The application of classification tree analysis to soil type prediction in a desert landscape

Transcription

1 Ecological Modelling 181 (2005) 1 15 The application of classification tree analysis to soil type prediction in a desert landscape P. Scull a,, J. Franklin b, O.A. Chadwick c a Department of Geography, Colgate University, 13 Oak Drive, Hamilton, NY 13346, USA b Department of Biology, San Diego State University, San Diego, CA , USA c Department of Geography, University of California, Santa Barbara, CA93106, USA Received 3 April 2003; received in revised form 13 May 2004; accepted 1 June 2004 Abstract Classification tree analysis is evaluated as a predictive soil mapping technique for developing a preliminary soil map for neighboring site from samples extracted from an existing soil map. The objective of the research is to help guide future soil mapping in a nearby area. In order to determine the best overall modeling approach several variations were explored: the dependent variable (soil map class) was grouped at several hierarchical levels (according to Soil Taxonomy), sensitivity analysis was performed on the predictor variables (environmental variables acting as surrogates for soil forming factors), and the study area was divided into meaningful sub-areas (mountains and basins). Soil great group was discovered the most parsimonious dependent variable based on model results (misclassification error rate of 30.0% based on a test data set). Geomorphology (as measured by several landform variables) best explains the distribution of soil types. The terrain analysis variables did not explain a large amount of variance within the models. Dividing the study area in two separate modeling units increased overall model accuracy. Our results suggest that soil taxonomic class can be predicted with reasonable accuracy from environmental variables. In addition, the technique can provide limited insight into the variables that are most responsible for driving soil development in a given area. This technique could be used in soil survey to extrapolate obvious soil landscape relationships from one site to another, allowing soil experts to concentrate their field mapping effort in unique areas Elsevier B.V. All rights reserved. Keywords: Soil survey; Classification tree modeling; Predictive soil mapping 1. Introduction Geographic information science (GIS) and technology has great potential to improve the efficiency and Corresponding author. Tel.: ; fax: address: pscull@mail.colgate.edu (P. Scull). quality of the methods used to gather spatial soil information (Hewitt, 1993; Gessler et al., 1995; McBratney and Odeh, 1997). GIS based predictive soil mapping is necessary because soil data are being used by scientists in increasingly sophisticated ways. For example, ecological and hydrological process models used to evaluate global change require chemical and physical soil data (Burrough and McDonnell, 1998). Technological /$ see front matter 2004 Elsevier B.V. All rights reserved. doi: /j.ecolmodel

2 2 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 advances in GIS and remote sensing have created a tremendous potential for improvement in soil resource inventory (McBratney, 1992; Scull et al., 2003). Research in the field of predictive soil mapping has led to many criticisms of the methods and products of traditional soil survey. The degree of soil variability observed in the field has always been difficult to characterize given the concept of soil survey (Beckett and Webster, 1971; Cambell, 1977; McSweeney et al., 1994). Recently, however, the fundamentals of soil survey (e.g. classification and the soil type) have come under scrutiny and many researchers have concluded that soil survey is an inadequate method of soil data collection because it does not produce the kinds of soil data required by modern users (McSweeney et al., 1994; Cook et al., 1996; Zhu et al., 1997). Still, soil survey remains the dominant means by which data on the spatial properties of soil are inventoried in the USA because most users accept the product s shortcomings and are largely satisfied (Indorante et al., 1996). Thus, there is a need to develop predictive soil mapping methods that are directly applicable to soil survey. One particular predictive mapping method, decision tree analysis (DTA), is being increasingly used in vegetation mapping (for example see Franklin et al., 2000) and habitat modeling in ecology (for a review see Guisan and Zimmermann, 2000). In contrast, the potential of DTA to contribute to soil survey has received limited consideration. The method has been used to create a map of soil class for an expanded area from a small reference area (Lagacherie et al., 1995; Lagacherie and Holmes, 1997), and to improve an existing soil map (Moran and Bui, 2002). Cialella et al. (1997) used DTA to predict soil drainage class from remotely sensed and digital elevation data, and McKensie and Ryan (1999) used regression trees to model individual soil properties. However, DTA has not been applied at landscape scales to map soil taxonomic class in desert ecosystems. Soil survey in the Mojave Desert has had low priority in the past, but recent concerns about biodiversity and species protection require an understanding of soil distribution (Butcher, 1981). Knowledge gained from the patchwork of existing, small-area soil surveys in the Mojave Desert can be used to assist soil mapping in the rest of the region. Predictive soil mapping has the potential to increase mapping efficiency by using the existing soil surveys to develop numerical predic- Fig. 1. Overview of methods. tors of soil occurrence. Here we use an existing level 4 soil map covering a 2590 km 2 tract of land in the central Mojave Desert to develop a prediction of soil distribution for a contiguous area recently scheduled to be mapped (the Expansion Area ). Our objective is to generate a preliminary soil map to help guide the field mapping effort. We used samples extracted from the existing digitized soil map in a multinomial classification tree model to produce a soil map for a neighboring, and assumed similar site. We determined the most appropriate dependent variable for the analysis, selected the best group of predictor variables to include in the model, explored the possibility of stratifying the study area into separate modeling units, and evaluated its applicability to the Expansion Area. In addition, we commented more generally on the use of decision tree modeling approaches in predictive soil mapping research. 2. Methods 2.1. Method overview An overview of the research methods is presented in Fig. 1. A GIS was used to manage the digital spatial data characterizing the environmental variables that are related to, or surrogates for, the soil forming processes. Four sources of data were input to the GIS: remote sensing, terrain analysis, pre-existing environmental maps (lithology, climate, a generalized statewide soil

3 P. Scull et al. / Ecological Modelling 181 (2005) database, and vegetation), and soil survey data. We developed a decision tree modeling approach using soil data as the dependent variable and environmental data from the GIS as independent variables. The result of model development is a set of rules defining where the dependent variable is located (relative to the environmental variables), based on the initial training data. The results are evaluated by passing an independent dataset through the models and once refined, can be applied to the environmental data for the Expansion Area to create a predictive map. The DTA procedure was designed to utilize information extracted from the existing digitized soil survey map. The other sources of information from the original survey (field collected data and expert knowledge) were either insufficient or unavailable. Additionally, the soil survey map is, in essence, a synthesis of both the expert knowledge and the survey point data; the amount of information contained in a soil map is more than simply the sample points that were collected during the production of the map. While soil maps were not intended to provide such geographically specific information, there is a precedent for using point samples extracted from soil maps in decision tree analysis (Lagacherie and Holmes, 1997; Cialella et al., 1997). We tested three aspects of the above procedures in order to determine the best overall approach to create a predictive map. First, three levels of aggregation of the dependent variable class (order, suborder, and great group) were defined to identify the most appropriate hierarchical level for predictive soil mapping. Once an appropriate dependent variable was selected, the second step was to determine the best group of predictor variables to use in model development. Third, we tested the potential of stratifying the study area into separate modeling units based on obvious landscape features (mountains versus basins) to improve model predictions Study area description The study area is located in the Mojave Desert Ecoregion of California, within a part of the larger Basin and Range Physiographic Province (see Fig. 2). The area comprises about 2590 km 2. The physiography of the region is dominated by isolated, fault-block mountain ranges rising abruptly from broad, alluviumfilled desert basins. Characteristic landforms of the area include alluvial fans, rock pediments, bajadas, fan remnants, alluvial flats, washes and playas (Schoenherr, 1992). Virtually no water exists on the surface, except locally after infrequent, heavy rainfall. Most of the runoff flows inward and drains internally into several large playas that occasionally flood to depths of a meter during large rainfall events (Enzel, 1992). There are four major vegetation types present within the study area. Creosotebush (Larrea tridentata) and white bursage (Ambrosia dumosa) dominate Mojave creosotebush scrub, which occurs on gently sloping alluvial fans and steep sideslopes of mountains and hills. Desert saltbush scrub is characterized by one or more species of saltbush (Atriplex sp.) in combination with other halophytes and occurs on basin floors adjacent to playas. Blackbrush scrub is dominated by blackbrush (Coleogyne ramosissima) and occurs at mid to higher mountain elevations. The variable composition of the Mojave wash scrub, which occurs in ephemeral channels, is influenced by the size of the watershed, slope gradient, parent material, soil texture and climate (Federal Geographic Data Committee, 1997). The climate of the study area is extremely arid. Precipitation ranges from 50 to 100 mm a year for most of the area, with higher elevations receiving as much as 180 mm in some years. Mean monthly temperatures range from 7.8 C in January to 29.4 C in July. The geology is highly variable in terms of both composition and age, ranging from pre-cambrian metamorphic to Cenozoic volcanic and sedimentary (Yount et al., 1994). Collectively, these factors yield an extremely heterogenous group of soils. Surface age varies greatly over very short distances, often resulting in weakly developed Entisols occurring next to 100,000-year-old Aridisols. Soil development is characterized by a lack of water and there is minimal organic matter available to be incorporated in the soil profile. Because insufficient water exists to leach material from the soil, the study site is collectively characterized by soils that have zones of soluble and semi-soluble salts, and clay accumulation at depth (Fahnestock and Lato, 1998) Data The USDA Natural Resources Conservation Service (NRCS) provided us with a Level 4 digitized soil map for the entire area defined by the current boundary of the study area. We sampled soil class directly from the map

4 4 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 Fig. 2. Study area showing the topography and material type. (see sampling scheme below). The order, suborder, and great group classifications of the dominant soil in each mapping class were used as the dependent variables in the models. An extensive search of existing data for the area yielded an environmental database that was used to characterize significant environmental factors that determine soil properties (see Table 1). The database was composed of all the information a soil surveyor would normally use to build a conceptual model of soil variation, including the data layers that most strongly drive soil development. For example, temperature and precipitation surfaces (January average daily minimum temperature, July average daily maximum temperature, average summer and winter precipitation) were used to estimate the climate soil-forming factor. While the direct connection between present climate variables (e.g. temperature and precipitation) and soil type distribution may seem tenuous given the time scale of soil development in the desert, present climate data is used explicitly in US Soil Taxonomy (Soil Survey Staff, 1975), making them an important variable to consider in predictive soil mapping of soil type. Climate data were derived from available climate station data and elevation values from a digital elevation model (J. Michaelsen, unpublished) using a universal kriging routine (described in Franklin et al., 2000). Additionally, local variations in the influence of climate were characterized using several terrain attributes: solar radiation, southwestness, and elevation. The California Gap Analysis map, a regional scale map of vegetation association was the best representation of vegetation available. Vegetation distribution was also computed using the Normalized Difference Vegetation Index (NDVI) from a 8 June 1996 TM image. Terrain attributes derived from digital elevation models (DEMs) are commonly useful explanatory variables in predictive soil models (Odeh et al., 1991; Moore et al., 1993; Gessler et al., 1995; Skidmore et al., 1996). The role of terrain analysis in soil mapping has been reviewed by McKensie et al. (2000). Relief was estimated by using variables derived by terrain analysis: topographic moisture index (TMI), solar

5 P. Scull et al. / Ecological Modelling 181 (2005) Table 1 Examples of inputs to the environmental database Variable a Resolution Source, description Range Soil Forming Factor b Landsat thematic mapper TM 30 m Digital numbers (DNs) from each DN O, PM, T (bands 1 5; 7; TM1-7) c individual band (8 June 1996) TM band ratios (5:7, 5:3, 3:1) 30 m Band ratios from TM (8 June 1996) DN O, PM, T TM texture variables (text5, text15) 30 m Covariance filter, window size 5 5 and (TM 8 June 1996) TM panchromatic 30 m TM bands 1+2+3(TM8June 1996) TM NDVI d 30 m Digital numbers (DNs) from each individual band (8 June 1996) July maximum temperature 1km 2 J. Michaelsen, interpolated by (julmaxt) kriging January minimum 1km 2 J. Michaelsen, interpolated by temperature (janmint) kriging Summer precipitation 1km 2 J. Michaelsen, interpolated by (sprecip) kriging Winter precipitation 1km 2 J. Michaelsen, interpolated by (wprecip) kriging Landsat MSS 1986 (bands 30 m Digital numbers (DNs) from each 1 4; MSS1 4) individual band (8 June 1996) Topographic moisture index 30 m Modeled from DEMs; (TMI) ln(a c /tan B); A c is upslope catchment area, b is slope (Moore et al., 1991) Potential solar radiation (solarad) 30 m Shortwave, modeled from DEMs using Solarflux (Hetrick et al., 1993) for one date (21 December) Southwestness (swness) 30 m From DEMs, cos(aspect-255); values range from 1 (southwest) through 0 (northwest and southeast) to 1 (northeast) Slope gradient (slope) 30 m From DEMs by first order finite difference Elevation (elevation) 30 m USGS digital elevation models (DEMs) 1:24,000 quadrangles Landform (landform, earth material, sediment type, age) 1:75,000 1:75,000; 10 ha mmu, TM/SPOT merge, photo-interpreted DN O, PM, T DN O, PM, DN O C CL C CL mm CL mm CL DN O, PM, T DN R Jm 2 Cl, R 1 to R Cl,R m Cl, R 18, 24, 2, and 7 classes O, PM, T STATSGO 1:250,000 General soil maps 12 classes PM Vegetation (veg) 1:250,000 CA gap map (USGS Biological 9 classes O Resources Division) Geology (geol) 1:250,000 Digitized CA geology map 7 classes PM a The names used to refer to the variables in the text are in parentheses. b CL: climate; O: organisms; R: relief; PM: parent material; T: time. c TM wavelength ranges: band 1 = m; band 2 = m; band 3 = m; band 4 = m; band 5 = m; band 7 = m. d NDVI = [(TM4 TM3)/(TM4 + TM3)].

6 6 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 radiation, southwestness, slope, and elevation. In order to account for the movement of water through the landscape TMI (upslope catchment area divided by slope gradient, assuming uniform hydraulic conductivity; Beven and Kirby, 1979) was used. Topographically modeled potential solar insolation (Dubayah and Rich, 1995) and southwestness (cos(aspect-225 ); Franklin et al., 2000) were used to account for the effect of slope aspect on potential evaporation. Slope gradient was used to capture subsurface soil moisture flow and soil texture. Many variables can be used to assess soil parent material (Table 1). Four separate attributes from the landform database were used: landform type, sediment type, earth material, and age. Collectively, these variables help to define the shape, composition, and origin of landforms. Several variables were derived from the TM data in order to help discern the geologic composition of the surficial material. The ratio of TM bands 5 and 7 (b5b7) has been shown to be a proxy for clay content and ratios 5:3 (b5b3) and 3:1 (b3b1) can reflect relative concentrations of iron (Vincent, 1997). These three ratios can help control for differences in the composition of the material found on the surface. Two texture variables were derived from TM band 5 to take advantage of the low absorption of that band and to measure landscape roughness. Parent material is also partly assessed by the regional geology (geol) and generalized soils maps (STATSGO). Age of landform is partially addressed in the model by the remote sensing data (both TM and MSS data), which can indicate surface age by detecting desert varnish (Anderson et al., 1993) Sampling scheme Sampling was necessary because an infinite number of points could have been extracted from the digitized soil map. Therefore, a sample scheme was developed to ensure adequate representation of smaller classes (Cliff and Ord, 1981). Three independent samples were drawn from the map to generate the decision tree models. The first was used to train the models (26,258 sample points), the second to prune them (9199 sample points), and the third to test model accuracy (4420 sample points). All soil map classes were randomly sampled proportional to their mapped area. This resulted in thousands of observations used for modeling. Fig. 3. Example of a pruning plot for the basin areas showing how training error rate declines with increasing tree size. Final node number determined by optimizing test error rate Decision tree analysis Decision tree analysis (Breiman et al., 1984; Quinlan, 1993) was used to predict soil taxonomic unit from environmental data. Decision tree modeling is a form of classification that involves recursively partitioning a data set into increasingly homogeneous subsets (Breiman et al., 1984). Once the partitioning has ceased, the subsets are called terminal nodes (Quinlan, 1993). Each terminal node is assigned the label of the majority class (Lees and Ritman, 1991). Splits, or rules defining how to partition the data, are selected based on information statistics that measure how well the split decreases impurity (heterogeneity or variance) within the resulting subsets (Clarke and Pregibon, 1992). The process is recursive, growing from the root node (the complete data set) to the terminal nodes in a dendritic fashion (Friedl and Brodley, 1997). Once the tree has been developed (or grown ), it encodes a set of decision rules that define the range of conditions (values of environmental variables) best used to predict each soil class. Pruning the tree is necessary to prevent the model from being over-fit to the sample data, and to reduce tree complexity. Pruning entails combining pairs of terminal nodes into single nodes to determine how the misclassification error rate changes as a function of tree size (see Fig. 3). We used cost-complexity pruning with an independent data set (a pruning data set) to produce a plot of training misclassification error rate versus tree size (Safavian and Norvig, 1991). The plot was used to

7 P. Scull et al. / Ecological Modelling 181 (2005) determine an approximate optimal tree size (byvisually determining the tree size that minimizes training errors from the plot). We then produced a series of tree models with various sizes near the value suggested by the plot. Each of these models was assessed with an independent test sample to determine their prediction accuracy. We continued to produce models with greater or smaller sizes until a tree size was found that minimized the test error rate (Fig. 3) Significance of independent variables In order to explore the predictive power of individual variables, two sets of models were generated for each predictor variable in the dataset. Excluding each variable one at a time from the potential pool of predictor variables created the first group of models, and using only a single variable at a time generated the second group of models. Subsets of similar predictors (e.g. remote sensing variables, terrain variables, etc.) were also both excluded from models and used alone in model generation. Mean misclassification error rates were noted to determine independent variable significance, as measured by influence on predictability Principal components analysis of independent variables Many of the quantitative predictor variables were derived from either the remote sensing data or the digital elevation models and are therefore highly correlated. This covariance and the large number of quantitative variables used (25) would make model interpretations difficult. In order to address this problem, we explored using principal components analysis (PCA) to orthogonalize the quantitative variables and reduce the total number of variables. A correlation matrix PCA was used because many of the variables had different numeric scales. We decided to use seven extracted components as predictor variables in the classification tree models because the first seven explained greater than 90% of the total variance Comparison of mountain and basin soils In desert ecosystems soil character and the factors influencing soil development differ dramatically between the basins and the mountains. For example, in terms of albedo or brightness, opposite relationships exist between reflectance and soil development in the basins versus the mountains. Areas with low total albedo are often varnished surfaces in the basins, which are therefore stable, and have well developed soils beneath them. Areas that appear bright are often dunes, washes, and other erosionally active surfaces. These sites are frequently composed of poorly developed soils (e.g. Entisols). Therefore, surface age (and, consequently, degree of soil development) and total albedo are inversely related in the basins. In the mountains, areas of low albedo are usually varnished rock outcrops, which can be surrounded by very thin soils. The brighter areas are usually pockets in between large areas of outcrops where the surface is slightly more stable and where thicker soils can support grass and shrub vegetation. This results in a positive relationship between albedo and degree of soil development in the mountains. Since soil-landscape relationships differ in mountains and basin areas, we explored modeling them separately in order to determine whether we could achieve a higher overall level of model accuracy. 3. Results 3.1. Model evaluation Dependent variables A summary of three models predicting the soil order, suborder, and great group of the majority soil type in each mapping class are shown in Table 2. Pruned decision tree sizes (optimal numbers of nodes based on cost-complexity pruning) were 40, 60, and 70 for the order, suborder, and great group models, respectively. The soil order tree model (only two classes) exhibited the best prediction accuracy of the group (misclassification error rate of 23.8% based on the test data set), followed by the great group model (30.0%) and the suborder model (30.3%) (Table 2). All three of the models had substantially lower ( 3%) training misclassification error rates. No consistent patterns were observed in terms of the variables selected in each of the models. Soil great group was used as the dependent variable in all further models based on these results. While the model predicting soil order was 6.2% more accurate than the great group model, a predictive soil great group map contains substantially more information than a predictive soil order map.

8 8 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 Table 2 Classification tree results for each dependent variable Taxonomic # Nodes Error rates class Training (%) Test (%) Order (2 classes) a Group (8 classes) b Subgroup (11 classes) c Sample total a Variables used: geol, landform, text15, stgo, material2, MSS4, age, sprecip, veg, janmint, tulmaxt, b5b7, ndvi, text3, slp, wprecip. b Variables used: material2, geol, wprecip, landform, julmaxt, TM2, MSS4, b5b3, stgo, TM1, dem, veg, slp, TM6, b5b7, texture15, MSS3, age, texture5. c Variables used: material2, landform, wprecip, veg, geol, sprecip, dem, TM1, janmint, TM2, b5b7, MSS4, age, slp, texture15, MSS3, stgo, julmaxt Predictor variables PCAresults. The component loadings from the output of the principal components analysis are shown in Table 3. No clear interpretable relationships were noted between the groups of variables associated with each component (although PC1 seemed like a brightness/dryness component, measuring the total albedo of the surface). Collectively, the first seven components account for 91.2% of the total variance present in the 25 quantitative variables from which they were derived. Misclassification error rates from unpruned models were used to compare the predictive power of the PCA variables to the original variables (Table 4). The misclassification error rate based on the training data of the great group model discussed above (using all variables) was 27.5%. Because the categorical variables were not included in the PCA transformation, they were used in combination with the seven components, achieving an error rate of 29.3%. A model using only the seven components had an error rate of 39.0%. Slightly better results were achieved when all 25 components from the PCA were used in model generation (35.0%). The number of nodes for these models is also shown in Table 4. All of the models had unpruned tree sizes of greater than 100 nodes with a negative relationship between the number of variables used in model formulation and unpruned model size (correlation coefficient of 0.64). PCA was not a useful method for addressing covariance among the predictor variables in this dataset at least when used in combination with decision tree modeling. Because the individual components were difficult to interpret, their use as predictors in a classification tree would have produced an even more obscure model. Additionally, model size barely decreased using the seven PCA components and the seven categorical variables (110 versus 112 nodes, unpruned), despite the fact that 18 fewer variables were used. Therefore, regardless of PCA transformation, classification tree interpretations would be hindered by the size of the models Significance of individual variables. Removal of 13 variables one at a time had no effect on training misclassification error rates (Table 5, left side). The individual removal of six of the variables (sediment age, slope, MSS4, TM5:7, TM6, and TM5:3) actually caused the misclassification error rate to drop slightly. The removal of the other 13 variables caused the misclassification error rate to rise very slightly. No patterns are evident between the types of variables that fell into each of the three categories (no effect, decrease and increase of error rate). The three variables that, when excluded from the model, caused the greatest increase in error rate were veg, landform, and earth material (see Table 5). When similar variables were grouped and collectively excluded the variables derived from the Landform Map caused the largest rise in error rate (from 27.5% to 30.8%). The terrain attributes collectively caused the smallest increase in error rate (less than 0.2%). Misclassification error rate rose by less than 1% when all four climate variables were excluded from model formulation. Training misclassification error rates for the models of soil great group that were developed using only one variable at a time varied from 41.7% to 48.4%

9 P. Scull et al. / Ecological Modelling 181 (2005) Table 3 PCA results component loadings for the first seven components Variable Component Dem Slp Pan Texture Texture Ndvi B5b B5b B3b TM TM TM TM TM TM Julmaxt Wprecip Sprecip MSS MSS MSS MSS Janmint TMi Swness Variance explained Eigenvalues for all 32 variables (see Table 5, right side). The four variables that performed best as single predictors of soil great group were wprecip, geol, landform, Table 4 Using principal components in classification tree model Variable combination a Tree size b Classification error c, rate (%) All (32) Categorical (7) Quantitative (25) components comp + categorical All 25 components Sample total a The predictor variables that were used in. each separate tree model. b Unpruned model size. c Soil subgroup used as dependent variable. and earth material. No strong patterns were observed among the types of variables that performed well versus those that performed poorly except that the two best predictors were both derived from the MDEP Landform map. When individual groups of predictors were used in model formulation (excluding the other groups) the worst performing group was the terrain attributes (44.0% training misclassification error rate; see Table 5). Contrasted with this the four landform variables used by themselves had an error rate of only 37.8%. Collectively, these results suggested that individual variables can be removed from the models with little impact on overall model accuracy. Therefore, interpreting the rules derived from the models (in terms of soil environment correlations) is difficult because no single model is clearly optimal and removing single variables could dramatically change the model rules while having little impact on model performance.

10 10 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 Table 5 Analysis of predictor variable significance Predictor variable Excluded error rate (%) Solo error rate (%) Earth material Landform Geol Wprecip STATSGO Sprecip TM B5b TM Elevation TM Janmint Julmaxt TM Veg TM TM Pan Texture Slope Swness Texture Sediment age MSS MSS MSS Ndvi B3b B5b MSS Sediment type Tmi Subset of variables Landform Geol + veg + STATSGO Climate Remote sensing Dem None Variables selected: material2, landform, wprecip, veg, geol; sprecip, dem, julmaxt, MSS3, stgo; TM6, b3b1, TM1, janmint, TM2; b5b7, MSS4, age, texture15, slp; MSS2, b5b3. Previous classification tree research has shown that using coarse resolution predictor variables (such as the 1 km 2 climate grids) often yields coarse resolution prediction surfaces (Gessler et al., 1995). Because the climate variables were not found to have great predictive power in terms of model accuracy (training mis- Table 6 Classification tree results for the mountain and basin subregions Taxonomic # Nodes Error rates class Training (%) Test (%) Mountain a (4 classes) Sample total 7619 Basin b (11 classes) Sample total Area weighted error rate a Variables used: geol, stgo, age, material2, landform, dem, slp, texture15, TM1. b Variables used: material2, landform, geol, age, MSS1, dem, MSS3, veg, TM1, TM2, MSS4, slp. classification error rate only increased by 0.6% when the climate variables were excluded in model formulation), we excluded them from further model development. All of the other variables were included in model development to maximize accuracy Mountain versus basin model comparison The three samples (train, prune, and test) were divided into two subsets based whether each map class occurred in the mountains or in the basins. A separate classification tree model was generated on each using soil great group as the dependent variable. The models were pruned using cost complexity pruning and the test samples were used to measure their accuracy. The two models had test error rates of 12.0% and 35.0% for the mountain and basin models respectively (Table 6). Only four of the eleven soil great group classes occurred in the mountains, whereas all eleven occurred in the basins. As a result the mountain classification models were smaller than the basin models (25 versus 51 nodes). When the two individual error rates are weighted relative to their area an overall study area error rate of 27.7% was achieved. This value is 2.3% higher than the error rate of the great group model predicting both the mountain and basin classes simultaneously. These results suggest that dividing the study area into meaningful subareas could improve overall prediction. Two separate models were used for the final analysis based on these results.

11 P. Scull et al. / Ecological Modelling 181 (2005) Table 7 Error matrix for basin classes User accuracy (%) Predicted class Observed class (great group) Row total Aquisalid Argidurid Calci Haplargid Haplocalcid Haplocambid Haplodurid Haplogypsid Natrargid Torriorthent Torripsamment argid Aquisalid Argidurid Calciargid Haplargid Haplocalcid Haplocambid Haplodurid Haplogypsid Natrargid Torriorthent Torripsamment Column totals Producer accuracy (%) Average producer s accuracy (weighted by class area): 65.2%, average user accuracy (weighted by class area): 64.9%, sample size: 3102, overall accuracy: 65.05%, kappa: Final model and predictive map Details of the accuracy of the two classification tree models for the basin and mountain sub-areas are shown in Tables 7 and 8. The basin model predicted 10 of the 11 classes of soil great group, the exception being the Natrargid soil types. The basin map had a producer and user accuracy (weighted by class area) very similar to the overall model accuracy, 65.2% and 64.9%, respectively. A 0.52 kappa statistic was calculated for the overall error matrix. In terms of producer s error (a measure of how well the test data are classified), the three best classes were Aquisalids, Haplogypsids, and Torriorthents. The three classes in the basin area with the lowest producer s accuracy were Natrargids, Haplocambids, and Argidurids. Slightly different patterns can be observed by looking at the best and worst individual classes in terms of user accuracy. Because the predictive map will be used as a preliminary soil map during a soil survey of the area, the user accuracy is a more relevant measure of modeling success in the context of our objectives. The three map classes with the highest user accuracy (a measure of how likely a test sample classified into a given category actually belongs in that category) were Aquisalids, Torriorthents, and Haplodurids. In contrast, the classes Natrargids, Calciargids, and Torripsamments had the lowest user accuracy for the basin area. While overall the model for the mountain area was more accurate than the basin model (88% versus 65%), two of the great group classes (Argidurid and Haplodurid) in the mountains had user and producer accuracyof0%(table 6). Of the four classes found in the mountain area, the Torriorthent class was most accurately predicted by the model (>90% for both user and producer accuracy). A kappa statistic of 0.44 was calculated for the mountain area error matrix. The rules defined by the two models were separately applied to the mountain and basin subregions and then combined to create a predictive great group soil map for the entire study area (Fig. 4). Within the study area the model results can be visually compared to the actual soil map and in the Expansion Area the map serves as preliminary soil map. General patterns between the predicted and actual maps are similar within the base with many minor exceptions. Torriorthents and Haplargids are often confused with one another, though they generally are predicted to occur in the correct

12 12 P. Scull et al. / Ecological Modelling 181 (2005) 1 15 Table 8 Error matrix for mountain classes Observed class (great group) Row total User accuracy (%) Argidurid Haplargid Haplodurid Torriorthent Argidurid Haplargid Haplodurid Torriorthent Column totals Producer accuracy (%) Average producer s accuracy (weighted by class area): 87.2%, average user accuracy (weighted by class area): 85.3%, sample size: 1218, overall accuracy: 88.0%, kappa: locations. They are the only two classes that are predicted to occur in the mountains, because the model failed to identify the other mountain classes (Argidurid and Haplodurid). Torriorthents seem to be overestimated everywhere and some of the smaller classes (by total area in actual soil map) are underestimated. The actual soil map also has more fine-scale detail then the predictive map. 4. Discussion decision tree analysis as a PSM tool in soil survey In desert ecosystems classification trees are useful predictive soil mapping tools. The resulting predictive great group soil map for the Expansion Area could have utility when actual field mapping commences. At that time we will address the accuracy of the predictive map, Fig. 4. Comparison of predicted to actual soil map for Fort Irwin. Includes the Expansion Area preliminary soil map.

13 P. Scull et al. / Ecological Modelling 181 (2005) but in the meantime these results demonstrate some of the advantages and disadvantages of using DTA to predictively map soil Advantages Many aspects of decision trees make them appealing models to use in predictive soil mapping research. DTA is an especially useful approach to use with archived soil maps when no quantitative point data exist (or they are difficult and/or expensive to collect). In this situation, samples can be extracted from digitized soil maps and used to develop and test the model. Provided that the target study area is composed of similar landscapes the models lead to reasonable predictions. Since a patchwork of surveys exist across the Mojave Desert, DTA can help to fill in the gaps and to identify areas that require more field mapping attention. The methods can be applied to active field surveys during the off season (summer fieldwork is limited due to excessive heat) to produce preliminary soil maps. Those maps would guide fieldwork the next season. Using DTA methods to predict soil type, Lagacherie et al. (1995) also reported the technique looked promising. They obtained slight worse overall accuracies working within the Mediterranean coastal plain in the south of France. Moran and Bui (2002) obtained similar accuracies (65 70%) using a boosting technique for the Murray-Darling Basin in eastern Australia. Boosting is an iterative procedure that involves working with the mis-classified data from previous iterations (Moran and Bui, 2002). Despite these studies we know of no other soil mapping application of DTA to compare our results (where the predictor variable is categorical). DTA is also a useful method for integrating a wide variety of predictor variables (both nominal and continuous). Because the availability of digital environmental data to serve as predictor variables in predictive soil models will vary from one location to another, the flexibility of DTA is very appealing Limitations The proposed methodology can only be used in situations where soil maps exist and the resulting predictions will only have significance in nearby areas composed of similar landscape. The analysis of variable significance suggests that DTA provides only limited insight into physical processes driving soil formation in the study area. Overall few of the individual variables were crucial in model formation. Excluding each variable one at a time caused very small increases in error rate (the greatest was the Earth Material variable, which increased error rate 2%). In addition, when individual variables were used as predictors the range between the best and worse predictors was only 6%. Therefore it is difficult to draw any conclusions about which variables, and the associated soil forming processes they purport to measure, are responsible for yielding the observed soil patterns. The results do suggest that geomorphology (as measured by the four landform variables) best explains the distribution of the soil types in the study area. In contrast, the terrain variables did not explain a large amount of deviance within the models. These results contradict a large amount of research documenting the value of using terrain analysis in predictive soil models (reviewed in McKensie et al., 2000). However, the size and location of the study area (2580 km 2 of desert landscape), and nature of the dependent variable (soil taxonomic class) differ from most previous studies. The results suggest that at the landscape scale in desert ecosystems (the scale of the original soil map was 1:65,000) topography is probably not related to soil class. To derive the dependent variable in the analysis, samples were drawn from individual soil polygons that were assigned the taxonomic class of their majority soil component. Topography probably varies within each polygon and is expressed by the distribution of the individual soil components. The fact that none of the individual variables appear critical in model formation for this dataset can be an advantage in decision tree analysis. Some authors have criticized the tendency for decision tree models to produce a stepped prediction surface (Gessler et al., 1995). Such a situation can result from mixing predictor variables with different scales and/or data types, or can be the result of individual variable splitting rules defined by the model. In either case, if the problematic variables (similar to the climate variables in this paper) are not critical in the overall model (in terms of predictability) than it can be excluded from the analysis.

14 14 P. Scull et al. / Ecological Modelling 181 (2005) Conclusion A classification tree approach used an existing digitized soil map to produce a predictive soil map for a neighboring, and similar area. The method combines a variety of environmental variables that serve as surrogates for soil forming factors in model development. Soil taxonomic class, derived from the dominant soil type in each soil map class, can be predicted from environmental variables with reasonable accuracy. In addition, the technique provides some insight into the environmental variables that are most responsible for driving soil development in a given area. In the future this technique could be used in soil survey to extrapolate soil landscape relationships from one site to another, allowing soil experts to concentrate their field mapping efforts in areas that exhibit unique soil landscape pattern. References Anderson, R.C., Beratan, K.K., Blom, R.G., Identification of geomorphic surfaces from Landsat data, Whipple Mountains, southeastern California, Abstracts with Programs Geological Society of America 25, Beckett, P.H.T., Webster, R., Soil variability: a review. Soils Fertilizers 34, Beven, K.J., Kirby, M.J., A physically based variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24, Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J., Classification and Regression Trees. Wadsworth, Belmont, California, 367 pp. Burrough, P.A., McDonnell, R.A., Principals of Geographic Information Systems (revised edition). Clarendon Press, Oxford, 333 pp. Butcher, R.D., The California Desert plan. Natl. Parks Conserv. Mag. 55, Cambell, J.B., Variation of selected properties across a soil boundary. Soil Sci. Soc. Am. J. 41, Cialella, A.T., Dubayah, R., Lawrence, W., Levine, E., Predicting soil drainage class using remotely sensed and digital elevation data. Photogrammetric Eng. Remote Sensing 63, Clarke, L.A., Pregibon, D., Tree-based models. In: Chamber, J.M., Hastie, T.J. (Eds.), Statistical Models. S. Wadsworth and Brooks, Pacific Grove, CA, pp Cliff, A.D., Ord, J.K., Spatial Processes: Models and Applications. Pion Ltd, London, 325 pp. Cook, S.E., Corner, R.J., Grealish, G., Gessler, P.E., Chartres, C.J., A rule-based system to map soil properties. Soil Sci. Soc. Am. J. 60, Dubayah, R., Rich, P.M., Topographic solar radiation for GIS. Int. J. Geographic Inf. Syst. 9, Enzel, Y., Flood frequency of the Mojave River and the formation of late Holocene playa lakes, Southern California, USA. Holocene 2, Fahnestock, P., Lato, L., Soil survey of Fort Irwin, California. US Department of Agriculture, Washington, DC, 211 pp. Federal Geographic Data Committee, National vegetation classification standard. Franklin, J., McCullough, P., Gray, C., Terrain variables for predictive mapping of vegetation communities in Southern California. In: Wilson, J., Gallant, J. (Eds.), Terrain Analysis: Principals and Applications. John Wiley and Sons, New York, 381 pp. Friedl, M.A., Brodley, C.E., Decision tree classification of land cover from remotely sensed data. Remote Sensing Environ. 61, Gessler, P.E., Moore, I.D., McKensie, N.J., Ryan, P.J., Soillandscape modelling and spatial prediction of soil attributes. Int. J. Geographical Inf. Sci. 9, Guisan, A., Zimmermann, N.E., Predictive habitat distribution models in ecology. Ecol. Model. 135, Hewitt, A.E., Predictive modelling in soil survey. Soil Fertilizers 56, Indorante, S.J., McLeese, R.L., Hammer, R.D., Thompson, B.W., Alexander, D.L., Positioning soil survey for the 21st century. J. Soil Water Conserv. 1, Lagacherie, P., Holmes, S., Addressing geographical data errors in a classification tree for soil unit prediction. Int. J. Geographical Inf. Sci. 11, Lagacherie, P., Legros, J.P., Burrough, P.A., A soil survey procedure using the knowledge of soil pattern established on a previously mapped reference area. Geoderma 65, Lees, B.G., Ritman, A.K., Decision-tree and rule induction approach to integration of remotely sensed and GIS data in mapping vegetation in disturbed or hilly environments. Environ. Manage. 15, McBratney, A.B., On variation, uncertainty and informatics in environmental soil management. Aust. J. Soil Res. 30, McBratney, A.B., Odeh, I.O.A., Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurement, and fuzzy decisions. Geoderma 77, McKensie, N.J., Ryan, P.J., Spatial prediction of soil properties using environmental correlation. Geoderma 89, McKensie, N.J., Gessler, P.E., Ryan, P.J., O Connell, D., The role of terrain analysis in soil mapping. In: Wilson, J., Gallant, J. (Eds.), Terrain Analysis: Principals and Applications. John Wiley and Sons, New York, p McSweeney, K., Gessler, P.E., Hammer, J., Bell, J., Peterson, G.W., Towards a new framework for modeling the soil landscape continuum. In: Bryant, R.B., Arnold, R.W., Factors of Soil Formation: a Fiftieth Anniversary Retrospective, Soil Science Society of America Special Publication 39. Soil Science Society of America, Madison, WI. Moore, I.D., Gessler, P.E., Nielsen, G.A., Peterson, G.A., Soil attribute prediction using terrain analysis. Soil Sci. Soc. Am. J. 57,