Accurate numerical weather forecasting is of great importance. Due to inadequate observations, our limited understanding of the physical processes of the atmosphere, and the chaotic nature of atmospheric flow, uncertainties always exist in modern numerical weather prediction (NWP). Recent developments in ensemble forecasting and ensemble-based data assimilation have proved that there are promising ways to beat the forecast uncertainties in NWP. This paper gives a brief overview of fundamental problems and recent progress associated with ensemble forecasting and ensemble-based data assimilation. The usefulness of these methods in improving high-impact weather forecasting is also discussed. 1. Introduction Numerical weather prediction (NWP) is an initial value problem: it forecasts the atmospheric state by integrating a numerical model with given initial conditions. Commonly, two fundamental factors account for an accurate numerical weather forecast: 1) the present state of the atmosphere must be characterized as accurately as possible; 2) the intrinsic laws, according to which the subsequent states develop out of the preceding ones, must be known [1]. These so-called laws are composed of a set of partial differential equations, including the laws of momentum, mass, and energy conservations. Since the first successful NWP in early 1950s by Charney et al. [2], much progress has been made in enhancing the skill of NWP. These include efforts in improving initial conditions through advances in observing systems and the development of atmospheric data assimilation techniques. Many studies also devoted to improve numerical modeling with advanced numerical methods, better representation of dynamics processes of the atmosphere, and improved physical parameterization schemes [3–5]. Today, NWP has become a major forecasting tool in many operational centers around the world. However, due to inadequate observations, our limited understanding of the physical processes of the atmosphere, and the chaotic nature of the atmospheric flow, uncertainties always exist in both initial conditions and numerical models. Thus, reducing forecast errors caused by theses uncertainties remains a large area of research and operational implementation. Recent developments have proved that ensemble forecasting and ensemble-based data assimilation are promising ways to beat the forecast uncertainties in NWP. The objective of this paper is to give a brief overview of the fundamental problems and recent progress associated with ensemble forecasting and ensemble-based data assimilation. The
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