Estimating Seasonally Frozen Ground Depth From Historical Climate Data and Site Measurements Using a Bayesian Model

We develop a Bayesian model to predict the maximum thickness of seasonally frozen ground (MTSFG) using historical air temperature and precipitation observations. We use the Stefan solution and meteorological data from 11 stations to estimate the MTSFG changes from 1961 to 2016 in the Yellow River source region of northwestern China. We employ an antecedent precipitation index model to estimate changes in the liquid soil water content. The marginal posterior probability distributions of the antecedent precipitation index parameters are estimated using Markov chain Monte Carlo sampling methods. We compare the results of our stochastic method with those obtained from the traditional deterministic method and find that they are consistent in general. The stochastic approach is effective for estimating the historical changes in the frozen ground depth (root‐mean‐square errors = 0.13–0.35 m), and it provides more information on model uncertainty regarding soil moisture variations. Additionally, simulation shows that the MTSFG has decreased by 0.31 cm per year over the last 56 years on the northeastern Qinghai‐Tibet Plateau. This decrease in frost depth accelerated in the 1990s and 2000s. Considering the lack of data on seasonally frozen soil monitoring, the Bayesian method provides a pragmatic approach to statistically model frozen ground changes using available meteorological data. Key Points A Bayesian model is developed to estimate seasonally frozen ground depth using air temperature and precipitation observations Uncertainty in soil water parameters explains 1.4% to 21.5% of the total uncertainty in seasonally frozen ground depth estimation Climate warming has caused a significant decrease in frost depth on the Tibetan Plateau, which accelerated in the 1990s and 2000s