Predicting soil thickness on soil mantled hillslopes

Abstract

Soil thickness is a fundamental variable in many earth science disciplines due to its critical role in many hydrological and ecological processes, but it is difficult to predict. Here we show a strong linear relationship (r² = 0.87, RMSE = 0.19 m) between soil thickness and hillslope curvature across both convergent and divergent parts of the landscape at a field site in Idaho. We find similar linear relationships across diverse landscapes (n = 6) with the slopes of these relationships varying as a function of the standard deviation in catchment curvatures. This soil thickness-curvature approach is significantly more efficient and just as accurate as kriging-based methods, but requires only high-resolution elevation data and as few as one soil profile. Efficiently attained, spatially continuous soil thickness datasets enable improved models for soil carbon, hydrology, weathering, and landscape evolution.

Fig. 1

Curvature and thickness of the mobile regolith plot and predictive map. a The thickness of the mobile regolith (TMR) varies as a strong linear function of curvature (C) in Johnston Draw. Black dots represent randomly selected build dataset (70% of sites). Gray dots represent test set to validate the model. The white dot is a location that was excluded owing to proximity to both a rock outcrop and a stream channel. Uncertainty is reported as the standard error by the Method of Moments. b Predicted TMR map for the granitic portion of Johnston Draw derived from the TMR-curvature function using a 3 m Light Detection and Ranging (LiDAR)-derived digital elevation model. Darker shades indicate larger TMR (2.75 + m) and lighter shades indicate smaller TMR (0 m) including those areas excluded as rock outcrops or streams. Hatched areas indicate non-granitic portions of the watershed that were not modeled

Fig. 2

Cross-site evaluation. a Cross-site evaluation of six catchments in which the thickness of the mobile regolith (TMR)-curvature (C) function is evaluated using a 5-m digital elevation model (DEM). b Depicts catchment curvature distributions based on a 5 m DEM centered on 0 m⁻¹. c Cross-site comparison of the slope of the TMR-curvature function (and associated standard error) with the local standard deviation in catchment curvature (σ_c). Nunnock River (light green squares) dataset was not included in plots b or c due to the lack of high resolution Light Detection and Ranging (LiDAR) data; curvature estimates for Nunnock River in a were derived from reported local observations. Note, the curvature distributions are derived from all cells within the catchment’s DEM

Fig. 3

Model validation. Validation of the thickness of the mobile regolith (TMR)-curvature (C) approach at Babbington Creek and Reynolds Mountain, Idaho (a) and Gordon Gulch, Colorado, USA (b). Solid white, gray, and black lines represent best-fit predicted vs. observed TMR values based on curvature calculated from a Light Detection and Ranging (LiDAR)-derived digital elevation model (DEM) and a single soil pit for Reynolds Mountain (c), Babbington Creek (d), and Gordon Gulch (e), respectively. Large dashed black lines represents the 1:1 predicted versus observed line. The best-fit slopes were not significantly different from one for Babbington Creek (|t| = 0.74 < critical t_0.05,5 = 2.571) and Reynolds Mountain (|t| = 0.01 < critical t_0.05,7 = 2.365), indicating unbiased models, whereas the slope was significantly lower than one for Gordon (p < 0.001, |t| = 3.64 < critical t_0.05,162 = 1.974), indicating over-prediction with higher TMR than observed. Small white, gray, and black dotted lines represent the 95% prediction intervals (PI)