Trends in Dryness Index Based on Potential Evapotranspiration and Precipitation over 1961 – 2099 in Xinjiang , China

Under the background of global warming, deep understanding for drought-related index is important. The spatial distributions and trends in annual mean (AM) climatic data, including PAM, ETo,AM, and DIAM in Xinjiang, China, were analyzed. Statistical downscaling model (SDSM) was applied. Future PAM, ETo,AM, and DIAM series were generated and used to analyze their temporal trends, along with the historical climatic data. The results showed that (1) over 1960–2010, DIAM varied greatly and ranged from 1.5 to 479.6. Trends in DIAM decreased significantly. The regional climate turned to be from arid to humid in the past; (2) over 2015–2099, DIAM ranged between 1.9 and 198.5 under A2 scenario and 1.6 and 130.4 under B2 scenario. Trends in DIWR decreased insignificantly under A2 scenario and significantly under B2 scenario, indicating a weak drought stress from the future climate; (3) the modified Mann-Kendal (MKK) test generally decreased the significance of the trends because it considered the limitation of serial autocorrelation. Robust trend test of MMK method was recommended considering its rigor property. In conclusion, the drought in Xinjiang tends to be relieved over 2015–2099 compared to 1960–2010.


Introduction
It has been widely recognized that the increment of greenhouse gases in the atmosphere is the primary cause of the observed global warming [1].Climate change is expected to have a range of crucial consequences including droughts [2], sea level rise, intense rain, and flooding, of which droughts are recognized as an environmental disaster and have raised the interest of scientists across various disciplines.Drought is generally characterized by a considerable decrease in water availability caused by a deficit in precipitation over a large area [3,4].Droughts are often classified into four categories including meteorological, hydrological, agricultural, and social-economic types [5].Drought indices were presented for assessing the severity of a drought and defining different drought parameters [6].There are some commonly used drought indices, for example, dryness index (DI) [7,8], Palmer Drought Severity Index (PDSI) [9], Crop Moisture Index (CMI) [10], Standardized Precipitation Index (SPI) [11], Soil Moisture Drought Index (SMDI) [12], and Vegetation Condition Index (VCI) [13].Other droughtrelated indices including Standardized Precipitation Evapotranspiration Index (SPEI) [14,15], monthly precipitation anomalies [16], and El Nino-Southern Oscillation (ENSO) are also used in drought analysis.Among the presented drought indices, DI, which is the ratio of potential evaporation (ET  ) to precipitation (), is useful for classifying the type of climate in relation to the water availability and has been utilized in different regions of the world [17][18][19].Climatic regimes can be divided into 4 groups including arid (12 > DI ≥ 5), semiarid (5 > DI ≥ 2), subhumid (2 > DI ≥ 0.75), and humid regions (0.75 > DI ≥ 0.375), respectively [8].
General circulation models (GCMs), which include numerical coupled models and represent various earth systems, are important tools to assessing climate change effects on droughts [20].However, they are unable to resolve significant subgrid scale feature [21].Downscaling technique is generally needed to translate large-scale GCMs output onto a finer resolution.Two fundamental approaches exist for downscaling: (1) a dynamical approach where a higher 2 Advances in Meteorology resolution climate model is embedded within a GCM and (2) a statistical method where empirical relationships could be established between GCM-resolution and local climate variables [22].In contrast, statistical downscaling (SDS) is computationally efficient and can be suitably used to perform the spatial downscaling and bias correction for a large amount of GCM outputs and has become a commonly used tool in climate impact studies.Various studies demonstrated that the overall performance of statistical and dynamic downscaling was similar in reproducing the present-day climate for the respective regions [23].
The SDS technique involves developing a quantitative relationship between large-scale climate variables (predictors) and local surface variables (predictands).SDS has many advantages.SDS can provide point-scale climatic variables from GCM-scale output; it can be used to derive variables not available from regional climate models (RCMs); it is easily transferred to other regions based on standard and accepted statistical procedures; and it is able to directly incorporate observations into method [22].Many techniques have been developed for SDS.Wilby et al. [24] introduced an SDS model (SDSM) to assess regional climate change impacts.Mehrotra and Sharma [25] presented a multisite rainfall downscaling model (MMM-KDE) and Mehrotra et al. [26] applied the model in projection of future rainfall in India combined with 5 GCMs.An analogue downscaling method was applied by Timbal [27] and has been used for simulating the decline in rainfall in various regions within Australia [28,29].Sunyer et al. [30] compared five SDS methods, including two statistical correction methods and three weather generators (WG).Chen et al. [31] assessed the uncertainty of six empirical downscaling methods in quantifying the hydrological impact of climate change over two North American river basins.Chandler and Wheater [32] proposed a Generalised Linear Model (GLM) for daily time series and used it to analyze and simulate spatial daily rainfall given natural climate variability influences in the UK [33].Hughes et al. [34] described a nonhomogeneous hidden Markov model.Tumbo et al. [35] assessed the validity of downscaling together with evaluation of GCM models (CGCM, CRNM, ISPL, and ECHAM) for projecting climate change in Same (Northeastern Tanzania) using a self-organizing maps technique.The empirical downscaling methods, which were grouped into change factor and bias correction approaches, were also commonly used [36].Support vector machine (SVM) and multivariate analysis were applicable in SDS [37].Frost et al. [38] compared six downscaling methods and evaluated those using Australia multisite rainfall data.It was considered that no single model performed well over all timescales/statistics and the user should beware of model limitations when applying downscaling methods for various purposes [38].
Xinjiang Autonomous Region has an area of 1.66 million km 2 and takes up roughly one sixth of the total area of China.It is located in the northwest inland of China and is distant from any coast.The climate in Xinjiang is dry with many hours of sunshine and large temperature differences between day and night.The surface water and groundwater resources in Xinjiang rank 14 and 4, respectively, out of 31 provinces in China with highly uneven spatial distributions.The average annual precipitation in Xinjiang is only 147 mm while the average annual evaporation is 1512 mm [39].Xinjiang is a typical and representative arid region in China and is also typical of other arid regions around globe.Under the global climate warming background [1], the climate in Xinjiang transforms from warm-dry to warm-wet trends [40,41], accompanied with the abrupt change of precipitation and its extreme indices [42].Although there has been research which focused on the historical variations of various climate elements [43] and specifically in Xinjiang [41], the changing trends of future precipitation in this region are still not clear.Because the variability of weather elements (including precipitation, air temperature, wind speed, relative humidity, etc.) is important for the early warning of water-related hazards, studies on the trends of both historical and future droughts in Xinjiang are necessary in order to keep stable development of the regional economy and the health of people's livelihoods.
The objectives of this study are (1) to project annual mean precipitation ( AM ), potential evaporatranspiration (ET ,AM ) at the multisite of the study region over 2015-2099 under A2 (medium-high carbon emissions) and B2 (medium-low carbon emissions) scenarios of the IPCC SRES (Intergovernmental Panel on Climate Change, Special Report on Emission Scenarios), using an SDS method, NECP (National Center for Environmental Prediction) reanalysis data and the observed weather data and to obtain annual mean dryness index (DI AM ) series over 2015-2099; (2) to analyze the trends of , ET  , and DI series over 1961-2099 using a modified Mann-Kendall (MMK) method, in which serial autocorrelations are taken into account.Regional trends of drought are given, which could be a reference for the climatic precaution and disaster control.

Data and Methodology
]), which gave moderate results compared to the other models [1], is employed in this study to provide future predictors.A2 and B2 scenarios of the IPCC SRES for the period 1961-2099 are chosen to give different possibilities.B2 describes a world with intermediate population and economic growth, emphasizing local solutions to economic, social, and environmental sustainability, and A2 describes a very heterogeneous world with high population growth, slow economic development, and slow technological change [1].Data from HadCM3 under A2 and B2 scenarios are used in this study because (1) HadCM3 generates the past climate for China better than the other GCMs [45] and (2) it provides daily outputs of the 26 atmospheric predictor variables and can be easily obtained from the SDSM website (http://copublic.lboro.ac.uk/cocwd/SDSM/).

Estimation of Standard Potential Evapotranspiration.
Potential evapotranspiration is based on the calculated rate of evapotranspiration from a hypothetical reference crop with a height of 0.12 m, an albedo of 0.23, and a fixed surface resistance of 70 s m −1 .FAO-56 Penman-Monteith equation is used for estimating ET  [46]: where ET  is the potential evapotranspiration (mm day where  oi is the observed precipitation at the th day,  pi is the produced precipitation for the th day obtained from SDSM software,  ave is the average value of the observed daily weather data, and  is the number of the observations.When  oi is equal to pi ,  ns is equal to 1.
The established empirical relationship, taking  as an example, is described as follows: where   is the th predictor derived by NCEP.Equation ( 3) is then applied to downscale ensembles of the same local variables for the future climate provided by HadCM3 under A2 and B2 scenarios over 2015-2099.The historical data from 1961 to 2010 and the consecutive 89-year time slices from 2015 to 2099 are used to examine the temporal trends of .
Daily precipitation variations in the whole region ( WR ) could be obtained by introducing a parameter-area weight (  ).  is the ratio of the representative area of each station to the area of the whole region.The representative area of each station is obtained using Thiessen polygon method. WR is calculated by where   is the daily precipitation over 2015-2099 at the th weather station.Estimations of ET  and DI in the whole region are similar to .

Estimation of Dryness Index. The dryness index (DI) is estimated by
Inverse distance weight (IDW) interpolation method in Arcmap 10.2 is used to interpret the spatial distributions of , ET  , and DI.

Trend Detection Test.
The existence of annual trends in the data series was analyzed based on the Mann-Kendall (MK) statistical test [47,48] for two periods of 1961-2010 and 2015-2099.Taking precipitation () as an example, the test statistic, Kendall's , is calculated as [48] where   and   are the values in the th and th year,  is the length of the data set, and sgn () is the sign function.The variance ( 2 ) is given by [49] The standardized test statistic  is computed by [50]   follows the standard normal distribution with a mean of zero and variance of one under the null hypothesis of no trend in the series.The null hypothesis is rejected if || ≥  1−/2 at the confidence level of , where  1−/2 is the (1 − /2)quantile.If  is positive (negative), the series  has an upward (downward) trend.At  = 0.05, if || > 1.96, then the trend is significant.A correction factor   for limiting the influence of serial autocorrelation on the MK test is introduced [51,52] to estimate the modified standardized MK statistic,  * : where where   is the sample autocorrelation coefficient for lag (order) −, calculated by where  is the average value of all   in the data sets and  is year number.If   falls inside the confidence limits, the hypothesis that   is zero is accepted using a two-tailed test.
The lower and upper limits of   at a confidence level of 95% are estimated as follows: The magnitude of the slope of the trend is estimated according to Sen [53].Sen's slope () is a robust estimate of the magnitude of monotonic trend and is calculated as [50]: Takelamagan desert was located in the middle south part of the region; there were sparse weather stations located within the desert zone.The annual mean weather conditions of the 41 sites are given in Table 1.

Spatial Distributions and Trends of Annual
Figure 2 shows the spatial variations of the multiyear average values for the main climatic elements in Xinjiang including hours of sunshine (), air temperature (), relative humidity (RH), and wind speed (). generally increased from the west to the east part of the region. generally decreased from the south to the north of the region with higher temperatures located in the desert zone and the site with low elevation (Tulufan).RH decreased from the north to the south of the region. generally decreased from the east to the west of the region.
The spatial distributions of annual mean precipitation ( AM ), ET ,AM , and DI AM estimated from the historical observed weather data are illustrated in Figure 3.
Overall decreasing distributions of  AM and DI AM and increasing distributions of ET ,AM from north to south were observed.Larger  AM was found in mountain areas. AM increased with increased elevations. AM ranged between 0.004 and 1.36 mm day −1 , ET ,AM ranged between 1.52 and 3.42 mm day −1 , and DI AM ranged between 1.5 (at Yining) and 479.6 (at Ruoqiang).DI AM exhibited a large variability in space.The largest DI AM was at Ruoqiang, with Tulufan, Minfeng, Qiemo, Hetian, and Bachu also having large DI AM values (>100), indicating high extent of droughts.DI AM values at Aheqi, Balikun, Hebukesaier, Tacheng, Qitai, Shihezi, Tuoli, and Wusu were less than 12.Over 1960-2010; DI AM in the whole region (DI WR ) could be estimated using the historical DI AM and the obtained   of each site (Table 2).The estimated historical mean DI WR was 16.0; thus Xinjiang should generally be an arid region according to Arora [8].
The calculated MK statistics  and the MMK statistics  * for  AM , ET ,AM , and DI AM over 1961-2000 are given in Table 3.
In Table 3, (1) there were general increasing trends in ET ,AM .ET ,AM series at 11 sites were temporally independent with the order of the autocorrelation coefficient  being equal to 0. The trends in series ET ,AM at 11 sites increased significantly both by the MK and MKK tests at a confidence level of 95%.The trends in ET ,AM at 26 sites were tested significantly by the MK method but insignificantly at 15 out of 26 sites by the MMK method when  ranged from 1 to 8. The existence of serial autocorrelation structures changed, in other words, decreased the significance of the trends, especially at high orders () of   .Consideration of serial 0 250 500 (km)      The spatial distributions of the final trends (using the combined MK and MMK test results) for  AM , ET ,AM , and DI AM of each site are visually shown in Figure 3.There were obvious differences.

Projection of Daily Precipitation and
ET  over 2015-2099 Using SDSM

Calibration and Validation of the Regressions for Daily
and ET  .Predictors were selected for the region (Table 4) so that regression functions could be established when using the SDSM 4.2 software.Table 4 shows that (1) daily  series were related to 500 hPa geopotential height at 29 out of 41 sites, to surface velocity at 24 sites, to 500 hPa velocity at 24 sites, to 500 hPa meridional velocity at 19 sites, and to relative humidity at 17 sites.In total, 21 predictors were related to daily  at a minimum of 1 site.(2) Daily ET  series were highly correlated to mean temperature at 2 m for all of the selected sites, to surface specific humidity at 25 sites, to 500 hPa geopotential height at 20 sites, to 850 hPa relative humidity at 14 sites, to mean sea level pressure at 13 sites, and to surface velocity at 12 sites.15 predictors were related to daily ET  at a minimum of 1 site and a maximum of The observed historical daily , ET  , and the NCEP reanalysis data were used for establishing the regression equations over the calibration period of 1961-1990 for each site using the SDSM software.Then the NCEP reanalysis data over the validation period of 1991-2000 were input to the established equations to simulate daily  and ET  series, which would be compared with the observed data over 1991-2000 to validate the goodness of the established regression equations.Taking Yiwu station as an example, for daily , six predictors, including surface velocity, 500 hPa airflow strength, 500 hPa velocity, 500 hPa geopotential height, 850 hPa relative humidity, and near surface relative humidity, were selected.The partial correlation coefficients between daily  and the above six predictors were −0.233, −0.175, 0.247, 0.088, 0.039, and 0.145, respectively, at a significance level of 0.0001.The  2 and  ns values for the established regression equations for predicting daily  of the 41 studied sites are listed in Table 5.There were generally high  2 (ranging from 0.877 to 0.998) and  ns values (ranging from  4. ET ,AM over 2015-2099 ranged between 1.77 and 2.71 mm day −1 under scenario A2 and between 1.65 and 2.72 mm day −1 under scenario B2.  AM over 2015-2099 ranged between 0.04 and 0.62 mm day −1 under scenario A2 and between 0.03 and 0.65 mm day −1 under scenario B2, which were generally larger than the historical  AM Table 5: Determination of coefficients ( 2 ) and Nash-Suttcliffe coefficients ( ns ) for prediction of rainfall at the selected 41 sites in the validation period (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000).

Site
drought when compared to the DI AM values from 1960 to 2010.
From the trend test results of  AM over 2015-2099 (data not shown), there were increasing trends in  AM at 22 out of 41 sites under scenario A2, of which half of the trends were significant.For the other 19 sites, trends in  AM at 3 sites decreased significantly.Under scenario B2, trends in  AM over 2015-2099 increased at 24 sites, with 6 sites having significant increasing  AM trends.Decreasing trends were detected in 17 sites, with 3 sites having significant decreasing  AM trends.Moreover, there were few stations where the predicted  AM showed autocorrelation structures.From 2015 to 2099,  AM under scenario A2 was found autocorrelated at 6 sites, but  AM under scenario B2 was autocorrelated at only 2 sites.Under scenario A2, high-order autocorrelations were found at Kelamayi ( = 17) and Wenquan ( = 20), and the significance of the trends in Kalamayi and Wenquan stations changed from significant to insignificant when tested by the MMK method.Under scenario B2, no high-order autocorrelation was found in  AM series.
ET ,AM series at only 8 out of 41 sites were temporally independent.The trend test results of ET ,AM over 2015-2099 (data not shown) indicated that over 2015-2099 under scenario A2, there were decreasing trends in ET ,AM at 40 out of 41 sites, of which, with 17 sites having significant decreasing trends.There were long-range autocorrelations of ET ,AM at 32 sites, for which the order  ranged from 6 to 27.Significant trends in ET ,AM tested by the MK test at 23 sites were changed to be insignificant when tested by the MMK test when  > 12.The corresponding  values ranged between −0.005 and 0.004.Under scenario B2 over 2015-2099; trends in ET ,AM decreased at all of the 41 sites, of which trends at 27 sites were significant.ET ,AM series at 18 out of 41 sites were temporally independent.Long-range autocorrelations of ET ,AM were also found at 17 sites under scenario B2, with  ranging from 5 to 21.The  values ranged between −0.004 and 0.
DI AM series at 31 out of 41 sites were temporally independent.As to the trends in DI AM over 2015-2099 (data not shown) under scenario A2, there were decreasing trends in DI AM at 32 out of 41 sites, of which, with 18 sites having significant decreasing trends.There were no longrange autocorrelations of DI AM at the other 8 out of 10 sites ( < 7).The  values ranged between −0.231 and 0.447.Under scenario B2 over 2015-2099, trends in DI AM decreased at 30 sites, of which trends at 16 sites were significant.DI AM series at 35 sites were temporally independent.The order for autocorrelation ranged between 2 and 8 at 5 sites.Values of  ranged between −0.121 and 0.156.6.

Variations of ET
In Table 6 and Figure 5,

Discussions
Uncertainty exists when assessing climate change impacts on hydrologic or meteorological elements.Several studies affirmed that GCMs were the largest uncertainty contributors [54][55][56].Li et al. [18] compared the uncertainties from five raw monthly outputs of GCMs under three emission scenarios and concluded that GCMs projected different change trends and magnitudes for rainfall data.Sunyer et al. [30] concluded that the uncertainties were partly due to the variability of the RCM projections and partly due to the variability of the statistical downscaling methods.The results from Chen et al. [31] showed that a large uncertainty envelope is associated with the choice of a given empirical downscaling method, as well as the choice of a regional climate model simulation for quantifying the climate change impacts on hydrology.Besides GCMs and downscaling methods, emission scenarios were also a contributor to the model uncertainties, but less important [18,54].For hydrologic applications, the uncertainty due to the hydrological model parameters was also considered minor, and the abrupt changes in lowflow cumulative distribution functions were attributed to uncertainty in statistically downscaled summer rainfall [54].
Only one statistical downscaling method was used in this study.Uncertainty was not assessed but could refer to the other research mentioned above.SDSM 4.2 software is convenient for projecting future daily  and ET  data if historical data is available.Khan et al. [57] concluded that SDSM is the most capable of reproducing various statistical characteristics of observed data in its downscaled results with 95% confidence level compared to Long Ashton Research Station Weather Generator (LARS-WG) model and artificial neural network model.Frost et al. [38] pointed out that the simple scaling approach provided relatively robust results for a range of statistics when GCM forcing data was used.Although only one downscaling method was used in this study, the results obtained for projected precipitation could be used for future local disaster control and decision making.
The trends for  AM , ET ,AM , and DI AM series over 1961-2099 were detected using a more robust method based on the MK test, that is, the MMK test, which considered the autocorrelation effects of the serial structures on trends.From our results, trends changed from significant to insignificant if the lags of serial autocorrelation were high ( > 1).The trends of the series tended to be exaggerated using the MK test.This implied that the MK test gave apparent significance of the trends and may mislead the trend detector in understanding of the studied series.The MMK test is strongly recommended for obtaining actual trends of the data series because it removes the exaggerated trends caused by long-duration correlations.
Overall,  WR showed an increasing trend over 1961-2099.The projected  WR over 2015-2099 lost its autocorrelation structure, which was unexpected and also indicated that random components in the weather generator may be not enough.

Conclusions
The statistical downscaling model (SDSM), combined with HadCM3 data and NCEP reanalysis data, was used in this study to project future daily  data under scenarios A2 and B2 for 41 sites in Xinjiang, China.Over the period of 1960-2010, ET ,AM ,  AM , and DI AM ranged from 1.52 to 3.42 mm day −1 , 0.004 to 1.36 mm day −1 , and 1.5 to 479.6, respectively.Spatial distributions and the trends of ET ,AM ,  AM , and DI AM were investigated considering the autocorrelation structures of the data series.DI AM was small in the north and large in the southeast of the study region.DI AM varied considerably and generally decreased, indicating a general relief from historical drought.
Ranges of ET ,AM ,  AM and DI AM over 2015-2099 under scenario A2 were between 1.77 and 2.71 mm day −1 , 0.04 and 0.62 mm day −1 , and 1.9 and 198.5, respectively.Ranges of ET ,AM ,  AM and DI AM over 2015-2099 under scenario B2 were from 1.65 to 2.72 mm day −1 , from 0.03 to 0.65 mm day −1 and from 1.6 to 130.4, respectively.The obvious decrease in DI AM indicated a continuous relief of drought in the future 8 decades.
The robust trend test combining MK with MKK methods indicated that for the whole region in Xinjiang, trends in DI WR decreased significantly both over 1961-2010 and 2015-2099 under scenario A2 but decreased insignificantly over 2015-2099 under scenario B2.There was an overall relief of drought in Xinjiang both historically and in the coming decades.Robust trend detection method, that is, the MMK test is strongly recommend for autocorrelated data series, in order to detect an "actual" rather than an "apparent" trend and assess the trends objectively.

Figure 1 :
Figure 1: Digital elevation model (DEM) showing the geological location of the weather stations used in this study.
Mean ET  , , and DI Over 1961-2010.A total of 41 weather stations in Xinjiang, China, with observed datasets over 1961-2000 were selected.The longitude and latitude ranges of the 41 sites were between E36.9 and 48.1 ∘ and N75.2 and 94.7 ∘ , respectively.The elevation  varied from 30 to 3095 m.The basic geological locations and elevations of the selected sites are demonstrated in Figure 1.

Figure 3 :
Figure 3: Spatial distributions and trends of ET ,AM ,  AM , and DI AM over 1961-2010 in Xinjiang.DE: decrease, IN: increase, sig.: significant at a 95% confidence level, insig.: insignificant at a 95% confidence level (similar below).

− 0 .
755 to 0.022 for the various sites.A general decrease in DI AM showed a humid signal in drought evolution over 1960-2010, caused by increased  AM in the region.

( 1 )
the trend in ET ,WR over 1961-2010 decreased insignificantly ( = 10).The trends in ET ,WR over 2015-2099 under both scenarios A2 and B2 decreased insignificantly with both  = 0. (2) The trend in  WR during the period of 1961-2010 increased insignificantly ( = 12).The trend in  WR from 2015 to 2099 increased significantly under scenario A2 and insignificantly under scenario B2, both serial structures were time independent ( = 0).(3) The trend in DI WR from 1961 to 2010 decreased significantly ( = 6).The trend in DI WR over 2015-2099 under scenario A2 decreased but was insignificant under the influence of series autocorrelation ( = 15).The trend in DI WR over 1961-2010 under scenario B2 decreased significantly ( = 2).(3) Over the period of 1961-2010, DI WR decreased significantly, ET ,WR decreased insignificantly, and  WR increased insignificantly.The decreasing trends of DI WR indicate less drought stress in the study region.

Table 1 :
Basic information of meteorological stations., RH, , and  are multiyear mean air temperature, relative humidity, wind speed, and sunshine hour, respectively.
Spatial distributions of the multiyear mean climatic elements in the study region.autocorrelation structures was necessary when performing trend tests, in case the trends were exaggerated.For consistency, the final trend test results should adopt  values when  = 0 from MK test and  * values when  > 0 from MKK test, so that the tested trends considering the limitations of serial autocorrelation.By this principle, the trends in ET ,AM at 6 sites increased significantly and trends at 1 site decreased significantly.Overall, the trends in ET ,AM The trends in  AM at all sites increased.The trends in  AM at 29 sites were significant using the MK method but trends at only 16 sites were significant by the MMK method when  ranged from 1 to 9. Overall, the trends in  AM at 13 sites increased significantly.
1.19-1.501.50-1.771.77-1.971.97-2.23 2.23-2.552.55-2.942.94-3.413.42-4.00(d)Windspeed(m/s)Figure2: increased significantly at 9 sites, increased insignificantly at 18 sites, decreased significantly at 3 sites, and decreased insignificantly at 11 sites.Sen's slope () values of ET ,AM ranged from −0.005 to 0.006 for different sites (data not shown), which corresponded with the trends in the data series, also indicating that values of  were generally low when the trends were insignificant.(2)  AM series at 20 sites were temporally independent ( = 0).AM series at 23 sites were temporally independent.The trends in DI AM at 40 out of 41 sites decreased.The trends in DI AM at 29 sites tested significant using the MK method but trends at 9 out of 29 sites tested insignificant by the MMK method when  ranged from 1 to 10. Overall, the trends in DI AM at 21 sites decreased significantly.Sen's slope () values of DI AM ranged from

Table 2 :
Area weights (  ) of the studied sites in Xinjiang, China.

Table 4 :
The selected predictors used for developing a relationship between the predictand and predictor..566 to 0.988) for the selected 41 sites.The same procedure was used to predict daily ET  at the 41 chosen sites in the region.The established regression functions for predicting daily  and ET  in 2015-2099 in this region were generally good and could be used for projecting future daily  and ET  data using a weather generator.3.2.2.Projected Daily and ET  Using SDSM and Generated DI over 2015-2099.Daily  and ET  data over 2015-2099 were projected under A2 and B2 scenarios for the 41 sites using SDSM version 4.2.Daily DI values over 2015-2099 were estimated according to the projected daily  and ET  data. AM , ET ,AM , and DI AM were then estimated based on the projected daily  and ET  data.Spatial distributions and the tested trends of  AM , ET ,AM , and DI AM over 2015-2099 in Xinjiang are illustrated in Figure PR: Predictor, NPP and NPE: numbers of stations used for establishing predictor-predictand relationship of rainfall and ET  .0
,WR ,  WR , and DI WR over 2015-2099.Series of  AM , ET ,AM , and DI AM in the whole region (ET ,WR ,  WR , and DI WR ) gave the general variations.ET ,WR ,  WR , and DI WR over 2015-2099 could be obtained using (3).The serial autocorrelation at a confidence level of 95% and the temporal variations of ET ,WR ,  WR , and DI WR are shown in Figure 5.In Figures 5(a), 5(c), and 5(e), values of  for historical data series for ET ,WR ,  WR , and DI WR over 1961-2010 were less than 12; values of  for ET ,WR and  WR over 2011-2099 were all equal to 0, indicating their temporally independent serial structures; values of  for DI WR over 2011-2099 were 15 for scenario A2 and 2 for scenario B2, indicating DI WR was temporally dependent.In Figures 5(b), 5(d), and 5(f), decreased ET ,WR and increased  WR over 1961-2099 were obvious.The trend test results for ET ,WR ,  WR , and DI WR over 1961-2099 are presented in Table