Spatial distribution and temporal variation of reference evapotranspiration during 1961–2006 in the Yellow River Basin, China

Abstract

To explore the spatial and temporal variations of the reference evapotranspiration (ET_ref) is helpful to understand the response of hydrological processes to climate changes. In this study, ET_ref was calculated by the Penman-Monteith method (P-M method) using air temperature, wind speed, relative humidity and sunshine hours at 89 meteorological stations during 1961–2006 in the Yellow River Basin (YRB), China. The spatial distribution and temporal variations of ET_ref were explored by means of the kriging method, the Mann-Kendall (M-K) method and the linear regression model, and the causes for the variations discussed. The contribution of main meteorological variables to the variations of ET_ref was explored. From the results we found that: (1) the spatial distributions of ET_ref display seasonal variation, with similar spatial patterns in spring, summer and autumn; (2) temporal trends for ET_ref showed large variation in the upper, middle and lower regions of the basin, most of the significant trends (P = 0.05) were detected in the middle and lower regions, and, in particular, the upward and downward trends were mainly detected in the middle region and lower region of the basin, respectively; and (3) sensitivity analysis identified the most sensitive variable for ET_ref as relative humidity, followed by air temperature, sunshine hours and wind speed at the basin scale.

Citation Yang, Zhifeng, Liu, Qiang & Cui, Baoshan (2011) Spatial distribution and temporal variation of reference evapotranspiration during 1961–2006 in the Yellow River Basin, China. Hydrol. Sci. J. 56(6), 1015–1026.

Résumé

Pour explorer les variations spatiales et temporelles de l'évapotranspiration de référence (ET_ref), il est utile de comprendre la réponse des processus hydrologiques aux changements climatiques. Dans cette étude, ET_ref a été calculée par la méthode de Penman-Monteith (méthode P-M) en utilisant les données de température de l'air, de vitesse du vent, d'humidité relative et de durée d'ensoleillement de 89 stations météorologiques du bassin du Fleuve Jaune, en Chine, couvrant la période 1961–2006. La distribution spatiale et les variations temporelles de ET_ref ont été explorées au moyen de la méthode de krigeage, de la méthode de Mann-Kendall (M-K) et du modèle de régression linéaire, et les causes des variations discutées. La contribution des principales variables météorologiques aux variations de ET_ref a été explorée. D'après les résultats nous avons constaté que: (1) la distribution spatiale de ET_ref présente une variation saisonnière, avec des configurations spatiales similaires au printemps, en été et en automne; (2) les tendances temporelles de ET_ref présentent de grandes variations dans les régions supérieures, moyennes et inférieures du bassin, la plupart des tendances significatives ayant été détectées dans les régions moyennes et inférieures, en particulier les tendances à la hausse et à la baisse principalement détectées respectivement dans les régions moyenne et inférieure du bassin; et (3) l'analyse de sensibilité a identifié que la variable la plus sensible pour ET_ref est l'humidité relative, suivie par la température de l'air, la durée d'ensoleillement et la vitesse du vent à l'échelle du bassin.

Key words:

• reference evapotranspiration
• spatial distribution
• temporal trend
• sensitivity analysis
• Yellow River Basin
• China

Mots clefs:

• évapotranspiration de référence
• distribution spatiale
• tendance temporelle
• analyse de sensibilité
• bassin du Fleuve Jaune
• Chine

INTRODUCTION

In face of increasing water stress on the global scale, it is important to improve understanding of hydrological mechanisms underlying ecological patterns and processes (Rodriguez-Iturbe 2000, Zalewski 2000, Porporato et al. 2002). On the one hand, climate and soil control the vegetation dynamics; while on the other hand, vegetation exerts important control on the overall water balance and is responsible for many feedbacks with the atmospheric system (Rodriguez-Iturbe et al. 2001). Precipitation and evapotranspiration are regarded as the most important variables to diagnose climate change and reveal the environmental response to climate change on the basin scale (Yao et al. 2005, Cannarozzo et al. 2006, Liu et al. 2008). The temporal–spatial patterns of precipitation and evapotranspiration influence the eco-hydrological processes, which control the evolution of surface ecosystems (Cannarozzo et al. 2006, Oguntunde et al. 2006, McVicar et al. 2007, Zhan et al. 2008). This type of inquiry is fundamental to understand the coupling existing between ecosystem dynamics and the water cycle (Porporato and Rodriguez-Iturbe 2002, Rodriguez-Iturbe and Porporato 2005), which is important to explore the water needs of ecosystems and to optimize water resources allocation and management (Yang et al. 2005). Estimation of water needs must be adjusted to the atmospheric demand, which is related to the climatic conditions.

To deal with these issues, ET_ref was proposed by the United Nations Food and Agriculture Organization (FAO) for computing crop evapotranspiration, combined with crop coefficients (Allen et al. 1998, Jabloun and Sahli 2008). The ET_ref is defined as “the rate of evapotranspiration from a hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m^-1 and an albedo of 0.23, closely resembling the evapotranspiration from an extensive surface of green grass of uniform height, actively growing, well-watered, and completely shading the ground” (Allen et al. 1998). Now, ET_ref is regarded as one of the most important hydrological variables for scheduling irrigation systems, preparing input data to hydrological water-balance models, and calculating actual evapotranspiration for a region and/or a basin (Xu and Singh 2002, Xu and Li 2003, Gong et al. 2006, Kannan et al. 2007, Yin et al. 2008, Zhou et al. 2009). Furthermore, to obtain useful information for water resource regulation and management, accurate spatial and temporal patterns of ET_ref are also needed (Xu et al. 2006a). Xu et al. (2006a, 2006b) investigated the spatial distribution and temporal trends of ET_ref in the Changjiang (Yangtze River) Basin. The research showed that the highest and lowest values for ET_ref occurred in the upper region and in the middle region of the basin, respectively, and a significant decreasing trend was detected in ET_ref for the whole catchment because of a significant decreasing trend in net total radiation and, to a lesser extent, a significant decrease in the wind speed.

Considering the influence of topography and land-surface conditions on the forcing variables, McVicar et al. (2007) used an “interpolate-then-calculate” approach to obtain spatially-distributed ET_ref, and their results demonstrated that the distribution of monthly ET_ref with high spatial resolution can be spatially modelled while taking into account the influence of topography. In order to explore the spatial distribution of temporal trends on the basin scale, it is most important to understand the mechanism of interaction between climate, vegetation and hydrological processes, and to forecast the hydrological processes using hydrological models (Yao and Creed 2005). This can provide useful information to optimize the water resource management and maintain the ecosystem integrity. However, investigating the spatial distribution of temporal trends in ET_ref time series still remains a difficult task due to their complex and nonlinear nature in different regions, and relatively little research has been conducted on it (Cohen et al. 2002, Xu et al. 2006a, McVicar et al. 2007).

The objectives of this study are: (a) to calculate ET_ref with the Penman-Monteith (P-M) method using air temperature, wind speed, relative humidity and sunshine hours, and to analyse the spatial distribution of ET_ref in different seasons; (b) to explore temporal trends and their spatial distribution by the non-parametric Mann-Kendall (M-K) method and a linear regression model; and (c) to conduct sensitivity analysis to investigate the relative change in annual ET_ref due to relative change in the four meteorological variables: air temperature, wind speed, relative humidity and sunshine hours. All tests were based on ET_ref series calculated at 89 meteorological stations from the period 1961–2006 in the Yellow River Basin (YRB), China.

STUDY AREA

The Yellow River is about 5400 km long with a drainage area of 7.95 × 10⁵ km² (Fig. 1). It directly supports a population of 107 million people (McVicar et al. 2007). Originating from the Tibetan Plateau, the river flows through the Loess Plateau and North China Plain, and runs into the Bohai Sea. From the headstream to the estuary of the Yellow River, the watershed characteristics vary with the changes in topography and elevation. The area from upstream to Lanzhou, well covered by vegetation, is the main source of water resources, and about 54% of the river runoff is from this region (Jia et al. 2006). The headwater part of the Yellow River Basin, in particular, is covered by snow and frozen soil throughout the whole year. As the river flows through the Loess Plateau, most of the erosion is produced by the rainstorms that frequently occur in the flood season, combined with the loose soil texture and sparse vegetation in this region (Jia et al. 2006). As a result of high erosion rates from the Loess Plateau and the continuous presence of levees and dykes, the well-known suspended river has formed in the lower reach of the YRB—the bottom of the river bed is, in places, 20 m above the surrounding land surface (Li 2003). As most of the basin is located in arid and semi-arid regions, precipitation is concentrated in intense, but infrequent, storms (Yu 2002). The increase in agricultural and industrial water use, combined with a decrease in precipitation, has contributed to the decrease in runoff and drying-up in the YRB (Liu and Cheng 2000, McVicar et al. 2002, Liu 2004, Yang et al. 2004, Cong et al. 2009). According to Liu et al. (2008), precipitation in the YRB presented decreasing trends at most stations during 1961–2006. Yang et al. (2004) investigated the causes of drying up of the Yellow River and found that this can be attributed to the processes of precipitation and evaporation, as well as irrigation. Cong et al. (2009) found the simulated natural runoff follows a similar trend to the precipitation in the YRB during the last half century, and this implies that changes in the natural runoff are mainly controlled by the climate variability and change rather than land-use change. Chen et al. (2006) explored the variations of P-M ET_ref and its causes on the Tibetan Plateau. They detected negative trends in P-M ET_ref for the Tibetan Plateau. Changes in wind speed and, to a lesser degree, in relative humidity were found to be the most important meteorological variables affecting P-M ET_ref trends on the Tibetan Plateau while changes in sunshine duration played an insignificant role.

Fig. 1 Location of the YRB and the meteorological stations used in this study (▴). The two straight lines show the division of the basin into upper, middle and lower regions.

DATA AND METHOD

Data

The time series of the monthly records of air temperature, wind speed, sunshine hours and relative humidity for the period 1961–2006 at 89 meteorological stations in the YRB, China were used in this study. The data were provided by the National Climate Centre (NCC) of the China Meteorological Administration (CMA). The location of the stations in YRB is shown in Fig. 1. The annual values of ET_ref were obtained by summing monthly ET_ref at each of the 89 station for 1961–2006, calculated from the mean monthly data of air temperature, wind speed, sunshine hours and relative humidity by the P-M method.

In order to have a rough idea on the climate of the study region, the basin was divided into three parts, mainly according to the topography and elevation (Fig. 1). The dividing line for the upper and middle regions is mainly along the border of the Tibetan Plateau and the Loess Plateau, at about 2000 m above sea level (m a.s.l.), while that between the middle and lower regions is mainly along the dividing line of the Loess Plateau and the plains, at about 1000 m a.s.l. The mean elevations for the upper, middle and lower regions are 3693, 1403 and 677 m a.s.l., respectively.

The mean monthly values of the major meteorological variables were plotted (Fig. 2) for the upper, middle, and lower regions, and the whole basin. The variations in the meteorological variables indicate that: (a) the monthly variation of air temperature in the lower region is greatest, followed by that in middle and upper regions; (b) the relative humidity is higher in the lower region than in other regions in all months except for June, and the maximum relative humidity occurs in the period July–September in the basin; (c) the maximum wind speed occurs in April for all regions, and wind speed is higher in the lower region than that in other regions; and (d) sunshine hours present a similar pattern in the middle and lower regions with a maximum value occuring in June, but the value is relatively higher in April, August and November in the upper region of the YRB.

Fig. 2 Mean monthly variations of the key meteorological variables for: the upper, middle and lower regions (see Fig. 1) and whole YRB in the period 1961–2006: (a) air temperature; (b) relative humidity; (c) wind speed; and (d) sunshine hours.

METHOD

The Penman-Monteith method

The P-M method is a physically-based model for estimating ET_ref, which explicitly incorporates both radiative and aerodynamic parameters (Xu et al. 2006a, McVicar et al. 2007). It has been accepted as the most accurate method to estimate the ET_ref for its better results when compared with other equations in various regions of the world (López-Urrea et al. 2006), and recommended by the FAO as the best method to determine ET_ref (Allen et al. 1998). The P-M method (equation (1)(1)) was selected to estimate ET_ref in this study:

(1)

where ET_ref is the reference evapotranspiration (mm d^-1), R_n is the net radiation at surface (MJm^-2 d^-1), G is the soil heat flux density (MJm^-2 d^-1), T is the mean daily air temperature at 2 m height (°C), u ₂ is the wind speed at 2 m height (m s^-1), e_s is the saturation vapour pressure (kPa), e_a is the actual vapour pressure (kPa), e_s – e_a is the saturation vapour pressure deficit (kPa), Δ is the slope of the vapour pressure curve (kPa °C^-1), γ is the psychrometric constant (kPa °C^-1). If the time-step of all data is monthly then the resultant ET_ref is provided with units of mm month^-1 (Allen et al. 1998, McVicar et al. 2007). One can calculate Δ and R_n from the following equations:

(2)

(3)

(4)

(5)

where, n is the actual duration of sunshine hours; N is the potential sunshine hours; and R_a is the extra-terrestrial solar radiation (MJ m^-2 d^-1). The values of N and R_a can be obtained from standard tables (Allen et al. 1998) for different latitudes and months. Further, R _nl is the net outgoing longwave radiation (MJm^-2 d^-1); σ is the Stefan-Boltzmann constant (4.903 × 10^-9 MJK^-4 m^-2 d^-1); T _{max, K} and T _{max, K} are the maximum and minimum absolute temperature during a 24-h period (K = °C + 273.16); and a_s and b_s are regression constants.

Spatial interpolation

There are many algorithms available to interpolate spatially-distributed hydrological and climatic data (McVicar et al. 2007). In this study, kriging with spherical variogram (kriging method), inverse distance weighted (IDW) and spline method were selected to test annual ET_ref. These methods have been frequently used to interpolate data in hydrology (Yao and Creed 2005, Daly 2006). According to the spatial cross-validation, the correlation coefficients between the interpolated and original values of ET_ref were 0.96, 0.74 and 0.93 for the kriging method, IDW and spline method, respectively. So the kriging method was selected in the study for interpolating the mean seasonal and mean annual values at 89 stations at 30-km resolution.

The kriging method is a technique of making optimal, unbiased estimations of regionalized variables at unsampled locations, and has been preferred by researchers particularly when applied to data obtained from a low-density and irregularly spaced network (Goovaerts 2000, Campling et al. 2001, Xu et al. 2006a, Basistha et al. 2008). The description of kriging theory and its application can be found in Journel and Huijbregts (1978). The general equation of kriging estimator is:

(6)

where x denotes the set of spatial coordinates (x, y); and λ_i is the weight associated with the ith observation point, x_i .

Temporal trends

In order to test the significance of the trend existing in ET_ref series, both the non-parametric M-K method and the linear regression model were performed. The non-parametric M-K method is used to detect abrupt climate change against trend (Mann 1945, Kendall 1948), and has been widely used and tested as an effective method to evaluate the presence of a statistically significant trend in hydrological and climatological time series (e.g. Douglas et al. 2000, Birsan et al. 2005). The linear regression model is the most common technique of statistical diagnosis and forecasting in modern climate, and has been used to detect patterns in meteorological variables (Hameed et al. 1997, Wei 1999, da Silva 2004). In our study, the linear trends in the series of ET_ref were calculated by the least squares regression, and the estimated slopes were tested against the hypothesis of null slope by means of a two-tailed T test at the 95% confidence level (Serrano et al. 1999). The M-K method is expressed as described below.

Under the null hypothesis of no-trend, the time series of a variable has no change; the time series could be regarded as x ₁, x ₂, … , x_n . For each term, m_i is computed as the number of x_i in the series whose values exceeded x_j (1 ≤ j ≤ i). The test statistic is calculated as follows:

(7)

Assuming that the series is random and independent, the expected value E(d_k ) and variance of may be shown as follows:

(8)

We define:

(9)

The terms of u(d_k ) (1 ≤ k ≤ n) constitute curve C₁.

The null hypothesis of no trend will be rejected at a confidence level of α if the standard normal probability Pr(|u| < |u(d_k )|) > α.

Applying the method to the inverse series, is computed as the number of x_i in the series whose values exceeds x_j (i ≤ j≤ N). When and we could obtain the series of as follows:

(10)

The terms of (1 ≤ k ≤ n) constitute curve C₂.

If C₁ exceeds the confidence line ±1.96 (P = 0.05), it means that there is a significant upward or downward trend in the series. Based on this, if the intersection point of curves C₁ and C₂ is between the two confidence lines, we can consider that abrupt climate change takes place at that point (Fu and Wang 1992).

Sensitivity analysis

As a synthetic climatic variable, ET_ref, reflects the combined effects of many climatological factors. Sensitivity analysis is important to understand the relative importance of climatic variables to the variation of ET_ref (Xu et al. 2006a). A simple but practical way of sensitivity analysis is to calculate and plot the relative changes of an input variable against the resultant relative change of the output variable as a curve (Goyal 2004, Gong et al. 2006, Xu et al. 2006a). Then the corresponding relative change of the outcome can easily be read from the sensitivity curve for a certain relative change of the variable.

In this study, seven scenarios are generated for each meteorological variable using equation (11)(11):

(11)

where X is the meteorological variable and t is the time in day.

RESULTS AND DISCUSSION

Spatial distribution of seasonal and annual reference evapotranspiration

The spatial distributions of seasonal and annual ET_ref are plotted in Fig. 3, which reflects the combined effects of meteorological variables in different regions. The results are as follows:

Fig. 3 Spatial distributions of mean seasonal and annual ET_ref during 1961–2006 in the YRB, China.

a.	ETref, influenced by the seasonal variations of meteorological variables, demonstrated different spatial patterns in all seasons and the year. The lowest seasonal and annual values for ETref were found in the upper region of the YRB. The relatively low air temperature and wind speed caused low ETref values in the upper region during the whole year.
b.	The distributions of ETref in spring, summer and autumn presented similar patterns in the whole basin. The relatively high values of ETref extend in the northeast portion of the middle region. As seen from Fig. 2, the relatively high air temperature, wind speed, sunshine hours and low relative humidity were the main causes for high ETref values in the middle region in spring, summer and autumn.
c.	In winter, the centre of high values of ETref moved to the lower region, while that of low ETref moved to the northern part of the middle region, compared to the other seasons. As air temperature presented similar temporal variations, it contributed little to the difference in spatial pattern in the three regions during different seasons. The higher wind speed and relative humidity mainly contributed to higher ETref in the lower region and lower ETref in the middle region, respectively, in the winter.

The spatial distribution of ET_ref, combined with land cover and soil water content, has been used to estimate the ecological water requirement (Yang et al. 2005), which can provide more valuable information for water resources planning and management at the basin scale (Xu et al. 2006a, Liu et al. 2010).

Trend analysis of annual reference evapotranspiration

The M-K method with a nominal rejection rate of 5% was applied to 89 annual ET_ref series. The Yangcheng station (113°53′E, 35°19′N) was selected as an example to demonstrate the abrupt change occurring in the time series of ET_ref. It revealed that the downward abrupt change occurred in 1986 (Fig. 4).

Fig. 4 The abrupt change tested by the Mann-Kendall method for annual ET_ref series of Yangcheng station for 1961–2006. Here, as the line C₁ is over the confidence line (P = 0.05), the cross-over point of C₁ and C₂ is the start point of abrupt change in this series.

Significant trends The significant trends for different stations are shown in Fig. 5: 79 of the 89 stations showed a significant trend (P =  0.05). Among these 79 stations with significant trend, 51 showed an upward trend, and 28 a downward trend. The distribution of temporal trend for ET_ref indicated that:

Fig. 5 The upward trends (▴), downward trends (▪), and no trends (○) in annual ET_ref in the YRB, China in the 1961–2006 period, detected by the Mann-Kendall method.

a.	Among 24 stations in the upper region, six showed a downward trend, 12 exhibited an upward trend, and the other six stations showed no significant trend (60% of all stations with no significant trend in the basin).
b.	Thirty-one (31) of 41 stations (61%) exhibited a significant upward trend in the middle region, only seven stations showed a downward trend, and three stations presented no trend
c.	In the lower region, 15 of 24 stations displayed a downward trend, only eight stations and one station showed an upward trend and no trend, respectively.

Time and frequency of abrupt changes The time and frequency of the abrupt changes in ET_ref tested by the M-K method are shown in Fig. 6. The results show that:

Fig. 6 The time and frequency of the abrupt changes in ET_ref detected by the M-K method in the YRB in the 1961–2006 period, with the years when abrupt changes occurred (where two abrupt changes were detected at one station, the years are in brackets).

a.	Of 79 stations, two abrupt changes occurred in 16 stations and one abrupt change in the other stations. The timing of the abrupt changes in ETref series was between 1963 and 2003.
b.	There were 95 abrupt changes in the 79 stations with significant trend: the number of these occurring during 1961–1970, 1971–1980, 1981–1990, 1991–2000 and 2001–2006 were 26, 24, 14, 25 and 6, respectively.
c.	Four of 24 (16.67%) and 11 of 41 (26.83%) stations were detected with two abrupt changes in the lower and middle regions, respectively, while there was only one station with two abrupt changes in the upper region.
d.	Between 1961 and 2006, the abrupt changes in the lower and middle regions were relatively earlier than those in the upper region of the YRB.

The reasons for temporal variation of ET_ref result mainly from the complicated watershed characteristics which influence the response of ET_ref to the climate changes in the different regions of the YRB. From east to west, the mean elevation in the lower, middle and upper regions is 677, 1403 and 3693 m a.s.l., respectively, which may influence the variations in regional climate; furthermore, the variation in the vegetation, presenting obvious regional characteristics, has an important influence on the regional climate (Li and Yang 2004). In addition, the Asian monsoon influences the meteorological conditions in different regions of the YRB (Ye and Gao 1979, Cui et al. 2006), and the Tibetan Plateau, in particular, plays an important role in forming and inducing the variations in regional weather and climate in the YRB (Liu and Yin 2002). Xu and Ma (2009) noted that, influenced by the global climate changes, the East Asian summer monsoon intensity had changed significantly in the past 50 years, leading to a response by the water cycle of the YRB. All these factors can result in regional characteristics in the meteorological variables, e.g. decreasing trends from east to west presented by precipitation in the YRB (Liu et al. 2008).

Fitted data to linear regression model

Figure 7 shows the results of the least-squares analysis. Thirty-eight stations showed a negative trend of ET_ref, with an average annual increase of –1.7 mm year^-2, while 51 stations had a positive trend, with an average annual change of 1.2 mm year^-2. About 47% of stations (42 of 89) showed significant trend at the 95% confidence level on a basin scale, and most trends revealed by the linear regression model were consistent with those obtained by the M-K method. As influenced by meteorological variables, the trends in ET_ref revealed by the linear regression model also showed different characteristics in different regions:

Fig. 7 Trends (mm year^-2) for the annual ET_ref from 1961 to 2006 in the YRB, China. Circles placed around the dots denote significant trend (0.05 level).

a.	In the upper region, the average trend of ETref was –1.7 and 1.0 mm year-2 for the seven negative and 17 positive trend stations, respectively. Only one station displayed negative trend among the eight significant trend stations, but its abrupt change was upward. One among the other seven stations with significant positive trends showed an abrupt downward change.
b.	The negative and positive trends were detected in 12 and 29 stations, respectively, in the middle region, with an average slope of –1.38 and 1.52 mm year-2 average change, which are larger than those in the upper region. Fourteen of the 23 significant trend stations displayed positive trend, with upward trend detected by the M-K method. Among the nine negative significant trend stations, one station showed no abrupt changes and one showed two upward changes (in 1963 and 1998).
c.	In the lower region, about 79% of stations (19 of 24) showed negative trends, with the average change of –1.9 mm year-2, and the remaining five stations displayed positive trend with an average increase of 0.9 mm year-2. Seven stations showed significant negative trend and four showed significant positive trend.
d.	The average slope for ETref is 0.19, 0.67 and –1.34 mm year-2 during 1961–2006 in the upper, middle and lower regions of the YRB, respectively.

Significant increasing trends (P = 0.05) in air temperature have been reported by Liu et al. (2010). The causes for the decreasing trends in pan evaporation and ET_ref with the increases in air temperature have been explored by several researchers (e.g. Roderick and Farquhar 2002, 2004, Roderick et al. 2007, 2009a, b). In China, some studies also have been performed to reveal this problem (e.g. Xu et al. 2006b, Cong and Yang 2008, Liu et al. 2010). Cong and Yang (2008) investigated causes for the changes in pan evaporation from 1956 to 2005; their results showed that pan evaporation decrease is caused by decreasing radiation and wind speed before 1985 and pan evaporation increase is caused by decreasing vapour pressure deficit due to strong warming after 1986. According to Liu et al. (2010), the decreasing trends in radiation and wind speed caused ET_ref to decrease, and significant decreasing trends (P = 0.05) in wind speed is the main cause for decreasing trends in ET_ref in the lower region of the YRB.

Sensitivity analysis of reference evapotranspiration

The relative change in annual ET_ref due to relative change in meteorological variables is presented in Fig. 8. This shows that the two most sensitive variables are relative humidity and air temperature, followed by sunshine hours and wind speed. In response to the change in temperature by ±30%, ET_ref varies between ±13%. The ET_ref is less sensitive to decreasing temperature in comparison to increasing temperature, e.g. ET_ref reduces by –12.72% when air temperature decreases by –30%, while it increases by 13.01% with an increase of 30% in air temperature. This result is consistent with that addressed by Goyal (2004). The ET_ref showed an increasing trend with the decrease in relative humidity (e.g. ET_ref increases by 14.52% with a decrease of 30% in relative humidity). Wind speed and sunshine hours affect ET_ref in a similar pattern, despite a little higher magnitude for sunshine hours. The ET_ref is more sensitive to the decreased wind speed and increasing sunshine hours in comparison to increasing wind speed and decreasing sunshine hours. The ET_ref increases by 4.09% and 7.02% with an increase of 30% in wind speed and sunshine hours; while it reduces by 4.62% and 6.71% with a decrease of 30% in wind speed and sunshine hours, respectively. All of these results indicate that, influenced by radiometric and aerodynamic variables, the changes of ET_ref with increasing or decreasing different meteorological variables presents a nonlinear relationship (McVicar et al. 2007, Liu et al. 2010). Furthermore, the contribution of changes in the meteorological variables to the change in ET_ref in the basin should be considered with the trends of ET_ref and meteorological variables. This will be explored in the future to obtain more useful information to regulate water allocation and management for the YRB.

Fig. 8 The relative change in ET_ref due to changes in air temperature, wind speed, relative humidity and sunshine hours, respectively.

CONCLUSIONS

The ET_ref was calculated by the Penman-Monteith (P-M) method using monthly air temperature, wind speed, relative humidity and sunshine hours at 89 standard meteorological stations from 1961 to 2006 in the YRB and then regionally mapped. Using the Mann-Kendall (M-K) method and linear regression model, temporal trends and the spatial distribution of the ET_ref were explored, and then the sensitivity of ET_ref to the main meteorological variables was investigated. The following conclusions can be drawn:

1.	As affected by seasonal variations in the meteorological variables, the spatial distribution of ETref presented seasonal variations. Similar spatial distribution patterns of ETref were found in the spring, summer and autumn. The ETref, influenced by the changes in meteorological variables, presented different spatial patterns in winter: the centres of the high and low values of ETref moved to the lower region and the northern part of the middle region of the basin, respectively.
2.	The results of the M-K method indicated that 79 stations experienced abrupt changes in the last 46 years, 51 with upward trends and 28 with downward trends. The distribution of temporal trend in ETref also displayed spatial variation in different regions of the basin. The time and frequency of the abrupt change in ETref demonstrated that stations featured two abrupt changes mainly in the middle and lower regions of the YRB, and the abrupt changes in the lower and middle regions were relatively earlier than those in the upper region of the YRB. The trends of ETref revealed by the linear regression model exhibited almost the same spatial distribution pattern as those detected by the M-K method, and 42 among the 89 stations got through the T test at the 95%. confidence level
3.	Sensitivity analysis showed that the most sensitive variable for ETref in the YRB is relative humidity, followed by air temperature, sunshine hours and wind speed. The ETref showed an increasing trend with the decrease in relative humidity and vice versa, and it was less sensitive to the decreasing temperature in comparison to increasing temperature. Wind speed and sunshine hours affect ETref in a similar pattern, despite a slightly higher magnitude for sunshine hours. The ETref was more sensitive to decreasing wind speed and increasing sunshine hours in comparison to increasing wind speed and decreasing sunshine hours.

Acknowledgments

This research is supported by the National Science Foundation for Distinguished Young Scholars of China (no. 50625926), the Major State Basic Research Development Programme of China (973 Program) (no. 2010CB951104 and no. 2006CB403303) and the National Natural Science Foundation of China (no. 40701189). The authors are also grateful to the National Meteorological Information Center, China Meteorological Administration for providing the meteorological data. The authors thank two anonymous reviewers and the editors for their detailed and constructive comments.