A Nonlinear Grid Transformation Method for Extrapolating and Predicting the Convective Echo of Weather Radar
Abstract
:1. Introduction
2. Nonlinear Grid Transformation Method
2.1. Matrix for Grid Transformation
2.2. Estimation of the Nonlinear Grid Transformation Matrix
- (1)
- Quadratic coordinates and distance derivatives are involved in the operation of Equation (11), which makes it possible for the value of the coefficient to span many orders of magnitude. Therefore, all the variables involved in the actual calculation should be at least double-precision floating-point numbers.
- (2)
- An underestimation of image change will occur if points of ΔQ2−1 = 0 are considered when preparing Equation (11) because when only points of ΔQ2−1 = 0 are used, the final obtained M6×6 will be a unit matrix, that is, the image is unchanged.
- (3)
- Although the time complexity for solving Equation (11) appears to increase quadratically with the number of grids, the size of the original image does not become a problem because the method is not based on detailed texture and rather requires a certain degree of coarse grid spacing. A current personal computer can complete the calculation in 1–10 s when the historical sequence length is approximately 10, and the number of grid points is less than 100 × 100.
- (4)
- After obtaining the transformation matrix and before extrapolating using Equation (14), the image and coordinates are replaceable. For example, the filtered coarse-resolution image can be replaced by the original fine-resolution image. However, the unit of coordinates cannot be replaced because the transformation matrix is based on the coordinates used. For example, the coordinates cannot be changed from rectangular coordinate distance to latitude and longitude once the transformation matrix is obtained or from the latitude and longitude of a region to another different region.
2.3. Practical Steps for Extrapolation Prediction
- (1)
- Prepare a set of time-continuous historical echo images prior to the start time of the prediction. Perform resolution reduction and two-dimensional Gaussian filtering if necessary.
- (2)
- For each pair of adjacent images, each Equation (11) from a grid in which ΔQ2−1 ≠ 0 is selected continuously to form a system of linear equations.
- (3)
- Solve the system of linear equations in the last step to obtain the transformation matrix M2×6. Obtain [X2, Y2] according to Equation (14), and subtract the origin orthogonal grid [X1, Y1] to obtain grid transformation vector fields u and v. Here, the u and v are generated one-time.
- (4)
- If a resolution reduction is applied in the first step, u and v are linearly interpolated to the original resolution.
- (5)
- Based on the original image at the start time of the prediction, u and v are used to conduct backward interpolation, and the extrapolation image at N steps is obtained.
3. Weather Radar Echo Prediction Experiments
3.1. Experimental Setting
3.1.1. Case Setting and Statistics
3.1.2. The Method for Comparison
3.2. Ideal Cases
3.3. Real Case 1: A Convective Line with Shape Evolution
3.4. Real Case 2: A Convective Event with Convective Line Formation
3.5. Real Case 3: A Mesoscale Convective Complex and Comparison with Previous Deep Learning Results
4. Conclusions
- (1)
- In the ideal experiments for simple targets, NGT can achieve better prediction results than OF when there are changes in the value and path of the image target.
- (2)
- For cases with a convective line, NGT is superior to OF, where the CSI for 40 dBZ of the echo prediction at 60 min is approximately 0.2 higher.
- (3)
- For the case of MCC, NGT is better than OF and a deep learning method for 20 and 30 dBZ, while the deep learning method produces the best skill score for 40 dBZ. However, the good performance of the deep learning method may be due to the overestimation of the stronger echo.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Threshold (dBZ) | POD | FAR | CSI | |||
---|---|---|---|---|---|---|
NGT | OF | NGT | OF | NGT | OF | |
20 | 0.84 | 0.75 | 0.23 | 0.26 | 0.68 | 0.60 |
30 | 0.41 | 0.29 | 0.38 | 0.44 | 0.33 | 0.23 |
40 | 0.42 | 0.08 | 0.61 | 0.90 | 0.25 | 0.04 |
Threshold (dBZ) | POD | FAR | CSI | |||
---|---|---|---|---|---|---|
NGT | OF | NGT | OF | NGT | OF | |
20 | 0.61 | 0.47 | 0.15 | 0.08 | 0.55 | 0.45 |
30 | 0.47 | 0.34 | 0.27 | 0.25 | 0.40 | 0.31 |
40 | 0.33 | 0.08 | 0.55 | 0.83 | 0.24 | 0.06 |
Threshold (dBZ) | POD | FAR | CSI | ||||||
---|---|---|---|---|---|---|---|---|---|
NGT | OF | Liang 2021 * | NGT | OF | Liang 2021 * | NGT | OF | Liang 2021 * | |
20 | 0.75 | 0.77 | 0.84 | 0.13 | 0.18 | 0.33 | 0.67 | 0.66 | 0.54 |
30 | 0.61 | 0.63 | 0.67 | 0.27 | 0.32 | 0.49 | 0.49 | 0.49 | 0.39 |
40 | 0.28 | 0.31 | 0.51 | 0.62 | 0.62 | 0.57 | 0.19 | 0.21 | 0.30 |
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Sun, Y.; Xiao, H.; Tian, Y.; Yang, H. A Nonlinear Grid Transformation Method for Extrapolating and Predicting the Convective Echo of Weather Radar. Remote Sens. 2023, 15, 1406. https://doi.org/10.3390/rs15051406
Sun Y, Xiao H, Tian Y, Yang H. A Nonlinear Grid Transformation Method for Extrapolating and Predicting the Convective Echo of Weather Radar. Remote Sensing. 2023; 15(5):1406. https://doi.org/10.3390/rs15051406
Chicago/Turabian StyleSun, Yue, Hui Xiao, Ye Tian, and Huiling Yang. 2023. "A Nonlinear Grid Transformation Method for Extrapolating and Predicting the Convective Echo of Weather Radar" Remote Sensing 15, no. 5: 1406. https://doi.org/10.3390/rs15051406