Landsat 7 ETM+ images (Worldwide Reference System 2, row 027 and path 031) of the study area were acquired from the Global Land-cover Facility and the Landsat Program. These images covered a span of three different years 2007, 2011 and 2015. This freely available data has a ground resolution is 30 m. A thematic RGB band combination of bands 7, 4 & 2 was used. Data obtained was

in the form of individual bands ranging from 1 to 7. Layer stacking created a new multiband file from the input bands which were resampled and re-pro- jected. These datasets were resampled using the nearest neighbor algorithm so that their pixel brightness values were preserved. Upon layer stacking of the Landsat scenes; they were georeferenced to UTM Zone 14 North, WGS-84 Datum, then data calibration was applied which converted the digital numbers of the image to reflectance values as a way of preprocessing the data. Supervised classification was performed using Maximum Likelihood algorithm. We used supervised classification because the data of the study area was available and we had a prior knowledge of the study area. Training site data was derived using digitization which was then converted to polygonal training data. A total of 50 training sites were chosen for each image to ensure that all spectral classes constituting each LULC category were adequately represented in the training statistics. Ten training sites for each of the five classes were chosen as ROIs (regions of interest). The reference data was collected from existing LULC maps that have been field-checked. Change detection statistics was performed on a remote sensing platform to generate a change matrix for the years 2007-2011, 2011- 2015, and 2007-2015. The statistics are presented in a cross tabulation format that compares the change between the two maps, that is, the base map and the final map. We generated change matrices for years 2007 to 2011, 2011 to 2015, and 2007 to 2015. Pixel count and areal extent data for each class within each period was also generated. The maps generated from the change detection statistics were used as inputs to generate confusion matrices as a measure of accuracy assessment. The final change images were overlain with a vector file of the study areas and the final maps were generated.

Reclassified images of 2007-2011, 2011-2015, and 2007-2015 were imported as raster datasets. The datasets were converted to ASCII using the raster conversion tool to generate the attribute table containing cell values. To estimate the land-use transition from forested land to non-forested land, the datasets were reclassified using spatial analyst. The USGS Anderson Land Classification Scheme [44] was used to classify all the remotely sensed datasets into new values. The categories included: 1) bare soil or barren land, 2) open waters, 3) cropland, 4) forested land, and 5) urban/built-up area. Tables 2-4 represent the areal extent of change within each land-use class for the study period 2007-2015. The amount of positive or negative change for each land-use class is shown in the tables.

The MCMC process was used for describing and projecting land-use information within the watershed from satellite imagery. Data compatibility, stationarity and statistical independence were accessed using the aforementioned MCMC process. The ASCII data generated for each year in the ArcGIS interface was imported into SemGRID 1.6.1 interface as a layer. SemGRID 1.6.1 was used to

generate the transitional probabilities of LULC data for years 2007 to 2011, 2011 to 2015, and finally 2007 to 2015. These probabilities were projected as 3D mesh plots using SigmaPlot® 10.0.

The testing of statistical independence hypothesis involved a procedure that compared the expected change with the actual change. If the number of LULC categories is M, then the statistic to be computed is Pearson’s χ2 with (M − 1)² degrees of freedom [45] . According to the MCMC hypothesis, the transition probability matrix governing the period 2007-2015 can be obtained by multiplying the 2007-2011 and 2011-2015 matrices. Table 5 shows the subset areal extent derived from the Markov Chain model where transition from each class is quantified in hectares as well as percentage value. Transition probability data derived is shown in Tables 6-8. Kappa coefficient of agreement was derived based on [46] [47] . Reclassified Landsat datasets from the years 2007, 2011, and 2015 were combined using the combine function in ArcGIS-Spatial Analyst. Datasets from 2007 and 2011, 2011 and 2015, and finally 2007 and 2015 were combined. The attribute table for each dataset contained the pixel count information for each land-use class. These attribute tables for each datasets were then exported to a database table file in MS-Excel. These were converted to text files and imported into MS-Access where a crosstab query was performed to format and compress the data such that the row and column headings had the same class description as the reclassified datasets. These tables were imported into Excel to derive the Kappa coefficients of agreement for each dataset.

The overall accuracy values based on the post classified images generated for 2007-2011, 2011-2015, and 2007-2015 using change detection statistics in ENVI 4.5® were 91.59 percent, 88.30 percent, and 89.43 percent respectively. Figure 3 shows the graphical representation of LULC change matrix from 2007 to 2011 where a likelihood of increment in 89.69% cropland, 28.81% open waters, and 1.16% urban area was prominent. The likelihood of decrement in forested land appeared to be at 77.16% along with a decrement of 9.06% for bare soil or barren land. Figure 4 represents the graph showing LULC change matrix from 2011 to 2015 where a likelihood of increment in cropland, urban area and bare soil or barren land at 71.17%, 4.09%, and 2.04% respectively was noted. A net negative change in forested land and open waters was observed at 34.27% and 9.24% respectively. Forested land to non-forested land transition was found to be high for 2007 to 2011 period but was slightly lower from 2011 to 2015 period. Positive change in croplands was noted and could be a probable cause to the growing demand for food grains and agricultural products in this area. Figure 5 represents the graph for change matrix from 2007 to 2015. About 89.90% likelihood of increment in agricultural land leading to a 77.44% likelihood of decrement in forested land in the area was noted.

Markov Chain simulations for the Pipestem Creek watershed showed continuity between the trends in change from forested land to other land-use classes (e.g. [47] ). The range of forested land to cropland change was significant. Table 6 represents the transition probabilities of years 2007 to 2011 derived by Markov chain simulation. It represents cropland to cropland transition at 0.36 and

forested land to cropland transition at 0.52. Figure 6 is graphical representations of the transition probability from the year 2007 to 2011 showing significant peak for categories 3 followed by 4 which represent cropland and forested

land respectively. Urban or built-up land generated a low transition probability of 12% from barren land. Table 7 represents the transition probabilities of years 2011 to 2015 derived by Markov chain simulation. Transition from forest to cropland was 44% and cropland to cropland was approximately 50%. Forested land transiting to cropland was relatively higher than that exhibited for the years 2007 to 2011. Barren land to urban area transition probability was high at 22%. Open waters did not show much transition throughout 2007 to 2015. Figure 7 is a visual representation of the tabular data from 2011 to 2015 where the only significant peak that can be seen is for cropland. Table 8 represents the transition probability data 2007 to 2015 in LULC over a period of 9 years where a significant transition probability from forested land to cropland was 41% for years. Figure 8 is a graphical representation of the same data where cropland showed up as a significant peak followed by forested land and urban land, indicating

a likelihood of increment. The Kappa coefficients of agreement for the datasets were at 53.28% for the years 2007 to 2011, 55.74% for the years 2011 to 2015 and 60.24% for the years 2007 to 2015. Figures 9-11 represent LULC maps of the Pipestem Creek in North Dakota for the years 2007-2011, 2011-2015, and 2007-2015 respectively. The western parts of Stutsman and Wells County showed significant transition from forest to cropland. The south-eastern part of Stutsman County showed a significant increase in urban or built-up land attributable to the location of small towns like Jamestown. Reference [47] used error matrices to study similarity between two datasets. A Kappa coefficient value would determine the similarity or dissimilarity between two images. In this study, a low Kappa value is indicative of low similarities between the datasets which could also imply significant transition between various LULC classes. This prediction assumes spatial independence of the area units [48] . Although Markov chains constitute a good tool for describing and projecting LULC quantities, they are insufficient for spatially explicit LULC predictions, because they also assume statistical independence of spatial units. In a similar study made by [48] , it was suggested that Markov transitions

can be used coupled with spatially explicit models like cellular automata and/or linear extrapolation models. The methodology presented in this study incorporated a spatial element along with a temporal model. The projections of future LULC changes on the basis of a MCMC model showed a continuing trend of increase in urban and agriculture land acreages, and the decline in forests and other natural vegetation covers. A similar study was conducted by [47] of statewide North Dakota which depicted a greater likelihood of forest to non-forested land transition especially along north central North Dakota. The prioritization map of North Dakota derived in reference [47] showed that part of the Pipestem Creek watershed was a high priority area for Forest Stewardship Program. The MCMC model transition probabilities estimated from 2007-2015 showing change from forested land to other land-use classes depicted a probability of future change and loss of forest acreage. The test of time homogeneity was performed to determine if that the process of land-use change was stable throughout the full study period. This was done by comparing the data from each sub-period transition matrix i.e. 2007 to 2011, 2011 to 2015 to the full period transition matrix and then comparing the full period of 2007 to 2015. The test of

time dependence in this dataset is evident in Tables 6-8 where the change from forested land to agricultural land was significant from the base year to the transitioning year. The transition probabilities estimated from the full study period with an interval of 4 years was assumed to be time-stationary Markov transition matrix. This may be used to predict the future land-use category distribution to provide answers to management problems as in reference [49] study. Reference [49] also points out that early MCMC models were parameterized using data observed and measured from field surveys and air photography. These data tended to be biased and costly. The use of satellite remote sensing has enabled us to calculate less biased training sites from the full extent of the landscape as in reference [50] . Thus, the issue of obtaining observed training sites is crucial. The Markov chain models have shown the capabilities of descriptive power and simple trend projection for LULC change, regardless of whether or not the trend actually persists. The analysis can serve as an indicator of the direction and magnitude of change in the future as well as a quantitative description of change in the past. However, there are several limitations in LULC change applications. First, these models are difficult to accommodate high-order effects [51] . Reference [51] suggests that these effects can be modeled by redefining the state space, so that new states are defined by both present and preceding states. A second- order model, for instance, would include j² states instead of j states in a first-or- der model [51] . Second, the influence of non-stationary variables cannot be incorporated in the model [51] . Reference [52] shows a method to conditioning changes to the initial states in different sites, as well as in the final states, and therefore introduces spatial dependence into Markov modelling. So higher ordered effects can be studied once the spatial adjustments are made. Table 5 shows results generated with transition states which was corroborated in the transition matrix shown in Tables 6-8 for years 2007 to 2015. Overall, areas used for all forms of agriculture increased by more than 50% of its original level at the first stage. The built-up areas doubled in area compared to the initial stage. The Markov probabilities estimated from the full study period proved to be useful to analyze and predict the distribution of land-use categories, though the land-use change process cannot always be assumed static because of its dynamic nature [52] [53] . The MCMC model, combined with the geospatial analysis proved to capacitate trend projections of the changing land-use [54] . This spatio-temporal model provides not only a quantitative description of change in the past but also the direction and magnitude of change in LULC in the future [55] [56] [57] .

In terms of the quantitative accuracy, error rates for forest and agricultural land are particularly low indicating that nonparametric models can be successfully implemented in a further study of similar agricultural watersheds. In terms of the spatial accuracy for forest, and agricultural land, a confusion matrix generated low accuracy assessment as discussed earlier which were acceptable indicators. This indicates that the MCMC model can predict land-use patterns objectively.