Rwizi catchment lies in South- western Uganda between 29˚55'E 0˚55'S and 30˚55' 0˚16'S. River Rwizi originates from Buhweju hills (S00˚21.983', E030˚26.363') and Ntungamo hills (S00˚45.151', E030˚20.139'). It then flows downstream through Sheema (S00˚35.907', E030˚21.726') and Mbarara (S00˚37.095', E030˚38.630') and continues draining into lakes Nakivale in Isingiro and lake Kakyera in Lyantonde then to Lake Victoria through river Kagera, as shown in Figure 1. The catchment lies between 1300 - 2170 meters above sea level with annual precipitation of 690 mm - 1300 mm per year, experiencing two rainy and two dry seasons.

Satellite images for the years 1989, 1999, 2009 and 2019 (Table 1), with a 30 m spatial resolution were processed and analyzed for LULCC of the catchment. Landsat data were downloaded from U.S Geological Survey (USGS) center for Earth Resources Observation and Science (EROS) (http://earthexplorer.usgs.gov/). ASTER GDEM measuring 30 m per cell was also obtained from Aster Global Digital Elevation Map (http://gdex.cr.usgs.gov/gdex/), Rwizi flow data was obtained from the Directorate of Water Resource Management (DWRM), rainfall and temperature data was obtained from Uganda National Meteorology Authority (UNMA), population, production and other district specific data was obtained from Uganda Bureau of Statistics (UBOS) and Ministry of Agriculture Animal Industry and Fisheries (MAAIF), soil data was obtained from FAO, and district statistical abstracts were also used to obtain supplementary district specific data. Primary data was obtained from field visits/observations, key informant interviews and focus group discussions.

Data preparation involved unzipping of the downloaded images and combining selected bands (2, 3, 4, 5, 6, and 7) and stacking them to create multi-band images. Landsat image synthesis and classification was done in QGIS using random forest classifier algorithm. This clipped out the area of interest from the composite image which was then classified into different land use/cover categories (Table 2).

The software used for image processing was ArcGIS 10.2.2 and ERDAS IMAGINE 14. Before georeferencing to a datum in which river Rwizi falls, the images were first converted into Universal Transfer Mercator and image quality was improved by applying histogram equalizations. Thereafter, classification of the Rwizi catchment land cover classes was done followed by detection of change between 1989-2019 as well as between each ten year interval and catchment land cover maps for the four satellite years drawn as shown in Figure 3. Supervised image classification was used because of prior knowledge about activities and features of the catchment. The classification was done using Random Forest Classifier algorithm due to its robustness and high level accuracy when handling large data quantities [33] [34] . The obtained land cover classes are described in Table 2 below.

This process was done to identify the segments that were not classified correctly. Due to the fact that training samples were not picked from every segment, there were some segments that had wrong classes. The methods used to perform validation involved integrating a number of satellite imagery from ESA-Sentinel-2 images for 2019 land cover and other sources such as Google Maps, Bing maps and also the use of expert judgement based on the experiences about the subject area. The final LULC map obtained in ERDAS IMAGINE was fine-tuned by the Clump and Eliminate process. This process was important as it removes sliver polygons.

This was done to ascertain the reality on the ground and measure precision of the classified maps, and used randomly sampled reference data for LULC for the years 1989, 1999, 2009 and 2019. Accuracy was assessed using producer accuracy, user accuracy, overall accuracy and kappa coefficients [35] [36] [37] . Overall accuracy was calculated using Equation (1) while kappa coefficient was calculated using Equation (2).

Overallaccuracy = 1 N ∑ i = 1 n x i i (1)

where, x = individual cell values, x_ii = the total number of observations in row i and column i, n = total number of classes, N = total number of samples.

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

where, K is Kappa coefficient, r is the number of rows in the matrix, x_ii is the number of observations in row i and column i, x_i+ are the marginal totals of row i, x_+i are the marginal totals column i, and N is the total number of observations. The computed overall accuracy of the maps was 84.46% (1989), 89.69% (1999), 90.64% (2009) and 90.76% (2019); and kappa coefficients of 0.80 (1989), 0.83(1999), 0.84 (2009) and 0.85(2019) (Table 3). All overall accuracy values (84.46% - 90.76%) and kappa indices (0.8 - 0.85) fell in the range that indicates very good representation of ground truth by the images i.e. above 85% and (0.70 – 0.85) [38] , thus the validation data set reveals very good accuracy of the classified maps.

The formula used to calculate overall accuracy has limitations; when the degree of variation between sensitivity and specificity rises and/or when the prevalence moves away from 50%, overall accuracy presents significant challenges as a validity indicator. The overall accuracy and either sensitivity or specificity deviate more and more in both cases.

Limitations of using Equation (2) and kappa coefficient for accuracy assessment

One statistical metric that is frequently used to evaluate the precision of image classification is the kappa coefficient. When analyzing the results, one should

keep in mind that it has certain limits. A research paper [39] claims that the kappa coefficient measures the degree of agreement between a classification and a reference dataset over and beyond what would be predicted by chance, rather than the quality of an image classification. The kappa coefficient’s sensitivity to the prevalence of various classes in the dataset is one of its primary drawbacks. Furthermore, because the kappa coefficient’s magnitude might have a large range of values that don’t always correlate to different levels of accuracy, it can be challenging to interpret.

In conclusion, the kappa coefficient should be utilized cautiously and its limits should be considered when interpreting its results, even if it might be a valuable indicator of agreement between an image classification and a reference dataset.

The aim of this was to quantify the rate and trend of land use/land cover from the remotely sensed data at different times. Markov chain model in Idrisi software and Land Change Modeler, incorporating Random Forest Classifier Algorithm were used to compute the extent of change in each land cover class, obtained from Landsat photos of the catchment for the years: 1989, 1999, 2009 and 2019. The Land Change Modeler is a robust tool in analyzing spatial change, net change and its drivers as well as change trends and forecasts.

Transition Potentials

This parameter facilitated computation of the area of change. If the underlying sources of change for each transition were common, their transitions were grouped together into sub-models and the changes in land cover influenced by the same variables were also grouped into a sub-model. This process involved deciding transitions to be modelled based on similarity of driver variables followed by collecting transition potential maps. The variables input in the model were either static if they didn’t change over time for example elevation or slope or were dynamic if they changed over time taking an example of infrastructure and proximity to existing developments. This transition was run by using the process embedded in the Multi-Layer Perceptron (MLP).

The Land Change Modeler (LCM) incorporating Markov chain were used for land cover prediction. The LCM based on artificial neural network, Markov chain matrices and transition suitability maps predicts changes from the thematic raster images having the same number of classes in the same sequential order. This model was used to forecast the future land cover changes in the Rwizi catchment for the years 2030 and 2040. In complimenting the LCM, Markov chain model represents a stochastic approach to LULCC modeling. It projects future land use/cover by using transition probability matrix and transition area matrix from time t =1 to time t + 1. The product matrix is a measure of the degree of chance that a land cover class converts to another one during the stated interval. Transition probability maps are estimates of the probability of converting each pixel into a different land cover class or remain unchanged over annual time steps.

The model was constructed by considering factors and constraints; where factors favour conversion to another class and constraints hinder conversion to a given class [40] [41] , among these were: suitability for conversion to another class, distance to towns, distance to major roads, elevation, slope and proximity to water bodies (Table 4). The suitability for conversion was measured on a scale from 0 (no likelihood of conversion) to 1 (high likelihood of conversion). The ranks were arrived at by synthesising data from key informant expert opinions, Focus Group Discussions and desk review of several secondary documents. It was observed that conversion to cropland and built up area had slope as a key

Model validation

For any modeling activity, model validation is a vital step [2] [42] [43] [44] . To ascertain the suitability of the Markov model in predicting future land changes, model validation was done [45] [46] [47] by simulating the 2019 LULC status with the help of the 1999 and 2009 processed images. There after the simulated and actual land cover maps for the year 2019 were compared using the VALIDATE tool of IDRISI module. Furthermore, kappa indices namely: K_location = 0.9554, K_standard = 0.9275, K_{location strata} = 0.9345 and K_no = 0.9421, were applied to validate the predictive accuracy of the model.

LULCC analysis is key in exhibiting patterns of change that informs the need and direction for sustainable land management practices, policies and decision making. This required at least two satellite imagery years [48] [49] , from which computed land area for the different categories was analyzed to compute the percentage land cover change [50] as well as the annual rate of land cover change per decade and for the entire thirty year period using Equations (3) and (4) respectively. Furthermore, rate and trend of LULC change was projected for the periods 2019-2030 and 2030-2040 and interpreted accordingly. The named changes can be determined by using the following ways [51] .

Total LULC change in hectares calculated as: Total LULCC = Area of a final year − Area of initial year. Positive values denote an increase while negative values denote a decrease.

Percentage LULC change calculated using the following equation:

PercentageofLULCC= AreaofaFinalYear − AreaofInitialYear AreaofInitialYear ∗ 100 % (3)

➢ An annual rate of LULC change: computed as:

r = Q 2 − Q 1 t (4)

where r = the rate of change, Q2 = recent year LULC in ha, Q1 = initial year LULC in ha, and t = interval year between initial and recent year.

Drivers of LULC changes, were assessed using key informant interviews with district and catchment management experts and focus group discussions with farmers and large-scale landlords.

Land use land cover (LULC) change rate and trend for the period 1989-2019 in the Rwizi catchment, showed a total increase of 947.19% for built up area, 171.80% for forestland, 25.74%, for cropland 21.47% wetland and 4.43% open water bodies, with a decrease registered only in grazing land (−29.73%), (Table 5). Maps of the Rwizi catchment showing the extent of different land use/land cover classes in the four satellite years (1989, 1999, 2009 and 2019) were drawn as shown by Figures 3(a)-(d) respectively. However, each land use/land cover showed varying trends of change in each of the three decades (Table 5). Built up area increased continuously from 0.18% of the total catchment area in 1989 to 1.67 % by 2019. During the periods 1989-1999, 1999-2009 and 2009-2019 built up area increased by 28.82%, 146.68% and 229.53% respectively, and increased by 381.819 ha/year (Table 6).

Built up area registered highest percentage increase of 229.53% between 2009-2019, attributed to elevation of several administrative units to Town council, Municipality and City stati, as mentioned by majority of the respondents, and Mbarara District showed the highest rate of increase across all decades. Cropland area showed cyclic changes (Table 5), with 1989-1999 showing the highest rate of increase, with an annual rate of change of 2288.35 ha/year. Forestland area increased highest between 2009-2019 and overall change rate was 1287.43 ha/year. The sharp decline in the period 1999-2009 was due to pressure for fuel wood for many upcoming small scale industries, human settlement, more land for crop cultivation and clearing forests for construction materials owing to the anticipated elevation of administrative units attracting peri- urban settings. From interviews and focus group discussions, the highest percentage increase (370.03%) (2009-2019) was as a reversal to the drastic impacts of deforestation in the previous decade, where all district local governments embarked on a large-scale re-afforestation campaign. Grazing land changed cyclically (Table 5). The decade percentage change was only positive in the 1999-2009 period, though overall change rate was −4183.183 ha/year. The decline in grazing area in the last decade was attributed to the shift to zero grazing, food security at household level and commercial crop husbandry which required less land area than traditional grazing. Open water bodies area decreased only between 1989-1999, (Table 5), and overall change rate was 21.66 ha/year, while Wetland area only decreased between 2009-2019 (Table 5), and the overall change rate was 204.15 ha/year. According to key informants and focus group discussants,

the observed decline in wetland cover in 2009-2019 was attributed to encroachment for industrial parks, prolonged drought, a rise in population and increased demand for food that led to increased shortage of land for cultivation and loss of soil fertility in the available arable land but with no financial capacity to rejuvenate it, and people across the divide resorted to encroachment on wetlands for cultivation of seasonal crops.

An analysis of the annual rate of land cover change in hectares per year (Table 7) established that grazing land showed the highest rate (1999-2009) followed by cropland (1989-1999) and forest land (2009-2019). The three major land cover types showing maximum annual rate of increase in different decades point to a shift in policy that promote different priority investments inconsistently. Builtup area and wetland area showed the highest Pearson correlation coefficients between inter-decade annual rates of change and the highest R² values all showing that builtup area and wetland area changes are largely explained by a change in time in years, while other land cover changes are explained by other factors not largely time series.

These research findings conform to results from previous studies; [52] [53] [54] [55] [56] , all in the upper Rwizi catchment, where cropland, built up area and forestland increased overall while grazing land and wetland area decreased. Further investigations by [57] [58] , in the Mt. Elgon catchment, [59] , in somodo watershed south western, Ethiopia, [60] , in Tana River Basin, Kenya, [44] , in Kilombero catchment in Tanzania, [61] , in the Gaborone dam catchment, Botswana , [56] [62] , in the uMngeni river catchment, South Africa and [63] , in the Andassa watershed in the Upper Blue Nile basin of Ethiopia, all reported a positive change in cropland and built up area while grazing land registered a negative change, forest cover increased in some and decreased in others in their respective analysis periods. The observed trends point to a high degree of universality in both proximate and underlying drivers of land cover changes across different spatial distributions in Africa.

There were marked Land Use Land Cover conversions during 1989-2019 in the Rwizi catchment.

Only built-up area increased irreversibly throughout the entire period while Cropland, wetland and forestland showed cyclic falls and rises while grazing land showed a continuous decrease.

A trend of increase in built-up area, forestland and open water bodies is expected by 2030 and 2040 while wetland and grazing land are projected to decrease. In contrast, cropland is projected to decrease by 2030 and rise again by 2040. The projected trends threaten food security, river hydrology and soil quality in the catchment. Thus, management and planning should be oriented towards minimizing the likely adverse effects of this trend to the river and livelihood of catchment inhabitants. The major drivers of change in Land Use Land Cover were socio economic due to population pressure followed by hydro-climatic factors and Land Use Land Cover Change accounted for more variation in river flow than climate variability. Therefore the extent of enforcement of sustainable land management practices in the Rwizi catchment should be an area for further research.

There is need for catchment management planning and implementation to prioritise the cropland and grazing land, being the dominant land use/land cover types.

There is need for increased recurrent budget allocation at national, catchment and district levels for natural resources protection, management and education every financial year.

There is also a need for consistency in government’s programmes of popularising agricultural production and environmental conservation.