# Assessing Near Real-Time Satellite Precipitation Products for Flood Simulations at Sub-Daily Scales in a Sparsely Gauged Watershed in Peruvian Andes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}and a mean annual discharge of 130 m

^{3}/s. Its relief is predominantly rugged, characteristic of the Cordillera Vilcanota, with a mean slope and elevation of 15.6° and 4176 masl, respectively. Annual precipitation ranges from 800 to 1000 mm. The Vilcanota basin is located in a transition zone with tropical, sub-, and extratropical climates, a short wet season (November to March), and a long dry period during the rest of the year [28]. The basin continually suffers from floods that severely harm people’s health, private property, and result in large economic losses to the local community and the Cusco region [29]. Therefore, there is an urgent need to implement a monitoring and flood forecasting system in the basin in quasi-real time. However, the low density and short recording times of the current network of rain gauge stations in the basin makes this task difficult [28]. Therefore, the use of estimated hourly satellite precipitation products with fine spatiotemporal resolution is a promising alternative for short-term flood simulations.

#### 2.2. Ground-Based Data

#### 2.3. Satellite Precipitation Products (SPPs)

## 3. Methods

#### 3.1. Statistical Evaluation of SPPs against Rain Gauges

#### 3.2. Bias Correction of SPPs

#### 3.3. Semi-Distributed GR4H Model

#### 3.3.1. Model Description and Setup

_{HR}) and potential evapotranspiration (ETP

_{HR}) data for each sub-basin. The mean P

_{HR}of each sub-basin was calculated for each time interval as the mean of the bias-corrected SPP grids, while the ETP

_{HR}was estimated by the Hargreaves–Samani method [38] from the disaggregation of the daily climatic data (1981–2016) of the mean air temperature from the Peruvian Interpolated data of SENAMHI’s Climatological and hydrological Observations (PISCO) product. The PISCO product is a gridded database of precipitation and temperature that coverage throughout the Peruvian territory for the period 1981-2016. The temperature product is generated by applying geostatistical techniques to combining air temperature data from MODIS images and observations from weather stations nationwide and is available online: http://iridl.ldeo.columbia.edu/SOURCES/.SENAMHI/.HSR/.PISCO/ (accessed on 7 April 2019). Hydrological modeling was performed using the “airGR” package [39] in R language.

#### 3.3.2. Model Calibration, Validation, and Verification

## 4. Results

#### 4.1. Validation of SPP against Rain Gauges

#### 4.2. Evaluation of SPP’s Hydrological Performance Using GR4H Model

^{3}/s in the calibration to 34.593–38.343 m3/s in the validation. During the evaluation of the full simulation period, the results of the GR4H model forced by HE’, IMERG-E’, and CMORPH’ produce underestimations of runoff on the order of −7.8%, −4.2%, and −0.7%, respectively, while with GSMaP-NRT’, overestimates of 2.4% are produced. In terms of RMSE, the error of the simulations ranges between 28.052–30.338 m

^{3}/s. Regarding the KGE index, the highest performance is achieved with GSMaP-NRT’ (KGE = 0.843), but there are values close to 0.812, 0.783, and 0.777 with CMORPH’, IMERG-E’, and HE’, respectively. In the case of MARE, the simulations with CMORPH’ (0.743) slightly exceed those of IMERG-E’ (0.731), followed by HE’ (0.703) and GSMaP-NRT’ (0.680). On the other hand, when evaluating the ensemble mean in the total period, high values of KGE and MARE of 0.816 and 0.730 are observed, respectively, added to a BIAS of −2.6% and an RMSE of 28.052 m

^{3}/s.

^{2}and RMSE) account for the degree of fit of the observations and simulations at the different time scales. In all cases, the SRL models indicate a slight underestimation of the observed flow rates; however, at the hourly and daily time scale, moderate underestimations by more than 350 m3/s in flow rates are seen. At the hourly scale, the highest R

^{2}and lowest RMSE are obtained in the simulations with GSMaP-NRT’ (R

^{2}= 0.709 and RMSE = 27.319 m

^{3}/s). This pattern continues at the daily scale (R

^{2}= 0.748 and RMSE = 25.725 m

^{3}/s); however, at the monthly scale, the simulation with CMORPH’ (R

^{2}= 0.766 and RMSE = 21.860 m

^{3}/s) slightly exceeds GSMaP-NRT’ (R

^{2}= 0.760 and RMSE = 22.128 m

^{3}/s). The results using the mean of the simulation datasets always show higher R

^{2}(hourly = 0.718, daily = 0.730 and monthly = 0.763) and lower RMSE (hourly = 27.776 m

^{3}/s, daily = 26.619 m

^{3}/s and monthly = 21.970 m

^{3}/s) with respect to IMERG-E’ e HE’; and in some cases, better than CMORPH’ (daily and monthly) and GSMaP-NRT’ (monthly).

## 5. Discussion

^{2}) makes it difficult to verify and validate the spatial patterns of hourly precipitation and would increase the uncertainty in the bias-corrected SPP. Therefore, the correction applied in this work also considered the stations located outside the basin; however, in the near future, this work would incorporate evaluating the effect of different bias-correcting methods on reducing the uncertainty of the SPPs.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Huggel, C.; Raissig, A.; Rohrer, M.; Romero, G.; Diaz, A.; Salzmann, N. How useful and reliable are disaster databases in the context of climate and global change? A comparative case study analysis in Peru. Nat. Hazards Earth Syst. Sci.
**2015**, 15, 475–485. [Google Scholar] [CrossRef] [Green Version] - Min, X.; Yang, C.; Dong, N. Merging Satellite and Gauge Rainfalls for Flood Forecasting of Two Catchments Under Different Climate Conditions. Water
**2020**, 12, 802. [Google Scholar] [CrossRef] [Green Version] - INDECI. Evaluación Del Impacto Socio-Económico de la Temporada de Lluvias 2010 en la Región Cusco; Instituto Nacional de Defensa Civil del Perú: Lima, Peru, 2012; ISBN 201201354.
- Belabid, N.; Zhao, F.; Brocca, L.; Huang, Y.; Tan, Y. Near-Real-Time Flood Forecasting Based on Satellite Precipitation Products. Remote Sens.
**2019**, 11, 252. [Google Scholar] [CrossRef] [Green Version] - Wu, H.; Adler, R.F.; Tian, Y.; Huffman, G.J.; Li, H.; Wang, J. Real-time global flood estimation using satellite-based precipitation and a coupled land surface and routing model. Water Resour. Res.
**2014**, 50, 2693–2717. [Google Scholar] [CrossRef] [Green Version] - Li, L.; Hong, Y.; Wang, J.; Adler, R.F.; Policelli, F.S.; Habib, S.; Irwn, D.; Korme, T.; Okello, L. Evaluation of the real-time TRMM-based multi-satellite precipitation analysis for an operational flood prediction system in Nzoia Basin, Lake Victoria, Africa. Nat. Hazards
**2009**, 50, 109–123. [Google Scholar] [CrossRef] - Aybar, C.; Fernández, C.; Huerta, A.; Lavado, W.; Vega, F.; Felipe-Obando, O. Construction of a high-resolution gridded rainfall dataset for Peru from 1981 to the present day. Hydrol. Sci. J.
**2020**, 65, 770–785. [Google Scholar] [CrossRef] - Thiemig, V.; Rojas, R.; Zambrano-Bigiarini, M.; De Roo, A. Hydrological evaluation of satellite-based rainfall estimates over the Volta and Baro-Akobo Basin. J. Hydrol.
**2013**, 499, 324–338. [Google Scholar] [CrossRef] - Ma, Z.; Tan, X.; Yang, Y.; Chen, X.; Kan, G.; Ji, X.; Lu, H.; Long, J.; Cui, Y.; Hong, Y. The First Comparisons of IMERG and the Downscaled Results Based on IMERG in Hydrological Utility over the Ganjiang River Basin. Water
**2018**, 10, 1392. [Google Scholar] [CrossRef] [Green Version] - Maggioni, V.; Massari, C. On the performance of satellite precipitation products in riverine flood modeling: A review. J. Hydrol.
**2018**, 558, 214–224. [Google Scholar] [CrossRef] - Andres, N.; Vegas Galdos, F.; Lavado Casimiro, W.S.; Zappa, M. Water resources and climate change impact modelling on a daily time scale in the Peruvian Andes. Hydrol. Sci. J.
**2014**, 59, 2043–2059. [Google Scholar] [CrossRef] [Green Version] - Zulkafli, Z.; Buytaert, W.; Onof, C.; Manz, B.; Tarnavsky, E.; Lavado, W.; Guyot, J.-L. A Comparative Performance Analysis of TRMM 3B42 (TMPA) Versions 6 and 7 for Hydrological Applications over Andean–Amazon River Basins. J. Hydrometeorol.
**2014**, 15, 581–592. [Google Scholar] [CrossRef] - Zubieta, R.; Getirana, A.; Espinoza, J.C.; Lavado-Casimiro, W.; Aragon, L. Hydrological modeling of the Peruvian-Ecuadorian Amazon Basin using GPM-IMERG satellite-based precipitation dataset. Hydrol. Earth Syst. Sci.
**2017**, 21, 3543–3555. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Satgé, F.; Bonnet, M.-P.; Gosset, M.; Molina, J.; Lima, W.H.Y.; Zolá, R.P.; Timouk, F.; Garnier, J. Assessment of satellite rainfall products over the Andean plateau. Atmos. Res.
**2016**, 167, 1–14. [Google Scholar] [CrossRef] - Rossa, A.; Haase, G.; Keil, C.; Alberoni, P.; Ballard, S.; Bech, J.; Germann, U.; Pfeifer, M.; Salonen, K. Propagation of uncertainty from observing systems into NWP: COST-731 Working Group 1. Atmos. Sci. Lett.
**2010**, 11, 145–152. [Google Scholar] [CrossRef] [Green Version] - Shrestha, P.K.; Shrestha, S.; Ninsawat, S. How significant is sub-daily variability of rainfall for hydrological modelling of floods? A satellite based approach to sub-daily downscaling of gauged rainfall. Meteorol. Appl.
**2019**, 26, 288–299. [Google Scholar] [CrossRef] [Green Version] - Mei, Y.; Nikolopoulos, E.I.; Anagnostou, E.N.; Zoccatelli, D.; Borga, M. Error Analysis of Satellite Precipitation-Driven Modeling of Flood Events in Complex Alpine Terrain. Remote Sens.
**2016**, 8, 293. [Google Scholar] [CrossRef] [Green Version] - Hong, Y.; Adler, R.F.; Negri, A.; Huffman, G.J. Flood and landslide applications of near real-time satellite rainfall products. Nat. Hazards
**2007**, 43, 285–294. [Google Scholar] [CrossRef] [Green Version] - Brocca, L.; Massari, C.; Pellarin, T.; Filippucci, P.; Ciabatta, L.; Camici, S.; Kerr, Y.H.; Fernández-Prieto, D. River flow prediction in data scarce regions: Soil moisture integrated satellite rainfall products outperform rain gauge observations in West Africa. Sci. Rep.
**2020**, 10, 12517. [Google Scholar] [CrossRef] [PubMed] - Soo, E.Z.X.; Jaafar, W.Z.W.; Lai, S.H.; Othman, F.; Elshafie, A.; Islam, T.; Srivastava, P.; Hadi, H.S.O. Evaluation of bias-adjusted satellite precipitation estimations for extreme flood events in Langat river basin, Malaysia. Hydrol. Res.
**2020**, 51, 105–126. [Google Scholar] [CrossRef] - Habib, E.; Haile, A.T.; Sazib, N.; Zhang, Y.; Rientjes, T. Effect of Bias Correction of Satellite-Rainfall Estimates on Runoff Simulations at the Source of the Upper Blue Nile. Remote Sens.
**2014**, 6, 6688–6708. [Google Scholar] [CrossRef] [Green Version] - Yeditha, P.K.; Kasi, V.; Rathinasamy, M.; Agarwal, A. Forecasting of extreme flood events using different satellite precipitation products and wavelet-based machine learning methods. Chaos
**2020**, 30, 063115. [Google Scholar] [CrossRef] - Moine, N. Le Bassin Versant De Surface Vu Par le Souterrain: Une voie D’amélioration Des Performances Et Du Réalisme Des Modèles Pluie-Débit? Ph.D. Thesis, Université Pierre et Marie, Paris, France, November 2008. [Google Scholar]
- Caligiuri, S.; Camera, C.; Masetti, M.; Bruggeman, A.; Sofokleous, I. Testing GR4H Model Parameter Transferability for Extreme Events in Cyprus: Evaluation of a Cluster Analysis Approach. Proceedings of the Geophysical Research Abstracts, EGU General Assembly Conference Abstracts. Vienna, Austria, 7–12 April 2019; Volume 21. Available online: search.ebscohost.com (accessed on 16 January 2020).
- Basri, H.; Sidek, L.M.; Razad, A.Z.; Pokhrel, P. Hydrological Modelling of Surface Runoff for Temengor Reservoir Using GR4H Model. Int. J. Civ. Eng. Technol.
**2019**, 10, 29–40. [Google Scholar] - Ficchì, A.; Perrin, C.; Andréassian, V. Hydrological modelling at multiple sub-daily time steps: Model improvement via flux-matching. J. Hydrol.
**2019**, 575, 1308–1327. [Google Scholar] [CrossRef] - Lavado Casimiro, W.S.; Labat, D.; Guyot, J.L.; Ardoin-Bardin, S. Assessment of climate change impacts on the hydrology of the Peruvian Amazon-Andes basin. Hydrol. Process.
**2011**, 25, 3721–3734. [Google Scholar] [CrossRef] - Salzmann, N.; Huggel, C.; Rohrer, M.; Silverio, W.; Mark, B.G.; Burns, P.; Portocarrero, C. Glacier changes and climate trends derived from multiple sources in the data scarce Cordillera Vilcanota region, southern Peruvian Andes. Cryosphere
**2013**, 7, 103–118. [Google Scholar] [CrossRef] [Green Version] - Drenkhan, F.; Carey, M.; Huggel, C.; Seidel, J.; Oré, M.T. The changing water cycle: Climatic and socioeconomic drivers of water-related changes in the Andes of Peru. Wiley Interdiscip. Rev. Water
**2015**, 2, 715–733. [Google Scholar] [CrossRef] - Huffman, G.J.; Bolvin, D.T.; Nelkin, E.J.; Tan, J. Integrated Multi-satellitE Retrievals for GPM (IMERG) technical documentation. NASA/GSFC Code
**2015**, 612, 47. [Google Scholar] - Kubota, T.; Aonashi, K.; Ushio, T.; Shige, S.; Takayabu, Y.N.; Kachi, M.; Arai, Y.; Tashima, T.; Masaki, T.; Kawamoto, N.; et al. Global Satellite Mapping of Precipitation (GSMaP) Products in the GPM Era. In Satellite Precipitation Measurement: Volume 1; Levizzani, V., Kidd, C., Kirschbaum, D.B., Kummerow, C.D., Nakamura, K., Turk, F.J., Eds.; Springer International Publishing: Cham, Switzerland, 2020; pp. 355–373. ISBN 9783030245689. [Google Scholar]
- Joyce, R.J.; Janowiak, J.E.; Arkin, P.A.; Xie, P. A Method that Produces Global Precipitation Estimates from Passive Microwave and Infrared Data at High Spatial and Temporal Resolution. J. Hydrometeorol.
**2004**, 5, 487–503. [Google Scholar] [CrossRef] - Scofield, R.A.; Kuligowski, R.J. Status and Outlook of Operational Satellite Precipitation Algorithms for Extreme-Precipitation Events. Weather Forecast
**2003**, 18, 1037–1051. [Google Scholar] [CrossRef] [Green Version] - Dinku, T.; Hailemariam, K.; Maidment, R.; Tarnavsky, E.; Connor, S. Combined use of satellite estimates and rain gauge observations to generate high-quality historical rainfall time series over Ethiopia. Int. J. Climatol.
**2014**, 34, 2489–2504. [Google Scholar] [CrossRef] [Green Version] - Perrin, C.; Michel, C.; Andréassian, V. Improvement of a parsimonious model for streamflow simulation. J. Hydrol.
**2003**, 279, 275–289. [Google Scholar] [CrossRef] - Li, Y.; Ryu, D.; Western, A.W.; Wang, Q.J. Assimilation of stream discharge for flood forecasting: The benefits of accounting for routing time lags. Water Resour. Res.
**2013**, 49, 1887–1900. [Google Scholar] [CrossRef] - Cunge, J.A. On The Subject Of A Flood Propagation Computation Method (Musklngum Method). J. Hydraul. Res.
**1969**, 7, 205–230. [Google Scholar] [CrossRef] - Hargreaves, G.H.; Samani, Z.A. Reference Crop Evapotranspiration from Ambient Air Temperature. In Proceedings of the American Society of Agricultural Engineers Meeting (Paper 85-2517), Chicago, IL, USA, 17 December 1985. [Google Scholar]
- Coron, L.; Thirel, G.; Delaigue, O.; Perrin, C.; Andréassian, V. The suite of lumped GR hydrological models in an R package. Environ. Model. Softw.
**2017**, 94, 166–171. [Google Scholar] [CrossRef] - Duan, Q.Y.; Gupta, V.K.; Sorooshian, S. Effective and Efficient Global Minimization. J. Optim. Theory Appl.
**1993**. [Google Scholar] [CrossRef] - Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol.
**2009**, 377, 80–91. [Google Scholar] [CrossRef] [Green Version] - Dawson, C.W.; Abrahart, R.J.; See, L.M. HydroTest: A web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ. Model. Softw.
**2007**, 22, 1034–1052. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Gupta, H.V. Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res.
**2007**, 43, 160. [Google Scholar] [CrossRef] - Yuan, F.; Zhang, L.; Soe, K.M.W.; Ren, L.; Zhao, C.; Zhu, Y.; Jiang, S.; Liu, Y. Applications of TRMM- and GPM-Era Multiple-Satellite Precipitation Products for Flood Simulations at Sub-Daily Scales in a Sparsely Gauged Watershed in Myanmar. Remote Sens.
**2019**, 11, 140. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Location of the Vilcanota river basin at INT gauge-station. Pluviometric and hydrometric network at the study domain.

**Figure 2.**The structure of the GR4H model, taken from [36].

**Figure 3.**Seasonal variability of the (

**a**) relative error (RE), (

**b**) coefficient of correlation (R), (

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

**d**) mean absolute error (MAE) metrics calculated using hourly data for all pluviometric stations in each monthly time-window.

**Figure 4.**Correlation between the diurnal cycle of rainfall from 15 rain-gauge stations and estimates from (

**a**) Integrated Multi-satellite Retrievals for GPM–Early (IMERG-E), (

**b**) Global Satellite Mapping of Precipitation–Near Real-Time (GSMaP-NRT), (

**c**) Climate Prediction Center Morphing Method (CMOPRH), and (

**d**) HydroEstimator (HE); considering only rainy days upper than 15 mm/day from the wet period (November to April).

**Figure 5.**Observed and simulated hourly discharges at PIS gauge-station during (

**a**–

**e**) calibration and (

**f**–

**j**) validation periods, using four SPPs with bias correction and an ensemble mean streamflow scenario.

**Figure 6.**(

**a**) KGE, (

**b**) MARE, (

**c**) PBIAS, and (

**d**) RMSE values for evaluating the hydrological performance of the GR4H model at PIS gauge-station during calibration, validation, and total period; using four SPPs with bias correction and an ensemble mean streamflow scenario.

**Figure 7.**Scatter plot of (

**a**–

**e**) hourly, (

**f**–

**j**) daily, and (

**k**–

**o**) monthly observed and simulated discharges at PIS gauge-stations; using four SPPs with bias correction and an ensemble mean streamflow scenario.

**Figure 8.**Observed and simulated hourly discharges at (

**a**–

**e**) SAL, (

**f**–

**j**) CHI, and (

**k**–

**o**) INT gauge-stations; using four SPPs with bias correction and an ensemble mean streamflow scenario.

**Figure 9.**(

**a**) Kling–Gupta efficiency (KGE), (

**b**) Mean Absolute Relative Error (MARE), (

**c**) Percentage Bias (PBIAS), and (

**d**) RMSE values for evaluating the hydrological performance of the GR4H model at SAL, CHI, and INT gauge-stations during the verification period; using four SPPs with bias correction and an ensemble mean streamflow scenario.

**Figure 10.**Example of simulated discharges in 11 Vilcanota’s river streams for the 22:00 and 02:00 hours from 6 and 7 February 2020, respectively; using four SPPs as meteorological forcing data of the GR4H model.

N° Subbasin | Station * | Area [km ^{2}] | Mean Elevation [masl] | Mean Slope [°] | Length [km] |
---|---|---|---|---|---|

1 | SAL | 2042 | 4753 | 11 | 45 |

2 | - | 1743 | 4167 | 13 | 41 |

3 | - | 290 | 4317 | 19 | 29 |

4 | - | 686 | 4635 | 18 | 17 |

5 | - | 42 | 3766 | 17 | 9 |

6 | - | 1192 | 4010 | 17 | 58 |

7 | PIS | 906 | 3725 | 17 | 3 |

8 | - | 1113 | 3858 | 20 | 59 |

9 | - | 766 | 3733 | 13 | 13 |

10 | CHI | 401 | 4091 | 23 | 17 |

11 | INT | 411 | 3791 | 27 | 7 |

Type | Station | Abrev. | Longitude [ºW] | Latitude [ºS] | Elevation [masl] | Coverage [%] |
---|---|---|---|---|---|---|

Pluviometric | Acjanaco Gore | AGR | 71.62 | 13.20 | 3466.11 | 85.63 |

Calca | CAL | 71.96 | 13.33 | 2921.24 | 94.01 | |

Casaccancha | CAS | 72.30 | 13.99 | 4033.16 | 84.62 | |

Huayllabamba | HUA | 72.45 | 13.27 | 2976.55 | 86.86 | |

Intihuatana H | INH | 72.56 | 13.17 | 1774.23 | 63.86 | |

Intihuatana M | INM | 72.56 | 13.17 | 1778.23 | 89.81 | |

Machupicchu | MAC | 72.55 | 13.18 | 2399.80 | 68.18 | |

Marcapata Gore | MAR | 70.90 | 13.50 | 1792.76 | 83.05 | |

Qorihuayrachina | QOR | 72.43 | 13.22 | 2517.25 | 96.41 | |

Salcca | SAC | 71.23 | 14.17 | 3920.10 | 87.75 | |

San Pablo | SPB | 72.62 | 13.03 | 1228.11 | 90.45 | |

Santa Teresa | STR | 72.59 | 13.13 | 1491.43 | 64.97 | |

Santo Tomas | STM | 72.10 | 14.45 | 3665.48 | 95.58 | |

Sicuani | SIC | 71.24 | 14.24 | 3534.95 | 99.53 | |

Soraypampa | SOR | 72.57 | 13.40 | 3842.32 | 97.78 | |

Hydrometric | Intihuatana km105 | INT | 72.53 | 13.18 | 1774.72 | 12.01 |

Chilca | CHI | 72.34 | 13.22 | 2475.28 | 36.57 | |

Pisac | PIS | 71.84 | 13.43 | 2791.65 | 98.33 | |

Salcca | SAL | 71.23 | 14.17 | 3918.71 | 31.39 |

Product | Version | Short Name | Institution | Resolution | Latency |
---|---|---|---|---|---|

Integrated Multi-satellite Retrievals for GPM | Early V06B | IMERG-E | NASA | 0.1º × 0.1º | 5 h |

Global Satellite Mapping of Precipitation | Near Real-Time V06 | GSMaP-NRT | JAXXA | 0.1º × 0.1º | 5 h |

Climate Prediction Center Morphing Method | v0.x & v1.0 | CMORPH | NOAA/CPC | 0.08º ×0.08º | 8 h |

HydroEstimator | - | HE | NOAA/NESDIS | 0.05º ×0.05º | 3 h |

**Table 4.**Statistical metrics and their corresponding equations used for evaluating the meteorological performance of SPPs.

Statistical Metric | Unit | Equation | Optimal Value |
---|---|---|---|

Relative Error (RE) | - | $RE=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({S}_{i}-{G}_{i}\right)}{{{\displaystyle \sum}}_{i=1}^{n}{G}_{i}}$ | 0 |

Coefficient of Correlation (R) | - | $R=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left[\left({S}_{i}-\overline{S}\right)\left({G}_{i}-\overline{G}\right)\right]}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({S}_{i}-\overline{S}\right)}^{2}}\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({G}_{i}-\overline{G}\right)}^{2}}}$ | 1 |

Root Mean Square Error (RMSE) | mm/h | $RMSE=\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left({S}_{i}-{G}_{i}\right)}^{2}}$ | 0 |

Mean Absolute Error (MAE) | mm/h | $MAE=\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left|{S}_{i}-{G}_{i}\right|$ | 0 |

_{i}, precipitation from rain gauges; S

_{i}, precipitation estimates from satellite products.

**Table 5.**Statistical metrics and their corresponding equations used for evaluating the hydrological performance of SPPs.

Statistical Metric | Unit | Equation | Optimal Value |
---|---|---|---|

Kling–Gupta efficiency (KGE) | - | $KGE=1-\sqrt{{\left(r-1\right)}^{2}+{\left(\alpha -1\right)}^{2}+{\left(\beta -1\right)}^{2}}$$\phantom{\rule{0ex}{0ex}}$$\phantom{\rule{0ex}{0ex}}$ | 1 |

Mean Absolute Relative Error (MARE) | - | $MARE=1-\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\frac{\left|{X}_{i}-{O}_{i}\right|}{{O}_{i}}$ | 1 |

Percentage Bias (PBIAS) | % | $PBIAS=100\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({X}_{i}-{O}_{i}\right)}{{{\displaystyle \sum}}_{i=1}^{n}{O}_{i}}$ | 0 |

Root Mean Square Error (RMSE) | m^{3}/s | $RMSE=\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left({X}_{i}-{O}_{i}\right)}^{2}}$ | 0 |

_{i}, observed streamflow; X

_{i}, simulated streamflow.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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**

Llauca, H.; Lavado-Casimiro, W.; León, K.; Jimenez, J.; Traverso, K.; Rau, P.
Assessing Near Real-Time Satellite Precipitation Products for Flood Simulations at Sub-Daily Scales in a Sparsely Gauged Watershed in Peruvian Andes. *Remote Sens.* **2021**, *13*, 826.
https://doi.org/10.3390/rs13040826

**AMA Style**

Llauca H, Lavado-Casimiro W, León K, Jimenez J, Traverso K, Rau P.
Assessing Near Real-Time Satellite Precipitation Products for Flood Simulations at Sub-Daily Scales in a Sparsely Gauged Watershed in Peruvian Andes. *Remote Sensing*. 2021; 13(4):826.
https://doi.org/10.3390/rs13040826

**Chicago/Turabian Style**

Llauca, Harold, Waldo Lavado-Casimiro, Karen León, Juan Jimenez, Kevin Traverso, and Pedro Rau.
2021. "Assessing Near Real-Time Satellite Precipitation Products for Flood Simulations at Sub-Daily Scales in a Sparsely Gauged Watershed in Peruvian Andes" *Remote Sensing* 13, no. 4: 826.
https://doi.org/10.3390/rs13040826