**By Water Research Commission**

This is the latest in our series on rainwater harvesting. This month we look at models for calculating various aspects of rainwater harvesting to create the perfect system.

A number of scholars have developed RWH models through the years: Jenkins and Pearson (1978) developed the yield after spillage (YAS) and yield before spillage (YBS) release rules; Dixon (1999) developed a daily time-step model that simulates tank size, water quality, quantity, and cost of the RWH system; Van der Zaag (2000) developed a spreadsheet-based model which calculates storage capacity when daily water use and roof area are known; Roebuck and Ashley (2007) developed an Excel-based mass balance transfer model that predicts future financial and hydraulic performance of RWH systems.

Ndiritu et al. (2011) developed a daily time-step simulation of household water supply and a frequency analysis of the resulting number of days that the household gets supply for every year of the analysis; Raimondi and Becciu (2014) developed a model which uses analytical probabilistic approaches to the modelling of rainwater tanks.

As previously alluded, the storage tank greatly affects the initial capital cost and the volume of the rainwater collected because it is the most expensive component of a RWH system. Proper tank sizing is therefore important in order to avoid extra costs incurred when the tank is over sized and for avoiding low efficiency when it is under sized (Ghisi, 2010).

It is a daunting task to review all existing RWH models. Thus, while a number of models presented in the literature are listed (**Table 5.2**), only those that were accessed are discussed in more detail.

**Table 5.2:** Existing RWH models, their developers, spatial and temporal resolutions, as well as their availability

*Roof*

*Roof*

Roof is a spreadsheet-based water balance model that calculates storage capacity when daily water use and roof area are known; the model requires a complete series of daily rainfall data for at least three consecutive years. Roof uses the following water balance equation:

ππππ‘=π_{π}+π_{π‘}βπ_{πππ }βπ_{0} Equation 5.5

*Where:* V = volume of water stored in the tank [m^{3}], Q = roof run-off into the tank [m^{3 }d^{-1}], QT = additional inflow into the tank [m^{3} d^{-1}], Q_{abs} = water abstracted from the tank [m^{3} d^{-1}], Q_{o} = Overflow from the tank [m^{3} d^{-1}], and t = time [day].

With roof run-off equal to:

π_{π}= π Γ π΄_{π} Γ π_{π} Equation 5.6

*Where:* P = precipitation (m d^{-1}), A_{r} = roof area (m^{2}), and c_{r} = roof run-off coefficient.

The model produces a storage capacity graph which provides guidance in selecting the best tank size for a given geographical area. The relative storage capacity graph consists of the relative water consumption (RWC) expressed in mm water layer per day on the horizontal axis, and the relative development of resource guidelines for rainwater harvesting storage capacity (RSC) expressed in mm water layer on the vertical axis. The model is based on the following equations:

π ππΆ=ππ΄ Equation 5.7

π ππΆ=ππ΄ Equation 5.8

*Where:* RWC = relative water consumption [mm d^{-1}], RSC = relative storage capacity [mm], Q = daily water consumption [10^{-3} m^{3}d^{-1}], A = roof area [m^{2}], S= storage capacity [10^{-3} m^{3}], A = roof area [m^{2}]

The storage capacity graph represents a combination of the RWC and RSC for a given satisfaction level. The satisfaction level refers to the days where the daily water demand will be fully satisfied and it is expressed in a percentage; a 30% satisfaction level means that daily water demand will be fully satisfied for 30% of all the days. For a given combination of daily water demand and roof area the RWC value is known, therefore the RSC value can be obtained from the graph by multiplying the obtained RSC value by the roof area, thereby obtaining the storage capacity in the certain situation. The roof model was used on a study by Mwenge Kahinda et al. (2010) where the optimum tanks size for the area studied was found to be 0.5m^{3}.

*The SamSamWater rainwater harvesting tool*

SamSamWater rainwater harvesting tool is a global online RWH tool used for determining the optimum size of a rainwater harvesting system. The tool requires inputs of the location, roof size, roof type, and water demand of the household. The rainfall data set used in the tool is based on the CRU CL 2.0 dataset which is adopted from New et al. (2002). The tool provides outputs of monthly rainfall for an average year, water availability and water demand throughout the year, water level in the tank throughout the year. The value of the volume of water harvested at a certain month is represented in equation 5.

π_{β }= π΄ Γ π_{π }Γ π
_{ππ£π }Equation 5.9

*Where:* V_{h} = volume harvested by the roof [m^{3}]; r_{c} = run-off coefficient, and R_{avg} is the average rainfall [m]

These outputs are then used to conclude the size of the tank that would be suitable for the specific location.

*Yield reliability analysis model*

The yield reliability analysis (YRA) is a daily continuous simulation model developed by Ndiritu et al. (2011a), the model is based on an approach towards volumetric reliability by Su et al. (2009) who applied daily continuous simulation modelling to obtain relationships between storage size, deficit, and its exceedance probability, which allows for the selection of a confidence level associated with a specific yield and tank size. Ndiritu et al. (2011a) used the above-mentioned approach by Su et al. (2009) determining exceedance probabilities using the frequency analysis of the number of days of supply each year using a plotting position formula. The model calculates the number of days in a year that a household water demand is met by a RWH system, ROR (run-of-river), and the combination of the two. An optimal tank volume is described as the minimum tank size giving the highest number of days of supply for the specific roof area.

The yield reliability analysis model has been used in three case studies to date:

- β’ The yield-reliability analysis of rural domestic water supply from combined rainwater harvesting and run-off river abstraction in Nzhelele village, Limpopo province (Ndiritu et al., 2011a)
- β’ Incorporating hydrological reliability in rural rainwater harvesting and run-of-river supply (Ndiritu et al., 2011b)
- β’ Probabilistic assessment of the rainwater harvesting potential of schools in South Africa (Ndiritu et al., 2014).

*Raincycle*

Raincycle is a Microsoft Excel-based mass balance transfer model that predicts future financial and hydraulic performance of RWH systems (Roebuck and Ashley, 2007). The model is applicable for RWH systems in domestic, commercial, public or industrial buildings, and makes use of the YAS spillage algorithm as described by Jenkins and Pearson (1978). The model accounts for the change in water demand throughout working days, weekends and holidays. The models can provide daily simulations of the proposed design for up to 100 years of operation. The main result of the model is expressed as the percentage of demand fulfilled by harvested water. The model was validated by comparing the hydraulic outputs of the model with the methodology described by Fewkes and Warm (2001).

**Evaluation criteria of RWH models**

To evaluate RWH models, a set of evaluation criteria has been developed, after Cunderlik (2003) who developed evaluation criteria for hydrologic models. The selection of an existing model to be used in this project depends therefore on a range of criteria rather than the personal preferences of the project team. A number of criteria are informative while others are ranked and included in the evaluation process.

Criteria are ranked from either 1 to 3 or 1 to 2, with: rank 1-Bad, 2-Average and 3-Good. A summary of the comparison between the four models is presented in **Table 5.3**, according to:

- β’ Temporal scale β refers to the time step of the input data and used in the model [sub-hourly (+/-), hourly (+/-), daily (+/-), monthly (+/-), annually, flexible]. Rank [1-3]: models with flexible time step that include the daily time step receive the highest rank 3; models working at the daily time step get 2; and models with time steps higher than the daily time step get 1.
- β’ Length of rainfall input data β refers to the length of the rainfall time series used to run the model [1 year; 10 years; > 10 years]. Rank [1-3]: 3 for models with long time series (> 10 years), 2 for models with time series longer than 5 years but shorter or equal to 10 years, and 3 for models with short time series (1 year).
- β’ Length of water demand input data β refers to the volume of water extracted from the tank [flexible, time series, fixed value]. Rank [1-3]: 3 for models with flexible demand (both fixed and time series), 2 for time series of water demand, and 1 for fixed water demand.
- β’ Process modelled β refers to all processes that are modelled (reliability, optimum tank size). Rank [1-6]: (1-3 for each process); 6 if both processes are modelled, 4 if only one process is modelled, and 1 if none of the processes are modelled.
- β’ Cost β refers to the price of the model in rands and the cost of the required system to run it. Rank [1-3]: 3 for public domain models with free or cheap platform, 2 for public domain models running on expensive platforms, 1 for models which cost money.
- β’ Data requirements β refers to the input data (beside the roof area, the rainfall time series and the water demand) that the model requires in order to run. Rank [1-3]: 1-high, 2-medium, 3-low.
- β’ Expertise β refers to the scientific skills required to use the model adequately [low, medium, high]: 3-low, 2-medium, 1-high.
- β’ Technical support β support available for setting up the model, calibration and use. Rank: [1-3]: 3-if full support is available, 2-if limited support is available, 1-if there is no support.
- β’ Documentation β refers to the available documents of a model, such as reference manuals, user guides, web pages [good, medium, bad]. Rank [1-3]: 3-good, 2-medium, 1-bad.
- β’ Ease of use β refers to the user friendliness of the computer-based model, taking into consideration graphical user interface (GUI), input-output (I/O) operations, and visualisation options [easy, medium, and difficult]: 3-easy, 2-medium, 1-difficult.
- β’ Operating system β refers to the operating system required for the effective use of the model [Linux, UNIX, MAC, Windows CE, 95, 98, 2000, XP, 7, 8]. Rank [1-3]: 3 for Windows-based applications since Windows 7, 2 for DOS applications and windows operating systems before Windows 7, and 1 for other operating systems.
- β’ Validation β indication of whether or not the model results can be validated against observed data. Rank [1-3]: 3-validated, 1βnot validated.
- β’ Advantages and disadvantages β summarises the merits and demerits of a given model. Rank: [-].
- β’ References β lists the key reference(s) to the model in the literature. Rank: [-].
- β’ The total score gives the sum of all ranked criteria.

**Table 5.3: Comparison of selected RWH models, following evaluation criteria developed after**

**Modelling using the shortlisted RWH models**

The roof, SamSamWater rainwater harvesting tool, yield reliability analysis, and the raincycle model were used to estimate the optimum tank sizes of households across the country using existing daily rainfall time series 1989 to 1998, with the exception of SamSamWater rainwater harvesting tool which has its own rainfall data set. Four sites where selected for this analysis namely: Pretoria University, Cape Town fire service station, Stellenbosch, and Durban botanical garden. The following parameters were used for various sites across the country: roof area of 150m^{3}, daily demand of 50 litres per capita per day (an average of four inhabitants per household), and a run-off coefficient of 0.8.

The results of the modelling exercise provided a variety of optimum tank sizes for the range of models used. While there was no agreement between most model outputs, the raincycle and YRA models were in agreement in some areas. The SamSamWater rainwater harvesting tool underestimated the optimum tank sizes because it uses monthly rainfall data.

**Figure 5.1: Modelling results of the roof, YRA, SamSam, and raincycle in Cape Town, Durban, Pretoria, and Stellenbosch.**

** **

A number of models have been developed to optimise RWH systems and quantify their water savings. There are however no guidelines to verify which model is more relevant for which reasons, given that they are not validated against observed data. Model validation is the process of demonstrating that a given site-specific model is capable of making sufficiently accurate predictions (Refsgaard, 1997).

A model is said to be validated if its accuracy and predictive capability in the validation period/area have been proven to lie within the predefined acceptable limits. It is therefore a necessary step that is almost totally overlooked by the developers of the RWH models discussed above.

Capturing the processes operating in RWH systems is not sufficient to ensure that the model is good, as the functional form for the processes, and how these link together to form a system, cannot be derived from first principles. Several methods are indeed used to size RWH systems and, there is no way of determining which one is the most relevant. To verify which model is more relevant, model outputs have to be compared with observations. Unfortunately, there is a tremendous lack of data, both with which to run the models, especially demand from the tank, and to validate them.

*Next month we look at tank material.*

**Sources:**

*Development of resource guidelines for rainwater harvesting, *a report to the Water Research Commission by Jean-Marc Mwenge Kahinda, Shirley Malema, Eunice Ubomba-Jaswa, Luther King Akebe Abia and Adesola Ilemobda.