The entire LULC change process started with retrieval and clipping of Landsat images of 1990, 2000, 2010 and 2020 using the imported Mbagathi River catchment shapefile. For a supervised classification to be carried out, training sites were developed for the four land cover types (forest, grassland, urban and bare ground). In order to ensure proper classification, a minimum of 60 training sites was ensured for each of the four classes. Classification of images was done using supervised classification method where maximum likelihood algorithm was applied with training sites developed for the various land cover types (Muriuki et al., 2023) [7] .

Maximum likelihood is a parametric classifier which is very popular in LULC classification and is extensively used across the world over time. This classic algorithm is chosen to compare the accuracy of other algorithms by many researchers. The classifier measures the Gaussian distribution of each of the spectral classes based on input data by using a covariance matrix. The covariance matrix is used to weight the gaps between spectral clusters and the image pixels (Karan and Samadder, 2018 [8] ). Maximum likelihood calculates the probability distribution of classes which is related to Bayes’ theorem. Class probability distributions in this method are assumed to have the form of multivariate normal models (Richards and Jia, 2006) [9] .

Google earth images formed an important reference in the process of developing training sites and validation of classified image outputs. The validation process also involved ground truthing for the forest, grassland, urban and bare ground land covers.

To ensure that pixels were as accurately classified, an accuracy assessment was carried out. The assessment aimed at attaining the correct thresholds of: overall accuracy, producer’s accuracy, user’s accuracy and Kappa coefficient in an error matrix. Overall accuracy was computed by dividing the sum of all correct values in the diagonal of the error matrix by the total number of values in the matrix. The producer’s accuracy was computed by dividing the correct number of pixels in the class by the total number of pixels in the reference data. On the other hand, Users’ accuracy was computed by diving the correctly classified pixel values in a class by the total number of pixel values in the classification data. The Kappa coefficient which measures the agreement between the classified and reference map was computed based on the Equation (1) (Yesuph and Dagnew, 2019) [10] .

K = N ∑ i = 1 r x i i − ∑ i = 1 r ( x i + ) ( x + i ) N 2 − ∑ i = 1 r ( x i + ) ( x + i ) (1)

where K is the Kappa coefficient, N is the total number of values, r is the rows in the matrix, i is the column, x_ii is the number of values in the row i and column i, x_i+ is the total of row i, and x_+i is the total values in column i (Yesuph and Dagnew, 2019) [10] . After attaining acceptable users and producer’s accuracies, the areas of each of the four land covers (forest, grassland, urban, bare ground) were computed and changes were assessed by imagery and area subtraction between two subsequent years.

LULC change detection followed a successful classification process. This was carried out in online GEE platform with the help of appropriate java codes and algorithms. This involved computation of the sum of pixels/area for each class in each of the 1990, 2000, 2010 and 2020 classified image. Resulting areas and corresponding percent coverage were tabulated and checked against errors from the sum totals. The temporal changes for each LULC were determined by subtracting the previous from subsequent areas/percent coverage (2000-1990, 2010-2000 and 2020-2010). Spatial changes were assessed by subtracting two classified images. The change detection results from GEE were validated using similar approach and ground truthing.

The GEE codes and algorithms were used in computing the areas under each LULC classification in the entire catchment. Change in land covers between two subsequent years was determined by subtraction of areas for the corresponding land covers. Further changes were assessed by computing the areas of the four LULC types within 3 Km radius from the epicentre of an urban development. This was aimed at detecting the changes due to the rapid urban development.

A multivariate error matrix criterion was applied in the assessment of accuracy for the classification process. The accuracies included producer’s accuracy (PA), user’s accuracy (UA) and overall accuracy (OA) in addition to Kappa coefficient. Table 1 gives summary results of error matrix while the detailed individual confusion matrices are given in Appendices.

From the analysis of error matrix, the classifications gave overall accuracies of 92.16%, 90.77%, 92.0% and 80.67% with kappa coefficient values of 0.856, 0.776, 0.856 and 0.733 for 1990, 2000, 2010, and 2020 classifications respectively. The high values of overall accuracies and Kappa Coefficient indicated good classification and agreement between the classification and validation classes (Islami et al., 2022) [11] . The results also revealed that forest cover largely covering Ngong Hill Forest, Ngong Lenana Forest, Dagoretti Forest, Oloolua forest and Nairobi National Park was the best classified among all the four LULC.

UA = User’s Accuracy, PA = Producer’s Accuracy and OA = Overall Accuracy.

Figure 2 shows the results of the percent area changes in the catchment between year 1990 and 2020. The total area for the catchment was estimated at approximately 510 Km². An analysis of percentage change revealed that forest and grass land cover decreased between 1990 and 2020 while urban and bare-ground cover increased over the same period. Forest cover decreased from 32.2% to 14.4% while grassland reduced from 53.5% to 30.2%. On the other hand, urban and bare ground land covers increased from 4.1% to 17.5% and 10.1% to 37.9% respectively.

The increase in urban LULC would be attributed to the growing population and low land prices within the satellite towns (Ongata Rongai, Kiserian, Ngong and Tuala). The rapid urban development could also be related to good roads and connectivity between the satellite towns along with closeness to Nairobi town which attracts high labour force but has minimal provision for residential services. Most of the people work in Nairobi but live in these satellite towns.

Figure 3 shows the areas under urban development based on LULC analysis.

The LULC analysis established that urban development was on the increase at each of the four selected sites namely Ongata Rongai, Kiserian, Ngong and Tuala alongside Langata suburbs. The urban area under 3 Km radius increased from as low as 3% in Kiserian and Taula to a high of 14% and 22% in Tuala and Kiserian respectively. In Ngong town, urban area under 3 Km radius increased from 6.5% to 26% while Ongata Rongai recorded an increase in urban area from 9% to 32% for the 3 km radius coverage. Shawul et al., (2019) [12] reported similar findings in Awash basin where vegetation changes were highly occasioned by social developments and population growth. Additionally, Muriuki et al., (2023) [7] also recorded related findings in Lagha-Bor catchment in Wajir County, Kenya.

Similar spatial and temporal patterns and trend were reflected in the GHSL multi-temporal built-up information layer derived from Landsat image collections GLS1975, GLS1990, GLS2000, and Landsat 8 2015. Figure 4 shows the spatial-temporal patterns of built-up area. Visual inspection of the multi-temporal changes in built-up area re-affirmed changes occurred around Ongata Rongai, Kiserian, Ngong, Tuala and Mlolongo.

Results from the LULC change were used in assessing the level of catchment destruction within Mbagathi catchment. From Figure 5, the study observed that forest cover in the whole catchment reduced from 32.2% to 14.4%. Forest cover was also observed to reduce within the surroundings of Kiserian, Ngong and Ongata Rongai towns. The findings were confirmed by a forest officer at Ngong.