Towards improved depth to bedrock modeling beneath hillslopes
Guilherme José Cunha Gomes1; Jasper Alexander Vrugt2; Eurípedes do Amaral Vargas Jr.1
1 Pontifícia Universidade Católica do Rio de Janeiro; 2 University of California, Irvine
Resumo
Knowledge of the spatial heterogeneity of depth to bedrock (DTB) in a watershed is of crucial importance in many different fields of study, including hydromechanics, geotechnical engineering, and watershed hydrology. Direct measurement of the bedrock depth is rather time consuming, and much effort and human commitment would be required to characterize adequately bedrock depth variations at spatial scales of hillslopes and watersheds. Thus, a model that can be used to simulate high-resolution spatial maps of the depth to bedrock is of great importance. This paper builds on the assumption of the bottom-up control on fresh-bedrock theory of Rempe and Dietrich (2014) and includes a few modifications to the analytic formulation. Our model assumes that regolith thickness depends on the interplay between erosion, which removes unconsolidated material from the ground surface, and weathering, which promotes rock fragmentation in the soil-bedrock interface. The DTB model is strongly influenced by rock mass properties, such as porosity, permeability and rate of incision channel. The model also describes quantitatively the bedrock profile from the upslope zone to the channel, including a significant loss of regolith at steep slopes. Bayesian analysis was used to synthesize the output of the DTB model with spatially distributed field observations. This approach uses Markov chain Monte Carlo simulation (MCMC) simulation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm (Vrugt, 2008; 2009) to search efficiently the model parameter space in pursuit of so called posterior samples that honor best the observed data. The quality of fit is measured by a likelihood function which summarizes in a single value the distance between the observed and simulated bedrock depths. The prior distribution summarizes all our knowledge about the model parameters before the field data is collected. This distribution should honor soft data, geologic observations, field expertise and literature findings. Marginal distributions an
Palavras-chave: Depth to bedrock; Bayesian Inference; Parameter uncertainty; Markov chain Monte Carlo simulation