Selecting Time Scale Resolution to Evaluate Water Saving and Retention Potential of Rainwater Harvesting Tanks Academic research paper on "Earth and related environmental sciences"

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Procedia Engineering 70 (2014) 218 - 227

12th International Conference on Computing and Control for the Water Industry, CCWI2013

Selecting time scale resolution to evaluate water saving and retention potential of rainwater harvesting tanks

A. Campisanoa *, C. Modicaa

aDepartment of Civil and Environmental Engineering, University of Catania, Viale Andrea Doria, 6, 95125 Catania, Italy

Abstract

Water saving and stormwater retention benefits from Rainwater Harvesting (RWH) tanks can be evaluated by the use of behavioural models able to simulate the long-term water balance of the rainwater tank. However, simulation results may be affected by the computational time step, that is normally chosen according to the aim of the analysis and to the available data. The objective of the paper is to analyse the influence of the time-step on the evaluation of the performance of RWH systems. Results of the investigation may help modellers deriving indications to select the appropriate time scale resolution when evaluating water saving and retention efficiencies of rainwater tanks.

The analysis was carried with reference to a household case study in the south of Italy. High resolution rainfall data were used to run the water balance simulation of the tank at different daily and sub-daily time steps. In parallel, event-based data of toilet flushes collected during the field monitoring of the household residential water demands were used to derive long-term toilet water demand patterns at the different time scales of aggregation.

Simulations of the tank showed that the daily time step may be reliably chosen for accurate evaluation of both the water saving and the volumetric stormwater retention efficiency of the rainwater tank with the exception for small tanks and high water demand values for which inaccuracies may occur unless higher time resolution are adopted.

© 2013 The Authors.PublishedbyElsevierLtd.

Selection andpeer-reviewunder responsibility ofthe CCWI2013Committee

Keywords: Behavioural models; Rain water tanks; Storm water retention; Time scale resolution; Water saving.

* Corresponding author. Tel.: +39(0)957382730; fax: +39(0)957382748. E-mail address: acampisa@dica.unict.it

1877-7058 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of the CCWI2013 Committee

doi: 10. 1016/j .proeng .2014.02.025

1. Introduction

The use of rainwater tanks is an old practice that is reviving nowadays for its potential to address a number of environmental and social issues. In countries coping with water scarcity, rainwater tanks can help reducing the potable water consumption from mains. The volume of potable supply substitution is the primary reason that motivate households to equip houses with rain water harvesting (RWH) systems having the typical function of back-up supply source (Mitchell et al., 2008). Collected rainwater is basically used for local external or internal non-potable consumption (i.e. toilet flushing, garden irrigation, terrace cleaning, car washing, etc.). Although RWH may result expensive, the implementation of such systems in developed countries is increasing more and more, being often considered as a symbol of environmental involvement.

Rainwater tanks can also take part to the mitigation of environmental impacts of urbanization on storm water drainage systems and receiving waters. The increase of distributed retention storage throughout urban catchments can help reducing the frequency and volume of storm water runoff conveyed by drainage systems and contribute to partially restore the altered water balance of the catchment. From this viewpoint, RWH operates as a storage-based source control solution: during storm events, part of the rainfall is stored in the rainwater tank and used locally with the effect of abstracting such rainfall from the runoff component of the water cycle. However, differently from usual storm water storages, the water abstraction from rainwater tanks is demand-driven (Petrucci et al., 2012) with demand magnitude and patterns having a clear effect on the design and efficiency of RWH systems (Mitchell et al., 2008).

Household-scale experiments on water saving performance of rain water tanks have been conducted in various countries, basically using the collected rain water to flush toilets in private or public buildings (Chilton et al., 1999; Fewkes, 1999; Zaizen et al., 1999; Aylward et al., 2006; Ward et al., 2012). Findings of such studies clearly indicate that RWH systems offer significant water saving potential. However, these studies also show that the harvesting system performance is markedly influenced by site-specific variables such as local rainfall, roof area, rainwater tank size, potable water demand and number of people in the household.

Besides, recent experimental analyses based on the monitoring of implemented systems to assess storm water runoff control benefits of RWH show various results. Specifically, the results concerning the impact of a number of small rain water tanks in a suburban catchment of Paris, France show that RWH alone is not able to prevent overflows from the storm water drainage system (Petrucci et al., 2012). Differently, studies on the performance of twelve rainwater tanks in Australia (Burns, personal communication) have shown that, under regular and sufficiently large demands, RWH systems may achieve storm water retention performance approaching that of the same area under the pre-development condition.

Multiple benefits from RWH tanks have also been explored with the use of behavioural modeling methods based on the simulation of the long-term water balance of the tank (Fewkes and Butler, 2000; Villareal and Dixon, 2005; Ghisi and Ferreira, 2007; Mitchell et al., 2007; Coombes and Barry, 2008; Palla et al., 2011; Burns et al., 2012; Brodie, 2012; Campisano and Modica, 2012a; Campisano et al., 2013a, Campisano et al., 2013b). Results from such studies basically show the potential for exploitation of rainwater harvesting. However, findings reveal also that simulation results may be significantly affected by the model structure and parameters such as the computational time step. Although time step selection often depends on the objective of the analysis and on the availability of data, a sensitivity analysis conducted by Mitchell et al. (2008) has shown that it may influence the estimation of the tank volumetric reliability (up to about 8%) depending on the algorithm used to run the water balance simulation.

Early results by Fewkes and Butler (2000) point out that simulations with monthly time steps may provide inaccurate evaluation of the RWH system water saving performance and suggest to use the daily time step resolution for such an evaluation.

However, to obtain more accurate estimation of the tank potential to both reduce potable water volumes and control storm water volumes to the drainage system, higher time resolutions may be required under several conditions. Absolutely, high time resolutions become mandatory if the reduction of storm water flow peaks due to the tank is explored. Clearly, contraindications may emerge due to an increased computational effort to treat extended rain data sets and to arrange detailed information on the demand patterns.

The influence of the modelling time step on the performance estimation of rainwater tanks in terms of both water saving and stormwater retention efficiency is explored in this paper. The analysis was carried with reference to a household case study in the south of Italy and local rainfall data at high temporal resolution were used to run the water balance simulation of the tank at different daily and sub-daily time steps. Also, event-based data of toilet flushes collected during the household water demand monitoring were analysed with the basic aim to derive long-term toilet water demand patterns at different time scales of aggregation.

Simulations of the tank were run to derive indications on the appropriate time scale for the analysis of the benefits of RWH for both water saving and retention purposes.

2. Case study

The RWH system case study is located in Patti, Italy. The selected household is described in Campisano and Modica (2010) and it is located in a private apartment hosting a family of five people (four employees and one housewife). In march 2006 the homeowner was contacted to ask for permission to monitor consumptions at the house toilet. After agreement, a 2-week long monitoring campaign (from 1 May 2006 hour 19:30 to 15 May 2006 hour 19:30) was launched to determine the toilet water demand patterns (i.e. frequency of use, daily averages, etc.). Data were acquired using a simple electric sensor connected to the toilet cistern push button and equipped with a data logger (logger Series HOBO U-11). The device allowed to record the times the toilet was flushed with the accuracy of 1 s.

A total of 345 flushes was observed during the monitoring period with average 4.93 flushes/day capita. Findings resulted in good agreement with other existing studies in literature (Buchberger and Wells, 1996, Garcia et al., 2004). Fig. 1 reports the cumulated toilet flush events f (per capita) monitored during the whole experimental campaign. The quasi-linear trend of the curve points out the uniform use of the toilet during the two weeks period without significant differences between weekdays and weekend days, then confirming that the campaign duration was sufficiently long for establishing the demand pattern.

Fig. 1. Cumulated per capita toilet flushes monitored during the two-weeks period.

Rainfall data for the investigation were provided by the Sicilian Department of Water and Waste and consisted of the high resolution precipitation series recorded at the rainfall gauging station of Elicona a Falcone, located about 9 Km east of the case study site at about 14 m a.s.l. The gauge operates remotely since year 2002 and long-term precipitation patterns show average rainfall of about 577.0 mm. Precipitation of the year 2006 was taken into account correspondingly to the year of the monitoring campaign and because it has a complete series of records. For such a year 2006 total observed precipitation was 475.0 mm, prevalently concentrated during the semester October-March, as usual for Mediterranean climate.

3. Methods

3.1. Rainfall-runoff module

Row data concerning precipitation events registered during the year 2006 were filtered and aggregated in order to obtain 4 rainfall yearly series characterized by different time step resolution. To account for the intra-annual pattern of precipitation the whole year was analyzed and time steps of 5 min, 15 min, 1 h and 24 h (daily) were chosen, with resulting series respectively formed by 105120, 35040, 8760 and 365 data.

Considering the rainwater tank to be filled exclusively by the rainwater precipitated on the building rooftop and assuming zero initial losses and evaporation from the rooftop surface, the rainfall-runoff process was modeled simply by the equation:

Qt = A • Rt (1)

where subscript t indicates the current time step, Qt [m3] is the inflow volume to the tank at time step t; A [m2] is the effective rooftop area for rain water collection and Rt [m] is the rainfall at time step t.

3.2. Demand pattern module

A specific module was developed to derive the toilet demand pattern for the whole year 2006 at the 4 resolution time scales from the toilet demand pattern observed during the monitoring campaign. The module is based on a two-step procedure.

The first step allows the probabilistic generation of the number of toilet flushes for each of the 365 days of the year. In particular, the probability distribution function (PDF) of the fourteen values of daily toilet flushes was evaluated. For such a purpose, a normal PDF was fitted to data with mean 24.64 flushes/day and standard deviation 2.87 flushes/day (Fig. 2). Then, 365 random picks from such a normal distribution allowed to obtain the number of toilet flushes for each day of the year.

P, F (-) 0,8

15 20 25 30 35

daily flushes

Fig. 2. Fit of PDF function to the observed frequency of daily total flushes.

The second step of the procedure allows to scale the obtained daily toilet demand pattern up to higher temporal resolutions of 1 h, 15 min and 5 min. To achieve such a purpose, a intra-daily pattern for the frequency of toilet use was constructed starting from the daily pattern of the monitored flushes. Firstly, observed flush events of each monitored day were aggregated using time steps of 1 h, 15 min and 5 min. Secondly, the fourteen days were

"overlapped" and data are aggregated at the different time steps. Finally, aggregated data were normalized to the total number of observed flushes and cumulated. Consequently, the cumulated relative frequency distributions (CFDs) of toilet-use during the day was obtained.

As an example, the graph of Fig. 3 shows the obtained frequency distribution for the 5 min time step. As also pointed out by other authors in the literature, the graph shows that the toilet use is influenced by the users' habits. Basically, a strong relation is observed to whether people are at home or not and if they are asleep, getting up or preparing for bed (Blokker et al., 2010).

CFD o,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0

daytime

Fig. 3. Cumulated relative frequency distribution of toilet use during the day for the 5 min time step.

Similarly to step one of the procedure, random picks (in number equal to the total flushes for each day) from the obtained frequency distributions allowed to determine the 5 min, 15 min and 1h time steps relevant to each flush of the day. Such a procedure was conducted for the whole 365 days of the year. The obtained series were used to derive toilet water demand series at 5 min, 15 min and 1h time steps which were finally used as input for the water balance simulation of the tank at the various time scales.

0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 0.00

3.3. Behavioural storage module

The scheme of domestic RWH system considered in the present study is based on the collection of rain water precipitated on the building roof. Such water is temporary stored within a rainwater tank (Fig. 4). The demand for rain water in the house was limited to toilet flushing. Then, it was assumed that such a use is fulfilled primarily by water accumulated into the rainwater tank and only then, by water from the mains supply.

A specific module was implemented for the behaviour analysis of the tank (Campisano et al., 2012b). The module uses a continuous simulation to track the inflows and outflows, as well as the change in storage volume, according to the yield-after-spillage (YAS) algorithm as tank release rule (Jenkins et al., 1978):

Q (Vt-i + A • Rt - S

Qnt = maxj 0 (2)

Yt = mini D (3)

[Vt -1

V • V- + A ■ Rt - Yt

Vt = mi n (4)

t 1 S - Yt

where QDt (m3) is the volume discharged as overflow from the storage tank, V, (m3) is the volume in store, Yt (m3) is the yield from the storage tank, D, (m3) is the toilet water demand, and S is the tank storage capacity (Fig. 4).

Fig. 4. Schematic of the house rooftop rainwater harvesting system.

In the last decades, the performance of rainwater tanks has been analysed by literature using a number of performance measures, which were recently compared by McMahon et al. (2006).

Normally, the selection of the performance measure is dependent on the objective of the study. Water saving is one of the main motivation for RWH, expecially for urban areas characterised by reduced fresh water availability. Then, the water saving efficiency of the rainwater tank was evaluated by using the tank volumetric reliability (%) (Mitchell et al., 2008) as a measure of the tank performance:

Ews = A-l -100

where sums are extended to all time steps of the simulated year. Water saving assumes value zero as the yield from the rainwater tank is zero (only water from mains is used) and it assumes the value 1 when only the stored rainwater is used.

Moreover, to evaluate the volumetric retention performance of the tank, the retention efficiency (%) was used:

I A • Rt

which provides the volume of runoff that is retained by the tank during the storm even with respect to the tank rainwater inflow volume. Equation (6) clearly shows that ER tends to 0 when the sum of overflow discharges QDt from the tank tends to sum of ARt, that may occur in case of small tanks and/or reduced toilet demands.

3.4. Modelling scenarios

The performance of rainwater tanks as part of RWH systems is affected by several variables. Basically, the characteristics of the installation (i.e. rainwater tank storage capacity) and of the building (effective rooftop area) together with the household demand patterns and with the rainfall characteristics of the installation site (average precipitation, dry weather inter-event period) result crucial to evaluate water saving and storm water retention efficiencies.

There is also the potential for interdependency between the variables and the sensitivity of behaviour analysis results. However, it would be an onerous task to investigate such interdependencies because the number of

modelling scenarios to be conducted would be extremely high. Then, to consider different combinations of tank storage capacity, roof area rain water demand and precipitation, two dimensionless parameters, namely demand fraction and storage fraction (Campisano and Modica, 2012b) were taken into account to run the simulations:

with Dd and Rd being the average daily values of toilet water demand and rainfall.

Although rainfall and demand patterns are specified for the monitored site, the introduction of parameters (7) and (8) allows to generalize the results in order to extend the obtained results to other sites/systems characterized by other values of Dd and Rd.

A preliminary investigation was conducted to evaluate the scenarios of simulation based on the analysis of the practical application ranges of values of water demands for toilets, tank storage capacities, potential roof areas and precipitation.

As for water demand scenarios, the analysis was carried out with respect to five values of d. In particular, two values of d below one (respectively equal to 0.2 and 0.5) were selected thus corresponding to limited demand fraction. Three other scenarios (d = 1.0, d = 2.0 and d = 4.0) were also examined as representative of high toilet demand with respect to stored rainwater.

Concerning storage scenarios, the analysis was carried out considering seven storage fraction values for each demand scenario. In particular values of s equal to 1, 2, 3, 5, 10, 20 and 40 were used. The choice of the minimum adopted value (s = 1) allowed to comply with constraints suggested by Fewkes and Butler (2000) to avoid inaccuracies in simulation results at the daily time scale.

The behavioural analysis was carried out using a proprietary software code developed at the University of Catania specifically for the study of RWH systems.

4. Results and discussion

4.1. Water saving efficiency

Results of the simulations are presented in the following dimensionless graphs of Fig. 5. The figure reports the curves of water saving efficiency of the rainwater tank versus the storage fraction s for the different time scale resolutions adopted in the analysis. The graphs for d = 0.5, d = 1.0, d = 2.0 and d = 4.0 are reported. Globally looking to the water saving system performance, the figure points out that EWS tends to decrease as d increases (i.e. as demand for toilet flushing increases and/or as roof area and daily rainfall decrease).

Moreover, results of the simulations show that at high demand fractions (d = 2.0 and d = 4.0) the water saving efficiency is limited in the ranges 0-0.50 and 0-0.25 respectively, with the tank storage fraction having a reduced influence on the system performance. Oppositely, for the other two demand scenarios (d = 0.5 and d =1.0) the water saving efficiency is much more affected by the tank size and by the rainfall volume. Specifically, the graphs show that values of EWS significantly increase as the storage fraction increases (i.e. as S increases and/or A and Rd decrease). In particular, for the demand scenario d = 0.5 (and also for the lowest scenario d = 0.2 not shown here) the water saving efficiency quickly rises up to the maximum value. That is, in case of low demand at the toilet, the highest harvesting performance can be obtained with relatively small-size tanks.

Finally, it should be stressed that curves tend to flatten (derivatives tend to decrease) as s increases, revealing that reduced marginal water saving benefits can be obtained as the storage fraction increases.

Obtained results are in agreement with those previously published by Campisano and Modica (2012a) concerning the application of behavioural models for the analysis of RWH performance in the same region of the case study site here presented.

100 90 80 70 60 50 40 30 20 10 0

100 WS 90 (%) 80 70 60 50 40 30 20 10 0

EW'\ 90 (%) 80 70 60 50 40 30 20 10 0

100 WS 90 (% ) 80 70 60 50 40 30 20 10 0

d = 4,0

d = 1.0

W \ \ . 24h............................

■M.......................

15 min

-24b............

"1'h................

-15' ' min

-5 min

Fig. 5. Simulation time-step influence in the evaluation of the water saving efficiency for the various demand and storage scenarios.

As the time step resolution of the simulation is considered, Fig. 5 clearly shows that differences between the results of the simulation increase as s decreases and d increases. In particular, simulations run with high resolution time steps (5 min, 15 min and 1 h) provided slightly increased tank efficiencies than those run using the daily time scale. However, differences among the curves start to be significant (more than 5%) for the high values of d (larger than d=1) and for the small values of s (lower than s = 10). Such results are in agreement with Mitchell et al. (2008) and confirm that the efficiency of the tank is appreciably affected by the time-step only for the small storage capacities.

4.2. Retention efficiency

Dimensionless graphs similar to those of water saving were carried out concerning the tank retention efficiency and are reported in Figure 6. As expected, all the figures show that ER increases as d increases. In fact, higher water demands and small precipitations maintain the tank empty and avoid overflows to occur potentially reducing runoff volumes to convey to the drainage system.

Besides, results of the simulations show that the values of ER increase as the storage fraction increases. Such an increasing trend is much less evident for the small demand fractions with the curve of ER being almost flat for scenarios characterized by d lower than 0.5. On the opposite, variations of ER with s are higher for d=4.0 with 100% efficiency for the highest simulated values of s.

The analysis of the time step influence on the simulations reflects more evident differences among the curves obtained with the 4 plotted time steps. In agreement with results concerning the water saving efficiency, the graphs of Figure 6 show that differences between the results of the simulations increase as s decreases and d increases. In

particular, curves obtained using smaller simulation time steps differ significantly (up to 7.5% for d = 1.0 and to 17.5% for d = 4.0) from those associated to the daily time step scale showing that the down scaling to high time resolutions can increase the behavioural model estimation accuracy.

However, curves related to 5 min, 15 min and 1 hour time steps practically overlap one each other revealing that, for the analysed case study, it is not convenient (in terms of computational efforts) to analyse the tank volumetric retention performance down to the hourly time scale.

Fig. 6. Simulation time step influence in the evaluation of the retention efficiency for the various demand and storage scenarios.

5. Conclusions

In this paper the influence of the time-step on the use of behavioural models to evaluate the performance of rainwater harvesting tanks was explored. In particular, the analysis was developed using four temporal resolutions (daily, 1 hour, 15 min and 5 min time steps) to assess potential benefits of RWH tanks in terms of water saving and retention efficiencies.

A procedure previously developed by the authors and based on data monitored in a real household was applied to derive long-term patterns of water demands at the toilet at the different time scales of aggregation. Also high resolution rainfall data were used to run the water balance simulation of the tank at different daily and sub-daily time steps.

The simulations were run using a dimensionless approach and showed the time step to significantly affect the results for the small rain water tanks and for the high toilet water demand with increased inaccuracies using the daily time step resolution. In particular, larger differences among the used time resolutions were found in results concerning the evaluation of the volumes retained by the tank with up to 17% deviation between the daily and the 5 minutes time step scale.

Results of the investigation may be used by modellers to select the appropriate time scale resolution in order to evaluate the water saving and the volumetric retention efficiency of rainwater tanks. Moreover, the used approach

with the higher temporal resolution (5 min) opens also to the possibility to evaluate the potential of RWH systems in reducing peak flow rates to the drainage system.

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