Digital Terrain Models derived from SRTM data and kriging

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1 Digital Terrain Models derived from SRTM data and kriging T. Bernardes 1, I. Gontijo 1, H. Andrade 1, T. G. C. Vieira 2, H. M. R. Alves 3 1 Universidade Federal de Lavras, Lavras, Minas Gerais, Brasil, tiago@epamig.ufla.br 2 CTSM, Empresa de Pesquisa Agropecuária de Minas Gerais, Lavras, MG, Brasil, tatiana@epamig.ufla.br 3 EMBRAPA CAFÉ, Empresa Brasileira de Pesquisa Agropecuária, Brasília, DF, Brasil, helena@ufla.br Abstract The objective of this work is to define procedures to improve spatial resolution of SRTM data and to evaluate their applicability in the Serra Negra region, in the district of Patrocínio, state of Minas Gerais in Brazil. The region's structure is a result of past tectonic processes that have arched it into a dome shape. Besides the already existing agriculture exploitation, Serra Negra also has strong tourism and mining potential. The Digital Elevation Model (DEM) was done using different interpolation methods in a resolution of 30 meters or l arcsec, among them kriging, ideally used to manipulate random spatial variations due to its capacity for dealing with spatially variable components. The accuracy of the resulting DEM and slope maps modelled were evaluated based on slope measured in the field. The correlation coefficients were determined from the field data and those derived from the DEM. Analyses and tests with SRTM data, divulged for South America are presented to better adequate the model to the study area. The correlation coefficients in the estimates by kriging and by bicubic interpolator were similar, with a slight difference in favour of kriging. Therefore, kriging is an interesting alternative in elaborating Digital Elevation Models that are in keeping with the dome structure of the Serra Negra region. In order to measure operational aspects of the preprocessing methods, the study area data were prepared under a resolution

2 2 Digital Terrain Models derived from SRTM data and kriging of 30 meters and evaluated through statistical analysis and visualizations of the DEMs and slope. The data presented strong restrictions to being used in their original form due to the low spatial resolution. However, the pre-processing allows their use in relatively detailed scales. Based on the results, a proposal for the development of a DEM with the SRTM data for the Serra Negra region is presented. Introduction Many aspects of the landscape of terrestrial systems have been evaluated viewing a disciplined management of the information on natural resources. A large part of the features of the landscape is due to the shapes of the terrain derived from topographic variables when we assume that the different geographic phenomena on the Earth's surface establish occupation patterns associated to implicit and explicit inter-relation mechanisms. Points of correspondence can be traced between a region s relief, soil and vegetation. It is known, for example, that the soil presents distribution patterns in the landscape associated to soil formation factors, as shown in Jenny s equation: S = f(cl, O, R, P, T), where relief (R) can be modelled computationally to contribute to the elaboration of detailed maps at low costs and relative precision. Intrinsically, climate (Cl), organisms (O) and time (T) are also incorporated to the model, as they are responsible for the relief modelling when they act upon the geologic substratum or parent material (P). Climate and vegetation, at the same time that alter and denounce development stages in the soils in interaction with the relief, are also influenced by alterations on the earth surface. Precipitation data are related to relief by mechanisms resulting from the relief's influence allied to the dynamics of air masses that condition precipitation. Aspects related to shadows geometry in more mountainous portions of the landscape result in a trend towards the evolution of microclimates favourable to frost, for example. In Brazil, there is a lack of data on the topography of the terrain due to the extension of the lands, which makes their mapping by conventional planialtimetric survey more difficult. However, the development of hardware engineering, allied to powerful data processing systems and the advances of automatized cartography, have modified earth surface detailing methodologies. Added to the collection of earth surface data by technologies such as remote sensing, an astounding amount of information is generated daily. As an example, there are the 12 Terabytes of data collected by interferometry by the SRTM Project (Shuttle Radar Topographic Mission) during a period of 11 days and 176 orbits of the

3 Obtaining and preparation of data 3 Earth. Studies applied to the characterization of the landscape with morphologic variables have been aided by the development of automatic methods of extraction of topographic variables. It is important, in this sense, to define procedures of extraction of digital information on topography and relief units in a computational environment. Location of the area The study area is situated in the southeast region of the state of Minas Gerais, in the watershed of Alto Paranaíba. It is geographically referenced by coordinates and latitude S and to longitude W. The area can be distinguished from the regional context in orbital images, aero photographic surveys and other cartographic documents. The total study area is km2 (16,8 km in the east-west by 13,8 km in the north-south) and is approximately 280 meters above the local base level, with a maximum altitude of 1270 meters to the southwest, on the border of the dome structure, and 1160 meters in the centre, where the lagoon Chapadão de Ferro is located. Access from Belo Horizonte, capital of the state, is by highway BR 262 to the district of Ibiá, where the highway MG 187 leads to an earth road 2 km from the town, in the direction of the district of Cruzeiro da Fortaleza, which cuts the whole complex in the Western-Eastern direction. Obtaining and preparation of data The SRTM data are available on the USGS (United States Geological Survey) site, in a resolution of approximately 90 meters, and were obtained in TIFF format. Among the undesirable characteristics of the original data, only the extremely high or low points (peaks and vortices) were removed using the ENVI (Research Systems Inc., 2002) software, from where the data were exported in two different formats, ASCII and TIFF. Eventual objects on the terrain surface, such as edifications or even different land cover types, are incorporated into the model, giving a false impression of the relief. These features were not removed because the filtering techniques available cause an indistinct softening of the relief, leading to a loss of information. According to Valeriano (2003), unnecessary softening of the MDE hinders the performance of the slope algorithms. Moreover, the interpolation processes by kriging present a capacity for dealing with

4 4 Digital Terrain Models derived from SRTM data and kriging the components of spatial variability, providing an interesting way of manipulating such random spatial variations. Treatment of the data The objective was to modify the resolution of the original data from 3arcsec to 1arcsec, or from 90 to 30 meters approximately. To this end, the interpolations were carried out: bicubic, available in SPRING/INPE software, and kriging according to a flux of operations in different softwares. After removing the out liers in the original file, this was directly imported to SPRING/INPE in TIFF format where a new grade was generated, by bicubic interpolation, with a resolution of 30 meters. For the kriging, this same file was exported from ENVI in ASCII format with 3 columns representing coordinates X, Y and Z, where Z are the height values to be read by Software R (GeoR package) for exploratory analysis of the data. After exploratory analysis, the GS+ (Gamma Design Software, 2000) was used in geostatistical analysis which allowed the choice of a semivariogram model that better represented the data. The file containing all the digitalized points was then imported by the Surfer (Golden Software Inc., 1995), where interpolation by kriging was carried out. Field observations The field work consisted of measuring the slope in 40 sample points distributed in the whole study area. The observations were carried out manually using a clinometer and the points were georeferenced with a GPS Promark II. The GPS model allowed post-processing of the data improving their precision. The position errors were then confined to values less than 2 meters. These errors were considered satisfactory to the work as in all the points observed the slope remained the same in greater radius than these values. These georeferenced points were plotted on slope grades derived from the DEMs for comparison. Slope was measured according to Östman (1987), as the use of digital elevation models relapses especially on obtaining variables derived from altimetry (slope being the most frequent example). According to Valeriano (2004), slope is a more rigorous test because derivative calculations evidence structures that are too subtle to be perceived in the first order variable.

5 Trend and semivariogram analysis 5 Correlations with field data The DEM with 30 meters resolution obtained by the bicubic interpolator and by kriging were transformed into slope. The data were tabulated to obtain the correlation coefficients between the field data and those obtained from the DEMs interpolated by the two methods. Both methods were also compared to each other to verify their similarities. For this, the SAEG statistical software was used.trend and semivariogram analysis Exploratory analysis showed no trend in the data, so spatial analysis could be carried out without altering the data. As shown in Figure 1, the spheric model was the one adjusted, presenting the following parameters: nugget (Co): 10 m 2, sill (Co+C): 1480 m 2 and range (A) of m. Figure 1: Semivariogram model fitting The C0 parameter (nugget) represents undetected variability, according to the distance used, and can refer to an analytic error indicative of an unexplained variability. As nugget (Co) is very low in relation to sill (Co+C), there is a strong spatial dependence in the data in question (Cambardella et al., 1994). The C0 + C parameter, called sill, is the value in which the semivariogram stabilizes itself. The parameter A is the amplitude of dependence and indicates the limit distance between the samples that have, and those that do not, a spatial autocorrelation.

6 6 Digital Terrain Models derived from SRTM data and kriging Prepared models Both interpolation methods improved the definition of slope features in relation to the original data with 3 arcsec resolution. As shown in Figure 2 subtle variations were observed in the generated models such as softening of wrinkled flat areas and of artificial features in the terrain. (a) (b) (c) Figure 2: (a) DEM original resolution (3arcsec); (b) DEM by bicubic interpolation (1arcsec); (c) DEM by kriging interpolation (1arcsec) In both cases, features of objects on the earthy surface such as edifications, deforestation and irregularities in the area corresponding to the lagoon, due to aquatic macrophyte, remained in the products obtained. However, as was expected, kriging was more efficient in the treatment due to its capacity for dealing random spatial variations such as these. Bicubic interpolation highlighted the more mountainous features of the landscape, but it also highlighted the variations provoked by the dossel of the cerrado 1 vegetation in detriment of the topographic information. Similar results were obtained by Valeriano (2004), when the high frequency 1 Cerrado is a type of savanna vegetation of the central Brazil.

7 Prepared models 7 features represented by edifications in urban areas were enhanced by the triangular irregular network (TIN). When the data were transformed to slope grouped in classes, as shown in Figure 3, there were also few differences in terms of general distribution. Here also, the softening generated by the kriging model was fundamental in the performance of the slope algorithm, especially in determining flat areas, between 0 and 3%, reducing the modeling of areas with slopes between 3 and 12% distributed within flat areas. (a) (b) (c) Figure 3: (a) Slope derived from original; (b) DEM Slope derived from bicubic interpolation; (c) Slope derived from kriging interpolation

8 8 Digital Terrain Models derived from SRTM data and kriging Correlation with field data Table 1 shows the number of observations and correlation coefficients (R 2 ) between kriging and field data, bicubic interpolation and field data and kriging and bicubic interpolation. Table 1: Correlations coefficients between different interpolation methods and field data Interpolation Methods Number of observations R 2 Kriging and field data Bicubic interpolation and field data Kriging and bicubic interpolation As in the visual analysis of the models generated, the scatter plot of the field data with the data simulated by both interpolation methods used (Figures 4, 5 and 6) showed a slight improvement of the data treated with geostatistical techniques. The model generated by kriging presented a slightly superior correlation than the method of bicubic interpolation, with correlation values of and at 1% significance level. The similarity between the two methods can also be verified by the high correlation coefficient among them, at 1% significance level. In fact, according to Diggle et al (2002) and Diggle et al (2003), when working with regular samples and with interest limited to on the dot predictions, this similar behavior is justified due to the use of total neighborhood. Figure 4: Scatter plot for correlations between bicubic interpolation and field data

9 Conclusions 9 Figure 5: Scatter plot for correlations between kriging and field data Figure 6: Scatter plot for correlations between bicubic and kriging interpolation Conclusions In their original form, the SRTM data present a strong limitation to detailed terrain modeling, due to their low spatial resolution and the incorporation of objects on the landscape surface that mask the real aspects of the relief. They must also be treated to remove very discrepant values or out liers that can interfere in the performance of the slope algorithms, contaminating the really valid information. Interpolation by kriging and by the bicubic interpolator improved spatial resolution of the original data from 3 arcsec to 1 arcsec. The data obtained by kriging were more efficient in softening the artificial features and other objects on the surface of the terrain, and also in generating derived

10 10 Digital Terrain Models derived from SRTM data and kriging products such as slope thematic mapsthe slope classes derived from the DEMs were better simulated in more mountainous areas. Considering the similarity in the performance of both interpolation methods, the decision to use one of them should be based on the presence or absence of non relief features in the terrain, such as edifications, forest remnants within grazing lands and/or deforestation in areas occupied by high canopy vegetation. In such cases kriging is recommended because of its capacity to softening these noisy features. When this is not a problem, the bicubic interpotator is easier to be used. References Cambardella, C. A.; Moorman, T. B.; Novak, J. M.; Parkin, T. B.; Karlen, D. L.; Turco, R. F.; Konopka, A. E Field-scale variability of soil properties in central Iowa soils. Soil Science Society of America Journal, Madison, Vol. 58, No. 5, pp Diggle, P. J.; Ribeiro Jr, P. J.; Christensen, O. F An introduction to model based geostatistics. In: Jesper Möller. (Org.). Spatial statistics and computational methods. Springer Verlag, Vol.173, pp Diggle, P. J.; Ribeiro Jr, P. J Bayesian Inference in Gaussian model based geostatistics. Geographical And Environmental Modelling, Vol. 6, No.2, pp Instituto Nacional de Pesquisas Espaciais INPE SPRING 4.2 São José dos Campos, CD ROM. Golden Software Surfer Version 6.01 Surface mapping system. Golden: Golden Software, Inc. GS+ Geostatistical for Environmental Sciences Version Beta, Professional Edition, Plainwell, Gamma Design Software. Östman, A Quality control of photogrammetrically sampled Digital Elevation Models. Photogrammetric Record, Vol.12, No.69, pp Research Systems Inc Environment for Visualizing Images ENVI Version 3.6. Colorado: Boulder, p. Valeriano, M. M.; Carvalho Júnior, O. A Geoprocessamento de modelos digitais de elevação para mapeamento da curvatura horizontal em microbacias. Revista Brasileira de Geomorfologia, Vol.4, No.1, pp Valeriano, M. M Modelo digital de elevação com dados SRTM disponíveis para a América do Sul. INPE: Coordenação de Ensino, Documentação e Programas Especiais (INPE RPQ/756), São José dos Campos, SP. 72p.