The study area adopted is Gilgil constituency shown in Figure 1. It is an electoral region of Nakuru County with a population of 152,102 with five wards Kiambogo, Malewa West, Gilgil, Mbaruk and Murindat [15] . It lies on latitude 0 degrees 16 minutes South and longitude 36 degrees 04 minutes East with an administrative area of about 1348 Sq. Km within Universal Transverse Mercator (UTM) of zone 37 South.

The study area is covered by rivers and consists of Lake Elementaita and surrounded by Lake Naivasha and Lake Nakuru. The rocks underlying the study area are volcanic rock deposits which have low permeability and storage capacity that feeds the groundwater system from high precipitation at higher altitudes

[16] . Groundwater gained from recharge flows longitudinally from these highland areas to the valley floor, following surface elevation contours [13] . The rainfall pattern in Gilgil is bimodal with rainy seasons from April to June (long rain) and from October to November (short rain) and the mean annual temperature lies between 10 and 21 degrees Celsius conditions that are likely to promote rainfall shortages [17] [18] .

Gilgil constituency was selected since a water study on accessibility has not been conducted though many studies have been done on the lakes within and around the area, considering the geology of the area that has resulted in high fluorides being experienced in the groundwater. This study used water points tested and accepted by Water Resource Management Authority (WRMA) to establish accessibility to these water points by pedestrians. The area was also suitable for accessibility study due to its diverse terrain that enabled assessment of different walk speeds with different slope angles.

Datasets used in this research were landcover, Digital Elevation Model (DEM) where slope was extracted, household locations; where semi-permanent structures were extracted from aerial photos through digitization. Vector datasets used were: transport network (road and railway), water facility points which included boreholes and a few springs and areas demarcated and set aside for specific usage under government directives which may deter or encourage settlement with or without water facilities present; Table 5 shows these datasets and their sources.

Household data was digitized from geo-rectified and geo-referenced aerial imagery of 15 m spatial resolution. All buildings were identified and semi-permanent structures differentiated from permanent households by use of size, shape, height and proximity of the structures. The study is interested with semi-permanent structures since it’s the population that is likely to use potable water. These semi-permanent structures were captured as polygons and represented as points by use of a conversion tool that captures the points as centroids.

Water facility locations which included mainly boreholes were obtained from Water Resource Management Authority (WRMA) and these water points are

monitored and controlled for quality hence the aspect of quality was not examined in the study. The points had locational information and was obtained in form of an excel sheet and captured as a shapefile to map them within the study area as shown in Figure 2.

The road network was obtained from United Nations Office for the Coordination of Humanitarian Affairs (UNOCHA) Rosea open source portal. The road network was categorized into classes of main road, secondary road and tracks. These classes were given pedestrian walk speeds as shown in Table 2 while the main road was eliminated from analysis since it’s not expected for people to actively use that class of road while on foot. Documented data on travelling times in Kenya is very limited hence travelling times were adopted from the work of Pozzi and Robinson [19] as shown in Table 2.

The slope on the other hand was obtained from the digital elevation model

(DEM) of a Shuttle Radar Topography Mission (SRTM) of 15 m. The slopes were allocated walking speed as shown in Table 3 with walk speeds assigned at specific degree of slope adopted from Alegana’s work [20] . As for land cover, various speeds were also allocated and the speeds were borrowed from previous studies that had estimated walk speeds on different land covers as adopted from Pozzi and Robinson [21] as shown in Table 4. The study also sought to determine why people would settle in areas with scarce water resource hence areas that the government has demarcated for other activities like forests, wetlands,

settlement schemes were established and used in the logistic regression analysis.

The study adopted cost distance analysis using time as the cost. Cost distance tool was selected due to its capability to combine weights of different surfaces as one moves through each cell location and create a suitable model for walking analysis. We evaluated focal statistics values for land cover layer, slope and built-up area developed from the aerial image that were converted to raster and accorded varying importance using Visual Basic (VB) script. We eliminated primary roads from the road data as they cannot serve as walkable routes. The resulting raster was then classified from 1 to 10 based on difficulty of travel, with a value of 1 being easiest to travel and 10 being most difficult.

The weighted sum overlay of the layers involved set conditions such that if a cell contained a variable like a water body which is not conducive for walking then the summation with the other cell values still acquired or retained the level of difficulty of the water body cell or other variable used containing highest difficulty rate; otherwise the cell values were averaged to obtain the new values. Thereafter, groundwater locations were loaded and a path distance raster was created showing the travel costs. The cost distance tool requires source locations which were the water points and a cost raster which was the combined weight raster as input shown in Figure 4.

For raster cells with the value of 10, which are areas with difficulty of movement like water bodies, when a weighted overlay was done the overall value after the evaluation remains 10 regardless of the other cell values allocated to the other features as shown in Table 6. In this evaluation land cover had the biggest

influence followed by slope value. Service areas from water facilities were created within travel time zones of 10, 20 and 30 minutes of walk time using road network speeds as an impedance having eliminated the main roads from the analysis referring to walk speeds in Table 3.

Restricted layers were also used during the generation of service areas shown in Figure 5 which included forested areas and lakes. The Service areas were created to establish settlements that lived outside these zones and try to establish other sources of water for these settlers. Once the service areas were identified the study set to examine other factors that influence settlement apart from groundwater points since there were plenty of settlements in areas that had no groundwater points.

A predictive analysis using logistic regression was used to determine factors affecting settlement and the predictors used were; slope, agricultural areas (selected from land cover), transportation (roads and railway), groundwater points, government policy (forests and settlement schemes) and soil type. Logistic regression was used because the response to whether a variable affects settlement in an area was a dichotomy with a response of either yes or no. Logistic Regression was well suited to describe and test hypothesis about existing relationships from the categorical outcome variable and several predictor variables [22] .

The analysis used 240 observations which were generated randomly in the study and the values generated were binary (1, 0) where Yes responses represented 1 and No 0. R software was used in the analysis using Logistic regression since the response values were either yes or no (settlements were present in certain conditions).

Null deviance and the residual deviance from Table 9 shows how well the model fits against the null model which is a model with only the intercept whereas the gap widens the better the fit. The drop in the deviance value is experienced when adding a variable which reduces the value of the residual deviance.

When a variable has p-value that has no significance shown by Table 7, Table 8 and Figure 6, the variable should be dropped from the model to further improve the model fit and a better fit will reflect to a significant drop in deviance and Akaike information criterion (AIC) and a lower AIC means the model is closer to the truth.

The results of Figure 4 and Table 10 show a cost surface which was generated using weighted sum overlay that allowed for variables to be allocated varying importance and therefore logic was observed especially in areas that pedestrians could not walk over due to the presence of water bodies, swamps or very high

peak slopes. The use of Visual Basic scripts during the overlay outperforms a normal overlay that does not create conditions and simply averages all the raster’s cell values that are involved in the analysis.

Cost surface was generated to explain ease of pedestrians moving across the wards in Gilgil constituency. Table 10 depicts that Kiambogo ward had the

highest surface friction covering 37.9% of the total friction surface and Mbaruk Ward the lowest surface friction of 6.9%.

From the three service walk zones created, consideration was given to the maximum walk time that WHO recommended would be good for pedestrian to endure which was 30 minutes. From Figure 7 out of a total of 36,109 semi-permanent structures in the study area, only a total of 8195 households were within the 30-minute walk time which is 23%.

Households that are within 30-minutes form the bulk with 4335 households while those within 10 minutes of walk time are 3828. The service areas are well concentrated in regions that have croplands which are Murindat, Malewa West and Kiambogo while areas with no service area have wooded and open grassland, lake and forests which explains lack of settlements in those areas demonstrated in Figure 3. The areas in Murindat and Kiambogo with settlements and no service areas have huge river networks hence presence of alternative water sources. The study was concerned with groundwater sources only, thus excluded other available water sources.

From the prediction analysis, there was a decrease in deviance from the null value of 334 to residue deviance of 279 which is a reduction of 53.06 points on 5 degrees of freedom which is a significant reduction. Such reduction in deviance shows a good fit of the model. The Akaike Information Criterion (AIC) is another result obtained in R and it assesses model quality; where a low AIC would depict greater model quality. In the study the AIC was 291.38 as shown in Table 9 and we further improved the model by eliminating any variable that was not significant. In this study, slope has no significance as shown from its p value not having an asterisk hence was removed and the AIC value reduced to 283.41.

The variable having the highest influence as shown in Table 7 is Infrastructure given its p-value has significance indicated by the 3 asterisks. Other variables with influence are Agricultural Zones, Water locations and Government Policy. From analysis, slope and soil do not necessarily control settlement especially if other factors override them like the government policy. Example; in Kiambogo the government created a settlement scheme; Eburru Settlement Scheme

(Olrajai Scheme) at the top of Eburru range which attracted settlement though the area has less water facilities.