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According to Pothiraj and Rajagopalan, (2013), the equation used to calculate groundwater recharge potential map weightage using the Boolean logic technique is as follows;
geomorphology * 12 + drainage * 9 + lineament * 5 + geology * 8 + land use * 2 + relief * 4 (eq. 1)
The map weights and class weights of each parameter are assigned based on the significance each parameter has on groundwater recharge. Relative weight is assigned to each parameter and each parameter is rated according to a category or range of values to get the class weight. Map weights are always constant; however, class weights vary as mentioned above.
Boolean logical analysis is the most common and simplest model that has been used to delineate groundwater resources. It consists of four operators namely; AND, OR, NOT and XOR, therefore since the study is on integration of thematic layers to produce the groundwater recharge potential zone map, the AND operator is used to integrate thematic layers. However, like any other models this model also has its own downsides since the language used is complex, unfamiliar and takes time learning it, hence, results in errors (Zaidi et al., 2015).

Pinto et al., (2017) also demonstrate how a groundwater recharge potential map is calculated using the analytical hierarchy process technique;
GPM = (MC1w * SC1r) + (MC2w * SC2r) + (MC3w * SC3r) + (MC4w * SC4r) + (MC5w * SC5r) + (MC6w * SC6r) + (MC7w * SC7r) + (MC8w * SC8r) (eq. 2)
where GPM is groundwater recharge potential map, MC1–MC8 represent the main criteria (1–8 thematic layer map), w is weight of a thematic map, SC1–SC8 are the sub-criteria of each thematic layer map and r is the sub-criteria class rating of each thematic layer map.
The analytical hierarchy process assigns normalized weights to each parameter by first assessing the geometric mean. The geometric mean is derived from the total sum of score of a specific parameter given by the following equation; (Kaliraj et al. 2014)

Geometric mean=( total scale weight )/(total number of parameter) (eq. 3)

The corresponding geometric mean weights have been used to derive a normalized weight given by the following equation; (Kaliraj et al., 2014)

Normalized weight = Assigned weight of a parameter feature class / geometric mean

Two layers can be integrated using pair-wise comparison matrix and the original weights of polygons of two layers are summed to get the weight of each polygon of the integrated layer. The process is continued for the remaining layers to obtain a final integrated layer. The sum of the weights in the final integrated layer is divided into three equal classes to delineate groundwater recharge potential zones (Chowdhury et al., 2009).

The normalized weights for the theme and their features obtained are examined for consistency by calculating consistency ratio (CR) by first assessing the consistency index (CI) given by the following equation; (Jha et al. 2010)

Consistency Index (CI) =( ?max – n )/(n – 1) (eq. 4)

where n represent the number of factors

Consistency ratio (CR)=( Consistancy Index (CI))/(Random Consistancy Index (RI)) (eq. 5)

Lastly the parameters along with their normalized weights are integrated to produce a groundwater recharge potential zone map using the given equations above.
Studies has shown that the analytical hierarchy process is the most common decision-making technique used over the years simply because it organizes and analyses complex decisions based on mathematics and psychology.
The weighted index overlay analysis technique is the simplest of them all since it only takes into consideration the relative importance of parameters and classes belonging to each parameter. As aforementioned, factor maps are first converted to raster format and raster classification is performed for all the layers. Each layer along with their classes are assigned weightage and score; hence, the higher the weightage and score values, the more favourable the zone to groundwater recharge potential (Nag and Ghosh, 2013). Each thematic layer along with their classes are assigned weights based on their relative contributions towards the output (Jasrotia et al., 2007). Reclassified and weighted maps are integrated using weightage overlay equation (Danee and Helen, 2014).

The average score is given by the following equation; (Nag and Ghosh, 2013)
S= ???(Sij x Wi)?/ ??Wi (eq. 6)
where S represents weight score of an object, Wi represents weight for the i input and Sij represents rating score of j class of i map

Pothiraj and Rajagopalan (2013) stated that in order to produce a groundwater recharge potential zone map the following steps have to be followed; gathering of data; analysis of data and lastly integration of data. According to Arkropovo et al., (2012) and Magesh et al., (2012), multi-influencing factor is found to be the most cost-effective and time efficient technique ever used to delineate groundwater recharge potential zone in any area. The equation used to calculate the score for each influencing factor is given by; (Thapa et al., 2017).
Proposed Score=( A + B)/( A + B )*100% (eq. 7)
where A represents the major effect of factors and B represents the minor effect of factor
After calculating the weights and ranks and subclasses for each parameter, the values are then used to calculate the groundwater recharge potential zonation through the use of weighted overlay method given by the following equation; (Thapa et al., 2017).
GWPZ = ? GXGY + GMXGMY + SXSY + LUXLCY + DDXDDY + SIXSIY + EXEY + RXRY + FLXFLY + STXSTY (eq. 8)
where GWPZ represents groundwater recharge potential zonation, ‘x’ and ‘y’ represent factor maps and factor subclass, G represents geology, GM represents geomorphology, S represents soil, LULC represents land use or land cover, DD represents drainage density, Sl represents slope, E represents elevation, R represents Rainfall, FL represents fault, and lineament density and ST represent soil texture. The study area is situated in the Mpumalanga Province of Republic of South Africa. It falls within the Steve Tshwete Local Municipality of the Nkangala District. It is located on the eastern part of the Middelburg Basin which covers an approximate area of 1626 km2, lying between the longitudes 25,430 E and 25,800 E and latitudes 29,170 S and 29,600 S (Figure 4.1). Middelburg experiences warm summers and cold winters representative of the Highveld climate, i.e., rainfall commonly occurs as thunderstorms. It experiences an annual average rainfall of 740 mm (Figure 4.2.1) and varies from an average of 132 mm in summer to 9 mm during winter. Rainfall mostly occurs between November and February. It experiences severe frosts during winter; however, it experiences hail storms during summer. Water is lost in the system due to mean annual potential evaporation of 2 060 mm. The temperature of Middelburg is representative of the temperatures occurring on the Highveld with the lowest temperature being 3 0C in July and a maximum of 31 0C in January. The average annual winter temperature is 15 0C whereas the average summer temperature is 27 0C (Figure 4.2.2). The Proterozoic Wilgerivier Formation of the Waterberg Group forms the only stratigraphic unit in the Middelburg Basin. It unconformably overlies the Pretoria Group, Silverton Formation and Loskop Formation and is turn overlain unconformably by the sedimentary rocks of the Karoo Supergroup (Table 4.2.3). The Wilgerivier Formation has a maximum thickness of 2000 m (Callaghan et al., 1991). The Wilgerivier Formation comprises arenaceous clastic sedimentary rocks. The red-brown sandstone and quartzite rocks resemble an immature texture and mineralogy that dip towards the north at angles of 10º to 15º. It is intruded by a number of diabase sills and dykes of several metres (STLM, 2008).

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