中文摘要：

模式变量初始场误差和模式误差都是制约数值天气预报准确性提高的重要因素,传统数值预报和变分同化均忽略模式误差的影响。随着研究的深入,关于模式误差对数值预报影响的研究显得尤为重要。本文从非线性动力方程出发,推导出在模式存在参数误差和物理过程描绘缺失误差情况下的模式预报误差演变方程及短时间内误差平方均值近似表达式,并利用Liouville方程推导说明模式误差演变并不服从马尔科夫链分布,该结论对于任意模式系统均成立;利用Hopf分岔动力系统及Lorenz系统进行数值实验,结果表明,短期内模式预报误差均值随时间呈二次增长;随着时间增长,模式预报误差平方均值趋于稳定饱和值;参数误差和物理过程描绘缺失误差在一定意义下等价。这将为模式预报误差订正及弱约束变分同化研究提供重要理论指导和参考价值。

英文摘要：

Initial errors and model errors are the limiting factors to the improvement of the numerical weather prediction （NWP）. Traditional NWP and variational data assimilation （VDA） always ignore the influence of model errors, but it is important to investigate the dynamics of model errors for deep research. Based on the nonlinear dynamic model, the model error equation and the mean quadratic error expression for short time which are independent of the particular model are obtained on the assumption that there exist model parameters error and physical processes lacking error in the prediction model, and the non-Markovian character of the probability density of the model error is proved with Liouville equation. Taking the Hopf bifurcating system and Lorenz low-order atmospheric systems as examples, the results indicate that the mean quadratic error is bound to behave like t2 in a short time; the mean quadratic error tends to a stable value after a long time; the parameters error is equivalent to the physical processes lacking error under certain condition. It will afford valuable information for the research of forecasting error correction and weak constraint VDA from the theoretic aspect.