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Support Vector Machines Based-Modeling of Land Suitability Analysis for Rainfed Agriculture

Fereydoon Sarmadian*, Ali Keshavarzi, Azin Rooien, Ghavamuddin Zahedi, Hossein Javadikia, Munawar Iqbal

Department of Soil Science, University of Tehran, Karaj, Iran

Abstract: Soil evaluation plays important role in the sustainable agriculture development. Based on the value of several soil and environment indicators, the agricultural land evaluation methodology is applied to land mapping units in order to compute the suitability index. This index characterizes these land-mapping units. However, there are different methodologies which have been reviewed for land capability and suitability evaluation. In the present study, the potential use of support vector machines (SVMs) algorithm was evaluated for land suitability analysis for rainfed wheat based on FAO land evaluation frameworks (FAO, 1976, 1983, 1985) and the proposed method by Sys et al. (1991). The study area was divided into thirteen land units (with thirty two representative soil profiles) and ten land characteristics including climatic (precipitation, temperature), topographic (relief and slope) and soil-related (texture, CaCO₃, OC, coarse fragment, pH, gypsum) parameters were considered to be relevant to rainfed wheat. In this study economic factors have been excluded and moderate management has been assumed. The data points were divided by randomization technique and 80% data was selected to train the model and the remaining 20% was used to test the model. The Root Mean Square Error (RMSE) and coefficient of determination (R²) were used as evaluation criteria. The results showed that the corresponding values for RMSE and R2 between the measured and predicted land suitability indices using the SVMs model were 3.72 and 0.84 respectively. Moreover, the most important limiting factors for rainfed wheat cultivation are climatic and topographic conditions, and 84.38% of total lands are classified as S₂ class (moderately suitable) while the remaining 15.62% are classified as S₃ class (marginally suitable). It appears that SVMs approach could be a suitable alternative to performance of land suitability scenarios.

Keywords: SVM, land characteristics, land suitability analysis, rainfed wheat

Received July 27, 2014; Revised August 15, 2014; Accepted August 19, 2014

Citation: Fereydoon Sarmadian, Ali Keshavarzi, Azin Rooien, Ghavamuddin Zahedi, Hossein Javadikia, Munawar Iqbal, Support Vector Machines Based-Modeling of Land Suitability Analysis for Rainfed Agriculture. Journal of Geosciences and Geomatics, 2 (4). 165-171. January 2014. doi:10.12691/jgg-2-4-4

1. Introduction

Due to constant decrease in farmlands, it is important to identify the best lands for sustainable agriculture (productive and profitable agriculture that protects the environment and that is socially equitable). This requirement has resulted in the development of land suitability scenarios for agriculture (Mendas and Delali, 2012). Land evaluation procedures focus increasingly on the use of quantitative procedures to enhance the qualitative interpretation of land resource surveys. Crucial to the estimation of land suitability is the matching of land characteristics with the requirements of envisaged land utilization types. Land evaluation results from a complex interaction of physical, chemical, and bioclimatic processes and evaluation models are reliable enough to predict accurately the behaviour of land (Held et al., 2003; Ball and De la Rosa, 2006).

The FAO (1976) first developed a common framework for land evaluation that was based on biophysical factors and the socioeconomic characteristics of an area. However, this approach was difficult to apply over large areas before the development of geographical information systems (GIS), which permitted the use of computerized techniques for assessing and mapping land suitability. These techniques have become increasingly important as integral components of urban planning (Marull et al., 2007), agricultural utilization (Olivas et al., 2007), habitat selection (Manton et al., 2005), and environmental planning (Oleszczuk, 2007). Many studies have assessed the potential suitability of land and guide the selection of areas that are suitable for a particular use. There are two general kinds of land suitability evaluation approaches: qualitative and quantitative. A qualitative approach is used to assess land potential at a broad scale, or employed as a preliminary to more detailed investigations . The results of classification are generally given in qualitative terms only, such as highly suitable, moderately suitable, and not suitable. The second approach is that using parametric techniques involving more detailed land attributes which allow various statistical analyses to be performed.

In recent years, soft computing techniques have been successfully developed for soil and land evaluation. Support vector machines (SVMs) algorithm is one of new mathematic tools which is used as a universal constructive learning procedure based on the statistical learning theory developed by Vapnik (Vapnik, 1995) and have attracted greater interest recently in geosciences and agricultural engineering. It provides non-linear solutions to regression and classification problems by transforming the input variables in a large-dimension space, whose inner product is given by positive definite kernel functions. SVMs are trained using dual optimisation techniques with constraints. Recently several research groups about engineering have shown excellent performance of SVMs on different problems of regression and classification. SVMs are a promising machine learning method originally developed for pattern recognition problem based on structural risk minimization (Li et al., 2009). Basically, SVMs are closely related to artificial neural networks (ANNs). In fact, SVMs model using sigmoid kernel function is equivalent to a two-layer perceptron neural network. Using a kernel function, SVMs are alternative training methods for polynomial, radial basis function, and multilayer perceptron classifiers in which the weights of the network are found by solving a quadratic programming problem with linear constraints, rather than by solving a non-convex, unconstrained minimization problem as in standard ANN training (Huang et al., 2010).

To our knowledge, the land suitability assessment using SVMs algorithm has not previously been used for the modelling of cultivated wheat. The main objective of this study was to investigate the potential use of the SVMs algorithm for land suitability analysis for rainfed wheat in a hilly plateau region of Iran.

2. Materials and Methods

2.1. Study Area

A hilly area in the northwestern province of Qazvin (Kouhin region), Iran was selected for this study (Figure 1). Height amplitude varies from 1300 m to 1600 m above sea level with 1 to 6 percent slope. This belt covers about 1000 hectares, situated between latitudes 36° 20' and 36° 23' North and longitudes 49° 34' and 49° 38' East. The climate is semi-arid in nature. Soil temperature and moisture regimes are mesic and xeric, respectively (Newhall and Berdanier 1996). The soils have been developed on alluvial deposits of marl and brown to grey limestone parent materials and are plateau from east to west direction. According to US Soil Taxonomy system, the soils have been classified as Entisols and Inceptisols (Soil Survey Staff, 2006) and are used for rainfed farming. During 1993-2006, the average annual rainfall and average annual temperature were recorded to be 327 mm and 11.2°C, respectively (Iran Meteorological Organization).

Figure 1. Location of study area and representative soil profiles

2.2. Data Collection and Soil Sample Analysis

As sampling is constrained by financial resources, efficient sampling strategies are desirable. In this paper, Soil-Land Inference Model (SoLIM) with respect to environmental covariates (soil and terrain attributes) was used for sampling design optimization (Yang et al., 2012). A Digital Elevation Model (DEM) with grid size of 10×10m was extracted from a paper-based topographic map using GIS platform with scale of 1:25000 and contour lines interval of 10 meter (, 2010). The terrain attributes such as slope value, aspect, elevation and plan curvature were extracted from a digital elevation model (DEM) with a resolution of 10 meter (Wilson and Gallant, 2000). A total of 120 soil samples were collected from different horizons of thirty two representative soil profiles located in Kouhin region in . Geographical location of sampling points was recorded by Global Positioning System (GPS). The soil samples were air dried, crushed and sieved using 2 mm sieve size and subjected to laboratory analysis using standard methods (Sparks et al., 1996).

2.3. Physical Land Suitability Procedure

The basis of the present methodology lies in the traditional qualitative land evaluation, and land qualities/characteristics are matched with each specific crop requirements in order to find the suitability class of land for the same crop (FAO, 1976). The methodology comprises two key steps: Step 1 is to identify land units with a similar topography and soil conditions, Step 2 is to match the properties of the land units with crop requirements including the traditional matching process, as described in the FAO qualitative land evaluation system (FAO, 1976, 1983, 1985) used to compare land qualities/ characteristics of topography, erosion hazard, wetness, soil physical properties, soil fertility and chemical properties, soil salinity and alkalinity with each specific crop requirements developed by Sys et al. (1991). The physical land suitability evaluation consists of a model that assigns a score to every land quality and characteristic. Land quality is a complex attribute of land, which in a distinct manner influences its suitability for a specific kind of use, while land characteristics are any measurable features of land that can be used to characterize a land unit. In this study, the land indices were calculated based on parametric method according to the square root equation (Samir, 1986; Bagherzadeh and Mansouri Daneshvar). In parametric method, a quantitative classification is allocated to each characteristic of land. If a characteristic of land for a specific product was completely desired and provided optimum conditions for that, maximum degree 100 would belong to that characteristic and if it has limitation, the lower degree will be given to it. Later, allocated ranks will be used in calculation of the land index.

2.4. Crop Requirements

A requirement table for rainfed wheat is established using the structure of the FAO framework for land evaluation. Both previously established requirement tables and conditions proper to Kouhin area were considered.

2.5. Support Vector Machines (SVMs) Methodology

Among many machine-learning methods, SVMs, originally developed by Vapnik (1995), are considered to be a new generation of learning algorithms. SVMs have several appealing characteristics for modellers, including: they are statistically based models rather than loose analogies with natural learning systems, and they theoretically guarantee performance (Cristianini and Scholkopf, 2002). SVM have been applied successfully to text categorization, handwriting recognition, gene-function prediction, remote sensing classification and ecology (Guo et al., 2005) demonstrating the utility of the method across disciplines, and proving that SVM produce very competitive results with the best available classification methods, and require just a minimum amount of model tuning (Huang et al., 2010). Typically, SVMs are designed for two-class problems where both positive and negative objects exist. For these classification problems, two-class SVM seek to find a hyper plane in the feature space that maximally separates the two target classes. The basic idea of SVMs is to use a linear model to implement non-linear class boundaries through nonlinear mapping of the input vector into a high-dimensional feature space. The linear model constructed in the new space can represent a non-linear decision boundary in the original space. In this study, MATLAB 8.2 (The MathWorks, Inc.) software was used for the design and testing of SVMs model. Data points were randomized by Excel software and 80% of data was applied as training data, while remaining 20% set as a test data. For more details about SVMs algorithm, one can refer to Xu et al. (2012).

2.6. Performance Criteria

The model performance was evaluated using test data points that were not used in the training stage. The parameters used for the evaluation of model were root mean square error (RMSE) and coefficient of determination (R²), which were calculated using equations 1 and 2 (Wosten et al., 2001):

[picture] | (1)

[picture] | (2)

where is the measured value, is the predicted value, is the mean value, and N is the total number of data points. RMSE was used to measure accuracy and validity of the training and test data sets.

3. Results and Discussion

The crop requirements in terms of soil and land characteristics are presented in Table 1. The study area was divided into thirteen land units (with thirty two representative soil profiles) and ten land characteristics including climatic (precipitation, temperature), topographic (relief and slope) and soil-related (texture, CaCO₃, OC, coarse fragment, pH, gypsum) parameters were considered to be relevant to rainfed wheat. In similar study, Kamkar et al. (2014) studied a GIS-based plan to assess the possibility and performance of a canola- soybean rotation in Golestan province, one of the most important agricultural production regions of . They used precipitation, temperature, aspect, slope, texture, pH and EC layers in GIS platform. According to their results, 11.82% of total lands are very suitable to rotate soybean after canola while most agricultural lands in the study area fell into the moderate and low suitability classes.

Table 1. Soil and land characteristics for rainfed wheat in Kouhin region

Table 2. soils classification in the study area (Soil Survey Staff, 2006)

In the present study, economic factors have been excluded and moderate management has been assumed. Soils classification in the study area is presented in Table 2. As it is highlighted in Table 2, 7.69% of soils are classified as Entisols order, whereas the remaining 92.31% are classified as Inceptisols order. Land suitability classes and land indices in Kouhin region are shown in Table 3. According to Tables 1 and 3, the most important limiting factors for rainfed wheat cultivation are climatic and topographic conditions, and 84.37% of total lands are classified as S₂ class (moderately suitable) while the remaining 15.62% are classified as S₃ class (marginally suitable). Emphasis should be placed on soil management techniques that conserve organic matter and enhance nutrient and water-holding capacity of the soil. In order to assess the SVMs algorithm performance, test data points were used to predict land suitability indices and the predicted values were plotted against measured values (Figure 2). The plot approximates a straight line, confirming normality of the data and angle close to 45 degrees (one to one line) also indicates a high accuracy of the SVMs algorithm for the estimation of land suitability indices. The RMSE and R² between the measured and predicted land suitability indices using the SVMs model were 3.72 and 0.84 respectively.

Figure 2. The scatter plot of the measured versus predicted values for land indices

Table 3. Land suitability classes and land indices in Kouhin region

There are limited published studies dealing with the use of SVMs in soil sciences especially in land evaluation. Lamorski et al. (2008), for instance, estimated soil hydraulic parameters from measured soil properties using SVMs. They reported that SVMs performed generally better than or/with the same accuracy as ANNs. Twarakavi et al. (2009) developed SVM models for estimating the hydraulic parameters describing the soil water retention and hydraulic conductivity. They stated that the SVM-based method predicted the hydraulic parameters better than the ANN-based method. Wang et al. (2009) compared different artificial intelligence methods for forecasting monthly discharge time series. They concluded that SVM model was able to obtain better forecasting accuracy in terms of the various evaluation measures during the both training and validation phases.

In compare to this new method in land evaluation, the earlier fuzzy model has been used by many researchers in land suitability evaluation (Tang et al., 1991; Van Ranst et al., 1996; Keshavarzi and Sarmadian, 2009). Most of the researchers, have been compared the results of this evaluation with other conventional methods such as maximum limitation, parametric and multiple regression methods in order to predicting the yield of production. The weakest part of the fuzzy set methodology for land evaluation is the way in which membership functions, class centers, cross-over values and weight values are chosen (Keshavarzi and Sarmadian, 2009). The problem of how to define the parameters of the fuzzy membership functions is more complicated than the boolean equivalent because it requires not only specifications of what kind of membership function and class boundary values, but also the widths of the transition zones. Another critical issue is the choice of weights which clearly have a major impact on results. Some guidance can be obtained from the literature and expert experience on land properties relevant to particular crops, but ultimately subjective decisions have to be made.

4. Conclusions

In this study, SVMs ―a novel machine learning algorithm― was evaluated for land suitability analysis for rainfed wheat using the Root Mean Square Error (RMSE) and coefficient of determination (R²). The results showed that the most important limiting factors for rainfed wheat cultivation are climatic and topographic conditions. According to the advantages associated with the use of the SVM over this research, It appears that SVMs approach could be a suitable alternative to performance of land suitability scenarios and studies on this approach should continue in an effort to relate soil properties to the basic soil characteristics and its advantages should motivate soil scientists to work further on it in the future.

Acknowledgements

This study was supported by the Center of Excellence Division, Department of Soil Science, University of Tehran, Iran.

References

[1]   | Bagherzadeh A, Mansouri Daneshvar MR. 2011. Physical land suitability evaluation for specific cereal crops using GIS at Mashhad Plain, Northeast of Iran. Frontiers of Agriculture Journal, 5(4): 504-513.
[2]   | Baja S, Chapman MD, Dragonvich D. 2002. A conceptual model for defining and assessing land management units using a fuzzy modeling approach in GIS environment. Environmental Management, 29: 647-661.
[3]   | Ball A and De la Rosa D. 2006. Modelling possibilities for the assessment of soil systems. In: Uphoff N, Ball A, Fernandes E, Herren H, Husson O, Laing M, Palm Ch, Pretty J, Sanchez P, Sanginga N, Thies J (Eds.), Biological Approaches to Sustainable Soil Systems. CRC Press, BocaRaton, FL, USA.
[4]   | Chong Xu, Fuchu Dai, Xiwei Xu, Yuan Hsi Lee. 2012. GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed, China. Geomorphology, 145: 70-80.
[5]   | Cristianini N and Scholkopf B. 2002. Support vector machines and kernel methods-the new generation of learning machines. AI Magazine, 23: 31-41.
[6]   | Djurić U, Marjanović M, Šušić V. 2013. Land-Use Suitability Analysis of Belgrade City Suburbs Using Machine Learning Algorithm. Geoinformatics for City Transformation, January 21- 23, Ostrava.
[7]   | FAO. 1976. A framework for land evaluation. FAO Soils Bulletin No. 32, Rome.
[8]   | FAO. 1983. Guidelines: Land evaluation for rainfed agriculture. FAO Soils Bulletin. No. 52, Rome.
[9]   | FAO. 1985. Guidelines: Land evaluation for irrigated agriculture. FAO Soils Bulletin, No. 55, Rome.
[10]   | Guo QH, Kelly M, Graham CH. 2005. Support vector machines for predicting distribution of Sudden Oak Death in California. Ecological Modelling, 182, 75-90.
[11]   | Held M, Imeson A, Montanarella L. 2003. Economic Interests and Benefits of Sustainable Use of Soils and Land Management. Joint Res. Centre Press, Ispra, Italy.
[12]   | Huang Y, Lan Y, Thomson SJ, Fang A, Hoffmann WC, Lacey RE. 2010. Development of soft computing and applications in agricultural and biological engineering. Computers and Electronics in Agriculture, 71: 107-127.
[13]   | Kamkar B, Dorri MA, Teixeira da Silva JA. 2014. Assessment of land suitability and the possibility and performance of a canola (Brassica napus L.) - soybean (Glycine max L.) rotation in four basins of Golestan province, Iran. The Egyptian Journal of Remote Sensing and Space Sciences, In press.
[14]   | Keshavarzi A, Sarmadian F. 2009. Investigation of fuzzy set theory`s efficiency in land suitability assessment for irrigated wheat in Qazvin province using Analytic hierarchy process (AHP) and multivariate regression methods. Proc. ‘Pedometrics 2009’ Conf, August 26-28, Beijing, China.
[15]   | Lamorski K, Pachepsky Y, Sawiñski C, Walczak RT. 2008. Using support vector machines to develop pedotransfer functions for water retention of soils in Poland. Soil Science Society of America Journal, 72: 1243-1247.
[16]   | Li H, Liang Y, Xu Q. 2009. Support vector machines and its applications in chemistry. Chemometrics and Intelligent Laboratory Systems, 95: 188-198.
[17]   | Manton MG, Angelstam P, Mikusinski G. 2005. Modelling habitat suitability for deciduous forest focal species. A sensitivity analysis using different satellite land cover data. Landscape Ecology, 20: 827-839.
[18]   | Marull J, Pino J, Mallarach JM, Cordobilla MJ. 2007. A land suitability index for strategic environmental assessment in metropolitan areas. Landscape and Urban Planning, 81: 200-212.
[19]   | Mendas A and Delali A. 2012. Support system based on GIS and weighted sum method for drawing up of land suitability map for agriculture. Application to durum wheat cultivation in the area of Mleta (Algeria). Spanish Journal of Agricultural Research, 10(1): 34-43.
[20]   | National Cartographic Center. 2010. Research Institute of NCC. Tehran, Iran (www.ncc.org.ir).
[21]   | Newhall F and Berdanier CR. 1996. Calculation of soil moisture regimes from the climatic record. Natural Resources Conservation Service, Soil Survey Investigation Report, No. 46, Pp13.
[22]   | Oleszczuk P. 2007. The evaluation of sewage sludge and compost toxicity to Heterocypris incongruens in relation to inorganic and organic contaminants content. Environmental Toxicology, 22: 587-596.
[23]   | Olivas GUE, Valdez LJR, Aldrete A, Gonzalez GMdJ, Vera CG. 2007. Suitable areas for establishing maguey cenizo plantations: definition through multicriteria analysis and GIS. Revista fitotecnia mexicana, 30: 411-419.
[24]   | Samir MK. 1986. A statistical approach in the use of parametric system applied to the FAO framework for land evaluation. Ph.D. thesis, State University of Ghent, Belgium, 141pp.
[25]   | Soil Survey Staff. 2006. Keys to Soil Taxonomy, 10th ed. United States Department of Agriculture, Washington.
[26]   | Sparks DL, Page AL, Helmke PA, Leoppert RH, Soltanpour PN, Tabatabai MA, Johnston GT, Summer ME. 1996. Methods of soil analysis. Soil Science Society of America, Madison, Wisconsin.
[27]   | Sys C, Van Ranst E, Debaveye IJ. 1991. Land evaluation. Part I: Principles in Land Evaluation and Crop Production Calculations. General Administration for Development Cooperation, Agricultural publication, No. 7, Brussels-Belgium, 274pp.
[28]   | Sys C and Debaveye J. 1991. Land evaluation, part 1: Principles in land evaluation and crop production calculation. In: General administration for development cooperation. Brussels, Belgium.
[29]   | Tang H, Debaveye J, Ruan D, Van Ranst E. 1991. Land suitability classification based on fuzzy set theory. Pedologie, 3: 277-290.
[30]   | Twarakavi NKC, Simunek J, Schaap MG. 2009. Development of pedotransfer functions for estimation of soil hydraulic parameters using support vector machines. Soil Science Society of America Journal, 73: 1443-1452.
[31]   | Van Ranst E, Tang H, Groenemans R, Sinthurahat S. 1996. Application of Fuzzy logic to land suitability for rubber production in Peninsular Thailand. Geoderma, 70: 1-19.
[32]   | Vapnik V. 1995. Nature of statistical learning theory. John Wiley and Sons Inc., New York.
[33]   | Wang WC, Chau KW, Cheng CT, Qiu L. 2009. Acomparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. Journal of Hydrology, 374: 294-306.
[34]   | Wilson JP and Gallant JC. 2000. Terrain analysis, principle and applications. John Wiley and Sons Inc., New York.
[35]   | Wosten JHM, Pachepsky YA, Rawls WJ. 2001. Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics. Journal of Hydrology, 251: 123-150.
[36]   | Yang L, Zhu AX, Qi F, Qin C, Li B, Pei T. 2012. An integrative hierarchical stepwise sampling strategy for spatial sampling and its application in digital soil mapping. International Journal of Geographical Information Science, 27: 1-23.