两类滤波方法在估算土壤湿度方面的对比研究
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摘要
集合卡曼滤波(EnKF)利用蒙特卡罗方法统计背景场的误差协方差矩阵,解决了卡曼滤波在数据同化时需要对模型算子和观测算子线性化的缺点,易于使用,被广泛地应用到陆面数据同化中来估算土壤湿度廓线。
EnKF虽然可以用非线性模式产生集合背景预报场,但是最优分析场是建立在模式误差间关联为线性且误差为高斯分布的假设上,而实际土壤湿度方程为高度非线性。同时,土壤湿度又存在固定取值范围；过干和过湿都会造成集合样本偏斜。为了考查这些不利因素可能的影响,特引入非线性粒子滤波,来定量比较它们在估算土壤湿度廓线的速度和精度等方面异同。
首先,本论文引入了基于贝叶斯原理计算粒子的后验概率分布的粒子滤波中采样重要性重采样算法(Sampling importance Resampling, SIR),它不需模式误差为正态以及误差为线性关联的假设,并且可以提供误差分布的高阶矩信息；它在更新背景场样本时每个粒子的权重不同,而集合卡曼滤波粒子的权重都是相同的。其次,为了评估土壤湿度样本在土壤过干或过湿时出现的偏斜性甚至双模态,考虑到西北黄土高原陆面过程的重要性,本论文选取黄土土壤的逐渐变干过程来进行观测模拟同化试验。最后,选用2003年土壤湿度试验(SMEX03)的站点观测资料进行实际大气观测驱动下同化试验。通过上述实验可以得出：
1、估算土壤湿度的EnKF同化方案虽然不满足集合卡曼滤波最优解需要的条件,但它却能快速地估算出土壤湿度廓线,加之所需粒子样本较少,计算量也较小；而SIR虽然无此限制,但只有在大样本的条件下才能达到相同的土壤湿度估算精度,因此无论从速度和计算量来看都比EnKF逊色。
2、两者样本统计分布随同化过程也完全不同,EnKF的样本集合的边缘概率密度分布始终保持为一个单峰分布,而SIR方法的样本粒子却经历了从一个峰值到两个再到一个分布的变化过程。
3、EnKF同化方案在改进土壤湿度廓线估计的同时也使计算的地表感热和潜热通量更接近真值。
基于上述结论,EnKF基本满足陆面数据同化系统对同化算法的要求,可用于同化表层土壤湿度观测(或微波量温)来估算土壤湿度廓线。
The ensemble Kalman filter(EnKF) calculates background error covariance matrix using Monte-Carlo method and is able to resolve the nonlinearity and discontinuity exist within model operator and observation operator.At the same,it is an easy to use, flexible, and efficient data assimilation algorithm widely used in Soil moisture Assimilation System.
Although EnKF can use non-linear models to gain the background forecast field, but it based on the normality approximation of model error and observational error which is the assumption of Gaussian distribution. However, the soil moisture equation is highly nonlinear, and soil moisture is a fixed range,The sample can be highly skewed toward the wet or dry ends. In order to examine the possible impact of these negative factors,This paper gives the results from the EnKF are compared with those obtained from a sequential importance resampling (SIR) particle filter that is one of nonlinear filters.
First, this thesis introduces the Sampling importance Resampling, It based on Bayesian posterior probability distribution of particles in particle filter.It needn't the normality approximation of model error and observational error which is the assumption of Gaussian distribution,and it can provide information on higher order moments.When it updates the background field of a sample weight of each particle different but the EnKF weight is the same. Secondly, in order to evaluate the soil moisture in the soil samples had dry or too wet even when the skew of dual-mode, taking into account the northwest Loess Plateau importance of land surface processes. in this thesis, dry loess soil in the process of gradually come to be observed Simulation of assimilation test. Finally, the use of soil moisture experiment in 2003 (SMEX03) the actual site observation data assimilation of atmospheric observations driven test. the conclusion are:
1、Although The EnKF estimates of soil moisture assimilation scheme does not meet the collection needs of Kalman filtering conditions, but it can quickly estimate the soil moisture profile, coupled with the required small particle samples, computation is also small; and SIR Although no such restrictions, but only under the conditions of a large sample to achieve the same estimation accuracy of soil moisture, so in terms of speed and computation of view less than EnKF.
2、Statistical distribution of the two samples are quite different along the process, the EnKF edge of the sample set of probability density distribution always remains a single peak distribution, but the SIR method has experienced a sample of particles from one peak to two and then to a distribution of changes process.
3、EnKF assimilation scheme to improve estimates of soil moisture profiles and also to calculate the surface sensible heat and latent heat flux is closer to EnKF observaty value.
Based on the result, EnKF can basically meet the land surface data assimilation system to assimilate the requirements of algorithms can be used for assimilation of surface soil moisture observations (or microwave or temperature) to estimate the soil moisture profile.
EnKF虽然可以用非线性模式产生集合背景预报场,但是最优分析场是建立在模式误差间关联为线性且误差为高斯分布的假设上,而实际土壤湿度方程为高度非线性。同时,土壤湿度又存在固定取值范围；过干和过湿都会造成集合样本偏斜。为了考查这些不利因素可能的影响,特引入非线性粒子滤波,来定量比较它们在估算土壤湿度廓线的速度和精度等方面异同。
首先,本论文引入了基于贝叶斯原理计算粒子的后验概率分布的粒子滤波中采样重要性重采样算法(Sampling importance Resampling, SIR),它不需模式误差为正态以及误差为线性关联的假设,并且可以提供误差分布的高阶矩信息；它在更新背景场样本时每个粒子的权重不同,而集合卡曼滤波粒子的权重都是相同的。其次,为了评估土壤湿度样本在土壤过干或过湿时出现的偏斜性甚至双模态,考虑到西北黄土高原陆面过程的重要性,本论文选取黄土土壤的逐渐变干过程来进行观测模拟同化试验。最后,选用2003年土壤湿度试验(SMEX03)的站点观测资料进行实际大气观测驱动下同化试验。通过上述实验可以得出：
1、估算土壤湿度的EnKF同化方案虽然不满足集合卡曼滤波最优解需要的条件,但它却能快速地估算出土壤湿度廓线,加之所需粒子样本较少,计算量也较小；而SIR虽然无此限制,但只有在大样本的条件下才能达到相同的土壤湿度估算精度,因此无论从速度和计算量来看都比EnKF逊色。
2、两者样本统计分布随同化过程也完全不同,EnKF的样本集合的边缘概率密度分布始终保持为一个单峰分布,而SIR方法的样本粒子却经历了从一个峰值到两个再到一个分布的变化过程。
3、EnKF同化方案在改进土壤湿度廓线估计的同时也使计算的地表感热和潜热通量更接近真值。
基于上述结论,EnKF基本满足陆面数据同化系统对同化算法的要求,可用于同化表层土壤湿度观测(或微波量温)来估算土壤湿度廓线。
The ensemble Kalman filter(EnKF) calculates background error covariance matrix using Monte-Carlo method and is able to resolve the nonlinearity and discontinuity exist within model operator and observation operator.At the same,it is an easy to use, flexible, and efficient data assimilation algorithm widely used in Soil moisture Assimilation System.
Although EnKF can use non-linear models to gain the background forecast field, but it based on the normality approximation of model error and observational error which is the assumption of Gaussian distribution. However, the soil moisture equation is highly nonlinear, and soil moisture is a fixed range,The sample can be highly skewed toward the wet or dry ends. In order to examine the possible impact of these negative factors,This paper gives the results from the EnKF are compared with those obtained from a sequential importance resampling (SIR) particle filter that is one of nonlinear filters.
First, this thesis introduces the Sampling importance Resampling, It based on Bayesian posterior probability distribution of particles in particle filter.It needn't the normality approximation of model error and observational error which is the assumption of Gaussian distribution,and it can provide information on higher order moments.When it updates the background field of a sample weight of each particle different but the EnKF weight is the same. Secondly, in order to evaluate the soil moisture in the soil samples had dry or too wet even when the skew of dual-mode, taking into account the northwest Loess Plateau importance of land surface processes. in this thesis, dry loess soil in the process of gradually come to be observed Simulation of assimilation test. Finally, the use of soil moisture experiment in 2003 (SMEX03) the actual site observation data assimilation of atmospheric observations driven test. the conclusion are:
1、Although The EnKF estimates of soil moisture assimilation scheme does not meet the collection needs of Kalman filtering conditions, but it can quickly estimate the soil moisture profile, coupled with the required small particle samples, computation is also small; and SIR Although no such restrictions, but only under the conditions of a large sample to achieve the same estimation accuracy of soil moisture, so in terms of speed and computation of view less than EnKF.
2、Statistical distribution of the two samples are quite different along the process, the EnKF edge of the sample set of probability density distribution always remains a single peak distribution, but the SIR method has experienced a sample of particles from one peak to two and then to a distribution of changes process.
3、EnKF assimilation scheme to improve estimates of soil moisture profiles and also to calculate the surface sensible heat and latent heat flux is closer to EnKF observaty value.
Based on the result, EnKF can basically meet the land surface data assimilation system to assimilate the requirements of algorithms can be used for assimilation of surface soil moisture observations (or microwave or temperature) to estimate the soil moisture profile.
引文
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[1]黄洪峰.土壤-植物-大气相互作用原理及模拟研究,北京：气象出版社,1997.
[2]孙淑芬.陆面过程的物理、生化机理和参数化模型,北京：气象出版社,2005：27-71.
[3]张述文,李得勤,邱崇践.三类陆面模式模拟土壤湿度廓线的对比研究,高原气象,2009：28(5),987-996.
[4]Walker J P, Willgoose G R, Kalma J D.One-dimensional soil moisture profile retrieval by assimilation of near-surface observations:a comparison of retrieval algorithms.Advances in Water Resources,2001,24 (6):631-650.
[5]Entekhabi D, Nakamura H, Njoku E G. Solving the Inverse Problem for Soil Moisture and Temperature Profiles by Sequential Assimilation of Multifrequency Remotely Sensed
Observations. IEEE Transactions on Geoscience and Remote Sensing,1994,32:438-448.
[6]张述文.土壤含水量和地表热通量估算方法研究.兰州大学,2004：80-95.
[7]王夏晖,王益权,Kuznetsov M S.黄土高原几种主要土壤的物理性质研究.水土保持学报,2000,4：99-103.
[8]张文煜,袁九毅。大气探测原理与方法。北京：气象出版社,2007：112-124.
[1]郑婧,谢正辉,戴永久,等.陆面过程模型CoLM与区域气候模式RegCM3的耦合及初步评估.大气科学,2009,33(4)：737-750.
[2]罗斯琼,吕世华,张宇,等.CoLM模式对青藏高原中部BJ站陆面过程的数值模拟.高原气象,2008,27(2)：125-133.
[3]王澄海,师锐,左洪超,等.青藏高原西部冻融期陆面过程的模拟分析.高原气象,2008,27(2)：186-194.