Error Analysis and Modeling of GPM Dual-Frequency Precipitation Radar Near-Surface Rainfall Product

Zhixuan Wang aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Leilei Kou aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China
bCollaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Yinfeng Jiang aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Ying Mao aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Zhigang Chu aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Aijun Chen aSchool of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China
bCollaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China

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Abstract

The error characterization of rainfall products of spaceborne radar is essential for better applications of radar data, such as multisource precipitation data fusion and hydrological modeling. In this study, we analyzed the error of the near-surface rainfall product of the dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement Mission (GPM) and modeled it based on ground C-band dual-polarization radar (CDP) data with optimization rainfall retrieval. The comparison results show that the near-surface rainfall data were overestimated by light rain and slightly underestimated by heavy rain. The error of near-surface rainfall of the DPR was modeled as an additive model according to the comparison results. The systematic error of near-surface rainfall was in the form of a quadratic polynomial, while the systematic error of stratiform precipitation was smaller than that of convective precipitation. The random error was modeled as a Gaussian distribution centered from −1 to 0 mm h−1. The standard deviation of the Gaussian distribution of convective precipitation was 1.71 mm h−1, and the standard deviation of stratiform precipitation was 1.18 mm h−1, which is smaller than that of convective precipitation. In view of the precipitation retrieval algorithm of DPR, the error causes were analyzed from the reflectivity factor (Z) and the drop size distribution (DSD) parameters (Dm, Nw). The high accuracy of the reflectivity factor measurement results in a small systematic error. Importantly, the negative bias of Nw was very obvious when the rain type was convective precipitation, resulting in a large random error.

Significance Statement

This study first compares the total and different rain types of near-surface rainfall measured by DPR and ground-based radar CDP, then separates the error of DPR near-surface rainfall into systematic and random errors and analyzes the possible causes of the error. The purpose of this study is to better apply the error model to applications such as optimal data fusion and hydrological modeling, and the analysis of the error can also provide a basis for improving the spaceborne precipitation retrieval algorithm.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Leilei Kou, cassie320@163.com

Abstract

The error characterization of rainfall products of spaceborne radar is essential for better applications of radar data, such as multisource precipitation data fusion and hydrological modeling. In this study, we analyzed the error of the near-surface rainfall product of the dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement Mission (GPM) and modeled it based on ground C-band dual-polarization radar (CDP) data with optimization rainfall retrieval. The comparison results show that the near-surface rainfall data were overestimated by light rain and slightly underestimated by heavy rain. The error of near-surface rainfall of the DPR was modeled as an additive model according to the comparison results. The systematic error of near-surface rainfall was in the form of a quadratic polynomial, while the systematic error of stratiform precipitation was smaller than that of convective precipitation. The random error was modeled as a Gaussian distribution centered from −1 to 0 mm h−1. The standard deviation of the Gaussian distribution of convective precipitation was 1.71 mm h−1, and the standard deviation of stratiform precipitation was 1.18 mm h−1, which is smaller than that of convective precipitation. In view of the precipitation retrieval algorithm of DPR, the error causes were analyzed from the reflectivity factor (Z) and the drop size distribution (DSD) parameters (Dm, Nw). The high accuracy of the reflectivity factor measurement results in a small systematic error. Importantly, the negative bias of Nw was very obvious when the rain type was convective precipitation, resulting in a large random error.

Significance Statement

This study first compares the total and different rain types of near-surface rainfall measured by DPR and ground-based radar CDP, then separates the error of DPR near-surface rainfall into systematic and random errors and analyzes the possible causes of the error. The purpose of this study is to better apply the error model to applications such as optimal data fusion and hydrological modeling, and the analysis of the error can also provide a basis for improving the spaceborne precipitation retrieval algorithm.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Leilei Kou, cassie320@163.com

1. Introduction

Precipitation is the core component of the global water and energy cycle and is the main atmospheric forcing variable driving surface hydrological and land surface processes (Le Coz and van de Giesen 2020). As two traditional methods to observe precipitation on the ground, rain gauge and ground radar play an important role in industrial and agricultural production and weather forecasting. (Liu et al. 2010; Wang and Wolff 2010). With the development of research, the density of station networks and the distribution of space–time and environmental factors will have an inevitable impact on both methods (Schwaller and Morris 2011; Dong and Liu 2012). Satellite precipitation observations are the only effective means to systematically understand global precipitation and its changes (Hou et al. 2014; Iguchi et al. 2018). The Tropical Rainfall Measuring Mission (TRMM) satellite, launched in 1997, carried the world’s first precipitation radar (PR), but it only sampled tropical rainfall. However, on 27 February 2014, the Global Precipitation Measurement (GPM) mission was launched, which provided more complete coverage in space and time. Compared with the TRMM PR, GPM carried a dual-frequency PR (DPR), and could thus use both the Ku and Ka bands to obtain information on the drop size distribution (DSD) and further improve the accuracy of precipitation retrieval. The addition of the Ka band in the DPR improved the measurement of light precipitation (Chandrasekar et al. 2008; Zhang et al. 2020).

To better utilize spaceborne radar rainfall products, it is important to validate the spaceborne radar precipitation data based on measured ground data (Gao et al. 2021; Wu et al. 2019; Chase et al. 2020; Watters et al. 2018; Fatemeh et al. 2020). For example, to validate the effectiveness of GPM DPR products in key climate areas with complex terrain (such as Italy), Petracca et al. (2018) compared DPR normal beam scan (NS) products with ground radar. Speirs et al. (2017) compared GPM DPR products with the three-dimensional precipitation rate measured by ground radar in the Swiss Alps and plateaus according to seasons and precipitation stages and found that the GPM consistently underestimated the precipitation. Liao et al. (2014) developed a framework based on DSD data and found that the DSD model of DPR retrieval (μ = 3) was reliable. Kirstetter et al. (2012) compared the TRMM PR quantitative precipitation estimation with the ground radar reference values from the National Oceanic and Atmospheric Administration and revealed the sensitivity to the processing steps with reference values, comparisons of rainfall detectability, and the distribution of rainfall rate. These studies are mainly aimed at interpreting the characteristics of rainfall products from different sensors, analyzing the applicability of rainfall products in some specific areas, or analyzing the sensitivity of precipitation data based on physical characteristics.

Aside from the research on ground validation and characteristic analysis of different precipitation products, the quantitative error analysis and mathematical modeling are more conducive to precipitation data applications like optimal multisource data fusion. Both ground-based and spaceborne radar precipitation estimation data have their own error structure characteristics. How to accurately describe the systematic and random errors of precipitation estimation is the key problem to obtain the optimal fusion with different sensors. Quantitatively characterizing the error characteristics of precipitation retrieval from spaceborne radar can further improve the applications of rainfall products, such as multisource precipitation data fusion, data assimilation, and hydrological modeling. For instance, the optimal fusion of multisource data is generally based on unbiased data. The Bayesian method generally takes the random error and systematic error of input data as likelihood function, and their values will directly affect the quality of the final fusion results. In addition, the analysis of error sources also provides a basis for improving the spaceborne precipitation retrieval algorithm and the accuracy of precipitation retrieval.

The C-band dual-polarization radar (CDP) data in Nanjing, China, from 2015 to 2017 were selected for matchup and statistical comparison with GPM DPR data in this paper, to analyze the error of DPR precipitation measurement. First, the quality of CDP data was controlled, and the optimal precipitation estimation was obtained by determining the optimal precipitation relationships based on neural network and establishing logistic multiple regression prediction model. The approximate true value of near-surface rainfall of CDP was filtered and obtained by comparing with the rain gauge data. Then, the DPR and CDP precipitation data were quantitatively compared, including the comparison of total precipitation, and of stratiform precipitation and convective precipitation. According to the comparison results, the error structure was modeled as systematic and random error, and the quantitative mathematical models were given respectively. The possible causes of the error were analyzed from two aspects of reflectivity factor measurement and the DSD parameters. The analysis of error structure and error causes can better help the optimal fusion of multisource precipitation data and the improvement of spaceborne radar data retrieval algorithm.

2. Data description

a. GPM DPR near-surface rainfall product

The DPR of GPM is composed of Ku- and Ka-band precipitation radar. The frequency of the Ku band is 13.6 GHz and that of the Ka band is 35.5 GHz. The two bands of precipitation radar are abbreviated as KuPR and KaPR, in which KuPR is very similar to TRMM PR. One of the main error sources in TRMM PR rainfall estimation is the uncertainty of radar reflectivity factor conversion to rainfall rate. This uncertainty is due to the change of DSD with the region, season, and rain type. One of the purposes of adding the Ka band to DPR is to provide DSD information obtained from the non-Rayleigh scattering effect with higher frequency, so as to further improve the precision of quantitative precipitation measurement by using double frequency measurement.

The main module of the DPR precipitation retrieval algorithm mainly contains six submodules including the preparation module, vertical profile module, classification module, DSD module, surface reference technique module, and solver module (Chen and Guan 2018). The main module reads and writes all input and output files and variables by calling the submodule, while the submodule cannot call other submodules. When the submodule terminates, the processing results will be returned to the main module. The secondary standard rainfall products of GPM DPR mainly include 2AKu, 2Aka, and 2ADPR. The 2AKu is the precipitation product of the KuPR single frequency retrieval, 2AKa is the precipitation product of the KaPR single-frequency retrieval, and 2ADPR is the precipitation product of the dual-frequency retrieval. The 2ADPR is divided into MS (matched beam scan), NS (normal beam scan), and HS (high-sensitivity beam scan). HS products are designed to work in the KaPR high-sensitivity interleaved sampling mode, with a vertical spatial resolution of 250 m and scanning width of 120 km. In MS products, the Ku and Ka bands are used for retrieval of relevant parameters, with a scanning width of 125 km and vertical spatial resolution of 250 m. NS products are retrieval products in the Ku band, with a scanning width of 245 km, and each scanning line should have 49 pixels. The 13–37 pixels in NS mode are Ku and Ka bands, and the pixels next to it are approximately dual frequency.

The 2ADPR product was selected due to the dual-frequency retrieval having better accuracy compared with the single-frequency retrieval (Gao et al. 2017; Zhang and Fu 2018; Petracca et al. 2018). In the three kinds of dual-frequency retrieval products, the scanning width of the NS product is close to twice that of the MS and HS products. This paper focuses on the error analysis and modeling of the near-surface precipitation in the 2ADPR NS products.

b. Ground-based dual-polarization radar near-surface rainfall product

The dual-polarization radar used in this study is in Nanjing University of Information Science and Technology, which works in C-band with a wavelength of 5.3 cm and a beamwidth of 0.54°. The original range resolution is 75 m. To investigate the error of DPR rainfall measurements, the most important thing is to get approximate true ground rainfall as the benchmark. Considering that there is no true precipitation product in reality, this paper selected the optimal retrieval and filtered CDP rainfall data as the approximate true value. The near-surface rainfall data of CDP were obtained in mainly three aspects: radar measured data quality control, optimal precipitation retrieval, and radar precipitation data filtering.

First, the quality control of the original measured radar data is carried out.

  1. Low-elevation radar reflectivity factor data are often contaminated by nonprecipitation echoes (ground clutter, anomalous propagation echo, etc.). We applied the fuzzy logic method to identify and remove clutter.

  2. Ten-point median filtering was applied to the two-way differential propagation phase ϕDP variable to filter the high-frequency random fluctuation of polarization measurement in the radar radial direction (Wang et al. 2018).

  3. We used the filtered ϕDP to calculate the difference propagation phase shift KDP to reduce the error caused by KDP with least squares method.

  4. The attenuation correction of the reflectivity factor of CDP measurement was carried out by KDPZH joint correction method (Park et al. 2005).

  5. In addition to the correction of the reflectivity factor, the differential reflectivity factor was corrected by the KDPZDR joint correction method (Liu et al. 2002).

  6. Median filtering was done for KDP and ZDR to improve the data quality.

Then, after the quality control of CDP measurement data, the optimal near-surface rainfall retrieval of CDP was carried out by using DSD data from raindrop disdrometer.

  1. The CDP data of the PPI scanning mode were selected to carry out optimal precipitation retrieval. The lowest elevation angle was taken outside the radar range of 30 km, while the third elevation angle was taken within the radar range of 30 km to avoid ground clutter.

  2. Only the values of KDP and ZDR greater than 0 were considered and the parameters with abnormal data were removed.

  3. Using raindrop size distribution data as training data, three kinds of polarization radar precipitation estimation relations were obtained by using a neural network algorithm: R(ZH), R(ZH, ZDR), and R(KDP).

  4. By comparing the precipitation results obtained from R(ZH), R(ZH, ZDR), and R(KDP) with the rain gauge data, the absolute bias between them was obtained. If the absolute bias between R(KDP) and the rain gauge was the smallest, the matching pixel was judged to be 1; otherwise, it was 0, and the 0–1 distribution of the binary dataset was obtained.

  5. Based on the binary classification results in step 4, the parameters of ZH and KDP on the matching point were used as input parameters, and the binary data of 0–1 distribution were used as output parameters to establish the logistic multiple regression prediction model.

  6. The sample was input into a logistic multiple regression model for prediction. If the prediction result was 1, R(KDP) was selected as the precipitation retrieval formula for the sample. If the prediction result was 0 and ZDR was greater than 0.5 dB, R(ZH, ZDR) was selected as the precipitation retrieval formula. Otherwise, R(ZH) was selected for the precipitation retrieval.

The rain gauge can provide high-precision observation of ground rainfall measurement. In this paper, the original reference rainfall (Rref) was compared with the rain gauge in the Nanjing area to further filter out the approximate true ground rainfall. The CDP rainfall data and rain gauge data are temporal–spatial matched. The matched rainfall data are hourly rainfall. Since the radar has 7–8 volume scans in 1 h, the radar data are averaged in 1 h in order to temporal match with the rain gauge data. For a spatial matchup, we find the nearest grid point according to the longitude and latitude of each rain gauge, and match the CDP rainfall on the grid point with the rainfall of the rain gauge. Figure 1 shows the scatter comparison of ground-based rainfall and rain gauge data. Since many low precipitation amounts would be better appreciated on a logarithmic scale, we have logarithmically processed the values.

Fig. 1.
Fig. 1.

Comparison of rainfall estimation results with adaptive retrieval algorithm and traditional retrieval algorithms, combined retrieval algorithm: (a) R(ZH), (b) R(ZH, ZDR), (c) R(KDP), (d) R(KDP, ZDR), (e) combined retrieval, (f) adaptive optimization retrieval. The rainfall with the adaptive retrieval algorithm is closest to that of rain gauge data, and the scatterplot shows a high correlation.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Compared with the rain gauge, the rainfall from the R(ZH) and R(ZH, ZDR) retrieval algorithms show that the scatter points are seriously downward-biased, which makes the rain gauge value larger overall, while the abnormal values of R(KDP) and R(KDP, ZDR) retrieval algorithms are obvious. The combined retrieval algorithm improved the problems caused by the traditional retrieval algorithm, but the scatter was still more downward-biased compared with the rain gauge. Figure 1f shows the scatter of rain gauge data compared with the CDP rainfall obtained by the adaptive optimal retrieval algorithm. The scatter points are almost distributed near the dotted line (y = x). The quantitative statistical comparison parameters are shown in Fig. 2. The figure shows that the correlation coefficient (CC) of the data obtained by the six algorithms is relatively small and the CC obtained by the adaptive optimal retrieval algorithm is slightly higher. Meanwhile, compared with the absolute deviation (bias) of the traditional retrieval algorithms greater than 2 mm h−1, the bias of the combined retrieval algorithm was slightly reduced, while the bias of the adaptive optimal retrieval algorithm was significantly reduced to less than 1 mm h−1. In addition, the root-mean-square error (RMSE) of the adaptive optimal retrieval algorithm was also significantly reduced compared with the other algorithms. In general, the adaptive optimal retrieval algorithm has the highest retrieval accuracy among the six retrieval algorithms and is suitable for the following analysis.

Fig. 2.
Fig. 2.

Statistical comparisons between rain gauge data and near-surface rainfall obtained by CDP radar with different rainfall retrieval algorithms. CC, bias, and RMSE show that the adaptive optimization algorithm of CDP radar rainfall performs better than the traditional retrieval algorithm and the combined retrieval algorithm.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

To make the ground rainfall closer to the true value, the matching pairs with correlation above 0.9 were selected. Figure 3a shows that rainfall with a correlation above 0.9 accounts for approximately 83% of the total, which indicates that the filtered sample data not only improves the accuracy but also retains a relatively rich amount of data.

Fig. 3.
Fig. 3.

(a) Correlation of rain gauge and CDP matching pairs. The correlation of rainfall between them is 0.6–0.7, 0.7–0.8, 0.8–0.9, and above 0.9, respectively, after the matching of ground-based radar and rain gauge. The matching points with correlation above 0.9 were selected. (b) Scatter comparison of rain gauge and CDP with a correlation of more than 0.9.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

After the above series of filtering, the final matching points obtained in this paper are about 40% of the original data. These matching points correspond to the approximate true ground rainfall.

3. Analysis and modeling of the error of DPR near-surface rainfall

To analyze the error of GPM DPR near-surface rainfall, the ground-based radar and the satellite radar should be matched in time and space. In this paper, the method of grid matching was used to match the near-surface rainfall measured by DPR with the approximate true ground rainfall (Rtrue) obtained in section 2b. We also set a minimum threshold of 0.1 mm h−1 and a maximum threshold of 60 mm h−1 for both CDP and DPR near-surface precipitation. After matching, the resolution of the two is 5 km × 5 km, and the number of matched samples in 2015–17 is 10 326. The matching pair is the matching of the rainfall used in the comparative study of DPR and CDP near-surface rainfall.

a. Comparison of CDP and DPR near-surface rainfall

Figure 4 shows the scatterplot and probability distribution of total near-surface rainfall and rainfall of different rain types measured by DPR and CDP from 2015 to 2017, with the rain type depending on the DPR classification module. As in section 2b, in order to better appreciate the low precipitations, we still perform logarithmic processing on the value, which is specifically shown on the scatterplot. The statistical quantitative comparison results are shown in Table 1, and the black dotted line is the trend line y = x.

Fig. 4.
Fig. 4.

Comparative scatterplot and probability distribution of near-surface rainfall from DPR and CDP. (a) Scatterplot of total rainfall; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation; (d) probability distribution of total rainfall; (e) probability distribution of stratiform precipitation; and (f) probability distribution of convective precipitation.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Table 1

Statistical comparison results of near-surface rainfall between CDP and DPR during 2015–17. Stratiform precipitation and convective precipitation pixels are obtained based on DPR precipitation classification. The error modeling will be carried out based on these comparison results.

Table 1

As shown in Fig. 4a, the scattered points are inclined upward as a whole; that is, the rainfall measured by the DPR was larger than the CDP as a whole. According to the probability distribution (Fig. 4d), the trend and distribution of rainfall measured by CDP and DPR were relatively consistent, while DPR was more likely to measure light rain. GPM DPR has a significantly improved ability to measure weak precipitation compared with TRMM PR. However, it is still sensitive to light rain because the band of DPR is in the millimeter band. Based on point-to-point, the CC between the near-surface rainfall estimated by CDP and DPR was 0.62, and bias was 3.42 mm h−1, as shown in Table 1.

The information about DSD is necessary for accurate rainfall retrieval, while the DSD is relate to the type of rainfall (Liu and Lei 2006). Therefore, rain type classification plays an important role in GPM DPR algorithm (Fu et al. 2012). When the classification module in DPR detects bright bands at the 0°C level, the rain type is stratiform precipitation if the reflectivity factor of the rain area does not exceed a specific convective threshold. When there is no bright band at the 0°C level and the reflectivity factor exceeds the conventional convective threshold, the rain type is convective precipitation (Minda and Chandrasekar 2012). There are some differences in the measurement results for different rain types, and the classification of precipitation can improve the accuracy of remote sensing precipitation estimation (Awaka et al. 2016). The classification results of stratification and convection precipitation were based on DPR rain type products.

Figures 4b and 4c shows the comparison results of stratiform and convective rainfall, respectively. Figure 4b shows that most of the stratiform precipitation is light to moderate rain, with less heavy rain. The rainfall intensity of DPR was slightly higher in light rain and similar to the measured total precipitation scatter. From the probability distribution in Fig. 4e, we can see that the near-surface rainfall of stratiform precipitation by CDP and DPR is consistent with CC reaching 0.63, while the probability of light rain by DPR was slightly higher. The results of the quantitative statistical comparison are presented in Table 1. Compared with the total precipitation, DPR has higher accuracy in measuring stratiform precipitation, with the CC improving and the RMSE reducing by 1.82 mm h−1. Figure 4c shows the scatterplot of convective precipitation measured by DPR and CDP, in which there are more samples of moderate to heavy rain. The probability distribution of convective precipitation measured by CDP and DPR (Fig. 4f) shows that the two are relatively consistent, but there is a large gap in the distribution. The distribution gap can be further analyzed using bias and the RMSE.

According to the statistical results in Table 1, the bias between CDP and DPR was 6.14 mm h−1 and the RMSE reached 9.49 mm h−1. As with the overall and stratiform precipitation, Fig. 4f shows that DPR was significantly more likely to measure light rain. Compared with stratiform precipitation, the bias of convective precipitation was about 2.5 times that of stratiform precipitation, and the RMSE was close to 10 mm h−1, which shows that the error of DPR near-surface rainfall in convective precipitation was much larger. The error may be due to the faster falling of particles and larger raindrops in convective precipitation of DPR, which makes Mie scattering easier to appear. In other words, the DSD changes more in convective precipitation.

b. Quantitative error modeling and analysis

1) Total error model

Based on the rainfall comparison results, the difference (diff) between rainfall measured by DPR (R) and the approximate true ground-based rainfall (Rtrue) was modeled as a quantitative mathematical function. Only the nonzero pairs of Rtrue and R are considered in the calculation to emphasize the ability of the DPR to quantify precipitation when it rains. Quantile regression studies the relationship between the conditional quantiles of independent and dependent variables, and the corresponding regression model can estimate the conditional quantiles of the dependent variables from the independent variables. Compared with the traditional regression analysis, which can only obtain the central trend of the dependent variable, quantile regression can infer the conditional probability distribution of the dependent variable. In this study, the model fitted is represented by a conditional quantile line, which is divided into 11 quantile regression curves. The y1y10 represent the diff (DPR−CDP) that can be included in the regression curve of conditional quantiles from 5% to 95%, and x1x10 are the rainfall measured by CDP corresponding to these differences. With increases in x, the range of y changes to varying degrees. For instance, when y9 is 0.9 quantile regression, it is hoped that 90% of data points (y = diff, x = CDP) can be included under the regression curve, and the formula shows that with the increase of x, the change range of 90% of diff under the regression curve also increases. The 0.9 quantile regression model is as follows:
y9=0.2274x9+1.8498.

Figure 5 shows the scatter of diff with CDP and the overall error model. The model is established by quantile local fitting with the difference as a function of Rtrue, with the conditional quantiles from top to bottom ranging from 5% to 95% (5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%).

Fig. 5.
Fig. 5.

The overall error model with diff (DPR − CDP) as a function of Rtrue established by quantile local fitting and the scatter of diff with CDP. The probability density of scatter points shows that DPR overestimates light rain (the median of residual error is positive and the distribution density is large), and underestimates the heavy rain. The fitting total error model is represented by (5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%) conditional quantile line.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Figure 5 shows that most of the scatter points with a high probability density gather in the position of light rain. When Rtrue increased gradually, the probability density of the scatter points decreased and extended to a negative difference. DPR slightly overestimated the light rain (the median of difference was positive) and underestimated the high rainfall rate (the median of the difference was negative). As DPR is in the millimeter band, it is very sensitive to light rain. In addition to the influence of the band itself, there may be some other factors, such as an incorrect ZR relationship, uneven beam filling, and insufficient correction of DPR attenuation for heavy rain rates.

2) Error separation and modeling

Understanding the error attributes, including system components and random components, has been the basis for the development of precipitation retrieval algorithms, uncertainty models, and bias adjustment techniques (Grimes 2009; Tian et al. 2009). In addition to the error separation modeling of total rainfall, it is necessary to separate and model the errors of different rain types because the rain type classification affects the DSD in the DPR algorithm. The error of DPR rainfall was modeled as an additive model [Eq. (2)], where s was the systematic error and ε was the random error. The terms a, b, and c were the fitting parameters of linear regression, which are called the regression coefficient and regression constant, respectively, and are used to explain the systematic error. Variable x represents the approximate true CDP rainfall:
error=s+ε,s=ax2+bx+c.

Systematic error is caused by some fixed reasons in the analysis process, including the measurement error of reflectivity factor Z, rain or rain-free reflectivity threshold, and distance from radar. Owing to the existence of systematic error, the average value of the measured data deviates significantly from its true value. Ideally, the systematic error should be eliminated or minimized to reduce the overall uncertainty.

Figure 6a shows the systematic error of the total rainfall compared with the approximate true rainfall of the CDP. It can be seen that the systematic error of DPR near-surface rainfall is directly proportional to the rainfall intensity and presents the distribution form of a quadratic function. The results show that the greater the rainfall intensity, the greater the systematic error of the DPR. Figure 6b presents the systematic error model of stratiform precipitation, showing that the systematic error is small with a maximum value of only 1.12 mm h−1. The systematic error of convective precipitation was also proportional to the rainfall intensity. Compared with the systematic error of stratiform precipitation, 1.12 mm h−1, the minimum system error of convective precipitation was 3.02 mm h−1. As a whole, the systematic error of convective precipitation (Fig. 6c) was larger than that of stratiform precipitation. Moreover, the growth range of the systematic error of convective precipitation was obviously greater than that of the total precipitation.

Fig. 6.
Fig. 6.

Systematic error and random error models of total near-surface rainfall and rainfall with different rain types: (a) systematic error model of total rainfall; (b) systematic error model of stratiform precipitation; (c) systematic error model of convective precipitation; (d) random error model of total rainfall; (e) random error model of stratiform precipitation; and (f) random error model of convective precipitation.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Based on the error distribution in Fig. 6, the systematic error was modeled in the form of a quadratic polynomial function in Eq. (3), where S1, S2, and S3 represent the systematic error of total, stratiform, and convective precipitation, and t1, t2, and t3 represent the rainfall measured by the corresponding CDP, respectively:
S1=0.0058t12+0.1607t1+1.2321,S2=1.2996×104t220.0253t2+1.1172,S3=0.0040t32+0.2189t3+3.0172.
There are many reasons for random errors, and it is difficult to reduce the random error (Habib et al. 2009). Figures 6d–f show the models of random error for total rainfall, stratiform precipitation, and convective precipitation, respectively. The probability density function can estimate the variability of the variable and give the corresponding confidence level. Therefore, this study uses a probability distribution function to find the relative probability of a value within the range of random error. Our results showed that the random error of total precipitation and different rain types of precipitation were all in the form of a Gaussian distribution, that is, N(μ, σ2). The μ is the expected value and σ2 represents the variance. We use standard deviation σ instead of variance to match the errors in bias and RMSE. The model of random error is shown in Eq. (3), where r1, r2, and r3 represent the random error of total, stratiform, and convective precipitation, respectively. The random error of the total near-surface rainfall showed a Gaussian distribution with a μ of −0.76 mm h−1 and a σ of 1.58 mm h−1. The μ of the random error of stratiform precipitation and convective precipitation were −0.42 and −0.96 mm h−1, and the σ were 1.18 and 1.71 mm h−1, respectively:
f(r1)=0.21exp{[(r1+0.76)2.23]2},f(r2)=0.28exp{[(r2+0.42)1.67]2},f(r3)=0.15exp{[(r3+0.96)2.41]2}.

Currently, most adjustment algorithms are based on correcting the amount of rainfall over a certain period of time (Aghakouchak et al. 2012). Although this method can adjust the total amount of rainfall, it may lead to underestimation or overestimation of rainfall peak. The quantification of systematic error and random error component can promote the further development of bias elimination algorithm, among which the most important is the ratio of error to rainfall rate and the distribution of error itself.

3) Analysis of possible causes of error

There are many reasons that lead to errors when estimating near-surface rainfall of DPR, such as uneven beam filling, attenuation of DPR radar signal, variation of DSD and so on. The separation of rain and no rain boundary is also a driving factor of DPR rainfall error, which may be related to the lack of sensitivity of the most uneven and brighter part of the rain area edge. But the most important mistake is probably the DPR precipitation retrieval formula. The working principle of spaceborne precipitation radar is similar to that of general ground-based radar. Precipitation retrieval algorithms are based on the relationship between radar echo and precipitation intensity (ZR):
Ze1(N*,D*)=λ14π5|K|2σb1(D)N(D;N*,D*)dD,Ze2(N*,D*)=λ14π5|K|2σb2(D)N(D;N*,D*)dD.

The effective radar reflectivity factor Ze could be expressed in terms of the backscattering cross section σb(D) of a precipitation particle of diameter D and the particle size distribution N(D). The basic idea of rainfall estimation with a dual-wavelength radar was to use two parameters to better represent the change of N(D). In other words, if N(D) is characterized by two parameters N* and D*, Ze at two wavelengths Ze1 and Ze2 become functions of N* and D*. Once Ze1 and Ze2 were given, we could solve Eq. (5) for N* and D*, and R could be calculated from N (D; N*, D*). Therefore, the most important parameters in DPR precipitation retrieval formula are likely to be Z and DSD parameters. The reflectivity factor Z is closely related to the systematic error of DPR, while the uncertainty of DSD will mainly lead to random error.

To further explore the influence of Z measurement on DPR precipitation detection, this study selected the reflectivity factors matching DPR and CDP from 2015 to 2017 for comparison. The detection threshold of reflectivity factor measured by DPR Ku band was 18 dBZ, and the matching effect was improved by setting the reflectivity factor threshold of CDP and DPR to 18 dBZ. Due to the different detection bands and scanning methods, there are some differences in the reflectivity factors detected by CDP and DPR (Liu et al. 2018; Kou et al. 2016). To eliminate the influence of wave band, the reflectivity factor of C–, Ku–, and Ka–wave band detection must be simulated first.

Figure 7 shows the comparison results of the C-, Ku-, and Ka-band detection reflectivity factors based on the T-matrix scattering simulation. The detection result of the Ku band was slightly less than that of the C band at the weak echo. With an increase in the reflectivity factor intensity, the detection result of the Ku band became gradually greater than that of the C band, which may be because the NS mode can detect a stronger echo and the detection ability of the weak echo is insufficient (Jiang et al. 2020). The reflectivity factor of C-band detection was taken as the independent variable and the reflectivity factors of Ku- or Ka-band detection were taken as the dependent variable:
ZCKu=anZCn+an1ZCn1++a1ZC1+a0,ZCKa=anZCn+an1ZCn1++a1ZC1+a0.
Fig. 7.
Fig. 7.

The results of reflectivity factor in C, Ku, and Ka band by Mie-scattering simulation. (The solid blue line represents the C band, the red is the Ku band, and the yellow is the Ka band.) The x axis is Z simulated by C band and the y axis is Z simulated by Ku/Ka band. The simulation results are conducive to the band correction.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

The term ai(i = 1, 2⋯n) represents the fitting coefficient, ZC→Ku, ZC→Ka respectively means that the reflectivity factor of the C-band detection was converted to the Ku and Ka bands, so the equivalent reflectivity factor of different bands was converted to the same band, that is, band correction was realized.

A comparison of the total and different rainfall types of the reflectivity factor after attenuation and band correction is shown in Fig. 8. Figure 8a shows a comparison of the total reflectivity factors, it can be observed that the most scattered points are concentrated. The error statistical parameters in Table 2 show that the CC between CDP and DPR reaches 0.84 and the reflectivity factor detected by DPR in stratiform precipitation is less affected than convective precipitation, and the CC between CDP and DPR reaches 0.86 because the echo intensity is relatively uniform.

Fig. 8.
Fig. 8.

Comparison between reflectivity factors measured by CDP and DPR: (a) Scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. The scatter points of all figures are relatively concentrated, and the quantitative statistical comparison parameters can refer to Table 2.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Table 2

The statistical comparison of reflectivity factors from CDP and DPR with total, stratiform, and convective precipitation samples during 2015–17.

Table 2

Compared to stratiform precipitation, convective precipitation is generated under atmospheric instability conditions. The echo intensity of convective precipitation is high, and it is more easily affected by attenuation, signal processing, radar parameters, and other factors. However, the CC between the CDP and DPR of convective precipitation was only slightly reduced compared to that of stratiform precipitation, despite the attenuation and other influences, indicating that different rain types only have a small impact on the reflectivity factor of DPR detection. Therefore, the accuracy of the reflectivity factor of the DPR was high, meaning that the measurement error was small. Because the precipitation measured by spaceborne radar is largely dependent on the reflectivity factor and retrieval of R, it can be seen from the analysis of Z that the overall consistency of the measurement of DPR and CDP reflectivity factors was good.

The uncertainty of DSD has a great influence on the rainfall estimation error due to the precipitation retrieval parameters are directly affected by DSD. The DSD of N(D) in DPR algorithm is in the form of gamma distribution as follow (Gorgucci and Baldini 2018; Chen et al. 2020):
N(D)=Nwf(μ)(DDm)μexp(ΛD).

In the DPR algorithm μ takes fixed parameter 3. From the research of Liao et al. (2014), we can find the DSD model of DPR retrieval (μ = 3) is reliable, so the sources of error are most likely Dm and Nw. The term Dm is defined as the ratio of the fourth moment to the third moment of DSD, and Nw is the normalized intercept parameter (Laroche 2002). After obtaining the true value of the raindrop disdrometer data, the variation retrieval method was used to obtain the DSD parameters of CDP (Cao et al. 2013; Mahale et al. 2019; Zhang et al. 2001).

To demonstrate the reliability of ground-based radar variational retrieval of DSD parameters, we used time series data to compare with measured DSD data. In this study, retrieval results from 0300 to 1400 local time (LT) 10 August 2015, were selected to draw a time sequence diagram, and the calculation results of the raindrop disdrometer data at Jiangning station in the Nanjing area were taken as the true values to test the retrieval results. Figure 9 shows that the results based on variational retrieval are closer to the true value than those of the conventional retrieval method. Unlike the conventional retrieval method, the variational retrieval method considered the error of observation data and the uncertainty of raindrop size distribution, which can minimize the error.

Fig. 9.
Fig. 9.

Comparison of Dm from CDP with different retrieval algorithm between 0300 and 1400 LT 10 Aug 2015. The time sequence diagram of Dm retrieval results shows that the results based on the variational method are closer to the results of the raindrop disdrometer, while the Dm obtained by the conventional retrieval method will have large fluctuations. The results obtained by the variational method will be used for validation of Dm from DPR.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

The statistical results in Table 3 showed that CC between the results obtained by variational retrieval and those obtained by raindrop disdrometer is higher and the bias is smaller. Hence, the DSD parameters retrieved based on variational method were used as the standard for comparison with DPR.

Table 3

The statistical comparison results of the DSD parameters Dm from disdrometer and CDP radar from 0300 to 1400 LT 10 Aug 2015. Based on the DSD data from disdrometer, the results obtained by the method of variational retrieval algorithm.

Table 3

The comparison scatters of the matching DSD parameters Dm and Nw from DPR and CDP are shown in Figs. 10 and 11. Figure 10 shows the overall comparison of Dm between CDP and DPR from 2015 to 2017, as well as the comparison, scatterplot of different rain types. By analyzing the comparison of total Dm in Fig. 10a, the Dm value measured for CDP is approximately 2.5 mm at most, and there are few points distributed between 2 and 2.5 mm. The GPM value of Dm was high. The reason for this phenomenon is that the NS mode is sensitive to strong echo and has insufficient detection ability for weak echo. The Dm measured by the NS mode showed a slightly lower bias, especially in stratiform precipitation.

Fig. 10.
Fig. 10.

Comparison of DSD parameter Dm from CDP and DPR: (a) Scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. The GPM value of Dm is obviously higher, and all the scatterplots show upward trend, which may because NS mode is sensitive to strong echo and has insufficient ability to detect weak echo. For quantitative comparison, please refer to Table 4.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Fig. 11.
Fig. 11.

Comparison of DSD parameter Nw from CDP and DPR: (a) scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. Compared with Dm, Nw has an obvious negative bias, especially in convective precipitation.

Citation: Journal of Hydrometeorology 23, 2; 10.1175/JHM-D-21-0173.1

Table 4 shows the comparison statistics of Dm and Nw in general and convective and stratiform precipitation. The Dm had a relatively large bias of 1.26 mm in convective precipitation and the RMSE reached 1.62 mm. In addition, Fig. 10c shows that DPR obviously overestimated Dm in convective precipitation.

Table 4

The statistical comparison results of the DSD parameters Dm and Nw (Dm/Nw) from DPR and CDP. The comparison of DSD parameters for different rain types can better analyze the possible causes of errors since DSD is particularly relevant to rain types.

Table 4

Figure 11 shows a comparison of Nw between CDP and DPR. We found that the overall scatter in Fig. 11a shows an upward trend; that is, the GPM value of Nw was slightly underestimated compared with CDP, which may be due to the inverse relationship between Nw and Dm (Gatlin et al. 2020). Therefore, a retrieval method with a positive Dm bias, such as 2ADPR, may produce a negative Nw bias. The 3-yr Nw comparison statistics presented in Table 4 show that compared with Dm, the bias of Nw increases to 3.49 mm−1 m−3 and the RMSE reaches 4.48 mm−1 m−3. The bias of Nw was much larger than that of the previously detected reflectivity factor. The value of Nw had a particularly serious negative bias for convective precipitation. This may mainly be due to the optimization method used in searching 2ADPR DSD, including simulating Ka-band attenuation, which may be affected by multiple scattering and uneven beam filling in convection.

From the above analysis of error reasons, we can determine reflectivity factor Z, as the contributor of systematic error, has high measurement accuracy and is almost unaffected by rain type classification. The DSD parameters contribute to the random error, with their sensitivity significantly impacting the random error. The DSD parameters are sensitive to rain types, and the retrieval results for different rain types are obviously different. Among the two DSD parameters, Dm had a significantly higher retrieval accuracy and was less affected by different rain types. Compared with Z, the retrieval accuracy of Nw was obviously lower and there was an obvious negative bias of Nw from convection precipitation. At the same time, the CC of Nw was very low, at only 0.14 for convective precipitation and the RMSE reached up to 6.01 mm−1 m−3. Therefore, the overall retrieval error of Nw was large.

4. Summary and discussion

In this study, the error of the 2ADPR near-surface rainfall product was analyzed and modeled by comparing it with rainfall retrieval results from the CDP radar in the Nanjing area. The initial retrieval comparison results showed that the near-surface rainfall from DPR and CDP were consistent, with a CC of 0.62 and a bias reaching 3.42 mm h−1. DPR had a larger error when measuring convective precipitation than stratiform precipitation, and for both precipitation types, light rain was slightly overestimated and heavy rain slightly underestimated. The systematic error of near-surface rainfall estimated by DPR was proportional to the CDP rainfall intensity, and it presented as a quadratic function. For stratiform precipitation, the systematic error was small with a maximum value of 1.12 mm h−1, while the systematic error of convective precipitation was large, with a minimum value of 3.02 mm h−1. The probability distributions of random error of total, stratiform, and convective precipitation all present the form of a Gaussian distribution. Among them, the mean value of convective precipitation had the largest bias from 0 of −0.96 mm h−1, and its standard deviation reached 1.71 mm h−1.

Based on the above error modeling, we analyzed the error of the measurement reflectivity factor and DSD of the DPR. Our results showed that the ground-based and spaceborne radar measurements of the reflectivity factor had good consistency. A high-accuracy reflectivity factor leads to a small systematic error. Two DSD parameters in DPR were compared with the parameters retrieved by CDP based on the variational retrieval algorithm. The results showed a positive bias in Dm of the DPR, which in turn produced a negative bias in Nw. For convective precipitation, the biases of Dm and Nw were very obvious. In addition, the CC of Nw was very low and the RMSE reached 6.01 mm−1 m−3.

Many factors affect the comparison between DPR and CDP, such as band, attenuation, effective sampling volume, and filling effect. It is difficult to accurately quantify the measurement or retrieval errors. DPR has potential advantages in evaluating other radars owing to its ability to retrieve microphysical parameters and high-accuracy quantitative estimation of precipitation. The significance of this study is that it characterizes the error of DPR relative to ground-based radar and quantifies the systematic and random error model, which is useful for further applications. For example, the optimal fusion of multisource precipitation based on artificial intelligence usually needs to understand the uncertainty of multisource observations and quantify its error characteristics, and hydrological simulations and predictions are based on the determined error quantitative model. However, this study was aimed at precipitation measurement in Nanjing and its applicability in other areas requires further research and verification. Moreover, this study mainly quantified the DPR error characteristics statistically and analyzed the main possible error causes. In the future, we should analyze the sources of radar estimation error from the physical mechanism and quantify the error estimation results for each source.

Acknowledgments.

This study is jointly sponsored by the National Natural Science Foundation of China (41975027), and the National Key Research and Development Program of China (2017YFC1501401).

Data availability statement.

The rain gauge data and raindrop disdrometer data are from China National Meteorological Information Center. The CDP data are available from Nanjing University of Information Science and Technology. The DPR rainfall data are available at https://www.nasa.gov/mission_pages/GPM/main/index.html.

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    • Crossref
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  • Cao, Q., G. F. Zhang, and M. Xue, 2013: A variational approach for retrieving raindrop size distribution from Polarimetric radar measurements in the presence of attenuation. J. Appl. Meteor. Climatol., 52, 169185, https://doi.org/10.1175/JAMC-D-12-0101.1.

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  • Fig. 1.

    Comparison of rainfall estimation results with adaptive retrieval algorithm and traditional retrieval algorithms, combined retrieval algorithm: (a) R(ZH), (b) R(ZH, ZDR), (c) R(KDP), (d) R(KDP, ZDR), (e) combined retrieval, (f) adaptive optimization retrieval. The rainfall with the adaptive retrieval algorithm is closest to that of rain gauge data, and the scatterplot shows a high correlation.

  • Fig. 2.

    Statistical comparisons between rain gauge data and near-surface rainfall obtained by CDP radar with different rainfall retrieval algorithms. CC, bias, and RMSE show that the adaptive optimization algorithm of CDP radar rainfall performs better than the traditional retrieval algorithm and the combined retrieval algorithm.

  • Fig. 3.

    (a) Correlation of rain gauge and CDP matching pairs. The correlation of rainfall between them is 0.6–0.7, 0.7–0.8, 0.8–0.9, and above 0.9, respectively, after the matching of ground-based radar and rain gauge. The matching points with correlation above 0.9 were selected. (b) Scatter comparison of rain gauge and CDP with a correlation of more than 0.9.

  • Fig. 4.

    Comparative scatterplot and probability distribution of near-surface rainfall from DPR and CDP. (a) Scatterplot of total rainfall; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation; (d) probability distribution of total rainfall; (e) probability distribution of stratiform precipitation; and (f) probability distribution of convective precipitation.

  • Fig. 5.

    The overall error model with diff (DPR − CDP) as a function of Rtrue established by quantile local fitting and the scatter of diff with CDP. The probability density of scatter points shows that DPR overestimates light rain (the median of residual error is positive and the distribution density is large), and underestimates the heavy rain. The fitting total error model is represented by (5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%) conditional quantile line.

  • Fig. 6.

    Systematic error and random error models of total near-surface rainfall and rainfall with different rain types: (a) systematic error model of total rainfall; (b) systematic error model of stratiform precipitation; (c) systematic error model of convective precipitation; (d) random error model of total rainfall; (e) random error model of stratiform precipitation; and (f) random error model of convective precipitation.

  • Fig. 7.

    The results of reflectivity factor in C, Ku, and Ka band by Mie-scattering simulation. (The solid blue line represents the C band, the red is the Ku band, and the yellow is the Ka band.) The x axis is Z simulated by C band and the y axis is Z simulated by Ku/Ka band. The simulation results are conducive to the band correction.

  • Fig. 8.

    Comparison between reflectivity factors measured by CDP and DPR: (a) Scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. The scatter points of all figures are relatively concentrated, and the quantitative statistical comparison parameters can refer to Table 2.

  • Fig. 9.

    Comparison of Dm from CDP with different retrieval algorithm between 0300 and 1400 LT 10 Aug 2015. The time sequence diagram of Dm retrieval results shows that the results based on the variational method are closer to the results of the raindrop disdrometer, while the Dm obtained by the conventional retrieval method will have large fluctuations. The results obtained by the variational method will be used for validation of Dm from DPR.

  • Fig. 10.

    Comparison of DSD parameter Dm from CDP and DPR: (a) Scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. The GPM value of Dm is obviously higher, and all the scatterplots show upward trend, which may because NS mode is sensitive to strong echo and has insufficient ability to detect weak echo. For quantitative comparison, please refer to Table 4.

  • Fig. 11.

    Comparison of DSD parameter Nw from CDP and DPR: (a) scatterplot of total precipitation; (b) scatterplot of stratiform precipitation; (c) scatterplot of convective precipitation. Compared with Dm, Nw has an obvious negative bias, especially in convective precipitation.

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