# Optimal Temporal Resolution of Rainfall for Urban Applications and Uncertainty Propagation

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## Abstract

**:**

## 1. Introduction

^{2}in England is used to perform cross-validation and verify the methodology. Twelve combinations of different accumulation and downscaling resolutions are tested. Additionally, an example of application to urban modelling is presented. The optimal accumulation and downscaling resolutions for a specific model are identified by comparing different products with 14 combinations of accumulation resolutions and downscaling resolutions in a case study in the Netherlands. The generated rainfall products are tested, using an InfoWorks urban hydrological model. The case study is based on a high-intensity convective rainfall event that occurred in the Municipality of Twenterand, in the east of the Netherlands, causing severe flooding in the village of Vroomshoop. The InfoWorks model of the Vroomshoop area and water level measurements are used to identify the optimal combination of accumulation and downscaling resolutions for the specific model, by comparing the deterministic KED predictions. For the selected product, the uncertainty propagation is studied, producing an ensemble from the probabilistic KED result and using it in the InfoWorks model.

## 2. Dataset and Model

#### 2.1. Case Study 1: United Kingdom

#### 2.1.1. Rain Gauges

^{2}, and 226 rain gauges managed by the Environment Agency (EA) are available upon request [26]. The dataset has been quality checked manually and consists of a uniform set of tipping bucket rain gauges with a bucket resolution of 0.2 mm and the time series are provided at a temporal resolution of 15 min. For this work, the request at the EA National Request Service [26] was for all the 15-minute data for all England, from January to September 2016; subsequently, only the rain gauges in the study area have been selected. The dataset is indicated as EA in this work and the position of the rain gauges is shown in Figure 1.

#### 2.1.2. Radars

#### 2.2. Case Study 2: The Netherlands

#### 2.2.1. Rain Gauges

#### 2.2.2. Radars

#### 2.2.3. Vroomshoop InfoWorks Model and Water Level Data

^{2}, composed of 1227 nodes, 1282 links, 12 pumps, 17 weirs and 65 storm overflows. The model has been calibrated according to the C2100 guideline [33]. The InfoWorks model is a 1-D full hydrodynamic urban sewer flow model. It solves the 1-D Saint-Venant equations (shallow water equations) in a conduit system. Rainfall flows into the system through catchment areas that are connected to the manholes (nodes). Any area drains to the closest manhole. The catchment areas are divided into different types of surfaces: closed (asphalt) or open (bricks) pavement and flat or sloped roofs. Unpaved areas are assumed not to drain to the sewer system. The catchment areas were surveyed during the setup of the model, in 2012. The rainfall runoff model consists of several components with different parameters for the four surface types: depression storage, evaporation (open pavement only), infiltration (Horton) and routing delays (linear reservoir). The tuning of the rainfall runoff parameters is part of the calibration procedure of the model. The results of the model are compared to the water level measurements from the three sensors available for this work, provided by the Municipality of Twenterand. The position of the sensors is reported in Figure 2, in the low-right corner as stars, and in Figure 3, as red squares. Figure 3 is a simplified representation of the model, reporting the main components.

## 3. Methods

#### 3.1. Data Pre-Processing and Accumulation

#### 3.1.1. Radar

^{6}/m

^{3}) is necessary. Then, the rainfall rate is calculated using the Z-R relationship [32]:

#### 3.1.2. Rain Gauges

#### 3.2. Variogram Calculation

- For the Dutch case study, the number of rain gauges is limited, and their resolution highly variable, therefore a reliable time-variant variogram calculation based on ground measurements is difficult to calculate.
- The variogram for KED needs to be calculated on rainfall residuals, rather than on the rainfall field itself [37].

- The rain gauges are interpolated applying ordinary kriging with the calculated variogram.
- The residuals are calculated subtracting the radar field from the interpolated rain gauge field.
- The variogram of the residuals is calculated with the FFT approach.

#### 3.3. Merging Using Kriging with External Drift

#### 3.4. Rain Gauge Error Modelling

#### 3.4.1. Tipping Bucket Rain Gauge Error Model

#### 3.4.2. KNMI Automatic Rain Gauges

#### 3.4.3. KNMI Manual Rain Gauges

#### 3.5. Downscaling

#### 3.5.1. Downscaling the KED Prediction

#### 3.5.2. Downscaling the KED Variance

- The variance of a sum is the sum of the covariance between all summed elements (Equation (16)).

#### 3.6. Ensemble Generation and Propagation

## 4. Results

#### 4.1. Case Study 1: Evaluation of the Optimal Combination in Terms of Rainfall Product Quality

#### 4.2. Case Study 2: Identification of the Optimal Accumulation and Downscaling Resolution

#### 4.3. Case Study 2: Ensemble Generation and Propagation

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Schilling, W. Rainfall data for urban hydrology: What do we need? Atmos. Res.
**1991**, 27, 5–21. [Google Scholar] [CrossRef] - Berne, A.; Delrieu, G.; Creutin, J.; Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. J. Hydrol.
**2004**, 299, 166–179. [Google Scholar] [CrossRef] - Gabellani, S.; Boni, G.; Ferraris, L.; von Hardenberg, J.; Provenzale, A. Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator. Adv. Water Resour.
**2007**, 30, 2061–2071. [Google Scholar] [CrossRef] - Fletcher, T.D.; Andrieu, H.; Hamel, P. Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art. Adv. Water Resour.
**2013**, 51, 261–279. [Google Scholar] [CrossRef] - Berne, A.; Krajewski, W.F. Radar for hydrology: Unfulfilled promise or unrecognized potential? Adv. Water Resour.
**2013**, 51, 357–366. [Google Scholar] [CrossRef] - Islam, T.; Rico-Ramirez, M.A. An overview of the remote sensing of precipitation with polarimetric radar. Prog. Phys. Geogr.
**2013**, 38, 1–24. [Google Scholar] [CrossRef] - Villarini, G.; Krajewski, W.F. Review of the different sources of uncertainty in single polarization radar-based estimates of rainfall. Surv. Geophys.
**2010**, 31, 107–129. [Google Scholar] [CrossRef] - Peleg, N.; Ben-Asher, M.; Morin, E. Radar subpixel-scale rainfall variability and uncertainty: Lessons learned from observations of a dense rain-gauge network. Hydrol. Earth Syst. Sci.
**2013**, 17, 2195–2208. [Google Scholar] [CrossRef] - Wang, L.P.; Ochoa-Rodríguez, S.; Van Assel, J.; Pina, R.D.; Pessemier, M.; Kroll, S.; Willems, P.; Onof, C. Enhancement of radar rainfall estimates for urban hydrology through optical flow temporal interpolation and Bayesian gauge-based adjustment. J. Hydrol.
**2015**, 531, 408–426. [Google Scholar] [CrossRef] - Seo, B.C.; Krajewski, W.F. Correcting temporal sampling error in radar-rainfall: Effect of advection parameters and rain storm characteristics on the correction accuracy. J. Hydrol.
**2015**, 531, 272–283. [Google Scholar] [CrossRef] - Thorndahl, S.; Nielsen, J.E.; Rasmussen, M.R. Bias adjustment and advection interpolation of long-term high resolution radar rainfall series. J. Hydrol.
**2014**, 508, 214–226. [Google Scholar] [CrossRef] - Goudenhoofdt, E.; Delobbe, L. Evaluation of radar-gauge merging methods for quantitative precipitation estimates. Hydrol. Earth Syst. Sci. Discuss.
**2009**, 5, 2975–3003. [Google Scholar] [CrossRef] - Haberlandt, U. Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event. J. Hydrol.
**2007**, 332, 144–157. [Google Scholar] [CrossRef] - Jewell, S.A.; Gaussiat, N. An assessment of kriging-based rain-gauge-radar merging techniques. Q. J. R. Meteorol. Soc.
**2015**, 141, 2300–2313. [Google Scholar] [CrossRef] - Schuurmans, J.M.; Bierkens, M.F.P.; Pebesma, E.J.; Uijlenhoet, R. Automatic prediction of high-Resolution daily rainfall fields for multiple extents: The potential of operational radar. J. Hydrometeorol.
**2007**, 8, 1204–1224. [Google Scholar] [CrossRef] - Wilson, J.W. Integration of radar and rain gauge data for improved rainfall measurement. J. Appl. Meteorol.
**1970**, 9, 489–497. [Google Scholar] [CrossRef] - Li, J.; Heap, A.D. A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors. Ecol. Inform.
**2011**, 6, 228–241. [Google Scholar] [CrossRef] - Nanding, N.; Rico-Ramirez, M.A.; Han, D. Comparison of different radar-raingauge rainfall merging techniques. J. Hydroinform.
**2015**, 17, 422–445. [Google Scholar] [CrossRef] - Berndt, C.; Rabiei, E.; Haberlandt, U. Geostatistical merging of rain gauge and radar data for high temporal resolutions and various station density scenarios. J. Hydrol.
**2014**, 508, 88–101. [Google Scholar] [CrossRef] - Panziera, L.; Gabella, M.; Zanini, S.; Hering, A.; Germann, U.; Berne, A. A radar-based regional extreme rainfall analysis to derive the thresholds for a novel automatic alert system in Switzerland. Hydrol. Earth Syst. Sci.
**2016**, 20, 2317–2332. [Google Scholar] [CrossRef] - Sideris, I.V.; Gabella, M.; Erdin, R.; Germann, U. Real-time radar-rain-gauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland. Q. J. R. Meteorol. Soc.
**2014**, 140, 1097–1111. [Google Scholar] [CrossRef] - Ferraris, L.; Gabellani, S.; Rebora, N.; Provenzale, A. A comparison of stochastic models for spatial rainfall downscaling. Water Resour. Res.
**2003**, 39, 1–8. [Google Scholar] [CrossRef] - Liu, X.; Coulibaly, P.; Evora, N. Comparison of data-driven methods for downscaling ensemble weather forecasts. Hydrol. Earth Syst. Sci. Discuss.
**2007**, 4, 189–210. [Google Scholar] [CrossRef] - Simões, N.E.; Leitão, J.P.; Ochoa-rodríguez, S.; Marques, A.S.Á. Stochastic Urban Pluvial Flood Mapping Based Upon a Spatial—Temporal Stochastic Rainfall Generator. In Proceedings of the 13th International Conference on Urban Drainage, Sarawak, Malaysia, 7–12 September 2014. [Google Scholar]
- Peleg, N.; Blumensaat, F.; Molnar, P.; Fatichi, S.; Burlando, P. Partitioning the impacts of spatial and climatological rainfall variability in urban drainage modeling. Hydrol. Earth Syst. Sci.
**2017**, 21, 1559–1572. [Google Scholar] [CrossRef] - Environment Agency National Requests. Available online: https://www.gov.uk/government/organisations/environment-agency (accessed on 11 January 2017).
- Met Office 1 Km Resolution UK Composite Rainfall Data from the Met Office Nimrod System. Available online: http://catalogue.ceda.ac.uk/uuid/27dd6ffba67f667a18c62de5c3456350 (accessed on 1 January 2017).
- Harrison, D.L.; Driscoll, S.J.; Kitchen, M. Improving precipitation estimates from weather radar using quality control and correction techniques. Meteorol. Appl.
**2000**, 7, 135–144. [Google Scholar] [CrossRef] - Harrison, D.L.; Kitchen, M.; Scovell, R.W. High-resolution precipitation estimates for hydrological uses. Proc. ICE Water Manag.
**2009**, 162, 125–135. [Google Scholar] [CrossRef] - Witteveen+Bos. Available online: www.witteveenbos.com (accessed on 1 October 2016).
- Brandsma, T. Comparison of Automatic and Manual Precipitation Networks in the Netherlands; Wetenschappelijke Publicatie: De Bilt, The Netherlands, 2014. [Google Scholar]
- Overeem, A.; Holleman, I.; Buishand, A. Derivation of a 10-year radar-based climatology of rainfall. J. Appl. Meteorol. Climatol.
**2009**, 48, 1448–1463. [Google Scholar] [CrossRef] - Rioned. Leidraad Rionlering. Module C2100: Rioleringsberekeningen, Hydraulisch Functioneren; Rioned: Mildenhall, UK, 2004. [Google Scholar]
- Peleg, N.; Marra, F.; Fatichi, S.; Paschalis, A.; Molnar, P.; Burlando, P. Spatial variability of extreme rainfall at radar subpixel scale. J. Hydrol.
**2016**. [Google Scholar] [CrossRef] - Zhang, Y.; Adams, T.; Bonta, J.V. Subpixel-Scale Rainfall Variability and the Effects on Separation of Radar and Gauge Rainfall Errors. J. Hydrometeorol.
**2007**, 8, 1348–1363. [Google Scholar] [CrossRef] - Sideris, I.V.; Gabella, M.; Sassi, M.; Germann, U. The CombiPrecip experience: Development and operation of a real-time radar-raingauge combination scheme in Switzerland. In Proceedings of the International Symposium Weather Radar and Hydrology, Washington, DC, USA, 7–9 April 2014. [Google Scholar]
- Cressie, N.A.C. Statistics for Spatial Data; Kohn Wiley & Sons: Hoboken, NJ, USA, 1993. [Google Scholar]
- Marcotte, D. Fast variogram computation with FFT. Comput. Geosci.
**1996**, 22, 1175–1180. [Google Scholar] [CrossRef] - Nerini, D.; Besic, N.; Sideris, I.; Germann, U.; Foresti, L. A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform. Hydrol. Earth Syst. Sci.
**2017**, 21, 2777–2797. [Google Scholar] [CrossRef] - Mazzetti, C.; Todini, E. Combining Weather Radar and Raingauge Data for Hydrologic Applications. In Flood Risk Management: Research and Practice; Taylor & Francis Group: London, UK, 2009; ISBN 9780415485074. [Google Scholar]
- Clark, I. Statistics or geostatistics? Sampling error or nugget effect? J. S. Afr. Inst. Min. Metall.
**2010**, 110, 307–312. [Google Scholar] - Chiles, J.-P.; Delfiner, P. Geostatistics: Modeling Spatial Uncertainty; Wiley-Interscience Publication: New York, NY, USA, 1999. [Google Scholar]
- Ciach, G.J. Local Random Errors in Tipping-Bucket Rain Gauge Measurements. J. Atmos. Ocean. Technol.
**2003**, 20, 752–759. [Google Scholar] [CrossRef] - Wauben, W.M.F. KNMI Contribution to the WMO Laboratory Intercomparison of Rainfall Intensity Gauges; Koninklijk Nederlands Meteorologisch Instituut: De Bilt, The Netherlands, 2006. [Google Scholar]
- Ciach, G.J.; Krajewski, W.F.; Villarini, G. Product-Error-Driven Uncertainty Model for Probabilistic Quantitative Precipitation Estimation with NEXRAD Data. J. Hydrometeorol.
**2007**, 8, 1325–1347. [Google Scholar] [CrossRef] - Kirstetter, P.-E.; Delrieu, G.; Boudevillain, B.; Obled, C. Toward an error model for radar quantitative precipitation estimation in the Cévennes-Vivarais region, France. J. Hydrol.
**2010**, 394, 28–41. [Google Scholar] [CrossRef] - Villarini, G.; Krajewski, W.F. Sensitivity Studies of the Models of Radar-Rainfall Uncertainties. J. Appl. Meteorol. Climatol.
**2010**, 49, 288–309. [Google Scholar] [CrossRef] - Gires, A.; Onof, C.; Maksimovic, C.; Schertzer, D.; Tchiguirinskaia, I.; Simoes, N. Quantifying the impact of small scale unmeasured rainfall variability on urban runoff through multifractal downscaling: A case study. J. Hydrol.
**2012**, 442, 117–128. [Google Scholar] [CrossRef] - Ochoa-Rodriguez, S.; Wang, L.P.; Gires, A.; Pina, R.D.; Reinoso-Rondinel, R.; Bruni, G.; Ichiba, A.; Gaitan, S.; Cristiano, E.; Van Assel, J.; et al. Impact of spatial and temporal resolution of rainfall inputs on urban hydrodynamic modelling outputs: A multi-catchment investigation. J. Hydrol.
**2015**, 531, 389–407. [Google Scholar] [CrossRef] - Emmanuel, I.; Andrieu, H.; Leblois, E.; Flahaut, B. Temporal and spatial variability of rainfall at the urban hydrological scale. J. Hydrol.
**2012**, 430–431, 162–172. [Google Scholar] [CrossRef] - KNMI. Available online: https://data.knmi.nl/datasets/etmaalgegevensKNMIstations/1?bbox=53.7,7.4,50.6,3.2&dtstart=2016-06-12T23:00Z&dtend=2016-06-17T22:59Z (accessed on 4 October 2016).
- KNMI. Available online: https://www.knmi.nl/nederland-nu/klimatologie/monv/reeksen (accessed on 1 October 2016).
- KNMI. Product: RAD_NL25_RAC_MFBS_5min. Available online: ftp.knmi.nl (accessed on 1 October 2016).
- Het Weer Actueel. Available online: www.hetweeractueel.nl/overijssel (accessed on 1 October 2016).
- De Niet, A.C. Coasts, Rivers and Land Reclamation PMC, Witteveen + Bos. Available online: http://witteveenbos.com/ (accessed on 1 October 2016).

**Figure 1.**The UK study area is presented, including the Environment Agency (EA) rain gauges and the three radars available in the area.

**Figure 2.**The Dutch study area is presented, including all the available rain gauge datasets. In the bottom-right panel, the three available water measurement points are shown.

**Figure 4.**The methodology followed in this work is reported in the figure. In particular, the six numbered passages are discussed in the Methods Sections.

**Figure 6.**Rank histograms for the tested accumulation (${T}_{1}$) and downscaling (${T}_{2}$) combinations in the UK case study.

**Figure 7.**The 14 rainfall products are used as an input for the InfoWorks model and the results are compared to the water level observations in three distinct locations as reported in Figure 2. The names of the products describe the accumulation resolution (A) and the downscaling resolution (D) in minutes. Rad5 and Rad15 are the radar products at 5 and 15 min resolution, respectively, and Obs is the water level observation.

**Figure 8.**Using the rainfall ensemble as an input for the InfoWorks model, an ensemble of water level estimations is obtained. The ensemble is compared with the observations at three different locations. The ensemble is represented with the deterministic prediction (kriging mean), with the 5–95% quantile band, and the minimum–maximum band.

Network | Number | Accumulation | Type |
---|---|---|---|

Twenterand (TWE) | 3 * | 3 min | Tipping bucket |

HWA amateur (HWA) | 14 * | 5 min to 5 h | Variable tipping bucket |

knmi hourly (KNMI-H) | 2 | 60 min | Floating device |

knmi daily (KNMI-D) | 20 | 24 h | Water level reading |

ID | Networks | N. Gauges | Accumulation ${\mathit{T}}_{1}$ | Downscaling ${\mathit{T}}_{2}$ |
---|---|---|---|---|

1 | EA | 226 | 1 h | 15 min |

2 | EA | 226 | 1 h | 30 min |

3 | EA | 226 | 1 h | 1 h |

4 | EA | 226 | 3 h | 15 min |

5 | EA | 226 | 3 h | 30 min |

6 | EA | 226 | 3 h | 1 h |

7 | EA | 226 | 12 h | 15 min |

8 | EA | 226 | 12 h | 30 min |

9 | EA | 226 | 12 h | 1 h |

10 | EA | 226 | 24 h | 15 min |

11 | EA | 226 | 24 h | 30 min |

12 | EA | 226 | 24 h | 1 h |

**Table 3.**Different sub-daily accumulations and downscaling intervals are tested with the available rain gauges at sub-daily resolution in the Dutch case study.

ID | Networks | N. Gauges | Accumulation ${\mathit{T}}_{1}$ | Downscaling ${\mathit{T}}_{2}$ |
---|---|---|---|---|

13 | HWA, TWE, KNMI-H | 19 | 1 h | 5 min |

14 | HWA, TWE, KNMI-H | 19 | 1 h | 15 min |

15 | HWA, TWE, KNMI-H | 19 | 1 h | 30 min |

16 | HWA, TWE, KNMI-H | 19 | 3 h | 5 min |

17 | HWA, TWE, KNMI-H | 19 | 3 h | 15 min |

18 | HWA, TWE, KNMI-H | 19 | 3 h | 30 min |

19 | HWA, TWE, KNMI-H | 19 | 12 h | 5 min |

20 | HWA, TWE, KNMI-H | 19 | 12 h | 15 min |

21 | HWA, TWE, KNMI-H | 19 | 12 h | 30 min |

**Table 4.**Daily accumulations are calculated with all the available rain gauges, including the daily ones in the Dutch case study.

ID | Networks | N. Gauges | Accumulation ${\mathit{T}}_{1}$ | Downscaling ${\mathit{T}}_{2}$ |
---|---|---|---|---|

22 | HWA, TWE, KNMI-H, KNMI-D | 39 | 1 day | 5 min |

23 | HWA, TWE, KNMI-H, KNMI-D | 39 | 1 day | 15 min |

24 | HWA, TWE, KNMI-H, KNMI-D | 39 | 1 day | 30 min |

**Table 5.**Non-corrected radar products are compared as well, at two different resolutions in the Dutch case study.

ID | Networks | N. Gauges | Accumulation ${\mathit{T}}_{1}$ | Downscaling ${\mathit{T}}_{2}$ |
---|---|---|---|---|

25 | - | - | 5 min | - |

26 | - | - | 15 min | - |

**Table 6.**The three indicators (bias, MRTE, and NSE) are reported for the 12 products of the UK case study, indicated with accumulation resolution (A) and downscaling resolution (D) in minutes. A conditional colour formatting is applied to easily compare the values, where green is a positive performance, and red a negative one.

BIAS | |||

A\D | 15 | 30 | 60 |

60 | 0.065 | 0.069 | 0.078 |

180 | 0.054 | 0.056 | 0.064 |

720 | 0.048 | 0.045 | 0.051 |

1440 | 0.045 | 0.043 | 0.045 |

MRTE | |||

A\D | 15 | 30 | 60 |

60 | 0.193 | 0.166 | 0.147 |

180 | 0.187 | 0.161 | 0.142 |

720 | 0.165 | 0.139 | 0.123 |

1440 | 0.147 | 0.127 | 0.113 |

NSE | |||

A\D | 15 | 30 | 60 |

60 | 0.46 | 0.52 | 0.58 |

180 | 0.46 | 0.51 | 0.55 |

720 | 0.51 | 0.55 | 0.59 |

1440 | 0.52 | 0.56 | 0.59 |

**Table 7.**The three indicators (bias, Mean Root Transformed Error—MRTE, and Nash-Sutcliffe Efficiency—NSE) are reported for the 14 products indicated with accumulation resolution (A) and downscaling resolution (D) in minutes, for the three measurement locations. Radar products are indicated with RD. A conditional colour formatting is applied to easily compare the values, where green is a positive performance, and red a negative one.

A | D | VW162 | VW984C1 | VW263 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

BIAS | MRTE | NSE | BIAS | MRTE | NSE | BIAS | MRTE | NSE | ||

1440 | 5 | 0.146 | 0.0092 | 0.58 | 0.052 | 0.0059 | 0.57 | 0.396 | 0.0177 | 0.02 |

1440 | 15 | 0.147 | 0.0093 | 0.58 | 0.052 | 0.0060 | 0.57 | 0.400 | 0.0182 | -0.01 |

1440 | 30 | 0.146 | 0.0093 | 0.58 | 0.051 | 0.0060 | 0.57 | 0.399 | 0.0180 | 0.01 |

720 | 5 | 0.159 | 0.0092 | 0.58 | 0.053 | 0.0059 | 0.57 | 0.310 | 0.0103 | 0.44 |

720 | 15 | 0.159 | 0.0092 | 0.58 | 0.053 | 0.0059 | 0.57 | 0.313 | 0.0104 | 0.44 |

720 | 30 | 0.158 | 0.0092 | 0.58 | 0.052 | 0.0060 | 0.57 | 0.313 | 0.0103 | 0.44 |

180 | 5 | 0.178 | 0.0061 | 0.73 | 0.070 | 0.0033 | 0.77 | 0.303 | 0.0088 | 0.53 |

180 | 15 | 0.178 | 0.0061 | 0.73 | 0.070 | 0.0033 | 0.77 | 0.304 | 0.0088 | 0.53 |

180 | 30 | 0.178 | 0.0059 | 0.74 | 0.071 | 0.0031 | 0.78 | 0.305 | 0.0089 | 0.53 |

60 | 5 | 0.183 | 0.0061 | 0.73 | 0.072 | 0.0033 | 0.77 | 0.272 | 0.0066 | 0.65 |

60 | 15 | 0.183 | 0.0061 | 0.73 | 0.071 | 0.0033 | 0.77 | 0.271 | 0.0066 | 0.65 |

60 | 30 | 0.182 | 0.0059 | 0.74 | 0.071 | 0.0031 | 0.79 | 0.274 | 0.0066 | 0.65 |

RD | 15 | 0.184 | 0.0093 | 0.58 | 0.074 | 0.0058 | 0.59 | 0.298 | 0.0101 | 0.46 |

RD | 5 | 0.184 | 0.0094 | 0.58 | 0.075 | 0.0058 | 0.59 | 0.297 | 0.0102 | 0.46 |

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**MDPI and ACS Style**

Cecinati, F.; De Niet, A.C.; Sawicka, K.; Rico-Ramirez, M.A.
Optimal Temporal Resolution of Rainfall for Urban Applications and Uncertainty Propagation. *Water* **2017**, *9*, 762.
https://doi.org/10.3390/w9100762

**AMA Style**

Cecinati F, De Niet AC, Sawicka K, Rico-Ramirez MA.
Optimal Temporal Resolution of Rainfall for Urban Applications and Uncertainty Propagation. *Water*. 2017; 9(10):762.
https://doi.org/10.3390/w9100762

**Chicago/Turabian Style**

Cecinati, Francesca, Arie C. De Niet, Kasia Sawicka, and Miguel A. Rico-Ramirez.
2017. "Optimal Temporal Resolution of Rainfall for Urban Applications and Uncertainty Propagation" *Water* 9, no. 10: 762.
https://doi.org/10.3390/w9100762