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1 Digital Terrain Analysis with Ilwis DTA (Digital Terrain Analysis) is the process of quantitatively describing terrain. DTA is also known as geomorphological analysis, landform parameterization and land surface analysis. In this process the data is extracted from image maps that show the topography of an area. These maps are also referred to as elevation maps and a digital terrain model is also referred to as the Digital Elevation Model (DEM). DTM (Digital Terrain Modeling) is the process of creating DEMs. The following terminology is used consistently in the digital terrain analysis process: DEM – Digital Elevation Map, i.e. representation of the Earth’s surface topography DTM – set of techniques used to derive or present a DEM DEM filtering – set of techniques used to improve the geomorphic resemblance of a DEM Terrain analysis or parameterization – set of techniques used to derive terrain patterns from a digital terrain model. This is the process of quantifying the morphology of a terrain. Terrain analysis (DTA) is a general term for derivation of terrain parameters and their application Terrain parameters – these are maps or images derived from a DEM using DTA e.g slope Topography or relief – is the shape or configuration of the land, represented on a map by contour lines, hypsometric unit and relief shading Terrain Analysis is accomplished by use of GIS packages like ArcGIS, IDRISI, ERDAS or ILWIS. In this application we will be using ILWIS. We will use ILWIS to run simple filter operations on already existing contour maps available for the different areas in this study. Modelling Terrain

Digital Terrain Analysis With Ilwis

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Digital Terrain Analysis with Ilwis

DTA (Digital Terrain Analysis) is the process of quantitatively describing terrain. DTA is also known as geomorphological analysis, landform parameterization and land surface analysis. In this process the data is extracted from image maps that show the topography of an area. These maps are also referred to as elevation maps and a digital terrain model is also referred to as the Digital Elevation Model (DEM). DTM (Digital Terrain Modeling) is the process of creating DEMs. The following terminology is used consistently in the digital terrain analysis process:

DEM – Digital Elevation Map, i.e. representation of the Earth’s surface topography

DTM – set of techniques used to derive or present a DEM DEM filtering – set of techniques used to improve the geomorphic

resemblance of a DEM Terrain analysis or parameterization – set of techniques used to derive

terrain patterns from a digital terrain model. This is the process of quantifying the morphology of a terrain. Terrain analysis (DTA) is a general term for derivation of terrain parameters and their application

Terrain parameters – these are maps or images derived from a DEM using DTA e.g slope

Topography or relief – is the shape or configuration of the land, represented on a map by contour lines, hypsometric unit and relief shading

Terrain Analysis is accomplished by use of GIS packages like ArcGIS, IDRISI, ERDAS or ILWIS. In this application we will be using ILWIS. We will use ILWIS to run simple filter operations on already existing contour maps available for the different areas in this study.

Modelling Terrain

In modeling we will be creating DEMs from the contour maps of Nyadero, Nyabondo and Nyamarumbe locations. The contours maps for the respective areas are shown below:

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FIGURE 1: NYADERO TOPO MAP

FIGURE 2: NYABONDO TOPO MAP

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FIGURE 3: NYAMARUMBE TOPO MAP

These visualized data sources are already raster maps (images) where each pixel contains information on elevation or terrain parameter and other features evident like water bodies, settlement areas and vegetation. The contour lines provide information about the terrain of the respective areas.

In modeling contour maps the technique used is called interpolation. Interpolation is the sampling of data at point locations or digitized from the contour lines. Interpolation is grouped into two where the interpolator can be exact or approximate or the interpolator can be local or global.

For accuracy purposes, the grid size, scale and resolution must be taken into account. Generally an increase in the detail in the DEM will resolve to more accurate terrain parameters and in overall accurate results in quantitative data.

In contour map data, the average grid size is determined by the length of the contour lines. In the above maps the grid sizes have been chosen with this fact in consideration and the limitation of the areas the study is focusing on. To give the data from the different a commensurate measure. A map with the greatest length of contour lines was chosen as a blue print for the rest of the areas.

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The largest grid area to work with should be at least the average spacing between the inflection points (a location at which the second derivative of a function changes sign i.e location at which the second derivative changes from being concave to convex and vice versa). Theoretically speaking this is provided by the following formula:

pmax ≤l

n(δz)

However, in most scenarios we are greeted with the (‘chicken-egg’ problem) and in particular this study, we had to select the study areas and extract the grid sizes from a larger map. The grid sizes are hence chosen as an estimate.

The grid resolution is given by the following formula:

p= A2 .∑ l

The grid resolution should be at least half the average spacing between the contours, where A is the total size of the study area and ∑l is the total cumulative length of all digitized contours.

Incorporation of water bodies is a step in improving the geomorphic plausibility of the DEM. This is a step in DEM filtering which increases the accuracy of the quantitative data.

The Practical Guide on Creating a DTM

Creating a DTM in ILWIS implies (1) digitizing contour lines from existing topographic maps and subsequently (2) interpolation between the contour lines to obtain a rasterized surface of topography. The contours will be digitized from a segment map which contains coordinate data.

Due to lack of proper digitized maps for analysis, the process of creating accurate DEMs involved use of other software applications like Golden Software Didger which provides a straight forward approach to digitizing the topographical maps.

Once you have installed and started Didger, you can start a new project and import your image map. Next you will need to vectorize it using the tools available. The software will analyze the map and create polygon lines which

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in this case will represent the contour lines shown on the map. The following are the digitized versions of the above topographic maps.

FIGURE 4: NYAMARUMBE DIGITIZED CONTOUR MAP

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FIGURE 5 NYABONDO DIGITIZED CONTOUR MAP

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FIGURE 6: NYADERO DIGITIZED CONTOUR MAP

Calculating the slopes

With the digitization of the topo maps, we can now use ILWIS tools to enhance, filter and evaluate the data. In this step we will calculate the slopes in each and every one of these maps and find out the coverage of high altitude terrain and how they affect population, vegetation coverage and water bodies present in the areas. It is common knowledge that high altitude areas are usually a source for water bodies (rivers and streams), as it is evident in the digitized maps the points marked in blue represent water bodies.

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In ILWIS, slope and aspect are calculated using the gradient of the slope, calculated from the DEMs at each pixel. The filters Dfdx and Dfdy are gradient filters in the X and Y coordinates respectively that yield the altitude differences in these directions on a pixel by pixel basis.

Calculating the slope is a two-step process: first the two filtered maps for the gradient in X and Y direction are calculated and used to obtain slopes:

1. Select from the main ILWIS menu the options: Operations, Image Processing, Filter. Select the filter Dfdx and the map. The output is dx

2. Repeat the procedure for filter Dfdy. Output is Dy.3. Type the following formula on the command line of the main ILWIS

window to create the map Slope

Slope = ((hyp(Dx,Dy))/50)*100

4. Display the slope map on the screen and overlie the fault pattern. You should see the above patterns.

Green Vegetation Indexing

To determine the vegetation coverage we will use the green vegetation index. The most used vegetation index is the Normalized Difference Vegetation Index (NDVI) defined as:

NDVI = (TM 4 – TM 3)/(TM 4 + TM 3)

The NDVI is calculated using the NDVI function NDVI = NDVI (TM3, TM4)*127+128 in ILWIS. This command is input in the ILWIS command line and pressing enter then selecting the image map.

TM3 and so on represent areas of high threshold color composition representing the vegetative areas.

This technique however was not applied to this situation since the topographic maps do not have areas of high threshold to represent the vegetative areas. We will therefore assume that the lack of the vegetative regions means that these areas are bare or have very little vegetation, which could not be digitized.

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Analysis of the Data Collected

From the data collected from the initial topographic maps through the process of modeling and generation of digitized contour maps we can conclude that the presence of water bodies are determined by the presence of high altitude areas. In areas like Nyamarumbe which is mostly a low altitude area does not have any water bodies present, if any then they are just secondary water bodies which dry out in times of low rainfall. It is also evident from the topographic map of this area that human population is higher here. This is in comparison to the higher altitudes of Nyadero and Nyabondo areas.

Even though digitization of Nyadero’s topographic map did not reveal any vegetative areas. It is evident through basic map reading that the high altitude of this area has a high vegetative cover with very minimal human settlement. Settlement is concentrated in the lower areas of the map.

Modeling Land Use and Land Cover Change in Nyakach

Before one can start any analysis on image maps they must be matched to a coordinate system. The georeferencing process matches features in your scanned map image to real world coordinates on the ground. An example of reference systems are Longitude and Latitude, Universal Transverse Mercator (UTM) and State Plane Coordinate System. If you have specific geospatial data you want to use, then it would be best to reference your image to the coordinate system of your data.

Finding Ground Control Points (GCPs)

To georeference an image you need GCPs which are visible in the photographs. Some examples of good GCPs are road intersections, stone wall boundaries, building corners, and solitary trees. These points will be used to “tell” the GIS software:

where your image is in the world how to correctly orient the photograph correct for errors in photo-geometry.

These errors are probably caused by the inherent problems of taking aerial photographs, such as airplane tilt and problems with the lens. The better your GCPs the better your resulting image will be referenced to the real world.

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The number of GCPs you choose will depend on the amount of distortion in your photograph and your desired level of accuracy. The process of registering your photograph applies a mathematical formula to each pixel in the photo. The process of rectification can be thought of making a regression equation that says where a image coordinate corresponds to real world coordinates. The simplest formula is a linear equation, which does not distort the picture but cannot correct any photo-geometry distortion except for skew. Higher order (more complex) equations can correct more serious cases of photo-geometry distortion but they can also seriously distort your final image. As you make the equation more complex you have to add more GCPs.

A linear equation requires a minimum of 3 points, a second-order equation requires 6 points, and a third-order equation requires a minimum of 10 points. In general you should find at least double the number points so that you can discard bad points and you can also lower the error in fitting the equation.

At the map library we have a collection of maps called USGS Topographic Quadrangle Sheets (quad sheet). These maps cover the entire U.S. at a scale of 1:24,000. By using a coordinate grid and a quad sheet, you can get coordinates for GCPs in Lat/Long, UTM, and State Plane. The map library has a reference map for New England which gives the name for the quad sheets. Once you have your quad sheet(s) you can put the coordinates into a GIS and georeference your image. To learn how to get coordinates off a quad sheet please read: CHOOSING GCPS and READING COORDS OFF A COORDINATE SHEET.

Getting the coordinates into a GIS

The first step in georeferencing your image is to open a Correspondence File. This file will be used by Idrisi to reference your image. The best idea is to call the file <YourImageName>.cor, where YourImageName corresponds to the name of your scanned image. Open the Windows Notepad (or any ASCII text editor). The format of the file is as follows

5

65 4225 429043 541801

1702 1657 460102 449235

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3424 4470 538868 527318

2605 3199 501868 492297

5951 1782 597383 425079

The first line of the file denotes how many GCPs there are in the file (5 in this instance). The following lines are:

originalX originalY newX newY

Where the original X and Ys correspond to the column and row numbers of the GCP from the photograph after it has been imported into Idrisi. The new X and Ys correspond to the coordinates for the same GCP read off the quad sheet (CT State Plane in this instance).

Save the .cor file and begin the Idrisi RESAMPLE module. This process will put your photograph into real world coordinates.

A prediction methodology using Markov-Cellular Automata Model

Land cover change models have been developed for predicting landscape change at different levels of complexity. Most techniques predict future scenarios based on the logistic regression, multi-agents and cellular automation. Prediction models can also be viewed as either stochastic or process based. Stochastic models include Markov, Cellular Automata and Logistic Regression, while process based models include the dynamic eco-system model. These spatial models consist of three components: multitemporal maps, a transition function, and a simulated map of future land cover changes. The Markovian Cellular Automata model has gained standing as one of the most powerful means of projecting land use/cover trends.

Markov Cellular Automaton modeling of land use/cover changes

A Markov-cellular automaton is a robust spatially explicit hybrid model which integrates the Markov Chain Analysis and Cellular automata and is an improvement in spatio-temporal dynamic modelling. The integration of the

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Markov process and the cellular automaton mechanism offers significant modelling advantages. Whereas the Markov process directs temporal dynamics among the land cover classes by means of transition probabilities the cellular automaton mechanism addresses the local rules relating to neighbourhood configuration. In tandem with the transition probability, it determines the spatial dynamics of land cover types.

Although the Markov chain analysis operates under fairly restrictive assumptions such as independence and stationarity, it is mathematically easy to implement. In addition, the land use/cover transition probability results can serve as an indicator of the direction of land use/cover processes. Deficits in the Markov Analysis are compensated through the integration of the cellular automata, which facilitates the spatial interactions of the land covers through proximity modeling.

Data and methodology

The datasets used for predicting the land use/cover changes include land use/cover maps previously generated for Nyadero, Nyabondo and Nyamarumbe areas from satellite maps images for the respective areas.

The 1960, 1970 and 2010 classified maps were used for the projection to 2019. 2030 and, 1997. Idrisi Andes software was used for performing the Markovian Cellular Automata model and model validation. This remote sensing and GIS software was selected for its advanced environmental modeling capability. Idrisi has both GIS, IPS as well as advanced modeling functions including:

Land Change Modeling Earth Trends Modeling Markov Analysis and Markov Analysis combined with Cellular Automata

Markovian simulation

The Markovian Cellular Automata model was implemented to predict land use/cover changes in this study. This model was chosen based on its simplicity to implement in a GIS environment. Markov Chain Analysis is suitable to use when changes and processes in the landscape are complex to describe. A Markov process is defined as one in which the future state of a system is projected entirely on the basis of the immediately preceding state. The process involves computing the transition probability matrix of land cover change from time one to time two, which is then considered to be the basis upon which to assign to a later time period.

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In this study, the Markov chain method was implemented to analyse the 1966 and 1974 pair of classified images and to generate a transition probability matrix, a transition area matrix, and a set of conditional probability maps. A transition probability matrix indicates the probability of inter-class transitions among different land use/cover types, while a transition area matrix shows the quantity of land that is expected to transform from one class to another over a 13 year period (up to 2019). Conditional probability images show the probability of existence of a particular land use/cover type over the 13 year period; these images are computed as temporal projections based on the 1966 and 1974 input land use/cover images. The 1966 and 1974 classified maps were used as the earlier and later land cover images respectively. The prediction is purely based on the state of land cover in 1966 and 1974; the background cells were assigned a value of 0.0. A proportional error of 0.11 was assigned to the prediction based on an overall accuracy of 89% for 1974. Land use/cover is considered to be temporally persistent over 10-15 year intervals (Lambin et al., 1999; Gómez-Mendoza et al., 2006), thus a 13 year prediction used in this study was within the required range.

A summary of the computations involved in the Markov projections is shown below, where land use/cover is considered as stochastic process of which the different classes are regarded as the states of a chain.

A Markov chain is expressed as follows:

P( X t j∨Xo io , X1 i1, …, X t 1it1)

P( X t j∨X t1 it 1)

(1)

If a Markov sequence of random variable Xn takes the discrete values a1 ....a N, then

P( Xn ain∨X n1ain 1

, …, X1al1)

P( Xn a¿∨Xn1a¿1)

(2)

Where the sequence Xn is called a Markov chain.

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The initial transition area matrix of the different land use/cover classes is shown in expression.

X11 X 12… X ln

X21 X 22… X2n

X n1 Xn2… Xnn

(3)

Where Xij indicates the quantity of land use/cover type i transforming to land use/cover j over a particular period of time, n denotes the number of land use/cover types. This calculation simplifies to:

∑jl

n

X ij X i ,∑i1

n

X ij X j

(4)

Pij X ij∨X i

(5)

Pij shows the ratio of the quantity of land use/cover type i transforming into the land use/cover class j in the period of time. Using the equations of the Markov process and Bayesian principles of conditional probability, the

above equations are further simplified to. j(k)∑i1

n

i(k 1)P ij( j1,2 , …, n)

(6)

Where j(k) denotes the area of land use type j at the kth state.

Integration of the Markov Chain analysis and Cellular Automata

Markov Chain analysis results were further processed using the Markov Cellular Automata algorithm to bring a spatial sense not considered in the Markov Chain projection. The Markov Cellular Automata function integrates the Cellular Automata, Markov Chain and Multi-Objective Land Allocation which takes consideration of spatial contiguity and a sense of the likely spatial distribution of the transitions to Markov chain analysis. The 2006 land cover classification was used as a basis land cover image for change

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0 0 1 0 00 1 1 1 01 1 1 1 1

0 1 1 1 00 0 1 0 0

simulation. A transition area file derived from the Markov Chain analysis was incorporated into the Markov Cellular Automata computation, which determines the quantity of potential land allocated to each land cover class over a 13 year period. A 5x5 contiguity filter shown in equation (7) was chosen for the cellular automata. The filter down-weights the suitability of pixels that are far from existing areas of each land cover class.

(7)

The role of the contiguity filter is to ensure the ideal choices for land cover transformation are restricted to cells that are both inherently suitable and in close proximity to existing areas of that land cover class; this gives preference to contiguous suitable areas. A total of 13 iterations were used in the simulation. The multi-objective land allocation (MOLA) procedure was used in each time step to resolve the land allocation conflicts. All land use/cover classes act as claimant classes and contend for land within the host class.

Results

Predicted land cover transformations from 2006 to 2019

Transition probabilities and areas tables are shown in Table 1 and Table 2. The transition probabilities indicate a probability of 0.4474 for vegetation to remain in its current state and a probability of 0.5132 for vegetation to transform to degraded vegetation. The conversion of vegetation to degraded vegetation state is accompanied by an area migration of 455.036km2. A lower probability of 0.0195 is associated with direct vegetation migration to bare and degraded soil, accompanied by a transition area of 17.262 km2.

A probability of 0.0488 and a transition area of 74.179 km2 is associated with a further degradation of degraded vegetation into bare and degraded soil. A higher probability of

0.4889 exists that bare and degraded soil will recover to degraded vegetation with area coverage of 35.222km2. Probabilities of 0.2343 and

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0.179 exist for bare and degraded soils and degraded vegetation respectively to recover to fully vegetated areas with transition areas of 16.884 km2 and 271.991 km2 respectively associated with the recovery. The change detection matrix statistics in Table 3 reveal that 23.576% of the vegetation cover will transform to degraded vegetation, whilst a mere 3.217% of degraded vegetation is going to recover to full vegetation cover. A further 8.147% of degraded vegetation will degrade to bare and degraded soil whilst only 3.62% of bare and degrade soil will transform to degraded vegetation.

Table 1 Land use/cover transition probabilities, 2006-2019.

Probability of changing: 2019:

Vegetation

Degraded Vegetation

Bare and Degraded Land

Vegetation 0.4474 0.5132 0.0195

Degraded Vegetation

0.179 0.612 0.0488

Bare and Degraded Land

0.2343 0.4889 0.0283

Table 2 Land use transition area matrix (in km2) 2006-2019.

Expected transition: 2019

Vegetation Degraded Vegetation Bare and Degraded LandVegetation 396.7236 455.0364 17.262

Degraded Vegetation

271.9908 929.6919 74.1789

Bare Degraded Land

16.884 35.2224 2.0421

A net decrease of 17.993% was recorded for vegetation. Significant increases of 78.46% and 52.841% were projected for settlement, bare and degraded land whilst a marginal net growth of 0.0115% for degraded vegetation is predicted. The change detection statistics confirm considerable degradation to bare and degraded soil and conversion of vegetation to settlements. Although a minor net change in degraded vegetation is predicted, examination of the change detection matrix reveals that important land use/cover class interchanges are concealed by viewing the net changes per land use/cover class alone. The changes in degraded

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vegetation are characterized by significant losses to bare and degraded soils which are compensated by gams from intact vegetation; such a scenario indicates an increase in land degradation.