A Bayesian analysis of sensible heat flux estimation: Quantifying uncertainty in meteorological forcing to improve model prediction.

The influence of uncertainty in land surface temperature, air temperature, and wind speed on the estimation of sensible heat flux is analyzed using a Bayesian inference technique applied to the Surface Energy Balance System (SEBS) model. The Bayesian approach allows for an explicit quantification of the uncertainties in input variables: a source of error generally ignored in surface heat flux estimation. An application using field measurements from the Soil Moisture Experiment 2002 is presented. The spatial variability of selected input meteorological variables in a multitower site is used to formulate the prior estimates for the sampling uncertainties, and the likelihood function is formulated assuming Gaussian errors in the SEBS model. Land surface temperature, air temperature, and wind speed were estimated by sampling their posterior distribution using a Markov chain Monte Carlo algorithm. Results verify that Bayesian-inferred air temperature and wind speed were generally consistent with those observed at the towers, suggesting that local observations of these variables were spatially representative. Uncertainties in the land surface temperature appear to have the strongest effect on the estimated sensible heat flux, with Bayesian-inferred values differing by up to ±5°C from the observed data. These differences suggest that the footprint of the in situ measured land surface temperature is not representative of the larger-scale variability. As such, these measurements should be used with caution in the calculation of surface heat fluxes and highlight the importance of capturing the spatial variability in the land surface temperature: particularly, for remote sensing retrieval algorithms that use this variable for flux estimation.

Figure 13: Observed and Bayesian-inferred values of meteorological variables for a (a, c, e, and g) soybean tower (WC162) and (b, d, f, and h) corn tower (WC152). The gray lines in the top three rows represent the observed values for the other 11 flux towers. (bottom) The observed, deterministic calculated, and stochastic generated sensible heat fluxes are shown. The x axis for all plots indicate hour of the day (local time) for day-of-year 173.