Short-Term Dynamic Radar Quantitative Precipitation Estimation Based on Wavelet Transform and Support Vector Machine

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  • Corresponding author: Changjiang ZHANG, zcj74922@zjnu.edu.cn
  • Funds:

    Supported by the National Natural Science Foundation of China (41575046), Project of Commonweal Technique and Application Research of Zhejiang Province of China (2016C33010), and Project of Shanghai Meteorological Center of China (SCMO-ZF- 2017011)

  • doi: 10.1007/s13351-020-9036-7

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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Short-Term Dynamic Radar Quantitative Precipitation Estimation Based on Wavelet Transform and Support Vector Machine

    Corresponding author: Changjiang ZHANG, zcj74922@zjnu.edu.cn
  • 1. College of Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004
  • 2. Shanghai Meteorological Center, Shanghai 200030
Funds: Supported by the National Natural Science Foundation of China (41575046), Project of Commonweal Technique and Application Research of Zhejiang Province of China (2016C33010), and Project of Shanghai Meteorological Center of China (SCMO-ZF- 2017011)

Abstract: Currently, Doppler weather radar in China is generally used for quantitative precipitation estimation (QPE) based on the ZR relationship. However, the estimation error for mixed precipitation is very large. In order to improve the accuracy of radar QPE, we propose a dynamic radar QPE algorithm with a 6-min interval that uses the reflectivity data of Doppler radar Z9002 in the Shanghai Qingpu District and the precipitation data at automatic weather stations (AWSs) in East China. Considering the time dependence and abrupt changes of precipitation, the data during the previous 30-min period were selected as the training data. To reduce the complexity of radar QPE, we transformed the weather data into the wavelet domain by means of the stationary wavelet transform (SWT) in order to extract high and low-frequency reflectivity and precipitation information. Using the wavelet coefficients, we constructed a support vector machine (SVM) at all scales to estimate the wavelet coefficient of precipitation. Ultimately, via inverse wavelet transformation, we obtained the estimated rainfall. By comparing the results of the proposed method (SWT-SVM) with those of Z = 300 × R1.4, linear regression (LR), and SVM, we determined that the root mean square error (RMSE) of the SWT-SVM method was 0.54 mm per 6 min and the average Threat Score (TS) could exceed 40% with the exception of the downpour category, thus remaining at a high level. Generally speaking, the SWT-SVM method can effectively improve the accuracy of radar QPE and provide an auxiliary reference for actual meteorological operational forecasting.

1.   Introduction
  • Highly accurate rainfall estimations are required by both policymakers and researchers when making decisions. Currently, quantitative precipitation estimation (QPE) methods are mainly divided into two categories: one utilizing the Z–R relationship, and the other known as the radar–rain gauge merging (R–G) method that combines rain gauge and radar to estimate precipitation.

    The reflectivity Z of Doppler weather radar is closely related to the concurrent rainfall intensity R. Traditional radar QPE algorithms used Z as the main source for rainfall field retrieval and the feedback-derived radar QPE algorithm (Gou et al., 2019). From 1941 to 1946, Ryde (1946) used 10- and 5-cm weather radar echoes in an attempt to predict various weather processes. Researchers such as Jones (1956) and Fujiwara (1965) discovered the droplet distribution and Z–R relationship for different precipitation types. The Z–R relationship, however, cannot be rectified in a timely fashion when there are errors in either the radar measurements or rainfall data. Moreover, radar detection height, the super-refractive index, wind, and other factors inevitably affect the measurement of precipitation and reflectivity.

    The conventional method, for converting radar reflectivity into rainfall rates primarily relies on the Z–R relationship. It is difficult, however, to satisfy the strict ideal conditions required for this physical model. In order to reduce the error and avoid the limitations of the Z–R relationship, Brandes (1975) used a calibration factor derived from the ratio of radar estimations and rain gauge measurements to correct the systematic errors of radar estimations. Since then, several studies have shared similar ideas (Seo, 1998; Chumchean et al., 2006; Thorndahl et al., 2014). Ramli et al. (2011) utilized the optimization method in order to obtain the regional Z–R relationship, while Gou et al. (2018) developed two radar QPE schemes using observations from 11 Doppler weather radars and 3,264 rain gauges on the eastern Tibetan Plateau. The consequences of these Z–R relationship methods are not suitable for all regions. Statistical approaches, such as linear regression (LR; Jung et al., 2008; Kusiak et al., 2013; Kou et al., 2018) and frequency analysis (Eldardiry et al., 2015), can also be employed to estimate precipitation, although these methods have low estimation accuracy. In recent years, data-driven methods for radar QPE have become feasible, such as artificial neural networks (ANNs; Xiao and Chandrasekar, 1997; Kusiak et al., 2013; Kou et al., 2018), nonparametric methods (Ayat et al., 2018), support vector machines (SVMs; Sehad et al., 2017), and random forests (RFs; Li et al., 2011; Kuang et al., 2016). In contrast to the Z–R relationship, these methods attempt to capture the relationship between radar reflectivity and rain gauge measurements. Taking into consideration the entire vertical distribution of reflectivity, Yang et al. (2017) estimated and calculated the 1-h rainfall in Hangzhou, China using the terrain-based weighted random forest method. Moreover, a new model (Tang et al., 2018) has been proposed to further improve the accuracy of precipitation estimation by introducing the geographical and temporal attention continuous conditional random field (GAT–CCRF). They constructed a 6-min interval QPE model using reflectivity (6-min) and rain gauge (1-min) data. Most of the above methods adopted single-polarization radar for QPE. In recent years, dual-polarization applications in QPE have made great progress and achieved good results (Cifelli et al., 2011; Chen et al., 2017). In this study, the reflectivity of single-polarization radar in combination with gauge rainfall from automatic weather stations (AWSs) were used to model and verify the performance of the proposed method.

    Many techniques for estimating precipitation based on radar data have been proposed. However, neither the Z–R relationship of fixed parameters nor a simple neural network can avoid the problem of large errors in radar QPE. In addition, the estimated interval of precipitation is usually 1 h or longer. Compared with these models, 6-min precipitation estimation is more drastic and more vulnerable to external factors such as noise, especially during light rain (Habib et al., 2001; Villarini et al., 2008; Chen and Chandrasekar, 2015a). In the case of heavy rain cases, however, these factors should not matter much (Chen and Chandrasekar, 2015b). In order to address the existing problems in radar QPE and prediction algorithms, based on the June 2017 radar and precipitation data from East China, this study presents a dynamic quantitative precipitation estimation method with a 6-min interval based on the stationary wavelet transform (SWT) and SVM. We refer to the proposed method as the SWT-SVM. In order to verify the performance of the proposed method, we then conducted a sufficient 1-yr evaluation and compared it with Z = 300 × R1.4 (Crosson et al., 1996), LR, and SVM. The results confirm the superiority of our proposal.

2.   Data
  • All of the data used in this study were obtained from the Shanghai Meteorological Center, including the Z9002 Doppler radar reflectivity and AWS data from January to December 2017 (UTC + 8) in Shanghai. In this region, most of the precipitation is concentrated in June–August (flood season). The resolution of gauge rainfall is 0.1 mm per 5 min, and the maximum error is ± 3%. As shown in Table 1, the Doppler weather radar Z9002 was located in Qingpu, Shanghai (31º4'30''N, 120º57'28''E), and had a scanning radial distance of 230 km. The radar completed 9 elevations of scanning in 6 min: 0.5°, 1.45°, 2.4°, 3.35°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°, and its volume scanning mode was VCP21. Therefore, the radar files were updated about every 6 min. In this study, the maximum reflectivity of the radar at 0.5°, 1.45°, and 2.4°, also known as the combined reflectivity, was used as input. Correspondingly, there were about 74 AWSs within the coverage of this radar, as seen in Fig. 1. Data from the AWSs were calculated every 5 min. In order to match precipitation with reflectivity, we averaged the precipitation data over 5 min, and obtained the precipitation data per minute. Finally, we labeled all of the reflectivity and precipitation data based on the time. We read the radar reflectivity file, then located the corresponding precipitation data, and gathered the corresponding gauge rainfall over 6 min (assuming the radar data file generation time is T, the corresponding precipitation filename is T + 1 min, T + 2 min,..., T + 6 min). We then matched the reflectivity with precipitation according to longitude and latitude. Precipitation and reflectivity data were also labeled based on time. There were approximately 10 gauge rainfall and reflectivity files per hour, at intervals of approximately 6 min. The data preprocessing is illustrated in Fig. 2.

    CharacteristicValue
    Position31º4'30''N, 120º57'28''E
    Height (above ground level)39 m
    Polarization typeSingle-polarization
    Wavelength10 cm (S-band)
    Maximum range460 km
    Useful range230 km
    Bin resolution1 km
    Scan interval (VCP21)6 min
    No. of elevations (VCP21)9 (0.5° –19.5°)

    Table 1.  Technical characteristics of Doppler radar Z9002

    Figure 1.  Locations of the AWSs in the radar coverage.

    Figure 2.  Data matching process.

    In this study, we focused on rainfall estimation. The snowfall processes will be addressed in future work. The start of each rainfall process was chosen such that there was significant rainfall over a spatially coherent area. The end of each rainfall process was determined to be the time at which there was no longer any significant rainfall occurring in the area. A total of 16 rainfall events were analyzed, with 6-min radar–gauge data from each event consisting of no fewer than 10,000 sets.

3.   Proposed method
  • In this study, the precipitation estimation model consisted of 4 steps. First, the historical times of the dynamically selected training samples were determined, and the SWT was used to obtain the wavelet coefficients at different scales and different frequency channels. Second, the wavelet coefficients at different scales and different frequency channels were input into corresponding SVM models as training data. Third, the wavelet coefficients of the estimated reflectivity were input into the corresponding SVM model, thus obtaining the wavelet coefficients of the estimated rainfall at the corresponding scales. Finally, the estimated rainfall was obtained using the inverse wavelet transform. The overall process is shown in Fig. 3.

    Figure 3.  Structure of the SWT-SVM method.

  • Given that rainfall prediction has a stronger correlation with the meteorological conditions of the previous period of the time series, even though the historical data further removed from the prediction time also contain some future rainfall information, we believe that this information is also included in the vicinity of the time series (He et al., 2017). Therefore, We utilized the data of the previous period to train the dynamic precipitation model, instead of using all the data to build a static model in this study. In order to determine the optimal training data period for the dynamic precipitation model, this study examined the estimated results by the proposed method for different training data during the past 6, 12, …, 120 min. The processing method is shown in Fig. 4.

    Figure 4.  Rainfall estimation processing with training data during the past 6 × S min.

  • Wavelet analysis is a mathematical model that transforms an original signal (especially with a time domain) into a different domain for analysis and processing. Using the characteristics of high- and low-frequency separation of wavelet transform, the high-frequency components can be filtered without losing the important information components of the original signal. Modified components are then reconstructed by using inverse wavelet transformation in order to improve the quality of the signal. There exist various choices for wavelet analysis such as continuous wavelet transform (CWT), discrete wavelet transform (DWT), wavelet packet transform (WPT), dual-tree complex wavelet transform (DT-CWT), and SWT. Many studies have proven that SWT and DT-CWT are more suitable for signal denoising than CWT, DWT or WPT (Mortazavi and Shahrtash, 2008; Jamaluddin et al., 2015; Luo and Yang, 2018). Furthermore, compared with DWT, SWT can detect faint signal changes, which are not well implemented by DT-CWT. Additionally, the choice of wavelet basis function also has a pronounced influence on the calculation results. Some representative wavelet basis functions include: Haar, Daubechies, Symlets, Meyer, and others. Figure 5 shows their function curves in the time domain. Compared to the other three wavelet functions, the Haar wavelet is the simplest and is also the most sensitive to abrupt signals (Fig. 5a) (Quek et al., 2001). Most importantly, its transform is sufficient for radar reflectivity. For these reasons, we selected Haar as our analysis wavelet. Based on the continuity and mutagenicity of the Z and R series, this study chose the SWT with the Haar wavelet to extract their features.

    Figure 5.  Four wavelet basis functions: (a) Haar, (b) Daubechies, (c) Symlets, and (d) Morlet.

    If the reflectivity and rainfall data in the past 1 h are as follows:

    The estimated reflectivity and rainfall data are

    Since the input signal length of the SWT must be an integer power of 2 (set n), the number of wavelet transform layers is not more than n. The latest $\left({{2^{\rm{n}}} \leqslant n1 < {2^{n + 1}}} \right)$ data are taken as training samples. That is

    The low-frequency and high-frequency coefficients of (Z1, R1) at n scales can be obtained by applying the SWT with the Haar wavelet:

    where Za and Ra respectively represent the low-frequency information of Z and R; Zd and Rd represent high-frequency information of Z and R, respectively.

    In order to ensure wavelet transform consistency between the estimated and sample data, the estimated reflectivity and the latest reflectivity are arranged in an array of 2n. If q = n1 + n2 − 2n + 1, the array is as follows:

    In the same way, the reflectivity can be changed by SWT, yielding:

    The 2n~n2 columns in expressions (3) and (4) are then estimated for reflectivity wavelet coefficients at high and low frequencies:

  • Cortes and Vapnik (1995) defined the ε-insensitive function on the basis of the original SVM, and proposed the ε-SVM. Compared with the SVM, the ε-SVM adds a penalty term ε to prevent overfitting. The ε-SVM can solve the non-linear problem very well, especially in the case of small samples, which have low computational complexity and a fast convergence speed. This study utilized data within the previous 1 h for training, an approach that is very suitable for modeling with the ε-SVM.

    It is known that N-independent identically distributed sample datasets satisfy $\left\{ {\left({{{x}_1},{{y}_1}} \right),\left({{{x}_2},{{y}_2}} \right), \cdots,\left({{{x}_{N}},{{y}_{N}}} \right)} \right\} \subseteq$$ {{\bf R}^D} \times {\bf R} $, where RD is the D-dimensional real space. On the basis of defining the ε-insensitive loss function, the ε-SVM looks for the objective function,

    where ω, xRD, and bR. Minimizing the predicted expected risk R(ω),

    In the above formula, ε is the insensitive loss function, and ${\left\| {\rm{\omega }} \right\|^2}$ is the structural risk, which represents the complexity of the regression model. Rεemp is the empirical risk, which represents the error of the regression model, and C is the penalty factor, which is used to balance the structural error and empirical error, and to control the robustness of the regression model. Minimizing R(ω) is equivalent to determining the following objective function,

    where ξi and ξi* are the upper and lower limits of the slack variable, respectively. After introducing the Lagrange coefficient, the objective function is converted to its dual form:

    The variable ω is as follows:

    The regression objective function is as follows:

    In order to avoid complex high-dimensional calculations, kernel functions are introduced into the formula. Therefore, the final form of the regression function is as follows:

    In this study, we utilized the n-scale wavelet coefficients of historical hourly gauge rainfall and reflectivity as samples to train 2n SVM models. Then, the wavelet coefficients of the reflectivity to be estimated [expressions (5) and (6)] were input into the SVM model of the corresponding scale and channel, providing us with the rainfall wavelet coefficients of the corresponding scale and channel. The estimated rainfall was then obtained using inverse wavelet transformation.

  • The root mean square error (RMSE), correlation coefficient (CC), mean bias (MB), and mean absolute error (MAE) are commonly used in QPE to reflect the total error of estimation results. In addition, the Threat Score (TS) is usually used to test the quality of precipitation estimation results. All of these parameters indicate the overall error of the estimation results both quantitatively and qualitatively.

    The formulas for calculating the RMSE, CC, MB, and MAE are as follows:

    where Rg is the gauge rainfall and ${\bar R_{\rm{g}}}$ indicates the average of Rg. Analogously, Re is the estimated rainfall and ${\bar R_{\rm{e}}}$ indicates the average of Re. The RMSE describes the overall precision of the precipitation estimation. The CC demonstrates the linearity between the estimated results and the gauge results. A value of MB > 0 indicates that the estimated result is greater than that obtained by the rain gauge, i.e., there is an overestimation. Conversely, an MB value < 0 indicates underestimation, for which the smaller the MB, the greater the degree of underestimation. The MAE, reflecting the estimation error to some extent, can avoid the mutual cancellation of positive and negative errors.

    In meteorology, the TS is commonly used to determine the quality of estimated rainfall. Generally speaking, precipitation is divided into five categories: light rain, moderate rain, heavy rain, rainstorm, and downpour, allowing the TS for precipitation of all intensities to be determined. As shown in Table 2, this study classified 6-min rainfall into 5 different grades according to the suggestions from the Shanghai Meteorological Center, since there are no classification criteria for 6-min rainfall totals. The number of hits, false alarms, and misses could then be calculated, which were recorded as NA, NB, and NC, respectively. The TSs are given by

    CategoryDrizzleLight/moderate rainHeavy rainRainstormDownpour
    6-min rainfall (mm)[0, 0.1)[0.1, 0.7)[0.7, 1.5)[1.5, 4)[4, +∞)

    Table 2.  Categories of 6-min rainfall

    where the k values ranged from 1 to 4, representing 6-min rainfall forecasts of ≥ 0.1 mm, ≥ 0.7 mm, ≥ 1.5 mm, and ≥ 4 mm, respectively. The TS values ranged from 0 to 1, reflecting effective precipitation prediction accuracy.

4.   Results
  • This study selected the first 10 rainfall events for training and the last 6 events for testing. In order to demonstrate the relative merit of the SWT-SVM, we compared the results of this proposed method with the results of Z = 300 × R1.4, LR, and SVM. The training and testing processes were performed on a Dell Intel® CoreTM i7 CPU computer and the MATLAB2017b platform.

  • First, this study determined the optimal training data period for the dynamic precipitation model, as described in Section 3.1. Figure 6 shows the RMSE curve of the proposed method for different training data during the past 6, 12, ···, and 120 min. From Fig. 6, we can discern that when using training data during the previous 30 min, the RMSE will be the smallest. Since the RMSE describes the overall accuracy of the estimated rainfall, this implies that the precipitation model trained with data during the previous 30 min is the best.

    Figure 6.  RMSE for different training data during the past 6, 12, ···, and 120 min.

  • The SWT-SVM proposed in this study was used to estimate the dynamic precipitation for 6 rainfall events. Figures 7 and 8 show the comparison of the estimated 6-min rainfall and TSs from Z = 300 × R1.4, LR, SVM, and SWT-SVM methods with the gauge values. The evaluation results of these four methods are listed in Table 3.

    MethodRMSE
    [mm (6 min)–1]
    MB
    [mm (6 min)–1]
    MAE
    [mm (6 min)–1]
    CC
    (%)
    Z–R1.12 0.260.5352.74
    LR0.69–0.390.5854.32
    SVM0.85–0.350.3852.14
    SWT-SVM0.54–0.210.3774.72

    Table 3.  Evaluation results of estimated rainfall using different methods

    Figure 7.  Scatter plots for comparison of the estimated 6-min rainfall (mm) from (a) Z = 300 × R1.4, (b) LR, (c) SVM, and (d) SWT-SVM methods with the gauge 6-min rainful (mm). The black solid line shows a 1 : 1 relationship.

    Figure 8.  TSs of estimated rainfall for four category rainfall using different methods (colored bars): Z = 300 × R1.4, LR, SVM, and SWT-SVM.

    From Figs. 7, 8, and Table 3, it is clear that the RMSEs and MBs of the Z = 300 × R1.4 algorithm are the largest. This indicates that estimated rainfall amounts from Z = 300 × R1.4 are higher than the gauge rainfall, and the corresponding error is the greatest. While the TSs of heavy rain, rainstorm, and downpour of Z = 300 × R1.4 are much better than the corresponding values of the LR and SVM, the relatively high TSs are also one of the reasons that Z = 300 × R1.4 is an efficient algorithm for QPE. In all of the evaluation results, the estimated rainfall using the LR method is generally lower than the gauge rainfall. In addition, the corresponding TSs are only better than those of the SVM, a machine learning method commonly used in recent years. Even though the overall RMSE of the precipitation estimation using the SVM is lower, its TSs are not as good as those from Z = 300 × R1.4. There are two reasons for this result. First, the precipitation model using the SVM may be overfitting due to a large amount of training data, as well as the presence of abnormal cases. Second, the generally low-quantity rainfall data in the training samples lead to the underestimation of rainfall.

    Considering the temporal dependence of precipitation and the advantages of the SVM for small samples, this study proposed the SWT-SVM method. Compared with the gauge values, estimated rainfall using the proposed method exhibited a strong correlation with a small error rate. On the whole, however, the estimated rainfall tended to be lower than that measured by the rain gauges, particularly in the case of downpours. In addition, the TSs of precipitation estimations by the proposed method are significantly improved compared to those of the other methods, particularly for the TSs of rainstorms and downpours, which increased by approximately 20% compared with those from Z = 300 × R1.4. Moreover, the TSs of the other categories increased by about 5%. These results also support the conclusion that the SWT-SVM method is superior to the basic precipitation estimation methods.

    The average performance of six precipitation events was analyzed above. Figures 9ah show the evaluation result for 74 AWSs using the proposed SWT-SVM method, Z = 300 × R1.4, LR, and SVM, respectively. The numbers of the AWSs are not continuous due to occasional missing AWS data. The abscissa of Fig. 9 shows the AWS numbers at intervals of 2. In Fig. 9a, the RMSE of most AWSs using the proposed method ranges from 0.5 to 0.6, reflecting the relatively high precision of QPE compared with the other methods. Figure 9b shows the CC of the estimated rainfall with the gauge rainfall, in which it can be seen that the CC of the proposed method does not fall below 60%, indicating a strong correlation between the estimated and gauge rainfall. The MB and MAE curves both illustrate the degrees of underestimation or overestimation. Figures 9c and 9d are consistent with the average MB and MAE values analyzed above. From Figs. 9eh, the TSs of four categories have been improved, while the TS improvement is less significant for light/moderate rain and heavy rainfall. An increase of 10% has been attained for the rainstorm TS and 20% for downpours. Similarly, the TSs of the four categories are consistent with the average TSs analyzed above.

    Figure 9.  Evaluation results of (a) RMSE, (b) CC (%), (c) MB, (d) MAE for the estimated rainfall [mm (6 min)–1], and TSs (%) of (e) light/moderate rain, (f) heavy rain, (g) rainstorm, and (h) downpour for 74 AWSs using the proposed SWT-SVM, Z = 300 × R1.4, LR, and SVM.

  • In the previous section, we discussed the results of QPE using different methods, and summarized the advantages of the proposed SWT-SVM method. In this section, two cases of the six precipitation events (Figs. 10, 11) will be analyzed.

    Figure 10.  Choropleth maps from 0706–0712 local time (LT) on 10 June 2017 of (a) radar reflectivity, (b) gauge rainfall, and QPE by (c) the proposed SWT-SVM method, (d) Z = 300 × R1.4, (e) LR, and (f) SVM.

    Figure 11.  Choropleth maps from 1124–1130 LT 12 August 2017 of (a) radar reflectivity, (b) gauge rainfall, and QPE by (c) the proposed SWT-SVM method, (d) Z = 300 × R1.4, (e) LR, and (f) SVM.

    (1) Case 1

    Figure 10a shows a 6-min radar map from 0706 to 0712 local time (LT) on 10 June 2017. Figures 10bf show the choropleth precipitation maps of 6-min gauge rainfall and estimated rainfall. By comparing the map of East China with Fig. 10b, it can be seen that the 6-min gauge totals surpassed 2 mm in most areas of Suzhou and the Yangtze River Delta, even reaching 4 mm in some areas of Suzhou. By comparing the QPE results of the four different methods, it can be seen that the proposed SWT-SVM method was more accurate in estimating the location of the rainband as well as precipitation lighter than heavy rainfall. However, this method noticeably underestimated the precipitation > 4 mm. The rainband distribution of the Z–R relationship precipitation estimation results was consistent with that of the radar reflectivity, but different from that of the gauge rainfall. The QPE results of the LR and SVM methods exhibited varying degrees of underestimation, and their estimated rainband locations also deviated from the gauge rainfall.

    (2) Case 2

    In Fig. 11, the choropleth maps of reflectivity, gauge rainfall, and estimated precipitation from 1124 to 1130 LT 12 August 2017 using the same QPE methods as Case 1 are illustrated. Although the distribution of radar reflectivity is related to the actual gauge rainfall, it does not determine it. The 6-min gauge rainfall measurements were more intense in the vicinity of Shanghai and Jiangsu Province. Rainfall estimated by the Z–R relationship at the major AWSs was noticeably higher than the gauge rainfall, while the estimates of the other three methods were all lower than the actual rainfall. Therefore, there were more false alarms for QPE from the Z–R relationship. In addition, the QPE results from the Z–R relationship, LR, and SVM deviated slightly in terms of rainband location. Relatively speaking, the proposed SWT-SVM method was found to be superior to the other techniques, both in terms of precipitation location and precipitation estimation.

5.   Summary and Conclusions
  • Taking into consideration both the time dependence and abrupt changes of precipitation, and recognizing the advantages of the SWT in signal feature extraction and the SVM in prediction involving small samples, a dynamic radar QPE method based on both the SWT and SVM was proposed. First, given the time dependence and abrupt changes of precipitation, this study selected the data during the previous 30-min period for training, which were used to determine a dynamic precipitation estimation model. Second, small training samples that utilized the data from the previous 30 minutes highlighted the advantages of the SVM. Finally, creatively combining the SWT with the SVM, QPE in the wavelet domain was found to greatly improve the accuracy of precipitation estimation. Experimental results in East China verified that the proposed SWT-SVM method is clearly superior to the basic estimation methods.

    In order to further improve the performance of this model, future work should include the following: (1) the respective construction of different models for different automatic weather stations, (2) the consideration of correlations between neighborhood grids and the grid to be estimated, and (3) the utilization of additional precipitation features.

    Acknowledgments. The authors wish to thank Shanghai Meteorological Center for providing the data used in this paper.

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