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2 Ecological Informatics 16 (2013) 1 9 Contents lists available at SciVerse ScienceDirect Ecological Informatics journal homepage: Assessing the spatial uncertainty in soil nitrogen mapping through stochastic simulations with categorical land use information Mingkai Qu a,b, Weidong Li c,, Chuanrong Zhang c a Department of Resource and Environmental Information, Huazhong Agricultural University, Wuhan , China b Key Laboratory of Soil Environment and Pollution Remediation, Institute of Soil Science, Chinese Academy of Sciences, Nanjing , China c Department of Geography and Center for Environmental Sciences and Engineering, University of Connecticut, Storrs, CT 06269, USA article info abstract Article history: Received 16 July 2012 Received in revised form 30 March 2013 Accepted 3 April 2013 Available online 12 April 2013 Keywords: Sequential Gaussian simulation Land use type Uncertainty assessment Soil nitrogen Predictive mapping This study explores the capability of an extended sequential Gaussian simulation algorithm with incorporation of categorical land use information (SGS-CI) for simulating spatial variability of soil total nitrogen (TN) contents and assessing associated spatial uncertainty. 402 sampled data in soil TN contents in a county scale region and the categorical land use map data of the study area were used to perform sequential simulations for comparing the SGS-CI algorithm and the conventional SGS algorithm, and 135 validation samples were used to assess the improvement of SGS-CI over SGS in prediction accuracy and uncertainty reduction. Results showed that the validation data were more strongly correlated with the optimal prediction (i.e., E-type estimates) data of SGS-CI than with those of SGS, and the mean error and the root mean square error of the optimal prediction using SGS-CI were smaller than those using SGS. SGS-CI also performed slightly better than SGS in uncertainty modeling in terms of accuracy plots and goodness statistic G. In addition, because demands for soil total nitrogen by different crops are usually different in agricultural practice, we showed that SGS-CI could be used to assess spatial uncertainty of deficiency or abundance degrees of soil TN based on demands of different crops in different land use types. Therefore, SGS-CI may provide an effective method for improving prediction accuracy and reducing uncertainty in soil TN prediction Elsevier B.V. All rights reserved. 1. Introduction Soil nitrogen is an important nutrient for maintaining the earth's ecosystems. Besides the nitrogenous fertilizers widely applied to farmlands for improving crop production, atmospheric deposition also represents an important source (Galloway et al., 2008; Kaiser, 2001). Sometimes the content of soil nitrogen may exceed the requirement of plant growth. This generally results in low nitrogen use efficiency and high nitrogen loss (Li and Zhang, 1999). The nitrogen loss from soils may further lead to negative impacts on the environment. For example, nitrogen losses to water bodies often cause water eutrophication a serious ecological issue facing the environment nowadays (Carpenter et al., 1998; Lu et al., 2007; Smith et al., 2001). Therefore, effectively mapping the spatial distribution of soil nitrogen contents and the associated uncertainties inherent in spatial prediction are crucial to agricultural management, environmental management, and ecological management. Geostatistics comprises a set of spatial statistical techniques, which have been widely used to characterize spatial variability of soil properties (Burgess and Webster, 1980; Ferguson et al., 1998; Li and Heap, 2011; Tutmez and Hatipoglu, 2010). However, besides spatial prediction, geostatistics also concerns quantifying the uncertainty associated with Corresponding author. Tel.: address: weidongwoody@gmail.com (W. Li). a spatial prediction (Bourennane et al., 2007; Diodato and Ceccarelli, 2006; Qu et al., 2013). Currently uncertainty assessment is mainly conducted using stochastic simulation algorithms (Bourennane et al., 2007; Goovaerts, 2001; Zhao et al., 2005). Sequential Gaussian simulation (SGS) is one of the most frequently used stochastic simulation algorithms for continuous variables. The increasing utilization of stochastic simulation algorithms in modeling uncertainties is justified by the fact that interpolation algorithms, such as kriging, yield a unique response the interpolated map, which usually smoothes out local details of spatial variability of the attribute being mapped (Goovaerts, 1997). This shortcoming of kriging results in overestimation of small values and underestimation of large values. For these reasons, stochastic simulations are generally preferred to interpolations for applications where the spatial variation of the measured field needs to be preserved and uncertainty assessment is required. Indeed, stochastic simulation techniques, that provide multiple possible realizations of an unknown spatial distribution, do not aim to minimize a local error variance. Fluctuations between realizations provide a quantitative measure of the uncertainty about the underlying phenomenon. An important issue, which we should not ignore, is the effect of some categorical factors (e.g., geological formations, land use types, or soil types) on the spatial variability of the target environmental or ecological variable. Earlier studies suggested that soil type information could be used to improve the prediction accuracy of some soil properties. For /$ see front matter 2013 Elsevier B.V. All rights reserved.

3 2 M. Qu et al. / Ecological Informatics 16 (2013) 1 9 Fig. 1. Soil sample locations and land use type distribution. example, Voltz and Webster (1990) and Van Meirvenne et al. (1994) used a method called stratified kriging (i.e., first stratify the survey area based on soil types and then perform kriging independently within each stratum) to improve the prediction accuracy of soil properties; Goovaerts and Journel (1995) used simple indicator kriging with varying means and indicator cokriging to incorporate the effect of soil types on interpolation of soil heavy metals, and found that the incorporation could improve the delineation of deficient areas; Liu et al. (2006) suggested a kriging combined with soil map-delineation (KSMD) method for incorporating the effect of soil types on several soil properties, and also took into account the contributions of both hard data and soil type data to the estimation variance. Recently, Goovaerts (2011) presented two approaches to incorporate both point and areal data in spatial interpolation of continuous soil attributes. Goovaerts (2010) also presented a general formulation of area-and-point kriging and demonstrated the effect of geological formations on soil heavy metals. Qu et al. (2012) recently investigated the effect of land use types on the spatial prediction of soil nitrogen using the area-and-point kriging method. However, all of these studies focused on optimal interpolations rather than sequential simulations. As aforementioned, stochastic simulation algorithms such as SGS have the advantages in quantifying and visually displaying the uncertainty associated with spatial predictions. Given the influence of categorical factors such as land use types on local values of many soil properties, it is desirable to integrate the related categorical information into a geostatistical stochastic simulation algorithm such as SGS. Therefore, a satisfactory stochastic simulation for these variables should include two components the spatial variation between different categories and the variability within each category. However, related studies in literature have been very rare so far. In this study, the conventional SGS algorithm was combined with categorical land use information for simulating the spatial distribution of soil total nitrogen (TN) contents in a study area and assessing the Table 1 Soil TN content (g kg 1 ) statistics for different land use types a. Land use type Number Range Minimum Maximum Mean SD Skew Kurt CV Total Paddy field Dry farmland Other land use type Validation data a SD standard deviation; Skew skewness; Kurt kurtosis; CV coefficient of variation (%).

4 M. Qu et al. / Ecological Informatics 16 (2013) associated spatial uncertainty. The extended simulation method was denoted as SGS-CI for the convenience of presentation. In the Jianghan Plain in Hubei Province, major crops are rice and wheat, which are cultivated under different land use types. While wheat grows only in dry farmlands, rice requires ample water to submerge the fields. These two different land use types usually cause differencesinmanysoilpropertiessuchascontentsofsoilorganicmatterand nitrogen (Qu et al., 2012). This means that incorporation of categorical land use information into spatial prediction and uncertainty assessment of soil nitrogen would be desirable. Furthermore, the demands of soil nitrogen by crops are also related to specific receptors (e.g., wheat and rice) of fertilization. Therefore, spatial uncertainty assessment of deficiency or abundance degrees of soil nitrogen concentration in a study area should take into account different receptors, which usually occur as different land use types. The objectives of this study are: (1) to explore the capability of SGS-CI in improving prediction accuracy of soil TN and reducing associated uncertainty in prediction, compared with the conventional SGS; and (2) to assess the spatial uncertainty of deficiency and abundance degrees of soil TN contents based on demands of different crops in different land use types in the study area. The general purpose is to find a more effective method for mapping soil nutrients and their spatial uncertainty for precision farming and environmental management. 2. Materials and methods 2.1. Study area The study was conducted in Hanchuan County, Hubei Province, an agricultural region in central China. The study area is bounded by the longitudes of and east, and the latitudes of and north, with an area of 1659 km 2. It belongs to the northern subtropical monsoonal climate zone, with a temperate-humid climate throughout the year and four distinct seasons. The annual average temperature is 16.1 C and the average annual precipitation is approximately 1198 mm. In this region, there are generally four land use types (or groups) paddy field, dry farmland, water body, and others. Fig. 1 shows the spatial distribution of land use types. Paddy field is the dominant land use type in the county, a major crop production base in the province Soil sampling and lab analysis The topsoil samples consist of the prediction points (n = 402) and the validation points (n = 135). Among the 402 samples for prediction, 215 were taken from paddy fields, 130 from dry farmlands and the remaining samples from other land use types (Table 1). The validation Fig. 2. Histograms of original TN data (a), normal score transformed data (b), residual data (c), and normal score transformed residual data (d).

5 4 M. Qu et al. / Ecological Informatics 16 (2013) 1 9 samples cover the same three land use groups, although they were collected with consideration of randomness and homogeneity in the area. Sample locations were recorded using a hand-held global position system (GPS). All samples were taken in fall after harvest and before next cropping season so as to avoid the effect of fertilization during crop cultivation. During sampling, soils in the top layers (0 15 cm) of six to eight points at each site within an area of approximately 0.01 ha were collected and then mixed. A portion of 1 to 2 kg for each sample was delivered to a laboratory for analysis. All samples were air-dried at room temperature (20 22 C).After stones or otherdebriswereremoved,samples were sieved to ensure the soil particles to be smaller than 2 mm in diameter. A portion of about 100 g for each sample was ground in an agate grinder and sieved through a mm mesh. TN was determined using the Kjeldahl method with H 2 SO 4 +H 2 O 2 digestion (Kim, 2005) Variogram estimation Variogram is an effective tool for characterizing spatial variability (Boyer et al., 1991; Cahn et al., 1994; Webster and Oliver, 1990). The spatial pattern of a soil attribute following the intrinsic stationarity assumption can be described using an experimental variogram estimated by ^γ ðhþ ¼ 1 2NðhÞ XN ðhþ i¼1 ½zðx i Þ zðx i þ hþš 2 ; ð1þ where N(h) is the number of data pairs separated by distance lag h, and z(x i )andz(x i + h) are the measured values for the regionalized variable Z(x) at the locations of x i and x i + h, respectively Sequential Gaussian simulation Sequential Gaussian simulation is the most frequently used sequential simulation algorithm for simulating continuous variables. After a regularly spaced grid covering the region of interest is defined, the procedure of SGS involves the following steps: (1) Transform the sample data into standard normally distributed data using normal score transformation if they do not meet a Gaussian distribution. (2) Compute and model the variogram of the normal score transformed data. (3) Establish a random path through all of the grid nodes, in a way that each node is visited only once in each sequence. (4) At each node x 0 : (a) Estimate the parameters (mean and variance) of the Gaussian conditional cumulative distribution function (ccdf) of the studied variable using the simple kriging estimator with the normal score variogram model. The conditioning data includes a specified number of both the original sample data and previously simulated data within a neighborhood of the location being simulated. (b) Draw a simulated normal score value from the estimated ccdf and then add it to the conditioning dataset to be used for simulating other nodes. (c) Proceed to the next grid node along the random path and repeat steps (a) and (b) until the entire grid nodes are simulated. (5) Back-transform the simulated normal score data into the values of the target variable in the original data space. These sequential steps build up only the first realization, {z (1) (x 0j ), j =1,, M}, which is only one model of TN spatial distribution. To generate multiple, say L, realizations, {z (l) (x 0j ), j =1,, M, l =1,, L}, steps 3 to 5 should be repeated with different random paths passing through all nodes. Detailed introduction on this method can be found in Goovaerts (1997) and Remy et al. (2009) SGS-CI Liu et al. (2006) suggested the KSMD method for incorporating the effect of soil types in interpolation of soil properties. The method separated an observation at a location into two components the mean value over the soil type polygon and the residual, similar to Goovaerts and Journel (1995). The residual data were further interpolated using the ordinary kriging, rather than using the indicator kriging as done in Goovaerts and Journel (1995). Thus, the final estimate at an unsampled location was the sum of the mean value and the interpolated residual value, and the variance was also estimated as the sum of contributions of the two components. However, similar to other earlier studies, the KSMD method did not perform stochastic simulations. The SGS-CI method suggested in this study is similar to the KSMD method to some extent in its structure. It also separates an observation at a location into two components the mean value over the land use type polygon and the residual. But the residual data are used as samples for sequential simulation by SGS, rather than for interpolation by ordinary kriging. A final simulated realization is the sum of a simulated residual realization and the mean values at all locations. Thus, a number of simulated realizations incorporating land use effect can be generated and the associated uncertainty with the optimal prediction (i.e., the E-type estimate) can be assessed. Therefore, the SGS-CI algorithm is essentially an extension of KSMD. The spatial variability of a soil attribute is partially owing to the complex distribution of land use types in the study region, which increases the prediction uncertainty. To reduce this uncertainty, the value z(x kj ) of each sample can be divided into two portions: mean value u(s k ) under the land use type s k, to which the sample belongs, and the corresponding residual r(x kj ), that is, z x kj ¼ uðs k Þþr x kj ; ð2þ where x kj is the location of the sample z(x kj ). Therefore, the variance σ z 2 of z(x kj ) can be estimated as the sum of the two components: σ s 2 between land use types and σ r 2 within a land use type, which indicate the influence of land use types on the soil attribute and the variation of the soil attribute within a land use type, respectively (Liu et al., 2006). That is, we have σ 2 z ¼ σ 2 s þ σ 2 r : Then, the residual r(x kj ) can be treated as a new stationary regionalized variable and be simulated using SGS. Results of SGS-CI are essentially composed of the SGS simulated residuals and the corresponding mean values under the different land use types Evaluation criteria The Pearson's correlation coefficients (r), the mean errors (ME) and root mean square errors (RMSE) between validation data and optimal prediction maps from the two methods SGS and SGS-CI can be used to evaluate their prediction performance. Here the optimal prediction maps refer to the E-type estimates, which are the point-by-point averages of a number of simulated realizations. ME and RMSE are calculated using the following equations ME ¼ 1 X N v zðx N i Þ z ðx i Þ v i¼1 ð3þ ð4þ

6 M. Qu et al. / Ecological Informatics 16 (2013) Fig. 3. Experimental variograms of normal score transformed data (a) and normal score transformed residual data (b). vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 X Nv RMSE ¼ t zðx N i Þ z 2 ðx i Þ v i¼1 respectively, where N v is the number of validation points, and z(x i ) and z*(x i ) are the measured and predicted values at the validation points, respectively. The ME provides a measure of bias, and the RMSE provides a measure of accuracy. The greater r and the lower ME and RMSE values indicate the higher prediction accuracy. The accuracy and goodness of the reproduction of the single-point conditional probability distributions by the set of realizations also can be examined to evaluate the simulation performance. At any location x, knowledge of the ccdf F(x, z (n)) allows the computation of a series of symmetric p-probability intervals (PI) bounded by the (1 p)/2 and (1+p)/2 quantiles of the ccdf. According to Goovaerts (2001),a probability distribution is considered accurate if the fraction of values of a validation dataset falling in the symmetric p-pi interval exceeds p for all p [0, 1]. Considering a validation set, z(x j ), j =1,, N v, and the corresponding independently predicted ccdfs F(x j, z (n)), the fraction of true values falling into a given symmetric p-pi interval can be computed as ξðpþ ¼ 1 X N v N v with ξ x j ; p j¼1 ξ x j ; p ð5þ p ½0; 1Š ð6þ ( ¼ 1; if F 1 x j ; ð1 pþ=2 bz x j 0; otherwise F 1 x j ; ð1þpþ=2 : The scattergram of the calculated fractions vs the set of probabilities p is called accuracy plot (Goovaerts, 2001). The accuracy of a probabilistic model can be visually assessed through an accuracy plot; for an accurate case, most of the points must fall above the 45 line, i.e. ξðpþ > p for most p. Deutsch (1997) suggested assessing the closeness of the estimated and theoretical fractions using the following goodness statistics G [0, 1] h i G ¼ 1 1 0½3aðpÞ 2Š ξðpþ p dp; ð8þ where the indicator function a(p) is defined as ap ð Þ ¼ 1 if ξðpþ p: 0 otherwise As shown in Eq. (8), twice more importance is given to deviations when ξðpþbp (inaccurate case). The greater G value indicates the higher prediction uncertainty. ð7þ ð9þ 2.7. Uncertainty evaluation Given a variogram model and a neighborhood search rule, stochastic simulation methods such as SGS-CI can generate many simulated realizations. From these realizations local and spatial uncertainties may be quantified, and these realizations and uncertainty data may be further used to assist in decision-making, such as appropriate fertilization program. Because it is difficult to acquire sufficient sampling data to objectively characterize the real spatial patterns, particularly in the field of environmental study, conditional stochastic simulation methods were especially proved to be superior to interpolation methods in dealing with this complexity and uncertainty. Because arable lands are the targets of fertilization, uncertainty assessment of TN status was focused on arable lands (i.e., paddy fields and dry farmlands) in this study, where major crops are rice and wheat. In addition, crop demands to soil TN contents are also related to specific receptors (e.g., wheat and rice) of fertilization. Hence, uncertainty assessment of deficiency or abundance degree of soil TN concentration in the study area should take into account the specific receptors in different land use types Local uncertainty evaluation The uncertainty of an estimate at a specific location x can be defined as the probability that unknown z(x) at location x is greater (or smaller) than a given specific critical threshold. In this study, we only assess the uncertainty of deficiency or abundance degree of soil TN concentration for different crop types in the study area. Therefore, we use two thresholds a high threshold c hi and a low threshold c li for the i-th crop land use type, and assess the probabilities of soil TN being higher than c hi (abundance) and lower than c li (deficiency) at each location. These probabilities can be calculated using the following equations: Pzx ½ ð Þ>c hi Š ¼ nðxþ ; if x A ðcrop type iþ ð10þ N t N t Pzx ½ ð Þbc li Š ¼ nðxþ ; if x A ðcrop type iþ ð11þ Here n(x) is the number of realizations in which the simulated values by SGS-CI at the location x were greater (or smaller) than their respective thresholds c hi (or c li ), and N t is the total number of simulated realizations Spatial uncertainty evaluation Spatial uncertainty (multi-location uncertainty) means the joint uncertainty of estimates at several locations or in an area, which can be used to assess the reliability of the high (or low) value areas determined by P[z(x m )>c(x m )] (or P[z(x m ) b c(x m )]) at a given critical probability

7 6 M. Qu et al. / Ecological Informatics 16 (2013) 1 9 Fig. 4. Four randomly selected realizations of TN spatial distribution generated by SGS (a, b) and SGS-CI (c, d). (Goovaerts, 1997; Zhao et al., 2005). Suppose there are j locations, x 1, x 2,, x j,inareaa; the probability of all values at the j locations in area A being greater (or smaller) than their respective critical limits c(x 1 ),, c(x j ) can be calculated using the following equation: h P zðx 1 Þ > cðx 1 Þ; zðx 2 Þ > cðx 2 Þ; ; z x j >c x j h i P zðx 1 Þbcðx 1 Þ; zðx 2 Þbcðx 2 Þ; ; z x j bc x j i n x 1 ; x 2 ; ; x j ¼ N t n x 1 ; x 2 ; ; x j ¼ N t ð12þ ð13þ where N t is the total number of simulated realizations in the study, and n(x 1, x 2,, x j ) is the number of realizations that have values at those locations all being higher (or lower) than their respective critical limits c(x 1 ),, c(x j ). 3. Results and discussion In this study, geostatistical simulation was performed on a regular square grid of 400 m 400 m, and the S-GeMS software (Remy et al., 2009) and the statistical analysis tool Matlab R2007b were used to perform the computations. Both the SGS-CI simulation and the SGS simulation were carried out 500 times (i.e., generated 500 realizations). For assessing the uncertainty of deficiency or abundance degree of soil TN concentration under different crop types (also the major land use types in the study area), 2 g kg 1 and 1.5 g kg 1 were chosen as the high thresholds, respectively, for rice and wheat (i.e., paddy field and dry farmland), and 1 g kg 1 Fig. 5. Optimal prediction maps generated by SGS (a) and SGS-CI (b).

8 M. Qu et al. / Ecological Informatics 16 (2013) Fig. 6. Scatter plots between soil TN validation data and optimal prediction data using different methods: (a) SGS and (b) SGS-CI. and 0.8 g kg 1 were chosen as the low thresholds, respectively, for rice and wheat Explanatory data analysis The descriptive statistics for TN contents of soil samples are given in Table 1. The mean TN content of all samples is 1.46 g kg 1,andtheir coefficient of variation (CV) is 37.14%. Samples were classified into three groups based on the land use types of their locations, of which the average TN contents in descending order are 1.62 g kg 1 for paddy fields, 1.25 g kg 1 for dry farmlands and 1.38 g kg 1 for other land use types (i.e., non-arable lands). This indicates that land use types affect the content level of soil TN. Among the three groups, the soil TN CV for the non-arable lands is the highest (41.80%) and that for the paddy fields is the lowest (33.82%). The original TN content data and the residual data after removing mean values are both approximately normally distributed (Fig. 2). The TN contents of soil samples are apparently correlated with land use types; such a result is consistent with the previous studies (Wang et al., 2009). In general, the paddy fields have higher TN contents as a result of more fertilizer input and organic matter accumulation under the persistent wet condition, whereas the dry farmlands have lower TN contents because of less fertilizer input and fast organic matter mineralization. This implies that categorical land use data should be valuable auxiliary information to the stochastic simulation and incorporating them may improve spatial prediction accuracy and reduce prediction uncertainty. The variogram provides a description of the spatial autocorrelation structure of the variable under study and some insights into possible processes affecting the spatial distribution of the variable (Paz Gonzalez et al., 2001). Because no apparent anisotropy was found for soil TN contents, experimental variograms were estimated omni-directionally in this study. Experimental variograms for the normal score transformed data of soil TN and the normal score transformed data of soil TN residuals are presented in Fig. 3. The two experimental variograms were both fitted well by spherical models. The C 0 /(C 0 +C)ratiois usually used as a criterion to describe the spatial auto dependence of a variable. Ratio values lower than 25% and higher than 75% correspond to strong and weak spatial dependencies, respectively, while ratio values between 25% and 75% indicate moderate spatial dependence. Strong spatial dependence of soil properties may be attributed to intrinsic factors and weak spatial dependence may be attributed to extrinsic factors (Cambardella et al., 1994). The C 0 /(C 0 + C) ratio of the variogram model for the normal score transformed data of soil TN is 63%, exhibiting moderate spatial auto dependency which may be attributed to both the intrinsic factors such as other soil properties and the extrinsic factors such as human activities (e.g., land use). After land use based mean values were removed from the original soil TN data, the variance reduced from 0.33 to 0.29 because the structural variance deriving from the land use effect was eliminated. Fig. 7. Accuracy plots and G statistics for simulated results by (a) SGS and (b) SGS-CI.

9 8 M. Qu et al. / Ecological Informatics 16 (2013) 1 9 Fig. 8. Probability maps of soil TN (a) deficiency (less than 1 g kg 1 for paddy fields and less than 0.8 g kg 1 for dry farmlands) and (b) abundance (greater than 2 g kg 1 for paddy fields and greater than 1.5 g kg 1 for dry farmlands) in arable lands Spatial distribution of soil TN Four randomly selected realizations generated by SGS and SGS-CI, respectively, are displayed in Fig. 4. Each realization represents a possible realistic spatial distribution of soil TN without the smoothing effect. The realization maps generated by SGS and SGS-CI using the same random path do not show much difference. One major reason may be that many land use polygons are too complex in shape due to the spatial connection of farmland pieces under the same land use type (see Fig. 1). Another reason may be that the effect of land use types on soil TN contents is not very large in this case. Fig. 5 shows the optimal prediction maps (i.e., E-type estimates) by SGS and SGS-CI. Both maps show similar trends, with higher TN values appearing in the northwest region and lower values mainly occurring in the mid-south region of the county. However, the optimal prediction map generated by SGS-CI illustrates more details in texture compared with the one generated by SGS due to the influence of land use types, and it shows the lower and higher contents more accurately as expected on different land use types. For example, while the land use type implies lower TN contents in the top-left corner of the study area where no sample data are available, the SGS-CI optimal prediction map indeed shows some low values but the SGS optimal prediction map indicates high values (see Figs. 1 and 5). In general, despite that the SGS-CI method gives more accurate prediction as quantitatively evaluated later, this improvement is not visually obvious probably due to the complexity of land use polygons Prediction accuracy analysis The correlation coefficients r, ME values and RMSE values between the 135 observed validation data and the optimal prediction maps by SGS and SGS-CI are shown in Fig. 6. Larger r values and smaller ME and RMSE values indicate more accurate prediction. The r values are 0.53 and 0.69 for the optimal prediction maps generated by SGS and SGS-CI, respectively. The optimal prediction map generated by SGS has a ME value of and a RMSE value of 0.43, while the one by SGS-CI has a ME value of and a RMSE value of Apparently, SGS-CI provides higher prediction accuracy. Accuracy plots related to the SGS and SGS-CI simulated results were computed and depicted in Fig. 7. Compared with the SGS results, Table 2 Assessment of spatial uncertainty of soil TN deficiency and abundance areas based on joint probability. Critical probability (p c ) Number of cells Joint probability Deficiency Abundance the SGS-CI results have more points falling above the 45 line. This means SGS-CI generated higher accuracy in modeling uncertainty compared with SGS. Both simulation algorithms have some points below the 45 line, especially for the larger p-values (p > 0.7), indicating their inaccuracy in the higher probability intervals. A relatively higher (i.e., better) G value was thus obtained from the simulated realizations by SGS-CI, compared with the G value from the simulated results by SGS. This reveals again that SGS-CI performed better than SGS did and thus reduced the estimation uncertainty Uncertainty evaluation of soil TN The probability maps for soil TN deficiency (less than 1 g kg 1 for rice and less than 0.8 g kg 1 for wheat) and abundance (greater than 2gkg 1 for rice and greater than 1.5 g kg 1 for wheat) were estimated (Fig. 8). TN deficiency (p > 0.6) mainly appears in the middle of the study area along a river where dry farmlands (i.e., mainly wheat fields) dominate, and TN abundance (p > 0.6) scatters around mainly in the paddy fields (see Figs. 1 and 8). If a critical probability of 0.6 is used to delineate the deficiency and abundance areas, 33 and 161 cells (not including cells in which sampling points are located) can be obtained respectively for deficiency and abundance, and their corresponding joint probabilities are just 2% and 3% (Table 2). Therefore, there is a large spatial uncertainty although the critical probability is high (p c =0.6)for the locations selected for delineating the TN deficiency and abundance areas. 4. Conclusion Land use types are related to the local level of soil TN contents, as shown by our data in the study area where the average soil TN content in the paddy fields is apparently higher than that in the dry farmlands. This study proposed and explored the SGS-CI algorithm, which incorporates categorical land use information into the conventional SGS algorithm, for simulating spatial distribution of soil TN contents. A simulation case study was performed in Hanchuan County, Hubei Province, China, with a comparison to SGS, for evaluating the merits of SGS-CI. The optimal prediction map (i.e., E-type estimate) of soil TN content generated by SGS-CI indicates an improvement in prediction accuracy over that generated by SGS, as represented by the correlation coefficients r, ME and RMSE values. This means that incorporation of categorical land use information is valuable for more accurately assessing the spatial distribution of soil TN. The accuracy plots and G statistics of simulated realizations by SGS and SGS-CI demonstrate again that SGS-CI can increase predictive accuracy and reduce uncertainty in soil TN spatial mapping through incorporating categorical land use information. Probably because of the complexity of land use polygons

10 M. Qu et al. / Ecological Informatics 16 (2013) in this case study, the accuracy improvement of SGS-CI over SGS in the simulated results is not visually obvious. Uncertainty assessment of soil TN was performed using a number of simulated realization maps generated by SGS-CI. As different crops are planted in the arable lands of different land use types and they have different demand levels for soil nutrients, incorporating their information is also necessary in uncertainty assessment of soil nutrient status in the arable lands. For a given probability threshold, areas of soil TN deficiency and abundance can be delineated using a number of simulated realizations and such delineation represents a quantitative assessment of spatial uncertainty in soil TN distribution. Our study shows that the areas of soil TN deficiency mainly concentrate in the dry farmlands in the middle of the study area, and the areas of soil TN abundance mainly scatter around in the paddy fields. 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