# ORGANICS: A QGIS Plugin for Simulating One-Dimensional Transport of Dissolved Substances in Surface Water

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}],

_{x}: longitudinal fluid flow velocity is the input velocity [L/T].

^{2}/T].

^{−1}].

_{0}= 0 [L] (the inlet point of a surface water body reach) at the initial time (t

_{0}= 0) [T], for each x > 0 and t > 0 the Equation (1) may be reduced to the following analytical solution (2) [10,37].

_{0}= 0 [T] the initial condition is C(

_{x},

_{0}) = 0 [M/L

^{3}] along all the simulated domains.

#### 2.1. Software Development

#### 2.2. Data Needs

- a *.csv file specifying the water average longitudinal velocity (U) and concentration values at the inlet of the watercourse (constant concentration boundary condition), and the time these data refer to. The file must comply with the template format defined for the plugin. In particular, the file must contain data relating to (at least) one dataset, specifying:
- -
- starting date and time, in YYYY-MM-DD HH: MM: SS format;
- -
- average flow velocity in the surface water body, in m · s
^{−1}. This value will be used at all the node of the surface water body; - -
- the concentration of the source at the inlet point.

- an ESRI linear Shapefile representing the surface water body. The file may consist of one or more segments. The line must be digitized towards the flow direction. When more segments are used, the topology must be respected (all the lines must be connected).

#### 2.3. Model Implementation and Run

^{−1});

^{2}/s);

- Select a position (distance in m from the entry point): this option will create a graph displaying the concentration trend in a point defined by the user at a certain distance from the starting point, as a function of time (Figure 4);
- Use the selected position on the layer: this option allows to view the same result as above, but in this case the position is provided by selecting, using the classic selection tools on the map, one or more points of the output layer (Figure 5);
- Select a time: this graph will display the concentration values, at a given simulated time, as a function of the distance from the inlet (Figure 6). The times available for selection correspond to the discretization obtained with the time step chosen in input by the user.

## 3. Results and Discussion

#### 3.1. Model Validation

^{−1}(no decay is simulated)

^{2}/s

_{(0,0)}= C

_{0}, and

_{(x,0)}= 0 at x > 0

#### 3.2. Example Problem

_{0}mass injection, constant over time;

_{0}mass injection;

_{0}mass input, variable over time (multi-pulse input condition).

#### 3.2.1. C_{0} Mass Injection, Constant over Time

_{0}= 100 ng/L constant over time. The solution is presented at the end of the simulation time, which is the time needed for the mass to reach the outlet.

#### 3.2.2. Time-Limited Pulse C_{0} Mass Injection

_{0}= 100 ng/L mass injection for a 2 h duration. This time-limited pulse case, at constant concentration, can be implemented by defining in the *csv file an initial period (of known duration, with concentration C

_{0}; first line in the *csv file) followed by a second period with zero concentration (second line in the *csv file). In this test, the second input is then two hours long with concentration set at C

_{2h}= 0 ng/L. The solution is then displayed in Figure 9 at an infinite time (that is, the time needed for the dissolved substance to reach the outlet of the water course considered). The solution is presented at x = 500 m (Figure 9). At this distance, mass arrival is recorded after 30 min from the beginning of the simulation.

#### 3.2.3. C_{0} Mass Input, Variable over Time (Multi-Pulse Boundary Condition)

_{0}mass input, variable over time (multi-pulse input condition) according to data presented in Table 2. The global solution works as the superposition of the several pulses, each one having a constant condition for a specified time interval. Superposing each “pulse-solution” makes the model able to consider time-dependent boundary conditions. Results are shown at x = 400 m, x = 800 m, and x = 1200 m from the inlet point for time step length of:

#### 3.3. Case Study Application

_{w}= 0 m) and the outlet (point PSM

_{z}= 420 m) of the channel reach (Figure 13) in low-flow conditions. Analytical determinations were performed following the method described in [48]. Mean longitudinal flow velocities were measured by means of an acoustic digital current meter (OTT Messtechnik GmbH, Kempten; Germany). Data for CBZ and mean longitudinal flow velocities are presented in Table 3.

_{z}, 420 m from the inlet point. The Simulated value (PSM

_{z_sim}) column in Table 3 presents the simulated value against the measured ones (Outlet (PSM

_{z}) column). In Figure 13 CBZ simulated concentrations are themed with color scales depending on the concentration value.

^{2}= 0.95) between simulated and measured concentrations with values of the longitudinal dispersion coefficient of 35 m

^{2}/s and decay rate equal to 3 · 10

^{−5}s

^{−1}. Good fit (R

^{2}> 0,9) was also obtained varying these two parameters within the range of 30 and 35 m

^{2}/s for longitudinal dispersivity and between 2.5 · 10

^{−5}and 3 · 10

^{−5}s

^{−1}for the decay rate coefficient. The values of the longitudinal dispersion coefficient are coherent with values found in [49,50] for similar open channels. The calibrated values of the decay rate are slightly higher than calculated values from half-life time data for CBZ reported in [51].

## 4. Conclusions

^{2}/s and 3 · 10

^{−5}s

^{−1}for the pharmaceutical compound carbamazepine. Another potential application could be in the feasibility stage of the design of water-related green infrastructures for the improvement of water quality [46,52]. On the other hand, the increasing number of integrated geographical databases (including surface water bodies characteristics) along with the increasing availability of sensors gathering and distributing quasi real-time monitoring data (such as surface water heads) may allow for the combined use of monitoring and modelling to set up early warning systems to track pollution events [53,54,55]. To this aim, further research and pilot experimental sites are needed.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Example graph: solution at a selected points as function of time. Two points selected by using the GIS selection tools.

**Figure 7.**Computed simplified analytical solution implemented in Organics in time at x = 100 m and x = 1000 m.

**Figure 8.**C

_{0}mass injection, constant over time: concentration values at selected points of the reach.

**Figure 10.**Simulated concentration at x = 400 m, x = 800 m, and x = 1200 m from the inlet point with 20 min time step length.

**Figure 11.**Simulated concentration at x = 400 m, x = 800 m, and x = 1200 m from the inlet point with 10 min time step length.

**Figure 12.**Simulated concentration at x = 400 m, x = 800 m, and x = 1200 m from the inlet point with 5 min time step length.

**Figure 14.**Simulated concentration at x = 20 m, and x = 420 m from the inlet point with 10 min time step length.

Parameter | Value | Units |
---|---|---|

Total length of the reach | 1200 | m |

Simulation length | 50 | m |

Time step | 10 | min |

Velocity (U) | 0.1 | m/s |

First order decay rate (k) | 0.00005 | s^{−1} |

Longitudinal dispersion (E) | 5.0 | m^{2}/s |

Initial time | 28 May 2018 00:00 | dd/mm/yyyy hh:mm |

**Table 2.**Data used in the test presented in Section 3.2.3.

Date and Time | C_{0} (ng/L) |
---|---|

28 May 2018 0:00 | 0 |

28 May 2018 0:20 | 100 |

28 May 2018 2:00 | 50 |

28 May 2018 2:30 | 25 |

28 May 2018 3:30 | 75 |

28 May 2018 4:00 | 0 |

**Table 3.**Carbamazepine concentrations at the inlet (PSMw) and outlet (PSMz) points of the vegetated channel on 28 May 2018, and simulated results.

Time | Inlet (PSM_{w}) (ng/L) | Outlet (PSM_{z})(ng/L) | Flow Velocity (m/s) | Simulated Value (PSM_{z_sim}) (ng/L) |
---|---|---|---|---|

07:20 | 123 | - | 0.025 | - |

09:50 | 181 | - | 0.026 | - |

11:00 | - | 105 | - | 112 |

12:20 | 162 | - | 0.026 | - |

13:10 | - | 112 | - | 116 |

14:20 | 162 | - | 0.021 | - |

15:40 | - | 115 | - | 119 |

16:50 | 150 | - | 0.029 | - |

18:00 | - | 125 | - | 122 |

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## Share and Cite

**MDPI and ACS Style**

Rossetto, R.; Cisotto, A.; Dalla Libera, N.; Braidot, A.; Sebastiani, L.; Ercoli, L.; Borsi, I.
ORGANICS: A QGIS Plugin for Simulating One-Dimensional Transport of Dissolved Substances in Surface Water. *Water* **2022**, *14*, 2850.
https://doi.org/10.3390/w14182850

**AMA Style**

Rossetto R, Cisotto A, Dalla Libera N, Braidot A, Sebastiani L, Ercoli L, Borsi I.
ORGANICS: A QGIS Plugin for Simulating One-Dimensional Transport of Dissolved Substances in Surface Water. *Water*. 2022; 14(18):2850.
https://doi.org/10.3390/w14182850

**Chicago/Turabian Style**

Rossetto, Rudy, Alberto Cisotto, Nico Dalla Libera, Andrea Braidot, Luca Sebastiani, Laura Ercoli, and Iacopo Borsi.
2022. "ORGANICS: A QGIS Plugin for Simulating One-Dimensional Transport of Dissolved Substances in Surface Water" *Water* 14, no. 18: 2850.
https://doi.org/10.3390/w14182850