Comparison analysis of sampling methods to estimate regional precipitation based on the Kriging interpolation methods: A case of northwestern China

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1 Scieces i Cold ad Arid Regios Volume 8, Issue 6, December, 016 Citatio: Wu JK, Liu SW, Ma LP, et al., 016. Compariso aalysis of samplig methods to estimate regioal precipitatio based o the Krigig iterpolatio methods: A case of orthwester Chia. Scieces i Cold ad Arid Regios, 8(6): DOI: /SP.J Compariso aalysis of samplig methods to estimate regioal precipitatio based o the Krigig iterpolatio methods: A case of orthwester Chia JiKui Wu 1,*, ShiWei Liu **, LePig Ma 3, Jia Qi, JiaXi Zhou, Hog Wei 1. Laboratory of Watershed Hydrology ad Ecology, Northwest Istitute of Eco-Eviromet ad Resources, Chiese Academy of Scieces, Lazhou, Gasu , Chia. State Key Laboratory of Cryospheric Scieces, Northwest Istitute of Eco-Eviromet ad Resources, Chiese Academy of Scieces, Lazhou, Gasu , Chia 3. Shule River Basi Water Resources Admiistratio Bureau of Gasu Provice, Yume, Gasu 73500, Chia *Correspodece to: JiKui Wu, Northwest Istitute of Eco-Eviromet ad Resources, Chiese Academy of Scieces. No. 30, West Doggag Road, Lazhou, Gasu , Chia. jkwu@lzb.ac.c **Co-first author Received: March 18, 016 Accepted: July 1, 016 ABSTRACT The accuracy of spatial iterpolatio of precipitatio data is determied by the actual spatial variability of the precipitatio, the iterpolatio method, ad the distributio of observatories whose selectios are particularly importat. I this paper, three spatial samplig programs, icludig spatial radom samplig, spatial stratified samplig, ad spatial sadwich samplig, are used to aalyze the data from meteorological statios of orthwester Chia. We compared the accuracy of ordiary Krigig iterpolatio methods o the basis of the samplig results. The error values of the regioal aual precipitatio iterpolatio based o spatial sadwich samplig, icludig ME (0.1513), RMSE (95.91), ASE (101.84), MSE ( ), ad RMSSE (1.0397), were optimal uder the premise of abudat prior kowledge. The result of spatial stratified samplig was poor, ad spatial radom samplig was eve worse. Spatial sadwich samplig was the best samplig method, which miimized the error of regioal precipitatio estimatio. It had a higher degree of accuracy compared with the other two methods ad a wider scope of applicatio. Keywords: Krigig iterpolatio method; samplig methods; spatial sadwich samplig; precipitatio; orthwester Chia 1 Itroductio Precipitatio is oe of the most essetial variables of meteorology ad hydrology (Rui, 004). It is also the oe essetially required for a umber of applicatios such as atural resource maagemet, agriculture maagemet, irrigatio schedulig, ecosystem modelig, ad hydrological modelig (Ashiq et al., 010). Precipitatio data are usually available at certai locatios where weather statios are set up. For the majority of locatios, such as moutaious, marie ad oceaic regios, it is difficult ad expesive to acquire cotiuous spatial data (Wag et al., 014). Iterpolatio is a spatial aalysis method that costructs ew data poits withi the rage of a discrete set of kow data poits. I meteorology ad hydrology, by usig geographical (e.g., weather statios) ad temporal data from observatio poits, iterpolatio is used to predict climate variables i areas where there are o weather observatio data available (Alvarez et

2 486 al., 014). The precisio of spatial iterpolatio of precipitatio is related to the actual spatial variability of the precipitatio, the distributio of the statios, ad the iterpolatio methods used (Kog ad Tog, 008). The spatial variability of precipitatio is determied by atural properties, which are ot cotrollable. Therefore, to estimate precipitatio accurately, it is ecessary to have rai gauges distributed i optimal locatios ad to apply appropriate iterpolatio techiques for estimatig importat parameters (Yavuz ad Erdoğa, 01). May spatial iterpolatio methods have bee developed to estimate the values of evirometal variables at umeasured locatios for creatig a cotiuous surface from sampled poit values, ad over the last decade they have bee icreasigly used i a wide rage of studies, icludig ecology, hydrology, fire modelig, ad water resources (Bosta et al., 01; Alvarez et al., 014). The iterpolatio methods ca be divided ito two kids: determiistic ad geostatistical iterpolatio techiques. Determiistic iterpolatios use mathematical fuctios to geerate gridded data from the measured poits based o either the extet of similarity or the degree of smoothig (Johsto et al., 001; Ashiq et al., 010). Amog various determiistic iterpolatio techiques, iverse distace weighted, local polyomial iterpolatio, ad radial basis fuctios are used to geerate models. Geostatistic iterpolatios are based o the theory of regioalized variables ad rely o both statistical ad mathematical fuctios. A variogram model is used to describe the spatial cotiuity of the iput data to estimate values at usampled locatios. From this group, ordiary Krigig ad its multivariate extesio, ordiary co-krigig, are used to geerate models (Ashiq et al., 010). Regardig precipitatio, much of the effort has bee focused o idetifyig appropriate iterpolatio methods. Lloyd (005) studied the effect of elevatio o estimatio of mothly precipitatio i Great Britai by comparig movig widow regressio, iverse distace weight (IDW), ordiary Krigig (OK), simple Krigig with a locally varyig mea, ad Krigig with exteral drift (KED), ad cocluded that KED provided the most accurate estimates of precipitatio whe judged by cross-validatio estimatio error summary statistics. Che et al. (010) focused o idetifyig a accurate method to produce gridded daily precipitatio i Chia based o the observed data at 753 statios for the period They used ad compared five iterpolatio methods, icludig ordiary earest eighbor, local polyomial, radial basis fuctio, iverse distace weightig, ad ordiary Krigig. Cross-validatio showed that the ordiary Krigig based o seasoal semi-variograms gave the best performace. Wei et al. (005) compared iterpolatio approaches, statistical models, ad comprehesive approaches, icludig ie methods to estimate precipitatio resources for raiwater harvestig for agriculture i semi-arid lads i Chia. Their results idicated that the simulatig precisio of the comprehesive method was the best of the ie approaches, while amog the seve iterpolatio approaches, the precisio of the ordiary Krigig method was the best. These researches idicated that there is o absolutely best iterpolatio method; the best method ca be chose by takig the actual situatio of the study area ito accout. Amog the various iterpolatio methods, o method is always optimal; the best iterpolatio method for a specific situatio ca oly be obtaied by comparig their results (Su et al., 009). I studies of precipitatio iterpolatio i orthwester Chia, ordiary Krigig ad co-krigig performed better (Fag et al., 005; Chu et al., 008; He et al., 008). I this paper, we used the OK method to estimate the regioal surface precipitatio i orthwester Chia. The distributio of meteorological statios also impacts the precisio of precipitatio iterpolatio (Yavuz ad Erdoğa, 01). Numerous studies have show that the accuracy of the iterpolatio methods is comparatively more reliable i areas of greater observatio site desity (Che et al., 010). The distributio of precipitatio statios is subject to atural factors ad socio-ecoomic coditios, ad if the represetativeess of some statios is relatively poor, it will limit the accuracy of the precipitatio iterpolatio. Curretly, the samplig model method ca aggregate weather statios to optimize the umber ad locatio of the statios, ad the resultig samples will have a higher accuracy of iterpolatio ad greater represetativeess tha others i regioal precipitatio estimatio. Therefore, this method reders the iterpolatio results of regioal precipitatio more accurate. The samplig model maily icludes simple radom samplig, systematic samplig, cluster samplig, spatial radom samplig, spatial stratified samplig, ad spatial sadwich samplig, ad has bee widely used i fields such as sociology, atural scieces, ecoomics, ad populatio studies (Cao et al., 008; Jiag et al., 008). The sadwich samplig method will stratify the sample layer accordig to prior kowledge, which ca improve the accuracy of statistical results. For example, Wag et al. (00, 013) used the spatial sadwich method to estimate the proportio of cultivated lad i Shadog Provice, Chia i 000, ad they suggested certai situatios where sadwich estimatio might be expected to do better tha block Krigig estimatio ad hierarchical Bayesia estimatio. The sadwich samplig method is well applied i soil evaluatio ad forest area estimatio. For example, Che et al. (01) ivestigated the soil Cr cotet i Zegcheg City,

3 487 Guagdog Provice of Chia, with three differet methods for samplig aalysis: spatial radom samplig, spatial stratified samplig, ad spatial sadwich samplig. They foud that the regioal distributio result error of ordiary Krigig iterpolatio by sample poits which were obtaied by the sadwich samplig method was the miimum of the three methods. Zhag J ad Zhag Y (011) used differet samplig methods to estimate forest areas, ad their results showed that the accuracy of the sadwich model of spatial samplig was the highest, followed by the spatial stratified samplig ad the spatial radom samplig methods. Northwest Chia (31 35'N 49 15'N, 73 5'E 'E) is located i the cetral part of the Eurasia cotiet, ad icludes Xijiag, Qighai, Gasu, Nigxia, ad Shaaxi provices (Liu et al., 013). The total area is approximately 3.04 millio km, accoutig for more tha 30% of Chia's total terrestrial area. The Kulu Moutais ad the ortheaster Qighai-Tibet Plateau are the souther boudary of the area, ad they block the vapor from the Idia Ocea. The Altai Moutais are the orther boudary, blockig the vapor from the Arctic Ocea. The Tiasha Moutais lie i the middle of Xijiag ad form ladscapes of alpie meadows, ilad basis, gobi deserts, ad widespread sady deserts. This regio is cotrolled by a cotietal climate ad the average aual precipitatio is oly 130 mm, with a icreasig tred durig (Shi et al., 00; She et al., 013). The Loess Plateau is the easter boudary, which blocks the vapor from the Pacific Ocea. This regio is cotrolled by a mosoo climate, ad the average aual precipitatio is about 500 mm with a egative chagig tred ( 9.11 mm/(50a)) (Wag et al., 01). The Hexi Corridor is the middle area, coectig the Tiasha Moutais ad the Loess Plateau, whose aual precipitatio is about 00 mm with a icreasig tred (3.95 mm/(10a)) (Meg et al., 01). However, the aual precipitatio is still relatively sparse i souther Xijiag ad the Hexi Corridor, while relatively abudat i orther Xijiag ad the Loess Plateau. Aalyzig the differeces of precipitatio i a etire regio ad evaluatig whether the existig meteorological statios adequately reflect the regioal precipitatio ca help to grasp the actual regioal precipitatio ad pla idustry developmet accordig to idustrial water cosumptio, ad optimize the use of precipitatio resources i various regios. I additio, the spatial iterpolatio of precipitatio ca also provide basic data for the simulatio of area ruoff, ad predictio ad maagemet of droughts, floods, ad other hydrological problems. I this study, three samplig methods were used to sample the meteorological statios i orthwester Chia: spatial radom samplig, spatial stratified samplig, ad spatial sadwich samplig. The samples were iterpolated with the ordiary Krigig method to estimate the regioal precipitatio, ad the accuracy of the differet samples were compared to attempt to select a group of statios that are more represetative i the study area. Materials ad methods.1 Spatial autocorrelatio aalysis Spatial autocorrelatio refers to the relevace of the same property or pheomeo i differet spatial locatios, that is, the spatial heterogeeity of the same property or pheomeo (Zhag S ad Zhag K, 007). Mora's I coefficiet method is a commoly utilized idex to measure spatial autocorrelatio (Mora, 1948, 1950): I = S w 1 1 i, jziz i= j= j 0 z i= 1 i (1) where z i is the deviatio of the attribute of elemet i ad its average; w i,j is the spatial weight of elemets i ad j; ad S 0 are the total umber of elemets ad aggregatio of all spatial weights, respectively. S 0 is: S = w () 0 i, j i= 1 j= 1 The value of Mora's I is typically betwee 1 ad 1. If I is a positive umber, it idicates spatial elemets for clusterig distributio, ad for discrete distributio if I is a egative umber. A larger value of I idicates greater correlatio of spatial distributio, ad meas spatial elemets are more gathered i space ad more approximate i attribute value.. Samplig methods..1 Spatial radom samplig method Ulike simple radom samplig, the spatial radom samplig method takes the spatial autocorrelatio ito accout; the variace of the mea value estimatio eeds to be adjusted accordig to the degree of correlatio i the spatial samplig objects (Wag et al., 009). The mea ad variace are: 1 yi i = 1 y = (3) (, ) 1 1 σ E p C X Y v ( ) = E yi ys ( ) ds = i A A (4)

4 488 σ p where is the discrete variace, C(X,Y) is the covariace, ad y i is the observed value... Spatial stratified samplig method Accordig to Cochra stratificatio criteria (Cochra, 1977) (small variace i ier layer, large variace amog differet layers), it is ecessary to stratify the elemets that have a relative approximate attribute value for the same layer, ad divide the etire regio ito L layers. First, the method calculates the total sample of the study area accordig to the stratified radom sample model. The it assigs samples ito each layer accordig to W z, the weight of each layer (z). The W z ca be distributed i such ways that ehace the samplig efficiecy successively accordig to equality, the area proportio, ad the discrete variace. Fially, it samples all the elemets with the simple radom samplig method withi each layer (Wag et al., 009). The formula of the mea value is: y z 1 z = y (5) z i = 1 where y z is the mea value of the samples i layer z; z is the umber of samples i layer z; ad y zi is the value of sample i i layer z. The formula of the variace of the mea value is: zi ( ) ( ) z z z v y = E y Y (6) where Y z is the populatio mea value of the observed samples. After obtaiig the mea ad variace of each layer, we ca calculate the mea ad variace of the whole study area: 1 L y z z z = 1 y = (7) L ( ) Wz v( yz) v y = (8) z= 1..3 Spatial sadwich samplig method Spatial sadwich samplig adds report uit layers combied with the actual applicatio. Its model framework cosists of the sample layer, the kowledge layer, ad the report layer based o space delamiatio. I the spatial sadwich samplig model, the samples are partitioed by the kowledge layer, ad the sample mea ad variace of each kowledge layer will be calculated first. The, the report layer is cut with the kowledge layer, ad the mea ad variace of the kowledge layer are deduced to the report layer to obtai the mea ad variace of each report uit layer (Wag et al., 009). If the accuracy ad variace of each kowledge layer are give, the samplig capacity ad the optimal samplig size i each kowledge layer ca be calculated, as well as the mea value ad variace of each report uit layer. The mea value ad variace of each report layer are: y N rz = W y (9) r rz z z= 1 N rz ( r) rz ( z) V y = W V y (10) z= 1 W = N / N (11) rz rz r where N r represets the umber of populatio samples i the report layer r; N rz is the umber of samples i both the kowledge layer z ad the report layer r; W rz is the proportio of polygo rz accouted for i the report layer r; ad yz ad yr are the mea values of the kowledge layer z ad the report layer r, respectively..3 Spatial iterpolatio methods I cotrast with determiistic methods, Krigig is a powerful statistical iterpolatio method which has the capability of givig ubiased predictios with miimum variace ad takig accout of spatial correlatios ad statistical relatioships betwee measured poits (Krige, 1966). The OK estimate is a liear weighted average of the available o-observatios defied i Equatio (1) as: ( ) λ z( s ) Z s = (1) i i= 1 where Z(s) is the OK estimate at locatio s, λ i is the OK weight, ad s i are the observatio locatios. The weight of differet locatios is based o their spatial relatioship. Krigig uses the semi-variogram as a measure of dissimilarity betwee observatios. The semi-variogram is a fuctio of both distace ad directio, so it ca accout for directio-depedet variability (Yavuz ad Erdoğa, 01). However, Krigig methods ot oly provide predictios, but also quatify the predictio error. I this study, the performace compariso of differet samples was made usig a cross-validatio procedure. The root mea squared error (RMSE) is a accuracy performace measure that is frequetly used as a measure of magitude of errors (Equatio (13)) (Lloyd, 005): 1 i i = 1 i ( ( ) ( )) RMSE = Z s z s (13)

5 489 where Z(s) is the predicted value; z(s i ) is the observed value at the samplig poit s i ; ad is the umber of sample poits. The root mea square stadardized error (RMSSE) is a measure of the goodess of the assessmet of the predictio error. If the predictio error variace is correctly assessed, the the ratio should o average be close to 1 (Equatio (14)) (Bosta et al., 01): solves the samplig problem of multiple report uits. It ca divide the whole layer ito report layers accordig to the user's eeds, ad deduce the average ad variace of every report uit. The admiistrative layer was carried as the report layer i this paper, show i Figure 1. The kowledge layer is show i Figure. is the predictio error variace at loca- where σ tio s i. PE.4 Data source ( Z( s) z( s )) σ ( ) 1 i RMSSE = (14) s ( s ) i i= 1 PE i The precipitatio data were dowloaded from the Chia Meteorological Data Sharig Service System. The average aual precipitatio data of 155 meteorological statios i Northwest Chia were used for sample aalysis ad compariso. The distributio of these sites is show i Figure 1. Space stratificatio takes samples of the small variaces i the ier layer ad large variaces amog the differet layers, ad makes the spatial elemets have relatively approximate attribute values i the same layer. Accordig to Tobler's first law of geography (Tobler, 1970, 004), the closer distace of objects, the higher their degree of similarity, so the objects i space are cotiuous wholes. Thus, precipitatio i the study area was compreheded as beig larger i the southeast ad smaller i the Northwest, ad the souther Xijiag ad orther Gasu provices were foud to be the most arid regios i the area. We divided the whole Northwest Chia area ito five parts based o prior kowledge from local people to guaratee that the precipitatio differeces were small iside each layer ad large amog the other layers, ad all of the layers were spatially cotiuous. This stratificatio was called the kowledge layer (Wag et al., 00). The first strata icluded the souther regio of Shaaxi Provice ad a small regio i the southwest part of Qighai Provice; the secod strata icluded the middle area of Shaaxi, the souther regio of Gasu, ad the southwester regio of Qighai; the third strata icluded the orther regio of Shaaxi, the souther regio of Nigxia, the middle areas of both Gasu ad Qighai, ad a small part of the ortheast regio of Xijiag; the fourth strata icluded orther Nigxia, the middle Gasu ad Qighai, ad the orther Xijiag; ad the fifth strata icluded the orther regios of both Gasu ad Qighai. Sadwich samplig jois the report layer ad Figure 1 The distributio of meteorological statios ad partitio of report layer 3 Results Figure The partitio of the kowledge layer 3.1 Spatial autocorrelatio aalysis I this paper, Mora's I coefficiet method was used to measure the spatial autocorrelatio level of regioal precipitatio by ArcGIS 10.. The result showed the I idex as approximately 0.75, P<0.01, ad the Z score was approximately 17.. It idicated that there was a observable positive autocorrelatio of precipitatio i the study area at the 99% cofidece level, ad showed the state of aggregatio i the space. Each statio had a higher regioal represetatio if the high ad low values of precipitatio were aggregated i space rather tha havig a radom distributio. Samplig of the origial statios could thus determie which statio was highly represetative of the regio.

6 Samplig results I this paper, the pure radom samplig method proposed by Cochra was used to determie the sample capacity. The formula is: ( t S ) td = (15) d where is the capacity of sample; t is the stadard ormal deviatio accordig to sigificace level α; S td is the stadard deviatio of the samples; ad d is the product of the sample mea ad the relative error. The S td was 17.7 ad the sample mea was The t values were , , ad.5758 at the cofidece levels of 90%, 95%, ad 99%, respectively. Accordig to actual coditios, the relative error ad the cofidece level were set at 60% ad 99%, respectively. Eighty-five sample poits were chose to compare the spatial samplig. The software samplig package was used to sample the 155 statios by spatial radom samplig, spatial stratified samplig, ad spatial sadwich samplig. The cofidece iterval, spatial autocorrelatio coefficiet, populatio variace, ad absolute error of the spatial radom sample were set 0.05, 0.4, 17.7, ad 16, respectively. The cofidece iterval of the spatial stratified samplig was set 0.05 ad the variaces of each layer were, respectively, 138, 10, 95, 0, ad 109. The parameters of the sadwich samplig were the same as the stratified samplig, but with added report hierarchical iformatio. The samplig results are show i Table 1. Table 1 Sample distributio of kowledge layers based o differet samplig programs Spatial radom Spatial stratified Spatial sadwich Kowledge All statios samplig samplig samplig layer Amout Percetage Amout Percetage Amout Percetage Amout Percetage % % % % % % % % % % % % % % % % % % 4 8.4% 4 8.4% 3.3 Spatial iterpolatio Ordiary Krigig was utilized to iterpolate the regioal value of aual precipitatio with all of the statios ad samplig results. The iterpolatio results are show i Figures 3a d. Accordig to these results, the iterpolatio by spatial sadwich samples had the best result compared to the spatial radom ad spatial stratified samples. All three of the samplig types estimated that there was more precipitatio i the southeast, less i the orthwest, ad least i the middle area. The iterpolatio result of the spatial radom samples was gradually ad thily distributed, but could ot reflect the extreme values of the whole area, such as orthwester Xijiag, souther Shaaxi, ad cetral Gasu. The iterpolatio of the spatial stratified samples gave better estimates i souther Shaaxi, whereas the spatial radom samples gave worse estimates. However, oly the spatial sadwich samples estimated the extreme values i orthwester Xijiag ad cetral Gasu. 3.4 Report iformatio The three kids of samplig methods could all report the precipitatio iformatio of the study area. The spatial radom samplig method could oly report the mea value ad the stadard deviatio of precipitatio of the samples i whole area. The spatial stratified samplig method could report more iformatio, such as the mea value of each kowledge layer. Ad the spatial sadwich samplig method could ot oly report the iformatio of the kowledge layers, but also of the report layers. I the aalysis of regioal aual precipitatio with spatial sadwich samplig, we could obtai the iformatio of differet report layers, such as watershed layers, raster layers, ad admiistratio layers. The mea iterpolated values of Xijiag, Qighai, Gasu, Nigxia ad Shaaxi were , , 91.59, , ad 56.7, respectively, compared with observed values of , , 97.49, 51.75, ad The mea value of Nigxia had the largest deviatio because oly 4 samples from 10 statios i Nigxia were selected i the spatial sadwich samplig. 3.5 Error aalysis We used cross-validatio of the aual precipitatio iterpolatio of all 155 statios ad the three samplig methods to produce a error aalysis ad evaluate the accuracy of the samples. The results are show i Table.

7 491 Figure 3 The ordiary Krigig iterpolatio of precipitatio uder differet distributios of the samplig methods Table The predictive accuracy of ordiary Krigig uder differet samplig methods Samplig methods All statios Spatial radom samplig Spatial stratified samplig Spatial sadwich samplig ME MSE Comparig the errors of the three types of samplig results of aual precipitatio, the mea error (ME) of the spatial sadwich samplig was , the earest to 0; the.0870 error of the spatial radom samplig was the largest, idicatig that the arithmetic mea of all the predictio errors of the spatial radom samples was the miimum. Accordig to RMSE, ASE ad RMSE ASE, the iterpolatio result of the spatial sadwich samples was closest to the real level. The mea stadardized error (MSE) of the spatial sadwich samples was closest to 0, followed by stratified samples ad spatial radom samples; this idicated that i the spatial sadwich samplig, the degree of differece betwee the sample mea ad the populatio mea was the lowest. Stadardizatio of root mea square stadardized error (RMSSE) idicated the effectiveess of the stadard deviatio of the predictio value. If the stadard error of predictio is valid, RMSSE should be close to 1. If RMSSE is greater tha 1, the the predictio of variability is uderestimated, ad if RMSSE less tha RMSSE RMSE ASE RMSE ASE , the the predicted variability is overestimated. Here, the RMSSE of the spatial sadwich samplig was , which was closest to 1, idicatig that its predicted variability was the most valid. Cosiderig the capacity of all the statios, the optimal error idex of all the statios showed the highest predictio accuracy. The iterpolatio predictio accuracy of the spatial radom samples was the optimal, followed by spatial stratified samplig; spatial radom samplig had the worst result. The predicted values of the 155 statios iterpolated by the 85 differet samples were compared with the observed aual precipitatio values at the 155 statios. Figure 4 is scatter diagram of the observed values ad predicted values; three abormal values were discarded. The regressio coefficiet ad the correlatio efficiet of the spatial radom samplig were ad , respectively, idicatig that the spatial radom samples had the highest predictio accuracy.

8 49 Figure 4 Scatter diagram of observed values ad predicted values at 15 statios Accordig to the iterpolatio error calculatio method of leave-oe-out cross-validatio, ad the scatter diagram of predicted values ad observed values, the correlatio efficiecy of the spatial sadwich samples was , which was closer to 1 tha were the spatial stratified samples ad the spatial radom samples. Thus, the spatial sadwich samples had greater represetativeess tha the two other types. I order to verify the precipitatio iterpolatio of the sample statios i raiy years ad dry years, the sample statios were used to iterpolate surface precipitatio i a raiy year (007) ad a dry year (008). The iterpolatio results ad error of cross-validatio are show i Table 3 ad Figure 5, respectively. The spatial radom samples estimated well i the middle area of moderate precipitatio, but performed badly i the southeast i 007 ad i both the southeast ad orthwest i 008. Spatial stratified samples performed better i the southeast tha did spatial radom samples i both raiy years ad dry years, but worse i the middle area i 008. Spatial sadwich samples estimated the high values i both the southeast ad orthwest i the raiy year (007) ad dry year (008), but did ot perform better tha spatial radom samples at souther Xijiag, orther Qighai, ad ortheaster Gasu which had the least precipitatio. Geerally speakig, the spatial sadwich samples performed better tha the other two methods i both the orth ad the south. However, accordig to the error of cross-validatio, the spatial sadwich samples did ot perform much better tha spatial radom samples i the dry year (008). Therefore, we thik spatial sadwich samples gave a better estimatio of aual precipitatio ad performed well regardig extreme values amog the average years, dry years, ad raiy years. Table 3 The predictive accuracy of ordiary Krigig uder differet samplig programs i 007 (raiy year) ad 008 (dry year) Samplig methods ME MSE RMSSE RMSE ASE RMSE ASE All statios (007) Spatial radom samplig Spatial stratified samplig Spatial sadwich samplig All statios (008) Spatial radom samplig Spatial stratified samplig Spatial sadwich samplig

9 493 Figure 5 The ordiary Krigig iterpolatio of precipitatio uder differet distributios of sample poits i 007 (raiy year) ad 008 (dry year) 4 Coclusio I the samplig ivestigatio of regioal aual precipitatio, the spatial radom samplig method, the spatial stratified samplig method, ad the spatial sadwich samplig method were set at the same sample size, ad the samplig efficiecy was measured by evaluatig the precisio of ordiary Krigig iterpolatio. We foud that the spatial sadwich samplig method had the highest samplig efficiecy, followed by the spatial stratified samplig method, ad the spatial radom samplig method did the worst. The spatial sadwich samplig ad spatial stratified samplig fully cosidered the prior kowledge of people i the study area, while the spatial sadwich samplig imported the report layer, makig the samplig results adjust to the report layer. Also, spatial sadwich samplig could report the iformatio i the report layer accordig to the user's eed. The alpie zoe of orthwester Chia is cold ad sparsely populated, makig it difficult to collect precipitatio data ad do other scietific research. Therefore, whe we set up the rai gauges i the glacier basi, we cut dow the umber of gauges ad the represetativeess was improved by adoptig the spatial sadwich samplig method. This suggests that optimizatio of the existig meteorological statios, for example, by usig 85 represetative spatial sadwich samples, performed better tha other groupigs. There are, however, some problems i this study. For example, the acquisitio of the kowledge layer was difficult, ad it will be ecessary to acquire additioal iformatio ad visit the study site to icrease awareess of the study area. The spatial sadwich samplig oly showed its superiority i the estimatio of regioal aual precipitatio.

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