**By Water Research Commission**

Several methods are used to size the tanks of rainwater harvesting (RWH) systems. The main methods include simplified methods, critical period, probability matrix methods, statistical methods, and procedures based on stochastic data generation.

Methods used to size RWH systems:

**Simplified methods**

The simplified method, used for preliminary design, is based on user defined relationships (Ward et al., 2010). Though they are used with relative ease, their results are not reliable due to poor modelling of rainfall and/or water storing processes (Raimondi and Becciu, 2014).

The supply side approach assumes that the required tank is large enough to store the maximum amount of rainwater in the wet season. Limitations of the method are that it ignores the water demand, which lead to inaccuracies when sizing the system. The method does not account for the seasonal variation in rainfall. The tank design is only based on the water needs and the period of water shortage.

The demand side approach assumes that the storage requirement is equal to the largest demand to be supplied by the tank. The method does not take into account water demand and uses only the water availability for the design of the storage tank (Ward et al., 2010). The main limitation is the assumption that there will be enough rains to fill the tank before the dry period commences.

** ****Critical period method**

The critical period method is based on the continuity equation wherein the required storage is equal to the maximum difference between the outflow and inflow of the reservoir during a critical period (McMahon and Adeyole, 2005). The term critical period refers to the period from a full reservoir condition to emptiness (McMahon and Adeyole, 2005). It identifies and uses sequence of flows where demand exceeds supply to determine the storage capacity (Fewkes and Butler, 2000). The critical period methods base the reservoir capacity on a single worst critical period or a synthesized one (Ndiritu et al., 2011).

**Behavioural analysis**

The continuous simulation method (behavioural analysis) uses a simple mass balance equation. This approach is popular because it can be applied with simple mathematical tools as spreadsheet applications and incorporates seasonal changes with relative ease (Raimondi and Becciu, 2014). The limitations of the model are that: depending on the length of the annual inflow data, storage size for high reliabilities cannot be estimated (McMahon et al., 2007). Considering stochastically generated annual streamflows, Pretto et al. (1997) found that biases occur in the mean and higher order quantiles of storage estimates before the estimated storage size converges to a stationary value after a long sequence (typically 1 000 years or more).

Behavioural models simulate the operation of the reservoir with respect to time by routing the simulated mass flows through an algorithm which describes the operation of the reservoir (Fewkes and Butler, 2000).The input data, which is in time series format, is used for the simulation of the mass flows through the model and will be based upon a time interval of either a minute, hour, day or month (Fewkes and Butler, 2000) — they have found more preference (McMahon and Adeyole, 2005; Ndiritu et al., 2011a, Raimondi and Becciu, 2014), because they represent the storage behaviour more realistically than other methods and it can be adapted with ease to model complex configuration and operating rules (McMahon and Adeyole, 2005).

The operation of the system is usually simulated over a given period of time using a time step of a minute, hour or month (Fewkes and Butler, 2000). Several models that can be used for the design and modelling of the storage tank have been developed (Fewkes and Butler, 2000; Su et al. 2009; Ndiritu et al., 2011). The difference in the models is the release rule which may be YAS or YBS as explained later. Fewkes and Butler (2000) investigated the accuracy of behavioural models using different time steps with the YAS and YBS release rule for both small and large storages. Each model run was one year; the results of this preliminary analysis indicated that a YAS model using either hourly or daily input time series could be used to predict system performance. Some models have been incorporated into software packages while others operate in Excel.

There are two releases rules mainly involved in behavioural models, namely yield after spillage (YAS) or yield before spillage (YBS) algorithm. The two release rules were originally developed by Jenkins, et al. (1978), but later further development was done by Fewkes (2000).

The yield after spillage operating rule:

Yt=min {Dt Vt−1

Qt=min{Vt−1+Qt−Yt S−Qt

The yield before spillage operating rule is:

Yt=min{Dt Vt−1+Qt

Qt=min{Vt−1+Qt−Yt S

*Where*: Rt= Rainfall [m] during interval, t; Qt= Rainwater run-off [m^{3}] during time interval, t; Mt= Mains supply make-up [m^{3}] during time interval, t; Ot= Overflow from store [m^{3}] during time interval, t; Vt= Volume in store [m^{3}] during time interval, t; Yt= Yield from store [m^{3}] during time interval, t; Dt= Demand [m^{3}] during time interval, t; S= Store Capacity [m^{3}] and; A= Roof Area [m^{2}].

In the YBS rule, the water is supposed to be abstracted for use before the inflow at each time step and which leads to underestimation of the storage volume that is needed. The opposite is the case with the YAS, which is more conservative and then is usually preferred (Raimondi and Becciu, 2014). Fewkes and Butler (2000) found that a YAS model using either hourly or daily input time series could be used to predict system performance.

Mitchel (2007) used a 6-min time step over a 50-year simulation period, and concluded that the selection of either the YAS or YBS operating rule has negligible impact on the estimation of yield and volumetric reliability. There are however other algorithms rather than YAS and YBS; Ghisi (2010) estimated rainwater tank sizing and potential for potable water savings using an algorithm of the Neptune computer program which is neither YAS nor YBS.

**Mass curve method**

The mass curve methods use a mass balance of the worst drought recorded, thereby assuming that a more severe drought will not occur in the future (Ndiritu et al., 2014). The method further assumes that the tank is initially full at the beginning of the flow record and hence will be full at the start of the critical period (McMahon and Adeyole, 2005). Restriction control curves that are a function of storage content cannot be handled by the method (McMahon and Adeloye, 2005) and no estimate of the expected reliability is provided (Ndiritu et al., 2014). Moreover, the algorithm does not account for storage losses.

**Procedures based on stochastic data generation**

Storage estimates are made based on stochastic or synthetic streamflow data in conjunction with one of the critical period methods (McMahon and Adeyole, 2005). One of the methods based on this procedure is the behavioural analysis method discussed earlier.

**Probability matrix methods**

The probability matrix method is based on analytical derivation of probability distribution functions of design parameters; probabilistic modelling of the storage process is possible without the need of continuous simulations (Raimondi and Becciu, 2014). The method considers a maximum of two isolated rainfall events rather than the entire time series and it assumes that the tank is full at the end of the first rainfall event (Raimondi and Becciu, 2014).

The limitation in this method is that each year of the record is simulated separately, thereby ignoring serial correlation of the hydrological variables involved (Ndiritu et al., 2011a).

Next month we take an in-depth look at RWH models.