Bayesian performance evaluation of evapotranspiration models for an arid region in northwestern China

Abstract. Evapotranspiration (ET) is a major component of the land surface process involved in energy fluxes and balance, especially in the hydrological cycle of agricultural ecosystems. While many models have been developed to estimate ET, there has been no agreement on which model has the best performance. In this study, we evaluate four widely used ET models (i.e., the Shuttleworth Wallace (SW) model, Penman-Monteith (PM) model, Priestley-Taylor and Flint-Childs (PT-FC) model, and Advection-Aridity (AA) model) by using half-hourly ET observations obtained at a spring maize field in an arid region. The model evaluation is based on Bayesian model comparison and ranking using the Bayesian model evidence (BME), which balances between goodness-of-fit to data and model complexity. The BME-based model ranking (from the best to the worst) is SW, PM, PT-FC, and AA. The residuals between observations and corresponding model simulations are also analyzed, and the same model ranking is also obstained by using residual-based statistics, i.e., the coefficient of determination (R2), index of agreement (IA), root mean square error (RMSE) and model efficiency (EF). The PM and SW models overestimate ET, whereas the PT-FC and AA models underestimate ET in the study period. The four models also underestimate ET during the periods of partial crop cover. Especially during the late maturity stage, the PT-FC and AA models consistently produce an underestimation, and provide the worst simulated ET. As a result, at the half-hourly time scale, the SW model is the best model and recommend as the first choice for evaluating ET of spring maize in arid desert oasis areas.

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Bayesian performance evaluation of evapotranspiration models based on eddy covariance systems in an arid region

Hydrology and Earth System Sciences ◽

10.5194/hess-23-2877-2019 ◽

2019 ◽

Vol 23 (7) ◽

pp. 2877-2895 ◽

Cited By ~ 4

Author(s):

Guoxiao Wei ◽

Xiaoying Zhang ◽

Ming Ye ◽

Ning Yue ◽

Fei Kan

Keyword(s):

Extinction Coefficient ◽

Land Surface ◽

Arid Region ◽

Hydrological Cycle ◽

Model Performance ◽

Integration Algorithm ◽

Energy Imbalance ◽

Physical Mechanisms ◽

Available Energy ◽

Spring Maize

Abstract. Evapotranspiration (ET) is a major component of the land surface process involved in energy fluxes and energy balance, especially in the hydrological cycle of agricultural ecosystems. While many models have been developed as powerful tools to simulate ET, there is no agreement on which model best describes the loss of water to the atmosphere. This study focuses on two aspects, evaluating the performance of four widely used ET models and identifying parameters, and the physical mechanisms that have significant impacts on the model performance. The four tested models are the Shuttleworth–Wallace (SW) model, Penman–Monteith (PM) model, Priestley–Taylor and Flint–Childs (PT–FC) model, and advection–aridity (AA) model. By incorporating the mathematically rigorous thermodynamic integration algorithm, the Bayesian model evidence (BME) approach is adopted to select the optimal model with half-hourly ET observations obtained at a spring maize field in an arid region. Our results reveal that the SW model has the best performance, and the extinction coefficient is not merely partitioning the total available energy into the canopy and surface but also including the energy imbalance correction. The extinction coefficient is well constrained in the SW model and poorly constrained in the PM model but not considered in PT–FC and AA models. This is one of the main reasons that the SW model outperforms the other models. Meanwhile, the good fitting of SW model to observations can counterbalance its higher complexity. In addition, the detailed analysis of the discrepancies between observations and model simulations during the crop growth season indicate that explicit treatment of energy imbalance and energy interaction will be the primary way of further improving ET model performance.

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Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection

Water ◽

10.3390/w11081579 ◽

2019 ◽

Vol 11 (8) ◽

pp. 1579 ◽

Cited By ~ 3

Author(s):

Elshall ◽

Keyword(s):

Model Selection ◽

Bayesian Model ◽

Goodness Of Fit ◽

Transport Model ◽

Model Complexity ◽

Accurate Estimation ◽

Observation Data ◽

Sampling Errors ◽

Groundwater Transport ◽

Model Evidence

Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods.

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Detecting episodes of star formation using Bayesian model selection

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab138 ◽

2021 ◽

Vol 502 (3) ◽

pp. 3993-4008

Author(s):

Andrew J Lawler ◽

Viviana Acquaviva

Keyword(s):

Star Formation ◽

Bayesian Model ◽

Model Comparison ◽

Density Ratio ◽

Model Complexity ◽

Spectral Energy ◽

Analytic Approximation ◽

Nested Models ◽

Bayesian Model Comparison ◽

Correct Model

ABSTRACT Bayesian model comparison frameworks can be used when fitting models to data in order to infer the appropriate model complexity in a data-driven manner. We aim to use them to detect the correct number of major episodes of star formation from the analysis of the spectral energy distributions (SEDs) of galaxies, modelled after 3D-HST galaxies at z ∼ 1. Starting from the published stellar population properties of these galaxies, we use kernel density estimates to build multivariate input parameter distributions to obtain realistic simulations. We create simulated sets of spectra of varying degrees of complexity (identified by the number of parameters), and derive SED fitting results and pieces of evidence for pairs of nested models, including the correct model as well as more simplistic ones, using the bagpipes codebase with nested sampling algorithm multinest. We then ask the question: is it true – as expected in Bayesian model comparison frameworks – that the correct model has larger evidence? Our results indicate that the ratio of pieces of evidence (the Bayes factor) is able to identify the correct underlying model in the vast majority of cases. The quality of the results improves primarily as a function of the total S/N in the SED. We also compare the Bayes factors obtained using the evidence to those obtained via the Savage–Dickey density ratio (SDDR), an analytic approximation that can be calculated using samples from regular Markov Chain Monte Carlo methods. We show that the SDDR ratio can satisfactorily replace a full evidence calculation provided that the sampling density is sufficient.

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Bayesian model comparison

Bayesian Cognitive Modeling ◽

10.1017/cbo9781139087759.009 ◽

2014 ◽

pp. 101-117

Author(s):

Michael D. Lee ◽

Eric-Jan Wagenmakers

Keyword(s):

Bayesian Model ◽

Model Comparison ◽

Bayesian Model Comparison

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A Bayesian model comparison approach to test the specificity of visual integration impairment in schizophrenia or psychosis

Psychiatry Research ◽

10.1016/j.psychres.2018.04.061 ◽

2018 ◽

Vol 265 ◽

pp. 271-278 ◽

Cited By ~ 4

Author(s):

Tyler B. Grove ◽

Beier Yao ◽

Savanna A. Mueller ◽

Merranda McLaughlin ◽

Vicki L. Ellingrod ◽

...

Keyword(s):

Bayesian Model ◽

Model Comparison ◽

Visual Integration ◽

Bayesian Model Comparison ◽

Comparison Approach

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Bayesian model comparison for compartmental models with applications in positron emission tomography

Journal of Applied Statistics ◽

10.1080/02664763.2013.772569 ◽

2013 ◽

Vol 40 (5) ◽

pp. 993-1016 ◽

Cited By ~ 8

Author(s):

Yan Zhou ◽

John A.D. Aston ◽

Adam M. Johansen

Keyword(s):

Positron Emission Tomography ◽

Bayesian Model ◽

Model Comparison ◽

Compartmental Models ◽

Emission Tomography ◽

Bayesian Model Comparison ◽

Positron Emission

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Methods for Default and Robust Bayesian Model Comparison: The Fractional Bayes Factor Approach

International Statistical Review ◽

10.2307/1403706 ◽

1999 ◽

Vol 67 (3) ◽

pp. 267 ◽

Cited By ~ 8

Author(s):

Fulvio de Santis ◽

Fulvio Spezzaferri

Keyword(s):

Bayesian Model ◽

Model Comparison ◽

Bayes Factor ◽

Bayesian Model Comparison ◽

Fractional Bayes Factor

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Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

10.31219/osf.io/edh7j ◽

2021 ◽

Author(s):

John K. Kruschke

Keyword(s):

Posterior Distribution ◽

Bayesian Model ◽

Model Comparison ◽

Bayes Factor ◽

Bayes Factors ◽

Prior Model ◽

Bayesian Hypothesis Testing ◽

Bayesian Model Comparison ◽

Posterior Model Probability ◽

Model Probability

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

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