Methodology

A simple empirical approach to the determination of RWH potential was developed based on widely available datasets. The aim was to provide a spatially-relevant overview of agri- cultural water management requirements for national-scale policy-making, in regions where higher-resolution data can be scarce. A schematic representation of the methodological pro- cess is presented in Figure 3.3.

Figure ‎3.3 │Schematic representation of the methodological process followed to de- termine rainwater harvesting (RWH) benefits for crop yields.

3.2.2.1 Estimating crop water requirements

The water requirements of different crops vary both in quantity and in their temporal distri- bution. Crop water requirements were estimated for the 20-year historical and future month- ly climatic averages from the three GCMs across Africa. Crop water requirements, equiva- lent to crop evapotranspiration here (ETc), are defined by the empirical Equation 3.1 (Allen

et al., 1998):

𝑬𝑻

_𝒄

= 𝑲

_𝒄

∗ 𝑬𝑻

_𝟎

(‎3.1)

The reference evapotranspiration (ET0) values were estimated using CMIP5 climatic data.

While ET0 remains an important variable in hydrological models, it is not always calculated

directly in climate models. In order to estimate ET0, most hydrological models use the data

intensive and physically-based Penman-Monteith equation recommended by the FAO. Sim- pler equations have been shown to be as good, and sometimes better, at evaluating ET0

compared to the Penman-Monteith equation (Kay and Davies, 2008). In this context, due to limited data availability within GCM outputs, and due to computational limitations, an al-

ternative equation to calculate ET0 was selected (Oudin et al., 2005).That is shown in Equa- tion 3.2:

𝑬𝑻

𝟎

=

_𝝀𝝆𝑹𝒆 𝒘 𝑻𝒂+𝟓 𝟏𝟎𝟎

𝒊𝒇 (𝑻

𝒂

+ 𝟓) > 𝟎 (‎3.2)

𝑬𝑻𝟎= 𝟎 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 (𝒏𝒆𝒈𝒂𝒕𝒊𝒗𝒆𝒔 𝒗𝒂𝒍𝒖𝒆𝒔 𝒂𝒓𝒆 𝒃𝒆𝒊𝒏𝒈 𝒓𝒆𝒔𝒆𝒕 𝒕𝒐 𝒛𝒆𝒓𝒐)

Where Re is the extraterrestrial radiation (J/m

2_{/s), λ is the latent heat flux (taken as 2.45x10}6

J/kg), ρw is the density of water (1,000kg/m 3

), and Ta is the mean monthly air temperature

(°C).

Cropping calendars datasets based on typical national level and sometimes sub- national planting and harvest dates for the 1990s or early 2000s (Sacks et al., 2010) were used to produce weighed monthly crop evapotranspiration values based on the crop coeffi- cient (Kc) values of the different crops at the four crop growth stages (initial, crop develop-

ment, mid-season, late season). The cropping calendars were also used to estimate monthly values of the yield response factor (Ky), for yield impact evaluations. The yield response

factor is widely used in irrigation planning, and is at the core of the FAO’s crop water re- quirements models CropWat and AquaCrop. Each crop growth stage has differing sensitivi- ties to environmental stresses (e.g. grain filling and flowering, which occur mid-season, are the most sensitive stages to water stress), which in turn affect the Kc and Ky (c.f. Equation

3.4) values. Standard Kc and Ky values for maize (Table 3.1) were obtained from the FAO

(Allen et al., 1998).

Table ‎3.1 │Estimated Kc and Ky values for maize, millet, and sorghum from Allen et al. (1998). Crop Initial stage Crop development stage Mid-season stage Late season stage Maize Kc 0.40 0.80 1.15 0.70 Ky 0.40 1.50 0.50 0.20 Millet Kc 0.35 0.70 1.10 0.65 Ky 0.20 0.55 0.45 0.20 Sorghum Kc 0.35 0.75 1.10 0.65 Ky 0.20 0.55 0.45 0.20

Subsequently, the monthly water deficits were established from the difference be- tween estimated monthly crop water requirements (ETc) and the monthly rainfall amounts

having a probability of occurrence of 67% (i.e. minimum rainfall expected two years out of three). The latter is what is termed “design rainfall” when determining the sizing of RWH systems, and is discussed further in the next section. The “design rainfall” is used to account for the significantly greater inter-annual variability present with rainfall, than with solar ra- diation or temperature used to estimate crop water requirements.

3.2.2.2 Estimating rainwater harvesting system design requirements

The design of RWH systems has been described in Critchley and Siegert (1991), yielding Equation 3.3 to evaluate the optimal design catchment to cultivated area ratio (C:CA):

‎‎‎‎‎‎‎‎‎‎C:CA‎=‎

(𝑬𝑻𝒄−𝑫𝒆𝒔𝒊𝒈𝒏 𝑹𝒂𝒊𝒏𝒇𝒂𝒍𝒍)

(𝑫𝒆𝒔𝒊𝒈𝒏 𝑹𝒂𝒊𝒏𝒇𝒂𝒍𝒍 ∗𝑹𝒖𝒏𝒐𝒇𝒇 𝑪𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 ∗𝑬𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚)

(‎3.3)

Here the runoff coefficient is simply defined as the fraction of surface runoff to precipitation. While it is acknowledged that not all models produce reliable surface runoff from their land surface component (e.g. MRI-CGCM3), the use of gridded runoff data generated through GCMs is selected as it has been argued that runoff data generated through GCMs can be a desirable replacement option for macro-scale studies as they guarantee a closed hydrological cycle (Weiland et al., 2012). It was found that for the three models selected, the runoff coef- ficient remained within reasonable bounds over Africa (i.e. between 0.05 and 0.3 over rain- fed agricultural land for a key month of the growing season, Figure 3.1). As only the frac- tion of rainfall which is converted to surface runoff is of interest, as opposed to actual sur- face runoff values, this approach was deemed appropriate.

Finally, a relatively conservative value for the efficiency of the in situ RWH sys- tems was set to 0.6, where it can reasonably reach up to 0.75 for such short slope catch- ments (Critchley and Siegert, 1991). The efficiency factor takes into account the fact that not all harvested runoff can be used effectively by the crops, as there will be losses through deep percolation amongst others. The catchment to cultivated area ratios were calculated for each crop on a month-to-month basis, for both the historical and the future periods.

The maximum monthly value of the C:CA ratio required to fully bridge the crops water deficits was determined. Further consideration was given to the fact that RWH some- times requires an excessively large catchment area to harvest a sufficient amount of surface runoff to fully bridge crop water deficits. However, in arid environments where this situa- tion is more likely to occur, farmers already use very low cropping densities (e.g. Bationo et al., 1992), making the selected values here seem relatively conservative. In this study, the C:CA ratio (i.e. a calculated value used to optimize the design of RWH systems) is varied

spatially to values which are suited to the aridity of the different regions. It integrates the reality whereby drier regions often have lower cropping densities, and hence the use of larg- er catchment areas in those conditions does not necessarily reduce the availability of arable land for agricultural production. The aridity indices determined using the De Martonne Aridity Index (which ranges from 0 for very dry to 100 for very humid environments) (de Martonne, 1927), were calculated for both the historical and future period, as the range of reasonable C:CA ratios vary with aridity (Table 3.2).

Table ‎3.2 │Assumed maximum allowable C:CA ratios by aridity zone

Aridity zone Maximum allowable C:CA ratio

Arid 15:1

Semi-Arid 10:1

Dry sub-humid 5:1

Humid 3:1

If the C:CA value fell within a reasonable range as per Table 3.2 (e.g. positive value ≤ 15:1 for an arid zone), then that value was kept as such. Otherwise, it was assumed that RWH could only partially bridge the water deficit or was unnecessary. The gridded aridity indices were then used to re-assign the values of the C:CA ratio where only a partial bridg- ing of the water deficit could be accomplished. The dryer areas were assigned higher ratios, and wettest areas the lowest ratio of 3:1.

The actual evapotranspiration (ETa) of the different crops is equal to the design rain-

fall where there is no RWH. In the case where RWH is used, the C:CA ratios adjusted for aridity were used to estimate the amount of water actually harvested, which was then added to the design rainfall to obtain the total monthly ETa values for each crop.

3.2.2.3 Estimating impacts on crop yields

The yield gap (or yield decrease from water deficits) expected in the cases with and without RWH was estimated on a monthly basis, using Equation 3.4 (Doorenbos and Kassam, 1979):

(𝟏 −

𝒀𝒂

𝒀𝒑

) = 𝑲

𝒚

(

𝑬𝑻𝒂

𝑬𝑻𝒄

) (‎3.4)

Where Ya is the actual yield and Yp is the potential yield. The maximum value of the poten-

tial yield decrease caused by water deficits within a growing season was selected for the determination of potential for increasing crop yields through the bridging of that water defi- cit with the use of RWH. Due to the use of the 33rd percentile rainfall in the determination of

the actual evapotranspiration, the monthly maximum potential yield decrease value effec- tively represents the minimum yield gap that will occur in one of three growing seasons. Finally, to evaluate the future performance of RWH systems with respect to their historical performance, Equation 3.5 was developed:

𝒀

_{𝑰𝒏𝒅𝒆𝒙,𝒕}

= 𝑪𝑨

_𝒕

(𝟏 −

𝒀𝑮𝒂𝒑,𝒕

𝟏𝟎𝟎

) (𝟏 +

𝒀𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆,𝒕

𝟏𝟎𝟎

) (‎3.5)

Where YIndex,t is the yield index corrected for cropped area (CAt), percentage yield gap

caused by water deficits (YGap,t), and percentage yield increase associated with the use of

RWH (YIncrease,t) for the time period t (1986-2005 or 2046-2065). When YIndex,2046-2065 < YIn-

dex,1986-2005, the performance of RWH in the future is less than during the historical period,

and would point towards the need for different climate change adaptation strategies for the concerned regions.

In document Assessing the potential of rainwater harvesting as an adaptation strategy to climate change in Africa (Page 50-54)