# Surface Water Flow Balance of a River Basin Using a Shallow Water Approach and GPU Parallel Computing—Pescara River (Italy) as Test Case

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}and well representative of a typical medium-sized basin, was selected. The topography was described by a 10 × 10 m digital terrain model (DTM), covered by about 1,700,000 triangular elements, equipped with 11 rain gauges, distributed over the entire area, with some hydrometers and some fluviometric stations. Calibration, and validation were performed considering the flow data measured at a station located in close proximity to the mouth of the river. The comparison between the numerical and measured data, and also from a statistical point of view, was quite satisfactory. A further important outcome was the capability to highlight any differences between the numerical flow-rate balance carried out on the basis of the contributions of all known sources and the values actually measured. This characteristic of the applied modeling allows better calibration and verification not only of the effectiveness of much more simplified approaches, but also the entire network of measurement stations and could suggest the need for a more in-depth exploration of the territory in question. It would also enable the eventual identification of further hidden supplies of water inventory from underground sources and, accordingly, to enlarge the hydrographic and hydrogeological border of the basin under study. Moreover, the parallel computing platform would also allow the development of effective early warning systems, for example, of floods.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geographical and Geological Setting of the Selected Study Area (Pescara River Basin, Abruzzo, Italy)

^{2}. The river enters the narrow gorges of Popoli considerably swollen, squeezed by the mountains of the Gran Sasso to the north and the Morrone massif to the south. Figure 1 shows the hydrographic boundary, selected for the study discussed in this paper. Maintaining the north-east direction, the river then crosses the alluvial plain of Pescara Valley, laps the lower part of the city of Chieti and enters to Pescara, dividing it in two and finally flowing into the Adriatic Sea. In this context, the mountain range has a high relief characterized by resistant preorogenic carbonates (Mesozoic—Lower Tertiary) and synorogenic siliciclastic valleys (Tertiary), as well as by intramountain basins of continental Quaternary deposits (post-orogenic) [23]. The foothill area is to the east of the mountain range and looks like a hilly environment, characterized by Miocene, Pliocene and Quaternary terrigenous deposits (related to sin- and post-orogenic phases of the Apennines). Here the marine environment persisted until the lower Pleistocene. Later, during the Middle Pleistocene, a phase of tectonic uplift began which, together with a series of glacial-interglacial cycles linked to the climatic transition of the period, favored a phase of fluvial incision and deposition. In general, however, we can distinguish the area into two fundamental units: the chain and the foredeep [24,25]. The first is characterized by carbonate masses, mostly Mesozoic, with variable facies, and by deposits of the Messinian terrigenous facies. The deposits of the carbonate platform, generally calcareous, are quite homogeneous. Instead, the Messinian facies (ranging from arenaceous, pelitic and evaporitic lithotypes) and pelagic (calcareous, flint, marl and clayey lithotypes) present an important diversification. The Avanfossa area, on the other hand, is characterized by clayey, marly and sandy sediments relating to the Plio-Pleistocene. The tectonic style of the area in question is characterized by imbricated tectonic scales in eastern vergence, with evident overlaps on the surface in correspondence with the chain, but also in depth where deposits dating back to the Middle Pliocene are involved. In this scenario, the Majella Massif is of particular importance as it is characterized by one of the water reservoirs of the Abruzzo region [23], carrying the potable water supply of the region, and has therefore been the subject of many studies for evaluation and protection. The Majella has a wide asymmetrical anticline, with an eastern slant that presents a variable inclination, which grows up to be sub-vertical. This anticline is characterized by a rather wide hinge, with an axis that progressively rotates towards the South, presenting NW-SE orientations in the northern part, to NS in the central Majella, and to NNE-SSW in the southern part. Observing the area to the west, from Caramanico to the south, the Majella anticline is cut off by a fault called “Faglia della Majella”, with a NS direction, with a rejection that varies from a few meters in the Caramanico area, up to 4 km in the area between Passo S. Leonardo and Campo di Giove. To the west of this fault, we can observe the depression of the Orta Valley, which is filled with terrigenous sediments, and which develops for about 20 km with a NW-SE direction.

#### 2.2. Data Analysis

^{3}s

^{−1}) and the total rainfall (mm/d) measured at the experimental stations, ranging from 2000 to 2007. Further, inspection of the figures allow us to highlight when, in correspondence with a rainy event, there is the relative flood wave (or peak of flood).

^{3}s

^{−1}, 18 m

^{3}s

^{−1}and 14 m

^{3}s

^{−1}, respectively for the time series of January 2003, the two semesters of the 2000 and the first half of 2007. These increases were sufficient to compensate, at least in part, the discrepancies.

#### 2.3. Selected Mathematical–Numerical Approach

#### 2.3.1. Hydrodynamic Unsteady Flow Models

#### 2.3.2. Manning’s Coefficient

#### 2.3.3. Infiltration and Evapotranspiration

#### 2.3.4. Numerical Solver

_{i}is the volume of the i-th computational cell, whose area of the k-th edge face is ${A}_{k}$. Then, the approximate solution is always constructed as a sum of jumps or shocks, also involving rarefactions [14].

#### 2.3.5. Optimal Time-Step Computation

#### 2.4. Conceptual Model and Selected Inputs

#### 2.4.1. Numerical Meshing

#### 2.4.2. Rainfall

#### 2.4.3. Discharge Inputs

^{3}/s).

#### 2.5. The Calibration Process

#### 2.5.1. Infiltration-Evapotranspiration Calibration; Merged Model (InF_Ev)

#### 2.5.2. Manning’s Number Parametric Calibration

#### 2.5.3. Useful Features of the Selected Numerical Tool

#### 2.5.4. Parallel Platform through GPU

- Central Processing Unit (CPU) Intel i7-7700 3.6 GHz;
- #Cores: 4;
- #Threads: 8;
- GPU Nvidia GeForce GTX 1060 6 GB;
- #GPU Cores: 1280;
- Clock: 1506 MHz;
- Ram: 32 Gb.

## 3. Results and Discussion

^{3}/s were added to the base-flow of the 2000 time series, while 14 m

^{3}/s was added to the base-flow of the 2007 time series. Figure 7 shows the good match between the measured values and the numerical values predicted after calibrating the model and adjusting adequately the input, as described above.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Basin overview. Red dots reports the pluviometric station location, small green dot reports S.Teresa River Flow rate measurement stations.

**Figure 2.**Time series comparison of the river flow rate (Pescara, S. Teresa), river inflow rate (Pescara-Maraone increased by Tirino-Madonnina) and rainfall from year 2000 to 2007. Red line: river flow rate at Pescara S.Teresa; black line: river inflow rate; blue dashed line: rainfall. Red arrows indicate the maximum value of the exceptional river flow rate peaks: A = 336 m

^{3}/s, B = 360 m

^{3}/s, C = 285 m

^{3}/s, D = 190 m

^{3}/s, E = 240 m

^{3}/s.

**Figure 3.**Display of the triangular meshes tessellation of a selected area of the entire basin, shown in smaller windows, with the indication of their location: (

**a**) simulated water flow distribution due to rainfall at $t=30\text{}\mathrm{h}$ after 1 January 2000; (

**b**) simulated water flow distribution due to rainfall at $t=300\text{}\mathrm{h}$ after 1 January 2000.

**Figure 4.**Comparison plots between measured and numerical river flow rate data at S. Teresa station; red line: river measured flow rate; dashed green line: original numerical river flow rate; solid blue line: translated numerical river flow rate; (

**a**) simulations: S1 ($k=0.00115$, final Infiltration rate ${f}_{c}=1.94\cdot {10}^{-6}$; initial Infiltration rate ${f}_{0}=1.41\cdot {10}^{-5}$ ); (

**b**): S2 ($k=0.00115$, ${f}_{c}=2.78\cdot {10}^{-7}$, ${f}_{0}=2.78\cdot {10}^{-8}$ ); (

**c**): S3 (downstream area $k=0.00115$, ${f}_{c}=2.78\cdot {10}^{-8}$, ${f}_{0}=2.78\cdot {10}^{-9}$, upstream area, $k=0.00115$, ${f}_{c}=1.816\cdot {10}^{-8}$, ${f}_{0}=1.816\cdot {10}^{-9}$ ); Manning’s number M = 0.1.

**Figure 5.**Comparison plots between measured and numerical river flow rate at Pescara S. Teresa Station; river measured river flow rate (m

^{3}/s): red line; river numerical flow rate (m

^{3}/s) resulting from simulations obtained by selecting different Manning’s coefficients: $\mathrm{M}1=0.1$ (green short dashed line), $\mathrm{M}2=0.035$ and $\mathrm{M}2=0.03$, respectively, within the main drainage area surrounding the riverbed path and within the rest of the basin (dark pink, medium dash line), $\mathrm{M}3=0.02$ (blue solid line).

**Figure 6.**Comparison between the computation times related to simulation A (red medium dashed line: CPU Only) and simulation B (blue solid line: CPU + GPU), for a simulated period of the developed model, equal to 216 h.

**Figure 7.**Comparison of measured river flow data at S. Teresa station and the numerical river flow rate data resulting from the validation test related to the years: (

**a**) 2000 and (

**b**) 2007. Dashed dark blue line: total rainfall (mm); solid red line: measured river flow rate (m

^{3}/s); solid blue line: numerical river flow rate (m

^{3}/s).

**Figure 8.**Regression between numerically predicted and measured flow rate at S. Teresa Station, during the selected time periods; days: (

**a**) from 1 January 2003 to 31 January 2003 (calibration); (

**b**) from 1 January 2000 to 30 June 2000 (validation); (

**c**) from 1 July 2000 to 31 December 2000 (validation); (

**d**) from 1 January 2007 to 30 June 2007 (validation).

**Figure 9.**Relative Differences between measured river flow rate and predicted numerical flows data: RDMN (%); days and hours: (

**a**) from 1 January 2003 to 31 January 2003 (calibration); (

**b**) from 1 January 2000 to 31 December 2000 (validation); (

**c**) from 1 January 2007 to 30 June 2007 (validation).

**Figure 11.**RDMN histograms based on the Freedman–Diaconis rule for each selected time period; μ is the distribution mean; σ is the standard deviation of the selected distribution.

$\mathit{n}$ | ${\mathit{q}}_{1}$ | ${\mathit{q}}_{3}$ | $\mathit{m}\mathit{i}\mathit{n}(\mathit{x})$ | $\mathit{m}\mathit{a}\mathit{x}(\mathit{x})$ | Bins | |
---|---|---|---|---|---|---|

January 2003 | 31 | −5.87 | 18.85 | −31.12 | 35.04 | 4 |

1 semester 2000 | 181 | −3.77 | 2,41 | −23.69 | 22.21 | 21 |

2 semester 2000 | 183 | −9.13 | −1.15 | −53.69 | 28.65 | 29 |

1 semester 2007 | 181 | −3 | −1 | −15 | 10 | 35 |

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**MDPI and ACS Style**

Pasculli, A.; Longo, R.; Sciarra, N.; Di Nucci, C.
Surface Water Flow Balance of a River Basin Using a Shallow Water Approach and GPU Parallel Computing—Pescara River (Italy) as Test Case. *Water* **2022**, *14*, 234.
https://doi.org/10.3390/w14020234

**AMA Style**

Pasculli A, Longo R, Sciarra N, Di Nucci C.
Surface Water Flow Balance of a River Basin Using a Shallow Water Approach and GPU Parallel Computing—Pescara River (Italy) as Test Case. *Water*. 2022; 14(2):234.
https://doi.org/10.3390/w14020234

**Chicago/Turabian Style**

Pasculli, Antonio, Roberto Longo, Nicola Sciarra, and Carmine Di Nucci.
2022. "Surface Water Flow Balance of a River Basin Using a Shallow Water Approach and GPU Parallel Computing—Pescara River (Italy) as Test Case" *Water* 14, no. 2: 234.
https://doi.org/10.3390/w14020234