Assessing the spatial optimality of land use and land cover in three European Capitals

Data set and computational and data matching Fortran codes for calculation spatial distribution of land use and land cover (LULC) optimality (LULCO) as a compromise expressing the maximum relative representation of individual LULC types in a spatial unit. This is an application of a novel game-theoretic method to assess the spatial distribution of the probability of Nash equilibrium interpreted as LULCO among LULC types within the functional urban areas of three European Capitals: Prague, Vienna, and Budapest. The calculated spatial distribution of LULCO shows trends consistent with the Shannon index, characterizing heterogeneity. However, the approach used provides additional information on the relative degree of optimality between LULC types and is significantly more sensitive to small LULC types representation changes. The method employed is an autonomous stochastic model grounded in the structure of linear games in normal form. It facilitates the calculation of the distribution of Nash equilibrium probabilities within data represented by spatial cases characterized by multiple attributes. This approach offers a novel perspective in multi-objective optimization methods, applicable to various environmental data in different contexts. Data and code description Default data are raster maps of land use - Prague, Vienna, Budapest (Copernicus Urban Atlas 2012, 2018) in 4m pixel resolution converted to ASCI - see "input_raster_asc_maps". These data are converted into final input files - see "input_hexagonal_cases" using Fortran code "readhex.f90". This code requires a specific coordinate setting for the loaded ASCI map and allows the selection of the size of the hexagons - cases. The input case files (see "input_hexagonal_cases.zip") contain in each line the identifier of the hexagon - case (in the raster map) and the number of pixels found for each evaluated LULC type (for the subsequent Nash Equilibrium - NE probability evaluation, the absolute values for payoff are not relevant and the found pixel counts are directly usable values). Input cases are the input data to the computational code "equs_sp" (as "inp.dat"). The equs_sp.f90 code published here to compute the NE probabilities of each case is a practical version (compilable in GFortran) containing only the most computationally efficient version - generating 3D, 4D and 5D game arrays with two formal strategies for each entity - player and computing the NE in pure strategies. Multiple code versions justifying the concept and its structure are available at github.com/vachm/equsis. A detailed description is formulated in (Vach, 2020), and for limited calculations (up to 32 dedicated cases and a maximum of 5 interacting entities) the website equsis.com is available. The output of "equs_sp" is an outst.dat (see "output_hexagonal_cases.zip") file containing the identifier of the hexagon - case on the map and the received NE probability - LULCO value on each line. The back-conversion of the calculated data ("..out.dat" must be split back into three cities) into an ASCI raster map suitable for display (see "output_asc_maps.zip") is provided by the code "writhex.f90" , which requires specific settings (the same as "readhex.f90").