Standardized Penman-Monteith Equation Research Articles

Reference Evapotranspiration Estimation Using Genetic Algorithm-Optimized Machine Learning Models and Standardized Penman–Monteith Equation in a Highly Advective Environment

Accurate estimation of reference evapotranspiration (ETr) is important for irrigation planning, water resource management, and preserving agricultural and forest habitats. The widely used Penman–Monteith equation (ASCE-PM) estimates ETr across various timescales using ground weather station data. However, discrepancies persist between estimated ETr and measured ETr obtained from weighing lysimeters (ETr-lys), particularly in advective environments. This study assessed different machine learning (ML) models in comparison to ASCE-PM for ETr estimation in highly advective conditions. Various variable combinations, representing both radiation and aerodynamic components, were organized for evaluation. Eleven datasets (DT) were created for the daily timescale, while seven were established for hourly and quarter-hourly timescales. ML models were optimized by a genetic algorithm (GA) and included support vector regression (GA-SVR), random forest (GA-RF), artificial neural networks (GA-ANN), and extreme learning machines (GA-ELM). Meteorological data and direct measurements of well-watered alfalfa grown under reference ET conditions obtained from weighing lysimeters and a nearby weather station in Bushland, Texas (1996–1998), were used for training and testing. Model performance was assessed using metrics such as root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and coefficient of determination (R2). ASCE-PM consistently underestimated alfalfa ET across all timescales (above 7.5 mm/day, 0.6 mm/h, and 0.2 mm/h daily, hourly, and quarter-hourly, respectively). On hourly and quarter-hourly timescales, datasets predominantly composed of radiation components or a blend of radiation and aerodynamic components demonstrated superior performance. Conversely, datasets primarily composed of aerodynamic components exhibited enhanced performance on a daily timescale. Overall, GA-ELM outperformed the other models and was thus recommended for ETr estimation at all timescales. The findings emphasize the significance of ML models in accurately estimating ETr across varying temporal resolutions, crucial for effective water management, water resources, and agricultural planning.

Evapotranspiration Climatology of Indiana Using In Situ and Remotely Sensed Products

AbstractAn intercomparison of multiresolution evapotranspiration (ET) datasets with reference to ground-based measurements for the development of regional reference (ETref) and actual (ETa) evapotranspiration maps over Indiana is presented. A representative ETref equation for the state is identified by evaluating 10 years of in situ measurements (2009–19). A statewide ETref climatology is developed using the ETref equation and high-resolution surface meteorological data from the gridded surface meteorological dataset (gridMET). For ETa analyses, MODIS, Simplified Surface Energy Balance Operational dataset (SSEBop), Global Land Evaporation Amsterdam Model (GLEAM) (versions 3.3a and 3.3b), and NLDAS (Noah and VIC) datasets are evaluated using AmeriFlux data. Thirty years of rainfall data from Climate Hazards Group Infrared Precipitation with Station Data Rainfall (CHIRPS) are used with the ET datasets to develop effective precipitation fields. Results show that the standardized Penman–Monteith equation performs as the best ETref equation with median symmetric accuracy (MSA) of 0.37, Taylor’s skill score (TSC) of 0.89, and r2 = 0.83. The analysis shows that the gridMET dataset overestimates wind speed and requires adjustment before a series of statewide ETref climatology maps are generated (1990–2020). For ETa, the MODIS and GLEAM (3.3b) datasets outperform the rest, with MSA = 0.5, TSC = 0.8, and r2 = 0.8. The state ETa dataset is generated using all MODIS data from 2003 and blending the MODIS data with GLEAM (3.3b) to cover data unavailability. Using the top-performing datasets, annual ETref for Indiana is computed as 1110 mm, ETa as 708 mm, and precipitation as 1091 mm. A marginal increasing climatological trend is found for Indiana’s ETref (0.013 mm yr−1) while ETa is found to be relatively stable. The state’s water availability, defined as rainfall minus ETa, has remained positive and stable at 0.99 mm day−1 (annual magnitude of +3820 mm).

Assessment of Reference Evapotranspiration by Regionally Calibrated Temperature-Based Equations

The Penman-Monteith (PM) method for estimation of reference evapotranspiration (ET0) uses numerous data that are often missing in many regions. In such circumstances, temperature-based equations can be used for estimating ET0. The primary objective of this note was to compare the calibrated temperature-based ET0 approaches with the standard PM equation using meteorological data from fifteen CLIMWAT stations located in the Pannonian Basin. The most of these locations are classified as humid. Twelve temperature-based equations were evaluated according to the PM method. The regionally calibrated Hargreaves equation (HT) gave the lowest RMSE at seven sites and the second lowest RMSE at three sites. New regionally calibrated Thornthwaite approach (TT) yielded the lowest RMSE three times and the second lowest RMSE seven times. These approaches resulted in the lowest average RMSE for all fifteen locations (0.28 and 0.30 mm day−1, respectively). The other temperature-based approaches significantly fall behind the HT and TT equations at most stations. The overall results show the advantage of the HT approach except for a few southeast stations where the TT approach is dominant. It can be concluded that the regionally calibrated temperature-based approaches (HT and TT) are the most suitable to estimate ET0 in the Pannonian Basin.

Satellite Psychrometric Formulation of the Operational Simplified Surface Energy Balance (SSEBop) Model for Quantifying and Mapping Evapotranspiration

Abstract.Remote sensing-based evapotranspiration (ET) can be derived using various methods, from soil moisture accounting to vegetation-index based approaches to simple and complex surface energy balance techniques. Due to the complexity of fully representing and parameterizing ET sub-processes, different models tend to diverge in their estimations. However, most models appear to provide reasonable estimations that can meet user requirements for seasonal water use estimation and drought monitoring. One such model is the Operational Simplified Surface Energy Balance (SSEBop). This study presents a formulation of the SSEBop model using the psychrometric principle for vapor pressure/relative humidity measurements where the “dry-bulb” and “wet-bulb” equivalent readings can be obtained from satellite-based land surface temperature estimates. The difference in temperature between the dry (desired location) and wet limit (reference value) is directly correlated to the soil-vegetation composite moisture status (surface humidity) and thus producing a fractional value (0-1) to scale the reference ET. The reference ET is independently calculated using available weather data through the standardized Penman-Monteith equation. Satellite Psychrometric Approach (SPA) explains the SSEBop model more effectively than the energy balance principle because SSEBop does not solve all terms of the surface energy balance such as sensible and ground-heat fluxes. The SPA explanation demonstrates the psychrometric constant for the air can be readily adapted to a comparable constant for the surface, thus allowing the creation of a “surface” psychrometric constant that is unique to a location and day-of-year. This new surface psychrometric constant simplifies the calculation and explanation of satellite-based ET for several applications in agriculture and hydrology. The SPA formulation of SSEBop was found to be an enhancement of the ET equation formulated in 1977 by pioneering researchers. With only two key parameters, improved model results can be obtained using a one-time calibration for any bias correction. The model can be set up quickly for routine monitoring and assessment of ET at landscape scales and beyond. Keywords: Dry-bulb, ET fraction, ET modeling, Remote sensing, Satellite psychrometry, Wet-bulb.

Partitioning Evaporation and Transpiration in a Maize Field Using Heat-Pulse Sensors for Evaporation Measurement

. Evapotranspiration (ET) is the sum of soil water evaporation (E) and plant transpiration (T). E and T occur simultaneously in many systems with varying levels of importance, yet it is often very challenging to distinguish these fluxes separately in the field. Few studies have measured all three terms (ET, E, and T), and in the few cases where such measurements have been obtained, E is typically determined via destructive lysimetery. For 43 days in a fully developed maize ( L.) field, we continuously measured E using heat-pulse sensors and soil sensible heat balance, T using sap-flow gauges, and ET using an eddy covariance system. Crop evapotranspiration (ET c ) was also calculated from the crop coefficient (K c ) and the reference evapotranspiration (ET o ), which was determined with the standardized Penman-Monteith equation. During the measurement period, E and T accounted for 13% and 87% of E+T, respectively. E responded to variations in soil moisture and net radiation, whereas T changed primarily with net radiation. All three ET estimation methods (individually measured E+T, eddy covariance ET, and crop ET c ) demonstrated similar temporal trends and strong correlations (R 2 of 0.76 for ET c vs. E+T and 0.77 for ET vs. E+T), with the values of individually measured E+T close to crop ET c but larger than eddy covariance ET during the measurement period. Disparities in measurements were likely due to variations in measurement scale, which did not reflect the full range of field variability for individually measured E and T, and differences in response to declining soil moisture among the three approaches. Overall, the results support the need for individual measurement of each term (E, T, and ET) when attempting to interpret ET partitioning and suggest that soil heat-pulse sensors provide a viable complement to previously tested approaches for continuously determining E for ET partitioning during wetting-drying periods.

Estimating Reference Crop Evapotranspiration with ETgages

Three years of daily reference evapotranspiration measured by atmometers ( ETg ) were compared to the values computed from the ASCE standardized Penman–Monteith equation ( ETr ) using co-located me...

Effects of Vapor-Pressure Deficit and Net-Irradiance Calculation Methods on Accuracy of Standardized Penman-Monteith Equation in a Humid Climate

The effects of some common vapor pressure deficit~VPD! and net irradiance sRnd calculation methods on the accuracy of ETo values estimated by using the standardized ASCE Penman-Monteith ~ASCE-PM! equation for short grass were examined by comparing the estimated ETo values with measured ETo values in a humid climate. Sensitivity analysis showed 17% and 84% change in the estimated daily ETo values per unit change in the calculated VPD and Rn values, respectively. A total of 12 VPD and 27 Rn calculation methods were examined. Analyses of variance indicated lack of equality in the means of estimated ETo values obtained by different VPD and Rn methods. The percent mean error in the estimated ETo values ranged from ˛0.9 to ˛ 8.4% for VPD methods and from ˛0.3 to ˛ 19.7% for Rn methods. On the basis of the coefficient of determination sr 2 d and the standard error of the estimated sSy/xd values, the VPD calculated from saturation vapor pressure sesd, estimated by averaging the es at the maximum and minimum daily air temperatures, and actual vapor pressure sead, estimated by using either the average of minimum and maximum relative humidity or the dew-point temperature, gave more accurate results. Net irradiance sRnd estimated by using a regression of relative short-wave solar irradiance, as well as a linear regression on the square root of ea, resulted in relatively more accurate estimates of ETo than that obtained by methods based on ea or clear-sky data alone. These results indicate that in a humid climate, some of the VPD and Rn methods have a significant effect on the accuracy of theETo estimated by using the standardized ASCE-PM equation.

Closure to “History and Evaluation of Hargreaves Evapotranspiration Equation” by George H. Hargreaves and Richard G. Allen

The authors welcome the discussion by Samani on our paper and appreciate his cautionary statements regarding the assumption of constancy of KRS in the original Eq. (6), especially in humid or equatorial climates. Samani’s findings, based on the prediction of monthly solar radiation from Knapp et al. (1980) using temperature range (TR) (daily maximum temperature minus daily minimum temperature), indicate the need for KRS larger than the 0.17 constant implicit to the original Eq. (8) when the TR is relatively small (less than about 7°C). It is worthwhile to note that in Samani’s Fig. 1, KRS appears to only be statistically different from 0.17 in the 8–16°C range. TR does tend to be smaller in humid and subhumid climates than in semiarid and arid climates. Samani’s findings differ from KRS–TR relationships found using daily solar radiation and air temperature data from some of the more humid stations evaluated by the ASCE-EWRI Task Committee on Standardization of Reference Evapotranspiration Calculation (EWRI 2001; Itenfisu et al. 2003). For example, for three agricultural weather stations near Wellsboro, Valatie, and Ithaca, New York, computed KRS averaged only about 0.14 throughout the range in TR of 5–14°C. Monthly values for KRS ranged from 0.11–0.17 and averaged 0.14. In a study on variation in KRS, Allen (1997) found KRS to reside within the range 0.16–0.175 for his two most humid stations, Gainesville, Fla. and North Baltimore, Ohio. Thus, it appears that more study is needed to determine a general relationship between KRS and TR or other parameters. What is important in terms of predicting evapotranspiration sETod, however, is not the deviation of KRS from 0.17, but in how well the integrated form of Eq. (8) performs in predicting ETo. In the ASCE-EWRI study, Eq. (8) overpredicted ETo as computed using the ASCE standardized Penman-Monteith equation (Itenfisu et al. 2003) by more than 15% for the relatively humid eastern United States weather stations of Wellsboro, Valatie, and Ithaca, N.Y., and Blairsville and Attapulgus, Ga. Eq. (8) predicted about 10% higher than the ASCE standardized Penman-Monteith equation at the other eastern or midwestern United States locations of Fort Pierce and Lake Alfred, Fla.; Griffen, Ga.; Bondville and Belleville, Ill.,; and Mead and Clay Center, Neb. This overestimation in humid climates might imply the need for a smaller KRS rather than a larger one. In comparisons between Eq. (8) and the Food and Agricultural Organization of the United Nations Penman-Monteith (FAO-PM) equation based on the World Water and Climate Atlas of the International Water Management Institute (IWMI), Droogers and

EVALUATI NG SURFACE RESISTANCE FOR ESTIMATING CORN AND POTATO EVAPOTRANSPIRATION WITH THE PENMAN–MONTEITH MODEL

The PenmanMonteith (PM) evapotranspiration (ET) model has been shown to be adequate for estimating dailyreference crop ET (ETo). However, the proper evaluation of surface resistance to vapor exchange (rs) has been a limiting factorfor using the model to directly estimate daily ET for other crops. A popular approach to quantify rs, referred to as canopyresistance (rc), is based on singleleaf resistance (rL) and leaf area index (LAI) but does not account for nonstomatalcontributions (excess resistance) to rs such as leaf boundary layer resistance and aerodynamic resistance within the canopy.Field measurements of ET, rL, and LAI for fullcanopy conditions were used to develop an empirical crop height andLAIdependent relation to estimate excess resistance (ro). An alternative rs term was defined as ro + rc and used in conjunctionwith an aerodynamic resistance term (ra) calculated from the top of the canopy. Using climatic data collected over corn andpotato canopies, three variations of daily PM ET were compared:PM1, which used the rs definition including excess resistance (rs = ro + rc), ra calculated from the top of the canopy, andvapor pressure deficit (VPD) and solar irradiance (Rs) functions to adjust rL.PM2, which was essentially identical to PM1 with no VPD or Rs adjustment to rL.PM3, which used standard rs (rS = rc) and ra (based on a zeroplane displacement height approximately 2/3 of cropheight) calculations with VPD and Rs adjustments to rL.All three methods of PM ET were compared with daily crop ET measurements made with a Bowen ratio energy balance(BREB) system. For corn, the results of this study suggested significant resistance to vapor transfer in excess of the rc usedin standard calculations of daily ET with the PM equation. This behavior was not seen with the calculation of daily ET forpotatoes. The direct application of the standard PM equation to estimate daily corn ET (i.e., PM3) is not recommendedbecause excess resistance not accounted for by this model will often lead to substantial ET overestimation. However,estimation of excess resistance based on canopy features was not found satisfactory (i.e., PM1 and PM2).