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--- tutorial:building_a_land-use_and_land-cover_change_simulation_model [2017/01/27 17:06]
francisco [Second step: Calculating ranges to categorize gray-tone variables]
+++ tutorial:building_a_land-use_and_land-cover_change_simulation_model [2017/10/17 03:23] (current)
admin
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 ==== Second step: Calculating ranges to categorize gray-tone variables ====
-The Weights of Evidence method [[http://dx.doi.org/10.1016/0040-1951(93)90011-8|(Goodacre et al. 1993]]
+The Weights of Evidence method [[http://dx.doi.org/10.1016/0040-1951(93)90011-8|(Goodacre et al. 1993]][[https://books.google.com/books?printsec=frontcover&vid=ISBN0080424201&vid=ISBN0080418678&vid=LCCN94028315#v=onepage&q&f=false|, Bonham-Carter 1994)]] is applied in Dinamica EGO to produce a transition probability map (fig. 3), which depicts the most favourable areas for a change [[http://dx.doi.org/10.1016/S0304-3800(02)00059-5|(Soares-Filho et al. 2002]][[http://dx.doi.org/ 10.1111/j.1529-8817.2003.00769.x|, 2004)]].
-[[http://www.rc.unesp.br/igce/geologia/GAA01048/papers/Bonham-Carter_Cap9.pdf|; Bonham-Carter, 1994)]] is applied in Dinamica EGO to produce a transition probability map (fig. 3), which depicts the most favourable areas for a change [[http://dx.doi.org/10.1016/S0304-3800(02)00059-5|(Soares-Filho et al. 2002]][[http://dx.doi.org/ 10.1111/j.1529-8817.2003.00769.x|, 2004)]].
 Weights of Evidence consists of a Bayesian method, in which the effect of a spatial variable on a transition is calculated independently of a combined solution. The Weights of Evidence represent each variable’s influence on the spatial probability of a transition i-j and are calculated as follows.
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-Since Weights of Evidence only applies to categorical data, it is necessary to categorize continuous gray-tone maps (quantitative data, such as distance maps, altitude, and slope). A key issue to any categorization process concerns the preservation of the data structure. The present method adapted from Agterberg & BonhamCarter (1990), calculates ranges according to the data structure by first establishing a minimum delta – specified as the increment in the graphical interface – (//Dx//) for a continuous gray-tone variable x that is used to build n incremental buffers (//Nx//) comprising intervals from //X<wrap lo>minimum</wrap>// to //X<wrap lo>minimum</wrap>// + //nDx//.Each //n// defines a threshold that divides the map into two classes: //(Nx)// and //(Nx2)//. //An// is the number of cells for a buffer (//Nx//) multiple of //n// and //dn// is the number of occurrences for the modeled event (//D//) within this buffer. The quantities An and dn are obtained for an ordered sequence of buffers //N(xminimum + nDx)//. Subsequently, values of //W+// for each buffer are calculated using equations 2 to 4. A sequence of quantities //An// is plotted against //An*exp(W+)//. Thereafter breaking points for this graph are determined by applying a line-generalizing algorithm (Intergraph, 1991) that contains three parameters: 1) minimum distance interval along //x, mindx//, 2) maximum distance interval along //x, maxdx//, and 3) tolerance angle //ft//. For //dx// (a distance between two points along x) between //mindx// and  //maxdx//, a new breaking point is placed whenever //dx >= maxdx// (an angle between //v// and //v’//- vectors linking the current to the last point and the last point to its antecedent, respectively) exceeds the tolerance angle //ft//. Thus, the number of ranges decreases as a function of ft. The ranges are finally defined by linking the breaking points with straight lines. Note that //An// is practically error-free whereas //dn// is subject to a considerable amount of uncertainty because it is regarded as the realization of a random variable. Since small //An// can generate noisy values for //W+//, [[http://dx.doi.org/10.1016/0040-1951(93)90011-8|Goodacre et al. (1993)]] suggest that, instead of calculating it employing equations 2 and 4, one should estimate //W+// for each defined range through the following expression:
+Since Weights of Evidence only applies to categorical data, it is necessary to categorize continuous gray-tone maps (quantitative data, such as distance maps, altitude, and slope). A key issue to any categorization process concerns the preservation of the data structure. The present method adapted from Agterberg & Bonham-Carter (1990), calculates ranges according to the data structure by first establishing a minimum delta – specified as the increment in the graphical interface – (//Dx//) for a continuous gray-tone variable x that is used to build n incremental buffers (//Nx//) comprising intervals from //X<wrap lo>minimum</wrap>// to //X<wrap lo>minimum</wrap>// + //nDx//.Each //n// defines a threshold that divides the map into two classes: //(Nx)// and //(Nx2)//. //An// is the number of cells for a buffer (//Nx//) multiple of //n// and //dn// is the number of occurrences for the modeled event (//D//) within this buffer. The quantities An and dn are obtained for an ordered sequence of buffers //N(xminimum + nDx)//. Subsequently, values of //W+// for each buffer are calculated using equations 2 to 4. A sequence of quantities //An// is plotted against //An*exp(W+)//. Thereafter breaking points for this graph are determined by applying a line-generalizing algorithm (Intergraph, 1991) that contains three parameters: 1) minimum distance interval along //x, mindx//, 2) maximum distance interval along //x, maxdx//, and 3) tolerance angle //ft//. For //dx// (a distance between two points along x) between //mindx// and  //maxdx//, a new breaking point is placed whenever //dx >= maxdx// (an angle between //v// and //v’//- vectors linking the current to the last point and the last point to its antecedent, respectively) exceeds the tolerance angle //ft//. Thus, the number of ranges decreases as a function of ft. The ranges are finally defined by linking the breaking points with straight lines. Note that //An// is practically error-free whereas //dn// is subject to a considerable amount of uncertainty because it is regarded as the realization of a random variable. Since small //An// can generate noisy values for //W+//, [[http://dx.doi.org/10.1016/0040-1951(93)90011-8|Goodacre et al. (1993)]] suggest that, instead of calculating it employing equations 2 and 4, one should estimate //W+// for each defined range through the following expression:
 {{:tutorial:lucc_11.jpg?200|}}  (5)
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 ==== Fourth step: Analyzing map correlation ====
-The only assumption for the Weights of Evidence method is that the input maps have to be spatially independent. A set of measures can be applied to assess this assumption, such as the Cramer test and the Joint-Uncertainty Information [[http://www.rc.unesp.br/igce/geologia/GAA01048/papers/Bonham-Carter_Cap9.pdf|( Bonham-Carter, 1994)]]. As a result, correlated variables must be disregarded or combined into a third that will replace the correlated pair in the model.
+The only assumption for the Weights of Evidence method is that the input maps have to be spatially independent. A set of measures can be applied to assess this assumption, such as the Cramer test and the Joint-Uncertainty Information [[https://books.google.com/books?printsec=frontcover&vid=ISBN0080424201&vid=ISBN0080418678&vid=LCCN94028315#v=onepage&q&f=false|(Bonham-Carter, 1994)]]. As a result, correlated variables must be disregarded or combined into a third that will replace the correlated pair in the model.
 Open model ''weights_of_evidence_correlation.egoml'' in ''setup_run_and_validate_a_lucc_ model\4_weights_of_evidence_correlation''.
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-This model performs pairwise tests for categorical maps in order to test the independence assumption. Methods employed are the Chi^2, Crammers, the Contingency, the Entropy and the Uncertainty Joint Information [[http://www.rc.unesp.br/igce/geologia/GAA01048/papers/Bonham-Carter_Cap9.pdf|( Bonham-Carter, 1994)]]. In addition to the links to be connected, the only parameter to be set in the Determine Weights of Evidence Correlation is the transition as follows:
+This model performs pairwise tests for categorical maps in order to test the independence assumption. Methods employed are the Chi^2, Cramer, the Contingency, the Entropy and the Uncertainty Joint Information [[https://books.google.com/books?printsec=frontcover&vid=ISBN0080424201&vid=ISBN0080418678&vid=LCCN94028315#v=onepage&q&f=false|(Bonham-Carter, 1994)]]. In addition to the links to be connected, the only parameter to be set in the Determine Weights of Evidence Correlation is the transition as follows:
 {{ :tutorial:lucc_26.2.jpg |}}\\
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 ==== Fifth step: Setting up and running a LUCC simulation model ====
-Let’s start setting up the deforestation simulation model by loading the input data. You will need //[[:Load Categorical Map]]// to load the initial landscape: ''original/23267_1997.ers'', //[[:Load Map]]// for ''originals/23267statics.ers'', //[[:Load Weights]]// for ''new_weights.dcf'', and //[[:Load Lookup Table]]// for the multi-step transition matrix: ''originals/multiple_steps.csv'' because you will run the model in annual time-steps. Add the following comments to each functor:
+Let’s start setting up the deforestation simulation model by loading the input data. You will need //[[:Load Categorical Map]]// to load the initial landscape: ''originals/23267_1997.ers'', //[[:Load Map]]// for ''originals/23267statics.ers'', //[[:Load Weights]]// for ''new_weights.dcf'', and //[[:Load Lookup Table]]// for the multi-step transition matrix: ''originals/multiple_steps.csv'' because you will run the model in annual time-steps. Add the following comments to each functor:
 {{ :tutorial:lucc_28.jpg |}}