# Dual Benefit of Rainwater Harvesting—High Temporal-Resolution Stochastic Modelling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Model Framework

_{t}) and yields (Y

_{t}) usually differentiate models from each other. Inflows are a function of rainfall and collection surface. Rainfall data are unique for each location, and could be used as-is if their attributes (timestep and number of records) is sufficient (e.g., [20]). Rainfall data could also be synthesized [16], or generated stochastically [25].

_{t}to the main rainwater tank is given by:

_{t}is rain depth (m); DL

_{max}is the maximum depth of the depression losses tank (m); η is gutter system losses (−); and A

_{roof}is the roof area (m

^{2}).

_{max}is the tank capacity.

_{t}> 0, S

_{t}is set to S

_{max}, and the timestep is completed after demands are fulfilled.

#### 2.2. Efficiency Estimators

_{t}is the is water demand of the designated use (toilet flushing in this study) for timestep t.

_{t}+ CR

_{t}) is the maximum sum of overflow and controlled release for a specific timestep from the storage tank recorded in a certain year, and max(O

_{t}, S

_{max}= 0) is the maximal recorded overflow for the same year where the tank volume (S

_{max}) is 0, i.e., the maximum roof runoff (with no RWH system).

#### 2.3. Real-Time Control (RTC)

_{t}) plus the current volume of water in the tank (S

_{t}) exceed the overall tank volume. If so, the module simulates the opening of a valve (conceptually installed at the bottom part of the tank) for releasing water in a controlled manner. The release flowrate is a function of the current water level in the tank and the orifice’s cross-sectional area:

_{CRt}is the controlled release rate of flow, C

_{d}is the coefficient of discharge, A is the orifice’s cross-sectional area, g is the gravitational acceleration and h is the height of water column above the orifice.

_{t}is calculated by implementing the numerical midpoint method and multiplying the resulting controlled release flow with the timestep duration.

_{CR}declines with time, as the height of the water above the release valve decreases. To investigate different release policies, a release decision parameter α ranging from 0 to 1 is introduced, and the valve will remain open and release water until the following term is satisfied:

#### 2.4. Water Demand

#### 2.5. Meteorological Data of the Case Study

#### 2.6. Stochastic Modelling Framework

## 3. Results and Discussion

#### 3.1. Storage Tank Sizing

^{3}carries little benefit. PFR (peak-flow reduction) values grow linearly and are scattered along the y axis from 0 to 1. The VRE (volume reduction efficiency) values suggest that a significant portion of the annual rainfall could be harvested and used even with relatively small tanks.

^{2}was modeled. The model was executed for 100 randomly selected rain seasons. WSE, PFR, and VRE were calculated (Figure 4).

^{3}/year, and the mean annual rainwater volume harvested (i.e., annual rain X roof area minus depression losses minus transfer losses; Equation (2)) was 341 m

^{3}. This corresponds with [7], who estimated the annual available rainwater volume from a 850 m

^{2}roof in an areas of Jordan with average rainfall of 500 mm per year to be 360 m

^{3}.

^{3}storage tank, the median WSE reaches 0.18 (25–75 percentiles from 0.16 to 0.22) of the total annual demand (including the rainy winter and the dry summer), which corresponds with the findings of [29] on RWH feasibility in apartment buildings. Another simulation was conducted on a building with 16 apartments with a roof area of 400 m

^{2}, similar to a building modeled by [25]. The results show similar correlations between WSE and tank volume, with WSE reaching a maximum value of 0.19 with a tank volume of 35 m

^{3}or above. Muklada’s results showed a maximum value of 0.2 for WSE for the same tank volume while also supplying rainwater for laundry. It should be noted that in Muklada’s study demand data were deterministic, and the model was executed on a daily timestep. These differences could have caused the difference in the maximum WSE between the current study and Muklada’s findings.

^{2}roof was simulated to check the model’s correspondence with the findings of Palla et al. [37], who examined the WSE of RWH systems in Catania, Italy (590 mm mean annual rainfall). According to Palla et al. a building with a 50 m

^{3}tank and similar annual rainwater volume to annual demands ratio would reach WSE of 0.4, while the present model estimated a WSE of 0.35. This difference could be explained by the fact that rainfall in Israel characterized by short and intense storms, scattered mainly from November to March. This is causes more frequent overflows and less rainwater availability to satisfy demands. The modeled building with a 50 m

^{3}tank is able to collect 75% of the annual rainwater while the rest overflows, compared with a building with the same attributes in Catania, which is expected to collect more than 90% of the annual rainfall according to Palla et al.

^{3}tank is capable to capture 54% of the annual rainfall. Therefore, 50 m

^{3}tanks can collect 95% (median value, 25–75 percentiles from 89% to 99%) of the annual rainfall, and all tank sizes larger than 25 m

^{3}enable the use of at least 80% (median value) of the annual rainfall, or in other words, an at least 80% reduction of the annual overflow volume.

#### 3.2. Efficiency Curves

^{2}and an apartment number of 30–60 were modelled under similar 100 rain-season simulation, resulting in 100 PFR, WSE and VRE results per building. Contour plots of the mean values of the estimators were charted as a function of storage tank volume and the normalized roof area (roof area (m

^{2}) divided by mean annual demands (m

^{3}); Figure 5).

^{2}, and an estimated annual toilet flushing water use of 1930 m

^{3}(the latter can be estimated by multiplying the number of tenants by the expected annual water use for toilet flushing per capita). This building has a roof area to annual demand ratio of 0.45 m

^{−1}. For the purpose of this demonstration, the main objective of installing the RWH system in this building is to reduce the expected peak flow from the roof by 40%. By examining the PFR curves, it can be deducted that a rainwater tank of 35 m

^{3}would reduce the annual peak flows by 40% (on average) and would be able to supply about 17% of the annual toilet flushing water demand (WSE). If the desired PFR is 0.5, a tank of 45 m

^{3}would be needed for the same building. A tank of such volume would supply 18% of the annual demand for toilet-flushing, and reduce by 90% the annual overflow volume (VRE) of the system.

#### 3.3. RTC Policies

^{3}tank. The simulation included 100 years, and a total of 11 systems were simulated. Each RWH system was modelled with similar rain seasons and supplied water to the same building with identical demands, with the only difference being the value of α (α = 0, 0.1, 0.2,…, 1).

^{3}and run for 100 years (as before).

^{3}/year, this decrease reduces the total volume of supplied rainwater by 40 m

^{3}. When setting α = 0.3, the VRE median value decreases by 19% (from 0.75 to 0.61).

## 4. Conclusions

- The model enables simulation of various buildings (varying in the number of apartments and dwellers), collection surface (roof) areas, rainwater tank volumes and time periods; from single rain events up to multi-seasonal simulations
- Model inputs (rainfall and demands) are used in a stochastic manner (sampling with replacement), which maintains their natural pattern while generating realistic noise and temporal variability. In this way, creating rainfall and demand data series does not require rigorous data analysis on the one hand, and does not degenerate input data to constant or deterministic values on the other.

- Estimating the short term benefits such as runoff reduction for specific storms, as well as long term evaluations of peak runoff flow reduction, overall annual overflow volume reduction, and rainwater supply efficiencies.
- Comparing the performances of different tank sizes under the same conditions
- Drawing design curves for a range of tank sizes and roof areas for specific rainfall data
- Inspecting different RTC policies and their effects on the system’s efficiency.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Campisano, A.; Butler, D.; Ward, S.; Burns, M.J.; Friedler, E.; DeBusk, K.; Fisher-Jeffes, L.N.; Ghisi, E.; Rahman, A.; Furumai, H.; et al. Urban Rainwater Harvesting Systems: Research, Implementation and Future Perspectives. Water Res.
**2017**, 115, 195–209. [Google Scholar] [CrossRef] [PubMed] - Ranaee, E.; Abbasi, A.A.; Yazdi, J.T.; Ziyaee, M. Feasibility of Rainwater Harvesting and Consumption in a Middle Eastern Semiarid Urban Area. Water
**2021**, 13, 2130. [Google Scholar] [CrossRef] - Farreny, R.; Morales-Pinzón, T.; Guisasola, A.; Tayà, C.; Rieradevall, J.; Gabarrell, X. Roof Selection for Rainwater Harvesting: Quantity and Quality Assessments in Spain. Water Res.
**2011**, 45, 3245–3254. [Google Scholar] [CrossRef] [PubMed] - Rahman, A. Recent Advances in Modelling and Implementation of Rainwater Harvesting Systems towards Sustainable Development. Water
**2017**, 8, 959. [Google Scholar] [CrossRef][Green Version] - Campisano, A.; Modica, C. Optimal Sizing of Storage Tanks for Domestic Rainwater Harvesting in Sicily. Resour. Conserv. Recycl.
**2012**, 63, 9–16. [Google Scholar] [CrossRef] - Semaan, M.; Day, S.D.; Garvin, M.; Ramakrishnan, N.; Pearce, A. Optimal Sizing of Rainwater Harvesting Systems for Domestic Water Usages: A Systematic Literature Review. Resour. Conserv. Recycl. X
**2020**, 6, 100033. [Google Scholar] [CrossRef] - Abdulla, F. Rainwater Harvesting in Jordan: Potential Water Saving, Optimal Tank Sizing and Economic Analysis. Urban Water J.
**2020**, 17, 446–456. [Google Scholar] [CrossRef] - Domínguez, I.; Ward, S.; Mendoza, J.G.; Rincón, C.I.; Oviedo-Ocaña, E.R. End-User Cost-Benefit Prioritization for Selecting Rainwater Harvesting and Greywater Reuse in Social Housing. Water
**2017**, 9, 516. [Google Scholar] [CrossRef][Green Version] - Dallman, S.; Chaudhry, A.M.; Muleta, M.K.; Lee, J. Is Rainwater Harvesting Worthwhile? A Benefit–Cost Analysis. J. Water Resour. Plan. Manag.
**2021**, 147, 04021011. [Google Scholar] [CrossRef] - Steffen, J.; Jensen, M.; Pomeroy, C.A.; Burian, S.J. Water Supply and Stormwater Management Benefits of Residential Rainwater Harvesting in U.S. Cities. J. Am. Water Resour. Assoc.
**2013**, 49, 810–824. [Google Scholar] [CrossRef] - Freni, G.; Liuzzo, L. Effectiveness of Rainwater Harvesting Systems for Flood Reduction in Residential Urban Areas. Water
**2019**, 11, 1389. [Google Scholar] [CrossRef][Green Version] - Vaes, G.; Berlamont, J. The Effect of Rainwater Storage Tanks on Design Storms. Urban Water
**2001**, 3, 303–307. [Google Scholar] [CrossRef] - United States Environmental Protection Greening CSO Plans: Planning and Modeling Green Infrastructure for Combined Sewer Overflow (CSO) Control U.S. Environmental Protection Agency. 2014. Available online: https://www.epa.gov/sites/production/files/2015-10/documents/greening_cso_plans_0.pdf (accessed on 20 January 2021).
- Campisano, A.; Modica, C. Selecting Time Scale Resolution to Evaluate Water Saving and Retention Potential of Rainwater Harvesting Tanks. Procedia Eng.
**2014**, 70, 218–227. [Google Scholar] [CrossRef][Green Version] - Palla, A.; Gnecco, I.; La Barbera, P. The Impact of Domestic Rainwater Harvesting Systems in Storm Water Runoff Mitigation at the Urban Block Scale. J. Environ. Manag.
**2017**, 191, 297–305. [Google Scholar] [CrossRef] [PubMed] - Quinn, R.; Rougé, C.; Stovin, V. Quantifying the Performance of Dual-Use Rainwater Harvesting Systems. Water Res. X
**2021**, 10. [Google Scholar] [CrossRef] [PubMed] - Burns, M.J.; Fletcher, T.D.; Duncan, H.P.; Hatt, B.E.; Ladson, A.R.; Walsh, C.J. The Performance of Rainwater Tanks for Stormwater Retention and Water Supply at the Household Scale: An Empirical Study. Hydrol. Process.
**2015**, 29, 152–160. [Google Scholar] [CrossRef] - Gee, K.D.; Hunt, W.F. Enhancing Stormwater Management Benefits of Rainwater Harvesting via Innovative Technologies. J. Environ. Eng.
**2016**, 142, 04016039. [Google Scholar] [CrossRef] - Oberaschermsn, M.; Rauch, W.; Sitzenfrei, R. Efficient Integration of LoT-Based Micro Storages to Improve Urban Drainage Performance through Advanced Control Strategies. Water Sci. Technol.
**2021**, 83, 2678–2690. [Google Scholar] [CrossRef] [PubMed] - Xu, W.D.; Fletcher, T.D.; Duncan, H.P.; Bergmann, D.J.; Breman, J.; Burns, M.J. Improving the Multi-Objective Performance of Rainwater Harvesting Systems Using Real-Time Control Technology. Water
**2018**, 10, 147. [Google Scholar] [CrossRef][Green Version] - Di Matteo, M.; Liang, R.; Maier, H.R.; Thyer, M.A.; Simpson, A.R.; Dandy, G.C.; Ernst, B. Controlling Rainwater Storage as a System: An Opportunity to Reduce Urban Flood Peaks for Rare, Long Duration Storms. Environ. Model. Softw.
**2019**, 111, 34–41. [Google Scholar] [CrossRef] - Labadie, J.W. Optimal Operation of Multireservoir Systems: State-of-the-Art Review. J. Water Resour. Plan. Manag.
**2004**, 130, 93–111. [Google Scholar] [CrossRef] - Zhang, J.; Cai, X.; Lei, X.; Liu, P.; Wang, H. Real-Time Reservoir Flood Control Operation Enhanced by Data Assimilation. J. Hydrol.
**2021**, 598, 126426. [Google Scholar] [CrossRef] - Liang, R.; Thyer, M.A.; Maier, H.R.; Dandy, G.C.; Di Matteo, M. Optimising the Design and Real-Time Operation of Systems of Distributed Stormwater Storages to Reduce Urban Flooding at the Catchment Scale. J. Hydrol.
**2021**, 602, 126787. [Google Scholar] [CrossRef] - Muklada, H.; Gilboa, Y.; Friedler, E. Stochastic Modelling of the Hydraulic Performance of an Onsite Rainwater Harvesting System in Mediterranean Climate. Water Sci. Technol. Water Supply
**2016**, 16, 1614–1623. [Google Scholar] [CrossRef][Green Version] - Nachshon, U.; Netzer, L.; Livshitz, Y. Land Cover Properties and Rain Water Harvesting in Urban Environments. Sustain. Cities Soc.
**2016**, 27, 398–406. [Google Scholar] [CrossRef] - Abdulla, F.A.; Al-Shareef, A.W. Roof Rainwater Harvesting Systems for Household Water Supply in Jordan. Desalination
**2009**, 243, 195–207. [Google Scholar] [CrossRef] - Fewkes, A. Modelling the Performance of Rainwater Collection Systems: Towards a Generalised Approach. Urban Water
**2000**, 1, 323–333. [Google Scholar] [CrossRef] - Morales-Pinzón, T.; Rieradevall, J.; Gasol, C.M.; Gabarrell, X. Modelling for Economic Cost and Environmental Analysis of Rainwater Harvesting Systems. J. Clean. Prod.
**2015**. [Google Scholar] [CrossRef] - Mitchell, V.G. How Important Is the Selection of Computational Analysis Method to the Accuracy of Rainwater Tank Behaviour Modelling? Hydrol. Process.
**2007**, 21, 2850–2861. [Google Scholar] [CrossRef] - Butler, D.; Friedler, E.; Gatt, K. Characterising the Quantity and Quality of Domestic Wastewater Inflows. Water Sci. Technol.
**1995**, 31, 13–24. [Google Scholar] [CrossRef] - Friedler, E. The Water Saving Potential and the Socio-Economic Feasibility of Greywater Reuse within the Urban Sector—Israel as a Case Study. Int. J. Environ. Stud.
**2008**, 65, 57–69. [Google Scholar] [CrossRef] - Shteynberg, D. Measurement and Simulation of the Diurnal Pattern of Domestic Water Demand on Micro-Component Scale. Master’s Thesis, Technion—Israel Institute of Technology, Haifa, Israel, 2015. Available online: https://www.graduate.technion.ac.il/Theses/Abstracts.asp?Id=29200 (accessed on 24 March 2021).
- Penn, R.; Schütze, M.; Gorfine, M.; Friedler, E. Simulation Method for Stochastic Generation of Domestic Wastewater Discharges and the Effect of Greywater Reuse on Gross Solid Transport. Urban Water J.
**2017**, 14, 846–852. [Google Scholar] [CrossRef] - Friedler, E.; Butler, D.; Brown, D.M. Domestic WC Usage Patterns. Build. Environ.
**1996**, 31, 385–392. [Google Scholar] [CrossRef] - Mayer, P.; DeOreo, W.B. Residential End Uses of Uses Water; AWWA Research Foundation: Denver, CO, USA, 1999; pp. 125–132. ISBN 978-1-58321-016-1. [Google Scholar]
- Palla, A.; Gnecco, I.; Lanza, L.G. Non-Dimensional Design Parameters and Performance Assessment of Rainwater Harvesting Systems. J. Hydrol.
**2011**, 392, 65–76. [Google Scholar] [CrossRef] - Basinger, M.; Montalto, F.; Lall, U. A Rainwater Harvesting System Reliability Model Based on Nonparametric Stochastic Rainfall Generator. J. Hydrol.
**2010**, 392, 105–118. [Google Scholar] [CrossRef] - Rahman, A.; Snook, C.; Haque, M.M.; Hajani, E. Use of Design Curves in the Implementation of a Rainwater Harvesting System. J. Clean. Prod.
**2020**, 261, 121292. [Google Scholar] [CrossRef]

**Figure 1.**Modeling framework of a rainwater harvesting system. The conceptual depression losses tank needs to overflow to initiate inflows to the main rainwater tank. The rainwater tank is gaining water when R

_{t}> 0, and lose water due to overflows, yield (demands) or controlled release (if the latter is modeled).

**Figure 2.**Rainfall data from Bet Dagan (Israel) meteorological station (

**a**) Box plot of annual rainfall. (

**b**) Frequency distribution and empirical cumulative distribution function (CDF) of rain events depth. (

**c**) Frequency distribution and empirical CDF of dry periods (within the rainy season).

**Figure 3.**Two days of toilet flushing demands for 40 apartments created by the stochastic water demand generator. Demands as liter for 10 min (dashed red) show erratic pattern, 3-h moving average reveal typical diurnal pattern.

**Figure 4.**WSE PFR and VRE as a function of rainwater tank volume for the modeled building. Median values are marked as circles, boxes represent 25th and 75th percentiles, and whiskers 10th and 90th percentiles. Outliers are marked as red crosses. (

**a**) WSE, (

**b**) PFR, (

**c**) VRE.

**Figure 5.**WSE PFR and VRE as a function of normalized roof area (roof area divided by annual demands), and rainwater tank volume. Contours represent constant WSE (

**a**), PFR (

**b**) and VRE (

**c**) values.

**Figure 6.**WSE, PFR, and VRE as a function of release parameter, α, for the modeled building with a 20 m

^{3}tank. WSE and VRE decline as more water is released from the tank (smaller α), while PFR increases as more storage is available for incoming roof runoff. (

**a**) WSE, (

**b**) PFR, (

**c**) VRE.

**Figure 7.**Overflow and controlled release as fractions of the total loss flow (overflows + controlled release). As more water is released from the tank, the fraction of the released water from the overall outflows increases.

System Losses | Depression Losses | Num of Apts. | Roof Area | Orifice Diameter (RTC) | Simulation Timestep |
---|---|---|---|---|---|

10% | 0.5 mm | 40 | 840 m^{2} | 1 cm | 10 min |

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Snir, O.; Friedler, E. Dual Benefit of Rainwater Harvesting—High Temporal-Resolution Stochastic Modelling. *Water* **2021**, *13*, 2415.
https://doi.org/10.3390/w13172415

**AMA Style**

Snir O, Friedler E. Dual Benefit of Rainwater Harvesting—High Temporal-Resolution Stochastic Modelling. *Water*. 2021; 13(17):2415.
https://doi.org/10.3390/w13172415

**Chicago/Turabian Style**

Snir, Ofer, and Eran Friedler. 2021. "Dual Benefit of Rainwater Harvesting—High Temporal-Resolution Stochastic Modelling" *Water* 13, no. 17: 2415.
https://doi.org/10.3390/w13172415