasonal scales, consistent with similar findings across various Indian agroecological regions. The decline in reference evapotranspiration (ETo) may be attributed to changes in climatic variables which counterbalance the effect of rising temperatures. However, further studies are needed to comprehensively confirm and quantify the individual impacts of different climatic factors on ETo variations. Shorter-term variations, including periods of stability and minor increases in some decades, reflect climatic fluctuations. These patterns highlight the evolving nature of atmospheric water demand and underscore the critical need for further detailed studies to better understand the driving factors and future behaviour of reference evapotranspiration under changing climate conditions. Continued and comprehensive research is essential to accurately quantify the influences of various climatic variables on ETo trends and to anticipate potential shifts due to ongoing climate change.

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