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Agricultural Feasibility Analysis in China: A GIS-based Spatial Fuzzy Multi-Criteria Decision Making Approach Presenter: Fei Carnes Date: July 17, 2013 Email: fmeng@cga.harvard.edu Glossary 1. Raster A raster consists of a matrix of cells (or pixels) organized into rows and columns (or a grid) where each cell contains a value representing information, such as temperature. Rasters are digital aerial photographs, imagery from satellites, digital pictures, or even scanned maps. cell • The entire area is divided into a uniform matrix of cells which are organized into a regular grid. • All space is represented by cells, even where there is nothing of interest • Rows and columns are used to designate their location. • All cells must have a value. The number inside a cell represents some value for that cell location. The cell value may be an ID for a feature or it may be an attribute value. • There is only one value for each cell. • Cells are independent data units. The computer does not know if they are connected or not, but knows their relative position. • Each cell has its size and area. 2. Raster vs. Vector • Raster allows to illustrate gradual changes and variation in attributes from one place to another. • Raster has a simple data structure—A matrix of cells with values representing a coordinate and sometimes linked to an attribute table. • Raster is better in advanced spatial and statistical analysis. • Raster allows to perform fast overlays with complex datasets 3. Spatial Modeling (Raster modeling) • Suitablity Analysis • Hydrologic Modeling • Distance Modeling ... ... 3. Spatial Modeling • Suitablity Analysis ( feasiblity \ vulnerability \ sensitivity analysis) Calculate optimal site locations by identifying possible influential factors. The optimal suitability map may provide new insight into the ideal areas where a new site should be located. To solve ... Where are the optimum locations for a new school, landfill? • Hydrologic Modeling • Distance Modeling ... ... 3. Spatial Modeling • Suitablity Analysis • Hydrologic Modeling Provide methods for describing the hydrologic characteristics of a surface. Using an elevation raster data set as input, it is possible to model where water will flow, create watersheds and stream networks, and derive other hydrologic characteristics. To solve ... Where will the water flow to? • Distance Modeling ... ... 3. Spatial Modeling • Suitablity Analysis • Hydrologic Modeling • Distance Modeling Determine the least expensive method for a new road, flight pattern, shipping route, or any factor that is affected by time and cost. To solve ... ... ... Where will be the areas which has the nearest distance from a emergency helicopter? 4. Fuzzy A method to standardized factors based on a series of specific mathematical functions. It reclassifies or transforms the input data to standardized scale ([0,1], [0,10] ,[0, 255], etc.). How to standarize? • Different approaches are used with continuous (quantitative) and categorical (qualitative) data • Different functions available (linear, sigmoidal, J-shaped, user-defined) 5. Multi-Criteria Decision Making (MCDM) • It considers multiple criteria in decision making environment. • It provides a framework to represent the decision groups into a single model. GIS-based MCDM integrates the MCDM approach and GIS techniques to solve spatial issues. It has been received considerable attentions among planners since 1990s. This method has been shown in studies related to site determination for a nuclear waste facility, forest conservation. Objective 1. The main aim of this project is to solve data confidentiality issue. 2. Develop multi-criteria decision making technique using fuzzy approach for agricultural feasibility analysis. 3. Help people understand raster GIS analysis (spatial modeling). Data & Software Data： Weather Annual Precipitation Accumulated Temperature >10 °C Source: Yu Deng, China Academy of Science Sunshine Hours Hydrology Water Resources Topography Elevation Soil Soil PH Soil Depth Soil Drainage Software: Source: CGA IDRISI is a GIS and image processing software, developed by Clark Labs, Clark University. In 1993, IDRISI introduced the first instance of MultiCriteria and Multi-Objective decision making tools in GIS. Eighteen years later, IDRISI is still the industry leader, responsible for: • The first implementation of the Ordered-Weighted Average for multi-criteria evaluation that allows one to balance the relative amount of tradeoff between criteria with decision risk in balancing discordant information. • The first implementation of the MOLA heuristic for multiobjective land allocation. • The first GIS software implementation of Saatys Analytical Hierarchy Process (AHP). ArcGIS is a platform for designing and managing solutions through the application of geographic knowledge. Methodology 1. Data Determination and Processing 2. Criteria Standardization (Fuzzy) 3. Weight Determination 4. Weighted Linear Combination (weighted overlay) Methodology 1. Data Processing 1) Denoise and reclassify imageries 2) Data transformation. e.g. river (shapefile) distance to river (raster); elevation slope(degree) 3) Make sure all the data have the similar extents , and the same coordinate system. …… Annual Precipitation Accumulated Temperature >10 °C Elevation Sunshine Hour Slope Soil PH Distance to River Soil Depth Soil Drainage Methodology 2. Fuzzy Fuzzy evaluates the possibility that each pixel belongs to a fuzzy set by evaluating any of a series of fuzzy set membership functions. --- Idrisi Selva Help Document “0” is assigned to those locations that are definitely not a member of the specified set, “1” is assigned to those values that are definitely a member of the specified set. All the in-between values receive some membership values based on the function. Fuzzy membership function Annual Precipitation （ml） Fuzzy Annual Precipitation [0,1] Methodology 2.1 Fuzzy (for continues\ quantitative data) In Idrisi: “ FUZZY” module provides 4 fuzzy membership function types * Sigmoidal * J-Shaped * Linear * User-defined (“ S-Shape”) Monotonically increasing Monotonically decreasing Symmetric . Control points Control Points: a = membership rises above 0; b = membership becomes 1; c = membership falls below 1; d = membership becomes 0 Methodology 2.1 Fuzzy (continues data) Annual Precipitation 0 1500ml Sigmoidal increasing Fuzzy Precipitation Accumulated Temperature>10°C -117 3200 4800 9600 Sigmoidal Symmetric Fuzzy Temperature Elevation 0 2700 m Linear Fuzzy Elevation Slope 0 7 Distance to River 0 max Sigmoidal decreasing Linear Fuzzy Slope Fuzzy Distance to River Sunshine Hour 0 max Linear Fuzzy Sunshine hour Methodology 2.2 Fuzzy (for categorical \ qualitiative data) Reclassify and assign new values to each category. For example, land use types. 1 0.8 0.6 0.2 0 Deciduous forest Coniferous forest Cropland Methodology 2. 2 Fuzzy (categorical data) New Values Old Values [5.8, 6.9) Soil Drainage Soil Depth Soil PH 1 New Values Old Values Very deep (150-300cm) 1 Deep (100-150cm) 0.8 [4.5, 5.5) or [7.2,8.5) 0.6 Moderately deep (50-100cm) 0.6 <4.5 or >8.5 0.2 Shallow (10-50cm) 0.4 Very shallow (<10cm) 0.1 Other 0 Fuzzy Soil PH Fuzzy Soil Depth Well 1 0.9 0.8 0.6 … 0.8 New Values … [5.5, 5.8) or [6.9,7.2) Old Values Low 0 Fuzzy Soil Drainage Methodology 2. Fuzzy Fuzzy Precipitation Fuzzy Temperature Fuzzy Elevation Feasibility Map Fuzzy Slope Fuzzy Soil PH Fuzzy Distance to River Fuzzy Soil Depth Fuzzy Sunshine hour Fuzzy Soil Drainage Methodology 3. Weight Determine --- How important is each factor? --- We can give different weights to different factors, and all the weights must add up to 1 Determine the weight intuitively BUT it requires looking at all criteria together, this will not allow for negotiation or compromise looking at criteria two at a time. Analytic Hierarchy Process (AHP) • It lets you compare criteria two at a time. • The user specifies the relative importance of one criteria compared to another and does this for all possible combinations of criteria. • The procedure will then tell you how consistent are all of your comparisons and it will develop weights for you for each criteria. Methodology 3. Weight Determine Analytic Hierarchy Process (AHP) Steps: 1. Estimate the pertinent data 2. Create pairwise comparison decision matrix 3. Calculate the weights and check consistency（CR<0.1) Table1. The fundamental scale Intensity of Definition Explanation 1 Equal importance Two activities contribute equally to the objective 3 Moderate importance Experience and judgments slightly favor one activity over another 5 Strong importance Experience and judgment strongly favor one activity over another 7 Very strong or demonstrated importance 9 Extreme importance 2，4，6，8 Intermediate value between the two adjacent judgments Importance An activity is favored very strongly over another and dominance is demonstrated in practice The evidence favoring one activity over another is of the highest possible order of affirmation When compromise is needed Methodology 3. Weight Determine * By hand * Idrisi --- “Weight” module * Klaus D. Goepel, Singapore http://bpmsg.com/ * …… Methodology 3. Weight Determine * Klaus D. Goepel, Singapore http://bpmsg.com/ Ratio 1 Weather 0.46 2 Hydrology 3 Topography 0.07 0.32 4 Soil Ratio 1.1 accumulated temperature 0.56 1.2 sunshine 0.09 1.3 annual precipitation 0.35 2.1 distance to river 1 3.1 elevation 0.25 3.2 slope 0.75 Rank 1 4 2 Texture 0.15 4. 1 PH 0.12 4.2 Depth 0.23 4.3 Drainage 0.65 3 Methodology 4. Weighted Overlay apply weights to several inputs and combine them into a single output. ∗ S = 0 ai: pixcel value of factor i； bi: weight of pixel i； n: numbers of factors 2.2 2.2 3.3 3 3 2 2.2 1.1 1.1 1 3 1 1.1 2.2 2.2 2 1 1 Factor 1 ( Weight = 0.75) = Factor 2 ( Weight = 0.25) Output (top left cell = 2.4) = 2.2*0.75 + 3* 0.25 2.4 2.4 3.0 1.9 1.6 1.1 1.3 2.4 1.9 Output Methodology 4. Weighted Overlay Weather Hydrology …… *0.46 *0.07 feasibility map *Wn Overview Criteria layer …… Standardize criteria …… *W’1 *W’n Suitability ratings from different hierarchy …… *W1 Final feasibility map *W2 *Wn Result Summary • There are a variety of possible answers to one suitability problem. • Different answers for the same problem result from: – Considering criteria to be a factor or constraint – How the factor is standardized (what function, what thresholds) – How each factor is weighted Limitation 1. Different fuzzy functions apply to different crop production areas. 2. Not considering seasonal influence. 3. Lack of data, such as soil texture. Thank You ! Questions and Comments?