Evaluation of Class A Pan Coefficients for Estimating Reference Evapotranspiration in Humid Location

Evaporation pans [Class A pan, U.S. Weather Bureau (USWB)] are used extensively throughout the world to measure free-water evaporation and to estimate reference evapotranspiration (ET0). However, reliable estimation of ET0 using pan evaporation (Epan) depends on the accurate determination of pan coefficients (Kpan). Two equations developed by Frevert et al. in 1983 and Snyder in 1992 to estimate daily Kpan values were evaluated using a 23-year climate dataset in a humid location (Gainesville, Florida). The ET0 data, calculated using daily Kpan values from these equations, were compared to the Food and Agricultural Organization (FAO)-Penman-Monteith (FAO56-PM) method. The two equations resulted in significantly different daily Kpan values that produced different daily, monthly, and annual total ET0 estimates. The ET0 values calculated using Frevert et al.’s 1983 Kpan coefficients were in very good agreement with the FAO56-PM method with daily, monthly, and annual mean percent errors (PE) of 5.8, 5.5, and 5.7%, respectively. The daily and annual mean-root-mean-square error (RMSE) of the estimates using this method were as low as 0.33 and 7.3 mm, respectively. Snyder’s 1992 equation overestimated FAO56-PM ET0 with daily, monthly, and annual mean PEs of 16.3, 13.8, and 13.2%, respectively. The daily and annual mean RMSEs for this method were higher (0.6 and 18 mm) than those obtained with Frevert et al.’s 1983 coefficients. The overestimations with Snyder’s 1992 method were highest in the peak ET0 month of May and in summer months. The performances of the Kpan equations were also evaluated using randomly selected individual years (1979, 1988, 1990, and 1994) of climate data that had different climate characteristics than the 23-year average dataset. Frevert et al.’s 1983 coefficients resulted in good ET0 estimates with lower annual mean PEs of 7.0, 0.1, 15.7, and 1.3% for 1979, 1988, 1990, and 1994, respectively, compared to Snyder’s 1992 equation, which resulted in considerably higher PEs of 17.6, 9.1, 26.2, and 14.3% in 1979, 1988, 1990, and 1994, respectively. It was concluded that using Frevert et al.’s 1983 equation to calculate daily Kpan provided more accurate ET0 estimates, relative to the FAO56-PM method, from Epan data compared to Snyder’s 1992 equation under the humid-region climatic conditions in this study. The method is very useful in computer calculations of ET0 since it does not require “table lookup” for Kpan values.     

Comparison of Some Reference Evapotranspiration Equations for California

Four reference evapotranspiration (ETo) equations are compared using weather data from 37 agricultural weather stations across the state of California. The equations compared include the California Irrigation Management Information System (CIMIS) Penman equation, the Penman–Monteith equation standardized by the Food and Agriculture Organization (FAO), the Penman–Monteith equation standardized by the American Society of Civil Engineers, and the Hargreaves equation. Hourly and daily comparisons of ETo and net radiation (Rn) are made using graphics and simple linear regressions. ETo values estimated by the CIMIS Penman equation correlated very well with the corresponding values estimated by the standardized Penman–Monteith equations on both hourly and daily time steps. However, there are greater differences between the Rn values estimated by the two procedures. Although there are exceptions, the Hargreaves equation compared well to the FAO Penman–Monteith method. Spatial variability of the resulting correlations between the different equations is also assessed. Despite the wide variability of microclimates in the state, there are no visible spatial trends in correlations between the different ETo and/or Rn estimates.     

Comparison of Standardized Reference Evapotranspiration Equations in Southern Spain

ASCE and FAO-56 standardized reference evapotranspiration (ET0) equations were compared using data from 31 meteorological stations in Andalusia, Southern Spain. Comparisons were made between daily ET0 obtained by summing hourly standardized ASCE–Penman–Monteith estimations and calculated from the addition of hourly FAO56–Penman–Monteith estimations, daily ET0 estimated on a daily basis, and calculated by the Hargreaves equation. On an hourly basis, the FAO-56 version estimated lower than the ASCE version as 6% in some locations, with a difference of 4% on the average, mainly due to the higher surface resistance (70?s?m?1) used in the FAO-56 version during daytime periods, as opposed to the 50?s?m?1 rs value used by the ASCE version. Differences between both estimates were higher when evaporative demand increases. The level of agreement improved when the two computational time steps were compared, because differences were lower (2% on the average) and did not depend on the wind speed or ET0 values. The Hargreaves equation showed a higher spatial variability. At coastal areas, the equation generally underpredicted ASCE Penman–Monteith ET0 and provided good estimations for inland locations. Accuracy of the equation was affected by annual averages of evaporative demand and wind speed.     

Simplified Estimation of Reference Evapotranspiration from Pan Evaporation Data in California

Evaporation pan (Ep) data are often used to estimate reference evapotranspiration (ET0) for use in water resource planning and irrigation scheduling. This paper reviews equations to estimate ET0 from Ep and provides a simpler method to make this conversion for arid climatic conditions like in California. The new method accounts for fetch differences by first adjusting the Ep rates to values expected for 100?m of grass fetch. Then it relies on an empirical relationship between ET0 and the adjusted Ep to determine Kp values; thus, eliminating the need for relative humidity and wind speed data that are often unavailable. The method is conceptually simpler, easier to code into computer applications, and within California, it gave better results than methods based on relative humidity and wind speed. However, the method might require calibration in more humid or windier climates.     

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 meteorological measurements at 19 locations across North Carolina. The atmometers underestimated daily ETr by an average of 21% across the study area. Linear regression models between ETg and ETr had intercepts significantly different from zero and slopes different from one, but would generally yield a gauge error within 1?mm?day?1. The ETg-ETr relationship was found to be highly sensitive to precipitation and wind speed, but rather insensitive to humidity, radiation, and temperature. Although wind speed is generally low in the study area, the insensitivity of ETgages to wind caused severe underestimation in those periods when wind speed was high. Mean absolute error increased from 17% when wind speed was below 1?m?s?1 to 64% when wind speed was greater than 5?m?s?1. Precipitation can temporarily disrupt ETgage evaporation and cause underestimation of ETr. The linear relationship between ETg and ETr in rainy days was significantly different than that of the clear days. Analysis of the local relationships suggested that they are sensitive to their major surrounding physiographic environment and to the strictly local surface conditions, but not to the intermediate mesoscale surface environment. As a result, different linear regression equations were developed to adjust ETg to ETr in three land regions and in dry or wet conditions.     

Using Modified Bellani Plate Evapotranspiration Gauges to Estimate Short Canopy Reference Evapotranspiration

Modified Bellani plate atmometer has been offered as an alternative and simpler technique to combination-based equations to estimate evapotranspiration (ET) rate from green grass surface. However, there is a lack of information on its’ accuracy in humid climates. The evaporation rate (EA) from one type of atmometer marketed under the brand name ETgage? (or ETG) with a Number 30 green canvas cover that simulates the ET rate from a green grass surface was tested against the reference ET of a short green grass canopy (ETo) computed using the Food and Agriculture Organization of the United Nations Paper No. 56 Penman–Monteith (FAO56-PM) equation in two sites in north-central Florida. The ETG underestimated the ETo as much as 27%. The root mean square error (RMSE) of daily estimates of EA ranged from 1.03 to 1.15?mm. Data analyses indicated that the most of the poor performances and underestimations of the ETG occurred on rainy days. Using only the nonrainy day EA versus ETo relationship, the daily RMSE was as low as 0.47?mm and r2 was as high as 0.89, and the underestimations were within 3% of the ETo. Averaging daily ETG readings over 3 and 7 day periods considerably improved (lower RMSE and percent error, %E, and higher r2) ETo estimates. The ETG performed quite well on nonrainy days. The adjustment factors were developed and tabulated as a function of rainfall amount to adjust the EA values on rainy days. Results showed that an average adjustment factor of 0.84?(EA/0.84 = ETo) can be used as a practical number if rainfall observations are not available. The underestimations of the ETG on rainy days were attributed, in part, to the wetting of the green canvas cover due to the rainwater accumulations on it and to the lower diffusivity (higher resistance) value of the canvas cover (112–294?s?m?1) compared to the diffusivity of a green grass surface used in the ETo definition (70?s?m?1). Although it is found that the ETG is feasible and practical device, the EA values measured on rainy days require careful interpretation in humid and rainy climates such as Florida. The rainy day EA values should be used cautiously with the proper regression equation and adjustment factors to estimate ETo for irrigation scheduling if the input variables are not available to use the FAO56-PM equation for ETo estimates.     

Pan Evaporation to Reference Evapotranspiration Conversion Methods

Reference evapotranspiration (ET0) is often estimated from evaporation pan data as they are widely available and of longer duration than more recently available micrometeorologically based ET0 estimates. Evaporation pan estimation of ET0 ( = KpEpan) relies on determination of the pan coefficient (Kp), which depends on upwind fetch distance, wind run, and relative humidity at the pan site. The Kp estimation equations have been developed using regression techniques applied either to the table presented in FAO-24 or to the original data upon which this table was based (from lysimeter studies in Davis, Calif.). Here, the relative performances of the FAO-24 table and six different Kp equations are evaluated with respect to reproducing the original data table using the FAO-24 table as a standard. Evaporation pan- and CIMIS-based estimates of ET0 are also compared for stations having ranges of mean humidities (48–66%) and mean wind runs (156–193 km/day) located in the Sacramento and San Joaquin valleys, and for a coastal station (Point Heuneme) near Ventura, Calif., having a greater mean humidity (71%). In comparing the means, standard deviations, root-mean-square errors, and linear regression coefficients, five of the six equations reproduced the original data table with approximately the same accuracy as the FAO-24 table. Use of either Kp table slightly underestimated measured ET0 at the coastal site, while the Cuenca, Allen-Pruitt, and Snyder Kp equations most closely approximated the average measured ET0 at all seven sites.     

Estimating Reference Evapotranspiration with Minimum Data in Florida

Reference evapotranspiration estimation methods that require minimal data are necessary when climatic data sets are incomplete, inaccurate, or unavailable. This study was conducted to evaluate temperature-based reference evapotranspiration methods in Florida. Using reference evapotranspiration estimates using satellite-derived radiation as the standard for comparison, the “reduced-set” Penman-Monteith, Hargreaves, and Turc equations were evaluated using monthly temperature data from 72 weather stations in Florida. The reduced-set Penman-Monteith equation requires maximum and minimum temperature only and uses recommended methods to estimate radiation, humidity, and wind speed. The reduced-set Penman-Monteith and Hargreaves equations were found to overestimate reference evapotranspiration while the Turc equation neither overestimated nor underestimated. The reduced-set Penman-Monteith equation showed greatest error in coastal stations while the Hargreaves equation showed greatest error at inland and island locations. In the absence of regionally calibrated methods the Turc equation is recommended for estimating reference evapotranspiration using measured maximum and minimum temperature and estimated radiation in Florida.     

Estimating Reference Evapotranspiration Using Limited Weather Data

The FAO-56 Penman-Monteith combination equation (FAO-56 PM) has been recommended by the Food and Agriculture Organization of the United Nations (FAO) as the standard equation for estimating reference evapotranspiration (ET0). The FAO-56 PM equation requires the numerous weather data that are not available in the most of the stations. This paper examines the potential of FAO-56 PM equation in estimating the ET0 under humid conditions from limited weather data. For this study, full weather data sets were collected from six humid weather stations from Serbia, South East Europe. FAO-56 reduced-set PM ET0 estimates were in closest agreement with FAO-56 full set PM ET0 estimates at the most of locations. The difference between FAO-56 full set PM ET0 estimates and FAO-56 PM reduced-set ET0 estimates generally increases by increasing the number of estimated weather parameters. Overall results indicate that FAO-56 reduced-set PM approaches mostly provided better results compared to Turc equation, adjusted Hargreaves equation and temperature-based RBF network. This fact strongly supports using the FAO-56 PM equation even in the absence of the complete weather data set. The minimum and maximum air temperature data and local default wind speed value are the minimum data requirements necessary to successfully use the FAO-56 PM equation under humid conditions.     

Simple Equation to Estimate Reference Evapotranspiration from Evaporation Pans Surrounded by Fallow Soil

Reliable estimates of reference evapotranspiration (ET0) are key elements for efficient water resource management, and estimating ET0, based on “Class ‘A’ pan evaporation” data is common in arid climates. A pan coefficient (Kp), which depends on the distance (or fetch) of green vegetation or fallow soil around the pan (F), wind run (U), and relative humidity (RH), is used to convert from pan evaporation to ET0. Several researchers have developed models for estimating Kp values for pans surrounded by green vegetated fetch, but there is only one equation to estimate Kp values for dry fetch conditions. The equation is complex, so the objective of this research was to develop a new simple equation to estimate Kp under fallow soil fetch conditions. The new Kp equation and the more complex equation were compared with tabular values published by the United Nations Food and Agriculture Organization. The new equation performed slightly better at matching the tabular Kp values than the complex equation. The equation derivation and evaluation are presented.     

Predicting Incoming Solar Radiation and Its Application to Radiation-Based Equation for Estimating Reference Evapotranspiration

This paper presents an inverse square weighted interpolation for predicting the incoming solar radiation (Rs) from nearby weather stations. The predicted Rs is applied to the well-known Priestley-Taylor equation for estimating reference evapotranspiration (ETo). This cross-validation estimated bias and error in the final model predictions of the Rs and ETo at the 21 meteorological weather stations in Korea Peninsula. The coefficient of determination and the root-mean-square error (RMSE) for monthly estimates of Rs was in the range of 0.83–0.95 and 17.90–76.34?MJ?m?2?day?1, respectively. The RMSE for monthly estimate of ETo values at inland and coastal areas was 11.08 and 15.01 mm respectively. The estimates of ETo using thus predicted Rs to provide reasonable accuracy. The study can provide further useful guidelines for crop production, water resources conservation, irrigation scheduling, and environmental assessment.     

Solar and Net Radiation-Based Equations to Estimate Reference Evapotranspiration in Humid Climates

Two equations for estimating grass reference evapotranspiration (ET0) were derived using the Food and Agriculture Organization Penman–Monteith (FAO56-PM) method as an index. The first equation, solar radiation (Rs) based, estimates ET0 from incoming Rs and maximum and minimum air temperature, and the second equation, net radiation (Rn) based, uses Rn and maximum and minimum air temperature. The equations were derived using 15 years (1980–1994) of daily ET0 values estimated from the FAO56-PM method using the measured and carefully screened weather data from near Gainesville, Florida. The performance of the derived equations was evaluated for 6 validation years (1995–2000), including dry and wet years, for the same site and for other humid locations in the Southeast United States. Comparisons of the performance of the derived equations with the other commonly used methods indicated that they estimate ET0 as good or better than those other ET0 methods. The Rs- and Rn-based equations resulted in the lowest 6 year average standard error of estimate (SEE) of daily ET0 (0.44 and 0.41 mm?day?1, respectively). Both equations performed quite well for estimating peak month ET0 and had the lowest 6 year average daily SEE for the peak month ET0 (0.24 mm?day?1 for both equations). Estimates for annual total ET0 were very close to those obtained from the FAO56-PM method. The 6 year average ratio of ET0?method to ET0?FAO56-PM were 1.05 and 1.03 for the Rs- and Rn-based equations, respectively. The derived equations were further evaluated in other humid locations in the Southeast United States, including two locations in coastal regions in Florida, one location in Georgia, and another location in Alabama. The comparisons showed that both equations are likely to provide good estimates of ET0 in humid locations of the Southeast United States. When the required input variables are considered, the Priestley–Taylor (PT) method was the closest method to the second derived equation (Rn based). Therefore, it was necessary to evaluate how the PT method would perform compared to the Rn-based equation relative to the FAO56-PM method after it is calibrated locally. Although the performance of the PT method improved slightly after the calibration, its performances for estimating daily and peak month ET0 remained poorer than the Rn-based equation in all cases. Considering the limitations associated with the availability and reliability of the climatological data, especially in developing countries, the derived equations presented in this study are suggested as practical methods for estimating ET0 if the standard FAO56-PM equation cannot be used because of the above-mentioned limitations. These equations are recommended over the other commonly used simplified temperature and radiation-based methods evaluated in this study for humid climates in the Southeast United States.     

Comparison of Measured and FAO-56 Modeled Evaporation from Bare Soil

This paper evaluates how well the FAO-56 style soil water evaporation model simulates measurements of evaporation (E) from bare soil. Seven data sets were identified from the literature and in all but one case, the individuals who took the measurements were contacted and they provided the writers with specific weather and soils data for model input. Missing weather and soils data were obtained from online sources or from the National Climatic Data Center. Simulations for three possible variations of soil data were completed and compared. The measured and the FAO-56 simulated E/ETo and cumulative evaporation trends and values were similar. Specifically, the average evaporation weighted percent difference between the measured and the simulated cumulative evaporation was between ?7.5 and ?0.5%. This evaluation suggests model accuracy of about ±15% with the use of sound weather data and a fairly generalized understanding of soil properties in the location being evaluated.     

Comparison of Priestley-Taylor and FAO-56 Penman-Monteith for Daily Reference Evapotranspiration Estimation in Georgia

The climate in Georgia and other southeastern states of the United States is considered to be humid and the annual precipitation is usually greater than the annual potential evapotranspiration (ET). However, during several months of the year, supplemental irrigation is needed to prevent yield reducing water stress due to the temporal rainfall variability and sometimes due to long-term droughts. The Priestley-Taylor (PT) equation has been used operationally in Georgia to compute ET for irrigation scheduling because of its simplicity, its general acceptable performance in humid regions, and its limited input requirements. A recent study for a site in the humid southeastern United States found that PT overestimated ET and was less accurate than the FAO-56 Penman-Monteith (PM) among some of the approaches that were evaluated. The objective of this study was to assess the potential improvement that can be achieved by replacing PT with FAO-56 PM in Georgia and other southeastern states in a humid climate. More than 70 weather stations across Georgia are available as part of the Georgia Automated Environmental Monitoring Network. Nine representative sites, including Blairsville in a mountainous area and Savannah in a coastal area, were selected to assess the potential improvements that may be achieved by replacing PT with FAO-56 PM. Each site had at least 10 years of daily records that included minimum and maximum air temperature, solar radiation, wind speed, and vapor pressure deficit. PT underestimated the daily and monthly ET during the winter months in the central and southwestern areas and overestimated the daily and monthly ET during the summer months in the coastal and mountainous areas. For the warm season, i.e., April through September, PT slightly overestimated the cumulative ET in the central and southwestern areas, moderately for the mountainous area and severely for the coastal area. Based on these results, it is anticipated that the use of FAO-56 PM for estimating ET will standardize the ET calculations and improve irrigation efficiency in Georgia, especially for the mountainous and coastal areas.     

Comparison of Reference Evapotranspiration Calculations as Part of the ASCE Standardization Effort

Comparison among commonly used reference evapotranspiration (ET) equations in the United States and the recently recommended ASCE standardized reference ET equation was made as part of the ASCE standardization effort. Analyses used hourly and daily weather data from 49 geographically diverse sites in the United States. Calculations were performed for both grass and alfalfa reference crops in a consistent manner, using weather data that passed integrity and quality assessment checks. Comparisons were made between reference ET computed by the various methods and the ASCE Penman-Monteith (PM) equation used for a daily calculation time step. In addition, calculations using hourly time steps and summed daily were compared with daily calculations for the same method as well as against the ASCE-PM method. Results showed that the ASCE standardized equation agreed best with the full form of ASCE-PM. The results provide a basis for objectively assessing the relative performance of reference ET equations in a variety of climates and support adoption of a standardized equation as recommended by the ASCE Task Committee.     

Testing Reference Evapotranspiration Estimation Methods Using Evaporation Pan and Modeling in Maritime Region of Canada

Four methods of estimating daily reference evapotranspiration (ETo) were evaluated with the data collected from 2004 to 2006 in a Maritime weather station, the Potato Research Centre, Fredericton, N.B., Canada. We tested two models [i.e., the FAO-56 Penman–Monteith (PM) and the Priestley–Taylor (PT) equations] and two Class A pan methods (Cuenca and Snyder equations). In order to assess the Evaporation Pan methods, an automatic Class A Pan system was installed in a grassed field surrounded by potato fields and continuously measured from 2004 to 2006. The results from three growing seasons (years 2004–2006) indicated that both evaporation pan methods generated lower estimations of ETo compared to the PM and PT methods. The PT method produced the highest ETo estimation. The Snyder method showed a better agreement with the PM (r2>0.56). However, the agreement varied from year to year with an r2 value range of 0.4–0.7. Kpan coefficients (a factor to convert pan observation to ETo) varied from 0.78 to 0.94. In general, the Cuenca generated lower Kpan values (0.83) than the Snyder method (0.87). Compared to the PM, the PT method overestimated ETo, which may be related to the absence of humidity adjustment in the model. Furthermore, the research suggested that the time step played an important role in the estimation of ETo in this region. The PM method at daily time step was simple but intended to overestimate ETo by 10% compared to the hourly time-step method. In summary, when Class A Pan data are available, the Snyder equation can be used to calculate Kpan with an acceptable accuracy. If the PM method is used to estimate ETo when pan observations are unavailable, a reduction of 10% to the calculated ETo at daily time step could be applied to improve the accuracy of ETo estimation.     

Performance Evaluation of Reference Evapotranspiration Equations across a Range of Indian Climates

Reference crop evapotranspiration (ET0) is a key variable in procedures established for estimation of evapotranspiration rates of agricultural crops. In recent years, there is growing evidence to show that the more physically based FAO-56 Penman–Monteith (PM) combination method yields consistently more accurate ET0 estimates across a wide range of climates and is being proposed as the sole method for ET0 computations. However, other methods continue to remain popular among Indian practitioners either because of traditional usage or because of their simpler input data requirements. In this study, we evaluated the performances of several ET0 methods in the major climate regimes of India with a view to quantify differences in ET0 estimates as influenced by climatic conditions and also to identify methods that yield results closest to the FAO-56 PM method. Performances of seven ET0 methods, representing temperature-based, radiation-based, pan evaporation-based, and combination-type equations, were compared with the FAO-56 PM method using historical climate data from four stations located one each in arid (Jodhpur), semiarid (Hyderabad), subhumid (Bangalore), and humid (Pattambi) climates of India. For each location, ET0 estimates by all the methods for assumed hypothetical grass reference crop were statistically compared using daily climate records extending over periods of 3–4 years. Comparisons were performed for daily and monthly computational time steps. Overall results while providing information on variations in FAO-56 PM ET0 values across climates also indicated climate-specific differences in ET0 estimates obtained by the various methods. Among the ET0 methods evaluated, the FAO-56 Hargreaves (temperature-based) method yielded ET0 estimates closest to the FAO-56 PM method both for daily and monthly time steps, in all climates except the humid one where the Turc (radiation-based) was best. Considering daily comparisons, the associated minimum standard errors of estimate (SEE) were 1.35, 0.78, 0.67, and 0.31 mm/day, for the arid, semiarid, subhumid, and humid locations, respectively. For monthly comparisons, minimum SEE values were smaller at 0.95, 0.59, 0.38, and 0.20 mm/day for arid, semiarid, subhumid, and humid locations, respectively. These results indicate that the choice of an alternative simpler equation in a particular climate on the basis of SEE is dictated by the time step adopted and also it appears that the simpler equations yield much smaller errors when monthly computations are made. In order to provide simple ET0 estimation tools for practitioners, linear regression equations for preferred FAO-56 PM ET0 estimates in terms of ET0 estimates by the simpler methods were developed and validated for each climate. A novel attempt was made to investigate the reasons for the climate-dependent success of the simpler alternative ET0 equations using multivariate factor analysis techniques. For each climate, datasets comprising FAO-56 PM ET0 estimates and the climatic variables were subject to factor analysis and the resulting rotated factor loadings were used to interpret the relative importance of climatic variables in explaining the observed variabilities in ET0 estimates. Results of factor analysis more or less conformed the results of the statistical comparisons and provided a statistical justification for the ranking of alternative methods based on performance indices. Factor analysis also indicated that windspeed appears to be an important variable in the arid climate, whereas sunshine hours appear to be more dominant in subhumid and humid climates. Temperature related variables appear to be the most crucial inputs required to obtain ET0 estimates comparable to those from the FAO-56 PM method across all the climates considered.     

Fuzzy Genetic Approach for Modeling Reference Evapotranspiration

This study investigates the ability of fuzzy genetic (FG) approach in modeling of reference evapotranspiration (ET0). The daily climatic data, solar radiation, air temperature, relative humidity, and wind speed from three stations, Windsor, Oakville and Santa Rosa, in central California, are used as inputs to the FG models to estimate ET0 obtained using the FAO-56 Penman-Monteith equation. A comparison is made between the estimates provided by the FG and those of the following empirical models: the California Irrigation Management System Penman, Hargreaves, Ritchie, and Turc methods. The FG results are also compared with the artificial neural networks. Root-mean-square errors (RMSE), mean-absolute errors (MAE), and correlation coefficient statistics are used as comparing criteria for the evaluation of the models’ performances. The comparison results reveal that the FG models are superior to the ANN and empirical models in modeling ET0 process. For the Windsor, Oakville, and Santa Rosa stations, it was found that the FG models with RMSEW = 0.138, MAEW = 0.098, and RW = 0.999; RMSEO = 0.144, MAEO = 0.102, and RO = 0.999; and RMSES = 0.167, MAES = 0.115, and RS = 0.998 in test period is superior in modeling daily ET0 than the other models, respectively.     

Reference and Crop Evapotranspiration in South Central Nebraska. I: Comparison and Analysis of Grass and Alfalfa-Reference Evapotranspiration

In Nebraska, historically, there have been differences among the water regulatory agencies in terms of the methods used to compute reference evapotranspiration (ETref) to determine actual crop water requirements and hydrologic balances of watersheds. Because simplified and/or empirical temperature or radiation-based methods lack some of the major weather parameters that can significantly affect grass and alfalfa-reference ET (ETo and ETr) the performance of these methods needs to be investigated to help decision makers to determine the potential differences associated with using various ETref equations relative to the standardized ASCE Penman–Monteith (ASCE-PM) equations. The performance of 12 ETo and five ETr equations were analyzed on a daily basis for south central Nebraska from 1983 to 2004. The standardized ASCE-PM ETo and ETr values were used as the basis for comparisons. The maximum ASCE-PM ETo value was estimated as 12.6?mm?d?1, and the highest ETr value was estimated as 19?mm?d?1 on June 21, 1988. On this day, the atmospheric demand for evaporation was extremely high and the vapor pressure deficit (VPD) reached a remarkably high value of 4.05?kPa. The combination-based equations exhibited significant differences in performance. The 1963 Penman method resulted in the lowest RMSD of 0.30?mm?d?1 (r2 = 0.98) and its estimates were within 2% of the ASCE-PM ETo estimates. The 1948 Penman estimates were similar to the 1963 Penman (r2 = 0.98, RMSD = 0.39?mm?d?1). Kimberly forms of alfalfa-reference Penman equations performed well with RMSD of 0.48?mm?d?1 for the 1972 Kimberly–Penman and 0.67?mm?d?1 for the 1982 Kimberly–Penman. The locally-calibrated High Plains Regional Climate Center (HPRCC) Penman method, ranked 6th, performed well and underestimated the ASCE-PM ET by 5% (RMSD = 0.56?mm?d?1). Most of the underestimations occurred at the high ET range (>11?mm) and this was attributed to the upper limits applied by the HPRCC on VPD, (2.3?kPa) and wind speed (5.1?m?s?1). The lack of ability of the radiation methods in accounting for the wind speed and relative humidity hindered the performance of these methods in the windy and rapidly changing VPD conditions of south central Nebraska. The 1977 FAO24 Blaney–Criddle method was the highest ranked (seventh) noncombination method (RMSD = 0.64?mm?d?1, r2 = 0.94). The FAO24 Penman estimates were within 4% of the ASCE-PM ETo. Overall, there were large differences between the ASCE-PM ETo and ETr versus other ETref equations that need to be considered when other forms of the combination or radiation and temperature-based equations are used to compute ETref. We recommend that the ASCE-PM ETo or ETr equations be used for estimating ETref when necessary weather variables are available and have good quality. The results of this study can be used as a reference tool to provide practical information, for Nebraska and similar climates, on the potential differences between the ASCE-PM ETo and ETr and other ETref equations. Results can aid in selection of the alternative method(s) for reasonable ETref estimations when all the necessary weather inputs are not available to solve the ASCE-PM equation.     

Estimating Evapotranspiration using Artificial Neural Network

This study investigates the utility of artificial neural networks (ANNs) for estimation of daily grass reference crop evapotranspiration (ETo) and compares the performance of ANNs with the conventional method (Penman–Monteith) used to estimate ETo. Several issues associated with the use of ANNs are examined, including different learning methods, number of processing elements in the hidden layer(s), and the number of hidden layers. Three learning methods, namely, the standard back-propagation with learning rates of 0.2 and 0.8, and backpropagation with momentum were considered. The best ANN architecture for estimation of daily ETo was obtained for two different data sets (Sets 1 and 2) for Davis, Calif. Using data of Set 1, the networks were trained with daily climatic data (solar radiation, maximum and minimum temperature, maximum and minimum relative humidity, and wind speed) as input and the Penman–Monteith (PM) estimated ETo as output. The best ANN architecture was selected on the basis of weighted standard error of estimate (WSEE) and minimal ANN architecture. The ANN architecture of 6-7-1, (six, seven, and one neuron(s) in the input, hidden, and output layers, respectively) gave the minimum WSEE (less than 0.3 mm/day) for all learning methods. This value was lower than the WSEE (0.74 mm/day) between the PM method and lysimeter measured ETo as reported by Jensen et al. in 1990. Similarly, ANNs were trained, validated, and tested using the lysimeter measured ETo and corresponding climatic data (Set 2). Again, all learning methods gave less WSEE (less than 0.60 mm/day) as compared to the PM method (0.97 mm/day). Based on these results, it can be concluded that the ANN can predict ETo better than the conventional method (PM) for Davis.