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The need to compare two maps spatially has been derived mostly from remote sensing applications where producers and users of the land-use classification want to know its accuracy. Remote sensing studies use the error matrix to quantitatively assess the accuracy of the land use classification (Jensen, 1996b) which Foody (2002) state as the “core of accuracy assessment”. The error matrix is the summary of the relationship between two sets of information, which in remote sensing application are typically: (1) a remote sensing derived classification map and (2) reference information map (Jensen, 1996b). A pixel-by-pixel comparison is performed and reported in the error matrix, and several statistics can be calculated such as, the overall accuracy, producer’s accuracy and user’s accuracy. The overall accuracy is calculated by dividing the total correct pixels by the total number of pixels in the error matrix (Jensen, 1996b). The producer’s accuracy is calculated by dividing the total number of correct pixels in that category by the total number of pixels in that category, while the user’s accuracy is calculated by dividing the total number of correct pixels in that category by the total number of pixels that were actually classified in that category (Jensen, 1996b). These statistics provide the producer of the map a measure of how well an area is classified and the user of the

map a probability that a pixel classified on the map actually represents that category on the ground (Jensen, 1996b).

The Kappa statistic is also a measure of agreement or accuracy, expressed as a single number, which can be calculated from the error matrix. It is a discrete multivariate technique therefore appropriate for use on remote sensing data because these data are discrete, not continuous and also binomially or multinomially distributed not normally distributed (Jensen, 1996b). The Kappa is the fraction of agreement, which is corrected for the fraction of agreement statistically expected from the random relocation of all pixels in the maps, using the observed frequency distribution for the classification map and reference map (Hagen, 2002). Fitzgerald and Lees (1994) conclude that the Kappa statistic is superior to the overall accuracy percentage, as it is able to test the null hypothesis that there is no agreement between the two maps.

Foody (2002) mentions that there has been a call for standard measures and reporting to be used in accuracy assessment however, this has not been achieved as there is a variety of different needs and interpretations that exist and in reality it is probably impossible to specify a single all-purpose measure. However, the Kappa statistics has been recommended by analysts to be adopted as one of the standard measures (e.g. Smits et al. 1999)(cited in Foody, 2002 pg.189). The Kappa statistic for comparing maps has been used extensively in remote sensing applications, some examples include Fitzgerald and Lees (1994), Michelson et al. (2000) and South et

al. (2004).

South et al. (2004) refer to Montserud and Leamans (1992) who evaluated Kappa statistics and classification methodologies and proposed that a Kappa value of 0.75 or greater indicates a very good to excellent classification performance. While Foody (2002) cite Thomlinson et al. (1999) who set a target of an overall accuracy of 85 percent with no class less than 70 percent accurate.

Fuzzy set theory (Zadeh, 1965) has also been used by several authors to assess the accuracy of maps or map comparisons (Metternicht, 1999; Power et al., 2001; Metternicht et al., 2005) and it was introduced to address some of the map comparison issues (Hagen, 2002). Issues include; allowing for some level of

positional tolerance, finding the spatial distribution of error and to differentiate the error magnitude (i.e. some errors are more significant than others) (Hagen, 2002). Fuzzy sets deal with inexact concepts in a definable way (Burrough and McDonnell, 1998b). Some classes for various reasons cannot, and do not, have sharply defined boundaries and fuzziness can characterise this imprecision (Burrough and McDonnell, 1998b). A pixel is given a grade of membership expressed in terms of a scale varying continuously between 0 and 1. The grade corresponds to the degree to which that pixel belongs to its class. There are different kinds of fuzzy membership functions and their selection depends on the user’s requirement in defining the partial membership.

For the application of accuracy assessment or the comparison of maps Hagen (2003) deals with two sources of fuzziness, fuzziness of location and fuzziness of category. Fuzziness of location allows for vagueness of a category’s spatial position, i.e. the category may be present somewhere in the proximity of that location. Fuzziness of category allows some categories in the map to be more similar to each other than others. In a similar manner to the Kappa statistics, the KFuzzy can also be calculated

which provides an overall value of similarity between two maps which results in values between 1 (identical maps) and 0 (total disagreement). KFuzzy corrects the

percentage of agreement for the expected percentage of agreement and differs from Kappa in its calculation of the expected similarity (Hagen, 2003). For further details of the KFuzzy derivation, readers are referred to Hagen (2003).

The need to assess the accuracy of a map or simply compare two maps derived from differing applications has been addressed by the Research Institute of Knowledge Systems in The Netherlands in their development of the Map Comparison Kit (MCK)(RIKS, 2005a). They have bundled together several spatial map comparison techniques, including Kappa and KFuzzy outlined above, into user friendly software

which handles a series of maps. The Kappa algorithm included in the MCK is dissected into further statistics; Kappa location (measuring the similarity of location) and Kappa histogram (measuring the similarity of quantity).

2. 5 Summary

The following provides a summary combining the subsections included in the literature review and their link to the following chapters.

Several classification techniques have been reviewed concluding that for this research the LMU classification will be an adaptation of the spatially constrained classification of Oliver and Webster (1989) which in this case has the ability to incorporate large datasets (i.e. high resolution remote sensing). The two stage methodology to classify LMUs is described in Chapter 7.

Soil properties, vegetation and topographic attributes have been identified as important inputs to the LMU classification. Soil properties that appear to be stable in time and influence plant growth have been identified, namely texture, structure, organic matter, nutrient availability, pH, salinity/sodicity balance, depth of topsoil and depth to restricted layer. The relevant properties have been further detailed, highlighting the relationships between the properties, which support scientists in understanding their effect on plant growth. The field collection and chemical analysis of soil properties is detailed in Chapter 4. The soil properties are analysed statistically in Chapter 6, which will assist in determining the appropriate soil properties to be used in the LMU classification.

Based on the evidence of soil sampling strategies, the design will be based on a DEM and remote sensing data to provide an indirect (surrogate) measure of soil variability providing the opportunity to optimise the strategy. A stratified random sampling pattern that uses bulk sampling of surface soil, respecting the size of support will be used in this research. The soil sampling design is presented and implemented in Chapter 4 along with methods for sampling vegetation attributes that are used in remote sensing studies.

The potential of remote sensing data to detect landscape variation based on the relationships that exist between remote sensing systems and soil and vegetation properties has been highlighted. It appears that the RI would be a useful index on bare soil, while the vegetation indices (in particular the NDVI) would be useful for cropped areas. Transect sampling through three crop types, common to the Western

Australian wheatbelt, will be conducted depicting variation in crop growth. An analysis between crop variability and high resolution remote sensing data is discussed in Chapter 4.

Three topographic attributes namely; landforms, compound topographic index (CTI) and slope have been identified as important drivers in soil forming processes and their uses in past studies has been discussed. Their generation utilising GIS software is detailed in Chapter 5 and their relationship with soil properties in this instance are examined in Chapter 6.

Based on the discussion of validation techniques appropriate for the LMU classification, it appears that the use of spatial and temporal yield maps would be the most appropriate method which is mentioned in Chapter 8. The sensitivity of the LMU classification to changing parameters (another form of validation) can be assessed with algorithms provided in the MCK (RIKS, 2005a) (Chapter 8). Specifically, the Kappa, with Kappa location and Kappa histogram provided in the MCK, will be useful in this research to assess the sensitivity of the LMU classification to differing parameters (i.e. distance applied in the spatial constraint). It is preferred over the KFuzzy in this case, for its simplicity.

The following chapter includes a description of the study area and existing data sets. The software and hardware used throughout this research are briefly noted.

CHAPTER 3

STUDY AREA AND DATA SETS

Chapter 2 provided appropriate background information and reviewed several approaches for classifying landscapes into spatial zones. It was concluded that a spatial weighted multivariate classification worth a case study. This chapter introduces the case study region and describes how the various data for the experimentation were derived, from the primary data sources; terrain, remote sensing and yield data along with the software used.

3. 1 Study Area

The study site selected is the Muresk Institute of Agriculture Farm, part of Curtin University of Technology. It lies between latitudes 31º 41’ and 31º 46’S and longitudes 116º 39’ and 116º 45E, and is approximately 100km north-east of Perth city in the mid southern region of the Shire of Northam in the south-west of Western Australia (WA) (Figure 3.1). It covers approximately 1,780ha of which approximately 1,250ha is arable (Muresk Institute of Agriculture, 2005).

Typical to its region in WA, the farm is dominated by dryland agriculture and regions of natural vegetation. The main crops are wheat (Triticum aestivum), barley (Hordeum vulgare), oaten hay (Avena sativa), canola (Brassica napus), and lupins (Lupinus angustifolius), and pastures for animal grazing. Animal production includes Merino sheep for prime lamb and wool production and beef cattle. The WA Pig Skills Centre Pty Ltd is also on the property.

Certain advantages arise from selecting Muresk farm; yield data have been collected in the past, a complete database of paddock history exists, the farm has a variety of crop types and has topographic variability. Being part of Curtin University creates cohesion between the campuses and departments, and fosters future research relationships in GIS and agriculture. The farm is close to Perth (approximately 1 ½ hours drive) and can provide accommodation.

Figure 3.1 Study Area Location