Choice between competitive pairs of frequency models for use in hydrology: a review and some new results

Abstract

The potential is investigated of the generalized regression neural networks (GRNN) technique in modelling of reference evapotranspiration (ET₀) obtained using the FAO Penman-Monteith (PM) equation. Various combinations of daily climatic data, namely solar radiation, air temperature, relative humidity and wind speed, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on ET₀. In the first part of the study, a comparison is made between the estimates provided by the GRNN and those obtained by the Penman, Hargreaves and Ritchie methods as implemented by the California Irrigation Management System (CIMIS). The empirical models were calibrated using the standard FAO PM ET₀ values. The GRNN estimates are also compared with those of the calibrated models. Mean square error, mean absolute error and determination coefficient statistics are used as comparison criteria for the evaluation of the model performances. The GRNN technique (GRNN 1) whose inputs are solar radiation, air temperature, relative humidity and wind speed, gave mean square errors of 0.058 and 0.032 mm² day^?2, mean absolute errors of 0.184 and 0.127 mm day^?1, and determination coefficients of 0.985 and 0.986 for the Pomona and Santa Monica stations (Los Angeles, USA), respectively. Based on the comparisons, it was found that the GRNN 1 model could be employed successfully in modelling the ET₀ process. The second part of the study investigates the potential of the GRNN and the empirical methods in ET₀ estimation using the nearby station data. Among the models, the calibrated Hargreaves was found to perform better than the others.     

Comparison of the Hargreaves and Samani equation and the Thornthwaite equation for estimating dekadal evapotranspiration in the Free State Province,South Africa

Reference evapotranspiration (ET) is an important parameter that needs to be estimated accurately to enhance its utility in numerous applications. Although the widely recommended procedure for calculating this index involves using the FAO Penman–Monteith equation (ETo), the latter’s effectiveness is constrained by its considerable data requirements. To overcome this constraint, alternative methods using the limited data available have to be explored. In this study the ability of the Hargreaves and Samani (ET_HS) and Thornthwaite (ET_T) equations to estimate ET was investigated using multi-year data (1999–2008) from eight weather stations in the semi-arid Free State Province of South Africa. Results for non-calibrated equations are closely correlated, with ET_HS tending to underestimate ET for the July to December period while ET_T underestimates ET for all months of the calendar year. Although estimates from calibrated equations are also closely correlated, they have smaller deviations compared to the original equations with the calibrated Hargreaves and Samani equation (ET_CHS) estimating reference evapotranspiration better than its calibrated Thornthwaite (ET_CT) counterpart. The former’s better performance suggests that in data-scarce areas, the Hargreaves and Samani model is capable of giving results within acceptable ranges of accuracy.     

Daily pan evaporation modelling using multi‐layer perceptrons and radial basis neural networks

This paper reports on investigations of the abilities of three different artificial neural network (ANN) techniques, multi‐layer perceptrons (MLP), radial basis neural networks (RBNN) and generalized regression neural networks (GRNN) to estimate daily pan evaporation. Different MLP models comprising various combinations of daily climatic variables, that is, air temperature, solar radiation, wind speed, pressure and humidity were developed to evaluate the effect of each of these variables on pan evaporation. The MLP estimates are compared with those of the RBNN and GRNN techniques. The Stephens‐Stewart (SS) method is also considered for the comparison. The performances of the models are evaluated using root mean square errors (RMSE), mean absolute error (MAE) and determination coefficient (R²) statistics. Based on the comparisons, it was found that the MLP and RBNN computing techniques could be employed successfully to model the evaporation process using the available climatic data. The GRNN was found to perform better than the SS method. Copyright © 2008 John Wiley & Sons, Ltd.     

Evapotranspiration modelling using support vector machines / Modélisation de l'évapotranspiration à l'aide de ‘support vector machines’

Abstract

This study investigates the accuracy of support vector machines (SVM), which are regression procedures, in modelling reference evapotranspiration (ET₀). The daily meteorological data, solar radiation, air temperature, relative humidity and wind speed from three stations, Windsor, Oakville and Santa Rosa, in central California, USA, are used as inputs to the support vector machines to reproduce ET₀ obtained using the FAO-56 Penman-Monteith equation. A comparison is made between the estimates provided by the SVM and those of the following empirical models: the California Irrigation Management System (CIMIS) Penman, Hargreaves, Ritchie and Turc methods. The SVM results were also compared with an artificial neural networks method. Root mean-squared errors, mean-absolute errors, and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. The comparison results reveal that the support vector machines could be employed successfully in modelling the ET₀ process.     

Comparison of the Penman‐Monteith method and regional calibration of the Hargreaves equation for actual evapotranspiration using SWAT-simulated results in the Seolma-cheon basin,South Korea

ABSTRACT

The Hargreaves method provides reference evapotranspiration (ET_o) estimates when only air temperature data are available, although it requires previous local calibration for an acceptable performance. This method was evaluated using the data from 71 meteorological stations in the Seolma-cheon basin (8.48 km²), South Korea, comparing daily estimates against those from the Penman‐Monteith (PM) method, which was used as the standard. To estimate reference ET_o more exactly, considering the climatological characteristics in South Korea, parameter regionalization of the Hargreaves equation is carried out. First, the modified Hargreaves equation is presented after an analysis of the relationship between solar radiation and temperature. Second, parameter (K_ET) optimization of the regional calibration of the Hargreaves equation (RCH) is performed using the PM method and the modified equation at 71 meteorological stations. Next, an application was carried out to evaluate the evapotranspiration methods (PM, original Hargreaves and RCH) in the SWAT (Soil and Water Assessment Tool) model by comparing these with the measured actual evapotranspiration (AET) in the basin. The SWAT model was calibrated using 3 years (2007–2009) of daily streamflow at the watershed outlet and 3 years (2007–2009) of daily AET measured at a mixed forest. The model was validated with 3 years (2010‐2012) of streamflow and AET. RCH will contribute to a better understanding of evapotranspiration of an ungauged watershed in areas where meteorological information is scarce.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR Not assigned     

A simple temperature method for the estimation of evapotranspiration

Accurate estimation of evapotranspiration (ET) is essential in water resources management and hydrological practices. Estimation of ET in areas, where adequate meteorological data are not available, is one of the challenges faced by water resource managers. Hence, a simplified approach, which is less data intensive, is crucial. The FAO‐56 Penman–Monteith (FAO‐56 PM) is a sole global standard method, but it requires numerous weather data for the estimation of reference ET. A new simple temperature method is developed, which uses only maximum temperature data to estimate ET. Ten class I weather stations data were collected from the National Meteorological Agency of Ethiopia. This method was compared with the global standard PM method, the observed Piche evaporimeter data, and the well‐known Hargreaves (HAR) temperature method. The coefficient of determination (R²) of the new method was as high as 0.74, 0.75, and 0.91, when compared with that of PM reference evapotranspiration (ET_o), Piche evaporimeter data, and HAR methods, respectively. The annual average R² over the ten stations when compared with PM, Piche, and HAR methods were 0.65, 0.67, and 0.84, respectively. The Nash–Sutcliff efficiency of the new method compared with that of PM was as high as 0.67. The method was able to estimate daily ET with an average root mean square error and an average absolute mean error of 0.59 and 0.47 mm, respectively, from the PM ET_o method. The method was also tested in dry and wet seasons and found to perform well in both seasons. The average R² of the new method with the HAR method was 0.82 and 0.84 in dry and wet seasons, respectively. During validation, the average R² and Nash–Sutcliff values when compared with Piche evaporation were 0.67 and 0.51, respectively. The method could be used for the estimation of daily ET_o where there are insufficient data. Copyright © 2013 John Wiley & Sons, Ltd.     

Parameterization of the Ångström–Prescott formula based on machine learning benefit estimation of reference crop evapotranspiration with missing solar radiation data

Accurately estimated reference evapotranspiration (ET₀) is essential to regional water management. The FAO recommends coupling the Penman–Monteith (P-M) model with the Ångström–Prescott (A-P) formula as the standard method for ET₀ estimation with missing R_s measurements. However, its application is usually restricted by the two fundamental coefficients (a and b) of the A-P formula. This paper proposes a new method for estimating ET₀ with missing R_s by combining machine learning with physical-based P-M models (PM-ET₀). The benchmark values of the A-P coefficients were first determined at the daily, monthly, and yearly scales, and further evaluated in R_s and ET₀ estimates at 80 national R_s measuring stations. Then, three empirical models and four machine-learning methods were evaluated in estimating the A-P coefficients. Machine learning methods were also used to estimate ET₀ (ML-ET₀) to compare with the PM-ET₀. Finally, the optimal estimation method was used to estimate the A-P coefficients for the 839 regular weather stations for ET₀ estimation without R_s measurement for China. The results demonstrated a descending trend for coefficient a from northwest to southeast China, with larger values in cold seasons. However, coefficient b showed the opposite distribution as the coefficient a. The FAO has recommended a larger a but a smaller b for southeast China, which produced the region's largest R_s and ET₀ estimation errors. Additionally, the A-P coefficients calibrated at the daily scale obtained the best estimation accuracy for both R_s and ET₀, and slightly outperformed the monthly and yearly coefficients without significant difference in most cases. The machine learning methods outperformed the empirical methods for estimating the A-P coefficients, especially for the sites with extreme values. Further, ML-ET₀ outperformed the PM-ET₀ with yearly A-P coefficients but underperformed those with daily and monthly ones. This study indicates an exciting potential for combining machine learning with physical models for estimating ET₀. However, we found that using the A-P coefficients with finer time scales is unnecessary to deal with the missing R_s measurements.     

Assessment of eight reference evapotranspiration (ETo) methods considering Köppen climate class in Iran

ABSTRACT

The performance of eight empirical equations for estimating ET_o at 80 weather stations in Iran is evaluated. The equations assessed are Hargreaves (HGS), Trajkovic (TKC), Berti (BTI), Ravazzani (RZI), Irmak (IMK), Turc (TRC) and two Valiantzas methods (VTS1 and VTS2). The FAO56 reference crop Penman-Monteith (PM) equation is used as a baseline to evaluate their performance. Also, a Köppen climate classification map for Iran is developed and the best ET_o method for each climate type identified. The updated Köppen climate map shows six climate sub-classes; BWh, BWk, BSh, BSk, Csa and Dsa in Iran with a percentage of land area covered by each sub-class of 43, 17, 7, 9, 11 and 13%, respectively. The best performing ET_o equation for each climate class in Iran was HGS for BSh, VTS1 for BWk, and VTS2 for BSk, BWh, Csa and Dsa.     

Eddy covariance‐based evapotranspiration for a subtropical wetland

The eddy covariance (EC) method was used in a 30‐month study to quantify evapotranspiration (ET) and vegetation coefficient (K_CW) for a wetland on a ranch in subtropical south Florida. To evaluate the errors in ET estimates, the EC‐based ET (ET_C‐EC) and the Food and Agricultural Organization (FAO) Penman–Monteith (PM) based ET (ET_C‐PM) estimates (with literature crop coefficient, K_C) were compared with each other. The ET_C‐EC and FAO‐PM reference ET were used to develop K_CW. Regression models were developed to estimate K_CW using climatic and hydrologic variables. Annual and daily ET_C‐EC values were 1152 and 3.27 mm, respectively. The FAO‐PM model underestimated ET by 25% with ET_C‐EC being statistically higher than ET_C‐PM. The K_CW varied from 0.79 (December) to 1.06 (November). The mean K_CW for the dry (November–April) season (0.95) was much higher than values reported for wetlands in literature; whereas for the wet (May–October) season, K_CW (0.97) was closer to literature values. Higher than expected K_CW values during the dry season were due to higher temperature, lower humidity and perennial wetland vegetation. Regression analyses showed that factors affecting the K_CW were different during the dry (soil moisture, temperature and relative humidity) and wet (net radiation, inundation and wind speed) seasons. Separate regression models for the dry and wet seasons were developed. Evapotranspiration and K_CW from this study, one of the first for the agricultural wetlands in subtropical environment, will help improve the ET estimates for similar wetlands. Copyright © 2013 John Wiley & Sons, Ltd.     

Evapotranspiration modelling from climatic data using a neural computing technique

Evapotranspiration is one of the basic components of the hydrologic cycle and essential for estimating irrigation water requirements. This paper investigates the modelling of evapotranspiration using the feed‐forward artificial neural network (ANN) technique with the Levenberg–Marquardt (LM) training algorithm. The LM algorithm has never been used in evapotranspiration estimation before. The LM is used for the optimization of network weights, since this algorithm is more powerful and faster than the conventional gradient descent. Various combinations of daily climatic data, i.e. wind speed, air temperature, relative humidity and solar radiation, from three stations in Los Angeles, USA, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on evapotranspiration. A comparison is made between the estimates provided by the ANN and those of the following empirical models: Penman, Hargreaves, Turc. Mean square error, mean absolute error and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modelling evapotranspiration process from the available climatic data. The results also indicate that the Hargreaves method provides better performance than the Penman and Turc methods in estimation of the evapotranspiration. The accuracy of the ANN technique in evapotranspiration estimation using nearby station data was also investigated. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of trends in reference evapotranspiration data in a humid climate

Abstract

Statistically significant FAO-56 Penman-Monteith (FAO-56 PM) and adjusted Hargreaves (AHARG) reference evapotranspiration (ET₀) trends at monthly, seasonal and annual time scales were analysed by using linear regression, Mann-Kendall and Spearman’s Rho tests at the 1 and 5% significance levels. Meteorological data were used from 12 meteorological stations in Serbia, which has a humid climate, for the period 1980–2010. Web-based software for conducting the trend analyses was developed. All of the trends significant at the 1 and 5% significance levels were increasing. The FAO-56 PM ET₀ trends were almost similar to the AHARG trends. On the seasonal time scale, for the majority of stations significant increasing trends occurred in summer, while no significant positive or negative trends were detected by the trend tests in autumn for the AHARG series. Moreover, 70% of the stations were characterized by significant increasing trends for both annual ET₀ series.

Editor Z.W. Kundzewicz; Associate editor S. Grimaldi

Citation Gocic, M. and Trajkovic, S., 2013. Analysis of trends in reference evapotranspiration data in a humid climate. Hydrological Sciences Journal, 59 (1), 165–180.     

A simple parameterization of bulk canopy resistance from climatic variables for estimating hourly evapotranspiration

This paper examines a model for estimating canopy resistance r_c and reference evapotranspiration ET_o on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ET_o values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance r_c as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable r_c were also computed according to two other approaches: with the r_c variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that r_c/r_a (where r_a is the aerodynamic resistance) presents a dependence on the square root of r*/r_a, as the best approach with empirically derived global parameters. When estimating hourly ET_o values, we compared the performance of the PM equation using those estimated variable r_c values with the PM equation as proposed by the Food and Agriculture Organization, with a constant r_c = 70 s m^?1. The results confirmed the relative robustness of the PM method with constant r_c, but also revealed a tendency to underestimate the measured values when ET_o is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ET_o were obtained when an estimated variable r_c was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for r_c as a function of the square root of r* may be considered as an alternative for modelling r_c, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.     

Elevation-dependent changes in reference evapotranspiration due to climate change

The Food and Agriculture Organizations' (FAO) Penman–Monteith reference evapotranspiration (ET₀) is a crucial index in the research of water and energy balance. Temporal and spatial variations in ET₀ from 1981–2017 were investigated in the Hengduan Mountains, China_. The results showed a change point around the year 2000 in ET₀ series. ET₀ decreased and increased significantly by +3.200 mm/year (p < 0.01) from 1981–2000 and by +4.109 mm/year (p < 0.01) from 2001–2017, respectively. The contribution analysis shows that the positive significant contribution of air temperature (TA) was offset by negative effects of decreases in downward shortwave radiation (R_s) and wind speed (WS) and an increase in actual vapour pressure (e_a), causing the decrease in ET₀ from 1981 to 2000. WS was the largest contributing factor for the decrease in ET₀ from 1981 to 2000 during spring, winter and annually, while R_s and e_a were the largest negative contributors in summer and autumn, respectively. An increase in TA was responsible for the increase in ET₀ in all seasons except winter and the annual scale in 2001–2017. The sensitivity analysis shows that ET₀ was most sensitive to TA, and WS was the least sensitive variable. The trends of ET₀ increased with elevation; we denote this as the elevation-dependence of ET₀ changes. The elevation-dependence was also noted for the trends of WS and e_a, with higher elevations showing larger changes in WS and lower changes in e_a. Besides, the sensitivities of TA, R_s and e_a decreased with elevation, while that of WS increased slightly with elevation. A comprehensive investigation into the trends of climatic drivers and their sensitivities revealed complex trends of the contributions of climatic variables on ET₀ with elevation, with no uniform trend existed in seasons. The results will contribute to our understanding of the response of ET₀ to climate change in a mountainous area, and provide a guideline for the water resources management under climate change.     

Validation and calibration of solar radiation equations for estimating daily reference evapotranspiration at cool semi-arid and arid locations

ABSTRACT

In this work, the applicability of 12 solar radiation (R_S) estimation models and their impacts on daily reference evapotranspiration (ET_o) estimates using the Penman‐Monteith FAO-56 (PMF-56) method were tested under cool arid and semi-arid conditions in Iran. The results indicated that the average increase in accuracy of the ET_o estimates by the calibrated R_S models, quantified by the decrease in RMSE, was 2.8% and 6.4% for semi-arid and arid climates, respectively. Mean daily deviations in the estimated ET_o by the calibrated R_S equations in semi-arid climates varied from ?0.283?mm/d^-1 for the Glover‐McCulloch model to 0.080?mm/d for the El-Sebaii model, with an average of ?0.109?mm/d^-1, and in arid climates, they ranged from ?0.522?mm/d^-1 for the Samani model to 0.668?mm/d for the El-Sebaii model, with an average of 0.125?mm/d^-1.

Editor D. Koutsyiannis; Associate editor Not assigned     

Trend analysis of reference evapotranspiration in Northwest China: The roles of changing wind speed and surface air temperature

Reference evapotranspiration (ET₀) is an important element in the water cycle that integrates atmospheric demands and surface conditions, and analysis of changes in ET₀ is of great significance for understanding climate change and its impacts on hydrology. As ET₀ is an integrated effect of climate variables, increases in air temperature should lead to increases in ET₀. However, this effect could be offset by decreases in vapor pressure deficit, wind speed, and solar radiation which lead to the decrease in ET₀. In this study, trends in the Penman–Monteith ET₀ at 80 meteorological stations during 1960–2010 in the driest region of China (Northwest China) were examined. The results show that there was a change point for ET₀ series around the year 1993 based on the Pettitt's test. For the region average, ET₀ decreased from 1960 to 1993 by ?2.34 mm yr^?2, while ET₀ began to increase since 1994 by 4.80 mm yr^?2. A differential equation method based on the Food and Agriculture Organization Penman–Monteith formula was used to attribute the change in ET₀. The attribution results show that the significant decrease in wind speed dominated the change in ET₀, which offset the effect of increasing air temperature and led to the decrease in ET₀ from 1960 to 1993. However, wind speed began to increase, and the amplitude of increase in air temperature also rose significantly since the mid‐1990s. Increases in air temperature and wind speed together reversed the trend in ET₀ and led to the increase in ET₀ since 1994. Copyright © 2012 John Wiley & Sons, Ltd.     

Potential evapotranspiration and its attribution over the past 50 years in the arid region of Northwest China

Evaporation paradox and its attribution have become a hot research topic in hydrology in recent years. This study estimates the potential evapotranspiration (ET₀) using modified Penman–Monteith method and analyzes the corresponding trend attribution based on the long‐term meteorological data collected at 81 ground‐based meteorological stations in Northwestern arid region of China during the period 1958–2010. The analysis results show: (1) The ET₀ has exhibited an obvious decreasing trend until the early 1990s; however, the downward trend has been reversed to an upward trend after then. (2) Decrease in diurnal temperature range (DTR) and wind speed (WS) may lead to the decrease of ET₀ during 1956–1993. The change of dominant factors in the ET₀ trend has differences after the early 1990s; observed increase in WS is the primary factor contributing to the reversion of ET₀. Copyright © 2012 John Wiley & Sons, Ltd.     

M5 model tree based modelling of reference evapotranspiration

This paper investigates the potential of M5 model tree based regression approach to model daily reference evapotranspiration using climatic data of Davis station maintained by California irrigation Management Information System (CIMIS). Four inputs including solar radiation, average air temperature, average relative humidity, and average wind speed whereas reference evapotranspiration calculated using a relation provided by the CIMIS was used as output. To compare the performance of M5 model tree in predicting the reference evapotranspiration, FAO–56 Penman–Monteith equation and calibrated Hargreaves–Samani relation was used. A comparison of results suggests that M5 model tree approach works well in comparison to both FAO–56 and calibrated Hargreaves–Samani relations. To judge the generalization capability of M5 model tree approach, model created by using the Davis data set was tested with the datasets of four different sites. Results from this part of the study suggest that M5 model tree could successfully be employed in modeling the reference evapotranspiration. Further, sensitivity analysis with M5 model tree approach suggests the suitability of solar radiation, average air temperature, average relative humidity, and average wind speed as input parameters to model the reference evapotranspiration Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of artificial neural network models for hydrologic predictions at multiple gauging stations in an agricultural watershed

This paper reports on an evaluation of the use of artificial neural network (ANN) models to forecast daily flows at multiple gauging stations in Eucha Watershed, an agricultural watershed located in north‐west Arkansas and north‐east Oklahoma. Two different neural network models, the multilayer perceptron (MLP) and the radial basis neural network (RBFNN), were developed and their abilities to predict stream flow at four gauging stations were compared. Different scenarios using various combinations of data sets such as rainfall and stream flow at various lags were developed and compared for their ability to make flow predictions at four gauging stations. The input vector selection for both models involved quantification of the statistical properties such as cross‐, auto‐ and partial autocorrelation of the data series that best represented the hydrologic response of the watershed. Measured data with 739 patterns of input–output vector were divided into two sets: 492 patterns for training, and the remaining 247 patterns for testing. The best performance based on the RMSE, R² and CE was achieved by the MLP model with current and antecedent precipitation and antecedent flow as model inputs. The MLP model testing resulted in R² values of 0·86, 0·86, 0·81, and 0·79 at the four gauging stations. Similarly, the testing R² values for the RBFNN model were 0·60, 0·57, 0·58, and 0·56 for the four gauging stations. Both models performed satisfactorily for flow predictions at multiple gauging stations, however, the MLP model outperformed the RBFNN model. The training time was in the range 1–2 min for MLP, and 5–10 s for RBFNN on a Pentium IV processor running at 2·8 GHz with 1 MB of RAM. The difference in model training time occurred because of the clustering methods used in the RBFNN model. The RBFNN uses a fuzzy min‐max network to perform the clustering to construct the neural network which takes considerably less time than the MLP model. Results show that ANN models are useful tools for forecasting the hydrologic response at multiple points of interest in agricultural watersheds. Copyright © 2008 John Wiley & Sons, Ltd.     

Assessing the effect of climate change on reference evapotranspiration in China

Reference evapotranspiration (ET ₀ ) is a key parameter in hydrological and meteorological studies. In this study, the FAO Penman–Monteith equation was used to estimate ET ₀ , and the change in ET ₀ was investigated in China from 1960 to 2011. The results show that a change point around the year 1993 was detected for the annual ET ₀ series by the Cramer’s test. For the national average, annual ET ₀ decreased significantly (P < 0.001) by ?14.35 mm/decade from 1960 to 1992, while ET ₀ increased significantly (P < 0.05) by 22.40 mm/decade from 1993 to 2011. A differential equation method was used to attribute the change in ET ₀ to climate variables. The attribution results indicate that ET ₀ was most sensitive to change in vapor pressure, followed by solar radiation, air temperature and wind speed. However, the effective impact of change in climate variable on ET ₀ was the product of the sensitivity and the change rate of climate variable. During 1960–1992, the decrease in solar radiation was the main reason of the decrease in ET ₀ in humid region, while decrease in wind speed was the dominant factor of decreases in ET ₀ in arid region and semi-arid/semi-humid region of China. Decrease in solar radiation and/or wind speed offset the effect of increasing air temperature on ET ₀ , and together led to the decrease in ET ₀ from 1960 to 1992. Since 1993, the rapidly increasing air temperature was the dominant factor to the change in ET ₀ in all the three regions of China, which led to the increase in ET ₀ . Furthermore, the future change in ET ₀ was calculated under IPCC SRES A1B and B1 scenarios with projections from three GCMs. The results showed that increasing air temperature would dominate the change in ET ₀ and ET ₀ would increase by 2.13–10.77, 4.42–16.21 and 8.67–21.27 % during 2020s, 2050s and 2080s compared with the average annual ET ₀ during 1960–1990, respectively. The increases in ET ₀ would lead to the increase in agriculture water consumption in the 21st century and may aggravate the water shortage in China.     

Spatiotemporal variations of reference evapotranspiration in recent five decades in the arid land of Northwestern China

Spatial and temporal variations of reference evapotranspiration (ET₀) are useful for regional agricultural and water resources management as well as required in most distributed hydrological modelling. In the current study, the Penman–Monteith estimated ET₀ in the arid land of Northwestern China has been explicitly explored using the Mann–Kendall test. Most stations in the study region exhibited significant decreasing trend of ET₀ (P < 0.05) with only few occasions showing significant increasing trend (P < 0.05), despite the increase of temperature in the entire region. Analysis results revealed that the overall decreasing wind speed contributed most to the decreasing trend of ET₀, whereas the contributions of relative humidity and sunshine duration were limited. Temperature played the second important role on determining ET₀ trend, but its effect was opposite to that of wind speed and was largely offset by the decreasing wind speed. Furthermore, sensitivity analysis suggested the impact of temperature to ET₀ was much larger than formerly reported if its effect on saturated vapour deficit was taken into account. The results obtained in the current study will help for better understanding of the effects of climate changes to water resource management in the arid land of northwest China. Copyright © 2013 John Wiley & Sons, Ltd.