基于MCMC方法的WOFOST模型参数标定与不确定性分析

    Markov Chain Monte Carlo based WOFOST model parameters calibration and uncertainty analysis

    • 摘要: 为探究作物生长模型参数的自动标定技术及其不确定性分析方法,该研究以郑州农业气象试验站为试验点,利用融入了snooker更新(snooker update)的DE-MC(differential evolution Markov chain,差分进化马尔科夫链)方法实现对WOFOST(world food studies)作物生长模型的参数标定和不确定性定量评价。snooker更新增加了DE-MC算法中候选样本的多样性,从而实现利用更少的并行链对多维参数空间进行有效采样,较适合于WOFOST模型参数众多的特性。结果表明:相比于模型默认值,采用MCMC(Markov chain Monte Carlo,马尔科夫链-蒙特卡洛)标定后的参数,叶面积指数(leaf area index,LAI)模拟精度可提高51.40%~53.07%,产量模拟精度提高8.25%~8.88%。标定参数中,SPAN、SLATB070、SLATB040、AMAXTB130和SLATB00的后验分布可近似为高斯分布,其中SPAN的不确定性最低。带入后验参数集合进行模型,LAI在三叶期至返青期之间以及拔节期至抽穗期之间模拟的不确定性较大;产量模拟的不确定性随时间不断增大,至乳熟期前后达到稳定。该方法能够实现对多参数复杂作物生长模型的参数标定和不确定性分析,对作物模型参数估计及提高模拟精度具有重要作用。

       

      Abstract: Abstract: It is generally accepted that the model parameters calibration is an essential step before application. However, the traditional methods of obtaining a set of "optional parameters" based on a certain number of observations, fail to represent the uncertainties and get reliable estimates. To overcome this problem, we introduced the DE-MC (differential evolution Markov chain) algorithm with snooker update into the WOFOST (world food studies) model parameters calibration. The main objectives were: 1) to calibrate the WOFOST model by DE-MC algorithm with snooker update; 2) to evaluate the uncertainty of the model parameters after calibration; 3) to evaluate the uncertainty of the model outputs after calibration. Observational data including LAI (leaf area index) in different growth stages and the final yield of winter wheat in Zhengzhou Agrometeorological Experimental Station, were used to calibrate WOFOST model at potential mode with this algorithm. The crop parameters related to accumulated temperature were calculated directly from the crop phenological development date and near-surface temperature. The remaining crop parameters were analyzed by Sobol method. Taking Sobol global sensitivity index greater than 0.05 as the threshold for sensitive parameters, 14 parameters were then selected. The calibrated parameters were defined as the uniform distribution over their value interval. The likelihood function represented the mismatch of the model output with the measured observations, by which the parameters' priori distribution converted to posterior distribution. The likelihood function for yield was set as a Gaussian distribution with the observational data as expected value and 10% of the observational data as standard deviation. Similarly, the likelihood function for LAI was set as a multidimensional Gaussian distribution with observational LAI as the expected vector and a diagonal matrix as the covariance matrix. At last, we found that: 1) Compared with the simulation results with model default parameters, the LAI simulation accuracy could be increased by 51.40%-53.07% after the parameter calibration, and the yield simulation accuracy is improved by 8.25%-8.88%; 2) The posterior distribution of life span of leaves growing at 35 Celsius (SPAN), specific leaf area at development stage of 0.7 (SLATB070), specific leaf area at development stage of 0.4 (SLATB040), maximum CO2 assimilation rate at development stage of 1.3 (AMAXTB130), and specific leaf area at development stage of 0 (SLATB00) could be approximated as a Gaussian distribution with SPAN having the minimum uncertainty; 3) Running model with the posterior parameters set, the uncertainty of simulated LAI from the three-leaf stage to the re-greening stage and from the jointing stage to the heading stage is larger; the uncertainty of the simulated yield increases with time before the milky ripe stage, stayed unchanged until maturity. It was concluded that DE-MC with snooker update was an effective algorithm for parameters estimation of WOFOST model, the calibration had the potential to reduce the uncertainty of the model parameters and the calibrated model was able to model the observational data with some degree of skill. The calibration data used in this study was the observation data from the agrometeorological site. Although the crop varieties were consistent, the inter-annual cultivation management measures were not strictly controlled (eg.: seeding density), and the accuracy of the calibration results might be affected. Subsequent experiments can be carried out in more areas using experimental data with quantitative control to further verify the effectiveness of this algorithm.

       

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