Estimating Evapotranspiration Using Artificial Neural Network and Minimum Climatological Data

The objective of this study was to test an artificial neural network (ANN) for estimating the reference evapotranspiration (ETo) as a function of the maximum and minimum air temperatures in the Campos dos Goytacazes county, State of Rio de Janeiro. The data used in the network training were obtained from a historical series (September 1996 to August 2002) of daily climatic data collected in Campos dos Goytacazes county. When testing the artificial neural network, two historical series were used (September 2002 to August 2003) relative to Campos dos Goytacazes, and Vi?osa, State of Minas Gerais. The ANNs (multilayer perceptron type) were trained to estimate ETo as a function of the maximum and minimum air temperatures, extraterrestrial radiation, and the daylight hours; and the last two were previously calculated as a function of either the local latitude or the Julian date. According to the results obtained in this ANN testing phase, it is concluded that when taking into account just the maximum and minimum air temperatures, it is possible to estimate ETo in Campos dos Goytacazes.     

Generalization of ETo ANN Models through Data Supplanting

This paper describes the application of artificial neural networks (ANNs) for estimating reference evapotranspiration (ETo) as a function of local maximum and minimum air temperatures as well as exogenous relative humidity and reference evapotranspiration in different continental contexts of the autonomous Valencia region, on the Spanish Mediterranean coast. The development of new and more precise models for ETo prediction from minimum climatic data is required, since the application of existing methods that provide acceptable results is limited to those places where large amounts of reliable climatic data are available. The Penman-Monteith model for ETo prediction, proposed by the FAO as the sole standard method for ETo estimation, was used to provide the ANN targets for the training and testing processes. Concerning models which demand scant climatic inputs, the proposed model provides performances with lower associated errors than the currently existing temperature-based models, which only consider local data.     

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.     

Distribution and Trends in Reference Evapotranspiration in the North China Plain

The distribution and trends in reference evapotranspiration (ETo) are extremely important to water resources planning for agriculture, and it is widely believed that rates of ETo will increase with global warming. This is a big concern in China, where water deficits are common in the North China Plain (NCP). In this study, Penman-Monteith reference evapotranspiration at 26 meteorological stations during 1961–2006 in and around the NCP was calculated. The temporal variations and spatial distribution of ETo were analyzed and the causes for the variations were discussed. The results showed that: (1) the NCP was divided into two climatic regions based on aridity values: a semiarid region that accounts for 69% of the area and subhumid regions that made of the remaining area; (2) over the entire NCP, the highest annual ETo occurred in the central and western areas and the lowest total ETo was observed in the east. Comparing the mean monthly ETo and annual ETo distributions, the high ETo values from May through July mainly determined the annual ETo distribution; (3) for the whole NCP, annual ETo showed a statistically significant decrease of 11.92 mm/decade over the 46 years of data collection in the NCP or approximately a 5% total decrease compared to the ETo values in 1961; (4) to determine which variable has the greatest effect on the decrease in ETo, decadal changes were observed for daily values of maximum air temperature (+0.16°C), minimum air temperature (+0.35°C), net radiation (?0.13?MJ?m?2), and mean wind speed (?0.09?m?s?1). These results indicate that the decreasing net radiation and wind speed had a bigger impact on ETo rates than the increases observed by the maximum and minimum temperatures.     

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.     

Daily Grass and Alfalfa-Reference Evapotranspiration Estimates and Alfalfa-to-Grass Evapotranspiration Ratios in Florida

Efficient use of natural water resources in agriculture is becoming an important issue in Florida because of the rapid depletion of freshwater resources due to the increasing trend of industrial development and population. Reliable and consistent estimates of evapotranspiration (ET) are a key element of managing water resources efficiently. Since the 1940s numerous grass- and alfalfa-reference evapotranspiration (ETo and ETr, respectively) equations have been developed and used by researchers and decision makers, resulting in confusion as to which equation to select as the most accurate reference ET estimates. Twenty-one ETo and ETr methods were evaluated based on their daily performance in a humid climate. The Food and Agriculture Organization Penman-Monteith (FAO56-PM) equation was used as the basis for comparison for the other methods. Measured and carefully screened daily climate data during a 23-year period (1978–2000) were used for method performance analyses, in which the methods were ranked based on the standard error of estimate (SEE) on a daily basis. In addition, the performance of the four alfalfa-based ET (ETr) equations and the ratio of alfalfa ET to grass ET (Kr values) were evaluated, which have not been studied before in Florida’s humid climatic conditions. The peak month ETo estimates by each method were also evaluated. All methods produced significantly different ETo estimates than the FAO56-PM method. The 1948 Penman method estimates were closest to the FAO56-PM method on a daily basis throughout the year, with the daily SEE averaging 0.11 mm?d?1; thus this method was ranked the second best overall. Although 1963 Penman (with the original wind function) slightly overestimated ET, especially at high ETo rates, it provided remarkably good estimates as well and ranked as the third best method, with a daily average SEE value of 0.14 mm?d?1. Both methods produced peak month ETo estimates closest to the FAO56-PM method among all methods evaluated, with daily peak month SEEs averaging 0.07 and 0.09 mm?d?1, respectively. Significant variations were observed in terms of the performance of the various forms of Penman’s equations. For example, the original Penman-Monteith method produced the poorest ETo estimates among the combination equations, with a daily SEE for all months and peak month averaging 0.50 and 0.35 mm?d?1, respectively and ranked 11th. An average value of 1.18 was used to convert ETr estimates to ETo values for alfalfa-reference methods. The Kr value of 1.18 resulted in reasonable estimates of ETo throughout the year by the Kimberley forms of the Penman equations. Another ETr-based equation, Jensen-Haise, gave consistently poor estimates. The Stephens-Stewart radiation method was the highest-ranked (10th) noncombination method overall. The temperature-based McCloud method (ranked 19th) produced the poorest ETo estimates among all methods with a daily SEE for all months and for the peak month averaging 1.93 and 1.22 mm?d?1, respectively. In general, the results obtained from the temperature methods suggest that all of the temperature methods, with the possible exception of the Turc method, can only be applicable for these climatic conditions after they are calibrated or modified locally or regionally. The FAO and Christiansen pan evaporation methods (ranked 17th and 18th, respectively) produced poor ETo estimates and had the largest amount of point scatter in daily ETo estimates relative to the FAO56-PM ETo. Both methods resulted in the highest daily SEE of 1.18 and 1.19 mm?d?1 for all months, after the McCloud method (1.93 mm?d?1), and with the highest SEE of 1.30 and 1.24 mm?d?1 for the peak month of all methods evaluated. The FAO56-PM method uses solar radiation, wind speed, relative humidity, and minimum and maximum air temperature to estimate ETo. It has been recommended that the FAO56-PM be used for estimating ETo when all the necessary input parameters are available. However, all these input variables may not be available, or some of them may not be reliable for a given location if the FAO56-PM equation is used, and one may need to choose other temperature, radiation, or pan evaporation methods based on the availability of data for estimating ETo. The results of this study can be used as a reference tool to provide practical information on which method to select based on the availability of data for reliable and consistent estimates of daily ETo relative to the FAO56-PM method in a humid climate.     

History and Evaluation of Hargreaves Evapotranspiration Equation

A brief history of development of the 1985 Hargreaves equation and its comparison to evapotranspiration (ET) predicted by the Food and Agricultural Organization of the United Nations (FAO) Penman-Monteith method are described to provide background and information helpful in selecting an appropriate reference ET equation under various data situations. Early efforts in irrigation water requirement computations in California and other arid and semiarid regions required the development of simplified ET equations for use with limited weather data. Several initial efforts were directed towards improving the usefulness of pan evaporation for estimating irrigation water requirements. Similarity with climates of other countries allowed developments in California to be extended overseas. Criticism of empirical methods by H. L. Penman and others encouraged the search for a robust and practical method that was based on readily available climatic data for computing potential evapotranspiration or reference crop evapotranspiration (ETo). One of these efforts ultimately culminated in the 1985 Hargreaves ETo method. The 1985 Hargreaves ETo method requires only measured temperature data, is simple, and appears to be less impacted than Penman-type methods when data are collected from arid or semiarid, nonirrigated sites. For irrigated sites, the Hargreaves 1985 ETo method produces values for periods of five or more days that compare favorably with those of the FAO Penman-Monteith and California Irrigation Management Information Services (CIMIS) Penman methods. The Hargreaves ETo predicted 0.97 of lysimeter measured ETo at Kimberly, Idaho after adjustment of lysimeter data for differences in surface conductance from the FAO Penman-Monteith definition. Monthly ETo by the 1985 Hargreaves equation compares closely with ETo calculated using a simplified, “reduced-set” Penman-Monteith that requires air temperature data only.     

Performance of Penman-Monteith FAO56 in a Semiarid Highland Environment

Reliable estimates of evapotranspiration are essential for irrigation and water resources planning and management. Although several methods are available for computing reference evapotranspiration (ETo), the provision of complete and accurate climate data is often a problem. Therefore, weighing lysimeter data from a semiarid highland environment were used to evaluate the performance of six commonly used reference evapotranspiration estimation methods with different data requirements (Penman-Monteith-FAO56, Priestley-Taylor, Radiation-FAO24, Hargreaves, Blaney-Criddle, Class A pan). The lysimeter experiments were conducted at Ankara Research Institute of Rural Services in Turkey, during the April–October cropping seasons of the years 2000–2002. The average ETo for the three seasons, computed from the lysimeter data, was 964 mm. The Penman-Monteith-FAO56 method was also evaluated for cases where relative humidity, wind speed, solar radiation, or all three parameters would be missing. This resulted in a total of 10 different methods. The RMS errors (RMSE) and index of agreement for the daily data and the monthly averages as well as the mean absolute error (MAE) for the seasonal totals were computed to compare these methods. The methods were ranked based on the sum of the ranks for all five evaluation criteria. The Penman-Montheith-FAO56 method with the full data set, with replacement of wind speed, and with replacement of relative humidity took the top three spots, with MAEs for the seasonal totals ranging between 40 and 70 mm. The Hargreaves method came in fourth (MAE 54 mm), followed by the Penman-Montheith-FAO56 method with replacement of all three parameters (MAE 57 mm). The RMSE for the monthly average ETo was 0.43 and 0.50?mm?days?1 for the Penman-Monteith-FAO56 without and with replacement of all three parameters and 0.48?mm?days?1 for Hargreaves. Thus, if only temperature data would be available, the much easier to use Hargreaves method would be preferred above the Penman-Montheith-FAO56 equation with replacement of humidity, radiation, and wind speed data, for this semiarid highland environment.     

基于卡尔曼滤波的迟滞神经网络风速序列预测

通过将迟滞特性引入神经元激励函数的方式,构造了一种前向型迟滞神经网络模型.结合卡尔曼滤波方法,将其应用于风速时间序列的预测分析中.在原始风速时间序列的基础上,构造出风速变化率序列.采用迟滞神经网络分别对两种序列进行预测分析,并将预测结果利用卡尔曼滤波方法进行融合,从而得到最优预测估计结果.仿真实验结果表明,迟滞神经网络具有更加灵活的网络结构,能够有效改善网络的泛化能力,预测性能优于传统神经网络.采用卡尔曼滤波方法对预测结果进行融合后能够进一步提高预测精度,降低预测误差.      

Potential Evapotranspiration for the Distributed Modeling of Belgian Catchments

To support a sensitivity analysis in the framework of catchment modeling, three potential evapotranspiration (ETp) scenarios were generated by means of two Food and Agriculture Organization (FAO) approaches, namely, the FAO-24 and the FAO-56 approaches. The crop ETp was estimated as a function of the reference evapotranspiration (ETo) by means of the kc-ETo approach. Scenario A was generated with the standard FAO-24 approach; Scenario B considered also the FAO-24 approach, but with some nonstandard parameters. Scenario C considered the standard FAO-56 approach. The ETo data were compared to point-scale ETo constraints. The annual cumulative value of ETo from Scenario A was on average approximately 200 mm larger than the values from Scenarios B and C. The research revealed similar ETo estimates for Scenarios B and C. The research also assessed the performance of the angstrom approach for estimating incoming solar radiation (Rs). In this context, a set of angstrom coefficients was derived by means of an optimization process that considered available Rs data.     

Comparison of Simplified Pan-Based Equations for Estimating Reference Evapotranspiration

Accurate estimation of reference evapotranspiration (ET0) is essential for irrigation practice. Conversion from pan evaporation data to reference evapotranspiration is commonly practiced. The objective of this study was to evaluate the reliability of simplified pan-based approaches for estimating ET0 directly that do not require the data of relative humidity and wind speed. In this study, three pan-based (FAO-24 pan, Snyder ET0, and Ghare ET0) equations were compared against lysimeter measurements of grass evapotranspiration using daily data from Policoro, Italy. Based on summary statistics, the Snyder ET0 equation ranked first with the lowest RMSE value (0.449?mm?day?1). The pan-based equations were additional tested using mean daily data collected in Novi Sad, Serbia. The Snyder ET0 equation best matched ET0 estimates by Penman-Monteith equation at Novi Sad with lowest root mean square error value of 0.288?mm?day?1. The obtained results demonstrate that simplified pan-based equations can be successful alternative to FAO-56 Penman-Monteith equation for estimating reference evapotranspiration. The overall results recommended Snyder ET0 equation for pan evaporation to evapotranspiration conversions. The Snyder ET0 equation consistently provides better results compared to FAO-24 pan equation, although required measurements of only one weather parameter pan evaporation.     

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.     

Aircraft Icing Detection, Identification, and Reconfigurable Control Based on Kalman Filtering and Neural Networks

Flight in all weather conditions has necessitated correctly detecting icing and taking reasonable measures against it. This work aims at the detection and identification of airframe icing based on statistical properties of aircraft dynamics and reconfigurable control protecting aircraft from hazardous icing conditions. A Kalman filter is used for the data collection for the detection of icing, which aerodynamically deteriorates flight performance. A neural network process is applied for the identification of icing model of the aircraft, which is represented by five parameters based on past experiments for iced wing airfoils. Icing is detected by a Kalman filtering innovation sequence approach. A neural network structure is embodied such that its inputs are the aircraft estimated measurements and its outputs are the parameters affected by ice, which corresponds to the aircraft inverse dynamic model. The necessary training and validation set for the neural network model of the iced aircraft are obtained from the simulations of nominal model, which are performed for various icing conditions. In order to decrease noise effects on the states and to increase training performance of the neural network, the estimated states by the Kalman filter are used. A suitable neural network model of aircraft inverse dynamics is obtained by using system identification methods and learning algorithms. This trained model is used as an application for the control of the aircraft that has lost its controllability due to icing. The method is applied to F16 military and A340 commercial aircraft models and the results seem to be good enough.     

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.     

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.     

Sensitivity Analyses and Sensitivity Coefficients of Standardized Daily ASCE-Penman-Monteith Equation

The sensitivity of the standardized ASCE grass-reference Penman-Monteith evapotranspiration (ASCE-PM ETo) equation to climate variables in different regions has not yet been studied. Sensitivity analyses for the standardized daily form of the ASCE-PM equation were conducted on wind speed at 2?m height (U2), maximum and minimum air temperatures (Tmax and Tmin), vapor pressure deficit (VPD), and solar radiation (Rs) in the following regions of the United States: semiarid (Scottsbluff, Nebraska, and Bushland, Texas), a Mediterranean-type climate (Santa Barbara, California), coastal humid (Fort Pierce, Florida), inland humid and semihumid (Rockport, Missouri, and Clay Center, Nebraska), and an island (Twitchell Island, California). The sensitivity coefficients were derived for each variable on a daily basis. In general, ETo was most sensitive to VPD at all locations, while sensitivity of ETo to the same variable showed significant variation from one location to another and at the same location within the year. After VPD, ETo was most sensitive to U2 in semiarid regions (Scottsbluff, Clay Center, and Bushland) during the summer months. The Rs was the dominant driving force of ETo at humid locations (Fort Pierce and Rockport) during the summer months. At Santa Barbara, the sensitivity of ETo to U2 was minimal during the summer months. At Bushland, Scottsbluff, and Twitchell Island, ETo was more sensitive to Tmax than Rs in summer months, whereas it was equally sensitive to Tmax and Rs at Clay Center. The ETo was not sensitive to Tmin at any of the locations. The change in ETo was linearly related to change in climate variables (with r2 ≥ 0.96 in most cases), with the exception of Tmin, at all sites. Increase in ETo with respect to increase in climate variable changed considerably by month. On an annual average, a 1°C increase in Tmax resulted in 0.11, 0.06, 0.16, 0.07, 0.11, 0.08, and 0.10?mm increases in ETo at Scottsbluff, Santa Barbara, Bushland, Fort Pierce, Twitchell Island, Rockport, and Clay Center. A 1?m?s?1 increase in U2 resulted in 0.42, 0.18, 0.37, 0.28, 0.31, 0.20, and 0.26?mm increases in ETo at the same locations. A unit increase in Tmax resulted in the largest increase in ETo at Bushland, and a unit increase in Rs caused the largest increases in ETo at Fort Pierce. A 1?MJ?m?2?d?1 increase in Rs resulted in 0.05, 0.08, 0.06, 0.11, 0.05, 0.06, and 0.06?mm increases in ETo at the same locations. A 0.4?kPa increase in VPD resulted in 1.13, 0.54, 1.29, 0.57, 1.04, 1.10, and 1.22?mm increases in ETo at the same locations. The U2 had the most effect on ETo at Scottsbluff and Bushland, the two locations where dry and strong winds are common during the growing season. The sensitivity coefficient for Rs was higher during the summer months and lower during the winter months, and the opposite was observed for VPD (except for Twitchell Island). The decrease of the sensitivity coefficients for Rs corresponding to an increase in the sensitivity coefficient for VPD is due to a decrease in the energy term in favor of the increase in significance of the aerodynamic term of the standardized ASCE-PM equation in summer versus winter months. Because the ASCE-PM and the Food and Agriculture Organization paper number 56 Penman-Monteith (FAO56-PM) equations are identical when applied on a daily time step, the results of the sensitivity analyses and sensitivity coefficients of this study should be directly applicable to the FAO56-PM equation.     

Sensitivity of the Food and Agriculture Organization Penman–Monteith Evapotranspiration Estimates to Alternative Procedures for Estimation of Parameters

Reference crop evapotranspiration (ETo) is a key variable in procedures established for estimating evapotranspiration rates of agricultural crops. As per internationally accepted procedures outlined in the United Nations Food and Agriculture Organization's Irrigation and Drainage Paper No. 56 (FAO-56), using the Penman–Monteith (PM) combination equation is the recommended approach to computing ETo from ground-based climatological observations. Applying of the PM equation requires converting input climate and site data into a number of parameters, and FAO-56 recommends exact procedures for estimating these parameters. However, a plethora of alternative procedures for estimating parameters exist in literature. As a consequence, it is likely that ambiguous results may be obtained from the FAO-56 PM equation because of the adoption of such alternative (nonrecommended) supporting equations. The purpose of the present study is to evaluate differences that could arise in FAO-56 ETo estimates if nonrecommended equations are used to compute the parameters. Using historical climate records from 1973 to 1992 of a station located in the humid tropical region of Karnataka State, India, monthly ETo estimates computed by FAO-56 recommended procedures were statistically compared with those obtained by introducing alternative procedures for estimating parameters. In all, 13 alternative algorithms for ETo estimation were formulated, involving modified procedures for parameters associated with weighting factors, net radiation, and vapor-pressure-deficit terms of the PM equation. For the 240-month period considered, nine of these algorithms yielded ETo estimates that were in close correspondence with FAO-56 estimates as indicated by mean absolute relative difference (AMEAN) values within 1% and maximum absolute relative difference (MAXE) values within 2%. The remaining four algorithms, involving nonrecommended procedures for the vapor-pressure-deficit and net-radiation parameters, yielded considerably different ETo estimates, giving rise to AMEAN values in the range of 2 to 8% and MAXE values ranging between 8 and 28%. The results of this study highlight the need for strict adherence to recommended procedures, especially for estimating of vapor-pressure-deficit and net-radiation parameters if consistent results are to be obtained by the FAO-56 approach.     

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.     

Estimation of Evapotranspiration of Different-Sized Navel-Orange Tree Orchards Using Energy Balance

Crop evapotranspiration (ETc) and crop coefficient (Kco) values of four clean-cultivated navel-orange orchards that were irrigated with microsprinklers, having different canopy features (e.g., age, height, and canopy cover) were evaluated. Half-hourly values of latent heat flux density were estimated as the residual of the energy balance equation using measured net radiation (Rn), soil heat flux density (G), and sensible heat flux density (H) estimated using the surface renewal method. Hourly means of latent heat flux density (LE) were calculated and were divided by the latent heat of vaporization (L) to obtain ETc. Crop coefficients were determined by calculating the ratio Kco = ETc/ETo, with reference evapotranspiration (ETo) determined using the hourly Penman–Monteith equation for short canopies. The estimated Kco values ranged from 0.45 to 0.93 for canopy covers having between 3.5 and 70% ground shading. The Kco values were compared with Kc values from FAO 24 (reported by Doorenbos and Pruitt in 1975) and FAO 56 (reported by Allen et al. in 1998) and with Kc values from research papers that estimated reference ET from pan evaporation data using the FAO 24 method. The observed Kco values were slightly higher than Kc values for clean-cultivated orchards with high-frequency drip irrigation in Arizona and were slightly lower than for nontilled orchards in Florida. The Kco values were considerably higher than Kc values from FAO 24 and FAO 56 and were higher than Kc values from border-irrigated orchards near Valencia, Spain.     

Uncertainty of Weekly Nitrate-Nitrogen Forecasts Using Artificial Neural Networks

Nonpoint source pollution affects the quality of numerous watersheds in the Midwestern United States. The Illinois State Water Survey conducted this study to (1) assess the potential of artificial neural networks (ANNs) in forecasting weekly nitrate-nitrogen (nitrate-N) concentration; and (2) evaluate the uncertainty associated with those forecasts. Three ANN models were applied to predict weekly nitrate-N concentrations in the Sangamon River near Decatur, Illinois, based on past weekly precipitation, air temperature, discharge, and past nitrate-N concentrations. Those ANN models were more accurate than the linear regression models having the same inputs and output. Uncertainty of the ANN models was further expressed through the entropy principle, as defined in the information theory. Using several inputs in an ANN-based forecasting model reduced the uncertainty expressed through the marginal entropy of weekly nitrate-N concentrations. The uncertainty of predictions was expressed as conditional entropy of future nitrate concentrations for given past precipitation, temperature, discharge, and nitrate-N concentration. In general, the uncertainty of predictions decreased with model complexity. Including additional input variables produced more accurate predictions. However, using the previous weekly data (week t?1) did not reduce the uncertainty in the predictions of future nitrate concentrations (week t+1) based on current weekly data (week t).