1. 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

2. 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 Factors of soil formation. McGraw-Hill, New York.
Jenny, H The soil resource: Original behavior. Springer-Verlag, New York, p. 377.

3. 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

4. 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)

5. 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

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

9. 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?

10. 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

11. Sampling Strategy FOR MORE INFO...
Beven, K., M. Kirby Hydrological Science Bulletin 24:

12. 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

13. 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

14. 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.

15. 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

16. 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

17. 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

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

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

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

21. … elevation, slope, aspect?
Carbon

22. … plan or profile curvature?
Carbon

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

25. Spatial Distribution of Carbon and Nitrogen in Soil LFH

26. 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

27. 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

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