Soil Depth Estimation

Estimation of soil depth is crucial for the assessment of hillslope hydrological processes (e.g.
Tromp van Meerveld and McDonnell, 2006) and landslide stability (e.g Lanni et al., 2011, 2012).  Is a topic that had a lot of attention in the community of geomorphologists but indeed it remain still an open. In a recent paper (e.g. Lanni et al., 2012, under the final stage of review in HESS) we wrote a very short review:

"The spatial distribution of soil depth is controlled by complex interactions of many factors (topography, parent material, climate, biological, chemical and physical processes) (e.g., Summerfield, 1997, Pelletier and Rasmussen, 2009, Nicotina et al., 2011). As a result, soil depth is highly variable spatially and its prediction at a point is difficult. Moreover, soil depth survey is time consuming and soil depth is difficult to measure even for small basins (Dietrich et al., 1995). Various methods have been explored to allow the estimation of soil depth over landscapes. A process-based approach was suggested by Dietrich et al. (1995) for predicting the spatial distribution of colluvial soil depth. Based on this approach, topographic curvature may be considered a surrogate for soil production. Heimsath et al. (1997, 1999) validated the relationship between curvature and soil production based on observations of cosmogenic concentrations from bedrock in their Tennessee Valley site in California. This approach was incorporated into a landscape evolution model by Saco et al. (2006) to evaluate the dependence of soil production on simulated soil moisture. Roering et al. (1999) supported the idea that soil production follows a non linear equation and, therefore, modified the dependence of soil depth relationships. However, the various modeling approaches for predicting soil depth over landscapes, described above, showed only partial success (Tesfa et al., 2009).

In contrast to the process-based approaches, a number of studies have applied statistical methods to identify relationships between soil depth and landscape topographic variables (e.g., slope, wetness index, plan curvature, distance from hilltop, or total contributing area) (e.g. Gessler et al., 1993, Tesfa et al., 2009, Catani et al., 2010). Some of these works reported good predictive capabilities for these statistical relationships. For instance, Tesfa et al. (2009) report that their statistical models were able to explain about 50% of the measured soil depth variability in an out-of-sample test. This is an important result, given the complex local variation of soil depth."

Our short review possibly miss some interesting reference as the one by D'Odorico (2000) on a possible bi-stable evolution equation, and our little work in Bertoldi et al. (2006) that generalize Heimsath's to include random variaility in depth. 

However, reduction of soil depth formation simply to a geometrical factor (as implied by using equations with homogenous parameters) is clearly not enough. Pedologists know it. But so far I found only a few able to enter in the strict path of learning our equations. 

Anyway,  looking for R based hydrological resources I found this explanatory map by Roudier and Beaudette:

Looking at it gives clearly the idea that soil depth does not depend (only) on geometry. Where slope and curvature remain constant, anyway soil depth varies.

It is easy to think that it depend on variability in the geologic substrate,  soil cover (grass, plants), and soil use (for instance grazing or the presence of animals). But there is any pedologist out there which could help us to built a consistent quantitative theory ?

As usual, the references could be a starting point for a more in-depth literature search.

References

Catani, F., Segoni, S., and Falorni, G.: An empirical geomorphology-based approach to the spatial prediction of soil thickness at catchment scale, Water Resour. Res., 46, W05508, doi:10.1029/2008WR007450, 2010. 

Dietrich, W. E., Reiss, R., Hsu, M.-L., and Montgomery, D. R.: A process-based model for colluvial soil depth and shallow landsliding using digital elevation data, Hydrol. Processes, 9, 383 – 400, doi:10.1002/hyp.3360090311, 1995.

D'Odorico, P. (2000), A possible bistable evolution of soil thickness, J. Geophys. Res., 105(B11), 25,927–25,935, doi:10.1029/2000JB900253.

Gessler, P. E., Moore, I. D., McKenzie, N. J., and Ryan, P. J.: Soil landscape modeling and spatial prediction of soil attributes, Int. J. Geogr. Inf. Syst., 9, 421– 432, doi:10.1080/02693799508902047, 1995.

Heimsath, A. M., Dietrich, W. E., Nishiizumi, K., Finkel, R. C.: The soil production function and landscape equilibrium, Nature, 388, 358– 361, doi:10.1038/41056, 1997.

Heimsath, A. M., Dietrich, W. E., Nishiizumi, K., Finkel, R. C.: Cosmogenic nuclides, topography, and the spatial variation of soil depth, Geomorphology, 27, 151– 172, doi:10.1016/S0169-555X(98)00095-6, 1999.

Lanni, C., McDonnell, J.J., and Rigon, R.: On the relative role of upslope and downslope topography for describing water flowpath and storage dynamics: a theoretical analysis, Hydrological Processes, 25(25), 2011.

Lanni, C., McDonnell, J., Hopp, L. and Rigon, R.: Simulated effect of soil depth and bedrock topography on near-surface hydrologic response and slope stability, Earth Surf. Process. Landforms, 2012, doi: 10.1002/esp.3267.

Lanni, C., Borga M., Tarolli P., Rigon R., Modelling shallow landslide susceptibility by means of a subsurface flow path connectivity index and estimates of soil depth spatial distribution , HESSD, 2012

Nicotina, L., Tarboton, D. G., Tesfa, T. K., Rinaldo, A.: Hydrologic controls on equilibrium soil depths, Water Resour. Res., 47, W04517, doi:10.1029/2010WR009538, 2011.

Liu, J., Chen, X., Lin, H., Liu, H., & Song, H. (2013). A simple geomorphic-based analytical model for predicting the spatial distribution of soil thickness in headwater hillslopes and catchments. Water Resources Research, n/a–n/a. doi:10.1002/2013WR013834

Pelletier, J. D. and Rasmussen, C.: Geomorphically based predictive mapping of soil thickness in upland watersheds, Water Resour. Res., 45, W09417, doi:10.1029/2008WR007319, 2009.

Roering, J.E., Kirchner, J.W., and Dietrich, W.E.: Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology, Water Resorces Research, vol. 35(3), 853–870, 1999.

Saco, P. M., Willgoose, G. R., and Hancock, G. R.: Spatial organization of soil depths using a landform evolution model, J. Geophys. Res., 111, F02016, doi:10.1029/2005JF000351, 2006.

Summerfield, M. A.: Global Geomorphology, 537 pp. Longman, New York, 1997

Tesfa, T. K., Tarboton, D. G., Chandler. D. G., and McNamara, J. P.: Modeling soil depth from topographic and land cover attributes, Water Resour. Res., 45, W10438, doi:10.1029/2008WR007474, 2009.

Tromp-van Meerveld, H.J., and McDonnell, J.J.: Threshold relations in subsurface stormflow: 2. The fill and spill hypothesis, Water Resources Research, 42, W02411. 2006.