# Incorporating Satellite Precipitation Estimates into a Radar-Gauge Multi-Sensor Precipitation Estimation Algorithm

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## Abstract

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## 1. Introduction

## 2. SRG Multi-Sensor Fusion System

#### 2.1. Multi-Sensor Precipitation Estimator (MPE)

#### 2.2. Enhanced SRG Fusion Module

#### 2.3. Local Bias Correction of Satellite Quantitative Precipitation

#### 2.4. RRI Calculation

_{1}is the radar coverage and the second circle O

_{2}represents the area of influence of the satellite QPE; their area of intersection is used to determine the RRI. To calculate it is actually a “crop circle” problem. So,

_{1}and R

_{2}are the radar QPE coverage radius and satellite QPE influence radius, respectively. Figure 2b shows the resulting RRI values as a function of distance from the radar, where R

_{1}and R

_{2}are set at 65 and 12 Hydrologic Rainfall Analysis Project (HRAP) pixels (approximately 4 km each), respectively. This is because WSR-88D precipitation products are on the Hydrologic Rainfall Analysis Project (HRAP) coordinate system. The digital precipitation array product for each radar is on a 131 × 131 HRAP pixel grid mesh with the radar situated in the center. The radius of coverage is therefore 65 HRAP pixels. The default value of R

_{2}is 12 HRAP pixels is determined using the radar data influence radius currently used in radar-gauge merging. This value is set based on the conditional correlograms of rainfall amount averaged over eight directions (refer to Figure 2 in the paper of Seo and Smith [25]). Sensitivity analysis suggests that R

_{2}varies is within a narrow range surrounding the 12 HRAP pixels for a specific geographical region, and therefore a fixed, rather than a spatially and temporally varying R

_{2}is used.

#### 2.5. Double Optimal Estimation (DOE) for Radar and Satellite

## 3. Evaluation Method

#### 3.1. Continuous Verification Statistics

#### 3.2. Categorical Verification Statistics

## 4. Experimental Design and Data

## 5. Results

#### 5.1. Case Study

#### 5.2. Statistical Verification

#### 5.2.1. Region I

#### 5.2.2. Region II

## 6. Discussion

## 7. Summary and Conclusions

- (1)
- The satellite-radar-gauge SRG MSF improves over using satellite-gauge or radar-gauge alone, mainly because the estimates of radar and satellite are corrected consulting with gauge before merging them together, this procedure makes SRG-MSF less biased than the radar and more highly correlated with gauges.
- (2)
- Within the radar coverage region (Region I) the merging of satellite data with radar and gauges improves the data quality during the warm season, apparently by compensating for degradation of the radar data in regions where the beam is at or above the melting level (See, Figure 5). Outside the radar coverage region (Region II) nearby radar rain rates can be used via SOE and DOE to create a merged field that improves over the LB-adjusted satellite rain rates.
- (3)
- Introducing the parameter RRI to express the degradation of radar data quality with distance from the radar (beam height) provides an effective strategy for merging satellite and radar data in the framework of MPE. The smooth transition, as well as improvement in PB and other evaluation metrics between radar and satellite in the final product map reveal that the new fusing algorithm is reliable and robust.
- (4)
- Although the MPE and the enhanced satellite data fusion software package are reliable, the quality of the merged fields is directly influenced by the quality of each component dataset; and some errors in the individual component data set (particularly satellite) will propagate into the merged fields. Consequently, pre-processing the component data to reduce its errors (e.g., using local bias correction based on gauge values) is necessary to minimize the final product errors, e.g., this study demonstrates the value of LB correction of the satellite QPEs used in this framework.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The new Multi-Sensor Fusion System, showing the existing MPE on the left, and new developed Multi-Sensor Fusion System on the right. Major features include the Radar Range Index (RRI) to quantify the radar data quality based on beam broadening and increase in beam height with distance from the radar, the Modified-Sensor Estimator which uses Double Optimal Estimation (DOE) to blend the satellite and radar data, and pre-processing to identify regions of low radar data quality region and to correct SQPE biases, here A: Radar mosaic (RM), B: Mean field bias correction (MB), C: Local bias correction (LB), D: Radar–gauge fusion (RG-MSF), E: Satellite local bias correction (LSQPE), H: Satellite-radar-gauge multi-sensor fusion (SRG-MSF).

**Figure 2.**Illustration of the RRI calculation. On the left, (

**a**) shows radar and satellite relative location, O

_{1}is the radar location, O

_{2}is the location for which the rain rate will be estimated, R

_{1}is the radar coverage radius, and R

_{2}is the range of influence of satellite QPE, it is updated cut-off lag distance (HRAP) with pre-defined correlation coefficient. On the right, (

**b**) shows an example of calculated radar range index as a function of distance from radar, the solid line is the Radar Range Index and the dashed line is the satellite supplemental index, the distance D between O

_{1}and O

_{2}on the left is same as the x-axis on the right.

**Figure 3.**Test area of offline MPE. The red stars are radar sites and the yellow points are HADS gauge locations. There are approximately 800 gauges in the study area. Half of them are used for MPE bias correction, the rest of them serve as independent validation gauge.

**Figure 4.**Estimates of total rainfall during 00:00:00 to 23:59:59 on 27 June 2007 from different algorithms in the MPE software package, (

**a**) satellite only (SQPE), (

**b**) satellite-gauge local bias correction (LSQPE), (

**c**) radar-gauge multi-sensor fusion (RG-MSF), and (

**d**) satellite-radar-gauge multi-sensor fusion (SRG-MSF).

**Figure 5.**Monthly average continuous statistical metrics from four different algorithms in the MPE software package vs. gauges over Region I for April through October of 2003–2007: (

**a**) Percentage bias, (

**b**) mean absolute error, (

**c**) root mean square error, and (

**d**) correlation coefficient.

**Figure 6.**Monthly average categorical statistical metrics from four different algorithms in the MPE software package vs. gauges over Region I for April through October of 2003–2007 (Bias score, POD, FAR, and CSI).

**Figure 7.**Monthly average continuous statistical metrics from three different algorithms in the MPE software package vs. gauges over Region II for April through October of 2003–2007: (

**a**) Percentage bias, (

**b**) mean absolute error, (

**c**) root mean square error, and (

**d**) correlation coefficient.

**Figure 8.**Monthly average categorical statistical metrics from three different algorithms in the MPE software package vs. gauges over Region II for April through October of 2003–2007 (Bias score, POD, FAR, and CSI).

**Table 1.**Area average and bias for estimated hourly rainfall from 26 June 2017 to 28 June 2007 vs. the amounts of the independent gauges from different algorithm in the MPE software package, (

**a**) SQPE, (

**b**) LSQPE, (

**c**) RG-MSF, and (

**d**) SRG-MSF, last two rows are correlation coefficient and RMSE, where ${Q}_{MPE}$ and ${Q}_{Gauge}$ are hourly rain rate of offline-MPE products and independent gauge, respectively.

(a) SQPE | (b) LSQPE | (c) RG-MSF | (d) SRG-MSF | |||
---|---|---|---|---|---|---|

Hit | Q_{MPE} ≥ 0.254 and Q_{Gauge} ≥ 0.254 | Q_{MPE} | 8.20 | 4.87 | 4.90 | 4.88 |

Q_{Gauge} | 5.37 | 5.44 | 4.32 | 4.36 | ||

R = Q_{MPE}/Q_{Gauge} | 1.53 | 0.89 | 1.13 | 1.12 | ||

Pairs | 294 | 283 | 446 | 443 | ||

False Alarm | Q_{MPE} ≥ 0.254 and Q_{Gauge} < 0.254 | Q_{MPE} | 3.98 | 2.94 | 0.67 | 0.77 |

Q_{Gauge} | 0.00 | 0.00 | 0.00 | 0.00 | ||

R = Q_{MPE}/Q_{Gauge} | NA | NA | NA | NA | ||

Pairs | 185 | 159 | 119 | 119 | ||

Miss | Q_{MPE} < 0.254 and Q_{Gauge} ≥ 0.254 | Q_{MPE} | 0.01 | 0.01 | 0.01 | 0.01 |

Q_{Gauge} | 1.68 | 1.74 | 0.95 | 0.90 | ||

R = Q_{MPE}/Q_{Gauge} | 0.01 | 0.01 | 0.01 | 0.01 | ||

Pairs | 283 | 294 | 131 | 134 | ||

Correct Null | Q_{MPE} < 0.254 and Q_{Gauge} < 0.254 | Q_{MPE} | 0.10 | 0.11 | 0.23 | 0.21 |

Q_{Gauge} | 0.00 | 0.00 | 0.00 | 0.00 | ||

R = Q_{MPE}/Q_{Gauge} | NA | NA | NA | NA | ||

Pairs | 49 | 69 | 47 | 58 | ||

Total | Q_{MPE} > 0.0 or Q_{Gauge} > 0.0 | Q_{MPE} | 3.89 | 2.31 | 3.07 | 3.00 |

Q_{Gauge} | 2.53 | 2.55 | 2.76 | 2.72 | ||

R = Q_{MPE}/Q_{Gauge} | 1.54 | 0.90 | 1.11 | 1.10 | ||

Pairs | 811 | 805 | 743 | 754 | ||

$\rho $ | 0.36 | 0.30 | 0.61 | 0.62 | ||

RMSE | 6.29 | 5.56 | 5.29 | 4.99 |

**Table 2.**Percentage bias (PB%), mean average error (MAE), root mean square error (RMSE), and correlation (r) between hourly rainfall from four different algorithms in the MPE software package vs. rain gauge for all of Region I during 2003 to 2007 from April to October.

PB (%) | MAE | RMSE | r | |
---|---|---|---|---|

SQPE | 22.04 | 4.78 | 7.28 | 0.57 |

LSQPE | −2.75 | 4.33 | 6.98 | 0.55 |

RG-MSF | 27.63 | 3.01 | 5.81 | 0.75 |

SRG-MSF | 16.49 | 2.83 | 5.15 | 0.74 |

**Table 3.**Same as Table 2, but area bias (BIAS), Probability of Detection (POD), False Alarm Ration (FAR), and Critical Success Index (CSI) for rain/no rain discrimination (the cut off threshold is 0.254 mm/h).

BIAS | POD | FAR | CSI | |
---|---|---|---|---|

SQPE | 0.99 | 0.42 | 0.58 | 0.27 |

LSQPE | 0.92 | 0.40 | 0.56 | 0.27 |

RG-MSF | 1.36 | 0.77 | 0.44 | 0.48 |

SRG-MSF | 1.47 | 0.77 | 0.48 | 0.45 |

**Table 4.**Same as Table 2, but for Region II.

PB (%) | MAE | RMSE | r | |
---|---|---|---|---|

SQPE | 14.56 | 4.76 | 7.15 | 0.56 |

LSQPE | −2.26 | 4.45 | 7.02 | 0.54 |

SRG-MSF | −10.72 | 4.04 | 6.48 | 0.56 |

**Table 5.**Same as Table 3, but for Region II.

BIAS | POD | FAR | CSI | |
---|---|---|---|---|

SQPE | 1.01 | 0.40 | 0.60 | 0.25 |

LSQPE | 0.93 | 0.38 | 0.59 | 0.25 |

SRG-MSF | 1.07 | 0.47 | 0.56 | 0.29 |

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## Share and Cite

**MDPI and ACS Style**

He, Y.; Zhang, Y.; Kuligowski, R.; Cifelli, R.; Kitzmiller, D. Incorporating Satellite Precipitation Estimates into a Radar-Gauge Multi-Sensor Precipitation Estimation Algorithm. *Remote Sens.* **2018**, *10*, 106.
https://doi.org/10.3390/rs10010106

**AMA Style**

He Y, Zhang Y, Kuligowski R, Cifelli R, Kitzmiller D. Incorporating Satellite Precipitation Estimates into a Radar-Gauge Multi-Sensor Precipitation Estimation Algorithm. *Remote Sensing*. 2018; 10(1):106.
https://doi.org/10.3390/rs10010106

**Chicago/Turabian Style**

He, Yuxiang, Yu Zhang, Robert Kuligowski, Robert Cifelli, and David Kitzmiller. 2018. "Incorporating Satellite Precipitation Estimates into a Radar-Gauge Multi-Sensor Precipitation Estimation Algorithm" *Remote Sensing* 10, no. 1: 106.
https://doi.org/10.3390/rs10010106