Comparative evaluation of eight simplified potential evapotranspiration methods against the FAO-56 penman–monteith benchmark in the Jayakwadi Command Area, Maharashtra, India: a seasonal and spatial analysis

1 Introduction

Evapotranspiration (ET) is the dominant water flux in agricultural landscapes, typically accounting for 70–80% of total rainfall in semi-arid regions (Allen et al., 1998a; Bandyopadhyay et al., 2011; Ding et al., 2012; Amatya et al., 2014). Accurate estimation of reference evapotranspiration (ET₀)—the atmospheric water demand of a standardized well-watered grass surface (Allen et al., 1998a)—is central to irrigation scheduling, crop water requirement modeling, hydrological water balance computation, and drought assessment. In irrigation command areas with limited groundwater recharge and high seasonal rainfall variability, the consequences of ET₀ estimation errors propagate directly into water allocation decisions, canal scheduling, and crop yield outcomes (Allen and Tasumi, 2007; Senay et al., 2007).

The FAO-56 Penman–Monteith (PM) method is the internationally recognized standard for ET₀ estimation, recommended jointly by the Food and Agriculture Organization (FAO) and the World Meteorological Organization (WMO) (Allen et al., 1998a; Wagle et al., 2017). Its physically based formulation explicitly accounts for energy availability (net radiation), atmospheric demand (vapor pressure deficit), and aerodynamic resistance (wind speed), yielding reliable ET₀ estimates across diverse climatic settings (Almorox and Hontoria, 2004; Khoob, 2008; Singh and Pawar, 2017; Lu et al., 2005; Liu and Lin, 2005; Chen et al., 2005; Berti et al., 2014; Oudin et al., 2005; Tegos et al., 2015; McMahon et al., 2016). However, the method requires simultaneous measurement of air temperature (maximum and minimum), relative humidity, wind speed at 2 m height, and solar radiation—inputs that are routinely unavailable at the spatial and temporal resolution required for operational irrigation management across large command areas in developing countries, including India (Al-Ghobari, 2000; De Bruin and Stricker, 2000; Garcia et al., 2004; Raziei and Pereira, 2013).

To address this data scarcity, a range of simplified empirical ET₀ methods has been developed, broadly classified as radiation-based or temperature-based. Radiation-based methods—including Makkink (Makkink, 1957), Priestley–Taylor (Priestley and Taylor, 1972), and Abtew (Abtew, 1996)—use solar or net radiation as the dominant driver, reflecting the energy-limited nature of ET₀ in most climates. Temperature-based methods—including Hargreaves–Samani (Hargreaves and Samani, 1985), Thornthwaite (Thornthwaite, 1948), Hamon (Hamon, 1961), Linacre (Linacre, 1977), and Blaney–Criddle (Brouwer and Heibloem, 1986)—use only temperature and daylight duration, making them highly applicable in data-scarce environments but potentially less accurate under high vapor pressure deficit or strong advection conditions.

Multiple studies have compared the performance of simplified ET₀ methods against the FAO-56 PM benchmark across various climates (Oudin et al., 2005; Xu and Chen, 2005; Xu and Singh, 2005; Xu et al., 2006; Gong et al., 2006; Allen et al., 2005; Djaman et al., 2016; Acharki et al., 2025). In subtropical and semi-arid environments, radiation-based methods have generally outperformed temperature-based approaches (Xu et al., 2006; Gong et al., 2006; Djaman et al., 2016), though results are highly site- and season-specific (Xu and Singh, 2005; Acharki et al., 2025). Critically, most published comparisons are confined to temperate, humid, or Mediterranean climates in Europe, North America, and China; systematic multi-seasonal, spatially disaggregated evaluations for Indian semi-arid irrigation command areas remain scarce (Allen et al., 2005; Jagadesh et al., 2024).

The Jayakwadi Command Area (JCA) in the Marathwada region of Maharashtra, India, is one of the largest irrigation command areas in the Deccan Plateau, covering approximately 237,000 ha and serving a predominantly kharif-based agriculture under the Godavari River system. The region is characterized by high summer temperatures (maximum ~42 °C), monsoon-dominant rainfall (650–750 mm year⁻¹, ≥80% concentrated in June–September), pronounced inter-seasonal vapor pressure deficit variability, and severely limited meteorological station density. Despite these management challenges, three specific gaps limit the applicability of the existing empirical ET₀ literature to the JCA. First, an empirical gap: no published study has quantified simplified ET₀ accuracy under the JCA's particular combination of monsoon-dominant rainfall, high pre-monsoon vapor pressure deficit, and Vertisol-dominated hydrology, so transferability from the temperate, humid, and Mediterranean settings that dominate the comparative literature (Oudin et al., 2005; Xu and Chen, 2005; Xu and Singh, 2005; Xu et al., 2006; Gong et al., 2006; Allen et al., 2005; Djaman et al., 2016; Acharki et al., 2025; Jagadesh et al., 2024) cannot be assumed a priori. Second, a methodological gap: prior comparative assessments, in India and elsewhere, have relied predominantly on single-station point comparisons evaluated at annual or monthly resolution, rather than on a spatially distributed multi-station network combined with explicit seasonal disaggregation; consequently, how model performance and its within-zone spatial consistency vary across multiple stations sampling local microclimate heterogeneity, and between monsoon and non-monsoon regimes, remains largely undocumented. Third, a practical gap: no season-specific operational guidance exists for selecting among simplified ET₀ methods in the JCA, leaving irrigation managers without an evidence base for choosing data-light alternatives to FAO-56 PM.

This study addresses these three gaps. The specific objectives are: (i) to evaluate the accuracy of eight simplified empirical ET₀ methods against the FAO-56 PM benchmark across annual and four seasonal time scales (spring, summer, autumn, winter) in the Head Reach Zone of the JCA; (ii) to identify season-specific best-performing models using a multi-metric evaluation framework comprising NSE, Re, NRMSE, R², and PBIAS; and (iii) to provide evidence-based model selection guidelines for operational ET₀ estimation in semi-arid irrigation command areas where comprehensive meteorological datasets are unavailable.

The novelty and contribution of this study are threefold. First, it constructs and independently validates a five-station virtual meteorological network within the Head Reach Zone of an Indian irrigation command area, capturing within-zone spatial heterogeneity in local microclimate rather than relying on a single gauged or synthetic point series as in most prior comparative assessments (Section 2.2). Second, it applies a multi-metric (NSE, Re, NRMSE, R², PBIAS), multi-seasonal evaluation framework to eight empirical ET₀ methods simultaneously, enabling season-specific rather than blanket method recommendations, and explicitly demonstrating where single-metric (R²-only) evaluation is misleading (Section 5.3). Third, it provides, to the authors' knowledge, the first published seasonally disaggregated evaluation of simplified ET₀ methods for any command area of the Godavari river basin, extending the evidence base beyond the temperate, humid, and Mediterranean climates that dominate the existing literature (Oudin et al., 2005; Xu and Chen, 2005; Xu and Singh, 2005; Xu et al., 2006; Gong et al., 2006; Allen et al., 2005; Djaman et al., 2016; Acharki et al., 2025; Jagadesh et al., 2024) and offering an explicit sampling rationale for constructing multi-station virtual meteorological networks in other data-scarce semi-arid command areas, together with a transparent account of which aspects of that construction (Section 2.2) remain to be independently validated. We note here, and return to in Sections 4.1 and 6, that this five-station network and all reported results are confined to the Head Reach Zone of the JCA; the study does not sample or report on the command area's middle or tail reaches, and the findings should be read as characterizing Head Reach conditions specifically rather than the JCA as a whole.

2 Study area and data

2.1 Study area

The Jayakwadi Command Area (JCA) is located in the Marathwada sub-region of Maharashtra, India, between latitudes 19°30′N−20°15′N and longitudes 75°30′E−76°45′E (Figure 1). The command area spans approximately 237,000 ha, served by the Jayakwadi Dam on the Godavari River and irrigated through the Left Bank and Right Bank canal systems. This combination of high evaporative demand and monsoon-concentrated rainfall makes accurate ET_° estimation directly consequential for irrigation planning in the JCA specifically; Sunil et al. (2021) modeled future irrigation water demands under climate change scenarios for this same command area, underscoring the practical stakes of the ET_° estimation accuracy this study addresses. Topographically, the region features flat to gently undulating terrain with elevations ranging from 400 to 600 m above mean sea level, underlain predominantly by medium-to-deep Vertisols (black cotton soils) with high clay content (40–60%) and substantial water-holding capacity.

The area experiences a tropical semi-arid climate (Köppen: BSh), influenced by the southwest monsoon. Mean annual rainfall ranges between 650 and 750 mm, with over 80% occurring between June and September. Summers are hot (mean daily maximum ~42 °C in May), winters are mild (mean daily minimum ~10 °C in January), and relative humidity ranges from 35% in the pre-monsoon season to 85% at monsoon peak. The cropping pattern is dominated by kharif crops (soybean, cotton, sorghum, pigeon pea) with limited rabi cultivation constrained by reservoir storage and canal scheduling.

2.2 Meteorological dataset

Five virtual meteorological stations were selected within the Head Reach Zone to represent local spatial and microclimatic variability within a single, hydraulically stable part of the Jayakwadi Command Area. This sampling strategy provides within-zone spatial representation while maintaining computational efficiency for long-term model evaluation; it does not extend to the command area's middle reach or tail-end, which are outside the scope of this study (Section 6). A 34-year study period (1990–2024) was selected to encompass substantial inter-annual climatic variability, including wet, normal, and drought years, thereby ensuring that the comparative assessment of empirical evapotranspiration models reflects a broad range of hydroclimatic conditions typical of the region.

Due to the absence of continuous long-term ground-based meteorological records at adequate station density across the JCA, a 34-year (1990–2024) monthly synthetic dataset was developed for five spatially representative virtual stations, all located within the Head Reach Zone of the command area. This zone was selected as the study's sole spatial focus because it experiences comparatively stable hydraulic conditions and minimal conveyance losses (Section 4.1), providing a consistent meteorological setting within which to isolate model-to-model performance differences without the confound of a superimposed aridity gradient. Five stations within this single zone, rather than one, were used to capture local microclimate heterogeneity—arising from small-scale variation in canal-distributary proximity, minor elevation differences, and land-cover patchiness—and to provide a basis for assessing within-zone consistency of model rankings, rather than to sample the command area's broader head-to-tail hydraulic gradient. This study does not sample or report on the JCA's middle reach or tail-end; extending the evaluation to those areas is identified as future work (Section 6). Each virtual station record was constructed by combining three data sources: (i) climatological statistics from the India Meteorological Department (IMD) Pune gridded dataset (Gridded Rainfall Data, 2023), spatially interpolated to each virtual station coordinate using inverse-distance weighting (IDW) with a power parameter of p = 1 and the four nearest IMD grid points; (ii) NASA-POWER Version 8 surface meteorology reanalysis time series (Sparks et al., 2023), used to impose inter-annual variability on the IMD climatological means, since the IMD product supplies long-term statistics rather than a continuous 1990–2024 monthly series at station resolution; and (iii) an additive adjustment against available historical ground observations from the Maharashtra Water Resources Department (WRD) where such records existed for the period of overlap—specifically, for each virtual station and each calendar month, a fixed monthly offset (observed WRD value minus IDW-interpolated value, averaged over the period of record common to both sources) was computed and added to the corresponding month's interpolated value in every year of the 1990–2024 series, i.e., 12 station-specific monthly offsets per station, applied uniformly across years rather than varying year to year. The IDW power parameter (p = 1) and neighbor count (4 nearest grid points) were adopted as reasonable, commonly used choices rather than selected through formal sensitivity analysis against alternative parameterizations (e.g., the more conventional p = 2, or 6 or 8 neighbors); the sensitivity of the resulting interpolated climatology, and of the downstream ET₀ estimates, to these specific parameter choices has not been tested. The corresponding author can provide the full processing scripts on request (see Reproducibility, below). The six meteorological variables derived through this procedure are: daily maximum and minimum air temperature (T_max and T_min, °C); mean daily relative humidity (RH, %); daily solar radiation (R_s, MJ m⁻² day⁻¹); wind speed at 2 m height (u₂, m s⁻¹); and sunshine duration (n, h). Because the resulting series blend interpolated climatology with reanalysis-derived variability rather than direct station observation, we refer to it throughout as a synthetic dataset rather than an observed record, and we treat all downstream model comparisons as conditional on this construction (Section 6).

The synthetic dataset was validated by comparing monthly FAO-56 PM ET₀ estimates computed from the synthetic data against ET₀ values derived from the five nearest IMD weather stations with available complete records over the 2000–2015 overlap period. Mean absolute error of monthly ET₀ between the two sources was 0.34 mm day⁻¹ (coefficient of variation 4.8%), which we consider acceptable fidelity for comparative, relative model ranking; this aggregate ET₀-level check is, however, the only validation statistic computed for this study. We did not independently validate the six individual input variables (Tmax, Tmin, RH, R_s, u₂, sunshine duration) against station observations, so we are not able to report variable-level RMSE, bias, or correlation, and we do not claim a specific magnitude of bias reduction attributable to the interpolation or bias-correction procedure. We flag this as a limitation in Section 6 and recommend that future work compute and report variable-level validation statistics once continuous automatic weather station records become available for the JCA.

Reproducibility: the authors will make the monthly synthetic dataset (five stations × six variables × 1990–2024) and the associated processing scripts available from the corresponding author upon reasonable request, subject to institutional data-sharing approval (see Data Availability Statement), and intend to deposit a de-identified version in a public repository upon acceptance. All empirical-method equations were implemented exactly as published in their original source (Table 1), with no locally fitted coefficients, so that any discrepancy between our results and a re-implementation should be attributable to input-data handling rather than to formula ambiguity; unit conventions and time-step handling (daily-basis Hargreaves–Samani, Hamon, Priestley–Taylor, Linacre, Makkink, and Abtew aggregated to monthly totals; monthly-basis Thornthwaite and Blaney–Criddle applied directly) are documented in Table 1 (Figure 2).

Table 1. Empirical PET estimation methods evaluated in this study, their equations, required inputs, and input data categories.

3 Methodology

3.1 Reference ET₀: FAO-56 penman–monteith

The FAO-56 PM method served as the independent benchmark for all model comparisons. It was computed from the full set of meteorological variables (T_max, T_min, RH, R_s, u₂, and derived net radiation R_n) using the standard formulation recommended by Allen et al. (1998b):

ET0=[0.408Δ(Rn-G)+γ(900/(T+273))u2(es-ea)]/

[Δ+γ(1+0.34u2)]

where Δ is the slope of the saturation vapor pressure–temperature curve (kPa °C⁻¹), γ is the psychrometric constant (kPa °C⁻¹), G is soil heat flux density [set to zero for monthly calculations per (Allen et al., 1998b)], T is mean air temperature (°C), and (e_s-e_a) is the vapor pressure deficit (kPa). Extraterrestrial radiation (R_a), net longwave radiation, and related variables were computed following the procedures in FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998b).

3.2 Empirical ET₀ methods

The eight empirical methods evaluated are listed in Table 1 with their equations, key parameters, and required inputs. Methods were applied in their original published formulations without local calibration, as calibration-free performance assessment is the primary objective of this study. Methods are grouped into daily-based (Hargreaves–Samani, Hamon, Priestley–Taylor, Linacre, Makkink, Abtew) and monthly-based (Thornthwaite, Blaney–Criddle) categories based on their temporal resolution requirements.

3.3 Statistical Evaluation Framework

Table 2 model performance was quantified using five complementary metrics computed on the monthly time series over the full validation period, aggregated by season (spring: March–May; summer/monsoon: June–September; autumn/post-monsoon: October–November; winter: December–February) and annually:

Table 2. Statistical metrics used for model performance evaluation.

Following Moriasi et al. (2007), model performance was classified as “very good” (NSE > 0.75, PBIAS ± 10%), “good” (NSE 0.65–0.75, PBIAS ±15%), “satisfactory” (NSE 0.50–0.65, PBIAS ± 25%), or “unsatisfactory” (NSE < 0.50). Statistical analyses were performed in Python 3.10 (NumPy 1.24, SciPy 1.10).

4 Results

4.1 FAO-56 PM benchmark ET₀ in the head reach zone

The FAO-56 PM method yielded a mean annual ET₀ of 1420 mm for the Head Reach Zone of the JCA, with clear seasonal variation (Table 3). Summer (monsoon) contributed the highest seasonal ET₀ (420 mm), driven by high net radiation and elevated temperatures, despite high relative humidity partially suppressing vapor pressure deficit. Winter ET₀ (340 mm) and spring ET₀ (310 mm) were similar, while autumn ET₀ (350 mm) reflected the post-monsoon transition with declining humidity and moderate radiation. The Head Reach Zone was selected as the reference zone for inter-model comparison because it experiences relatively stable hydraulic conditions and minimal conveyance losses, providing consistent meteorological forcing across the 34-year dataset.

Table 3. FAO-56 PM ET₀ estimates (mm) for the Head Reach Zone of the Jayakwadi Command Area, aggregated by season and annually.

4.2 Seasonal and Annual Model Performance

Table 4 presents the full statistical performance assessment for all eight empirical methods across annual and seasonal time scales. Key findings are described below and visualized in Figures 3, 4.

Table 4. Statistical performance of eight empirical ET₀ methods against the FAO-56 PM benchmark (Head Reach Zone, JCA).

Best values per season highlighted. Classification follows (Moriasi et al. 2007).

4.3 Seasonal performance summary

4.3.1 Spring (March–May)

Abtew achieved the highest NSE (0.664) and lowest NRMSE (0.129), with near-zero bias (Re = 0.075; PBIAS = +7.5%), rating as “good”. Makkink ranked second (NSE = 0.477, “satisfactory”). Despite PT exhibiting the highest R² (0.986), its high positive Re (+0.293) and NRMSE (0.298) indicate systematic overestimation and unsatisfactory performance, illustrating the danger of relying on R² alone.

4.3.2 Summer/monsoon (June–September)

Abtew achieved outstanding performance (NSE = 0.937, Re = 0.007, NRMSE = 0.076; “very good”), the highest NSE of any model in any season. The near-zero bias (PBIAS = +0.7%) is particularly noteworthy for an uncalibrated single-parameter model. Makkink ranked second (NSE = 0.691, NRMSE = 0.170; “good”) with the highest R² observed in this study (0.992). Hargreaves–Samani showed satisfactory summer performance (NSE = 0.560) despite an 18.1% positive bias. Temperature-only models (Tho, Ham, Lin, BC) performed unsatisfactorily.

4.3.3 Autumn/post-monsoon (October–November)

Makkink dominated (NSE = 0.630; “good”), with Hargreaves–Samani performing satisfactorily (NSE = 0.552). Abtew declined to unsatisfactory (NSE = 0.295), likely due to reduced solar radiation availability in the post-monsoon transition and declining evaporative demand not captured by a radiation-only model. Priestley–Taylor again showed high R² (0.981) but unsatisfactory NSE (−0.162) due to systematic positive bias.

4.3.4 Winter (December–February)

Makkink achieved the highest single-season NSE across the entire study (NSE = 0.886; NRMSE = 0.173; PBIAS = −14.8%; “very good”), confirming its consistently strong performance under cool-season, low-humidity conditions. Priestley–Taylor (NSE = 0.617, PBIAS = +28.6%) and Abtew (NSE = 0.611) showed good performance. Thornthwaite was the worst performer in winter (NSE = −2.097, PBIAS = −82.3%), as expected for a model calibrated for temperate humid climates.

4.3.5 Annual scale

All eight models produced negative NSE values at the annual scale, with Tho yielding NSE = −58.72, indicating catastrophic annual-scale failure. This confirms that annual aggregation masks the substantial seasonal heterogeneity in model behavior and that annual-only evaluations are insufficient for semi-arid monsoon climates. Even the best annual performers (Abt: NSE = −1.040; Mak: NSE = −1.857) failed to meet the “satisfactory” threshold.

5 Discussion

5.1 Radiation-based methods outperform temperature-based methods

The consistent superiority of radiation-based methods (Makkink, Abtew, and to a lesser extent Priestley–Taylor) over temperature-based methods across all seasons in the JCA confirms the findings of comparable studies in subtropical and semi-arid environments globally (Xu and Singh, 2005; Xu et al., 2006; Gong et al., 2006; Allen et al., 2005; Djaman et al., 2016). The physical basis for this pattern is clear: under semi-arid conditions, ET₀ is primarily energy-limited rather than water-limited, and its inter-seasonal variability is governed by the radiation regime and vapor pressure deficit rather than temperature alone (Allen et al., 1998a; Gong et al., 2006). Temperature-based models, which conflate heat availability with radiative energy input, systematically underperform when the two are decoupled, as occurs in the JCA during the monsoon season when high humidity suppresses vapor pressure deficit despite moderate temperatures.

These results are consistent with Xu and Singh (2005), who found radiation-based methods superior to temperature-based alternatives across multiple European stations, and with Djaman et al. (2016), who reported radiation-based methods performing significantly better in semi-arid western United States conditions. Within an Indian context, Jagadesh et al. (2024) similarly found radiation-based formulations outperforming temperature-only methods in a tropical highland climate, reinforcing the generalisability of this pattern across Indian agroclimatic zones.

5.2 Season-specific model performance

The strong summer performance of Abtew (NSE = 0.937, PBIAS = +0.7%) is explicable by the high and relatively stable solar radiation input during the June–September monsoon period, combined with the model's inherent simplicity (single solar radiation predictor), which minimizes error propagation from secondary meteorological inputs. The near-zero bias is noteworthy for an uncalibrated model and suggests that the Abtew coefficient (k = 0.53) developed originally for Florida wetlands (Abtew, 1996) is accidentally well-suited to the JCA summer energy balance, likely due to comparable latent heat flux regimes under high moisture conditions.

Makkink's dominance in autumn and winter is attributable to the Δ/(Δ+γ) weighting term, which functions as a temperature-modulated radiation partition coefficient. As temperatures decline post-monsoon, this term appropriately reduces the ET₀ estimate relative to radiation, providing a physically consistent adjustment that the simpler Abtew formulation lacks. This also explains why Makkink, despite being classified as a radiation-based method, performs well across a wider seasonal range than Abtew.

The consistently unsatisfactory performance of Thornthwaite (best seasonal NSE = −2.097 in winter) confirms its known limitations in semi-arid, non-temperate environments (Thornthwaite, 1948; Xu and Singh, 2005). Thornthwaite's derivation for eastern North America climate normals makes it structurally unsuited to highly seasonal, radiation-governed semi-arid climates where temperature and energy availability are decoupled (Allen et al., 1998a). Similarly, Linacre showed the most extreme negative NSE values at the annual scale (−34.18), consistent with its sensitivity to dew-point temperature estimation errors that amplify under semi-arid low-humidity conditions.

5.3 The R² vs. NSE discrepancy

A notable finding of this study is the systematic discrepancy between R² and NSE for the Priestley–Taylor method, which achieved high R² values (0.947–0.986 seasonally) while simultaneously producing negative or near-zero NSE values in spring and autumn. This discrepancy arises because R² measures only the linearity of the association between observed and estimated values, without penalizing systematic additive or proportional bias (Allen et al., 1998a; Moriasi et al., 2007). PT's consistent positive bias (Re = +0.277 to +0.295), attributable to its fixed α = 1.26 parameterisation that does not account for the strong aerodynamic resistance under JCA's high wind speed and low humidity conditions, translates into high bias despite tight linear correlation. This finding reinforces the recommendation of Moriasi et al. (2007) that NSE, PBIAS, and NRMSE should be evaluated jointly, with R² used as a supplementary rather than primary performance criterion.

5.4 Negative annual NSE and the necessity of seasonal evaluation

The universal failure of all eight models at the annual scale (all NSE < 0) is a critical finding with practical implications. Annual aggregation masks the strong seasonal pattern of both ET₀ magnitude and model error structure. The JCA's ET₀ regime is highly asymmetric: the monsoon season contributes approximately 30% of annual ET₀ while the pre-monsoon summer contributes the highest monthly values. Models that perform well in one season and poorly in another produce compensating errors that result in apparently poor annual performance despite seasonal utility. This pattern is consistent with the findings of Oudin et al. (2005), who demonstrated that seasonal model calibration substantially improves annual-scale performance for empirical ET₀ methods. The practical implication for the JCA is that empirical ET₀ methods should always be evaluated and applied at seasonal timescales, with season-appropriate model selection, rather than fitted and deployed for annual water balance computation.

5.5 Practical implications for JCA water management

The results provide direct guidance for operational ET₀ estimation in the JCA, conditional on the important caveat established in Appendix A: the Abtew and Makkink recommendation below assumes solar radiation data of comparable quality to the interpolated, bias-adjusted construction in Section 2.2, not arbitrary or uncorrected radiation inputs. Where such radiation data are available from the NASA-POWER product or MODIS satellite retrievals, Abtew is recommended for summer (June–September) canal scheduling and Makkink for post-monsoon and winter irrigation advisory systems. Appendix A demonstrates that this recommendation is not robust to uncorrected radiation data specifically: when the same eight methods were recomputed on live-fetched NASA-POWER data in which only temperature had been bias-corrected, Abtew and Makkink performed poorly while Hargreaves–Samani (which depends only on bias-corrected temperature) improved. Operational deployment of Abtew or Makkink should therefore be preceded by a check of the specific radiation data source's quality against the Section 2.2 construction, not assumed automatically from the results reported here. Where only temperature data are available, or where radiation data quality cannot be confirmed, Hargreaves–Samani is the recommended fallback for summer and autumn (NSE 0.56 and 0.55 respectively), despite its 15–18% positive bias, as it still meets the “satisfactory” threshold, and Appendix A's independent demonstration provides some additional support for its relative robustness. Temperature-only models Thornthwaite, Hamon, Linacre, and Blaney–Criddle are not recommended for operational use in the JCA under any season.

These model recommendations align with the framework for satellite-assisted ET₀ estimation proposed by Pareeth and Karimi (2023), who demonstrated operational deployment of simplified radiation-based ET₀ estimation across large irrigated basins using MODIS inputs. Integration of the Abtew and Makkink models with MODIS MOD11A2 (LST) and NASA-POWER radiation products would provide a fully data-light, operational ET₀ monitoring system for the JCA without dependence on ground-based meteorological infrastructure.

5.6 Hydrological interpretation in the context of recent comparative literature

Beyond the statistical ranking of methods, the seasonal reversal between Abtew (summer-dominant) and Makkink (autumn/winter-dominant) reflects a genuine shift in the hydrological control on ET₀ across the JCA annual cycle. During the June–September monsoon, net radiation and cloud-modulated shortwave input are the primary drivers of atmospheric demand, while high relative humidity suppresses the vapor pressure deficit and dampens the aerodynamic term; under these conditions a single-parameter radiation model with no temperature feedback (Abtew) captures the dominant flux with minimal error propagation. As the monsoon withdraws, declining soil moisture in the JCA's Vertisol-dominated command area, combined with falling temperatures and clearer skies, re-introduces a temperature-modulated partitioning between available energy and the vapor pressure deficit; Makkink's Δ/(Δ+γ) weighting term tracks this partitioning explicitly, which is the physical reason for its dominance in the post-monsoon and winter seasons rather than a statistical artifact of the calibration period. This mechanistic reading is consistent with the broader finding, reported across recent semi-arid evaluations worldwide, that no single empirical formulation is transferable across a full monsoon-to-dry-season cycle without season-specific selection or recalibration (Djaman et al., 2016; Acharki et al., 2025).

These results also refine, rather than simply reproduce, the existing Indian evidence base. Wable et al. (2019), working in a semi-arid basin of Maharashtra using only temperature-based formulations, found that a temperature-based Penman–Monteith variant outperformed the standard Hargreaves–Samani method, but did not evaluate radiation-based alternatives; the present results indicate that where solar radiation data are available, radiation-based methods (Abtew, Makkink) outperform any of the temperature-only formulations they considered, by a wide margin at the seasonal scale. Similarly, the recent 50-model temperature- and humidity-based intercomparison of Ramachandran et al. (2026) for a semi-arid station in Tamil Nadu identified Hargreaves-family and humidity-adjusted temperature models as the best-performing temperature-only alternatives to FAO-56 PM; the JCA results are consistent with this in showing Hargreaves–Samani as the only temperature-based method reaching “satisfactory” performance, while reinforcing that even the best temperature-only formulation remains inferior to a data-light radiation-based method (Abtew, Makkink) wherever solar radiation observations or reanalysis products are available. Read together, these studies and the present results suggest a general hydrological principle for Indian semi-arid command areas: radiation availability, not temperature, is the binding constraint on ET₀ estimation accuracy, and method selection should therefore be governed primarily by which input variable—radiation or temperature alone—is actually observable at the site, rather than by a single nationally or globally “recommended” empirical formula.

A useful point of contrast comes from Hernández-Bedolla et al. (2023), who compared 12 reference-ET methods against FAO-56 PM across five sub-basins of the semi-arid Jucar River Basin, Spain (2000–2022 record). In that setting, temperature-based Hargreaves-family methods, not the radiation-based Makkink or Priestley–Taylor, gave the best regional performance, with radiation-based methods showing larger positive bias at the higher-elevation, cooler sub-basins. This is the opposite ranking to the one reported here for the JCA, and the contrast is informative rather than contradictory: the Jucar basin spans a wide elevation range (21–1,053 m) and a Mediterranean, low-monsoon-influence climate in which the humidity-suppression mechanism driving Abtew's JCA summer performance (Section 5.1) is largely absent, so radiation alone is a weaker predictor of atmospheric demand there than in the JCA. Read alongside Hernández-Bedolla et al. (2023), the present results reinforce that no empirical ET₀ ranking transfers automatically between semi-arid climates with different moisture regimes, and that the empirical gap identified in Section 1—the untested applicability of published rankings to monsoon-dominant semi-arid systems specifically—is not a parochial concern but a documented source of disagreement in the international literature.

More broadly, the empirical, ground-based approach adopted here sits alongside a parallel and increasingly active literature on satellite-derived actual evapotranspiration (ETa) in semi-arid regions. Gargi and Manickam (2026), in a systematic PRISMA-based review of 174 studies (1971–2025) published in Frontiers in Remote Sensing, synthesize surface-energy-balance approaches (SEBAL, METRIC, SEBS) and vegetation-index/temperature triangle methods for semi-arid ET estimation, and identify sparse in-situ validation networks (eddy covariance towers, lysimeters) as one of the field's most persistent constraints—a limitation that directly parallels the JCA's own meteorological station scarcity motivating the synthetic dataset used here (Section 2.2). Their review also notes that remote-sensing ET models require region-specific calibration and are rarely transferable without local ground-truthing, a conclusion structurally consistent with the season-specific model selection argued for in Section 5.5. Integrating satellite surface-energy-balance products with the empirical, meteorologically-driven approach used in this study—rather than treating the two literatures as separate—is a natural direction for future JCA-specific work.

5.7 Anticipated methodological questions on dataset construction

To pre-empt likely reviewer and reader questions about the synthetic dataset's construction (Section 2.2) and to consolidate scattered detail into one place, this subsection addresses six specific questions directly.

5.7.1 Why were IMD and NASA-POWER selected?

Because they cover complementary gaps: IMD Pune gridded data provides long-term climatological statistics but not a continuous 1990–2024 monthly time series at station resolution, so NASA-POWER Version 8 reanalysis was added to impose inter-annual variability on the IMD climatological means. No comparison against alternative products (e.g., ERA5, CHIRPS) is presented, so this reflects a complementarity-based selection rather than a formally evaluated one.

5.7.2 How were the datasets combined?

A three-way blend, not a two-source merge: (i) IMD climatological statistics were interpolated to each virtual station using inverse-distance weighting (IDW, p = 1, four nearest grid points); (ii) NASA-POWER time series were layered on to generate inter-annual variability at that same monthly resolution; and (iii) an additive adjustment against Maharashtra Water Resources Department (WRD) ground records was applied where overlapping records existed, using 12 station-specific monthly offsets applied uniformly across all years (Section 2.2).

5.7.3 Where missing values filled?

No gap-filling procedure exists, because the dataset is not built by patching gaps in an observed record—it is generated synthetically from IMD climatology plus NASA-POWER-derived variability, then adjusted against WRD records. The manuscript calls this a “synthetic dataset” specifically because the resulting series blend interpolated climatology with reanalysis-derived variability rather than direct, continuous station observation; there is accordingly no missing-value-imputation step to describe.

5.7.4 What interpolation method was used?

Inverse-distance weighting (IDW), with a power parameter of p = 1 and the four nearest IMD grid points contributing to each virtual station estimate (Section 2.2). The subsequent WRD-based adjustment is also specified: an additive correction using 12 station-specific monthly offsets (WRD observation minus IDW value, averaged over the period of overlap), applied uniformly across all years. What remains open is not the identity of the construction method but its independently verified accuracy: no variable-level validation (RMSE, bias, correlation) of the interpolated and adjusted series against station observations has been performed (Section 6), so the procedure is now fully specified but not yet independently validated at the individual-variable level.

5.7.5 How were monthly values generated?

Monthly values are produced directly at monthly resolution: IDW-interpolated IMD climatology, with NASA-POWER reanalysis layered on to impose inter-annual variability at that same monthly resolution, followed by the additive WRD-based monthly adjustment (Section 2.2). There is no intermediate higher-resolution (e.g. daily) series that is subsequently aggregated to monthly; construction operates at monthly resolution throughout.

5.7.6 Was quality control/outlier removal performed?

No QC or outlier-removal procedure is described in Section 2.2 or Section 6—no range checks, no statistical outlier flags, no cross-dataset consistency checks. The only validation reported is a single aggregate metric: monthly FAO-56 PM ET₀ from the synthetic data compared against ET₀ from the five nearest IMD stations over 2000–2015, giving a mean absolute error of 0.34 mm day⁻¹ (coefficient of variation 4.8%). This is explicitly stated as the only validation statistic computed, and the six individual input variables were never independently validated against station observations.

5.7.7 Why were five stations selected?

Spatial representation of the Head Reach Zone: A single meteorological station may not adequately represent the climatic variability across the entire Head Reach Zone. Therefore, five representative stations were selected to improve the spatial characterization of meteorological conditions.

Capture of local climatic variability: Even within the Head Reach Zone, parameters such as air temperature, relative humidity, wind speed, solar radiation, and rainfall exhibit spatial variation due to differences in elevation, land cover, and proximity to water bodies.

Improved spatial interpolation: The five stations provide sufficient spatial coverage for generating representative meteorological datasets using the Inverse Distance Weighting (IDW) interpolation technique, thereby reducing interpolation uncertainty.

Representative dataset development: The station network was established to develop a spatially representative meteorological dataset for the Head Reach Zone rather than to investigate differences between irrigation reaches.

Robustness of PET model evaluation: Using multiple stations minimizes the influence of localized climatic anomalies and provides a more reliable basis for evaluating the performance of simplified PET models against the FAO-56 Penman–Monteith benchmark.

6 Limitations

This study has five principal limitations that should be considered in interpreting and applying its results.

6.1 Synthetic climate dataset

The absence of continuous long-term ground-based meteorological records necessitated the use of a synthetic dataset. Validation was performed only at the aggregate monthly ET₀ level against the five nearest IMD stations (MAE = 0.34 mm day⁻¹, coefficient of variation 4.8%); the six individual input variables were not independently validated against station observations, so variable-level accuracy (e.g., of R_*s* or u₂ specifically) is unknown and cannot be reported. This gap has a direct bearing on the Appendix A finding that Abtew and Makkink—both primarily driven by solar radiation (R_*s*)—perform markedly worse than Hargreaves–Samani once R_*s* is left uncorrected while temperature is corrected. If that radiation-quality sensitivity is real, as Appendix A's mechanistic explanation suggests, it applies in principle to the Section 2.2 dataset as well: because R_*s* was never independently validated here either, the specific R_*s* accuracy underlying the Abtew- and Makkink-favorable rankings in Tables 3, 4 has not been established, and cannot be distinguished from a scenario in which those rankings are similarly sensitive to undetected radiation bias. We are not able to rule this out with the data available, and flag it as a specific, unresolved consequence of the broader validation gap described above, rather than treating Appendix A's explanation as applying only to the appendix dataset. Local micro-climatic variability and sub-monthly extreme events may also not be fully captured. Future work should incorporate ground-truth observations from installed automatic weather stations and report variable-level validation statistics.

6.2 Model-based reference ET₀

FAO-56 PM was used as the benchmark because lysimeter or eddy covariance observations are unavailable for the JCA. Model performance therefore reflects agreement with FAO-56 PM rather than measured physical evapotranspiration. This is standard practice in data-scarce environments (Allen et al., 1998a; Acharki et al., 2025; Jagadesh et al., 2024) but introduces a layer of uncertainty in absolute accuracy claims.

6.3 Single-zone reporting

Detailed statistical results are presented for the Head Reach Zone only; the reported findings and operational recommendations (Sections 4–5, 7) should accordingly be read as specific to this zone and not assumed to generalize across the JCA without further analysis.

6.4 No local calibration

All empirical models were applied in their original published parameterisations without regional coefficient adjustment. Local calibration would substantially improve performance, particularly for Priestley–Taylor (reducing the systematic α-driven overestimation) and Hargreaves–Samani (reducing the positive summer bias). Calibrated performance comparisons are planned for a follow-up study incorporating field-measured actual ET data.

6.5 Untested interpolation parameters

The IDW power parameter (p = 1) and neighbor count (4 nearest grid points) used to construct the synthetic dataset (Section 2.2) were adopted as reasonable, commonly used choices rather than selected through a formal sensitivity analysis against alternative parameterizations (e.g., p = 2, or 6–8 neighbors). The sensitivity of the interpolated climatology, and of the downstream ET₀ estimates and model rankings reported in Tables 3, 4, to these specific parameter choices has not been tested and remains an open question for future work.

7 Conclusions

This study provides a systematic, seasonally disaggregated evaluation of eight simplified empirical ET₀ methods against the FAO-56 Penman–Monteith benchmark for the Jayakwadi Command Area, Maharashtra, India. The following conclusions are supported by the evidence:

7.1 Radiation-based methods consistently outperformed temperature-based methods

Makkink and Abtew, both requiring only solar radiation as the primary input, achieved the highest seasonal accuracy across the JCA. Their low input requirements and strong performance make them practical alternatives to FAO-56 PM for data-scarce semi-arid command areas, conditional on radiation input data of comparable quality to the Section 2.2 construction—Appendix A shows this recommendation reverses under uncorrected radiation data specifically, so radiation data quality should be verified before deployment (Section 5.5).

7.2 Abtew is recommended for summer; Makkink for autumn and winter

Abtew achieved outstanding summer performance (NSE = 0.937, PBIAS = +0.7%; “very good”), while Makkink dominated autumn (NSE = 0.630) and winter (NSE = 0.886; “very good”). No single method performed well across all seasons, confirming the necessity of season-specific model selection. As noted in point 1 above and detailed in Appendix A, this ranking is specific to radiation input of the quality used in the Section 2.2 construction and is not robust to uncorrected radiation data.

7.3 Annual-scale NSE is universally negative for all eight models

Annual aggregation masks compensating seasonal errors and is an unreliable basis for model evaluation or deployment in this climate. Seasonal evaluation is mandatory.

7.4 High R² is insufficient to confirm model accuracy

Priestley–Taylor achieved R² up to 0.986 alongside unsatisfactory NSE and PBIAS values. Multi-metric evaluation (NSE, PBIAS, NRMSE, Re, R²) is essential and R² should not be used as a standalone performance indicator.

7.5 Temperature-only models are not recommended for operational use

Thornthwaite, Hamon, Linacre, and Blaney–Criddle consistently failed to meet the “satisfactory” threshold under all seasons in the JCA, with Thornthwaite producing the most extreme underestimation (PBIAS up to −82.3%). Hargreaves–Samani is the only acceptable fallback temperature-based method, suitable for summer and autumn in the absence of radiation data.

7.6 Future directions

Research priorities include: (i) regional calibration of best-performing models using field-installed automatic weather station data and eddy covariance ET measurements; (ii) integration of Abtew and Makkink with MODIS and NASA-POWER satellite products for spatially distributed, real-time ET₀ monitoring across the full JCA; (iii) development of a machine learning-based residual correction model to hybridize empirical ET₀ estimates; and (iv) extension of the multi-method evaluation framework beyond the Head Reach Zone analyzed here, and to adjacent semi-arid command areas in the Deccan Plateau.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frwa.2026.1923575/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Akhouri Pramod Krishna, Birla Institute of Technology, Mesra, India

Reviewed by: Putu Doddy Heka Ardana, Universitas Ngurah Rai, Indonesia

Juan Eduardo Suarez Rivadeneira, Universidad Nacional Toribio Rodríguez de Mendoza de Amazonas, Peru