气象学报  2019, Vol. 77 Issue (1): 142-153 PDF
http://dx.doi.org/10.11676/qxxb2019.001

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#### 文章信息

KOU Leilei, WANG Zhenhui, SHEN Feifei, CHU Zhigang. 2019.

High resolution interpolation for weather radar data based on Gaussian-scale mixtures model in wavelet domain

Acta Meteorologica Sinica, 77(1): 142-153.
http://dx.doi.org/10.11676/qxxb2019.001

### 文章历史

2018-03-30 收稿
2018-06-21 改回

High resolution interpolation for weather radar data based on Gaussian-scale mixtures model in wavelet domain
KOU Leilei, WANG Zhenhui, SHEN Feifei, CHU Zhigang
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters/Key Laboratory of Meteorological Disaster and Ministry of Education/Joint International Research Laboratory of Climate and Environment Change, Nanjing University of Information Science and Technology, Nanjing 210044, China
Abstract: An interpolation algorithm for radar reflectivity data is proposed using the Gaussian-scale mixtures (GSM) in the wavelet domain as the prior model, which can accurately describe the statistical characteristics of radar precipitation reflectivity data. The objective is to improve the radar image resolution while effectively reproduce those important spatial statistical characteristics of the precipitation echoes like local extreme intensity values and small scale variation gradient. Firstly, the statistical characteristics of radar precipitation reflectivity data in the wavelet domain are analyzed and the reflectivity data are modeled with the GSM. Then, the wavelet coefficients of the radar reflectivity data are matched with the GSM in the wavelet domain, and the wavelet coefficients at smaller scale are estimated by Bayesian theory. The high resolution radar reflectivity image can be recovered from inverse wavelet transform of the estimated coefficients at smaller scale. The case study shows that the proposed algorithm can get the high frequency coefficients of the high resolution images through the parameters estimations of low resolution images and the model used considers the statistical characteristics of precipitation reflectivity data; the interpolation result can capture the non-Gaussian singularities and local correlated features of the precipitation echoes, and the local details of the high resolution radar reflectivity images can be well reproduced.
Key words: Radar reflectivity data     Wavelet coefficients     Gaussian-scale mixtures (GSM) model     Interpolation
1 引言

2 雷达回波强度数据小波域GSM建模 2.1 雷达回波强度数据小波域统计特性

 图 1 2008年5月27日04时59分(世界时)南京降水个例回波强度(a), 分解得到的水平向(b)、垂直向(c)和对角向(d)子带小波系数及相应的小波系数概率统计分布(e—g) Figure 1 Radar reflectivity image of the precipitation case in Nanjing at 04:59 UTC 27 May 2008 (a), wavelet coefficients for horizontal (b), vertical (c) and diagonal (d) sub-bands of the reflectivity image in (a), and the corresponding probability statistical distributions (e-g)

 图 2 2011年7月25日19时47分10秒(世界时)南京降水个例回波(a)及其水平子带的概率统计分布(b) Figure 2 Radar reflectivity image of another precipitation case in Nanjing at 19:47:10 UTC 25 July 2011 (a) and the probability statistical distribution for its horizontal sub-band wavelet coefficients (b)

 图 3 水平向(a)、垂直向(b)、对角向(c)小波系数5×5邻域协方差矩阵 Figure 3 Covariance matrices of neighborhoods of size 5×5 for horizontal (a), vertical (b) and diagonal (c) sub-bands wavelet coefficients

 图 4 水平向(a)、垂直向(b)、对角向(c)小波系数尺度间二维联合直方图 Figure 4 The 2D inter-scale joint histograms of the horizontal (a), vertical (b) and diagonal (c) sub-bands wavelet coefficients
2.2 雷达降水回波强度数据小波域GSM模型

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 图 5 水平子带小波系数一阶矩(a)和二阶矩(b)随尺度的变化关系 Figure 5 The scaling law of the first (a) and second (b) moments of the wavelet coefficients at horizontal sub-band

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3 雷达降水回波强度数据小波域GSM插值

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4 个例试验

 图 6 (a) MAP法估计得到的个例1的水平子带小波系数GSM模型中的z值, (b)估计得到的更精细尺度水平子带小波系数, (c)原始低分辨率图像分解得到的小波系数 Figure 6 (a) The estimated parameter z in GSM model for the horizontal sub-band wavelet coefficients of Case 1 with the MAP algorithm, (b) the estimated smaller scale horizontal sub-band wavelet coefficients, (c) the horizontal sub-band wavelet coefficients for original low resolution reflectivity image

 图 7 个例1插值前后结果对比(a.原始高分辨率图像, b. 4倍降分辨率图像, c.双线性插值后的图像, d.基于小波域GSM模型插值后的图像) Figure 7 Comparison of radar reflectivity images for Case 1 (a. original high resolution image, b. upscaled image by a factor of 4, c. image with bilinear interpolation, d. interpolated image with the GSM model in wavelet domain)

 整体像素(>0 dBz) 强回波(>40 dBz) GRin与GRori GRGSM与GRori GRin与GRori GRGSM与GRori 平均差(dB) 0.8370 0.2167 平均差(dB) 1.6025 0.0525 均方根误差(dB) 3.4352 3.7012 均方根误差(dB) 2.4877 2.2118 熵差 0.4494 0.0273 像素个数 1928与2899 2819与2899
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 图 8 个例2插值前后结果对比(a.原始高分辨率图像, b. 4倍降分辨率图像, c.双线性插值后的图像, d.基于小波域GSM模型插值后的图像) Figure 8 Comparison of radar reflectivity images for Case 2 (a. original high resolution image, b. upscaled image by a factor of 4, c. image with bilinear interpolation, d. interpolated image with GSM model in wavelet domain)

 整体像素(>0 dBz) 强回波(>40 dBz) GRin与GRori GRGSM与GRori GRin与GRori GRGSM与GRori 平均差(dB) 1.5012 0.5289 平均差(dB) 1.9227 -0.0710 均方根误差(dB) 4.6582 4.3849 均方根误差(dB) 3.2955 2.8979 熵差 0.3940 0.0145 像素个数 1418与1912 1864与1912
5 结论