SPATIAL ESTIMATION OF SOIL MOISTURE AND SALINITY WITH NEURAL KRIGING

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1 SPATIAL ESTIMATIO OF SOIL MOISTURE AD SALIITY WITH EURAL KRIGIG Zhong Zheng 1, 2, Fengrong Zhang 1,*, Xurong Cha 1, Zhanqang Zhu 1, Fuyu Ma 2 1 College of Resources and Envronment, Chna Agrcultural Unversty, Bejng, P. R. Chna College of Agrculture, Shhez Unversty, Shhez, Xnjang Provnce, P. R. Chna * Correspondng author, Address: College of Resources and Envronment, Chna Agrcultural Unversty, Bejng, P. R. Chna , Tel: , Fax: , Emal: zhangfr@cau.edu.cn, zhenglxx@gmal.com Abstract: Keywords: The study was carred out wth 107 measurements of volumetrc sol water content (SWC) and electrcal conductvty (EC) for sol profle (0-30 cm) and the estmatng accuracy of ordnary krgng (OK) and back-propagaton neural network (BP) was compared. The results showed that BP method predcted a slghtly better accurate SWC than that of OK, but dfferences between both methods were not sgnfcant based on the analyss of covarance (AOVA) test (P >0.05). In addton, BP performed much better n EC predcton wth hgher model effcency factor (E) and rato of predcton to devaton (RPD) (E= and RPD=3.54) than that of OK (E= and RPD=0.39). Moreover, a novel neural krgng (K) resultng from the ntegraton of neural network () and ordnary krgng (OK) technques was developed through a geographc nformaton system (GIS) envronment for obtanng trend maps of SWC and EC. There was no sgnfcance between results of K and OK through trend maps. Comparng wth OK, K gves better spatal estmatons for ts great advantage of establshng spatal nonlnear relatonshps through tranng drectly on the data wthout buldng any complcated mathematcal models and makng assumptons on spatal varatons. sol mosture, sol salnty, spatal estmaton, ordnary krgng, artfcal neural networks

2 1228 Zhong Zheng, Fengrong Zhang, Xurong Cha, Zhanqang Zhu, Fuyu Ma 1. ITRODUCTIO In recent years, agrcultural development on the oass plan of Magat, orthwest Chna, has beng threatened by sol secondary salnzaton rrgaton-nduced due to excessve and neffcent water use. Salt accumulaton and excessve salt concentraton n farmlands has led to land degradaton, crop yeld decrease, abandoned lands ncrease, water qualty deteroraton and envronmental degradaton (Ktamura et al., 2006). Therefore, consstent and early stage dentfcaton of sol salnty as well as assessment of sol mosture s vtal for crop producton, especally n ard areas where harsh clmatc condtons together wth rapdly ncreasng populaton denstes (Farfteh et al., 2007). In the farmland, t s mpractcal to sample all the ponts wth the desred temporal frequency n order to research the varablty of sol water and salnty content. Optmzng spatal samplng scheme to reduce samplng densty and estmaton of unsamplng values can save tme and money (Ferreyra et al., 2002; L et al., 2007). However, ts effectveness reles on the accuracy of the spatal nterpolaton used to defne the spatal varablty. Multvarate technques such as geostatstcs and artfcal neural network (A) have been wdely used as estmaton tools. Geostatstcs provdes descrptve tools such as krgng to drectly mplements the predcton of an attrbute at an unsampled locaton accordng to known data ponts wthn a local neghborhood surroundng (Emery & Ortz, 2007). A has the ablty to model extremely non-lnear and complcated relatonshps between a set of nputs, and are operated by usng the avalable nput and output responses wthout consderng nherent system parameters (Sarang et al., 2006). It can be used as an alternatve to predct regonalzed varables (RV) whch are functons on geographc locatons (Huang & Foo, 2002; Farfteh et al., 2007). The performances of dfferent nterpolaton methods such as ordnary krgng (OK), nverse dstance weghtng(idw), splnes and so on, have been analyzed n several studes, whereas there have been many conflctng reports concernng the performances of dfferent nterpolaton methods (Gotway et al., 1996; Patel et al., 2002; Brocca et al., 2007). In addton, many comparsons of varous nterpolaton technques have been made n respect to dfferent data sets used, dfferent mathematcal procedures and dfferent nput parameters (Boken et al., 2004; Robnson & Metterncht, 2006). Moreover, very few studes compare the performance of OK and A methods smultaneously (Rzzo & Dougherty, 1994). Hence, the am of ths paper s to: () dentfy the performance of OK and A for estmaton of sol mosture and salt content n a gven area wthn a threshold of error. () nvestgate the applcablty of neural krgng (K) resultng from the ntegraton of neural network () and ordnary krgng (OK) technques; () llustrate trend maps of sol mosture and salnty dstrbuton for study area.

3 Spatal Estmaton of Sol Mosture and Salnty wth eural Krgng METHODS 2.1 Ste descrpton The study ste s located at the west margn of Taklamakan desert n orthwest Chna. Feld research was conducted on a cotton farmland (30 14'29"-39 14'57", 78 06'21"-78 07'00" E), whch s located n northeast regon of Magat County of Xnjang (Fg. 1). The research feld covers 0.54 km 2 (900m x 600m) wth a 2-4% slope northwest to southeast. The area s 442 m above sea level and experences an ard clmate wth mean annual temperature, precptaton, evaporaton and frost-free perod of 12.4 C, 46.5 mm, 2526 mm and 212 d over a 20-year perod, respectvely. The sol texture s domnant sand sol and ts dstrbuton and varablty n the topsol are nfluenced by Taklamakan desert n ard regons. The farmland for the present study was reclamed n 2000 and cotton was planted from Snce the groundwater n the study ste has hgher mneral degree, sol secondary salnzaton and drought are the man lmtng factors for crop producton n ard regons. Fg.1: Research area locaton and map of the dstrbuton of sol samples. 2.2 Data acquston A grd samplng scheme (40-60 m samplng space) was mposed on the feld wth 107 sample measurements of volumetrc sol water content (SWC) and electrcal conductvty (EC). SWC was measured usng a portable Tme Doman Reflectometry (Sol Mosture Equpment Corp., TRASE TDR) and

4 1230 Zhong Zheng, Fengrong Zhang, Xurong Cha, Zhanqang Zhu, Fuyu Ma EC usng a portable WET sensor (Delta-T Devces Ltd., Cambrdge, UK). On each samplng pont, we nserted vertcally a trple wre TDR probe to montor sol mosture and a wre WET sensor probe for sol salnty n the sol profle (0-30 cm). Each EC and SWC measurement was geo-referenced usng a Dfferental Global Postonng System (DGPS). At each samplng grd pont, fve EC or SWC measurements were made wthn a 1-m dameter crcle. The average readng for each grd pont was computed as EC or SWC datum pont. Sample measurements were mplemented before cotton cultvaton at March 12, Among ths set of 107 measurements, a set of 75 data were selected to consttute valdaton samples, remanng set of 32 for testng samples (Fg. 1). 2.3 Spatal estmaton methods Krgng Krgng estmate reles on a weghtng scheme where closer sample locatons have greater mpact on fnal predcton. At an unsampled locaton and for a gven varogram, a krgng estmate s smply an optmally weghted average of the surroundng sampled data (Emery & Ortz, 2007). In ths study, the total numbers n sample ste were dvded nto tranng sets wth 70% of all samples used for developng a geospatal model, and testng sets wth the remanng 30% used to test the performance of the models (Fg. 1). Accordng to the ntegrated performance of dfferent krgng methods, ordnary krgng(ok), for ts better performance obtaned from a crossvaldaton procedure n the study, was selected to take part n performance comparson to the followng artfcal neural network (A) Artfcal neural network (A) In general, all estmaton technques requre the modelng of the functon Z=f(X, Y), where (X, Y) beng the staton coordnates (lattude longtude) and Z the regonalzed varable (RV). Spatal dstrbuton of sol mosture and salnty s generally related to geographc locatons(x coordnate, Y coordnate). Therefore, the network nput layer used n ths study relates to geographc X coordnate and Y coordnate, whle the network output layer relates to sol mosture and sol salnty. The number of neurons n the hdden layer s of great mportance, as too many neurons may cause overfttng problems, and t can be defned usng a formula recommended or usng a tral-and-error approach (Huang & Foo, 2002). Thus, a 3-layer feedforward back propagaton neural network (BP) (topology structure: 2 x 5 x 2) was establshed (Fg. 2) and used wthn eural etwork Toolbox of

5 Spatal Estmaton of Sol Mosture and Salnty wth eural Krgng 1231 Matlab 7.0 (The MathWorks Inc. atck, MA). Tan-sgmod transfer functons and log-sgmod transfer functons (non-lnear) were selected for the hdden and output layers, respectvely. The Levenberg-Marquardt algorthm, whch provdes a fast optmzaton, was used for network tranng. Total of 107 sol samples were dvded nto two groups as 75 for the development (tranng and valdaton) and 32 for the test (Fg.1). Smulated error s 3% and 0.02 ms/cm for SWC and EC n tranng and testng process, respectvely. However, A only allows the RV estmaton, but not the predctor varance, whch s possble wth krgng (Rzzo & Dougherty, 1994; Koke et al., 2001). In some applcatons A s coupled wth krgng estmaton, whch was called neural krgng (K) by Rzzo and Dougherty (1994). K s dvded nto two steps: the frst s neural and uses neural network, and the second uses OK. The fnal estmates are produced as a sum of estmates and OK estmates. Hence K s an ntegrated nterpolaton technque. In spatal estmaton ts utlzaton s justfed by the fact that t extracts ts knowledge only from data, whch contan nformaton about the spatal dstrbuton of the RV. The present paper follows the K approach to estmate sol mosture and salnty and compare the obtaned estmates wth OK technque, and then llustrate trend maps of SWC and EC. Fg.2: Three-layer feed forward back propagaton neural network structure. 2.4 Evaluaton crtera We used cross-valdaton to valdate the accuracy of nterpolaton algorthms and examne the dfference between the measured values and the predcted values usng mean absolute errors (MAE) or relatve MAE (MAE%) (Eq. (1)), root-mean-square error (RMSE) or relatve RMSE (RMSE%) (Eq. (2)), rato of predcton to devaton (RPD) (Eq. (3)) and model effcency factor (E)(Eq. (4)). The RPD ndcates strength of

6 1232 Zhong Zheng, Fengrong Zhang, Xurong Cha, Zhanqang Zhu, Fuyu Ma statstcal correlaton between measured and predcted values. MAE, RMSE and E values ndcate degree of agreement between measured and predcted values. Detaled descrptons and defntons of these model performance parameters are gven by Robnson & Metterncht (2006) and Farfteh et al. (2007). 1 MAE Z x Z x * ( ) ( ) MAE% MAE Z ( x ) 1 * ( ) ( ) 2 RMSE RMSE Z x Z x RMSE% 100 (2) Z ( x ) RPD E 1 Where * * 2 Z ( x ) [ Z ( x )] / /( 1) 2 * * 2 Z ( x ) Z( x ) [ ( Z ( x ) Z( x )] / /( 1) ( ) Z x * 1 * Z ( x ) Z( x ) Z ( x ) Z ( x ) Z( x ) Z ( x ) 2 s the observed (measured) value of Z at locatons x, 2 ( ) Z x Z * ( x ) (1) (3) (4) * ( ) Z x s the predcted value at the same locatons,, s the average measured and predcted value, respectvely. s the number of values n the dataset. Conventonal statstcal analyses were conducted usng the software package SPSS 12.0 for Wndows (SPSS Inc., MatLab, USA). Geostatstcal analyses and mappng were performed by usng ArcGIS 9.0 software package (Envronmental Systems Research Insttute, Redlands, CA). 3. RESULTS AD DISCUSSIO 3.1 Descrptve statstcs Based on above estmaton methods as dscussed, descrptve statstcs for SWC and EC used n the development and valdaton of BP and OK are summarzed n Table 1. It s observed than both varables are approxmately normal dstrbuton avodng the need for data transformaton accordng to the coeffcent of skewness. The sol of study area has wde ranges of SWC and EC wth % and ms/cm, respectvely. The predcted

7 Spatal Estmaton of Sol Mosture and Salnty wth eural Krgng 1233 values of SWC and EC wth BP method, rangng between % and ms/cm respectvely, have smaller range and dstrbutons closer to the average measured values than that of OK, whch rang between % and ms/cm respectvely. Besdes, there s less standard devaton of BP than that of OK. Hence, we prmarly conclude that BP method could perform somewhat better than OK from the descrptve statstcs obtaned from cross-valdaton. Table 1 Summary statstcs of SWC (%) and EC (ms/cm) Sol property Mean Maxmum Mnmum Std.Dev. Skewness Kurtoss SWC (%) Measured OK method BP method EC (ms/cm) Measured OK method BP method Spatal estmaton and ts performance SWC and EC can all be estmated by both methods whle the former varable yelds very good results (Fg.3a) and the latter shows a bad generalzaton (Fg.3b). Besdes, Fg.4a and Fg.4b also shows good performance of SWC by both methods, respectvely. The worse performance of EC can be seen n Fg.4c and Fg.4d, where measured and predcted values are more scattered. Comparng to coeffcent of determnaton (R 2 ) (Fg.4), R 2 between predctons and observatons ranges from to for SWC and from to for EC by both methods. Ths result reveals that SWC predcton value has better performance than EC. Furthermore, spatal varablty of EC s beng under-predcted, whch s n good agreement wth the feld fndng smlar to the study reported by L et al. (2007). It has to be ponted out that the qualty and quantty of the data used for the study were not adequate to the complexty of spatal varablty of sol propertes. Boken et al. (2004) consdered that the accuracy estmate can be mproved by enhancng the representaton of samplng stes as well as by lmtng the estmatons to rrgated areas wthn countes. Based on the statstcal parameters as dscussed, both OK and BP model are valdated usng the model effcency factor E and RPD of predcted values. The E and RPD between reference measurements,.e. accurate or good predcton f RPD and E values are hgher than 2.5 and 0.80 respectvely by Farfteh et al. (2007), suggest an accurate to good predcton. It s observed from Table 2 that BP method (wth E= and RPD=15.06) predcts an accurate SWC nearly smlar to that of OK (wth E= and RPD=16.76), whereas dfferent performances occurred n predctng EC.

8 1234 Zhong Zheng, Fengrong Zhang, Xurong Cha, Zhanqang Zhu, Fuyu Ma BP method wth much hgher E = and RPD=3.54 performs well whle OK wth E= and RPD=0.39 performs poorly n EC predcton. In addton to MAE% and RMSE%, t s consdered that OK performs slghtly better, but dfferences between BP and OK methods n predctons are not sgnfcant for both varables based on the analyss of covarance (AOVA) test (P >0.05). Fg.3: Comparson of the estmated and measured values wth both methods for (a) SWC and (b) EC. Fg.4: Plots of the measured versus predcted values and the ftted regresson lne and equaton for (a) SWC wth OK, (b) SWC wth BP, (c) EC wth OK and (d) EC wth BP method.

9 Spatal Estmaton of Sol Mosture and Salnty wth eural Krgng 1235 Table 2 Performance of predcted values usng OK and BP methods Sol property MAE MAE% RMSE RMSE% E RPD SWC (%) OK method BP method EC (ms/cm) OK method BP method Trend maps of SWC and EC by K and OK As explaned n secton 2.3, the data nonlnear trend can be estmated by neural krgng (K) better than the ordnary krgng (OK) estmator f neural networks are coupled wth krgng. The K approach presented here for spatal estmaton s the result of the ntegrated of two dfferent technques: BP evaluaton and ordnary krgng (OK). Fg.5: Trend maps obtaned from estmated values of (a) SWC by OK, (b) SWC by K, (c) EC by OK and (d) EC by K method. Trend maps of sol mosture and salnty produced by OK and K are llustrated n Fg.5. Postve values show areas where SWC or EC predctons are hgher and negatve values represent areas where predcton values are lower. By lookng at the maps of Fg.5, dfferences between results of OK and K are not sgnfcant. In addton, the smoothed contour maps n Fg.5a and Fg. 5b dsplay qute smlar patterns wth low sol mosture n the eastern secton and hgh n the western and southern parts of the study area, whereas contour maps n Fg.5c and Fg. 5d wth hgh salnty n the eastern secton and low n the western sectons ncludng northwestern and southwestern parts. Because of the research feld wth a 2-4% slope

10 1236 Zhong Zheng, Fengrong Zhang, Xurong Cha, Zhanqang Zhu, Fuyu Ma northwest to southeast and sol texture wth hgh sand content and permeablty, salt leachng wth rrgaton and upward transport wth evaporaton are frequent. Ths may be result n rapd salt leachng and accumulaton n the topsol n southeastern secton of ths feld. Therefore, water floodng for rrgaton should be reduced to a great extent and watersavng rrgaton should be promoted n rrgaton areas. 4. COCLUSIOS The key am of the work s to contrbute to the problem of spatal estmaton of sol propertes wth a novel soluton, through the combned utlzaton of statstcal, geostatstcal and artfcal neural network (A) technques. The approach of neural krgng(k), coupled neural network () wth ordnary krgng (OK), has a great potental for predctng and mappng sol propertes. The procedure of K requres nformaton on the coordnates (X, Y) of a survey pont n the nput. After the completon of tranng, the traned network s tested to estmate sol propertes for all sample locatons wthn the area of nvestgaton by producng a correspondng contour map wth krgng technque. The K results compare very well wth smlar contour maps generated usng OK technques. The man advantage of K approach s ts ablty n establshng patterns or nonlnear relatonshps through tranng drectly on the data wthout buldng any complcated mathematcal models and makng assumptons on spatal varatons. It can be seen that ths method yelds hgh and sgnfcant spatal relatons and gves better spatal estmatons. ACKOWLEDGEMETS Ths work s supported n part by grants from the atonal atural Scence Foundaton of Chna (o ) and from the Xnjang Bngtuan Scence & Technology Research Program of Chna (o.2007yd YD43 and 2006GJS13). The authors also wsh to thank the key oass eco-agrculture laboratory of Xnjang Bntuan for offerng research workstaton. REFERECES Boken, V. K., Hoogenboom G., Hook, J.E., Thomas, D.L., Guerra, L.C., Harrson, K.A.. Agrcultural water use estmaton usng geospatal modelng and a geographc nformaton system, Agrc. Water Manage, 2004, 67:

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