# Rainwater Harvesting for Urban Landscape Irrigation Using a Soil Water Depletion Algorithm Conditional on Daily Precipitation

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, blue water use, ecotoxicity, eutrophication, and human health (in terms of anticancer activity). However, RWH-based irrigation is a special kind of water-saving irrigation using much less water than conventional water-saving irrigation (also called “low-rate irrigation”), and water supplied to crops is generally limited to 10–15% of the total crop water consumption over the whole growing season [11]. The work of [12] demonstrated the suitability of sustainable rainwater harvesting to support domestic or small-community agriculture or assist in fighting small forest fires.

## 2. Methodology

#### 2.1. Rainfall Climatology

#### 2.2. The Behavioural Model

_{t}(L) is the precipitation amount, Q

_{t}(L

^{3}) is the volumetric rainwater inflow to the storage tank, S (L

^{3}) is the storage capacity of the system (or tank volume), V

_{t}(L

^{3}) is the actual rainwater volume stored in the system, Y

_{t}(L

^{3}) is the released volume, O

_{t}(L

^{3}) is the overflow volume, and D

_{t}(L

^{3}) is the water demand. The rainwater inflow to the storage tank Q

_{t}(L

^{3}) is evaluated based on the flow that is collected at each computational step t and conveyed to the storage tank using the rational formula:

^{2}) is the extension of a generic collection area.

_{t}and V

_{t}are defined as follows, according to the so-called Yield After Spillage (YAS) algorithm:

#### 2.3. Water Demand and Rainwater Collection Scenarios

_{t}) is obtained, at each time step t, as a function of the actual soil water content according to the following scheduling of irrigation and watering criteria:

- Irrigation is not activated if it rains to cover at least the daily water need or if, in dry days, the soil water content is at least 80% of the WHC;
- Irrigation is always activated when the soil water content drops below the threshold of 80% of the WHC;
- The WHC of soil is recovered only after sufficiently large precipitation events but not from irrigation, which is used to ensure that only the water need of vegetation is fulfilled.

_{t}, expressed in mm) at each time step t is obtained according to the following rule:

_{t}(m

^{3}), is, therefore, given by:

_{meadows}, A

_{shrubs}, and A

_{trees}are the surface areas of the irrigated portions covered with meadows, shrubs, and trees, respectively equal to 1369, 801, and 1400 m

^{2}. Per each area, the initial condition at the start of the simulation period is set as a soil water content equal to the WHC.

_{eq}is the equivalent runoff coefficient and A

_{tot}is the total extension of the collection area in each solution:

- Scenario 1: Rainwater collected from the drainage of ground surfaces with A
_{tot}= 7925.6 m^{2}and ϕ_{eq}= 0.4; - Scenario 2: Rainwater collected from a sheet metal roof with A
_{tot}= 1800 m^{2}and ϕ_{eq}= 0.95; - Scenario 3: Rainwater collected from a brick roof with A
_{tot}= 4960 m^{2}and ϕ_{eq}= 0.85.

- Sports field and skate area (synthetic membrane): 850 m
^{2}; - Staircases (impervious material): 125 m
^{2}; - Playground (anti-trauma paving): 220 m
^{2}; - Sand playground (sand): 30 m
^{2}; - Pedestrian and driveway area paving (resin gravel): 3280 m
^{2}; - Historical and existing paving (stone): 1347 m
^{2}; - Green areas (meadows): 2074 m
^{2}.

## 3. Results and Discussion

_{e}), and two volumetric reliability indices (efficiency, E

_{T}, and overflow ratio, O

_{T}).

_{t}> 0.

_{T}is defined as the ratio between the rainwater volume provided by the tank and the associated water demand over the simulation period, while O

_{T}is defined as the ratio between the overflow volume and the total rainwater volume collected over the simulation period.

_{T}is the annual released volume.

_{t}) and the rainwater volume stored in the tank at the previous time step (V

_{t−}

_{1}), based on the following algorithm:

^{3}are considered to identify the most suitable system design.

^{3}in Scenarios 1 and 3, the storage fractions are larger than 0.01, confirming the correct choice of the daily temporal scale to run the simulations (see [25]).

#### 3.1. Performance Indices

_{e}, top panels) and of the annual volumetric reliability indices (E

_{T}and O

_{T}, bottom panels) as a function of the storage fraction (S/Q). The box-and-whisker description is the same as that in Figure 1, while the continuous lines represent the regression functions calculated from the mean values of the investigated indices.

_{0}and a are two numerical coefficients obtained from the regression. The values of the obtained numerical coefficients and the Pearson coefficient (R

^{2}) are listed in Table 2.

_{e}) and the efficiency (E

_{T}) range between 0.2 and 1, and obviously increase with the tank size. Both are larger than 60% when the storage fraction is larger than 0.03, 0.1, and 0.02 in Scenarios 1, 2 and 3, respectively. This means that a much larger tank size (twice the volume) is required in Scenario 2 to achieve the same system reliability of the other two solutions. The most suitable design of the RWH system would, therefore, require an intermediate tank size, in the order of 120 m

^{3}.

_{T}/S decreases as the tank volume increases, since the added capacity is utilized less frequently (Figure 5, left-hand panel). The results show that by fixing the tank size, Scenario 3 and Scenario 1 exhibit higher mean values of U if compared with Scenario 2, which means that the adopted storage volume is much better exploited. The box-and-whisker description is the same as that in Figure 1, while the continuous lines represent the regression function calculated from the mean values of the investigated index. The best fit formulation is a power law, expressed as a function of the storage fraction S/Q as:

^{2}) are listed in Table 3.

#### 3.2. Detention Time

^{2}) are listed in Table 3.

^{3}) identified above is here also confirmed in terms of the resulting water quality, since it implies normalized detention times only slightly larger than one in all scenarios and thus close to the reference value assumed in this work. It is important to highlight that the detention time provides an indication of the water quality deterioration over time after it is collected in the tank, while this parameter does not account for the initial water quality conditions. Scenario 1, where part the collected rainwater is subject to infiltration in the soil, allows improved water quality conditions to be obtained thanks to the purifying capability of the terrain and vegetation.

## 4. Conclusions

^{3}, also considering the quality deterioration of the water in the storage tank and the economic benefit associated with the exploitation of the resource. Based on the assumed parameters, Scenario 1 and Scenario 3 exhibit similar performances. Scenario 1, which involves collecting rainwater from various ground surfaces in the park, requires a more complex drainage network below the various ground surfaces contributing rainwater to the storage tank if compared with the other two scenarios where a simple assembly of gutters and pipes can be employed. Pros include the quality of the collected rainwater thanks to the purifying potential of the terrain and vegetation in the collection areas. Scenario 2 involves collecting rainwater from the sheet metal roof, but with 40% of the effective surface area (ϕ

_{eq}· A

_{tot}) with respect to Scenario 3. Using Scenario 2 would require doubling the size of the storage tank to achieve efficiency values similar to those in the other two scenarios.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Quasi-bicentennial daily rainfall record as observed at the meteorological station of Genova Università, with continuous and dashed lines indicating the mean plus/minus the standard deviation of the whole series, respectively; (

**b**) seasonal variability of monthly precipitation. Boxes and whiskers encompass the central 50% and 80% of the dataset, respectively, while dots indicate the 5th and 95th percentiles of their non-parametric distribution. The mean and median values are depicted with thick and thin horizontal lines, respectively.

**Figure 2.**Schematics of the main elements of the simulated RWH system. P

_{t}is the precipitation amount; Q

_{t}is the rainwater inflow to the storage tank; S is the storage capacity of the system; V

_{t}is the rainwater volume stored in the tank; Y

_{t}is the released volume; O

_{t}is the overflow volume; and D

_{t}is the water demand.

**Figure 3.**Box-and-whisker plots of the variability of the annual demand fraction (D/Q) during the simulation period for the three investigated scenarios. The box-and-whisker description is the same as in Figure 1.

**Figure 4.**Box-and-whisker plots of the variability of the annual temporal reliability indices (R and R

_{e}in panels (

**a**) and (

**b**), respectively) and volumetric reliability indices (E

_{T}and O

_{T}in panels (

**c**) and (

**d**), respectively) as a function of the storage fraction (S/Q) in the three investigated scenarios. The box-and-whiskers description is the same as that in Figure 1. Continuous lines represent the logarithmic regression function calculated from the mean values of the investigated indices.

**Figure 5.**Box-and-whisker plots of the annual variability of the usage volume per unit of tank capacity (U = Y

_{T}/S, panel (

**a**)) and normalized detention time (τ/τ*, panel (

**b**)) as a function of the storage fraction (S/Q) in the three investigated scenarios. The box-and-whisker description is the same as that in Figure 1. Continuous lines represent the power law regression function calculated from the annual mean values.

**Table 1.**Storage capacity of the system (S) and storage fraction (S/Q) in the three investigated scenarios.

S (m^{3}) | S/Q (-) | ||
---|---|---|---|

Scenario 1 | Scenario 2 | Scenario 3 | |

30 | 0.007 | 0.014 | 0.006 |

60 | 0.015 | 0.028 | 0.011 |

120 | 0.030 | 0.055 | 0.022 |

240 | 0.060 | 0.111 | 0.045 |

480 | 0.119 | 0.221 | 0.090 |

**Table 2.**Coefficients (y

_{0}and a) and Pearson coefficient (R

^{2}) of the logarithmic regression function for the four reliability indices in each collection scenario.

R | R_{e} | E_{T} | O_{T} | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Scenario | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 |

y_{0} | 1.116 | 1.022 | 1.156 | 1.321 | 1.069 | 1.427 | 1.299 | 1.035 | 1.412 | 0.597 | 0.412 | 0.669 |

a | 0.072 | 0.065 | 0.075 | 0.198 | 0.179 | 0.203 | 0.201 | 0.181 | 0.208 | −0.063 | −0.103 | −0.049 |

R^{2} | 0.997 | 0.995 | 0.994 | 0.997 | 0.995 | 0.994 | 0.997 | 0.980 | 1.000 | 0.996 | 0.979 | 0.999 |

**Table 3.**Coefficients (α and β) and Pearson coefficient (R

^{2}) of the power law regression function for the usage volume per unit of tank capacity and the normalized detention time in each collection scenario.

Y_{T}/S | τ/τ* | |||||
---|---|---|---|---|---|---|

Scenario | 1 | 2 | 3 | 1 | 2 | 3 |

α | 0.706 | 0.829 | 0.629 | 40.60 | 22.07 | 51.34 |

β | −0.589 | −0.604 | −0.590 | 0.94 | 0.91 | 0.94 |

R^{2} | 0.994 | 0.997 | 0.994 | 1.000 | 1.000 | 1.000 |

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**MDPI and ACS Style**

Cauteruccio, A.; Lanza, L.G. Rainwater Harvesting for Urban Landscape Irrigation Using a Soil Water Depletion Algorithm Conditional on Daily Precipitation. *Water* **2022**, *14*, 3468.
https://doi.org/10.3390/w14213468

**AMA Style**

Cauteruccio A, Lanza LG. Rainwater Harvesting for Urban Landscape Irrigation Using a Soil Water Depletion Algorithm Conditional on Daily Precipitation. *Water*. 2022; 14(21):3468.
https://doi.org/10.3390/w14213468

**Chicago/Turabian Style**

Cauteruccio, Arianna, and Luca G. Lanza. 2022. "Rainwater Harvesting for Urban Landscape Irrigation Using a Soil Water Depletion Algorithm Conditional on Daily Precipitation" *Water* 14, no. 21: 3468.
https://doi.org/10.3390/w14213468