# Validation of GPM Precipitation Products by Comparison with Ground-Based Parsivel Disdrometers over Jianghuai Region

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{m}–Z

_{e}and N

_{w}–D

_{m}relationships were also derived preliminarily to improve the GPM rainfall estimates over Jianghuai region.

## 1. Introduction

## 2. Data and Methods

#### 2.1. Observational Sites and Datasets

#### 2.1.1. In Situ Parsivel^{2} Disdrometers

^{2}disdrometers from 2014 to 2018. The Parsivel

^{2}disdrometer used herein was a second-generation optical disdrometer manufactured by OTT Hydromet, Germany [31,32]. To minimize the measurement error, a data quality control procedure was implemented. Fallers with diameters over 8 mm or falling speeds outside ±60% of the empirical speed–diameter relationship for rain [33] were eliminated. In addition, 1-min samples with raindrop numbers less than 10 or rain rates less than 0.1 mm h

^{−1}were excluded [27]. Following the definition of a rain event proposed by Tokay and Bashor [34], 48 rain events incorporating 52,056 1-min effective DSD samples were identified for the summer season, 53 rain events incorporating 16,831 samples were identified for the winter season. For simplicity, herein, we only listed the DSD data collected in 2014 (Table 1). Notably, the present study only focused on rainfall samples, to endorse that there were no snow samples or mix-phased particles in the winter season, a phase identification method (velocity and diameter relations) proposed by Friedrich et al. [35] was adopted herein (Figure 2).

#### 2.1.2. GPM DPR Level-2 Products

^{−1}) with a 5 × 5 km

^{2}-footprint. It typically takes 1–2 min to cross the analysis domain (Figure 1). The matching between DPR and surface disdrometer observations depends both on the availability of the Parsivel composite and the presence of rainy events over the area. As a result, we have chosen 20 (25) effective observations from 40 (43) instantaneous cases in summer (winter) for the DPR–Parsivel comparisons. Table 2 simply shows the rain events observed by the GPM DPR during the summer season in June–July 2014 and the winter season in December–January 2015.

#### 2.2. Raindrop Size Distribution

^{2}disdrometer counts and the integral rainfall parameters, including the radar reflectivity factor Z (mm

^{6}m

^{−3}), rain rate R (mm h

^{−1}), rain water content W (g m

^{−3}) and total concentration of raindrops N

_{t}(mm

^{−3}), are derived from measured DSDs as described in Wen et al. [36].

_{0}, µ and Λ] gamma function model is widely used to represent the measured raindrop spectra [37] and is expressed as

_{0}is the intercept parameter, µ is the shape parameter, and Λ is the slope parameter. The truncated moment method has been well described in Wu et al. [22] to obtain the gamma model as well as other DSD parameters from Parsivel observations.

_{M}(mm), which can be used to measure the spectral width and shape of the DSD [38], is defined as

_{m}(mm) is the mass-weighted mean diameter [39], given by

#### 2.3. Calculated GPM DPR Variables

_{e}for each wavelength can be calculated as below:

_{b}(D

_{i},λ) is the backscattering cross section of a raindrop with diameter D

_{i}, which can be directly calculated based on Mie theory. K

_{w}

^{2}is the dielectric factor, which is related to the complex refractive index of the region and is conventionally taken to be 0.93.

_{w}and is defined as follows:

_{Ku}and Z

_{Ka}are the effective radar reflectivity factors at Ku- and Ka-band frequencies, calculated via Equation (4).

#### 2.4. GPM–Parsivel Comparison

## 3. Validation of GPM Precipitation Products

^{2}observations, we calculated the Ku-band (Ka-band) effective radar reflectivity factor Z

_{Ku}(Z

_{Ka}) for two seasons using Equation (4). Thereby, we can calculate the dual-frequency ratio (DFR) for the GPM–Parsivel comparison via Equation (5). The DFR provides valuable information that can be used to attain a better understanding of the microphysics associated with rain-retrieval algorithms. Thus, we analyzed and compared the relationship between the DFR and rain rate R from GPM and Parsivel observations. The comparison results are shown in Figure 3.

_{Ku}and Z

_{Ka}are in linear correlation. The values of the DFR from observation and derivation remain nearly constant at approximately 0.3 and 0.5 (dB) for winter, 0.1 and 0.5 (dB) for summer, respectively. We computed the GPM–Parsivel normalized bias (NB) via Equation (6). The comparison results (NB = 0.4 for winter, NB = 0.8 for summer) suggest that the GPM underestimate the DFR more in the summer season than in the winter season, which indicates that the GPM might have better performance for winter rain than summer rain over Jianghuai region.

_{M}–D

_{m}variations of the observed DSD samples in two seasons are analyzed via Equations (2) and (3) and are shown in Figure 4. These variations are represented in terms of the frequency of occurrence, as joint PDF where the colors represent the number of cases with the corresponding σ

_{M}–D

_{m}pairs. In two seasons, a similar variation is found that σ

_{M}generally increases with D

_{m}. The variation for each part precipitation samples was fitted to a power law, and the fitted curve is superimposed on a corresponding plot in Figure 4. The fitted power law equation for winter is given by:

_{M}= 0.295D

_{m}

^{1.50}

_{M}= 0.275D

_{m}

^{1.36}

_{M}–D

_{m}relations, the mean values of σ

_{M}and D

_{m}are smaller in winter rain than summer rain (σ

_{M}= 0.38, D

_{m}= 1.31 for winter and σ

_{M}= 0.40, D

_{m}= 1.44 for summer), resulting in a broader spectral width with more large droplets in summer. In addition, this further implies the microphysics variability between different seasons.

_{10}(N

_{w}) versus D

_{m}for the convective and stratiform rain types over Jianghuai region. The two outlined boxes on the scatterplot correspond to the maritime-like and continental-like convective clusters as defined by Bringi et al. [48]. Note that the stratiform rain samples of both seasons are very close to the stratiform line reported by Bringi et al. [48]. The convective precipitation in summer can be identified as both maritime-like and continental-like, which could be related to the abundant moisture transported from tropical ocean during summer, while that of winter is close to continental-like convective precipitation. In addition, this could be due to the typical dry and cold weather during winter monsoon season over Jianghuai region.

## 4. Improvement of GPM Retrieval Algorithms

_{m}. Nevertheless, when the DFR is negative, D

_{m}cannot be uniquely retrieved because of the well-known “dual value” problem as indicated in Meagher and Haddad [49], which is an obstacle for dual-frequency radar DSD retrievals. For our data, the dual-valued phenomenon also existed (Figure 3). To avoid such a dual-value problem, only the effective radar reflectivity was used in this work to obtain the empirical relationship of D

_{m}.

_{m}–Z

_{Ku}, D

_{m}–Z

_{Ka}and log

_{10}(N

_{w})–D

_{m}were obtained as shown in Figure 6. D

_{m}increase tends to be highly correlated with increasing Z

_{Ku}or Z

_{Ka}. There is an inverse relationship between log

_{10}(N

_{w}) and D

_{m}. Following a least squares method, we derived the second-degree polynomial relationships of D

_{m}–Z

_{Ku}, D

_{m}–Z

_{Ka}and log

_{10}(N

_{w})–D

_{m}as presented in Table 3. Using the three relations, the parameters N

_{w}and D

_{m}can be derived first. Then combined with the normalized gamma model described in Section 2.2, the DSD can be preliminarily reconstructed from the derived N

_{w}and D

_{m}given a local µ value. Thereby, the rain rate can be estimated eventually with the derived DSD. It was reported by Liao et al. [25] that a fixed-µ value (µ = 3) generally yields the smallest error. However, a single constant µ value may not exist. To acquire an optimized shape parameter, statistical results of gamma model parameters under different seasons, rain rates and rain categories are obtained from the Parsivel observations over Jianghuai region. The results are evaluated by comparison with Parsivel observations.

#### 4.1. Under Different Rain Rates

^{1}, 5 < R ≤ 10, 10 <R ≤ 20, 20 < R ≤ 40, and R > 40 mm h

^{−1}and large (small) drops are assumed to be D > 4 (D < 1) mm. The average raindrop spectra of two seasons in six rain rates are shown in Figure 7, which suggests that the particle number concentration and spectral width both increase with an increase in rain rate. Comparing the two seasons, the concentration of large drops is larger in winter season than summer season at the same rain rate class, which could be due to a stronger collision–coalescence process within small drops as well as the easier evaporation of small drops in drier winter conditions. The concentration of small drops is larger in the summer season than in the winter season, with an increase in rain rate that could be due to the stronger collision–breakup process within large drops.

_{0}and λ both increase with an increase in rain rate, while μ values increase to a maximum value first, then decrease to a minimum value. Comparing the two seasons, the three parameters of summer rain are slightly larger than winter rain at the same rain rate class. Such a difference could be attributed to the different rain categories in two seasons. The convective rain of the summer season was fed with moisture transported by the southwesterly monsoon. The winter rain is impacted by the northeasterly monsoon, causing large-scale frontal rainfall.

_{m}–Z

_{Ku}, D

_{m}–Z

_{Ka}and log

_{10}(N

_{w})–D

_{m}relationships and calculated the rain rate. The NB and NSE statistics are also computed via Equations (6) and (7) for evaluation (Table 5). Compared with a constant µ in Liao et al. [25], the rain rate-based µ performs better in Jianghuai region with a NB of −11.3% and a NSE of 33.2% for winter, and a NB of −13.1% and a NSE of 36.3% for summer.

#### 4.2. Under Different Rain Categories

_{R}) of the rain rate. In this work, two categorization schemes are combined together to separate total samples into convective and stratiform clusters. Specifically, for ten consecutive 1-min samples, if the R values of ten adjacent values are all less than 10 mm h

^{−1}and the standard deviation σ

_{R}is less than 1.5 mm h

^{−1}, then the rain is defined as stratiform, otherwise it is classified as convective clusters. Consequently, winter and summer consist of 94.7% (5.3%), 80% (20%) stratiform (convective) rainfall samples, respectively. The results indicate a dominant stratiform rain type in winter.

_{0}, µ and Λ] of the gamma model all exhibit larger values in summer than winter—both for convective rain and stratiform rain. Comparing the two rain types, the stratiform rain shows larger values of [N

_{0}, µ and Λ] than convective rain.

_{m}–Z

_{Ku}, D

_{m}–Z

_{Ka}and log

_{10}(N

_{w})–D

_{m}relationships and calculated the rain rate. The NB and NSE statistics are also computed via Equations (6) and (7) for evaluation (Table 5). Compared with a constant µ or a rain rate-based µ, the rain category-based µ performs best in Jianghuai region with a NB of −3.5% and a NSE of 17.9% for winter, and a NB of −5.3% and a NSE of 18.8% for summer.

#### 4.3. Possible Application of the µ–Λ Relationship

^{−1}and number concentration N > 1000 were fitted by the truncated moment method to obtain µ and Λ values in two seasons. A second-degree polynomial µ–Λ relationship was further derived. The relationship for winter is:

^{2}+ 0.437μ + 1.540

^{2}+ 0.724μ + 1.958

_{m}= 4 + μ [39]. Thus, given the D

_{m}and μ values, the corresponding Λ value can be estimated. As shown in Figure 8, compared to the fit of convective rain from Chen et al. [51], our fits appear in the lower D

_{m}region, which suggests that the DSDs in Meiyu precipitation have higher D

_{m}values than those observed in Jianghuai region.

_{m}value calculated from D

_{m}–Z

_{e}relationships presented in Table 3, given a reflectivity factor. Therefore, the rain rate can be eventually estimated with the derived normalized gamma model as described in Section 2.2. The performance of DSD retrieval using the above three equations should be assessed. However, the retrieval is mostly theoretical and needs more research in future work.

## 5. Summary and Conclusions

- GPM underestimates the DFR more in summer than winter, which indicates that GPM might have better performance in the winter than summer season over Jianghuai region with biases of 40% (80%) in winter (summer). Such a discrepancy could be due to the broader spectral width of the precipitation during summer than that of winter in this specific area.
- The shape parameters µ under different rain rates as well as rain categories are obtained from 5-year Parsivel observations over Jianghuai region. The retrieval errors of rain category-based µ (3–5%) are proved to be smaller than that of rain rate-based µ (11–13%) or a constant µ (20–22%) in rain-retrieval algorithms, with a possible application to rainfall estimations over Jianghuai region.
- The effective radar reflectivity factor Z
_{e}is calculated using Parsivel disdrometer data. Empirical D_{m}–Z_{e}and N_{w}–D_{m}relationships are further derived to improve the GPM rainfall estimates over Jianghuai region.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Locations of two observational sites (Nanjing (NJ) and Chuzhou (CZ)) over Jianghuai region. The superimposed rectangle represents Jianghuai region.

**Figure 2.**Identification and elimination of (

**a**) snow sample case and (

**b**) mix-phase sample case in total winter rainfall observations. The black curve represents the empirical fitting result of raindrops as reported by Friedrich et al. [35]. The black box represents rainfall area. The color mark represents particle number.

**Figure 3.**Scatterplots of the dual-frequency ratio (DFR) versus rain rate from DPR observations and raindrop size distribution (DSD) derivations on the same scale during winter (blue circles) and summer (red circles) over Jianghuai region. The left two panels represent results from GPM observations, and the right two panels represent results from DSD derivations. The probability density functions (PDF) of the DFR are also given in each panel.

**Figure 4.**σ

_{M}–D

_{m}two-dimensional PDF distributions and fitting results based on Parsivel disdrometer observations in two seasons. The resolution of PDF is 0.1 mm × 0.1 mm and the color mark value represents the frequency of occurrence (%) of σ

_{M}versus D

_{m}.

**Figure 5.**Distribution of log

_{10}(N

_{w}) and D

_{m}observed from the Parsivel disdrometer for convective (blue filled circles) and stratiform precipitation (red hollow circles) during (

**a**) winter and (

**b**) summer over Jianghuai region (along with ± standard deviation). The green symbol represents the average value of convective rain. The two outlined rectangles correspond to the maritime and continental convective clusters reported by Bringi et al. [48]. The black dashed line indicates the fitting result of stratiform rain [48].

**Figure 6.**Scatterplots of D

_{m}(mm) and Z

_{Ku}(dBZ); D

_{m}(mm) and Z

_{Ka}(dBZ); log

_{10}(N

_{w}) (mm

^{−1}m

^{−3}) and D

_{m}(mm) derived from the Parsivel disdrometer data for two seasons. The left ones stand for winter and the right ones for summer. The overlaid red lines represent the fitted curves.

**Figure 7.**The average DSDs from the Parsivel disdrometer data at six indicated rain rate classes in two seasons, as well as their comparison result, where dotted lines represent summer rainfall and solid lines represent winter rainfall.

**Figure 9.**µ–Λ relationship scatterplots and fitting curves based on Parsivel disdrometer observations in two seasons. The gray circles represent winter precipitation samples and the gray crosses represent summer precipitation samples. The dashed line represents the empirical μ–Λ relationship of convective rain during Meiyu from Chen et al. [51]. The gray lines correspond to the relationship ΛD

_{m}= 4 + μ [39] given the value of D

_{m}= 1.0, 1.5, 2.0, and 3.0 mm.

Seasons | Event No. | Date | Time (LST) | 1-min Samples (min) | Accumulated Precipitation (mm) | Max Rain Rate (mm h^{−1}) |
---|---|---|---|---|---|---|

Summer | 1 | 15 Jun 2014 | 04:54–06:15 | 62 | 13.7 | 19.6 |

2 | 15 Jun 2014 | 17:57–22:12 | 152 | 15.2 | 18.4 | |

3 | 16 Jun 2014 | 07:11–17:01 | 216 | 18.1 | 16.8 | |

4 | 25 Jun 2014 | 05:51–23:47 | 364 | 29.2 | 39.4 | |

5 | 26 Jun 2014 | 00:02–18:17 | 545 | 38.6 | 43.1 | |

6 | 1 Jul 2014 | 05:53–15:51 | 263 | 12.3 | 32.5 | |

7 | 1–2 Jul 2014 | 20:49–09:37 | 417 | 19.4 | 37.2 | |

8 | 4 Jul 2014 | 11:00–23:59 | 631 | 39.8 | 101.1 | |

9 | 5 Jul 2014 | 00:01–12:53 | 725 | 41.1 | 115.3 | |

10 | 12 Jul 2014 | 06:59–22:58 | 313 | 71.9 | 145.2 | |

Winter | 1 | 17 Dec 2014 | 11:10–13:36 | 146 | 3.5 | 3.9 |

2 | 19 Dec 2014 | 12:24–20:02 | 192 | 5.9 | 2.9 | |

3 | 21 Dec 2014 | 10:24–21:42 | 99 | 0.2 | 0.6 | |

4 | 22–23 Dec 2014 | 12:10–01:47 | 130 | 0.1 | 0.4 | |

5 | 24 Dec 2014 | 14:25–20:43 | 67 | 0.1 | 0.2 | |

6 | 26 Dec 2014 | 06:41–12:52 | 120 | 2.5 | 6.9 | |

7 | 29 Dec 2014 | 09:52–10:58 | 66 | 1.1 | 2.8 | |

8 | 30 Dec 2014 | 15:23–23:02 | 328 | 12.8 | 6.8 | |

9 | 1 Jan 2015 | 04:02–09:28 | 189 | 4.9 | 3.1 | |

10 | 2–3 Jan 2015 | 13:05–06:44 | 205 | 9.7 | 4.3 | |

11 | 3 Jan 2015 | 08:21–16:37 | 156 | 2.4 | 1.6 | |

12 | 8 Jan 2015 | 15:34–16:57 | 83 | 3.5 | 2.8 |

**Table 2.**Precipitation events observed by the Global Precipitation Measurement Dual-frequency Precipitation Radar (GPM DPR) when it overpasses Jianghuai region in two seasons of 2014.

Seasons | Pass No. | Date | Time (LST) | Rainfall Observations (√/×) | Max Rain Rate (mm h^{−1}) |
---|---|---|---|---|---|

Summer | 1 | 15 Jun 2014 | 02:56–04:29 | √ | 10.2 |

2 | 15 Jun 2014 | 12:11–13:44 | × | 0 | |

3 | 23 Jun 2014 | 00:41–02:13 | × | 0 | |

4 | 25 Jun 2014 | 23:39–01:11 | √ | 24.3 | |

5 | 26 Jun 2014 | 08:54–10:27 | √ | 32.1 | |

6 | 2 Jul 2014 | 06:50–08:23 | √ | 19.5 | |

7 | 6 Jul 2014 | 20:21–21:54 | × | 0 | |

8 | 12 Jul 2014 | 04:24–05:56 | √ | 62.4 | |

Winter | 1 | 9 Dec 2014 | 22:55–00:27 | √ | 1.5 |

2 | 10 Dec 2014 | 08:10–09:42 | √ | 0.7 | |

3 | 18 Dec 2014 | 05:50–07:22 | √ | 1.9 | |

4 | 20 Dec 2014 | 19:33–21:05 | × | 0 | |

5 | 21 Dec 2014 | 04:48–06:20 | × | 0 | |

6 | 23 Dec 2014 | 18:31–20:03 | √ | 0.3 | |

7 | 26 Dec 2014 | 03:35–05:08 | √ | 0.6 | |

8 | 8 Jan 2015 | 13:55–15:28 | √ | 0.4 | |

9 | 10 Jan 2015 | 13:44–15:18 | × | 0 | |

10 | 13 Jan 2015 | 12:42–14:15 | √ | 6.9 | |

11 | 27 Jan 2015 | 08:18–09:51 | √ | 6.8 |

**Table 3.**Second-degree polynomial relationships of D

_{m}–Z

_{Ku}, D

_{m}–Z

_{Ka}and log

_{10}(N

_{w})–D

_{m}derived in two seasons.

Relation | Data | a | b | c |
---|---|---|---|---|

D_{m} = aZ_{Ku}^{2} + bZ_{Ku} + c | Winter | 0.00093071 | 0.0027 | 0.5904 |

Summer | 0.00113070 | 0.0047 | 0.4911 | |

D_{m} = aZ_{Ka}^{2} + bZ_{Ka} + c | Winter | 0.00082581 | 0.0118 | 0.5011 |

Summer | 0.00092452 | 0.0213 | 0.4104 | |

log_{10}(N_{w}) = aD_{m}^{2} + bD_{m} + c | Winter | 0.2876 | –2.1543 | 5.7352 |

Summer | 0.2794 | –2.1347 | 5.8102 |

Season | Rain Rate Class | log_{10}N_{0} | μ | Λ |
---|---|---|---|---|

Winter | R ≤ 2 | 4.82 | 3.09 | 5.85 |

2 < R ≤ 5 | 4.71 | 2.88 | 5.04 | |

5 < R ≤ 10 | 4.45 | 3.14 | 4.28 | |

10 < R ≤ 20 | 4.27 | 3.52 | 4.14 | |

20 < R ≤ 40 | 4.11 | 1.87 | 2.88 | |

R > 40 | 3.91 | 1.22 | 2.41 | |

Summer | R ≤ 2 | 4.86 | 3.20 | 6.01 |

2 < R ≤ 5 | 4.73 | 3.41 | 5.23 | |

5 < R ≤ 10 | 4.65 | 3.79 | 5.01 | |

10 < R ≤ 20 | 4.42 | 3.61 | 4.55 | |

20 < R ≤ 40 | 4.27 | 2.85 | 3.54 | |

R > 40 | 3.98 | 1.34 | 2.39 |

**Table 5.**Statistical results of the GPM–Parsivel comparison for rain rate given as a constant µ, µ under different rain rates, as well as µ under different rain categories. NB and NSE (%) represent normalized bias and normalized standard error, respectively.

Season | NB (%) | NSE (%) | |
---|---|---|---|

µ = 3 | Winter | −20.7 | 58.3 |

Summer | −22.1 | 60.5 | |

µ (rain rate-based) | Winter | −11.3 | 33.2 |

Summer | −13.1 | 36.3 | |

µ (rain category-based) | Winter | −3.5 | 17.9 |

Summer | −5.3 | 18.8 |

**Table 6.**Statistical results of gamma model parameters in terms of two rain types. SD and SK represent standard deviation and skewness, respectively.

Rain Type | Season | log_{10}N_{0} | μ | Λ | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | SD | SK | Mean | SD | SK | Mean | SD | SK | ||

Convective | Winter | 4.26 | 1.39 | 0.79 | 3.81 | 3.31 | 0.89 | 4.37 | 2.68 | 1.07 |

Summer | 4.70 | 1.14 | 0.73 | 4.69 | 2.92 | 0.69 | 4.89 | 2.42 | 0.94 | |

Stratiform | Winter | 5.12 | 1.50 | 0.38 | 4.66 | 2.93 | 0.56 | 6.94 | 3.22 | 0.49 |

Summer | 5.41 | 1.45 | 0.34 | 5.92 | 2.87 | 0.38 | 7.60 | 3.07 | 0.44 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, Z.; Zhang, Y.; Zhang, L.; Hao, X.; Lei, H.; Zheng, H. Validation of GPM Precipitation Products by Comparison with Ground-Based Parsivel Disdrometers over Jianghuai Region. *Water* **2019**, *11*, 1260.
https://doi.org/10.3390/w11061260

**AMA Style**

Wu Z, Zhang Y, Zhang L, Hao X, Lei H, Zheng H. Validation of GPM Precipitation Products by Comparison with Ground-Based Parsivel Disdrometers over Jianghuai Region. *Water*. 2019; 11(6):1260.
https://doi.org/10.3390/w11061260

**Chicago/Turabian Style**

Wu, Zuhang, Yun Zhang, Lifeng Zhang, Xiaolong Hao, Hengchi Lei, and Hepeng Zheng. 2019. "Validation of GPM Precipitation Products by Comparison with Ground-Based Parsivel Disdrometers over Jianghuai Region" *Water* 11, no. 6: 1260.
https://doi.org/10.3390/w11061260