The Development of a Land Cover Change Model for Southern Senegal

Temporal and spatial Markov models were developed for characterizing land use/land cover change in south-central Senegal, as an early stage in the development of models for lulc change forecasting. The modeling effort is a component of a project carried out by the EROS Data Center and funded by the U.S.Geological Survey and the Senegal mission of the U.S.Agency for International Development. The Markov model results were compared to results obtained using other spatial analysis techniques including join-count statistics and landscape metrics. Though landscape change appears not to be strictly Markovian, pure and modified versions of both the temporal and spatial models appear to have potential for simulation of lulc cover.

This has been particularly apparent in the Sahelian countries. As population pressures, international economies, and mechanized agriculture have become more prominent, Sahelian Africans have been forced into land use practices that are often inappropriate and result in degradation of soils and forests.

Landscape change also has an influence at regional and global scales. Deforestation, desertification, erosion, and many other types of land cover change contribute directly to a loss in biodiversity and very likely global climate change. Reduced resource bases can lead to regional food shortages, political instability, and the humanitarian concerns related to both.

Of particular importance are the types and degree of changes in the landscape, which must be determined before any causal relationship can be postulated. Long term monitoring of key indicators is a prerequisite to such a study, with attention paid to physical, biological, and social phenomena (Wasson, 1987). Once the type and extent of land cover change has been determined, modeling efforts can be initiated that describe it and forecast future change.

The following paper discusses the early stages of the development of such a model. Specifically it addresses the use of Markov processes in characterizing temporal and spatial changes in land use/land cover as part of a long term environmental monitoring project in the West African country of Senegal.

The EROS Data Center (EDC) of the U.S.Geological Survey and the Senegal mission of the U.S.Agency for International Development (USAID) have begun a pilot effort to develop a long term environmental monitoring system. A major goal of the project is to design, test, and institutionalize a framework for monitoring changes in Senegal's natural and agricultural resource base.

As part of that effort, EDC is working with the Government of Senegal's Ministry of the Environment and Protection of Nature to determine the extent of land use/land cover change; the biophysical, social, economic and political factors related to that change; and developing models that both describe existing changes and forecast future changes in land use/land cover. Two key requirements of such models are that they are technically straightforward enough to be applied in interested government agencies and yet accurate enough to be of use in providing realistic simulations for policy makers.

A prerequisite in modeling land use/land cover change is the ability to characterize existing change both temporally and spatially using empirical data. This step is necessary for forecasting future change. In order to develop such a characterization, Markov models were chosen. In the past such models have been used for urban land use/land cover change modeling (Bell, 1974; Bourne, 1976), forest and vegetation succession modeling (Horn, 1975; van Hulst, 1979; Hall, 1991; Usher, 1992), and more recently in modeling landscape change (Baker 1989, Turner 1990, Flam and Turner 1994, Boerner et.al., 1996).

Markov models have substantial scientific appeal. They are mathematically compact, easily developed from observed data and serve as an effective tool for simulation exercises. However, these models are not without their problems, indications of which will be discussed later.

Other studies have attempted to model land use/land cover change in the region. Perhaps the most well known effort in Senegal is by Lake (1979). In this study, Lake projected both forward and backward the extent of agricultural expansion from 1929 to 2004, based on land use/land cover data from 1954 to 1979. More recently a model was developed by Gilruth et.al. (1995) to simulate the dynamics of shifting cultivation in the Guinea Highlands (Futa Djallon). Both studies provide a useful backdrops for present efforts.

The overall study area consists of four departments located in south-central Senegal (Kaffrine, Tambacounda, Kolda and Velingara). There are 30 departments in all of Senegal, these four being of particular interest in that they have abundant natural resources, fall within the zone of viable rainfed agriculture, and as a result are undergoing significant land use/land cover change. The initial investigation was carried out in the department of Velingara (Fig. 1) and is the focus of this paper.

The landscape of Velingara is a mosaic of upland dry Sudanian woodland, riparian or moist gallery forest in the fossil river valleys, and clearings for agriculture, with no major urban centers. Most of the department, 66%, is in the Sudanian woodland , with 26% of the area in agricultural land use. Upland soils are shallow and typically over laterite. On the average the annual precipitation ranges between 800 and 1200 mm. The population of the department was estimated to be 127,068 in the 1988 census, with a density of 28.6 / km², relatively low compared to many parts of Senegal.

The department faces a number of critical land use issues, including the effects of charcoal and fuelwood production, cultivation of cash crops (peanuts and cotton), excessive burning, and agricultural expansion.

The issue most related to absolute change in land use/land cover in Velingara is the tradeoff between the need for keeping the land in woody cover and the need for agricultural land. Agricultural expansion usually occurs at the expense of forested land in this department.

Land use/land cover classifications were derived from Landsat MSS images from 1973, 1978, and 1990. The resulting 15 classes were aggregated into 5 major classes (Fig. 2). The resulting vector coverage was gridded at 80 meters to echo MSS resolution. It should be noted, however, that parallel studies were carried out to determine the effects of different resolutions on the Markov and landscape metrics .

Using post-classification differencing, a number of change datasets were developed. The change data was then analyzed using two modified Fortran programs, the temporal program from Harbaugh and Bonham-Carter (1970), with the spatial version coming from Lin and Harbaugh (1984).

Markov Chain Models

The underlying tenet of a 1st order Markov process is based on the probability that the system will be in a given state (land class) at some time t₂ is deduced from the knowledge of its state at time t₁. Therefore, the probability does not depend on the history of the system before time t₁. When a Markov process moves from one time step to the next, the transition from one state to the next only depends on that given state and not on how the process has arrived in that state. In other words, history plays no role in the future. (Parzen, 1962)

For the scope of this work, the Markov process will be considered to have discrete states in the form of five classes of land cover and transitions occurring at discrete times. Also, a transition from one state to another can be thought of in either time or space in which space assumes the role of a discrete event or an individual pixel.

A Markov process is formally described by the transition probability function P(t|x,t₀) which represents the conditional probability that the state of the system will be at time t, given that at time t₀ (< t) the system is in state x. So the transition probability matrix describes the specific character of the system where the elements of the matrix are the individual transition probabilities of one state moving to another state after one time or space increment. The transition matrix is as follows:

A transition probability (p_ij) is then the probability that the class x will be in state j at time t+1 given it was in state i at time t.

P_ij^t+1 = Pr [ x_t+1 = j | x_t = i ]

The transition matrix is a powerful analytical tool in itself. It provides a method of probabilistically describing a succession of events in space or time. (Harbaugh and Bonham-Carter, 1970)

Calculation of Transition Probabilities

Transition probabilities are calculated based on the frequency distribution of the observations. Given the assigned land cover classes, a frequency table is developed where a count is made of the transition from one state to another over the specified increment. For example, a count is made of the number of times that forest land cover changes to agriculture for the whole scene from one time period to the next or in space from one grid square to the next. This procedure is continued for all classes and increments that have been collected. When completed the frequency table in each row is summed and the values in each matrix element or transition state are divided by the row sums to compute the transition probability values (Table 1). In each row, the probability values should sum to 1.0. The diagonal of the transition probability represent the self-replacement probabilities where as the off diagonal values indicate the probability of change occurring from one state to another state or class. When each of the row totals are divided by the total number of transitions the marginal probability for each row or class is obtained. The individual marginal probabilities indicate the relative proportion of each state/class at the starting point. Also if the all the rows are identical to the marginal probabilities, the process is independent and therefore non-Markov.

Markov Model Assumptions

There are a number of assumptions that must be met if a Markov modeling approach is meaningful. Listed below are three assumptions that should be addressed, two of which are critical from a mathematical standpoint whereas the third one needs to be tested for but does not compromise the approach.

1) independence/randomness

2) stationarity/homogeneity

3) order of the Markov process (Collins, 1975)

The inherent proposition of a Markov process is that there is some memory from one increment to the next but only from that last state. Where no memory exists, the process is independent and not Markovian. A statistical test of independence can be applied to test the null hypothesis. If the null hypothesis is accepted then the process is independent. If it is rejected then the process may form a first order Markov process. The test statistic is a log likelihood ratio criterion. The test statistic is:

p_ij = transition probabilities n_ij = transition frequencies

p_j = marginal probabilities of the j^th column m = number of states

where -2 ln [lambda] is distributed as [chi]² with where (m-1)² degrees of freedom. (Harbaugh and Bonham-Carter, 1970) This procedure with minor modifications can be used to test assumptions two and three.

Temporal Markov

The three matrices in Table 1 represent the transition probability values. The null hypothesis for independence was rejected, indicating that the process is Markovian. The probabilities at different steps do not, however, exhibit stationarity and the log likelihood ratio test for stationarity supports this conclusion through the acceptance of the null hypothesis. Intuitively, one can see this from looking at the transitions probabilities in both the 73-78 matrix and the 78-90 matrix, which have not remained constant. For example, the probabilities of agriculture in 1973 remaining in agriculture or transitioning into upland woodland in 1978 are 95% and 5% respectively. The same transitions for 1978 to 1990 are 74% and 24% respectively. Probabilities in the 1973-90 matrix resemble those of the 78-90 matrix.

These results suggest that some influence was present after 1978 that altered the land use/land cover change transition probabilities, though what that is has not been determined. It is possible that it is not entirely a land use phenomenon and that the unequal length of the time steps influences the results. A 1985 image is being acquired and classified to add an additional step and to standardize the step length.

The marginal probabilities help indicate the percentage of the landscape in each class at the beginning of the transition period , i.e. in 1973 nearly 15% of the landscape was in agriculture, 76% in upland woodland, and 6% in riparian/moist gallery forest. In 1990, those percentages had c
hanged to 19%, 72%, and 6% respectively.

Some practical results are the actual land use/land cover changes for the key classes of agriculture, upland woodland, and gallery / riparian forest. It is interesting to note that while 18% of upland woodland was converted to agriculture between 1973 and 1990, with 73% remaining the same, 25% of the land in agriculture was returned to woodland or scrub during the same period with 81% remaining the same.

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A = agriculture    B = upland woodland    C = riparian/moist gallery forest
D = shrub savanna      E = towns    

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Table 1. Transition probability matrices .

Spatial Markov

One of the shortcomings of the temporal Markov approach is its inability to account for the spatial context of a grid cell or patch in characterizing transition. Therefore, a spatial Markov approach was developed to determine if it better characterized change in the system. The frequency of class to class transitions between the grid cells were tallied for each pair of adjacent cells using the rook sampling pattern (4 neighbor).

The results show strong spatial autocorrelation as indicated by the extremely high frequencies and probabilities in the diagonals as opposed to the off-diagonals (Table 2). By looking at the off-diagonals in the matrices, one can determine the predominate adjacencies for each class. For example, there is notable adjacency between agriculture and upland woodland, but little between agriculture and the riparian/gallery forest which are in the fossil river valleys, though this conclusion is based on a very limited sample for the latter.

These results, however, are obviously influenced by grain size. The effects of different grain sizes on the spatial Markov transitions were calculated in order to better understand their influence. Resoultions ranging beginning with 40 m. and increasing in powers of 2 through 640 m., with an additional test at 1080 m. were used to determine differences in the results of the transition probabilities. There was no appreciable difference through 640m. At 1080m , the transition to "same state" increased, but only by a few hundredths percent with comparable decrease in the off diagonals.

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A = agriculture    B = upland woodland    C = riparian/moist gallery forest
D = shrub savanna      E = towns    

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Table 2. Spatial Markov transition probabilities.

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1 = agriculture         2 = upland woodland          3 = riparian / moist gallery forest

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Table 3. Join-count statistics.

Join-Count Statistics

As a way of comparing the results of the Markov models, the data were processed using other spatial analysis techniques. One such technique, join-count statistics, measures the number and type of joins between adjacent polygons on a map. The frequency of the joins yields information about clustering and spatial autocorrelation (Goodchild, 1986; Bonham Carter, 1994). In order to further investigate the spatial influence of these transitions and to eliminate the problems of grain, join-count statistics were derived for a vector coverage of the land use/land cover (Table 3). Results were generated for the 5 aggregated classes.

Table 3 shows the transitions between classes, with their respective number of patches and probabilities. Expected joins are the number expected if the distribution of patches was random. If the number of observed joins differ significantly from expected, we have what amounts to a proximity index. For example the agriculture - upland woodland transitions are significant as indicated by the corresponding Z scores. A strong proximity or spatial adjacency exists between agriculture and upland woodland. The join-counts indicate there is no significant relationship between agriculture and riparian/gallery forest. These results generally reflect those obtained using the spatial Markov approach.

Landscape metrics

Landscape metrics have been used by landscape ecologists to quantify attributes of spatial patterns (Flam and Turner, 1984; Wickham and Ritters, 1995). The landscape metrics for this study were derived using the program Fragstats (McGarigal and Marks, 1995).

Though  just a preliminary examination, a few of the landscape metrics were of particular interest. The most notable outcome was our ability to quantify increased fragmentation as shown by the positive trend in the level of the number of patches and edge density (ratio of edge to area) and the decrease in the mean patch size in both the landscape and individual class metrics (Table 4). There is utility in using these metrics for comparing different landscapes predicted by the modeling process. Additional work is required to determine the relationship between these metrics and the results form the Markov models. The effect of gridding resolution is also unclear, though Wickham and Ritters (1995) suggest there is little effect on the metrics in changing resolutions up to 80 meters.

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     A = agriculture                    B = upland woodland                   C = riparian / moist gallery forest

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Table 4. Landscape metrics

This transition of land use/land cover to and from agricultural use is of particular interest (Fig. 3). Based on data collected from a rapid rural appraisal and other interviews conducted in the department by project staff, certain land use trends began to surface. The farmers in Velingara are still maintaining a traditional fallow period up to six or more years in some instances. Part of the shift in and out of agriculture might be explained by this practice. The addition of a 1985 image should help to confirm this assertion. There is some indication, however, that because forest area is still abundant, it is being cleared rather than returning to fallowed land because of the relatively higher fertility (Freudenberger 1996). There is also indication that some clearing is occurring in forest areas to maintain the appearance of "les mettre en valeur" or "productive use", a key requirement of the Land Law to demonstrate one's right to claim user privileges on that land. These are tenure issues that are key to policy makers and managers in the region.

As mentioned, Markov models are mathematically compact, easy to implement with empirical data, and lend themselves well to simulation. But , as to be expected, they have their weaknesses. They operate under fairly restrictive assumptions such as stationarity and the temporal process does not account for spatial context. Results indicate that there has been notable change in the study area and that the frequency of this change has not remained constant, suggesting that landscape change is not strictly Markovian (Turner 1988) . The temporal Markov models capture that aspect of the change well, but changes to the spatial Markov model are necessary to make it as effective.

Both appear to have potential for the simulation of land use/and cover change. The bounds of the temporal and spatial Markov results can be used to define simulations. Ideally we will be able to capture the essence of the change through modeling based on the Markov properties of the landscape. The actual implementation, however, may require modification of the transition probability matrices. Defining this modification is the focus of future research.

In order to address the problems with meeting the assumptions of the first order Markov process, we are investigating Markov variations such as the semi-Markov model (Rogerson 1978, Acevedo 1995) which relaxes the stationarity assumption, or multiple order Markov models which carry memory of the system beyond one step. Another variation is to start with these initial matrices and modify them to increase their utility using a suite of techniques.

We are beginning to address the issue of spatial influence and neighborhood effects . This will include investigation of spatial weighting and is role in developing the spatial transition probability matrix. An attempt is being made to couple the temporal with the spatial models.

In an effort to assess the benefit of integrating socioeconomic and other categorical ancillary data, we are applying logistic regression techniques. Results from this approach will be compared to those from the simple Markov and modified Markov models. They will also be considered as input in the modification of the matrices and as input for a knowledge based approach.

Finally, we feel it is key to integrate both expert knowledge and the influence of socioeconomic factors such as policy reform, etc. not easily captured in the previously described modeling approaches.,e.g. using Markov and regression techniques. Therefore, we hope to develop a knowledge based or expert system that will better accomodate these data.

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