Collaborative Research: Scale-Recursive Estimation of Precipitation for Applications to Quantitative Precipitation Forecast (QPF) Verification and Multisensor Estimation

大气降水，无论是对流风暴还是准均匀分层云层，通常都是高度不均匀的，并且在几米到几百公里的尺度上表现出相当大的自然变率。各种传感器（如雨量计、雷达和卫星）用于监测降水率和总积累，并根据仪器分辨率和采样或分析策略提供不同尺度的直接和间接测量。基于物理的大气和固体地球的计算机模型依赖于这些观测数据进行初始化/同化以及预测验证。然而，由于降水的巨大尺度依赖性变率以及不同类型/来源的数据在尺度和分辨率上的差异，合并或比较不同尺度的观测值，或将模式输出与观测值进行比较是困难的。然而，降水定量估计和模式预报验证是大气和水文预报的基础。在合并或比较来自多个来源的信息时，为了解决与尺度可变性和尺度差异相关的问题，主要研究人员试图使用最近开发的尺度递归估计（SRE）框架。他们将利用SRE框架进行：(1)在与数值模式的尺度不同的一个或多个尺度上可获得观测资料时，进行定量降水预报（QPF）验证；（二）将不同尺度的观测和模式输出合并为一个场的推导产品或者分析；(3)通过比较不同尺度下的观测值和模型输出，估算出各场的背景误差协方差。要解决的问题需要在降水的统计多尺度分析、最优估计理论、雷达数据分析和解释、数据同化和数值天气预报建模方面结合专业知识。该合作小组包括两名统计水文学家和两名气象学家，他们在上述领域具有专业知识，并建立在先前成功合作的基础上，在单个对流风暴的尺度上预测和观测降水的时空结构分析。在之前的合作研究中，对预测和观测到的降水的时空结构进行了广泛的分析，重点是一个基本问题：风暴解决预测模型产生的降水场是否与观测值表现出相同的尺度不变结构？如果不是，原因是什么？典型的基于距离的确定性插值器（或平均算子）用于将数据从一个尺度转换为另一个尺度，即降尺度（上尺度）的缺点被记录下来，并且需要一种能够处理观测中与尺度相关的可变性和不确定性的严格方法。目前的跨学科建议建立在以前工作的基础上，并建议探索一个框架，在这个框架内，可变性和尺度依赖性问题可以适当地解决，以便进行QPF验证和多传感器降雨估计。

Atmospheric precipitation, whether in convective storms or quasi-uniformly stratified cloud layers, generally is highly inhomogeneous and exhibits considerable natural variability at scales ranging from a few meters to several hundreds of kilometers. A variety of sensors (e.g. rain gauges, radars, and satellites) are used to monitor precipitation rate and total accumulation and provide both direct and indirect measurements at different scales based upon instrument resolution and sampling or analysis strategies. Physically-based computer models, both of the atmosphere and solid earth, rely upon these observed data for initialization/assimilation as well as forecast validation. However, owing to the tremendous scale-dependent variability of precipitation and the discrepancies in scale and resolution among different types/sources of data, merging or comparing observations at different scales, or comparing model outputs to observations, is difficult. Yet, quantitative precipitation estimation (QPE) and model forecast verification are foundational aspects of both atmospheric and hydrologic prediction.In an effort to address issues associated with both scale variability and scale discrepancy in merging or comparing information from multiple sources, the Principal Investigators seek to use a recently-developed scale-recursive estimation (SRE) framework. They will utilize the SRE framework for (1) Quantitative Precipitation Forecast (QPF) verification when observations are available at one or more scales different than the scale of the numerical model; (2) derivation of products or analyses in situations where observations and model outputs at different scales are to be merged to produce a single field; and (3) estimation of background error covariances from fields produced via the comparison of observations and model outputs at different scales. The problems to be addressed require combined expertise in statistical multi-scale analysis of precipitation, optimal estimation theory, radar data analysis and interpretation, data assimilation, and numerical weather prediction modeling. This collaborative team involves two statistical hydrologists and two meteorologists having demonstrated expertise in the above areas, and builds upon a previous successful collaboration in the analysis of the spatio-temporal structure of forecasted and observed precipitation at the scale of individual convective storms. In previous collaborative research, an extensive analysis was made of the spatio-temporal structure of forecasted and observed precipitation with an emphasis on one fundamental question: Do storm-resolving forecast models produce precipitation fields that exhibit the same scale invariant structures as observations, and if not, why? The shortcomings of typical distance-based deterministic interpolators (or averaging operators) for converting data from one scale to another, i.e., downscaling (up-scaling), were documented, and the need for a rigorous methodology capable of handling scale-dependent variability and uncertainty in observations was demonstrated.The present interdisciplinary proposal builds upon this body of previous work and proposes to explore a framework within which issues of variability and scale-dependency can be properly addressed for the purpose of QPF verification and multi-sensor rainfall estimation.