# Probabilistic Precipitation Estimation with a Satellite Product

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## Abstract

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## 1. Introduction

## 2. Data

#### 2.1. Satellite-Based Precipitation

#### 2.2. Gauge-Based Precipitation

## 3. Analysis Methods

#### 3.1. General Approach

#### 3.2. Precipitation Amount Modeling

#### 3.3. Precipitation Occurrence Modeling

## 4. Results

**Figure 1.**Mean precipitation (mm·d${}^{-1}$) over 2001–2007 from the gauge-based APHRODITE product and from the satellite-based 3B42RT and 3B42 products for Nepal and vicinity.

**Figure 2.**Rank correlation of precipitation of the satellite-based 3B42RT and 3B42 products as a function of aggregation timescales: (

**a**) Correlation with the gauge-based APHRODITE product for 2001–2007 over aggregation timescales from 1 to 90 days; (

**b**) Correlation with automated weather stations for 2013–2014 over aggregation timescales from 3 hours to 90 days.

**Figure 3.**Mean precipitation diurnal cycle, 2013–2014, averaged across 3 stations in Nepal (5-minute values and a Fourier series smoothed fit are shown) and for satellite products with 3-hour resolution subsampled at the same grid points. Nepal Standard Time is 5:45 hours ahead of Universal Time.

**Figure 4.**Rank correlation of daily precipitation between the satellite-based 3B42RT product and APHRODITE as a function of both station data coverage (expressed as the number of 0.05°subcells in a 0.25°grid cell with precipitation gauges) and satellite data coverage (availability of higher-quality microwave (MW) sounder precipitation estimates for at least 4 of the daily 3-hour windows versus only lower-quality estimates based on infrared (IR) imagery). Error bars are 95% confidence intervals for the correlation coefficients.

**Figure 5.**Empirical probability density for APHRODITE daily precipitation amount at the 0.25°grid scale (conditional on occurrence) for the region 26°–31°N, 79°–89°E and for two time periods, compared with a hyperexponential distribution fit only to the 1981–2000 data.

**Figure 6.**Example probability density functions for daily precipitation amount at the grid point containing Kathmandu, Nepal (27.7°N, 85.3°E) for a heavy-rainfall monsoon day (2 September 2013): background PDF, climatology PDF taking into account location and season, and probabilities that incorporate data from the satellite precipitation product 3B42RT.

**Figure 7.**Example maps of regional precipitation for 2 September 2013: (

**a**) 3B42RT amount (mm); (

**b**) climatological mean (mm); (

**c**) probability of precipitation > 10 mm based on combined climatology + satellite model; (

**d**) probability of precipitation > 50 mm.

**Table 1.**Skill measures for probabilistic daily precipitation estimates relative to APHRODITE values averaged over Nepal and vicinity, 2001–2007. The models are B = baseline (same probability distribution for all locations and days), S = satellite (incorporates precipitation from 3B42RT), C = climatology (incorporates past patterns of precipitation location and seasonality), Comb = combined (both satellite and climatology predictors). NLL = negative log likelihood, RMSE = root mean square error. RMSE is in transformed precipitation units, while NLL is in bits. Smaller values denote more skill. Precipitation amount skill measures are averaged only over cases with nonzero precipitation in APHRODITE.

B | S | C | Comb | |
---|---|---|---|---|

Precipitation amount: | ||||

RMSE | 0.957 | 0.839 | 0.776 | 0.742 |

NLL | 2.064 | 1.875 | 1.759 | 1.715 |

Precipitation occurrence: | ||||

RMSE | 0.486 | 0.433 | 0.382 | 0.364 |

NLL | 0.961 | 0.776 | 0.641 | 0.588 |

**Figure 8.**Frequency of precipitation above different threshold values ((

**a**) 1; (

**b**) 10; (

**c**) 50 mm/day) as a function of modeled probability (combined satellite and climatology model). 1-1 lines indicating an ideally calibrated model are also shown.

## 5. Discussion and Conclusions

## Acknowledgements

## Author Contributions

## Appendix: Fitting a Hyperexponential Distribution to Data

## Conflicts of Interest

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**MDPI and ACS Style**

Krakauer, N.Y.; Pradhanang, S.M.; Panthi, J.; Lakhankar, T.; Jha, A.K.
Probabilistic Precipitation Estimation with a Satellite Product. *Climate* **2015**, *3*, 329-348.
https://doi.org/10.3390/cli3020329

**AMA Style**

Krakauer NY, Pradhanang SM, Panthi J, Lakhankar T, Jha AK.
Probabilistic Precipitation Estimation with a Satellite Product. *Climate*. 2015; 3(2):329-348.
https://doi.org/10.3390/cli3020329

**Chicago/Turabian Style**

Krakauer, Nir Y., Soni M. Pradhanang, Jeeban Panthi, Tarendra Lakhankar, and Ajay K. Jha.
2015. "Probabilistic Precipitation Estimation with a Satellite Product" *Climate* 3, no. 2: 329-348.
https://doi.org/10.3390/cli3020329