Artcle Adaptve Surface Modelg of Sol Propertes Complex Ladforms We Lu, *, Ha-Rog Zhag 2, *, Da-Peg Ya ad Sheg-L Wag School of Geography, Geomatcs ad Plag, Jagsu Normal Uversty, Xuzhou 226, Cha; dpy990jsu@26.com (D.-P.Y.); wsljsu@26.com (S.-L.W.) 2 School of Evromet Scece ad Spatal Iformato, Cha Uversty of Mg ad Techology, Xuzhou 226, Cha * Correspodece: 60200005@jsu.edu.c (W.L.); harog-zhag@cumt.edu.c (H.-R.Z.); Tel.: +86-30-393-9855 (W.L.); +86-58-9520-6587(H.-R.Z.) Academc Edtor: Wolfgag Kaz Receved: 24 Aprl 207; Accepted: 8 Jue 207; Publshed: 20 Jue 207 Abstract: Spatal dscotuty ofte causes poor accuracy whe a sgle model s used for the surface modelg of sol propertes complex geomorphc areas. Here we preset a method for adaptve surface modelg of combed secodary varables to mprove predcto accuracy durg the terpolato of sol propertes (ASM-SP). Usg varous secodary varables ad multple base terpolato models, ASM-SP was used to terpolate sol K + a typcal complex geomorphc area (Qgha Lake Bas, Cha). Fve methods, cludg verse dstace weghtg (IDW), ordary krgg (OK), ad OK combed wth dfferet secodary varables (e.g., OK-Laduse, OK-Geology, ad OK-Sol), were used to valdate the proposed method. The mea error (ME), mea absolute error (MAE), root mea square error (RMSE), mea relatve error (MRE), ad accuracy (AC) were used as evaluato dcators. Results showed that: () The OK terpolato result s spatally smooth ad has a weak bull's-eye effect, ad the IDW has a stroger bull s-eye effect, relatvely. They both have obvous defceces depctg spatal varablty of sol K +. (2) The methods corporatg combatos of dfferet secodary varables (e.g., ASM-SP, OK-Laduse, OK-Geology, ad OK-Sol) were assocated wth lower estmato bas. Compared wth IDW, OK, OK-Laduse, OK-Geology, ad OK-Sol, the accuracy of ASM-SP creased by 3.63%, 0.85%, 9.98%, 8.32%, ad 7.66%, respectvely. Furthermore, ASM-SP was more stable, wth lower MEs, MAEs, RMSEs, ad MREs. (3) ASM-SP presets more detals tha others the abrupt boudary, whch ca reder the result cosstet wth the true secodary varables. I cocluso, ASM-SP ca ot oly cosder the olear relatoshp betwee secodary varables ad sol propertes, but ca also adaptvely combe the advatages of multple models, whch cotrbutes to makg the spatal terpolato of sol K + more reasoable. Keywords: complex ladform; adaptve surface modelg; spatal terpolato; geostatstcs; sol propertes. Itroducto Scetfc maagemet ad utlzato of sol resources s predcated o correct uderstadg of the cotuous chages regoal sol propertes. Spatal terpolato s the ma method used to evaluate cotuous chages sol propertes [], as well as beg a mportat research tool the felds of dgtal sol ad pedometrcs mappg [2]. Curret spatal terpolato methods maly orgate from dscrete moder mathematcal theores (fucto theory ad dfferetal geometry), ad ca be largely classfed to three groups [3]: () determstc or o-geostatstcal methods (e.g., verse dstace weghtg, IDW), (2) geostatstcal methods (e.g., ordary krgg, ISPRS It. J. Geo-If. 207, 6, 78; do:0.3390/jg606078 www.mdp.com/joural/jg
ISPRS It. J. Geo-If. 207, 6, 78 2 of 6 OK), ad (3) combed methods (e.g., regresso krgg). These methods are ofte data- or eve varable-specfc ad ther performace depeds o may factors. No cosstet fdgs have bee acqured to detfy the best terpolato method, ad most are global models (.e., the same model s appled over the whole study area) [4,5]. However, areas of ladform complexty, the spatal dstrbuto of sol propertes s affected by secodary varables such as sol type, lad use type, ad ladform type, ad t s dffcult to satsfy the basc assumptos of curret models [6,7]. Further, owg to varous shortcomgs, sgle terpolato models restrct the mprovemet of predcto accuracy. I recet years, some mache learg methods have bee appled to the felds of data mg ad spatal terpolato ad have demostrated ther predctve accuracy; for example, artfcal eural etworks (ANN), radom forest (RF), ad support vector mache (SVM). Furthermore, ANN ad SVM have bee appled to daly mmum ar temperature ad rafall data some subjects [8,9]. However, all of these represet global terpolato models, whch are dffcult to adapt to ladform complexty areas. Utlzg the advatages of esemble learg for regresso, we combed a seres of terpolato models to carry out terpolato smulato of the spatal varato sol propertes ad verfed the relablty of mult-model tegrato [0]. Despte ths, ssues stll rema; for example, prevous work, we oly coducted a global regresso tegrato of varous terpolato models, wth lmted cosderato of dscotuous space ad spatal varato problems. Furthermore, remag terpolato models eed mprovemet ad optmzato before they ca be tegrated. I addto, a rage of studes have demostrated that terpolato accuracy ad mappg qualty ca be effectvely mproved by the use of secodary varables as supplemetary formato [4, 8]. Lad use, sol type, grasslad type, ad geology type mght be expected to play a sgfcat auxlary role cotrollg the spatal varato of sol propertes. Prevous work by Sh et al. [] demostrated the effectveess of corporatg lad use type ad sol type to mprove terpolato smulato of sol propertes. I addto, may studes have detfed topography as a mportat auxlary elemet [3,9], but prevous research results suggest t s ot a key factor the study area [0]. Therefore, tegrato of secodary varables ths study should have a mportat fluece o terpolato accuracy. I order to solve the global model ad secodary varable problems that had log troubled the terpolato method, ths study amed to address some of the outstadg ssues, wth a overall goal of mprovg the predcto accuracy of the sgle terpolato model areas wth complex ladforms, usg sol K + as a example. We appled aalyss of varace (ANOVA) to select secodary varables closely related to the spatal varato of sol K +, tegrated secodary varables, ad costructed a seres of sol property terpolato models. To deal wth the dscotuty ad spatal varato of sol propertes areas wth complex ladforms, error surfaces were costructed to eable adaptve parttog of terpolato surfaces for screeg sutable base terpolato models. Ths paper optmzed the screeed base terpolato models, ad bult ad coordated mult-model tegrato terpolato methods (dfferet combatos of terpolato models were selected for dfferet areas) to realze a hgh precso smulato of sol propertes. We evaluated the performace of the dfferet spatal terpolato methods IDW, OK, OK-Laduse, OK-Geology, OK-Sol, ad ASM-SP, ad aalyzed ther predctve capabltes terms of sol K + maps. 2. Method 2.. Study Area ad Datasets The study area (36 38 37 29 N, 99 52 00 50 E) s located the southeast part of the Qgha Lake Bas, o the Tbeta Plateau, Cha (Fgure ). The log-term combed acto of geologcal movemet ad exteral forces have formed a complcated ad dverse array of geomorphc features the area. The study area covers a total of 200 km 2, wth a alttude ragg betwee 3043 ad 456 m, ad s characterzed by complex ladforms, cludg moutas, hlls, tablelads, ad plas. Abudat agrcultural ad husbadry actvtes are carred out the area.
ISPRS It. J. Geo-If. 207, 6, 78 3 of 6 The study area s characterzed by 6 sol types (Fgure 2a); 2 geology types, cludg alluval terrace, deudate hgh terrace, ad dluval pla (Fgure 2b); ad 8 lad use types, cludg croplad, grasslad, ad potetal arable lad (Fgure 2c). The grasslad ca be dvded to 20 types, maly cludg Achatherum spledes, leymus, ad Blysmus socompressus (Fgure 2d). We calculated the statstcal characterstcs of sol K+ secodary varables usg 0 trag samples (Table ). Fgure. Locato of the study area, showg sample stes (crcles) ad elevato (shadg). Fgure 2. Characterstcs of the study area: (a) sol types, from the :,000,000 sol map of the Cha Sol Ivestgato Offce; (b) geology types, from the :500,000 geologc map of the Bureau of Geologcal Explorato ad Developmet of Qgha Provce; (c) lad use types; ad (d) grasslad types.
ISPRS It. J. Geo-If. 207, 6, 78 4 of 6 Table. Descrptve statstcal characterstcs of sol K + cotet dfferet secodary varables. Secodary Varable Subtype Number Mea Stadard Error Area/km 2 Area Proporto/% Alpe meadow sol 32.98 0.4 420.47 20.8 Chestut sol 54 2.0 0.8 360.4 67.3 Sol Flow sady sol 0.72 0.2 44.76 7.6 Meadow marsh sol 6.84 0.03 3.9.58 Sem-fxed sady sol 8.50 0.07 63.4 3.4 Alluval terrace 8 2.04 0.4 7.25 3.53 Deudate hgh terrace 0 2.5 0.07 266.73 3.22 Dluval pla 3 2.0 0.3 55.24 25.53 Hlly 3 2.4 0.05 3.76 0.9 Lacustre pla 20.94 0.7 333.33 6.52 Geology Lake beach 5.84 0.09 43.99 7.4 Large rollg alpe 0.89 0.2 32.64 6.57 Mddle rollg alpe 4.9 0.0 5.63 0.28 Sad due 4.63 0.4 93.5 9.57 Small rollg alpe 4 2.05 0.2 287.08 4.23 Valley pla 9.96 0.08 65.22 3.23 Croplad 0 2.4 0.08 77.6 3.83 Grasslad 4.99 0.3 72.65 58.7 Meadowlad 25 2.02 0.2 47.44 20.7 Lad use Potetal arable lad 6.88 0.4 229.32.38 Scrublad 0.9 0.22.8 0.05 Swamp meadowlad 5.84 0.04 32.09.59 Uused lad 3.64 0.09 86.43 4.29 Achatherum spledes 37.93 0.7 79.58 35.59 Artemsaarearadc 2.49 0.07 3.83.57 Blysmus socompressus 5.93 0.4 30.00.48 Bush cqefol 8 2.06 0.4 57.9 25.58 Coarse beak carex 2.86 0.04 20.0 0.99 Elymus utas 3.73 0.08 8.49 0.9 Ephedra.50 0 2.49 0.2 Gravel 4.68 0.0 35.38 6.70 Irs esata thub.96 0 34.47.70 Grasslad Leymus 6.94 0.27 28.95.43 Kobresa humls 4 2.02 0.08 28.30.40 Koelera tbetca 4.80 0.0 24.45.2 Kobresa capllfola 7 2.05 0.08 57.90 7.8 Kobresa myosurodes 3 2.6 0.06 82.99 4. Salx ortrepha 2 2.02 0.05 6.33 0.8 Serpet grass 2.94 0.08 4.29 0.2 Stpa krylov 3.82 0.05 5.77 2.56 Stpa purpurea 5 2.4 0.07.5 5.52 Water ba zh 2.08 0 5.64 0.28 Feld samplg of surface sol (0 30 cm) at 0 samplg pots was carred out September 203 to supplemet map data. The mea dstace betwee sol samplg locatos was approxmately 6.74 km. The samplg stes were desged to cover the whole area ad clude dfferet ladscapes. I order to esure ratoal dstrbuto of the samplg pots across the dfferet geo-evromets, a spatally stratfed samplg strategy was appled based o ladscape types [20]. Supported by the Qgha Evrometal Motorg Ceter, we recorded formato such as sol type, alttude, geology, ad lad use for each sample locato. Each posto was sampled three tmes ad the mea was recorded as the sample value. Sol samples were take back to the laboratory for aalyss. After ar dryg, grdg, ad screeg through a 2 mm seve, sol K + of the samples was measured usg sodum hydroxde meltg aalyss [2]. The secodary varables were compled ArcGIS 0.2, ad coverted to a resoluto rato of 30 m through resamplg. Sce the study area covers a comparatvely large rage of ladscape types, ad the umber of samples was relatvely small, the spatal dstrbuto of samples was ueve (Fgure ) ad some ladscape types wth a relatvely hgh degree of fragmetato are poorly
ISPRS It. J. Geo-If. 207, 6, 78 5 of 6 represeted. I the study area, the subtypes of secodary varables ot sampled aywhere covered oly a very small area (.e., scrublad; Fgure 2c; Table ). For ths area, we drectly used the earest fve-pot surroudg values for the subtype to calculate the mea value. 2.2. Methods for Spatal Iterpolato 2.2.. Iverse Dstace Weghtg IDW s a determstc method for multvarate terpolato usg a kow scattered set of pots. Values assged to ukow pots are calculated wth a weghted average of the values avalable at kow pots. Weghts are usually versely proportoal to the power of dstace [22], whch, at a usampled locato x, leads to a estmator: * Z ( x) = λz( x)= Z( x) = = / d = p / d p () where Z*(x) s the predcted value, Z (x) s the measured value, s the umber of closest pots (typcally 0 to 30), p s a parameter (typcally p = 2), ad d s the cut-off dstace. 2.2.2. Ordary Krgg Krgg terpolato s cosdered the best ubased lear estmato method [23]. Whe the mathematcal expectato of the regoalzed varable Z*(x) s ukow, t s termed ordary krgg. Z*(x), the estmated value of varables at pot x, s obtaed by the lear combato of Z (x)s, the effectve observed value, usg the expresso: * Z x λz x = ( ) = ( ) (2) λ s the weght gve to the observed value Z( x ) ad represets the cotrbuto of each where observed value to the estmated value Z*(x). It ca be calculated by the sem-varace fucto of the varables o the codto that the estmated value s ubased ad optmal. The sem-varace fucto ca be expressed by the equato: γ ( h) = N( h) [ Z( x ) Z( x + h)] 2 N( h) 2 (3) = where γ ( h) s the sem-varace, N(h) s the pot group umber at dstace h, Z( x ) s the umercal value at posto x, ad Z( x + h) s the umercal value at dstace ( x + h). 2.2.3. Base Iterpolato Models As a kd of geostatstcal model [24,25], each observato z(xm,ym) of a specfc sol K + at locato (x, y) the -th type of the m-th kd of secodary varable ca be expressed as: zx (, y ) = me ( ) + rx (, y ) (4) m m m m m where m(em) s the mea value of z(xm,ym) the -th type of the m-th kd of secodary varable, ad r(xm,ym) s the resdual computed by subtractg the mea value m(em) of the -th type of the relatve m-th secodary varable from the measured value of sol K +. We assumed that m(em) ad r(xm,ym) are mutually depedet ad that varato of r(xm,ym) s homogeeous over the etre study area. The resduals were the used to terpolate the surface of resduals over the whole study area by OK. Fally, the terpolated resdual values were summed to the sol K + meas of the relevat secodary varable as the fal terpolated values of OK wth secodary varable for the
ISPRS It. J. Geo-If. 207, 6, 78 6 of 6 sol K + ; that s, the mea was modfed wth surface modelg of resduals. See Secto 3.3. for the specfc modelg process of base terpolato models (.e., OK-Laduse, OK-Sol, OK-Geology). 2.3. Method for Adaptve Parttog A seres of terpolato surfaces of sol propertes were geerated from the base terpolato models to calculate smulato errors for sol samplg pots. The error surface, derved from lear terpolato, was used to determe whether the error of each raster cell exceeded a threshold value. Raster cells below the threshold value were clustered to determe the spatal rage of applcablty of each terpolato model after multple teratos. The dvdual steps are show Fgure 3a ad detaled below. Fgure 3. Adaptve parttog process (a) ad clusterg (b). Step oe: Raster cell smulato. For a specfc sol property terpolato model (e.g., M), sol propertes are calculated for the whole study area at a specfc resoluto rato C0 to gve the raster smulato value S0; Step two: The sol property smulato error at each samplg pot s calculated by subtractg the smulato value from the measured value; Step three: Error surface costructo. The error surface s costructed usg lear terpolato based o the smulato error obtaed step two; Step four: Calculate the smulato error of sol propertes at each raster cell, based o the error surfaces obtaed step three; Step fve: Determe whether e (=, 2, m), the error of each raster cell, satsfes e < ε, where ε s the error threshold. If t does, ths raster cell s marked as a clusterg cell; Step sx: Clusterg. Areas that meet the accuracy threshold are clustered based o the spatal locatos clusterg cells. R, R2, ad Rk, etc., are the cluster spaces of the terpolato model M (Fgure 3b); Step seve: Repeat the above steps for each terpolato model to determe ther applcable spatal rages. 2.4. Assessmet of Performace Idepedet valdato was appled to assess terpolato accuracy. The sol K + sample data were radomly splt to two groups, oe of whch was used for terpolato ad the other for
ISPRS It. J. Geo-If. 207, 6, 78 7 of 6 valdato. A total of 90 sol K + sample pots were used for terpolato ad the remag 20 were used for valdato. We assessed the accuracy of the dfferet terpolato methods by comparg the mea error (ME), mea absolute error (MAE), mea relatve error (MRE), root mea square error (RMSE), ad accuracy (AC) of predcted ad measured values. The specfc equatos used are as follows: ME = ( z( x ) z ( x )) = (5) MAE = = z ( x ) z ( ) x (6) MRE = = z ( x ) z ( x )/ z( x ) (7) = ( ( ) ( )) 2 z x z RMSE = x (8) 2 AC = RMSE (9) PEV 2 ( ) ( ) (0) PEV = z x o + z x o j= where s the umber of samples; PEV s the potetal error varace (PEV); z( ) ad z ( ) the measured ad predcted values, respectvely; ad o s the mea measured value. AC vares betwee 0 ad, wth larger values dcatg a better predcted result. Smaller values of ME, MAE ad RMSE, dcate greater terpolato accuracy. MRE s dmesoless ad smaller values dcate greater terpolato accuracy. 3. Results 3.. Parameter Specfcato ad Selecto of Secodary Varables Based o ftted ugget, sll, ad rage values, the sem-varogram model was selected for aalyss of spatal correlato. Other models were cosdered, cludg expoetal, sphercal, Bessel, crcular, ad Gaussa, whle expoetal ad K-Bessel models were selected for the OK ad base terpolato models as they better ftted the data/resduals (Fgure 4). To determe the umber of krgg samples, we chose the best samples from 5 to 30 at 5-step tervals. The spatal correlato of resduals showed good performace after removal of the local mea wth the dfferet secodary varables (Table 2). All of the sem-varograms of resduals teded to show a smaller sll ad a shorter rage, dcatg that drft had bee removed [26]. The ugget/sll rato (N/S) of resduals was <0.3 for all models except OK-Geology, whch dcates strog spatal correlato of the resdual data [27]; the spatal correlato creased after tred removal. Ths fdg suggests that the OK ad base terpolato models were approprate for the study area. x x are Table 2. Sem-varogram models. Parameter Resdue of OK_Laduse Resdue of OK_Sol Resdue of OK_Geology OK Model K-Bessel K-Bessel Expoetal Expoetal Rage/0 km.984.269.984 2.5058 Nugget (N) 0.0204 0.0324 0.866 0.2483 Sll (S) 0.4842 0.5043 0.4783 0.602 N/S 0.042 0.069 0.390 0.430
ISPRS It. J. Geo-If. 207, 6, 78 8 of 6 Fgure 4. Sem-varograms of sol K + resduals for: (a) OK-Sol; (b) OK-Geology; (c) OK-Laduse; ad (d) OK (orgal values). The secodary varables used for each method were aalyzed by ANOVA. The sol K + data were grouped to classes order to compare sol K + for the dfferet secodary varables. For example, terms of sol type, the sol K + data were grouped to fve classes: alpe meadow sol, chestut sol, flow sady sol, meadow marsh sol, ad sem-fxed sady sol, wth 32, 54, 0, 6, ad 8 samples each, respectvely. The sol K + varaces betwee ad wth sol types were determed by ANOVA usg SPSS 2.0 for Wdows. 3.2. ANOVA Aalyss of Sol Propertes for Dfferet Secodary Varables The ANOVA results comparg the fluece of dfferet secodary varables o Sol K + are show Table 3. Geology type, sol type, ad lad use type are strogly correlated wth the spatal varato sol K +, wth sgfcace at the 0.0 level. However, grasslad type s poorly correlated wth sol K + (sgfcace level of 0.2). Ths s maly due to the larger degree of fragmetato of the sol map of grasslad types, ad the lmted umber of sample pots for some grasslad, wth some subtypes of grasslad havg just or 2 samplg pots (Table ). Hece, grasslad type was ot used the process of costructg the base terpolato ad ASM-SP models. Table 3. ANOVA aalyss for testg the sgfcace of secodary varables o sol K + varace. Geo-Factors Sol Property Geology type Sol K + Sol type Sol K + Lad use type Sol K + Grasslad type Sol K + Sources of Varace Degree of Freedom Sum of Varace Mea Varace F Value p Value I-group 9.033 0.5 2.856 0.005 Betwee groups 0 4.060 0.04 Total 0 5.093 I-group 4 0.722 0.8 4.378 0.003 Betwee groups 06 4.37 0.04 Total 0 5.093 I-group 4 0.462 0.6 2.645 0.008 Betwee groups 06 4.63 0.044 Total 0 5.093 I-group 6 0.934 0.058.39 0.202 Betwee groups 94 4.59 0.044 Total 0 5.093 3.3. ASM-SP The ASM-SP was costructed three steps: frst, a umber of base terpolato models were produced (e.g., OK-Laduse, OK-Sol, ad OK-Geology); secod, the base terpolato models were parttoed by a adaptve method; thrd, the base terpolato models were combed usg a popular combato scheme. The models OK-Laduse, OK-Sol, ad OK-Geology were used as the base terpolato models. Adaptve parttog was coducted o the base terpolato models usg the method descrbed Secto 2.3 to costruct error surfaces; parttos that met the
ISPRS It. J. Geo-If. 207, 6, 78 9 of 6 accuracy requremet were screeed ad the ASM-SP was costructed based o raster cell optmzato. The specfc steps were as follows. 3.3.. Costructo of Base Iterpolato Models Step oe: Equato (4) was used to calculate mea sol K + for each geologcal factor ad obta mea surface m(em). The mea sol K + was correlated to the secodary varables, based o measured values of sol K + (Fgure 5). (a) (b) (c) Fgure 5. Mea surface m(em) of sol K + for dfferet secodary varables: (a) lad use; (b) geology; (c) sol type. Step two: The mea value of sol K + was subtracted from the measured value to calculate the resduals of sol K +. The resduals were the terpolated by OK to obta the resdual surface r(xm,ym) (Fgure 6). (a) (b) (c) Fgure 6. Resdual surfaces r(xm,ym) of sol K + for dfferet secodary varables: (a) lad use; (b) geology; (c) sol type. Step three: The mea (Fgure 5) ad resdual surfaces (Fgure 6) were added to gve z(xm,ym), the spatal terpolato result of sol K + that tegrates the secodary varables, whch s the base terpolato surface to be tegrated.
ISPRS It. J. Geo-If. 207, 6, 78 0 of 6 3.3.2. Adaptve Parttog of Iterpolato Surfaces Based o the method for costructg error surfaces outled Secto 2.3, the local polyomal terpolato was used to obta error surfaces for the dfferet terpolato models (Fgure 7) ad to determe the spatal rage of applcablty for each terpolato model. (a) (b) (c) Fgure 7. Error surfaces of base terpolato models: (a) lad use; (b) geology; (c) sol type. 3.3.3. Itegrato of Iterpolato Surfaces O the bass of raster cell optmzato, terpolato results of raster cells wth the mmum error were selected as the optmal raster cell to be tegrated. Fgure 8 dsplays the prcple of the raster cell optmzato method, ad Fgure 9 shows the optmal parttos correspodg to the dfferet terpolato models. Fgure 8. The raster cell optmzato process ( a ad b are dfferet models of raster terpolato, c ad d are the terpolato error, e s the optmal raster cell mosac result).
ISPRS It. J. Geo-If. 207, 6, 78 of 6 Fgure 9. Regoal dstrbuto of optmzed base terpolato models. 3.4. Comparso of Iterpolato Performace The accuracy of ASM-SP for smulatg the spatal varato of sol K + was evaluated by comparg the smulato effectveess of sx terpolato methods, amely OK-Laduse, OK-Geology, OK-Sol, IDW, OK, ad ASM-SP. Fve evaluato dexes, ME, MAE, RMSE, MRE, ad AC, were used to depedetly valdate the models (Table 4). As dcated Table 4, the ME of the terpolato methods that combed secodary varables (.e., OK-Laduse, OK-Geology, OK-Sol, ad ASM-SP) was closer to 0 tha those of the covetoal terpolato methods (.e., IDW ad OK). Ths mples that terpolatos that tegrate secodary varables are less based. The ASM-SP method had lower ME, MAE, RMSE, ad MRE values tha the other terpolato methods, dcatg better performace, ad ths was reflected ts greater AC (0.9950). The terpolato accuracy of ASM-SP was hgher overall for two reasos. Frst, the method combes secodary varables so t more accurately depcts sol K + boudares as they vary wth the chagg geo-evromet. Secod, based o gve accuracy thresholds, ASM-SP adaptvely screes the optmal predcto area of multple terpolato models ad regroups them a optmzed way. The other methods, OK-Laduse, OK-Geology, ad OK-Sol, oly cosder the fluece of secodary varables o the spatal varace of sol K +, but do ot further scree ad optmze the terpolato results. Thus, they are feror to ASM-SP terms of terpolato accuracy. Table 4. Comparso of the accuracy of OK, OK-Laduse, OK-Geology, OK-Sol, verse dstace weghtg (IDW), ad ASM-SP terpolato. Evaluato Idex OK-Laduse OK-Geology OK-Sol IDW OK ASM-SP ME 0.0030 0.0037 0.0024 0.0072 0.0093 0.007 MAE 0.0294 0.030 0.0236 0.0362 0.034 0.0072 RMSE 0.0742 0.0672 0.085 0.637 0.067 0.0586 MRE 95.9% 96.57% 95.87% 96.04% 95.34% 89.69% AC 0.9047 0.986 0.9242 0.8756 0.8976 0.9903 3.5. Comparso of Iterpolated Maps The predctve capabltes of the sx terpolato methods terms of the sol K + maps are compared Fgure 0. The IDW terpolato gves a good represetato of the overall patter of sol K + dstrbuto, but the accuracy of small scale varatos s low. Also, a relatvely strog
ISPRS It. J. Geo-If. 207, 6, 78 2 of 6 bull s-eye effect s created areas wth greater or fewer samplg pots. The smulato surface of OK s smoother ad ts terpolato rage s at a termedate level. Owg to the smoothg effect of krgg, the rage of varato sol K + s arrower tha the true value, whch s what has bee foud other studes [28 3]. The OK map also shows a weak bull s-eye effect. The OK-Laduse, OK-Geology, ad OK-Sol maps elmate the smoothg effect of OK terpolato relatvely well, ad ther terpolato accuracy s slghtly hgher. The ASM-SP method s most effectve depctg the patter of spatal varato sol K + ad has a moderate terpolato rage (.3 2.38), ad ca gve more detals of sol K + dstrbuto dfferet secodary varables, especally the abrupt boudary. I cotrast, sol K + values of OK ad IDW terpolato map dd ot have the dscrete formato. The method has stroger adaptablty to the spatal terpolato of sol propertes areas wth complex ladforms, whch allowed t to descrbe the patters of spatal varato sol propertes the study area more accurately. Fgure 0. Comparso of sol K + maps costructed usg dfferet terpolato methods: (a) OK-Laduse, where OK s ordary krgg; (b) OK-Geology; (c) OK-Sol; (d) verse dstace weghtg (IDW); (e) OK; ad (f) ASM-SP. 4. Dscusso 4.. Performace of Mult-Model Itegrato for Reducg Predctve Error Ulke more tradtoal spatal terpolato methods (e.g., IDW ad OK), whch use oe terpolato model to tra data sets, the ASM-SP method uses a seres of base terpolato models ad costructs error surfaces to adaptvely scree ad regroup the terpolato models a optmzed way. Its terpolato accuracy s usually hgher tha that of a sgle terpolato model [0]. Thus, t has great advatages for coductg terpolato wth multple models. The systematc
ISPRS It. J. Geo-If. 207, 6, 78 3 of 6 aalyss followed ths study dcates that the mproved performace of the ASM-SP terpolato s maly due to the followg reasos: () The sample data used to predct sol propertes caot usually provde the complete formato for dvdual terpolato models, requrg assumptos to be made about dfferet codtos. I other words, t s dffcult for a sgle terpolato model to accurately descrbe the spatal varace of sol propertes across the whole study area. For stace, usg samplg data for oe sol property, a umber of terpolato models mght share smlar terpolato accuraces, wth o optmal terpolato. The accuracy of spatal terpolato of sol propertes ca be well mproved by effectvely combg the advatages of multple base terpolato models. (2) The sample data used to predct sol propertes ofte caot accurately express patters of spatal varato. However, the tegrato of multple models s able to provde a better approxmato tha use of a sgle model. For example, the patters of spatal varace sol K + dry farmlad dffer greatly areas wth cherozem ad clay sols. Therefore, f lad use type s the oly secodary varable used the spatal terpolato of sol K + (e.g., OK-Laduse), t s usually mpossble to acheve a relatvely hgh predcto accuracy. A effectve soluto s to tegrate a seres of spatal terpolato methods (e.g., OK-Laduse, OK-Sol, OK-Geology, etc.) to realze smultaeous approxmato. Based o the above, t s clear that the terpolato results derved from the ASM-SP method provde a better physcal explaato of the spatal varato sol propertes. Also, the smulato accuracy of ASM-SP s greatly ehaced compared wth OK, OK-Laduse, OK-Sol, OK-Geology etc. Thus, ASM-SP s a more sutable method for applcato areas wth complex ladforms. 4.2. Effectveess of Secodary Varables for Spatal Iterpolato Dfferet lad uses, sol types, ad geology all fluece the spatal varato of sol propertes. Prevous research has also demostrated that there s a relatvely strog spatal correlato betwee secodary varables ad the spatal varato of sol propertes [4,32 34]. Work by [35,36] explaed the correlato betwee the spatal varato of sol propertes ad secodary varables, ad effectvely mproved the predcto accuracy of sol propertes usg secodary varables as secodary varables. I ths study, we compared spatal terpolato models that tegrate secodary varables as the secodary varables (e.g., ASM-SP) ad spatal terpolato models that do ot corporate ay secodary varables (e.g., IDW ad OK). The results dcated that a approprate tegrato of secodary varables ca effectvely mprove the spatal terpolato accuracy of sol propertes. Ths supports the cocluso of Goovaerts (999) that CoKrgg terpolato combg secodary varables usually acheves a better smulato effect tha OK. However, as poted out by [24], the Cokrgg terpolato result s oly better tha OK whe the correlato betwee secodary varables ad the sample data of sol propertes s greater tha 0.4. Whe the correlato s greater tha 0.75, the smulato accuracy of spatal terpolato methods that combe secodary varables s hgher tha OK. Nevertheless, as show by our prevous research, the tegrato of secodary varables does ot always effectvely crease the spatal terpolato accuracy, though there s a relatvely strog spatal correlato betwee secodary varables ad the sample data of sol propertes [0]. However, geeral, a approprate tegrato of geo-evrometal factors as secodary varables s able to effectvely depct sol property boudares that abruptly chage as the geo-evrometal factors chage. 5. Coclusos Affected by secodary varables, the spatal dstrbuto of sol propertes s subject to problems such as spatal dscotuty ad varablty. It s dffcult for a sgle global terpolato model to fully expla the spatal stablty of spatal varables of sol propertes, especally areas wth complex ladforms. Usg sol K + as a case study, we proposed a kd of adaptve surface modelg
ISPRS It. J. Geo-If. 207, 6, 78 4 of 6 that combes secodary varables (ASM-SP). Compared wth methods such as OK ad OK-Laduse, OK-Sol, ad OK-Geology that also combe secodary varables, ASM-SP s able to depct the spatal varato of sol propertes areas wth complex ladforms more accurately, ad reduce smulato errors more effectvely, owg to ts tegrato of multple base terpolato models. I addto, sce ASM-SP combes secodary varables ad ts smulato surface better accords wth geographcal laws, t provdes detaled formato about the spatal varato of sol propertes that s more accurate ad reasoable. Ths provdes greater opportuty for physcal explaato of the spatal varace characterstcs of sol propertes. However, ASM-SP s based o error mmzato surfaces; therefore, there s a rsk of over-fttg, whch wll be addressed future work. The terpolato accuracy of sol propertes areas wth complex ladforms has two ma challeges. Frst, there s a o-lear relatoshp betwee the sol propertes of samplg pots ad the secodary varables, ad the fttg precso of covetoal lear models s rather lmted. Secod, the selected terpolato model must have relatvely hgh smulato accuracy ad, preferably, provde the optmal terpolato. However, realty, every terpolato model has advatages ad dsadvatages. Eve though t s possble to fd a global optmum terpolato model through adequate data explorato ad aalyss, a smple global model s uable to expla the spatal stablty of sol property spatal varables. A feasble soluto s to combe secodary varables to tegrate multple models, so that dfferet combatos of terpolato models ca be selected for dfferet areas. Sol K + s comparatvely represetatve of sol propertes that vary severely wth a short horzotal dstace. The ASM-SP method would also be applcable to the terpolato of other sol propertes (e.g., sol P, PH, Ca, Mg, ad Z). Prevously, we verfed the advatages of a esemble learg algorthm the seral tegrato of multple models [0]. I future research, we pla to comprehesvely utlze the mache learg algorthm, combe secodary varables, ad buld ad coordate adaptve mult-model tegrato terpolato methods to solve over-fttg problems ad to coduct hgh accuracy surface modelg of sol propertes. Ackowledgmets: Ths study was supported by the Natoal Natural Scece Foudato of Cha (Grat No. 460405). We are grateful to the Qgha Evrometal Motorg Ceter for provdg topsol samplg approval. Thaks to the Cha Sol Ivestgato Offce ad the Bureau of Geologcal Explorato & Developmet of Qgha Provce for provdg secodary datasets. Author Cotrbutos: Coceved ad desged the expermets: Lu We; performed the expermets: Ya Da-Peg ad Wag Sheg-L; aalyzed the data: Lu We ad Zhag Ha-Rog; cotrbuted reagets/materals/aalyss tools: Wag Sheg-L; wrote the paper: Lu We ad Zhag Ha-Rog. Coflcts of Iterest: The authors declare o coflct of terest. Refereces. Sh, W.J.; Lu, J.Y.; Du, Z.P.; Yue, T.X. Hgh Accuracy Surface Modelg of Sol Propertes Based o Geographc Iformato. Acta Geogr. S. 20, 66, 574 58. 2. Sh, D.; Lark, R. A New Brach of Sol Scece-Pedometrcs Its Org ad Developmet. Acta Pedol. S. 2007, 44, 99 924. 3. L, J.; Heap, A.D.; Potter, A.; Daell, J.J. Applcato of Mache Learg Methods to Spatal Iterpolato of Evrometal Varables. Evro. Model. Softw. 20, 26, 647 659. 4. Yue, T.X.; Wag, S.H. Adjustmet Computato of Hasm: A Hgh-Accuracy ad Hgh-Speed Method. It. J. Geogr. If. Sc. 200, 24, 725 743. 5. Wag, J.F.; Ge, Y.; L, L.F.; Meg, B.; Wu, J.L.; Ba, Y.C. Spatotemporal Data Aalyss Geography. Acta Geogr. S. 204, 69, 326 345. 6. Goovaerts, P. A Coheret Geostatstcal Approach for Combg Choropleth Map ad Feld Data the Spatal Iterpolato of Sol Propertes. Eur. J. Sol Sc. 20, 62, 37. 7. Lu, T.L.; Juag, K.W.; Lee, D.Y. Iterpolatg Sol Propertes Usg Krgg Combed wth Categorcal Iformato of Sol Maps. Sol Sc. Soc. Am. J. 2006, 70, 200 209. 8. Glard, N. Mache Learg for Spatal Data Aalyss. Ph.D. Thess, Uversty of Lausae ad Dalle Molle Isttute of Perceptual Artfcal Itellgece, Lausae, Swtzerlad, 2002.
ISPRS It. J. Geo-If. 207, 6, 78 5 of 6 9. Rgol, J.P.; Jarvs, C.H.; Stuart, N. Artfcal Neural Networks as a Tool for Spatal Iterpolato. It. J. Geogr. If. Sc. 200, 5, 323 343. 0. Lu, W.; Du, P.J.; Zhao, Z.W.; Zhag, L.P. A Adaptve Weghtg Algorthm for Iterpolatg the Sol Potassum Cotet. Sc. Rep. 206, 6, 23889, do:0.038/srep23889.. Bashr, B.; Foul, H. Studyg the Spatal Dstrbuto of Maxmum Mothly Rafall Selected Regos of Saud Araba Usg Geographc Iformato Systems. Arab. J. Geosc. 205, 8, 5. 2. Borůvka, L.; Mládková, L.; Peížek, V.; Drábek, O.; Vašát, R. Forest Sol Acdfcato Assessmet Usg Prcpal Compoet Aalyss ad Geostatstcs. Geoderma 2007, 40, 374 382. 3. Florsky, I.; Elers, R.G.; Mag, G.; Fuller, L. Predcto of Sol Propertes by Dgtal Terra Modellg. Evro. Model. Softw. 2002, 7, 295 3. 4. Kurakose, S.L.; Devkota, S.; Rosster, D.; Jette, V. Predcto of Sol Depth Usg Evrometal Varables A Athropogec Ladscape, a Case Study the Wester Ghats of Kerala, Ida. Catea 2009, 79, 27 38. 5. L, B.; Zhag, Y.; Sh, X.; Zhag, K.; Zhag, J. Spatal Iterpolato Method Based o Itegrated Rbf Neural Networks for Estmatg Heavy Metals Sol of a Mouta Rego. J. Southeast Uv. 205, 3, 38 45. 6. Masy, B.; Mcbratey, A.B. Spatal Predcto of Sol Propertes Usg Eblup wth the Matér Covarace Fucto. Geoderma 2007, 40, 324 336. 7. Motealegre, A.; Lamelas, M.; Rva, J. Iterpolato Routes Assessmet Als-Derved Dgtal Elevato Models for Forestry Applcatos. Remote Ses. 205, 7, 863 8654. 8. Yag, S.H.; Zhag, H.T.; Guo, L.; Re, Y. Spatal Iterpolato of Sol Orgac Matter Usg Regresso Krgg ad Geographcally Weghted Regresso Krgg. Ch. J. Appl. Ecol. 205, 26, 649 656. 9. Lu, W.; Du, P.J.; Wag, D.C. Esemble Learg for Spatal Iterpolato of Sol Potassum Cotet Based o Evrometal Iformato. PLoS ONE 205, 0, e024383. 20. Zhag, H.; Lu, L.; Lu, Y.; Lu, W. Spatal Samplg Strateges for the Effect of Iterpolato Accuracy. ISPRS It. J. Geo-If. 205, 4, 2742 2768. 2. Sparks, D.L.; Page, A.L.; Helmke, P.A.; Loeppert, R.H.; Soltapour, P.N.; Tabataba, M.A.; Johsto, C.T.; Sumer, M.E. Methods of Sol Aalyss. Part 3 Chemcal Methods; Sol Scece Socety of Amerca, Ftchburg, WI, USA, 2009. 22. Burrough, P.A. Prcples of Geographcal Iformato Systems for Lad Resources Assessmet. Geocarto It. 987,, 02, do:0.080/006048609354060. 23. Mosammam, A. Geostatstcs: Modelg Spatal Ucertaty. J. Appl. Stat. 203, 40, 923 923. 24. Asl, M.; Marcotte, D. Comparso of Approaches to Spatal Estmato a Bvarate Cotext. Math. Geol. 995, 27, 64 658. 25. Odeh, I.O.; Mcbratey, A.; Chttleborough, D. Further Results o Predcto of Sol Propertes From Terra Attrbutes: Heterotopc Cokrgg ad Regresso-Krgg. Geoderma 995, 67, 25 226. 26. Hegl, T.; Heuvelk, G.; Ste, A. A Geerc Framework for Spatal Predcto of Sol Varables Based o Regresso-Krgg. Geoderma 2004, 20, 75 93. 27. Cambardella, C.A.; Karle, D.L. Spatal Aalyss of Sol Fertlty Parameters. Precs. Agrc. 999,, 5 4. 28. Log, J.; Zhag, L.M.; Zhou, B.Q.; Mao, Y.L.; Qu, L.X.; Xg, S.H. Spatal Iterpolat of Sol Orgac Matter Farmlads Areas Complex Ladform. Acta Pedol. S. 204, 5, 8 93. 29. Peížek, V.; Borůvka, L. Sol Depth Predcto Supported by Prmary Terra Attrbutes: A Comparso of Methods. Plat Sol Evro. 2006, 52, 424 430. 30. Tratafls, J.; Odeh, I.; Mcbratey, A. Fve geostatstcal models to predct sol salty from Electromagetc ducto data across rrgated cotto. Sol Sc. Soc. Am. J. 200, 65, 869 878. 3. Zhao, Y.F.; Su, Z.Y.; Che, J. Aalyss ad Comparso Arthmetc for Krgg Iterpolato ad Sequetal Gaussa Codtoal Smulato. J. Geo-If. Sc. 200, 6, 767 776. 32. L, Q.Q.; Wag, C.Q.; Yue, T.X.; L, B.; Zhag, X.; Gao, X.S.; Zhag, Y. Predcto of Dstrbuto of Sol Orgac Matter Based o Qualtatve ad Attatve Auxlary Varables: A Case Study Sata Couty Schua Provce. Progress Geogr. 204, 33, 259 269. 33. Qu, L.F.; Yag, C.; L, F.F.; Yag, N.; Zhe, X.H. Spatal Patter of Sol Fertlty Basha Tea Garde: A Predcto Based o Evrometal Auxlary Varables. Ch. J. Appl. Ecol. 200, 2, 3099 304.
ISPRS It. J. Geo-If. 207, 6, 78 6 of 6 34. We, W.; Zhou, B.T.; Wag, Y.F.; Huag, Y. Sol Orgac Carbo Iterpolato Based o Auxlary Evrometal Covarates: A Case Study At Small Watershed Scale Loess Hlly Rego. Acta Ecol. S. 203, 33, 6389 6397. 35. Hu, K.; L, H.; L, B.; Huag, Y. Spatal ad Temporal Patters of Sol Orgac Matter the Urba Rural Trasto Zoe of Bejg. Geoderma 2007, 4, 302 30. 36. Sh, W.; Lu, J.; Du, Z.; Ste, A.; Yue, T. Surface Modellg of Sol Propertes Based o Lad Use Iformato. Geoderma 20, 62, 347 357. 207 by the authors. Lcesee MDPI, Basel, Swtzerlad. Ths artcle s a ope access artcle dstrbuted uder the terms ad codtos of the Creatve Commos Attrbuto (CC BY) lcese (http://creatvecommos.org/lceses/by/4.0/).