Problem: Interpolation of soil properties Soil physical and chemical property data essential for modelling surface and subsurface phenomena Soil data are often lacking Soil scientists have focused on vertical relationships rather than horizontal relationships Soil maps are often displayed as choropleth maps, with discrete lines representing the boundaries between map units two problems with this approach: lines do not accurately depict boundaries between soil units the implied homogeneity within the soil unit boundaries does not exist for most soil properties needed for environmental modelling

Factors influencing soil formation: Jenny’s (1980) factors of soil formation (CLORPT): 1. Cl - climate 2. O - organism 3. R - topography or relief 4. P - parent material 5. T - time climate topography organisms parent material soil time Reference Citation ... Jenny, H. 1941. Factors of soil formation. McGraw-Hill, New York. Jenny, H. 1980. The soil resource: Original behavior. Springer-Verlag, New York, p. 377.

Statistical Surfaces: based on the catena concept a sequence of soils, where climate, parent material and age are similar, BUT, the soils differ because of variation in relief and in drainage for example, the following figure shows four soils of a drainage catena and their topographic association in the field - these soils are all developed from the same parent material and differ only in drainage and topography

Distributing soil properties based on the terrain analysis Soil properties are highly variable This variability places limits on the ability to predict spatial distribution of soil properties (~ 70%) Digital terrain analysis approaches improve explanation of variance in soil properties Explanation of variance in Approach soil properties (Reference) 10% General purpose soil survey (Webster 1977) Terrain analysis 41 to 64% (Moore et al. 1993) Terrain analysis 63 to 68% (Gessler et al. 1993) 70% Maximum predicted explanation of variance using terrain analysis (Moore et al. 1993)

Terrain attributes and their importance to soil development Elevation Temperature and moisture gradients Aspect Temperature and moisture gradients Slope Potential gradient of water transport Curvature Accumulation and dissipation of water and water-transported chemical constituents Plan Convergence or divergence of water Profile Rate of change of potential gradient of water transport Catenary position Differential drainage conditions; differential transport and deposition of suspended materials; differential leaching, translocation and redeposition of soluble materials Contributing area Amount of water flow

Example 1: A single hillslope Moore et al. (1993)

Example 2: A nested watershed Creed et al. (2000) Predicting nutrient export rates from catchments is essential to understanding the nutrient budget of watersheds. Spatial heterogeneity of C and N pools should influence the rates of accumulation, remineralization and transport of these compounds What are the best predictors of the spatial heterogeneity of the C and N pools within the watershed?

Sampling Strategy Since catenary processes are hypothesized to be a strong predictive variable, a catenary index was used as the basis for designing the soil sampling strategy Criteria for sampling strategy: 1. Sample evenly in attribute space 2. Sample randomly 3. Minimize inefficiencies due to errors in location between digital terrain model and real world 4. Minimize inefficiencies due to spatial dependence of soil properties

Sampling Strategy FOR MORE INFO... Beven, K., M. Kirby. 1979. Hydrological Science Bulletin 24: 43-69.

Frequency Distribution of Catenary Index A frequency distribution of the catenary index was divided into five sample populations based on the 20th, 40th, 60th, and 80th percentiles. 5 10 15 20 25 30 35 1 2 3 4 6 7 8 9 11 12 13 14 Catenary Index Percent (%) 40 60 80 100

Spatial Distribution of Sites Based on Catenary Index Percentiles 0-20th 20-40th 40-60th 60-80th 80-100th D i s t r b u o n f S a m p l g e B d C y I x P F c < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 1 7 1 5 1 3 1 5 2 1

Semi-variogram of Catenary Index Semi-variogram provides distance-based measures of spatial autocorrelation. 1.2 sill = 1 1.0 0.8 gamma 0.6 0.4 nugget = 0.3 0.2 range = 250 m 0.0 200 400 600 800 1000 h (m) nugget = measurement error or micro-scale variation range = distance at which data are not longer autocorrelated Four sites were discarded from further analysis based on the calculated variogram.

ELEVATION 600 m 525 m 450 m 375 m 300 m SLOPE 40 degrees 30 degrees < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 29 18 9 8 17 SLOPE 40 degrees 30 degrees 20 degrees 10 degrees 0 degrees Slope < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 17 9 11 13 30 ASPECT North West East Aspect South < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 14 10 14 23 20

PROFILE CURVATURE Convex Neutral Concave South PLAN CURVATURE Convex < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 20 17 18 12 14 PLAN CURVATURE Convex Neutral Concave Plan Curvature South < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 13 16 18 23 11

Spatial Distribution of Sites Based on Biological Attributes TOTAL BIOMASS 150 Mg C/ha 120 Mg C/ha 90 Mg C/ha 60 Mg C/ha 30 Mg C/ha Total Biomass South < 2 t h 2 - 4 t h 4 - 6 t h 6 - 8 t h > 8 t h 20 12 18 13 18

Measured distribution of carbon in the soil profile Concentration Mass Per Area (%) (g/m ) 2 2 5 5 7 5 1 5 1 L L FH FH 5 5 ) m 1 1 ( c m h t c ( p e h t D l 1 5 p i 1 5 Soil Depth (cm) e Soil Depth (cm) o Soil Depth (cm) o o D S l i o Soil Depth (cm) o S 2 2 2 5 2 5

Model Development Entire Population (exploratory data analysis) Univariate analyses Multivariate analyses Split Population (predictive analysis) Model development: Population A Model corroboration: Population B

Do terrain attributes explain the variability of the soil profiles? Carbon

… elevation, slope, aspect? Carbon

… plan or profile curvature? Carbon

Do forest attributes explain the variability of the soil profiles? Carbon

Spatial Distribution of Carbon and Nitrogen in Soil LFH

Regression Trees Regression trees are an alternative technique for exploratory data analyses have the advantage of permitting non-monotonic, non-linear, and non-parametric relationships among variables have the advantage of allowing nesting of variables Regression trees are designed to iteratively “split” the samples into a binary tree of subsamples the split is based on the goal of minimizing the variation within the resulting subsamples the splitting process continues until the samples are too small to separate statistically, at which point the sample is assigned a constant value

for Carbon in the Soil LFH layer: Regression Tree for Carbon in the Soil LFH layer: Carbon in the LFH layer 1607 Slope < 11.72 Slope > 11.72 1991 1416 Plan Curv < -12.5 Elevation < 403 Elevation > 403 Plan Curv > -12.5 1619 2094 1644 1207 Biomass < 58,682 Plan Curv < 8.5 Slope < 20.14 Plan Curv > 8.5 Biomass > 58,682 Slope > 20.14 2297 1688 1520 2066 1399 1014 Biomass < 46,038 Plan Curv < -4.5 Biomass > 46,038 Plan Curv > -4.5 2599 1996 1753 1392

Model Evaluation: How do you know which one is “best”?