基于不适定反问题求解的降水图像降尺度研究

doi:10.11867/j.issn.1001-8166.2017.10.1102

地球科学进展 ›› 2017, Vol. 32 ›› Issue (10): 1102 -1111. doi: 10.11867/j.issn.1001-8166.2017.10.1102

王根 ^1, ²(

), 盛绍学 ¹, 黄勇 ³, 吴蓉 ⁴, 刘惠兰 ¹

1.安徽省气象信息中心安徽省大气科学与卫星遥感重点实验室, 安徽合肥 230031
2.中国气象局沈阳大气环境研究所, 辽宁沈阳 110000
3.安徽省气象科学研究所,安徽合肥 230031
4.安徽省气候中心,安徽合肥 230031

收稿日期:2017-04-05 修回日期:2017-08-02 出版日期:2017-12-20
基金资助:
安徽省自然科学基金项目“广义变分同化AIRS水汽通道亮温及在安徽强对流天气预报中的应用研究”(编号:1708085QD89);淮河流域气象开放研究基金项目“基于地面和卫星观测反演的江淮流域降水资料融合算法研究”(编号:HRM201407)资助.

Study on Precipitation Image Downscaling Based on the Method of Ill-posed Problems Solving

Gen Wang ^1, ²( ), Shaoxue Sheng ¹, Yong Huang ³, Rong Wu ⁴, Huilan Liu ¹

1.Anhui Meteorological Information Centre Anhui Key Laboratody of Atmospheric Science and Satellite Remote Sensing, Hefei 230031, China
2.The Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110000, China
3.Anhui Institute of Meteorological, Hefei 230031, China
4.Anhui Climate Center, Hefei 230031, China

Received:2017-04-05 Revised:2017-08-02 Online:2017-12-20 Published:2017-10-20
About author:
First author:Wang Gen(1983-),male,Taizhou City, Jiangsu Province, Engineer. Research areas include satellite data assimilation, numerical simulation of GRAPES and multi-source data fusion.E-mail:203wanggen@163.com
Supported by:
Project supported by the Natural Science Foundation of Anhui Province“Generalised variational assimilation of AIRS water vapor channel brightness temperature and the application study in severe convective weather in Anhui Province”(No.1708085QD89);The Open Research Fund of Huai River Basin in Meteorological “Study of precipitation data fusion algorithm in Jianghuai Basin based on the ground and satellite observations”(No.HRM201407).

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遥感降水产品和环流模型预报降水降尺度研究一直是水文和气象学的热点。使用多源降水融合资料进行降水图像降尺度研究,其本质是提高低分辨率观测或模拟降水场分辨率,并适当增加其细节或高频特性。基于降水自相似结构性质,将不适定数学反问题求解法用于降尺度。在求解降尺度不适定反问题时,不同风暴环境的小规模组织内降水特征往往会重复出现这一性质,通过训练得到高、低分辨率的降水场,形成相应的 “完备字典”,用于正交匹配追踪贪婪法重构高分辨率降尺度的降水场。执行时,首先基于专家场(Fields of Experts,FoEs)模型进行缺测资料插补;其次采用文中方法进行降水图像降尺度应用研究。基于传统“保真度”度量指标和空间结构相似性度量法对该方法得到的试验结果进行评估,结果表明该方法可行。

关键词: 降尺度, 不适定反问题, 正交匹配追踪法, 自相似, 降水融合产品

Downscaling of remote sensing precipitation products and the forecasting of circulation model are always the intense interests in hydrology and meteorology. The essence of downscaling is primarily to enhance resolution of observation or simulated rainfall field, and to appropriately increase its details or high frequency characteristics. Precipitation, as the main driving factors of the earth’s hydrologic cycle, not only affects the moisture and heat condition of a certain river basin, but also affects the global water and heat circulation. Based on the properties of rainfall self-similarity structure, the mathematically ill-posed precipitation problem solving method was used in low resolution downscaling precipitation for high resolution reconstruction. When solving the downscaling ill-posed problem, the greedy method of orthogonal matching pursuit was introduced so as to get the best high-resolution estimation in an optimal sense. It is hard to imagine that we might be able to find very similar (in mathematical norms) precipitation patterns over relatively large storm-scales. However, finding similar features over sufficiently small sub-storm scales seems more feasible. Based on the characteristics that small scale organized precipitation features tend to recur across different storm environments, the precipitation of both high and low resolution was obtained by training, which could be used to reconstruct the desired high-resolution precipitation field. Multi-source merged precipitation products were used in this experiment. Given the consideration of incompleteness of merged precipitation dataset, it was firstly interpolated based on the method of Fields of Experts (FoEs), which could solve the problem that common interpolation method could hardly work on the interpolation for dataset where consecutive missing data exists. Secondly, ideal experiments of precipitation products downscaling were carried out, where smooth coupling sampling and resampling operator were adopted respectively. Assessment based on the metrics of fidelity and spatial structural similarity demonstrates that the method used in this paper is feasible.

Key words: Downscaling, Ill-posed problems, Orthogonal Matching Pursuit, Self-similarity, Merged precipitation products.

中图分类号:

P468

图1 FoEs模型插补效果分析

Fig.1 Interpolation effect analysis of FoEs model

图2 原始真实场(上图),基于平滑耦合重采样降尺度前(中图)和降尺度后(下图)降水分布

Fig.2 The original true field (above), the distribution of precipitation before downscaling based on smooth coupling resampling (middle) and after downscaling (below)

图3 基于重采样降尺度前(上图)和降尺度后(下图)降水分布

Fig.3 The distribution of precipitation before downscaling based on resampling (above) and after downscaling (below)

表1 降尺度场(结果)和高分辨率场(真值)误差统计比较分析

Table 1 Error statistics obtained by comparing the downscaling filed (result) with the high-resolution filed(true)

度量方法	退化结构算子:平滑+重采样			退化结构算子:重采样
度量方法	s=4		s=8		s=4	s=8
MSE	0.72	0.70		0.62	0.69
MAE	0.93	0.81		0.90	0.83
PSNR	36.54	33.59		34.91	31.48
SSIM	0.96	0.94		0.95	0.93

表1 降尺度场(结果)和高分辨率场(真值)误差统计比较分析

Table 1 Error statistics obtained by comparing the downscaling filed (result) with the high-resolution filed(true)

度量方法	退化结构算子:平滑+重采样			退化结构算子:重采样
度量方法	s=4		s=8		s=4	s=8
MSE	0.72	0.70		0.62	0.69
MAE	0.93	0.81		0.90	0.83
PSNR	36.54	33.59		34.91	31.48
SSIM	0.96	0.94		0.95	0.93

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