# Subdaily Rainfall Estimation through Daily Rainfall Downscaling Using Random Forests in Spain

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Information Sources

## 3. Methodology

#### 3.1. Beuchat’s Model

#### 3.2. RFB Model

#### 3.3. Model Evaluation

#### 3.4. Synthetic Rainfall Generation

## 4. Results

#### 4.1. Model Comparison

#### 4.2. Performance Analysis of RFB

#### 4.3. Performance of Simulated Rainfall

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Smith, J.; Baeck, M.; Meierdiercks, K.; Miller, A.; Krajewski, W. Radar rainfall estimation for flash flood forecasting in small urban watersheds. Adv. Water Resour.
**2007**, 30, 2087–2097. [Google Scholar] [CrossRef] - Michaud, J.; Sorooshian, S. Effect of rainfall sampling errors on simulations of desert flash floods. Water Resour. Res.
**1994**, 30, 2765–2775. [Google Scholar] [CrossRef] - Kun, Y.; Giuliano, D.B.; Florian, P. Flood Hazard Mapping in Data-Scarce Areas. In Global Flood Hazard; Schumann, G.J., Bates, P.D., Apel, H., Aronica, G.T., Eds.; American Geophysical Union: Washington, DC, USA, 2018. [Google Scholar]
- Cáceres, M.D.; Martin-StPaul, N.; Turco, M.; Cabon, A.; Granda, V. Estimating daily meteorological data and downscaling climate models over landscapes. Environ. Model. Softw.
**2018**, 108, 186–196. [Google Scholar] [CrossRef] - Krajewski, W.; Smith, J. Radar hydrology: Rainfall estimation. Adv. Water Resour.
**2002**, 25, 1387–1394. [Google Scholar] [CrossRef] - Noor, M.; Ismail, T.; Chung, E.S.; Shahid, S.; Sung, J.H. Uncertainty in Rainfall Intensity Duration Frequency Curves of Peninsular Malaysia under Changing Climate Scenarios. Water
**2018**, 10, 1750. [Google Scholar] [CrossRef] - Pui, A.; Sharma, A.; Mehrotra, R.; Sivakumar, B.; Jeremiah, E. A comparison of alternatives for daily to sub-daily rainfall disaggregation. J. Hydrol.
**2012**, 470–471, 138–157. [Google Scholar] [CrossRef] - Huffman, G.; Adler, R.; Bolvin, D.; Nelkin, E. The TRMM Multi-Satellite Precipitation Analysis (TMPA). In Satellite Rainfall Applications for Surface Hydrology; Gebremichael, M., Hossain, F., Eds.; Springer: Dordrecht, The Netherlands, 2010. [Google Scholar]
- Pfeifroth, U.; Mueller, R.; Ahrens, B. Evaluation of satellite-based and reanalysis precipitation data in the tropical pacific. J. Appl. Meteorol. Climatol.
**2013**, 52, 634–644. [Google Scholar] [CrossRef] - Austin, G.; Seed, A. Special issue on the hydrological applications of weather radar—Guest editors’ preface. Atmos. Sci. Lett.
**2005**, 6, 1. [Google Scholar] [CrossRef] - Kim, J.E.; Joan Alexander, M. Tropical precipitation variability and convectively coupled equatorial waves on submonthly time scales in reanalyses and TRMM. J. Clim.
**2013**, 26, 3013–3030. [Google Scholar] [CrossRef] - Del Jesus, M.; Rinaldo, A.; Rodríguez-Iturbe, I. Point rainfall statistics for ecohydrological analyses derived from satellite integrated rainfall measurements. Water Resour. Res.
**2015**, 51, 2974–2985. [Google Scholar] [CrossRef][Green Version] - Hershenhorn, J.; Woolhiser, D. Disaggregation of daily rainfall. J. Hydrol.
**1987**, 95, 299–322. [Google Scholar] [CrossRef][Green Version] - Glasbey, C.; Cooper, G.; McGechan, M. Disaggregation of daily rainfall by conditional simulation from a point-process model. J. Hydrol.
**1995**, 165, 1–9. [Google Scholar] [CrossRef] - Cowpertwait, P. Further developments of the neyman-scott clustered point process for modeling rainfall. Water Resour. Res.
**1991**, 27, 1431–1438. [Google Scholar] [CrossRef] - Burton, A.; Kilsby, C.; Fowler, H.; Cowpertwait, P.; O’Connell, P. RainSim: A spatial–temporal stochastic rainfall modelling system. Environ. Model. Softw.
**2008**, 23, 1356–1369. [Google Scholar] [CrossRef] - Bennett, J.C.; Robertson, D.E.; Ward, P.G.; Hapuarachchi, H.P.; Wang, Q. Calibrating hourly rainfall-runoff models with daily forcings for streamflow forecasting applications in meso-scale catchments. Environ. Model. Softw.
**2016**, 76, 20–36. [Google Scholar] [CrossRef][Green Version] - Kim, S.; Singh, V.P. Spatial Disaggregation of Areal Rainfall Using Two Different Artificial Neural Networks Models. Water
**2015**, 7, 2707–2727. [Google Scholar] [CrossRef][Green Version] - Li, X.; Meshgi, A.; Wang, X.; Zhang, J.; Tay, S.; Pijcke, G.; Manocha, N.; Ong, M.; Nguyen, M.; Babovic, V. Three resampling approaches based on method of fragments for daily-to-subdaily precipitation disaggregation. Int. J. Climatol.
**2018**, 38, e1119–e1138. [Google Scholar] [CrossRef] - Rodriguez-Iturbe, I.; Eagleson, P. Mathematical models of rainstorm events in space and time. Water Resour. Res.
**1987**, 23, 181–190. [Google Scholar] [CrossRef] - Cowpertwait, P. A spatial-temporal point process model of rainfall for the Thames catchment, UK. J. Hydrol.
**2006**, 330, 586–595. [Google Scholar] [CrossRef] - Gupta, V.; Waymire, E. A statistical analysis of mesoscale rainfall as a random cascade. J. Appl. Meteorol.
**1993**, 32, 251–267. [Google Scholar] [CrossRef] - Sharma, A.; Srikanthan, R. Continuous Rainfall Simulation: A Nonparametric Alternative. In Proceedings of the 30th Hydrology and Water Resources Symposium, Launceston, Tasmania, 4–7 December 2006. [Google Scholar]
- Lu, Y.; Qin, X. Multisite rainfall downscaling and disaggregation in a tropical urban area. J. Hydrol.
**2014**, 509, 55–65. [Google Scholar] [CrossRef] - Cowpertwait, P.; Kilsby, C.; O’Connell, P. A space-time Neyman-Scott model of rainfall: Empirical analysis of extremes. Water Resour. Res.
**2002**, 38, 6. [Google Scholar] [CrossRef] - Burton, A.; Fowler, H.; Blenkinsop, S.; Kilsby, C. Downscaling transient climate change using a Neyman-Scott Rectangular Pulses stochastic rainfall model. J. Hydrol.
**2010**, 381, 18–32. [Google Scholar] [CrossRef] - Cowpertwait, P.; O’Connell, P.; Metcalfe, A.; Mawdsley, J. Stochastic point process modelling of rainfall. II. Regionalisation and disaggregation. J. Hydrol.
**1996**, 175, 47–65. [Google Scholar] [CrossRef] - Marani, M.; Zanetti, S. Downscaling rainfall temporal variability. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef][Green Version] - Burlando, P.; Rosso, R. Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation. J. Hydrol.
**1996**, 187, 45–64. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman: San Francisco, CA, USA, 1982; Volume 982. [Google Scholar]
- Beuchat, X.; Schaefli, B.; Soutter, M.; Mermoud, A. Toward a robust method for subdaily rainfall downscaling from daily data. Water Resour. Res.
**2011**, 47. [Google Scholar] [CrossRef][Green Version] - Agencia Estatal de Meteorología (AEMET). Iberian Climate Atlas; Agencia Estatal de Meteorología (España) and Instituto de Meteorología (Portugal): Madrid, Spain, 2011. [Google Scholar]
- Tullot, I.F. El clima de las Islas Canarias. Anuario de Estudios Atlánticos
**1959**, 1, 57–103. [Google Scholar] - Herrera, R.G.; Puyol, D.G.; Martín, E.H.; Presa, L.G.; Rodríguez, P.R. Influence of the North Atlantic oscillation on the Canary Islands precipitation. J. Clim.
**2001**, 14, 3889–3903. [Google Scholar] [CrossRef] - Diez-Sierra, J.; del Jesus, M. A rainfall analysis and forecasting tool. Environ. Model. Softw.
**2017**, 97, 243–258. [Google Scholar] [CrossRef] - Peel, M.C.; Finlayson, B.L.; McMahon, T.A. Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci.
**2007**, 11, 1633–1644. [Google Scholar] [CrossRef] - Herrera, S.; Gutiérrez, J.; Ancell, R.; Pons, M.; Frías, M.; Fernández, J. Development and analysis of a 50-year high-resolution daily gridded precipitation dataset over Spain (Spain02). Int. J. Climatol.
**2012**, 32, 74–85. [Google Scholar] [CrossRef] - AEMET. Available online: http://www.aemet.es/en/portada (accessed on 4 July 2018).
- CMA. Available online: http://hispagua.cedex.es/instituciones/confederaciones/andalucia (accessed on 4 July 2018).
- CHS. Available online: https://www.chsegura.es/chs/index.html (accessed on 4 July 2018).
- CHMS. Available online: https://www.chminosil.es/es/ (accessed on 4 July 2018).
- CHC. Available online: https://www.chcantabrico.es/ (accessed on 4 July 2018).
- CHJ. Available online: https://www.chj.es/es-es/Organismo/Paginas/Organismo.aspx (accessed on 4 July 2018).
- CHE. Available online: http://www.chebro.es/ (accessed on 4 July 2018).
- OAPN. Available online: http://www.mapama.gob.es/es/parques-nacionales-oapn/ (accessed on 4 July 2018).
- SIAR. Available online: http://eportal.mapama.gob.es/websiar/SeleccionParametrosMap.aspx?dst=1 (accessed on 4 July 2018).
- SMC. Available online: http://en.meteocat.gencat.cat/?lang=en (accessed on 4 July 2018).
- Kalnay, E.; Kanamitsu, M.; Kistler, R.; Collins, W.; Deaven, D.; Gandin, L.; Iredell, M.; Saha, S.; White, G.; Woollen, J.; et al. The NCEP/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc.
**1996**, 77, 437–471. [Google Scholar] [CrossRef] - Saha, S.; Moorthi, S.; Pan, H.L.; Wu, X.; Wang, J.; Nadiga, S.; Tripp, P.; Kistler, R.; Woollen, J.; Behringer, D.; et al. The NCEP climate forecast system reanalysis. Bull. Am. Meteorol. Soc.
**2010**, 91, 1015–1057. [Google Scholar] [CrossRef] - Friedman, J.H. Multivariate adaptive regression splines. Ann. Stat.
**1991**, 1–67. [Google Scholar] - Friedman, J.; Roosen, C. An introduction to multivariate adaptive regression splines. Stat. Methods Med. Res.
**1995**, 4, 197–217. [Google Scholar] [CrossRef] [PubMed] - Craven, P.; Wahba, G. Smoothing noisy data with spline functions. Numer. Math.
**1978**, 31, 377–403. [Google Scholar] [CrossRef] - Alizadeh, Z.; Yazdi, J.; Kim, J.H.; Al-Shamiri, A.K. Assessment of Machine Learning Techniques for Monthly Flow Prediction. Water
**2018**, 10, 1676. [Google Scholar] [CrossRef] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] - He, X.; Chaney, N.; Schleiss, M.; Sheffield, J. Spatial downscaling of precipitation using adaptable random forests. Water Resour. Res.
**2016**, 52, 8217–8237. [Google Scholar] [CrossRef][Green Version] - Muñoz, P.; Orellana-Alvear, J.; Willems, P.; Célleri, R. Flash-Flood Forecasting in an Andean Mountain Catchment—Development of a Step-Wise Methodology Based on the Random Forest Algorithm. Water
**2018**, 10, 1519. [Google Scholar] [CrossRef] - Sultana, Z.; Sieg, T.; Kellermann, P.; Müller, M.; Kreibich, H. Assessment of Business Interruption of Flood-Affected Companies Using Random Forests. Water
**2018**, 10, 1049. [Google Scholar] [CrossRef] - Cowpertwait, P.; O’Connell, P.; Metcalfe, A.; Mawdsley, J. Stochastic point process modelling of rainfall. I. Single-site fitting and validation. J. Hydrol.
**1996**, 175, 17–46. [Google Scholar] [CrossRef] - Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Markatou, M.; Tian, H.; Biswas, S.; Hripcsak, G. Analysis of variance of cross-validation estimators of the generalization error. J. Mach. Learn. Res.
**2005**, 6, 1127–1168. [Google Scholar] - Cowpertwait, P. A generalized spatial-temporal model of rainfall based on a clustered point process. Proc. R. Soc. Lond. A
**1995**, 450, 163–175. [Google Scholar] [CrossRef] - Leonard, M.; Lambert, M.; Metcalfe, A.; Cowpertwait, P. A space-time Neyman-Scott rainfall model with defined storm extent. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef][Green Version] - Cowpertwait, P.; Ocio, D.; Collazos, G.; De Cos, O.; Stocker, C. Regionalised spatiotemporal rainfall and temperature models for flood studies in the Basque Country, Spain. Hydrol. Earth Syst. Sci.
**2013**, 17, 479–494. [Google Scholar] [CrossRef][Green Version] - Cowpertwait, P. A Poisson-cluster model of rainfall: High-order moments and extreme values. Proc. R. Soc. A Math. Phys. Eng. Sci.
**1998**, 454, 885–898. [Google Scholar] [CrossRef] - Hu, Z.; Hu, Q.; Zhang, C.; Chen, X.; Li, Q. Evaluation of reanalysis, spatially interpolated and satellite remotely sensed precipitation data sets in central Asia. J. Geophys. Res.
**2016**, 121, 5648–5663. [Google Scholar] [CrossRef]

**Figure 1.**(Left) Location of the hourly (735, black stars) rainfall gauges used in the present study with rainfall records in the period 1990–2015. (Right) Spatial distribution of Köppen–Geiger climate groups developed by AEMET [32]. The acronyms shown in the legend correspond to the following climatic subgroups: BWh (hot desert), BWk (cold desert), Bsh (hot semi-arid), Bsk (cold semi-arid), Csa (temperate hot-summer), Csb (temperate warm-summer), Csc (temperate cold-summer), Csa (temperate humid subtropical), Cfb (temperate oceanic climate), Dsb (Mediterranean-influenced hot-summer humid continental), Dsc and Dfc (Subarctic climates), Dfb (Warm-summer humid continental climate), and ET (tundra climate)

**Figure 2.**Scheme of the methodology. First, hourly rainfall data are aggregated into daily data. Second, supradaily and subdaily rainfall statistics are estimated. Third, monthly atmospheric series from reanalysis data over the period of observation of the corresponding hourly rainfall series are extracted in each gauge location. Then, monthly statistics (mean and variance) are estimated from atmospheric predictors. Daily and supradaily rainfall statistics together with monthly atmospheric statistics and elevation are used as a predictors. The regressor is trained to fit the observed statistics of hourly rainfall. SLP, sea-level pressure; MARS, multivariate adaptive regression splines.

**Figure 3.**Performance evaluation of the random forests-based model (RFB) for variance, proportion of dry intervals (Pdry), skewness coefficient, and autocorrelation lag-one (ACF-lag1) for 1-h intervals. The first and third columns show the scatter plots of the observed versus downscaled (predicted) values; colors indicate climate type; dashed black line correspond to the linear regression. The second and fourth columns show the relative error (%) distributions through a kernel density estimator representation ($err=(Ob{s}^{2}-Pre{d}^{2})/Ob{s}^{2}$).

**Figure 4.**Performance evaluation of the random forests-based model (RFB) for the transition probabilities dry-dry and wet-wet for 1-h intervals. Results are shown in the same way as defined in Figure 3.

**Figure 5.**Location of the hourly rainfall gauges used to perform the simulation of the rainfall by the Neyman–Scott rectangular pulse model (NSRPM).

**Figure 6.**One-hour rainfall performance of the NSRPM simulation of variance, Pdry, and skewness. Black color corresponds to the “exact scenario”; the line and squares represent, respectively, the observed and simulated 1-h statistics. Red color corresponds to the “target scenario”; the dashed-line and squares represent, respectively, the RFB-predicted and the simulated 1-h statistics. The blue-hatched area shows the range of statistics for the calibration in the “simple scenario”. Each row corresponds to a case study.

**Figure 7.**One-hour rainfall performance of the NSRPM simulation of ACF-lag1, ${\varphi}^{DD}$ and ${\varphi}^{WW}$. Black color corresponds to the “exact scenario”; the line and squares represent, respectively, the observed and simulated 1-h statistics. Red color corresponds to the “target scenario”; the dashed-line and squares represent, respectively, the RFB-predicted and the simulated 1h-statistics. The blue-hatched area shows the range of statistics for the calibration in the “simple scenario”. Each row corresponds to a case study.

**Figure 8.**Empirical intensity-frequency curves derived from observed and simulated rainfall at 1-h aggregation. Black dots represent exceedance probability values of the observed rainfall series. Black and red lines correspond to the exceedance probability of “exact scenario” and “target scenario”, respectively. The blue-colored area represents the range of exceedance probability values between the 10 calibrations in the “simple scenario”. Each panel corresponds to a case study.

Organization | Number of Gauges |
---|---|

AEMET [38] | 38 |

Cuenca Mediterránea Andaluza [39] | 109 |

C.H.Segura [40] | 114 |

C.H. Miño-Sil [41] | 89 |

C.H. Cantábrico [42] | 56 |

C.H. Jucar [43] | 185 |

C.H. Ebro [44] | 69 |

Organismo Autónomo Parques Nacionales [45] | 16 |

Sistema de Información Agroclimática para el Regadio [46] | 237 |

Servei Meteorològic de Catalunya [47] | 43 |

**Table 2.**Coefficient of determination (${R}^{2}$) computed through 10-fold cross-validation for the 1-h and 12-h variance, probability of a dry interval (Pdry), skewness, and lag-1 autocorrelation coefficient for Beuchat’s model (B) and for the random forests-based model (RFB) proposed in the present paper. Bold letters highlight the best performing model for every climate and statistic.

Variance | Pdry | Skewness | ACF-lag1 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 h | 12 h | 1 h | 12 h | 1 h | 12 h | 1 h | 12 h | |||||||||

B | RFB | B | RFB | B | RFB | B | RFB | B | RFB | B | RFB | B | RFB | B | RFB | |

BWh | 0.79 | 0.65 | 0.96 | 0.96 | 0.84 | 0.89 | 0.99 | 0.99 | 0.59 | 0.62 | 0.91 | 0.91 | −0.13 | 0.40 | −12.16 | 0.04 |

BWk | 0.65 | 0.72 | 0.98 | 0.98 | 0.53 | 0.75 | 0.98 | 0.98 | 0.62 | 0.68 | 0.94 | 0.93 | −0.54 | 0.00 | −52.59 | 0.32 |

BSh | 0.73 | 0.63 | 0.96 | 0.96 | 0.92 | 0.94 | 0.99 | 0.99 | 0.69 | 0.65 | 0.91 | 0.92 | −0.68 | 0.33 | −7.89 | 0.34 |

BSk | 0.72 | 0.75 | 0.97 | 0.97 | 0.92 | 0.93 | 0.99 | 0.99 | 0.65 | 0.65 | 0.93 | 0.93 | 0.14 | 0.49 | −13.83 | 0.38 |

Csa | 0.80 | 0.81 | 0.98 | 0.98 | 0.92 | 0.94 | 0.98 | 0.99 | 0.73 | 0.74 | 0.92 | 0.92 | 0.26 | 0.57 | −11.51 | 0.53 |

Csb | 0.84 | 0.85 | 0.99 | 0.99 | 0.93 | 0.97 | 0.98 | 0.99 | 0.65 | 0.65 | 0.92 | 0.91 | 0.14 | 0.67 | −8.11 | 0.65 |

Cfa | 0.61 | 0.70 | 0.95 | 0.94 | 0.79 | 0.84 | 0.97 | 0.97 | 0.37 | 0.42 | 0.87 | 0.87 | 0.27 | 0.63 | −11.45 | 0.44 |

Cfb | 0.69 | 0.72 | 0.97 | 0.97 | 0.93 | 0.95 | 0.99 | 0.99 | 0.59 | 0.62 | 0.93 | 0.93 | 0.29 | 0.65 | −7.16 | 0.57 |

D | 0.66 | 0.77 | 0.94 | 0.97 | 0.73 | 0.69 | 0.92 | 0.88 | −0.56 | 0.21 | 0.78 | 0.79 | 0.26 | 0.43 | −13.77 | 0.03 |

Total | 0.78 | 0.83 | 0.98 | 0.98 | 0.94 | 0.96 | 0.99 | 0.99 | 0.71 | 0.73 | 0.93 | 0.93 | 0.24 | 0.61 | −9.74 | 0.56 |

**Table 3.**Predictors used (first column of the table) by models B and RFB (heading row) for the prediction of each statistic (subheading row). Predictors are: average daily precipitation (${\mu}_{24}$), daily precipitation variance (${\sigma}_{24}^{2}$), probability of a dry day (${\varphi}_{24}$), probability of two consecutive dry days (${\varphi}_{48}$), daily rainfall skewness (${\gamma}_{24}$), lag-1 daily autocorrelation coefficient (${\rho}_{24}^{1}$), probability of two consecutive wet days (${\varphi}_{24}^{WW}$), probability of two consecutive dry days (${\varphi}_{24}^{DD}$), average surface air temperature (TAS), surface air temperature variance (${\sigma}_{TAS}^{2}$), relative air humidity (HUR), and elevation of the station. Predictands are: rainfall variance (${\sigma}_{T}$), probability of a dry interval (${\varphi}_{T}$), rainfall skewness (${\gamma}_{T}$), rainfall lag-1 autocorrelation coefficient (${\rho}_{T}^{1}$), probability of two adjacent wet intervals (${\varphi}_{T}^{WW}$), and probability of two adjacent dry intervals (${\varphi}_{T}^{DD}$) at the ${T}^{should}$ it be italics? (in hours) aggregation scale. A colored cell indicates that a predictor has been used to predict a given predictand for the specific model (B: Beuchat’s model, in red; RFB: random forests-based model, in green).

Predictors | Predictands ($\mathit{T}\in \left\{1,2,3,6,12\right\}$) | ||||||||
---|---|---|---|---|---|---|---|---|---|

B | RFB | ||||||||

${\sigma}_{T}$ | ${\varphi}_{T}$ | ${\gamma}_{T}$ | ${\sigma}_{T}$ | ${\varphi}_{T}$ | ${\gamma}_{T}$ | ${\rho}_{T}^{1}$ | ${\varphi}_{T}^{WW}$ | ${\varphi}_{T}^{DD}$ | |

${\mu}_{24}$ | |||||||||

${\sigma}_{24}$ | |||||||||

${\varphi}_{24}$ | |||||||||

${\varphi}_{48}$ | |||||||||

${\gamma}_{24}$ | |||||||||

${\rho}_{24}^{1}$ | |||||||||

${\varphi}_{24}^{WW}$ | |||||||||

${\varphi}_{24}^{DD}$ | |||||||||

TAS | |||||||||

${\sigma}_{TAS}^{2}$ | |||||||||

HUR | |||||||||

Elevation |

**Table 4.**Coefficient of determination (${R}^{2}$) computed through 10-fold cross-validation for the 1-h and 12-h variance for the random forests-based model (RFB) proposed in the present paper.

${\mathit{\varphi}}^{\mathit{DD}}$ | ${\mathit{\varphi}}^{\mathit{WW}}$ | |||
---|---|---|---|---|

1 h | 12 h | 1 h | 12 h | |

BWh | 0.97 | 0.99 | 0.59 | 0.72 |

BWk | 0.97 | 0.97 | 0.12 | 0.83 |

BSh | 0.96 | 0.98 | 0.59 | 0.85 |

BSk | 0.98 | 0.99 | 0.67 | 0.87 |

Csa | 0.97 | 0.99 | 0.75 | 0.86 |

Csb | 0.96 | 0.99 | 0.80 | 0.90 |

Cfa | 0.87 | 0.97 | 0.73 | 0.79 |

Cfb | 0.95 | 0.98 | 0.8 | 0.90 |

D | 0.61 | 0.93 | 0.04 | 0.20 |

Total | 0.97 | 0.98 | 0.77 | 0.89 |

**Table 5.**Set of statistics used to fit NSRPM and associated weights. d and h indicate daily and hourly level of aggregation, respectively.

Mean | Variance | Skewness | Proportion of Dry Intervals | Lag-1 Correlation | ${\mathit{\varphi}}^{\mathit{DD}}$ | ${\mathit{\varphi}}^{\mathit{WW}}$ | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Time scale | 1 d | 1 h | 1 d | 1 h | 1 d | 1 h | 1 d | 1 h | 1 d | 1 h | 1 d | 1 h | 1 d |

Weights | 5 | 4 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 4 | 2 |

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**MDPI and ACS Style**

Diez-Sierra, J.; del Jesus, M. Subdaily Rainfall Estimation through Daily Rainfall Downscaling Using Random Forests in Spain. *Water* **2019**, *11*, 125.
https://doi.org/10.3390/w11010125

**AMA Style**

Diez-Sierra J, del Jesus M. Subdaily Rainfall Estimation through Daily Rainfall Downscaling Using Random Forests in Spain. *Water*. 2019; 11(1):125.
https://doi.org/10.3390/w11010125

**Chicago/Turabian Style**

Diez-Sierra, Javier, and Manuel del Jesus. 2019. "Subdaily Rainfall Estimation through Daily Rainfall Downscaling Using Random Forests in Spain" *Water* 11, no. 1: 125.
https://doi.org/10.3390/w11010125