# On the Use of Satellite Rainfall Data to Design a Dam in an Ungauged Site

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}, which from now on will be referred as the Pietrarossa catchment. The dam was built on a plan with average altitude of 170 m a.s.l. and it was designed to have a capacity of 32 millions m

^{3}, corresponding to the maximum water level of 188 m a.s.l. The Pietrarossa catchment is located in the inner hilly area of the island (Figure 1b) and it is characterized by a mean yearly precipitation of 485 mm, which is below the corresponding mean regional value of 600 mm. Precipitation occurs mostly during autumn and winter seasons (September to March).

#### 2.2. Precipitation Data Sets

#### 2.3. Data Pre-Processing

## 3. Methodology

#### 3.1. Evaluation Indexes

#### 3.2. Intensity–Duration–Area–Frequency (IDAF) Curves

#### 3.2.1. VAPI Regionalization Approach

^{2}and the duration $d$ in hours.

^{2}, and for the fixed durations of 1, 3, 6, 12 and 24 h, the IDAF curves are built by multiplying IDF curves obtained with the regionalization approach (Equation (4)) and the ARF factor, as follows:

#### 3.2.2. CMORPH Observations

^{2}.

#### 3.3. Peak Flow and Spillway Dimension

^{2}; $C$ is the dimensionless runoff coefficient; $i$ is the average areal rainfall intensity of the design storm, expressed in mm/h; $\mathrm{k}$ is a dimensional correction factor equal to k = 1/3.6 to obtain ${Q}_{P}$ in m

^{3}/s. Rainfall intensity is computed applying Equations (6) and (8) for $t={t}_{c}$, i.e., considering a duration of the event equal to the concentration time of the catchment, in order to maximize the value of the peak discharge ${Q}_{P}.$ The concentration time of a catchment can be defined as the time that it takes a drop to arrive from the most hydraulically distant point of the catchment to the outlet section [60]. Many authors in literature proposed empirical formulations to evaluate the concentration time of a catchment (e.g., [61,62,63]). Due to the characteristics of the case study, we adopt the one proposed by Giandotti [61], which was developed using Italian catchments with extension between 170 and 70000 km

^{2}and thus fits our case. It can be expressed as:

^{2}and $\Delta H$ is the difference in meters (m) between the catchment average altitude and the outlet section elevation.

## 4. Results

#### 4.1. Evaluation Indexes

#### 4.2. Intensity–Duration–Area–Frequency (IDAF) Curves

#### 4.3. Peak Flow and Spillway Dimension

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Scatter plots of 30-min and daily observations of rain gauges and CMORPH. The blue points stand for the daily observations, the black line represents the bisect, the red continuous line stands for the interpolant of the daily observations and the red dashed line is the interpolant of the 30-min observations. Each scatter plot is referred to a station: (

**a**) Aidone; (

**b**) Caltagirone; (

**c**) Caltanissetta; (

**d**) Enna; (

**e**) Gela; (

**f**) Mazzarino; (

**g**) Mazzarrone; (

**h**) Mineo; (

**i**) Piazza Armerina; (

**l**) Riesi.

**Figure 3.**Intensity–duration–area–frequency (IDAF) curves built for different return periods using CMORPH time series (dashed lines, identified by C letter in the legend) and VAPI regionalization approach (continuous lines, identified with V letter in the legend).

**Table 1.**List of statistical metrics computed. The values marked in bold stand for perfect match between satellite and rain gauge observations. ${S}_{i}$ stands for the i-th satellite estimation, ${R}_{i}$ is the corresponding rain gauge observation, $N$ is the number of observations available for the station, $H$ stands for the number of times that both CMORPH and rain gauges detected rainfall, $M$ represents the number of times rainfall is observed in a rain gauge but it is not detected by the satellite product, $F$ gives the number of times precipitation is not observed in a rain gauge but it is detected by CMORPH, $cov\left(S,R\right)$ is the covariance between rain gauge and CMORPH time series, $\sigma \left(S\right)$ and $\sigma \left(R\right)$ are the standard deviation of satellite and rain gauge time series, respectively.

Statistical Metric | Symbol | Equation | Range of Values | Unit |
---|---|---|---|---|

Mean Absolute Error | MAE | $\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left|{S}_{i}-{R}_{i}\right|$ | $\left[\mathbf{0},+\infty \right)$ | mm |

Root Mean Squared Error | RMSE | $\sqrt{\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left({S}_{i}-{R}_{i}\right)}^{2}}$ | $\left[\mathbf{0},+\infty \right)$ | mm |

Normalized Standard Error | NSE | $\frac{\sqrt{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{\left({S}_{i}-{R}_{i}\right)}^{2}}}{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{R}_{i}}$ | $\left[\mathbf{0},+\infty \right)$ | - |

Mean Bias Error | MBE | $\frac{{{\displaystyle \sum}}_{i=1}^{N}{S}_{i}-{R}_{i}}{{{\displaystyle \sum}}_{i=1}^{N}{R}_{i}}\xb7100$ | $\left[\mathbf{0},+\infty \right)$ | - |

Correlation Coefficient | CC | $\frac{cov\left(S,R\right)}{\sigma \left(S\right)\xb7\sigma \left(R\right)}$ | $\left[-1,\mathbf{1}\right]$ | - |

Probability of Detection | POD | $\frac{H}{H+M}$ | $\left[0,\mathbf{1}\right]$ | - |

False Alarm Ratio | FAR | $\frac{F}{F+M}$ | $\left[\mathbf{0},1\right]$ | - |

Critical Success Index | CSI | $\frac{H}{H+F+M}$ | $\left[0,\mathbf{1}\right]$ | - |

**Table 2.**Continuous evaluation indexes for CMORPH: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Normalized Standard Error (NSE), Mean Bias Error (MBE), Correlation Coefficient (CC). The values represented are for each station and for the two temporal aggregations of 30 min and 24 h.

MAE | RMSE | NSE | MBE | CC | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Station | 30 min | Daily | 30 min | Daily | 30 min | Daily | 30 min | Daily | 30 min | Daily |

Aidone | 0.05 | 1.64 | 0.46 | 5.66 | 11.77 | 3.01 | −29.34 | −29.43 | 0.30 | 0.62 |

Enna | 0.05 | 1.44 | 0.45 | 4.94 | 14.67 | 3.34 | 0.34 | −0.65 | 0.30 | 0.66 |

Caltagirone | 0.05 | 1.40 | 0.44 | 5.06 | 13.94 | 3.32 | −5.82 | −5.18 | 0.28 | 0.65 |

Caltanissetta | 0.05 | 1.48 | 0.46 | 5.27 | 13.16 | 3.16 | −10.48 | −10.38 | 0.30 | 0.66 |

Gela | 0.04 | 1.36 | 0.45 | 4.93 | 14.85 | 3.36 | −5.99 | −6.05 | 0.29 | 0.69 |

Mazzarino | 0.05 | 1.43 | 0.45 | 5.09 | 14.66 | 3.44 | 5.00 | 5.44 | 0.29 | 0.67 |

Mazzarrone | 0.05 | 1.57 | 0.45 | 5.42 | 11.96 | 3.00 | −26.26 | −26.23 | 0.29 | 0.64 |

Mineo | 0.04 | 1.39 | 0.45 | 5.31 | 14.58 | 3.56 | −6.65 | −6.63 | 0.26 | 0.65 |

Piazza Armerina | 0.05 | 1.48 | 0.45 | 5.81 | 12.78 | 3.46 | −21.13 | −20.84 | 0.27 | 0.64 |

Riesi | 0.05 | 1.41 | 0.41 | 4.72 | 11.88 | 2.85 | −22.90 | −22.71 | 0.29 | 0.67 |

**Table 3.**Categorical evaluation indexes for CMORPH: Probability Of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI). The presented values are for each station and for the two temporal aggregations of 30 min and 24 h.

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

Station | 30 min | Daily | 30 min | Daily | 30 min | Daily |

Aidone | 0.22 | 0.45 | 0.49 | 0.20 | 0.18 | 0.40 |

Enna | 0.23 | 0.45 | 0.54 | 0.22 | 0.18 | 0.40 |

Caltagirone | 0.22 | 0.45 | 0.51 | 0.20 | 0.18 | 0.40 |

Caltanissetta | 0.23 | 0.46 | 0.49 | 0.22 | 0.19 | 0.41 |

Gela | 0.25 | 0.45 | 0.50 | 0.23 | 0.20 | 0.40 |

Mazzarino | 0.24 | 0.43 | 0.48 | 0.23 | 0.20 | 0.38 |

Mazzarrone | 0.22 | 0.38 | 0.46 | 0.19 | 0.19 | 0.35 |

Mineo | 0.25 | 0.41 | 0.49 | 0.22 | 0.20 | 0.37 |

Piazza Armerina | 0.24 | 0.40 | 0.48 | 0.21 | 0.20 | 0.36 |

Riesi | 0.21 | 0.43 | 0.47 | 0.22 | 0.18 | 0.39 |

**Table 4.**Sample size of each indicator for each station. Indicators are: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Normalized Standard Error (NSE), Correlation Coefficient (CC), Mean Bias Error (MBE), Probability Of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI).

Sample Size | ||||||||
---|---|---|---|---|---|---|---|---|

MAE, RMSE, NSE, CC, MBE | POD | FAR | CSI | |||||

Station | 30 min | Daily | 30 min | Daily | 30 min | Daily | 30 min | Daily |

Aidone | 271096 | 5606 | 10357 | 1713 | 10230 | 1138 | 12525 | 1908 |

Enna | 277955 | 5771 | 9525 | 1736 | 9914 | 1175 | 12147 | 1953 |

Caltagirone | 278038 | 5746 | 9809 | 1744 | 9900 | 1160 | 12106 | 1940 |

Caltanissetta | 279339 | 5785 | 10127 | 1649 | 9995 | 1100 | 12335 | 1865 |

Gela | 255197 | 5244 | 7589 | 1339 | 7618 | 915 | 9535 | 1523 |

Mazzarino | 277846 | 5759 | 9565 | 1711 | 9362 | 1192 | 11661 | 1929 |

Mazzarrone | 276200 | 5719 | 10564 | 1949 | 10217 | 1384 | 12541 | 2125 |

Mineo | 276521 | 5700 | 8796 | 1673 | 8689 | 1181 | 10847 | 1869 |

Piazza Armerina | 276542 | 5718 | 9676 | 1831 | 9467 | 1301 | 11782 | 2029 |

Riesi | 276562 | 5716 | 10748 | 1671 | 10483 | 1149 | 12745 | 1870 |

**Table 5.**Values of the radius of the confidence interval at 95% for each indicator and each station. Indicators are: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Normalized Standard Error (NSE), Correlation Coefficient (CC), Mean Bias Error (MBE), Probability Of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI).

Confidence Interval Radius (95%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

MAE, RMSE, NSE, MBE | CC | POD | FAR | CSI | ||||||

Station | 30 min | Daily | 30 min | Daily | 30 min | Daily | 30 min | Daily | 30 min | Daily |

Aidone | 0.001 | 0.124 | 0.003 | 0.016 | 0.007 | 0.020 | 0.008 | 0.020 | 0.006 | 0.018 |

Enna | 0.001 | 0.107 | 0.003 | 0.014 | 0.007 | 0.020 | 0.008 | 0.020 | 0.006 | 0.018 |

Caltagirone | 0.001 | 0.110 | 0.003 | 0.015 | 0.007 | 0.020 | 0.008 | 0.019 | 0.006 | 0.018 |

Caltanissetta | 0.001 | 0.114 | 0.003 | 0.015 | 0.007 | 0.020 | 0.008 | 0.021 | 0.006 | 0.019 |

Gela | 0.001 | 0.112 | 0.004 | 0.014 | 0.008 | 0.022 | 0.009 | 0.023 | 0.007 | 0.021 |

Mazzarino | 0.001 | 0.110 | 0.003 | 0.014 | 0.007 | 0.020 | 0.008 | 0.020 | 0.006 | 0.018 |

Mazzarrone | 0.001 | 0.117 | 0.003 | 0.015 | 0.007 | 0.018 | 0.008 | 0.017 | 0.006 | 0.017 |

Mineo | 0.001 | 0.116 | 0.003 | 0.015 | 0.008 | 0.020 | 0.009 | 0.020 | 0.006 | 0.018 |

Piazza Armerina | 0.001 | 0.126 | 0.003 | 0.015 | 0.007 | 0.019 | 0.008 | 0.019 | 0.006 | 0.018 |

Riesi | 0.001 | 0.102 | 0.003 | 0.014 | 0.006 | 0.020 | 0.008 | 0.020 | 0.006 | 0.019 |

$\mathit{d}$ (hours) | $\mathit{Q}$ (m3/s) | ||||||
---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{20}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{50}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{100}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{200}$ (years) | ${\mathit{T}}_{\mathit{R}}=500$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{1000}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{3000}$ (years) | |

1 | 1866.2 | 2160.2 | 2380.5 | 2600.0 | 2889.6 | 3108.5 | 3455.3 |

3 | 937.0 | 1084.6 | 1195.3 | 1305.5 | 1450.9 | 1560.8 | 1734.9 |

6 | 606.7 | 702.3 | 773.9 | 845.3 | 939.4 | 1010.6 | 1123.3 |

9 | 470.5 | 544.6 | 600.1 | 655.5 | 728.5 | 783.7 | 871.1 |

12 | 392.8 | 454.7 | 501.1 | 547.3 | 608.2 | 654.3 | 727.3 |

24 | 254.3 | 294.4 | 324.4 | 354.3 | 393.8 | 423.6 | 470.9 |

$\mathit{d}$ (hours) | $\mathit{Q}$ (m3/s) | ||||||
---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{20}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{50}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{100}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{200}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{500}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{1000}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{3000}$ (years) | |

1 | 1862.9 | 2276.3 | 2589.0 | 2901.7 | 3315.1 | 3627.8 | 3940.5 |

3 | 986.8 | 1206.9 | 1373.4 | 1540.0 | 1760.1 | 1926.6 | 2093.1 |

6 | 649.1 | 795.2 | 905.7 | 1016.2 | 1162.4 | 1272.9 | 1383.4 |

9 | 508.4 | 624.1 | 711.6 | 799.1 | 914.8 | 1002.3 | 1089.9 |

12 | 429.7 | 528.7 | 603.5 | 678.4 | 777.4 | 852.2 | 927.1 |

24 | 303.4 | 377.2 | 433.1 | 489.0 | 562.8 | 618.7 | 674.5 |

$\mathit{d}$ (hours) | $\mathit{M}\mathit{B}{\mathit{E}}_{\mathit{Q}}$ (%) | ||||||
---|---|---|---|---|---|---|---|

${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{20}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{50}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{100}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{200}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{500}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{1000}$ (years) | ${\mathit{T}}_{\mathit{R}}\mathbf{=}\mathbf{3000}$ (years) | |

1 | 0.2 | −5.1 | −8.1 | −10.4 | −12.8 | −14.3 | −15.6 |

3 | −5.0 | −10.1 | −13.0 | −15.2 | −17.6 | −19.0 | −20.2 |

6 | −6.5 | −11.7 | −14.6 | −16.8 | −19.2 | −20.6 | −21.8 |

9 | −7.5 | −12.7 | −15.7 | −18.0 | −20.4 | −21.8 | −23.0 |

12 | −8.6 | −14.0 | −17.0 | −19.3 | −21.8 | −23.2 | −24.5 |

24 | −16.2 | −22.0 | −25.1 | −27.5 | −30.0 | −31.5 | −32.8 |

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## Share and Cite

**MDPI and ACS Style**

Bertini, C.; Buonora, L.; Ridolfi, E.; Russo, F.; Napolitano, F.
On the Use of Satellite Rainfall Data to Design a Dam in an Ungauged Site. *Water* **2020**, *12*, 3028.
https://doi.org/10.3390/w12113028

**AMA Style**

Bertini C, Buonora L, Ridolfi E, Russo F, Napolitano F.
On the Use of Satellite Rainfall Data to Design a Dam in an Ungauged Site. *Water*. 2020; 12(11):3028.
https://doi.org/10.3390/w12113028

**Chicago/Turabian Style**

Bertini, Claudia, Luca Buonora, Elena Ridolfi, Fabio Russo, and Francesco Napolitano.
2020. "On the Use of Satellite Rainfall Data to Design a Dam in an Ungauged Site" *Water* 12, no. 11: 3028.
https://doi.org/10.3390/w12113028