Simultaneously assimilating multivariate data sets into the two-source evapotranspiration model by Bayesian approach: application to spring maize in an arid region of northwestern China

Abstract

Abstract. Based on direct measurements of half-hourly canopy evapotranspiration (ET; W m−2) using the eddy covariance (EC) system and daily soil evaporation (E; mm day−1) using microlysimeters over a crop ecosystem in arid northwestern China from 27 May to 14 September in 2013, a Bayesian method was used to simultaneously parameterize the soil surface and canopy resistances in the Shuttleworth–Wallace (S–W) model. Four of the six parameters showed relatively larger uncertainty reductions (> 50%), and their posterior distributions became approximately symmetric with distinctive modes. There was a moderately good agreement between measured and simulated values of half-hourly ET and daily E with a linear regression being y = 0.84 x + 0.18 (R2 = 0.83) and y = 1.01 x + 0.01 (R2 = 0.82), respectively. The causes of underestimations of ET by the S–W model was possibly attributed to the microscale advection, which can contribute an added energy in the form of downward sensible heat fluxes to the ET process. Therefore, the advection process should be taken into account in simulating ET in heterogeneous land surfaces. Also, underestimations were observed on or shortly after rainy days, which may be due to direct evaporation of liquid water intercepted in the canopy. Thus, the canopy interception model should be coupled to the S–W model in the long-term ET simulation.

Parameter sensitivity analysis and optimization for a satellite‐based evapotranspiration model across multiple sites using Moderate Resolution Imaging Spectroradiometer and flux data

“…We constructed a Bayesian inference framework to optimize the key parameters using the flux data sets simultaneously. But, an important issue in optimization is equifinality, where the same result might be caused by different parameter combinations [ Franks et al ., ; Zhu et al ., ]. Engeland et al .…”

“…According to the Bayes theorem, the posterior probability density function (PDF) of model parameters is proportional to their prior PDF and the likelihood function and can be calculated as where θ are the parameter sets; O are the observed data sets; p ( θ | O ) is the posterior probability distribution; p ( θ ) is the prior probability distribution of parameter θ , which is chosen as uniform distributions with specified prior ranges (Table ); and p ( O | θ ) is the likelihood function, which reflects the influence of the observation data sets on parameter identification. The likelihood function can be expressed as [ Zhu et al ., ] where T is the total length of observation; O ( t ) and S ( t ) are observed and simulated values at time t ( t = 1, 2, …, T ), respectively; and σ is the standard deviation of the model error that is assumed to be unchanged during the observation time [ Braswell et al ., ], and σ can be expressed as …”

A hierarchical Bayesian approach for multi‐site optimization of a satellite‐based evapotranspiration model

“…That is, very different combination of the parameter values (“trade‐off” between the parameters) can make the model generate similar total ET predictions, but with great uncertainties in the model's ET partitioning. This phenomenon is well known as equifinality or parameter identifiability (Beven & Freer, ; Zhu et al, , ). Thus, we cannot ensure the model's ET partitioning based on a single set of optimized parameters to be correct, even though the simulated total ET were in good agreement with measurements.…”

“…Understanding the influence of model parameters on model response is significant elements in the development of robust regional and global ET products (Bastola, Murphy, & Sweeney, ; Brigode, Oudin, & Perrin, ; McCabe et al, ; Zhang et al, ; Zhu et al, ). Previous studies have shown that model parameters may vary by PFTs and species because of the genetic or local environmental variation (Mu, Zhao, & Running, ; Wullschleger et al, ).…”

“…First, the PT‐JPL model is highly complex with some ecophysiological parameters that may vary with the environmental conditions, plant functional types (PFTs), and other factors (Zhang et al, ). The widely used method to estimate parameters is to calibrate the mechanistic process model independently for each site through simple Bayesian (SB) analysis (i.e., Samanta, Mackay, Clayton, Kruger, & Ewers, ; Zhu et al, , ; Zhang et al, ). However, the SB method aggregated all uncertainties into a single term (residual error), which makes it be sensitive to measurement noise (Clark, ).…”