Bayesian Uncertainty Analysis Of Saturated Soil Water Flux Measured By Heat Pulse Method

Soil water flux is an important parameter for agricultural irrigation regulation and sustainable regional water resource utilization. The rapid and accurate measurement of the soil water flux promotes the agricultural and ecological water resource management from theoretical research to practical application. Heat Pulse Time Domain Reflectometry technique has been widely used in the fast determination of soil water flux recently. Since the Heat Pulse Time Domain Reflectometry method is not limited by soil type, non-destructive to soil samples and capable of unattended monitoring, it is with wide application prospect and great value. However, there is little research on the uncertainty analysis of the determination of soil water flux by the Heat Pulse Time Domain Reflectometry method. In this paper, the numerical case studies and column experiments were implemented to measure the saturated soil water flux via the Heat Pulse Time Domain Reflectometry method. The Bayesian theory-based Markov Chain Monte Carlo (MCMC) was used to quantify the uncertainties in estimating the heating intensity, probe space and water flux during the implementation of Heat Pulse Time Domain Reflectometry. The results were compared to those of existing methods. The main conclusions are as follows:(1) Bayesian calibration of the Heat Pulse Time Domain Reflectometry data showed that the MCMC algorithm could accurately identify the errors of the heating and the probe spacing caused by the operation,and gave a reasonable range of uncertainty.(2) The numerical simulation results showed that the MAP estimation value given by the Bayesian method was very close to the true water flux value, and the uncertainty range could cover the true value. We also examined the traditional heat pulse analysis methods,which include the maximum dimensionless temperature difference (MDTD), ratio method (Td / Tu) and upstream or downstream maximum temperature time method. The MDTD and the ratio method could only give single optimal estimations,and the difference between the estimated value and the real value was larger than that of the Bayesian method. The upstream or downstream maximum temperature time method could not correctly estimate the water flux.(3) Results of column experiments showed that the estimated saturated soil water fluxes given by the Bayesian method and traditional methods all deviated from the actual measured water fluxes due to the existence of preferential flow. The MAP estimation given by the Bayesian analysis had a good linear relationship with the average water flux at different flow rates (the determinant coefficient is above 0.96).However, the Bayesian method used in this paper only considered the measurement errors, which were assumed to strictly follow the Gaussian distribution, and the model errors were not included. Thus, the results provided by the Bayesian method were not obviously superior to those given by other methods in dealing with experimental data.(4) The match of the temperature data showed that the uncertainty ranges given by Bayesian analysis could cover the actual measured data, and the traditional methods could only give a single data matching result. Thus Bayesian analysis provides a tool for quantifying the uncertainty of heat pulse signals.