^{1}

^{2}

In order to make a rational prediction of the Dead Sea shape, data were prepared for suitability map creation using Markov Chain analysis and Multi Criteria Evaluation (MCE). Then, Markov Cellular Automata model and spatial statistics were used in prediction and validation processes. The validation process shows a standard Kappa index of 0.9545 which means a strong relation between the model and reality. The predicted shapes of years 2020, 2030 and 2040 follow the same conditions from 1984 to 2010. The predicted areas of 2020, 2030 and 2040 were 610, 591 and 574 km2 which were considered a logical extension of the trend from 1984 till 2010. This study can be used as an environmental alert in order to keep the Dead Sea alive. Moreover, Markov-Cellular Automata model can be used to predict closed seas as the Dead Sea from remote sensed data.

Reference [

All landscape spatial transition models can be expressed in a simple matrix as in Equation (1) [

where LU_{t} is the distribution of land uses among the different types at the beginning of the period and LU_{t}_{+1} is showing the distribution of land use types at the end of the projection period [_{t} and LU_{t}_{+1} are vectors composed of the fractions of each landscape type at time t and time t + 1, respectively. Reference [_{ij} is the transition probability from landscape i to j during times t and t + 1, while [_{ij}, as the probability of moving from one state i to another state which could be represented in the form of a transition matrix, P. Equation (2) illustrates the P matrix. A transition areas matrix expresses the total area (in cells) expected to be changed in the next time period. A set of conditional probability images expresses the probability that each pixel will belong to the designated class in the next time period. They are called conditional probability maps since this probability is conditional on their current state [

The transition probabilities P in K steps are derived from the landscape transitions occurring during some time interval as shown in Equations (3) and (4) [

where N(i, j) is the observed data during the transition from state i to j, and n_{ij} is the number of years between time step i and step j, and the total number of years is m; P(i, j) is the yearly transition probability after normalizing the transition probability in multiyear and K is the number of steps [

One of the disadvantages of Markov chain is that it has a very limited spatial knowledge. To improve the spatial sense of these conditional probability images, using Cellular Automata model will be a good choice. Cellular Automata (CA) is a grid of cells with each cell updating its value based on its neighboring cell values [

where:

A number of previous studies regarding CA-Markov are shown in [

The Dead Sea is located on 31˚30'0"N, 35˚30'0"E, WGS84 coordinate system, bordering Jordan to the east, historical Palestine and the West Bank to the west as illustrated in

a sill elevation of about 400 m below the sea level [

This study aims to investigate and predict the shape of the northern part of the Dead Sea using CA-Markov analysis and Multi Criteria Evaluation. For this purpose, the classified data of three Landsat time series satellite images (1984, 2000 and 2010) are to be used. The Dead Sea shape at later dates of 2020, 2030 and 2040 will be created, but first 2010 map will be predicted and compared with the real 2010 classified imagery using the standard Kappa Index and other spatio-statistical parameters.

The methodology followed in this study consists of seven major stages;

1) Data collection: Landsat Imagery download and ASTGTM-DEM of the Dead Sea area.

2) Pre-processing: aims to normalize all imageries by converting Digital Number (DN) to spectral radiance.

Then, atmospheric effects are removed. Moreover, the resulted images are converted to reflectance. Finally, black gaps are removed; if exist.

3) Supervised Classification.

4) Change detection analysis: changes of the Dead Sea area and shape

5) Data preparation for prediction: This stage consists of three tasks:

a) Markov chain analysis.

b) Data generation for Multi Criteria Evaluation (MCE).

c) Suitability map creation.

6) Prediction and validation processes.

7) Results and discussion.

In order to achieve the mentioned methodology, the following software and supporting tools are used. ERDAS Imagine 10 is used for image pre-processing and normalization, supervised classification and bathymetric map creation. Arc-GIS 9.3 is used for spatio-temporal analysis, building models for area, change analysis and Multi Criteria Evaluation, calculating spatial parameters and cartographical representation. IDRISI Selva is used for Markov Cellular Automata prediction analysis and validation process. Stages from 1) to 4) are deeply discussed in [

In terms of future prediction, Markov-Cellular Automata (CA-Markov) model will be used. CA-Markov is a combined Cellular Automata, Markov Chain and Multi-Criteria Evaluation (MCE) land cover prediction procedure that adds an element of spatial contiguity as well as knowledge of the likely spatial distribution of transitions to Markov chain analysis. So, three main processes are required; Markov model, Cellular Automata model and validation and prediction.

Markov analysis needs two imageries as inputs to create a) a transition probability matrix, b) a transition

area matrix c) a set of conditional probability images. In data generation for MCE, two maps are created; bathymetric map which generated from TM imagery and slope map which generated from ASTGTM-DEM.

As discussed above bathymetric map is one of the essential criteria map for prediction. The measurement of bathymetry can be expected to be the best with Landsat TM data because that sensor detects visible light from a wider portion of the visible spectrum, in more bands, than other satellite sensors. In order to create a bathymetric zones map represents a very crude bathymetric map, the following steps have to be accomplished one by one: First, finding out the average DN values of deep water pixels for blue, green, red and infrared bands of the 2010 Landsat TM image [

The values 0, 63, 127, 191 and 255 are assigned to each zone in order to make it visually recognizable before cartographical presentation.

where

S: The suitability map.

W_{i}: Weight for a criteria i.

C_{i}: Criteria for suitability.

r_{i}: Restriction.

By applying weights to each rated factor, the suitability map of the Dead Sea Area was developed using three maps; the bathymetric map, the probability of classes map derived from Markov process and the slope map derived from ASTGTM-DEM. More than one trial is made to get the best results in validation.

Suitability map for water class | |||
---|---|---|---|

i = 1 | i = 2 | i = 3 | |

C_{i}: Criteria for suitability | Bathymetric zones map rated from 0.1 to 1 as very shallow to very deep water respectively. | The water class probability map of Dead Sea derived from Markov process. | Slope map derived from ASTGTM-DEM map rated from 0.1 to 1 as the highest slope to the lowest slope respectively. |

W_{i}: Weight for a criteria i | 34% | 33% | 33% |

r_{i}: Restriction | Area boundaries | ||

Suitability map for land class | |||

i = 1 | i = 2 | i = 3 | |

C_{i}: Criteria for suitability | Bathymetric zones map rated from 0.1 to 1 as deep to very shallow water respectively. | The land class probability map of Dead Sea derived from Markov process. | Slope map derived from ASTGTM-DEM map rated from 0.1 to 1 as the lowest slope to the highest slope respectively. |

W_{i}: Weight for a criteria i | 34% | 33% | 33% |

r_{i}: Restriction | Very deep water | Area boundaries |

see

Using the output data produced by the Markov chain analysis, the predicting model will apply a contiguity filter to grow out from imagery captured in the year of 2000 to a future time. This CA filter develops a spatially explicit contiguity-weighting factor to change the state of a cell based on its neighbors. Dead Sea shape at later

dates of 2020, 2030 and 2040 will be created, but first 2010 map will be predicted and compared with the real 2010 classified imagery using the standard Kappa Index and other spatio-statistical parameters. There are three outputs of Markov chain analysis for each predicted year. The following three outputs are resulted from using the classified imageries 1984 and 2000 as inputs in the process of predicting the 2010 map using CA-Markov analysis.

a) A transition areas matrix (1984-2000-2010):

The transition areas matrix (1984-2000-2010) expresses the total area (in cells) expected to change from the year of 2000 to the year of 2010 according to those changes happened from 1984 to 2000. Based on matrix above, there are 416 land classified cells (30 m/cell) will turn into water class, meanwhile there are 32316 water classified cells will turn into land class.

b) Transition probability matrix (1984-2000-2010):

The transition probability matrix (1984-2000-2010) expresses the likelihood that a pixel of a given class that will change to any other class (or stay the same) in the next time period. This could be derived from transition areas matrix by knowing the total cells of each class.

c) A set of conditional probability images/each class (1984-2000-2010)

These maps (

body for suitability but in order multiply overlaid layers by 1. Land restriction map is shown in

By using the output data produced by the Markov chain analysis and MCE analysis, the predicting model applied for the year of 2010. The expected 2010 map is shown in

Using VALADATE tool, IDRISI gave the standard Kappa of 0.9545, Kappa for no information of 0.9564, Kappa for grid-cell level location of 0.9981 and Kappa for stratum-level location of 0.9981 Which are all more than 0.7. More-over IDRISI offers quantity disagreement of about 0.0209, which is convenient with the outputs of the transition matrix. Transitional matrix shows that the water-body will decrease by 28.63 km^{2} from 2000 to 2010 to equal 613 km^{2}. However; the real 2010 map tells another story since the decrease from 2000 to 2010 was just 10.77 km^{2} to equal 631.27 km^{2}.

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The percentage between both areas is 2.8% which so close to quantity disagreement since the difference could be due to some pixels generated in arbitrary locations (not inside the water-body) when using these stochastic algorithms. Strata disagreement = 0 which is logical because the number of output classes is the same as the number of input classes. The allocation disagreement = 0.0009 which is so close to zero. Since overall disagreement is 0.0218, the overall agreement is 0.9782. The overall agreement consists of agreement due to chance, agreement due to quantity and agreement due to grid cell level location. The agreement due to chance is the agreement that a scientist could achieve with no information of location and no information of quantity. Therefore, it could be a good baseline upon which to compare the actual agreement. The agreement due to chance equals 0.5. While the agreement due to grid cell level location which is the additional agreement when the comparison map is somewhat accurate in terms of its specification of the grid cell-level location of each category within each stratum. The agreement due to grid cell level location equals 0.4575. The agreement is due to quantity which is the additional agreement when the comparison map is somewhat accurate in terms of its specification of quantity of each category. The agreement due to quantity equals 0.0207. There is no additional agreement when the comparison map is somewhat accurate in terms of its specification of quantity of each category within each stratum.

Another factor commonly used in the literatures which measures of agreement between maps called M(m). It describes the agreement between the reference map and the unmodified comparison map. It is the proportion of grid cells classified correctly. It confounds agreement due to quantity and agreement due to location. IDRISI gives M(m) = 0.9782 which is considered a good matching.

Based on these results, the suitability maps and model are valid and will be used to predict 2020, 2030 and 2040 maps as shown in ^{2} which are considered a logical extension of the trend from 1984 till 2010. The direction of this shrinkage is from the north, northwest and from the south direction of the northern part due to slopes of bathymetry. No shrinkage is considered from the east direction due to the same reason since the bathymetric slope is so sharp.

Markov-Cellular Automata is used in prediction process. The predicted shapes of 2020, 2030 and 2040 follow

the same conditions from 1984 to 2010. The areas of predicted 2020, 2030 and 2040 are 610, 591 and 574 km^{2} which are considered a logical extension of the trend from 1984 till 2010. So, Markov-Cellular Automata model can be used to predict closed seas as the Dead Sea. It is so recommended to use the result of this study in order to find strategies and solutions to keep the Dead Sea “alive”. The result of this spatial simulation model can be used as an environmental alert focusing on the Dead Sea case. It is so recommended to include hydrological parameters in prediction process and to use other surface water models to include Jordan valley in consideration that will give results more reliability.