一种基于预报集合的降维资料同化方法的数值试验研究

A Numerical Study of an Ensemble-Based Reduced-Dimensional Data Assimilation Method

对Qiu和Chou(2006)提出的一种基于预报集合的降维资料同化方法(4DSVD)给出了可行的实施方案,利用中尺度模式MM5产生的模拟资料进行数值试验并将其与MM5/3DVAR的同化结果进行比较,分析了不同的观测误差和观测点密度对同化结果的影响。试验表明:(1)和3DVAR相比该方法能更好地从有观测的变量推断无观测的变量(从温度的观测推测风和比湿);(2)该方法可以相当有效地滤除观测噪音;(3)该方法具有更好的将观测信息扩展到资料空缺地区的能力。

One of the major difficulties in data assimilation is that the degree of freedom in NWP model far exceeds the number of observations collected at any single time, so the problem is usually underdetermined. In order to reduce the degree of underdetermined problem, Qiu and Chou （2006） suggested that the solution should be restricted to the attractor of atmosphere dynamic equations in the phase space. Based on this idea, an ensemble-based reduce＆ dimensional data assimilation （ERDA） method was developed. In it, one set of short-range forecasts （include the simulated observations） is obtained with the different perturbation initial conditions. The ensemble of atmospheric state is generated by sampling in a time window. Then the singular value decomposition （SVD） technique is used to construct the orthogonal basis vectors from the ensemble. The assimilation is performed in the space spanned by a few leading basis vectors. In this paper the effect of performing data assimilation using ERDA is examined via comparison with three-dimensional variational technique （3DVAR） in an idealized environment. The experiments are performed using the Pennsylvania State University-NCAR Mesoscale Model version 5 （MM5） with 99 × 99× 31 grid points and the simulated observations. A set of 24-hour forecasts with 20 members is used to generate 180 samples of the ensemble following the precept of selecting a snapshot every 3 hours. The 3DVAR scheme used in the experiments is one designed for the MM5 model. In order to ensure a fair comparison, ERDA and 3DVAR both use the same observational data at a single time level only. Therefore, the four-dimensional data assimilation method proposed by Qiu and Chou （2006） is reduced to a three-dimensional scheme. In all experiments, it is assumed that only temperature observations are available at sparsely selected grid points. The numerical experiments are performed with the different number of truncated basis vectors, observed density and error level in the observation. The results indicate that （i） the quality of the analysis by ERDA is better evidently than that by 3DVAR. Though 3DVAR can produce a little more precise analysis for the temperature than that by ERDA in most cases, ERDA is more effectual than that of 3DVAR to recover winds, pressure, and humidity these unobserved variables from observed temperature; （ii） in ERDA the observed information can be reasonably extrapolated to the data-void areas by the basis vectors, which represent the basic special configuration of the atmospheric state （increment） ; （iii） in ERDA, the analysis increment is restricted in a space spanned by a few singular vectors and these vectors are dynamically constrained fields produced by the model while random noises in observations do not fit any of the dynamic constraints. Therefore the errors in the observation have even less damage to the analysis. Nevertheless some useful information in the observation is also lost. So the intensity of analysis increment is light usually than actual one. This is a weakness of ERDA.