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Spatial variation of climatology monthly crop reference evapotranspiration and sensitivity coefficients in Shiyang river basin of northwest China
Agricultural Water Management 97 (2010) 1506–1516
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Spatial variation of climatology monthly crop reference evapotranspiration and sensitivity coefficients in Shiyang river basin of northwest China Xiaotao Zhang a , Shaozhong Kang a,∗ , Lu Zhang b,∗∗ , Junqi Liu a a b
Center for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China CSIRO Land and Water, Christian Laboratory, GPO Box 1666, Canberra, ACT 2601, Australia
a r t i c l e
i n f o
Article history: Received 27 November 2009 Accepted 3 May 2010 Available online 12 June 2010 Keywords: Crop reference evapotranspiration Penman–Monteith ANUSPLIN Sensitivity analysis Shiyang river basin
a b s t r a c t Crop reference evapotranspiration (ET0 ) is often used to determine crop water requirement. ET0 maps are useful for regional agricultural and water resources management, and also play an important role in the distributed hydrological modeling. For generating spatial ET0 surfaces, ‘Interpolate-then-calculate (IC)’ approach is powerful in principle and is recommended especially for sparse weather station networks. The partial thin-plate smoothing spline incorporated in ANUSPLIN for interpolating climatic variables has been accepted widely across the world. In this paper, the climatology monthly ET0 data of Shiyang river basin, one of the three inner basins in northwest China, are developed by spatially modeling the input climatic parameters with ANUSPLIN, and from the interpolated climate and ET0 datasets, sensitivity coefficients of ET0 to the climatic variables of selected months are also spatially distributed. In the cool months (January, February, November and December), the spatial variability of ET0 is small and the value is rather low, whereas the warm season (May, June, July and August) is characterized by high values of ET0 and large spatial variations in the river basin. Vapor pressure deficit is the most sensitive variable during the cool months and in the mountainous area with lower temperature; mean air temperature is the least sensitive one during the year and a little variation is observed at the basin scale. In summer, available energy primarily forces ET0 as expected, and in winter, wind speed plays an important role and affects ET0 greater at the northern plain region where deserts are dominated by dunes and low shrubs. We conclude that for regions with isolated climate stations, ‘IC’ procedure by including topographic and geographic factors can effectively model spatially distributed ET0 . © 2010 Elsevier B.V. All rights reserved.
1. Introduction Crop reference evapotranspiration (ET0 ) is an important variable in the agrohydrological systems, which depends only on climatic parameters and provides the evapotranspiration of an ideal and well-watered grass surface. Actual crop evapotranspiration can be derived from ET0 by means of proper crop and water stress coefficients (Rana and Katerji, 2000; Kite and Droogers, 2000). A number of equations are available for estimating ET0 (e.g. Penman, 1948; Blaney and Criddle, 1950; Hargreaves and Samani, 1985; FAO-56 Penman-Monteith, 1998). Among these equations, FAO-56 Penman–Monteith equation (P–M) that incorporates both energy balance and aerodynamic theory, is considered to be the most appropriate model to predict ET0 and is recommended by the Food and Agriculture Organization of the United Nations (FAO) as
∗ Corresponding author. Fax: +86 10 6273 7611. ∗∗ Co-corresponding author. Fax: +61 2 6246 5800. E-mail addresses: [email protected] (S. Kang), [email protected] (L. Zhang). 0378-3774/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2010.05.004
the standard for computing ET0 from full climate records (Allen et al., 1998; Xu et al., 2006). Annual and monthly ET0 maps provide valuable information in regional management of cropping system, evaluation of agricultural water use, water resources monitoring and management and agro-climatic zoning. The spatial variability of ET0 is also useful for distributed hydrological modeling. Two different approaches, ‘Calculate-then-Interpolate (CI)’ and ‘Interpolate-then-Calculate (IC)’ (McVicar and Jupp, 2002; Stein et al., 1991), are compared by many researchers for generating spatial ET0 maps. Mardikis et al. (2005) evaluated the two procedures when plotting the long-term mean daily ET0 for each month in Greece using four interpolation methods, including Ordinary Kriging (OK), Inverse Distance Squared (IDS), Residual Kriging (RK) and Gradient plus Inverse Distance Squared (GIDS). They found that IC–GIDS combination ranked first with the lowest mean absolute error (0.1207 mm) and root mean squared error (0.0367 mm) averaged over all months, and had a slight superiority over CI–GIDS. Ashraf et al. (1997) concluded that the IC procedure provided lower root mean squared error of ET0 than the CI procedure. Although Bechini et al. (2000) stated that the IC procedure would increase the error of model application if
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Fig. 1. The meteorological stations in and around Shiyang river basin, and its digital elevation model (DEM) with a spatial resolution of 0.02◦ × 0.02◦ in longitude and latitude.
the spatial and temporal structures of the model inputs were not reliable, the IC approach is powerful in principle, for each of the input parameters may have the specific spatial correlation structure (Heuvelink and Pebesma, 1999). Using IC will provide accurate ET0 surfaces for partial station networks (Ashraf et al., 1997), as the near-surface elevation dependence is not equivalent for each climatic variable (McVicar et al., 2007). Various interpolation methods have been applied to spatially model the input climatic variables such as air temperature, precipitation, and wind speed; and those incorporating the topographical and geographical forcing factors (e.g. elevation, distance to the sea, latitude and longitude) affecting the spatial climate patterns often demonstrate better results (Goovaerts, 2000; Lloyd, 2005; Luo et al., 2008). ANUSPLIN, a software package developed by Hutchinson (2004), is a mathematical approach to generate hydrometeoro-
logical maps at varying spatial and temporal scales. It is based on the thin-plate smoothing spline methods, which is primarily described by Wahba and Wendelberger (1980). A key feature of ANUSPLIN is that it includes a linear covariate to represent the elevation effect on climatic data, being termed the partial thin-plate splines (Hutchinson, 1991). Price et al. (2000) compared ANUSPLIN with GIDS, which outperformed six other interpolation methods (Nalder and Wein, 1998) to spatially map monthly mean minimum and maximum air temperature and precipitation in Canada. The result showed that the root mean squared errors obtained using ANUSPLIN were lower than those of GIDS for most months. Jeffrey et al. (2001) have applied ANUSPLIN algorithm to construct the interpolated surfaces of daily maximum and minimum air temperature, solar radiation, vapor pressure and pan evapotranspiration of Australia. Shen et al. (2008) established annual and monthly
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Table 1 Descriptive statistics of elevation (m) for the 32 stations (4 stations in and 28 stations around Shiyang river basin).
4 stations 28 stations
the total water consumption by different sectors that totalled 28.54 × 108 m3 (Tong et al., 2007).
Max
Min
Mean
SD
3. Data and method
3045.1 3662.8
1367.0 1177.4
1979.8 2208.2
755.4 765.6
3.1. Climate data
SD is the standard deviation.
vapor pressure grid datasets of China through ANUSPLIN, and the resultant surfaces indicated a good linear correlation between the measured and the corresponding grid values. All the work provides strong support for using ANUSPLIN in climate interpolation. ANUSPLIN has been applied to generate spatial surfaces of monthly ET0 for Coarse Sandy Hilly Catchment located in Loess Plateau of China by McVicar et al. (2007), in which the forcing meteorological variables, including maximum and minimum air temperature, wind speed and vapor pressure, were interpolated using the partial thin-plate splines with a linear dependency on elevation. McVicar et al. (2007) showed how the near-surface elevation dependence (a lapse rate for air temperature) varies as a function of input variable and month of year. To validate their resultant ET0 surfaces they also interpolated pan evaporation rates from 20-cm diameter Chinese micro-pans, and calculated the pan coefficient (Kpan ) which varied from 0.44 in April to 0.65 in August. The slightly lower values of the Kpan (than what is expected for a Class A pan) were attributed to the different geometry of the micro-pan. Tong et al. (2007) spatially distributed the average seasonal crop evapotranspiration (ETc ) of spring wheat during the 1950s–2001 for Shiyang river basin, where a multiple regression relationship between ETc and elevation, latitude and aspect was used and the CI approach was performed. To understand the relative importance of climatic variables in the P–M model, a sensitivity analysis is required and the results from sensitivity analysis are of vital significance for determining the effect of climate change on ET0 . Several papers have carried out sensitivity analysis of ET0 to meteorological data in different climates (Saxton, 1975; Rana and Katerji, 1998; Goyal, 2004; Irmak et al., 2006), but they all restricted to a single station. Gong et al. (2006) conducted a sensitivity analysis of P–M ET0 to key meteorological variables (air temperature, wind speed, relative humidity and shortwave radiation) in Changjiang basin and derived the spatial variation of sensitivity coefficients by interpolating the station estimates. The objectives of this paper were: (1) to develop the climatology monthly crop ET0 maps of Shiyang river basin, an inner basin in northwest China with sparse data inside the area by interpolating the major input climatic variables with spline models incorporated in ANUSPLIN; and (2) to estimate the spatial variations of climatology sensitivity coefficients from the interpolated surfaces, in an attempt to understand the relative roles of main climatic variables in the P–M model at the regional scale. 2. Study area Shiyang river basin, located at the east part of the Hexi Corridor, Gansu Province of northwest China (Fig. 1), covers an area of 4.16 × 104 km2 . The basin is topographically variable. The Qilian mountains in the south, where the river originates, reach 5150 m above sea level; the middle of the basin is the plain region between the elevation of 1400 m and 2000 m; the elevation of Minqin oasis in the north, where the river ends, is 1256–1400 m. Due to the topographical differences, the basin exhibits typical semi-arid to arid climatic features from south to north, with the annual precipitation ranges 600–50 mm, and the annual pan evaporation is 700–2600 mm (Ma et al., 2008). Agriculture is the biggest water user in the river basin. In 2000, irrigation accounted for 86% of
The National Meteorological Centre of China operates 32 stations in and around Shiyang river basin (Fig. 1). The 4 stations in the basin are distributed in the upper, middle and lower reaches, with an elevation range of 1678.1 m (Table 1). Daily meteorological data of 32 stations were collected from China Meteorological Data Sharing Service System for the period of January 1959–December 2008 (50 years), with mean, maximum and minimum air temperature, relative humidity and bright sunshine hours at 2 m height, and wind speed measured at 10 m height. These measured daily data were converted to standard input parameters for the ET0 model (see the following section) and the standard daily means were averaged in each month for the 50 years. 3.2. Calculation of reference evapotranspiration The P–M method for estimating daily reference evapotranspiration (Allen et al., 1998) is: ET0 =
0.408(Rn − G) + (900/(Tmean + 273))u2 (es − ea ) + (1 + 0.34u2 )
(1)
where ET0 is reference evapotranspiration (mm day−1 ), the slope of the saturation vapor pressure curve (kPa ◦ C−1 ), Rn the net radiation at the surface (MJ m−2 day−1 ), G the soil heat flux (MJ m−2 day−1 ), Rn − G the available energy (MJ m−2 day−1 ), ␥ the psychrometric constant (kPa ◦ C−1 ), Tmean the mean temperature at 2 m height (◦ C), u2 the mean daily wind speed at 2 m height (m s−1 ), es the saturation vapor pressure (kPa), ea the actual vapor pressure (kPa) and es − ea is vapor pressure deficit (kPa).The computation of all data required for calculating daily reference evapotranspiration followed the procedures in FAO paper 56 (Allen et al., 1998). To obtain the total monthly evapotranspiration, Eq. (1) was multiplied by the number of days for a given month. Pearson correlation coefficients were calculated at the 32 stations between climatology monthly ET0 and geographical factors (latitude and elevation) to understand the spatial patterns of the ET0 surfaces. 3.3. Interpolation of climate data The spline models implemented in ANUSPLIN version 4.3 was used to interpolate monthly average daily climatic data of the 32 stations into a grid of 0.02◦ × 0.02◦ in longitude and latitude. In order to analyze the effect of elevation on the climatic variables of the observed stations, Pearson correlation coefficients were firstly computed between the monthly average daily climatic data and elevation at the 32 stations using SPSS 15.0. Based on the previous work (McVicar and Jupp, 2002; McVicar et al., 2007), a second-order or third-order partial thin-plate spline with latitude, longitude as independent variables and elevation as a covariate was chosen to interpolate all climatic variables because they produced lowest square root of generalised cross-validation (RTGCV) errors as compared with some other settings (e.g. secondorder spline with latitude, longitude and elevation as independent variables), and climatic data rarely exhibit high degree of spatial continuity by higher order spline (Hutchinson, 1998). By including elevation as a covariate, the partial thin-plate spline determines the approximately linear dependence of climate on elevation, which is termed a lapse rate for air temperature (mean, maximum and minimum) and the near-surface elevation dependence (NSED) for other meteorological variables (McVicar et al., 2007). As the spline
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Fig. 2. Monthly mean daily values of: (a) Tmean (◦ C); (b) Tmax (◦ C); (c) Tmin (◦ C); (d) Rs (MJ m−2 day−1 ); (e) ea (kPa); (f) u2 (ms−1 ); (g) VPD (kPa); (h) Rn − G (MJ m−2 day−1 ). The average of 32 stations (black solid line), the average of 4 stations in the river basin (red solid line), ±1 standard deviation (dashed lines), and the maximum and minimum (dash-dot lines) are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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models fit a continuous surface of the points, the smoothing surface does not necessarily go through each observed point (Hijmans et al., 2005). 3.4. Sensitivity analysis of the reference evapotranspiration to meteorological variables McKenney and Rosenberg (1993) and Goyal (2004) conducted sensitivity analyses on ET0 , in which the relative changes of an input climatic variable within a range against relative changes of the output ET0 were plotted as a sensitivity curve. Irmak et al. (2006) derived sensitivity coefficients by dividing the amount of increase/decrease in ET0 by the unit of increase/decrease in each climate variable on a daily basis as: SC =
ET0 CV
(2)
where SC is the sensitivity coefficient; CV is the unit change in the climatic variable; ET0 (mm day−1 ) is the change in ET0 with respect to changes in climatic variables. However such sensitivity coefficient is sensitive to the magnitude of ET0 and climatic variables. To get a non-dimensional sensitivity coefficient, we normalize SC as: SC =
ET0 /ET0 CV/CV
(3)
where SC is the dimensionless sensitivity coefficient; ET0 , CV are the base values before change. The SC value of −0.1 would suggest that a 10% increase in CV may be expected to decrease ET0 by 1%. In this study, sensitivity analyses for daily average ET0 in each month were firstly conducted at the four stations inside the study area from −20% to +20% at an interval of ±5% (eight scenarios) to each of the four variables (i.e. mean air temperature, vapor pressure deficit, wind speed at 2 m above the ground and available energy) while keeping all the other parameters constant. And then sensitivity curves for the average changes of the four stations were plotted. If the sensitivity curve is linear, the sensitivity coefficient is able to represent the change in ET0 caused by any perturbation of the climatic variable concerned (Gong et al., 2006). This is the basis for calculating spatially distributed sensitivity coefficient. At regional scale, sensitivity analyses were conducted at each grid cell from the interpolated climate data and ET0 maps and the sensitivity coefficient maps for each month were obtained by averaging grid values of the eight scenarios. 4. Results and discussion 4.1. Characteristics of climatic data and the interpolated climate surfaces General characteristics of the standard daily mean climatic data at the 32 observed stations for the 12 months are illustrated in Fig. 2. Monthly mean daily data of the four stations located in the basin are also averaged (Fig. 2). Unlike mean, maximum and minimum temperature (Tmean , Tmax , Tmin ) have the mono-peak in July (Fig. 2a–c), maximum Rs occurs in June (Fig. 2d), which is governed by the relative summer–winter daylength differences and modulated by increasing cloud cover associated with the summer monsoons (McVicar et al., 2007). The maximum ea is observed in the rainy season (July and August), and the minimum value is experienced in winter (January) (Fig. 2e). The monthly distribution of u2 has a strong peak in April and a weak peak in late autumn (November); see Fig. 2f. Vapor pressure deficit (VPD) is low in winter, increasing to the highest value in June and then declines (Fig. 2g). Fig. 2h shows that available energy (Rn − G) has a similar seasonal
Fig. 3. Correlations between monthly daily average climatic variables and elevation.
trend to vapor pressure deficit, both of which increase to their maxima before the arrival of monsoon rains. In addition, the trends of the averaged daily data for the 32 stations are in a good agreement with those for the 4 stations inside the basin. Seasonal patterns of the climatic data in Shiyang river basin basically represent the climate characteristics of North China (McVicar et al., 2007; Liang et al., 2010). Pearson correlation coefficients between elevation and the six climatic variables for the 12 months are in Fig. 3. Wind speed shows a low correlation with elevation, ranging from 0.091 in August to a maximum of 0.313 in February, because in summer mesoscale convective circulation caused by greater solar radiation dominantly controls wind, and in winter the elevation influence on wind is stronger (McVicar et al., 2007; Kossmann et al., 1998). Actual vapor pressure exhibits a negative and statistically significant correlation with elevation. For solar radiation, there is a positive and statistically significant correlation with elevation from November to February, but from May to September, this correlation is negative. For in winter solar radiation load is higher in the lower-latitude upper reaches, and in summer the strongly negative dependence on elevation stems from the important contribution of water vapor to the greenhouse effect. Water vapor decreases with increasing elevation (Marty et al., 2002). As expected, mean, maximum and minimum temperatures have high and statistically significant correlation with elevation. Our findings are consistent with those reported by other researchers (Goodale et al., 1998; Boer et al., 2001). Among the temperature variables, Tmax has the widest range of lapse rates from −3.65 ◦ C km−1 in winter to −7.77 ◦ C km−1 in summer (Fig. 4b), while the range of Tmin lapse rates is narrowest, from −4.04 ◦ C km−1 to −5.97 ◦ C km−1 (Fig. 4c). The variation of Tmean lapse rates is intermediate, between −3.89 ◦ C km−1 in winter and −7.02 ◦ C km−1 in summer (Fig. 4a). These are in accordance with Hong et al. (2005) who reported that monthly Tmax had greater lapse rates than Tmean and Tmin . The seasonality of NSED for ea agrees well with the results of McVicar et al. (2007); however, the seasonal variation of NSED for u2 is not obvious, with R2 = 0.2782. The annual average of NSED for u2 is 1.105 ms−1 km−1 , which is smaller than their annual mean of 1.33 ms−1 km−1 , considering the small standard deviation (0.17) for our range of u2 during the year (Fig. 2e). The NSED for Rs is steepest in June (−1.45 MJ m−2 km−1 ) and shallowest in November (0.073 MJ m−2 km−1 ). Marty et al. (2002) found similar temporal pattern for global radiation at Alpine Surface Radiation Budget stations, and the different gradients are due to higher and lower solar altitude in summer, respectively in winter.
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Fig. 4. Monthly values of the NSED for: (a) Tmean ; (b) Tmax ; (c) Tmin ; (d) Rs ; (e) ea ; (f) u2 . Lines of best fit (as a function of month) are shown by the dashed lines, with equations and statistics of the fit lines provided.
4.2. Spatial distribution of ET0 Monthly surfaces of ET0 for the multi-year data of the study area are shown in Fig. 5. These maps are obtained from the interpolated meteorological surfaces according to the method in Section 3.1. Statistics of the ET0 surfaces are provided in Fig. 6. In winter months (January, February, November and December), ET0 is rather low and the spatial distributions are fairly homogeneous, as can be seen in Fig. 6 that the standard deviations of these surfaces are quite small. From March to October, these ET0 maps show strong variability and marked differences between the southern mountain ranges and the north plain region. The contour stripes are along the direction of the mountain range in the south and gradually change to the eastern–western direction, which implies that both the elevation gradient and the latitude differences result in the fluctuation of ET0 . ET0 distributions of March and April have simi-
lar patterns with October and September respectively. The summer months (May, June, July and August) are characterized by high values of ET0 , and the standard deviations are relatively large with the largest of 30 mm in July. ET0 of the summer months accounts for 53% of the total annual amount, which is comparable to the percentages given by Tong et al. (2004) that varied from 52% at Wushaoling to 57% for Minqin station. The maximum ET0 and maximum mean monthly ET0 of the region both occur in July with the values of 203 mm and 154 mm, while the minimum values of 23 mm and 25 mm occur in January. The most significant differences between the maximum and minimum ET0 values appear in July with 120 mm, and in June the value is 119 mm, whereas the smallest differences occur in January with the value of 7 mm, followed by February with the value of 11 mm (Fig. 6). Higher values of ET0 are identified mainly at the northern part of the basin for most of months, but during the cool sea-
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Fig. 5. Monthly average ET0 from the multi-year data (mm month−1 ). Table 2 Pearson correlation coefficient between reference evapotranspiration and geographic factors at the 32 stations.
Latitude Elevation
Latitude Elevation * **
January
February
−0.265 0.343
−0.032 −0.012
March *
0.352 −0.456**
April
May **
0.613 −0.743**
June **
0.708 −0.790**
0.726** −0.801**
July
August
September
October
November
December
0.712** −0.798**
0.696** −0.777**
0.733** −0.708**
0.686** −0.582**
0.324 −0.214
0.359* −0.220
Correlation is significant at the 0.05 level (two-tailed). Correlation is significant at the 0.01 level (two-tailed).
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Fig. 6. Time series of the surface averaged monthly ET0 . The multi-year mean (black solid line), ±1 standard deviation (dashed lines), and the maximum and minimum (dash-dot lines) are shown.
son, the maxima are in the southern mountainous area for most cases, where net radiation is higher. Southern mountainous area has the minimum values of ET0 in the warm months (Fig. 5).
Fig. 7. Comparison between monthly daily averaged ET0 calculated from the observed meteorological data and the value extracted from the interpolated-thencalculated surfaces.
Fig. 8. Percent change in ET0 with respect to changes in climatic variables for the average of the four stations in the river basin.
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Fig. 9. Spatial distributions of sensitivity coefficient and their descriptive statistics for (a) mean air temperature, (b) vapor pressure deficit, (c) wind speed and (d) available energy.
Table 2 shows Pearson correlation coefficients between ET0 at the 32 stations and their geographical factors (latitude and elevation). From April to October, ET0 is significantly correlated with both latitude and elevation. It is positively correlated with latitude and negatively with elevation. And this could
be a validation to the spatial patterns of monthly ET0 in Fig. 5. A comparison was made between ET0 calculated from the observed data and the value extracted from the interpolated surfaces (4 data points each month, and 48 points in total) (Fig. 7),
X. Zhang et al. / Agricultural Water Management 97 (2010) 1506–1516 Table 3 The slope of the regression lines from sensitivity curves.
Tmean VPD u2 Rn − G
January
April
July
October
−0.0326 0.6985 0.3896 0.3015
0.0047 0.5178 0.2280 0.4822
0.0635 0.3144 0.1367 0.6856
0.0375 0.4376 0.2021 0.5624
The regression lines are in the form of Y = slope X (Y = percent change in climate variable and X = percent change in ET0 ).
and the consistency reflects high spatial fidelity of the interpolated climatic variables. 4.3. Sensitivity analysis Sensitivity curves for climate variables in January, April, July and October for an average of the four stations inside the study area are presented in Fig. 8, and the slopes of the linear regression lines for the curves (sensitivity coefficients) are listed in Table 3. The four months are selected to represent winter, spring, summer and autumn, respectively. It is seen that each climatic variable fluctuates during the year. Mean air temperature has the least effect on ET0 over the year. During summer months, higher temperature has larger effect on ET0 . In January, when the temperature is below zero at all stations, the slopes of sensitivity curves for mean air temperature is negative, because higher temperatures are obtained after the negative change of minus value. However at Minqin station in April and July with the increasing of mean air temperature, the value of ET0 also decreases. This is due to the fact that at Minqin in warm months, the aerodynamic term contributes more than the energetic term, and therefore the decreasing trend of aerodynamic term in these months controls the trend of ET0 . As the negative effect at Minqin counterbalances the positive variations of other stations, the affect of mean air temperature on ET0 in April is small (slope = 0.0047). Vapor pressure deficit and available energy both have positive effects on ET0 , and they exhibit opposite seasonal trends. In January, vapor pressure deficit is the most sensitive variable for the study area (slope = 0.6985); while in July available energy plays the most significant role (slope = 0.6856). It is noted that the sum of their slopes in the same month equals 1, for they represent the two component terms in P–M model. Saxton (1975) has noted the changing relative importance between net radiation and aerodynamic terms. And Rana and Katerji (1998) reported a sensitivity analysis of the P–M model for three crops on an hourly basis in a semi-arid climate of southern Italy, where available energy also showed an opposite behavior to vapor pressure deficit. During warm hours, the sensitivity coefficient for available energy is larger, but the coefficient for vapor pressure deficit is lower. Next to vapor pressure deficit, wind speed has the second largest effect on ET0 in January (slope = 0.3896). It has a similar temporal trend with vapor pressure deficit, with the slope of the regression line gradually decreasing to its minimum in July (slope = 0.1367) and then increasing. The sensitivity curves between the percent changes in each climate variable and the relative percent changes in ET0 are generally linear within the range of variability (r2 ≥ 0.98). Therefore the sensitivity coefficient for each climatic variable is approximately derived from the average value of the eight scenarios according to Section 3.4. Fig. 9 shows the spatial distributions of sensitivity coefficient for the four climatic variables and the statistics of each surface. Vapor pressure deficit is the most sensitive variable in January for the area, with the mean SC of 0.712. And in the southern mountain ranges, ET0 is sensitive to vapor pressure deficit over the year. Mean air temperature is the least sensitive parameter during the year, and higher mean SC (0.013) is seen in July. Variations between the upper and lower reaches in the region are obvious in warm months,
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with higher SD values. In July, available energy influences ET0 a lot (SC = 0.652) except southern mountain ranges where ET0 is most sensitive to vapor pressure deficit over the year. Wind speed plays an important role in winter compared with other months, when the mean value of SC is 0.398 and it affects ET0 greater at the lower reaches of the river basin, where two deserts (Badanjilin Desert and Tenggeli Desert) are located and the vegetation is sparse. 5. Conclusions The 50-year monthly ET0 climatology for the Shiyang river basin were calculated from the input climate surfaces interpolated by the partial thin-plate spline in ANUSPLIN, where longitude and latitude are independent variables; elevation is as a linear covariate. A comparison between the calculated station ET0 values and interpolated-then-calculated values for the 12 months indicated that the interpolated surfaces balanced smooth and fidelity of the station values; and the continuous surfaces of ET0 and their spatial structures for each month were well estimated. These ET0 maps obtained can be applied to predict the agricultural water demand and will assist water resources planning and management for this region. Sensitivity analysis for the P–M equation was conducted on the main climatic variables, including mean air temperature, vapor pressure deficit, wind speed and available energy at the four stations in the study area. Based on the spatially interpolated climatic variables and gridded ET0 data, maps of the sensitivity coefficient for the four major climatic variables are derived. For this arid and semi-arid environment, vapor pressure deficit is the most sensitive variable during the cool season, while in summer available energy becomes the predominant factor at most part of the region except the southern mountain ranges in the upper reaches where vapor pressure deficit has the largest effect on ET0 all over the year. And mean air temperature is the least sensitive parameter during the year. This provides a view on the response of ET0 to climate variability and climate change in the study area. Our results confirmed that for an area with sparse data points and complex topography, incorporation of elevation as a covariate or other geographic factors is important and effective for interpolating climatic variables and then calculating ET0 . To estimate crop evapotranspiration, ET0 is multiplied with crop coefficient, which considers the local condition (e.g. atmospheric attenuation, slope and aspect), but the accuracy of ET0 would be improved if incorporating the slope and aspect effect on the solar radiation at each grid cell. Acknowledgements We thank the State-Sponsored Study-abroad Scholarship Program of China Scholarship Council. Thanks to Li Lingtao in CSIRO for his assistance in this study and Prof. Michael Hutchinson in ANU for the helpful discussion. And this work is also supported by the Chinese National Natural Science Fund (Nos. 50939005 and 50679081), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0657) and the National High Tech Research Plan (No. 2006AA100203). The authors are grateful to the two anonymous reviewers for their detailed and constructive comments, which greatly improved the quality of the paper. References Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration – guidelines for computing crop water requirements. In: Irrigation and Drainage Paper 56. United Nations Food and Agriculture Organization, Rome, Italy. Ashraf, M., Loftis, J.C., Hubbard, K.G., 1997. Application of geostatistics to evaluate partial weather station networks. Agricultural and Forest Meteorology 84, 255–271.
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Agricultural Water Management journal homepage: www.elsevier.com/locate/agwat
Spatial variation of climatology monthly crop reference evapotranspiration and sensitivity coefficients in Shiyang river basin of northwest China Xiaotao Zhang a , Shaozhong Kang a,∗ , Lu Zhang b,∗∗ , Junqi Liu a a b
Center for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China CSIRO Land and Water, Christian Laboratory, GPO Box 1666, Canberra, ACT 2601, Australia
a r t i c l e
i n f o
Article history: Received 27 November 2009 Accepted 3 May 2010 Available online 12 June 2010 Keywords: Crop reference evapotranspiration Penman–Monteith ANUSPLIN Sensitivity analysis Shiyang river basin
a b s t r a c t Crop reference evapotranspiration (ET0 ) is often used to determine crop water requirement. ET0 maps are useful for regional agricultural and water resources management, and also play an important role in the distributed hydrological modeling. For generating spatial ET0 surfaces, ‘Interpolate-then-calculate (IC)’ approach is powerful in principle and is recommended especially for sparse weather station networks. The partial thin-plate smoothing spline incorporated in ANUSPLIN for interpolating climatic variables has been accepted widely across the world. In this paper, the climatology monthly ET0 data of Shiyang river basin, one of the three inner basins in northwest China, are developed by spatially modeling the input climatic parameters with ANUSPLIN, and from the interpolated climate and ET0 datasets, sensitivity coefficients of ET0 to the climatic variables of selected months are also spatially distributed. In the cool months (January, February, November and December), the spatial variability of ET0 is small and the value is rather low, whereas the warm season (May, June, July and August) is characterized by high values of ET0 and large spatial variations in the river basin. Vapor pressure deficit is the most sensitive variable during the cool months and in the mountainous area with lower temperature; mean air temperature is the least sensitive one during the year and a little variation is observed at the basin scale. In summer, available energy primarily forces ET0 as expected, and in winter, wind speed plays an important role and affects ET0 greater at the northern plain region where deserts are dominated by dunes and low shrubs. We conclude that for regions with isolated climate stations, ‘IC’ procedure by including topographic and geographic factors can effectively model spatially distributed ET0 . © 2010 Elsevier B.V. All rights reserved.
1. Introduction Crop reference evapotranspiration (ET0 ) is an important variable in the agrohydrological systems, which depends only on climatic parameters and provides the evapotranspiration of an ideal and well-watered grass surface. Actual crop evapotranspiration can be derived from ET0 by means of proper crop and water stress coefficients (Rana and Katerji, 2000; Kite and Droogers, 2000). A number of equations are available for estimating ET0 (e.g. Penman, 1948; Blaney and Criddle, 1950; Hargreaves and Samani, 1985; FAO-56 Penman-Monteith, 1998). Among these equations, FAO-56 Penman–Monteith equation (P–M) that incorporates both energy balance and aerodynamic theory, is considered to be the most appropriate model to predict ET0 and is recommended by the Food and Agriculture Organization of the United Nations (FAO) as
∗ Corresponding author. Fax: +86 10 6273 7611. ∗∗ Co-corresponding author. Fax: +61 2 6246 5800. E-mail addresses: [email protected] (S. Kang), [email protected] (L. Zhang). 0378-3774/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2010.05.004
the standard for computing ET0 from full climate records (Allen et al., 1998; Xu et al., 2006). Annual and monthly ET0 maps provide valuable information in regional management of cropping system, evaluation of agricultural water use, water resources monitoring and management and agro-climatic zoning. The spatial variability of ET0 is also useful for distributed hydrological modeling. Two different approaches, ‘Calculate-then-Interpolate (CI)’ and ‘Interpolate-then-Calculate (IC)’ (McVicar and Jupp, 2002; Stein et al., 1991), are compared by many researchers for generating spatial ET0 maps. Mardikis et al. (2005) evaluated the two procedures when plotting the long-term mean daily ET0 for each month in Greece using four interpolation methods, including Ordinary Kriging (OK), Inverse Distance Squared (IDS), Residual Kriging (RK) and Gradient plus Inverse Distance Squared (GIDS). They found that IC–GIDS combination ranked first with the lowest mean absolute error (0.1207 mm) and root mean squared error (0.0367 mm) averaged over all months, and had a slight superiority over CI–GIDS. Ashraf et al. (1997) concluded that the IC procedure provided lower root mean squared error of ET0 than the CI procedure. Although Bechini et al. (2000) stated that the IC procedure would increase the error of model application if
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Fig. 1. The meteorological stations in and around Shiyang river basin, and its digital elevation model (DEM) with a spatial resolution of 0.02◦ × 0.02◦ in longitude and latitude.
the spatial and temporal structures of the model inputs were not reliable, the IC approach is powerful in principle, for each of the input parameters may have the specific spatial correlation structure (Heuvelink and Pebesma, 1999). Using IC will provide accurate ET0 surfaces for partial station networks (Ashraf et al., 1997), as the near-surface elevation dependence is not equivalent for each climatic variable (McVicar et al., 2007). Various interpolation methods have been applied to spatially model the input climatic variables such as air temperature, precipitation, and wind speed; and those incorporating the topographical and geographical forcing factors (e.g. elevation, distance to the sea, latitude and longitude) affecting the spatial climate patterns often demonstrate better results (Goovaerts, 2000; Lloyd, 2005; Luo et al., 2008). ANUSPLIN, a software package developed by Hutchinson (2004), is a mathematical approach to generate hydrometeoro-
logical maps at varying spatial and temporal scales. It is based on the thin-plate smoothing spline methods, which is primarily described by Wahba and Wendelberger (1980). A key feature of ANUSPLIN is that it includes a linear covariate to represent the elevation effect on climatic data, being termed the partial thin-plate splines (Hutchinson, 1991). Price et al. (2000) compared ANUSPLIN with GIDS, which outperformed six other interpolation methods (Nalder and Wein, 1998) to spatially map monthly mean minimum and maximum air temperature and precipitation in Canada. The result showed that the root mean squared errors obtained using ANUSPLIN were lower than those of GIDS for most months. Jeffrey et al. (2001) have applied ANUSPLIN algorithm to construct the interpolated surfaces of daily maximum and minimum air temperature, solar radiation, vapor pressure and pan evapotranspiration of Australia. Shen et al. (2008) established annual and monthly
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Table 1 Descriptive statistics of elevation (m) for the 32 stations (4 stations in and 28 stations around Shiyang river basin).
4 stations 28 stations
the total water consumption by different sectors that totalled 28.54 × 108 m3 (Tong et al., 2007).
Max
Min
Mean
SD
3. Data and method
3045.1 3662.8
1367.0 1177.4
1979.8 2208.2
755.4 765.6
3.1. Climate data
SD is the standard deviation.
vapor pressure grid datasets of China through ANUSPLIN, and the resultant surfaces indicated a good linear correlation between the measured and the corresponding grid values. All the work provides strong support for using ANUSPLIN in climate interpolation. ANUSPLIN has been applied to generate spatial surfaces of monthly ET0 for Coarse Sandy Hilly Catchment located in Loess Plateau of China by McVicar et al. (2007), in which the forcing meteorological variables, including maximum and minimum air temperature, wind speed and vapor pressure, were interpolated using the partial thin-plate splines with a linear dependency on elevation. McVicar et al. (2007) showed how the near-surface elevation dependence (a lapse rate for air temperature) varies as a function of input variable and month of year. To validate their resultant ET0 surfaces they also interpolated pan evaporation rates from 20-cm diameter Chinese micro-pans, and calculated the pan coefficient (Kpan ) which varied from 0.44 in April to 0.65 in August. The slightly lower values of the Kpan (than what is expected for a Class A pan) were attributed to the different geometry of the micro-pan. Tong et al. (2007) spatially distributed the average seasonal crop evapotranspiration (ETc ) of spring wheat during the 1950s–2001 for Shiyang river basin, where a multiple regression relationship between ETc and elevation, latitude and aspect was used and the CI approach was performed. To understand the relative importance of climatic variables in the P–M model, a sensitivity analysis is required and the results from sensitivity analysis are of vital significance for determining the effect of climate change on ET0 . Several papers have carried out sensitivity analysis of ET0 to meteorological data in different climates (Saxton, 1975; Rana and Katerji, 1998; Goyal, 2004; Irmak et al., 2006), but they all restricted to a single station. Gong et al. (2006) conducted a sensitivity analysis of P–M ET0 to key meteorological variables (air temperature, wind speed, relative humidity and shortwave radiation) in Changjiang basin and derived the spatial variation of sensitivity coefficients by interpolating the station estimates. The objectives of this paper were: (1) to develop the climatology monthly crop ET0 maps of Shiyang river basin, an inner basin in northwest China with sparse data inside the area by interpolating the major input climatic variables with spline models incorporated in ANUSPLIN; and (2) to estimate the spatial variations of climatology sensitivity coefficients from the interpolated surfaces, in an attempt to understand the relative roles of main climatic variables in the P–M model at the regional scale. 2. Study area Shiyang river basin, located at the east part of the Hexi Corridor, Gansu Province of northwest China (Fig. 1), covers an area of 4.16 × 104 km2 . The basin is topographically variable. The Qilian mountains in the south, where the river originates, reach 5150 m above sea level; the middle of the basin is the plain region between the elevation of 1400 m and 2000 m; the elevation of Minqin oasis in the north, where the river ends, is 1256–1400 m. Due to the topographical differences, the basin exhibits typical semi-arid to arid climatic features from south to north, with the annual precipitation ranges 600–50 mm, and the annual pan evaporation is 700–2600 mm (Ma et al., 2008). Agriculture is the biggest water user in the river basin. In 2000, irrigation accounted for 86% of
The National Meteorological Centre of China operates 32 stations in and around Shiyang river basin (Fig. 1). The 4 stations in the basin are distributed in the upper, middle and lower reaches, with an elevation range of 1678.1 m (Table 1). Daily meteorological data of 32 stations were collected from China Meteorological Data Sharing Service System for the period of January 1959–December 2008 (50 years), with mean, maximum and minimum air temperature, relative humidity and bright sunshine hours at 2 m height, and wind speed measured at 10 m height. These measured daily data were converted to standard input parameters for the ET0 model (see the following section) and the standard daily means were averaged in each month for the 50 years. 3.2. Calculation of reference evapotranspiration The P–M method for estimating daily reference evapotranspiration (Allen et al., 1998) is: ET0 =
0.408(Rn − G) + (900/(Tmean + 273))u2 (es − ea ) + (1 + 0.34u2 )
(1)
where ET0 is reference evapotranspiration (mm day−1 ), the slope of the saturation vapor pressure curve (kPa ◦ C−1 ), Rn the net radiation at the surface (MJ m−2 day−1 ), G the soil heat flux (MJ m−2 day−1 ), Rn − G the available energy (MJ m−2 day−1 ), ␥ the psychrometric constant (kPa ◦ C−1 ), Tmean the mean temperature at 2 m height (◦ C), u2 the mean daily wind speed at 2 m height (m s−1 ), es the saturation vapor pressure (kPa), ea the actual vapor pressure (kPa) and es − ea is vapor pressure deficit (kPa).The computation of all data required for calculating daily reference evapotranspiration followed the procedures in FAO paper 56 (Allen et al., 1998). To obtain the total monthly evapotranspiration, Eq. (1) was multiplied by the number of days for a given month. Pearson correlation coefficients were calculated at the 32 stations between climatology monthly ET0 and geographical factors (latitude and elevation) to understand the spatial patterns of the ET0 surfaces. 3.3. Interpolation of climate data The spline models implemented in ANUSPLIN version 4.3 was used to interpolate monthly average daily climatic data of the 32 stations into a grid of 0.02◦ × 0.02◦ in longitude and latitude. In order to analyze the effect of elevation on the climatic variables of the observed stations, Pearson correlation coefficients were firstly computed between the monthly average daily climatic data and elevation at the 32 stations using SPSS 15.0. Based on the previous work (McVicar and Jupp, 2002; McVicar et al., 2007), a second-order or third-order partial thin-plate spline with latitude, longitude as independent variables and elevation as a covariate was chosen to interpolate all climatic variables because they produced lowest square root of generalised cross-validation (RTGCV) errors as compared with some other settings (e.g. secondorder spline with latitude, longitude and elevation as independent variables), and climatic data rarely exhibit high degree of spatial continuity by higher order spline (Hutchinson, 1998). By including elevation as a covariate, the partial thin-plate spline determines the approximately linear dependence of climate on elevation, which is termed a lapse rate for air temperature (mean, maximum and minimum) and the near-surface elevation dependence (NSED) for other meteorological variables (McVicar et al., 2007). As the spline
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Fig. 2. Monthly mean daily values of: (a) Tmean (◦ C); (b) Tmax (◦ C); (c) Tmin (◦ C); (d) Rs (MJ m−2 day−1 ); (e) ea (kPa); (f) u2 (ms−1 ); (g) VPD (kPa); (h) Rn − G (MJ m−2 day−1 ). The average of 32 stations (black solid line), the average of 4 stations in the river basin (red solid line), ±1 standard deviation (dashed lines), and the maximum and minimum (dash-dot lines) are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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models fit a continuous surface of the points, the smoothing surface does not necessarily go through each observed point (Hijmans et al., 2005). 3.4. Sensitivity analysis of the reference evapotranspiration to meteorological variables McKenney and Rosenberg (1993) and Goyal (2004) conducted sensitivity analyses on ET0 , in which the relative changes of an input climatic variable within a range against relative changes of the output ET0 were plotted as a sensitivity curve. Irmak et al. (2006) derived sensitivity coefficients by dividing the amount of increase/decrease in ET0 by the unit of increase/decrease in each climate variable on a daily basis as: SC =
ET0 CV
(2)
where SC is the sensitivity coefficient; CV is the unit change in the climatic variable; ET0 (mm day−1 ) is the change in ET0 with respect to changes in climatic variables. However such sensitivity coefficient is sensitive to the magnitude of ET0 and climatic variables. To get a non-dimensional sensitivity coefficient, we normalize SC as: SC =
ET0 /ET0 CV/CV
(3)
where SC is the dimensionless sensitivity coefficient; ET0 , CV are the base values before change. The SC value of −0.1 would suggest that a 10% increase in CV may be expected to decrease ET0 by 1%. In this study, sensitivity analyses for daily average ET0 in each month were firstly conducted at the four stations inside the study area from −20% to +20% at an interval of ±5% (eight scenarios) to each of the four variables (i.e. mean air temperature, vapor pressure deficit, wind speed at 2 m above the ground and available energy) while keeping all the other parameters constant. And then sensitivity curves for the average changes of the four stations were plotted. If the sensitivity curve is linear, the sensitivity coefficient is able to represent the change in ET0 caused by any perturbation of the climatic variable concerned (Gong et al., 2006). This is the basis for calculating spatially distributed sensitivity coefficient. At regional scale, sensitivity analyses were conducted at each grid cell from the interpolated climate data and ET0 maps and the sensitivity coefficient maps for each month were obtained by averaging grid values of the eight scenarios. 4. Results and discussion 4.1. Characteristics of climatic data and the interpolated climate surfaces General characteristics of the standard daily mean climatic data at the 32 observed stations for the 12 months are illustrated in Fig. 2. Monthly mean daily data of the four stations located in the basin are also averaged (Fig. 2). Unlike mean, maximum and minimum temperature (Tmean , Tmax , Tmin ) have the mono-peak in July (Fig. 2a–c), maximum Rs occurs in June (Fig. 2d), which is governed by the relative summer–winter daylength differences and modulated by increasing cloud cover associated with the summer monsoons (McVicar et al., 2007). The maximum ea is observed in the rainy season (July and August), and the minimum value is experienced in winter (January) (Fig. 2e). The monthly distribution of u2 has a strong peak in April and a weak peak in late autumn (November); see Fig. 2f. Vapor pressure deficit (VPD) is low in winter, increasing to the highest value in June and then declines (Fig. 2g). Fig. 2h shows that available energy (Rn − G) has a similar seasonal
Fig. 3. Correlations between monthly daily average climatic variables and elevation.
trend to vapor pressure deficit, both of which increase to their maxima before the arrival of monsoon rains. In addition, the trends of the averaged daily data for the 32 stations are in a good agreement with those for the 4 stations inside the basin. Seasonal patterns of the climatic data in Shiyang river basin basically represent the climate characteristics of North China (McVicar et al., 2007; Liang et al., 2010). Pearson correlation coefficients between elevation and the six climatic variables for the 12 months are in Fig. 3. Wind speed shows a low correlation with elevation, ranging from 0.091 in August to a maximum of 0.313 in February, because in summer mesoscale convective circulation caused by greater solar radiation dominantly controls wind, and in winter the elevation influence on wind is stronger (McVicar et al., 2007; Kossmann et al., 1998). Actual vapor pressure exhibits a negative and statistically significant correlation with elevation. For solar radiation, there is a positive and statistically significant correlation with elevation from November to February, but from May to September, this correlation is negative. For in winter solar radiation load is higher in the lower-latitude upper reaches, and in summer the strongly negative dependence on elevation stems from the important contribution of water vapor to the greenhouse effect. Water vapor decreases with increasing elevation (Marty et al., 2002). As expected, mean, maximum and minimum temperatures have high and statistically significant correlation with elevation. Our findings are consistent with those reported by other researchers (Goodale et al., 1998; Boer et al., 2001). Among the temperature variables, Tmax has the widest range of lapse rates from −3.65 ◦ C km−1 in winter to −7.77 ◦ C km−1 in summer (Fig. 4b), while the range of Tmin lapse rates is narrowest, from −4.04 ◦ C km−1 to −5.97 ◦ C km−1 (Fig. 4c). The variation of Tmean lapse rates is intermediate, between −3.89 ◦ C km−1 in winter and −7.02 ◦ C km−1 in summer (Fig. 4a). These are in accordance with Hong et al. (2005) who reported that monthly Tmax had greater lapse rates than Tmean and Tmin . The seasonality of NSED for ea agrees well with the results of McVicar et al. (2007); however, the seasonal variation of NSED for u2 is not obvious, with R2 = 0.2782. The annual average of NSED for u2 is 1.105 ms−1 km−1 , which is smaller than their annual mean of 1.33 ms−1 km−1 , considering the small standard deviation (0.17) for our range of u2 during the year (Fig. 2e). The NSED for Rs is steepest in June (−1.45 MJ m−2 km−1 ) and shallowest in November (0.073 MJ m−2 km−1 ). Marty et al. (2002) found similar temporal pattern for global radiation at Alpine Surface Radiation Budget stations, and the different gradients are due to higher and lower solar altitude in summer, respectively in winter.
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Fig. 4. Monthly values of the NSED for: (a) Tmean ; (b) Tmax ; (c) Tmin ; (d) Rs ; (e) ea ; (f) u2 . Lines of best fit (as a function of month) are shown by the dashed lines, with equations and statistics of the fit lines provided.
4.2. Spatial distribution of ET0 Monthly surfaces of ET0 for the multi-year data of the study area are shown in Fig. 5. These maps are obtained from the interpolated meteorological surfaces according to the method in Section 3.1. Statistics of the ET0 surfaces are provided in Fig. 6. In winter months (January, February, November and December), ET0 is rather low and the spatial distributions are fairly homogeneous, as can be seen in Fig. 6 that the standard deviations of these surfaces are quite small. From March to October, these ET0 maps show strong variability and marked differences between the southern mountain ranges and the north plain region. The contour stripes are along the direction of the mountain range in the south and gradually change to the eastern–western direction, which implies that both the elevation gradient and the latitude differences result in the fluctuation of ET0 . ET0 distributions of March and April have simi-
lar patterns with October and September respectively. The summer months (May, June, July and August) are characterized by high values of ET0 , and the standard deviations are relatively large with the largest of 30 mm in July. ET0 of the summer months accounts for 53% of the total annual amount, which is comparable to the percentages given by Tong et al. (2004) that varied from 52% at Wushaoling to 57% for Minqin station. The maximum ET0 and maximum mean monthly ET0 of the region both occur in July with the values of 203 mm and 154 mm, while the minimum values of 23 mm and 25 mm occur in January. The most significant differences between the maximum and minimum ET0 values appear in July with 120 mm, and in June the value is 119 mm, whereas the smallest differences occur in January with the value of 7 mm, followed by February with the value of 11 mm (Fig. 6). Higher values of ET0 are identified mainly at the northern part of the basin for most of months, but during the cool sea-
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Fig. 5. Monthly average ET0 from the multi-year data (mm month−1 ). Table 2 Pearson correlation coefficient between reference evapotranspiration and geographic factors at the 32 stations.
Latitude Elevation
Latitude Elevation * **
January
February
−0.265 0.343
−0.032 −0.012
March *
0.352 −0.456**
April
May **
0.613 −0.743**
June **
0.708 −0.790**
0.726** −0.801**
July
August
September
October
November
December
0.712** −0.798**
0.696** −0.777**
0.733** −0.708**
0.686** −0.582**
0.324 −0.214
0.359* −0.220
Correlation is significant at the 0.05 level (two-tailed). Correlation is significant at the 0.01 level (two-tailed).
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Fig. 6. Time series of the surface averaged monthly ET0 . The multi-year mean (black solid line), ±1 standard deviation (dashed lines), and the maximum and minimum (dash-dot lines) are shown.
son, the maxima are in the southern mountainous area for most cases, where net radiation is higher. Southern mountainous area has the minimum values of ET0 in the warm months (Fig. 5).
Fig. 7. Comparison between monthly daily averaged ET0 calculated from the observed meteorological data and the value extracted from the interpolated-thencalculated surfaces.
Fig. 8. Percent change in ET0 with respect to changes in climatic variables for the average of the four stations in the river basin.
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Fig. 9. Spatial distributions of sensitivity coefficient and their descriptive statistics for (a) mean air temperature, (b) vapor pressure deficit, (c) wind speed and (d) available energy.
Table 2 shows Pearson correlation coefficients between ET0 at the 32 stations and their geographical factors (latitude and elevation). From April to October, ET0 is significantly correlated with both latitude and elevation. It is positively correlated with latitude and negatively with elevation. And this could
be a validation to the spatial patterns of monthly ET0 in Fig. 5. A comparison was made between ET0 calculated from the observed data and the value extracted from the interpolated surfaces (4 data points each month, and 48 points in total) (Fig. 7),
X. Zhang et al. / Agricultural Water Management 97 (2010) 1506–1516 Table 3 The slope of the regression lines from sensitivity curves.
Tmean VPD u2 Rn − G
January
April
July
October
−0.0326 0.6985 0.3896 0.3015
0.0047 0.5178 0.2280 0.4822
0.0635 0.3144 0.1367 0.6856
0.0375 0.4376 0.2021 0.5624
The regression lines are in the form of Y = slope X (Y = percent change in climate variable and X = percent change in ET0 ).
and the consistency reflects high spatial fidelity of the interpolated climatic variables. 4.3. Sensitivity analysis Sensitivity curves for climate variables in January, April, July and October for an average of the four stations inside the study area are presented in Fig. 8, and the slopes of the linear regression lines for the curves (sensitivity coefficients) are listed in Table 3. The four months are selected to represent winter, spring, summer and autumn, respectively. It is seen that each climatic variable fluctuates during the year. Mean air temperature has the least effect on ET0 over the year. During summer months, higher temperature has larger effect on ET0 . In January, when the temperature is below zero at all stations, the slopes of sensitivity curves for mean air temperature is negative, because higher temperatures are obtained after the negative change of minus value. However at Minqin station in April and July with the increasing of mean air temperature, the value of ET0 also decreases. This is due to the fact that at Minqin in warm months, the aerodynamic term contributes more than the energetic term, and therefore the decreasing trend of aerodynamic term in these months controls the trend of ET0 . As the negative effect at Minqin counterbalances the positive variations of other stations, the affect of mean air temperature on ET0 in April is small (slope = 0.0047). Vapor pressure deficit and available energy both have positive effects on ET0 , and they exhibit opposite seasonal trends. In January, vapor pressure deficit is the most sensitive variable for the study area (slope = 0.6985); while in July available energy plays the most significant role (slope = 0.6856). It is noted that the sum of their slopes in the same month equals 1, for they represent the two component terms in P–M model. Saxton (1975) has noted the changing relative importance between net radiation and aerodynamic terms. And Rana and Katerji (1998) reported a sensitivity analysis of the P–M model for three crops on an hourly basis in a semi-arid climate of southern Italy, where available energy also showed an opposite behavior to vapor pressure deficit. During warm hours, the sensitivity coefficient for available energy is larger, but the coefficient for vapor pressure deficit is lower. Next to vapor pressure deficit, wind speed has the second largest effect on ET0 in January (slope = 0.3896). It has a similar temporal trend with vapor pressure deficit, with the slope of the regression line gradually decreasing to its minimum in July (slope = 0.1367) and then increasing. The sensitivity curves between the percent changes in each climate variable and the relative percent changes in ET0 are generally linear within the range of variability (r2 ≥ 0.98). Therefore the sensitivity coefficient for each climatic variable is approximately derived from the average value of the eight scenarios according to Section 3.4. Fig. 9 shows the spatial distributions of sensitivity coefficient for the four climatic variables and the statistics of each surface. Vapor pressure deficit is the most sensitive variable in January for the area, with the mean SC of 0.712. And in the southern mountain ranges, ET0 is sensitive to vapor pressure deficit over the year. Mean air temperature is the least sensitive parameter during the year, and higher mean SC (0.013) is seen in July. Variations between the upper and lower reaches in the region are obvious in warm months,
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with higher SD values. In July, available energy influences ET0 a lot (SC = 0.652) except southern mountain ranges where ET0 is most sensitive to vapor pressure deficit over the year. Wind speed plays an important role in winter compared with other months, when the mean value of SC is 0.398 and it affects ET0 greater at the lower reaches of the river basin, where two deserts (Badanjilin Desert and Tenggeli Desert) are located and the vegetation is sparse. 5. Conclusions The 50-year monthly ET0 climatology for the Shiyang river basin were calculated from the input climate surfaces interpolated by the partial thin-plate spline in ANUSPLIN, where longitude and latitude are independent variables; elevation is as a linear covariate. A comparison between the calculated station ET0 values and interpolated-then-calculated values for the 12 months indicated that the interpolated surfaces balanced smooth and fidelity of the station values; and the continuous surfaces of ET0 and their spatial structures for each month were well estimated. These ET0 maps obtained can be applied to predict the agricultural water demand and will assist water resources planning and management for this region. Sensitivity analysis for the P–M equation was conducted on the main climatic variables, including mean air temperature, vapor pressure deficit, wind speed and available energy at the four stations in the study area. Based on the spatially interpolated climatic variables and gridded ET0 data, maps of the sensitivity coefficient for the four major climatic variables are derived. For this arid and semi-arid environment, vapor pressure deficit is the most sensitive variable during the cool season, while in summer available energy becomes the predominant factor at most part of the region except the southern mountain ranges in the upper reaches where vapor pressure deficit has the largest effect on ET0 all over the year. And mean air temperature is the least sensitive parameter during the year. This provides a view on the response of ET0 to climate variability and climate change in the study area. Our results confirmed that for an area with sparse data points and complex topography, incorporation of elevation as a covariate or other geographic factors is important and effective for interpolating climatic variables and then calculating ET0 . To estimate crop evapotranspiration, ET0 is multiplied with crop coefficient, which considers the local condition (e.g. atmospheric attenuation, slope and aspect), but the accuracy of ET0 would be improved if incorporating the slope and aspect effect on the solar radiation at each grid cell. Acknowledgements We thank the State-Sponsored Study-abroad Scholarship Program of China Scholarship Council. Thanks to Li Lingtao in CSIRO for his assistance in this study and Prof. Michael Hutchinson in ANU for the helpful discussion. And this work is also supported by the Chinese National Natural Science Fund (Nos. 50939005 and 50679081), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0657) and the National High Tech Research Plan (No. 2006AA100203). The authors are grateful to the two anonymous reviewers for their detailed and constructive comments, which greatly improved the quality of the paper. References Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration – guidelines for computing crop water requirements. In: Irrigation and Drainage Paper 56. United Nations Food and Agriculture Organization, Rome, Italy. Ashraf, M., Loftis, J.C., Hubbard, K.G., 1997. Application of geostatistics to evaluate partial weather station networks. Agricultural and Forest Meteorology 84, 255–271.
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