# Performing Hydrological Monitoring at a National Scale by Exploiting Rain-Gauge and Radar Networks: The Italian Case

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Tools and Methods

#### 2.1. Study Area and Period

^{4}km

^{2}) located in the northern and central part of the country and many small- and medium-size steep catchments (drainage areas ranging from 10

^{1}to 10

^{3}km

^{2}) across the country. In the northern and north-eastern alpine and sub-alpine regions, climate is cold and temperate without a dry season [17]. While it is temperate with a dry season and arid all along the western coast and in the central and southern regions [17], with most of the rainfall in autumn and winter—a typical Mediterranean climate [18]. Consequently, annual maximum flows occur in late autumn and winter in Mediterranean regions, while during summer in the alpine ones [19], because of the snowmelt. Over recent years, Italy has faced several damaging hydrological events, such as flash floods and landslides associated with heavy rainfall events affecting its small, steep, and highly populated Mediterranean catchments [20,21] and spatially more extensive fluvial floods in larger catchments (http://polaris.irpi.cnr.it/event/, last accessed on 22 February 2021).

#### 2.2. Data

^{2}, with the highest value of 1/50 km

^{2}along the western coast and the lowest of 1/200 km

^{2}in southern Italy (Figure 2a) [20]. The temporal resolution changes from sensor to sensor but usually is 5–10 min. The Italian radar network was established for better monitoring capabilities of atmospheric phenomena [23,24], and the consequent detection and warning of severe weather related to hydrological risks. The network consists of 23 radars, covering the whole country (Figure 2b), and whose characteristics, in terms of location, band, polarization, and range, are reported in Table 1. The Marshall and Palmer relationship [25] is used to derive rainfall rates from radar reflectivity. Some portions of the domain are covered by more than one radar (Figure 2b), so it is possible to select a better estimate using the quality of the measures. The radar temporal resolution ranges from 5 to 10 min and QPE values are stored in pixels with spatial resolution 1 km × 1 km. Therefore, the radar network provides mosaiced products with 10 min temporal resolution and 1 km × 1 km spatial resolution.

_{obs}) and the corresponding simulated (Q

_{sim}) streamflow time series. Observed streamflow values exceeding the threshold on Q

_{obs}with corresponding simulated values less than the threshold on Q

_{sim}were marked as outliers, i.e., artifacts due to measurement errors, rather than real streamflow peaks, and removed. Moreover, step (ii) was thought to verify the coherence among upstream and downstream sections, and step (iii) with rainfall input data. Obviously, steps (i) and (ii) could be improved as they were basically qualitative checks. As a result of the quality check, we assigned a score between 0 to 5 to each section (0, very unreliable observations; 5, very reliable observations). We did not fill missing values, but we did not consider w.y. with more than 6 months of missing data, both because of unavailability of data or the outlier identification and removing procedure.

#### 2.3. Modified Conditional Merging

#### 2.3.1. Description of the Method

^{2}). In the last decade a radar network for a better rainfall estimation and monitoring was also set up. Both sets of data are available in real-time. Considering the spatio-temporal availability and the fact that rain gauges have good reliability but punctual observations, while radars have wide domains but with higher uncertainties (due to indirect measurement) the choice of a geostatistical approach must be the best one. Geostatistical methods are based on the evaluation of the spatial correlation of data and their goal is to evaluate the effect of the position of the measuring point on the variability of the observed data. Such variability is usually modeled by the semi-variogram, a mathematical function, which assesses the variation of the degree of correlation of points at increasing distances. The geostatistical methods get results by performing a recalibration of the field (i.e., radar map), forcing it to pass through the measuring points with certain characteristics of the covariance. Their advantage lies in the fact that they preserve the observed value in the control points, typically the rain-gauge values, which are assumed to be the more reliable evaluation of rainfall [35,36].

_{i}the observation of p-ith point, x the location of p-ith point, N the number of point couple at l lag distance, σ

^{2}the variance of the spatial domain where the correlation is evaluated, and μ the mean of the spatial domain where the correlation is evaluated. Obviously, the more information is available about involved lags, the better the estimation of correlation. In the MCM every pixel of the radar map is considered as a rain gauge, so it is possible to evaluate correlation for all the lags between the spatial resolution and the maximum distance for which rain gauges have influence (Figure 5a). In the case of CM, the limitation is that the correlation is estimated based on the ground-based rain gauges, that are in limited number, so the lags available for correlation estimation are few and generally similar to each other, with no information about smaller or greater values (Figure 5b) and this can lead to an inaccurate estimation of the kernel function.

#### 2.3.2. Analysis of Rainfall Fields

#### 2.4. Operational Hydrological Model at National Scale

_{th}is chosen as the 99 percentile of the observed hydrograph along the calibration period, and Q

_{m}(t) and Q

_{o}(t) are the modelled and observed streamflow at time t. In those portions of territory (catchments or sub catchments) where calibration was not possible, for example because of lack of data, we set parameters according to the similarity of that portion of territory to calibrated catchments, in terms of processes involved in the rainfall-runoff transformation. As an alternative, average values of parameters are assumed. This is coherent with what done and discussed in [44] for instance.

## 3. Results

#### 3.1. Analysis on Rainfall Fields

#### 3.1.1. Cross-Validation of MCM

#### 3.1.2. Catchment-Scale Comparison

#### 3.2. Performances of Hydrological Simulations

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- Rain-gauge rainfall accumulation on temporal domain (Figure A1).
- Radar observation accumulation over spatio-temporal domain (Figure A2);
- Interpolation of rain-gauge values (Figure A5);
- Interpolation of radar values sampled on rain-gauge locations and using the same local parameters as for rain-gauge interpolation (Figure A6);
- Difference between radar map and the interpolation of radar, to identify the small-scale structure of the event (Figure A7);
- Sum of the difference map (obtained in step 6) and the rain gauge interpolation, to force the output map passing through the rain gauge points with the structure from the radar observations (Figure A8).

**Figure A3.**Example of local window domain centered on the rain gauge location (

**a**) and on the radar map (

**b**). On this area, the correlation is evaluated and the best covariance kernel is identified.

**Figure A7.**Example of the difference between GRISO interpolation on radar and rainfall field. This map represents the small scale of the event.

## Appendix B

- Ground observations are preserved. This means that on the gauge location the output field maintains the measured values.
- Tendency to a selectable value. The field F(x, y) far from the gauge locations and their influence assumes a specific imposed value.
- Usage of a different structure of kernel. If information about the local field structure is available, it is possible to integrate it to improve the local estimation.

_{V}, or any other value. Moreover, the option (3) allows the local small spatial scale to be reproduced. This is difficult to be represented by a simpler interpolator.

**N**is the number of rain gauge used, so it has a unique solution.

_{K}

_{i}is the mean of Kxy, Vi is the observed rainfall accumulated value of the rain gauge I, μ

_{V}is the tendency imposed value, and Wi are the coefficients that solve the system.

_{Ki}is used, instead of values of 1. This simple difference brings out the aforementioned characteristic.

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**Figure 1.**Location of study sections (markers with violet edge are sections with available observed streamflow data).

**Figure 2.**Italian rain-gauge network (

**a**) and radar network (

**b**). In (

**b**), blue radar icons refer to C-band radars, while light blue ones to X-band radars.

**Figure 4.**Example of empirical 3D local structure evaluated from the radar observation. The values are between 0 (no correlation) and 1 (perfect correlation (located only on the rain-gauge location)).

**Figure 6.**Ensemble of statistical moments varying with density. The subplots indicate (

**a**) mean, (

**b**) standard deviation, (

**c**) skewness, and (

**d**) kurtosis.

**Figure 7.**Ensemble of power spectra slope mean along x directions of the interpolators (

**a**) and NSE (

**b**), varying with the density. The blue lines indicate MCM, while the black ones indicate CM.

**Figure 8.**Ensemble of PBIAS (

**a**) and RMSE (

**b**), varying with densities. The blue lines indicate MCM, while the black ones indicate CM.

**Figure 9.**Ensemble of the PDF of differences between run and original field. The subplots correspond to the different sampling percentage of gauge used: (

**a**) 10%, (

**b**) 25%, (

**c**) 50%, and (

**d**) 75%, while the numbers 1 and 2 are the MCM and CM simulations, respectively.

**Figure 10.**Scatterplot between daily areal mean rainfall from MCM and daily areal mean rainfall from ground-based data.

**Figure 11.**Maps of RMSE (

**a**) and PBIAS (

**b**) between daily areal mean rainfall from MCM and daily areal mean rainfall from ground-based data.

**Figure 12.**Frequency histograms of RMSE (

**a**) and PBIAS (

**b**) between daily areal mean rainfall from MCM and daily areal mean rainfall from ground-based data.

**Figure 13.**Frequency histograms of REHF (

**a**) and Nash–Sutcliffe (

**b**), considering all the study sections.

**Figure 14.**Frequency histograms of REHF (

**a**) and Nash–Sutcliffe (

**b**), considering only the calibrated sections.

**Figure 15.**Frequency histograms of REHF (

**a**) and Nash–Sutcliffe (

**b**), considering only the sections which observed discharge, is evaluated with a score greater than or equal to 3.

**Figure 17.**Comparison between observed and modelled hydrographs for a section not calibrated but with reliable observed streamflow data.

Longitude | Latitude | Band | Polarization | Range (km) |
---|---|---|---|---|

11.6239 | 44.6561 | C | double | 200 |

11.6739 | 45.3561 | C | single | 200 |

11.2072 | 46.4894 | C | single | 200 |

7.7239 | 45.0228 | C | double | 200 |

8.1906 | 44.2394 | C | double | 200 |

10.4906 | 44.7894 | C | double | 200 |

13.4739 | 45.7228 | C | double | 200 |

9.0072 | 40.4228 | C | double | 200 |

13.1800 | 42.0500 | C | single | 200 |

12.7906 | 45.6894 | C | single | 200 |

8.1700 | 40.5700 | C | double | 200 |

12.2300 | 41.9100 | C | single | 200 |

9.2800 | 45.3400 | C | single | 200 |

10.6072 | 43.9561 | C | double | 200 |

16.6239 | 39.3728 | C | double | 200 |

12.7906 | 42.8561 | C | double | 200 |

14.6239 | 41.9394 | C | double | 200 |

12.9739 | 46.5561 | C | double | 200 |

9.4938 | 39.8822 | C | double | 200 |

14.8239 | 37.1228 | C | double | 200 |

15.0498 | 37.4617 | X | double | 100 |

15.6500 | 38.0700 | X | double | 100 |

14.2750 | 40.8800 | X | double | 100 |

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**MDPI and ACS Style**

Bruno, G.; Pignone, F.; Silvestro, F.; Gabellani, S.; Schiavi, F.; Rebora, N.; Giordano, P.; Falzacappa, M.
Performing Hydrological Monitoring at a National Scale by Exploiting Rain-Gauge and Radar Networks: The Italian Case. *Atmosphere* **2021**, *12*, 771.
https://doi.org/10.3390/atmos12060771

**AMA Style**

Bruno G, Pignone F, Silvestro F, Gabellani S, Schiavi F, Rebora N, Giordano P, Falzacappa M.
Performing Hydrological Monitoring at a National Scale by Exploiting Rain-Gauge and Radar Networks: The Italian Case. *Atmosphere*. 2021; 12(6):771.
https://doi.org/10.3390/atmos12060771

**Chicago/Turabian Style**

Bruno, Giulia, Flavio Pignone, Francesco Silvestro, Simone Gabellani, Federico Schiavi, Nicola Rebora, Pietro Giordano, and Marco Falzacappa.
2021. "Performing Hydrological Monitoring at a National Scale by Exploiting Rain-Gauge and Radar Networks: The Italian Case" *Atmosphere* 12, no. 6: 771.
https://doi.org/10.3390/atmos12060771