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Comparing effects of different sizes of aggregation on spatial structure of remotely sensed data

Yu-Pin Lini*, Tung-po Teng2
1Association Professor, Department of Landscape Architecture
Chinese Culture University
55, Hwa-Ken Rd. Yangming Shan, Taipei, Taiwan 11114
Tel: 011-8862-2862-6433 Fax: 011-8862-2861-7507
E-mail:[email protected]

2Graduate student, Graduate institute of Geography
Chinese Culture University, Taiwan

Abstract
Remote sensing data can be aggregated to evaluate, model and monitor in environment and ecology from local to lager scaled region. The effects of aggregated data sometimes also display on the output of models or the results of monitoring. Meanwhile, variograms provides a model of the spatial correlation of data within a statistical framework, including spatial covariance functions and a means of quantifying the commonly observed relationship. Therefore, this study performed isotropic and anisotropic experimental variograms in 12.5m, 25m, 37.5m, and 50m resolutions NDVI data from a Spot image at three different land-cover sites that were an almost pure grass, a mixed grass and shrub, and a broad forest within the yangmingshan national park in Taiwan to evaluate the impact of aggregation on the spatial structure at different land-cover sites. The results indicated that the experimental variograms of the NDVI data in the above four different resolutions displayed identical spatial structure in both isotropic and anisotropic directions at the pure grass site. At the mixed grass and shrub site the NDVI experimental variograms in the 12.5m, 25m, 37.5m, and 50m resolutions displayed a similar spatial tendency but different spatial variations. The experimental variograms of NDVI of these four resolutions at the broad-forest site displayed different spatial patterns and spatial variations in both isotropic and anisotropic directions. The experimental variograms of the 25 m and 50 m resolutions of the broad forest site displayed a similar tendency. Moreover, the 12.5 m and 37.5 m resolutions NDVI data of the broad forest site exhibit a similar pattern on their variograms.

1. Introduction
Remote sensing data can be aggregated to evaluate, model and monitor in local or global environmental and ecological study. However, the aggregations of data increase each pixel size of data and reduce the number of pixel in a sampling site. Moreover, these aggregated data are often referred to having a coarser spatial resolution (Bian and Butler, 1999). The effects of aggregated data sometimes also display on the output of models. Therefore, many scientists recently focused on these data aggregation effects to evaluate different aggregation methods.

The normalized different vegetation index (NDVI) calculated by remote sensing data can be used to evaluate monitor the spatial and temporal vegetation change. Meanwhile, the NDVI is preferred to the simple index for global vegetation monitoring (Lillesand and Kiefer, 2000). Moreover, NDVI data are useful to identify land cover categories through the seasonal variation of greenness (Loveland et al, 1991 and Cihlar et al. 1996). In biophysical remote sensing, greenness can be measured in terms of the normalized different vegetation index (NDVI) that uses radiances or reflectances from a red channel around 0.66 and a near-IR channel around 0.86μm (Lo and Faber, 2000).

A great deal of collected environmental data, high spatial continuity, indicate that points that are closer in given direction display higher correlation values than those that are separated farther (Lin and Change, 2000). The above spatial structure analysis may be affected by aggregated data. Variography is usually performed by determine the estimated variogram of the data collected in time and space. Variogram provides a model of the spatial correlation of data within a statistical framework, including spatial and temporal covariance functions (Lin and Change, 2000). Not surprisingly, these models are defined in terms of the correlation between any two data points separated by either spatial or temporal distances. Variogram has been applied in many fields such as soil pollution, air pollution, hydrology, ecology, and remote sensing. These techniques have also recently been applied to characterize the spatial variability of pollutants and environmental monitoring.

This study performed isotropic and anisotropic experimental variograms in 12.5m, 25m, 37.5m, and 50m resolutions NDVI data from a SPOT image at three 0.1407 km2 different land-cover sites that are an almost pure grass, a mixed grass and shrub, and a broad forest within the Yang Ming Shan National Park in Taiwan to evaluate the impact of aggregation on the spatial structure at different land-cover site.

2. Materials and Methods
In order to analyze the aggregation effects on different resolutions the 12.5m, 25m, 37.5m, and 50m resolutions NDVI data calculated from the aggregated SPOT images at three different 0.1407 km2 land-cover sites that are an almost pure grass, a mixed grass and shrub, and a broad forest within the Yang Ming Shan National Park in Taiwan. These level 10 SPOT images were from the center for space and remote sensing research of the national central university in Taiwan. The three selected areas are displayed in Fig 1. The aggregated NDVI maps are displayed in Fig. 2. Moreover, the experimental variograms of NDVI data were calculated within GS+ (Gamma Design, 1995).

2.1 Greenness Index
High reflectance in the near-infrared part of the spectrum, together with chlorophyll absorption in the red wavelengths, is typical, green vegetation (Gates et al. 1965, O’neill, 1996). Vegetation areas will generally yield high value for either index because of their relatively high near-IR reflectance and low visible reflectance (Lillesand and Kiefer, 2000). The NDVI expresses the difference between the incident radiation reflected by photosynthetically active pigments in green leaves, and that portion reflected on the near-infrared part of the spectrum (Jelinski and Wu, 1996). NDVI is defined as:

where NIR and RED are wavelengths in the reflective infrared (~0.65-0.90μm) and red (~0.60-0.65μm) bandwidths, respectively (Quattrochi and Luvall, 1999). Thus NDVI is bounded ratio that varies between -0.1 and 0.1, with only active growing vegetation having positive values typically between 0.1 and 0.6 (Jelinski and Wu, 1996).
2.2 Spatial Structure
Variography is initiated by the grouping of the available pair-values into a number of lags or distance classes in accordance with their in between distances. Variograms provide a means of quantifying the commonly observed relationship where by samples close together will tend to have more similar values than samples farther apart. The variogram ?(h) is defined as:

g(h)=(1/2)Var[Z(x)-Z(x+h)]
where h is the lag distance separating pairs of data points, Var is the variance of the argument. Z(x) is the value of the regionalized variable of interest at location x, and Z(x + h) is the value at the location x + h.

An isotropic experimental variogram g*(h), is given by:

where g*(h) is variogram for interval lag distance class h, n(h) is the number of pairs separated by the lag distance h.

An anisotropic experimental variogram is defined as:

where q is the angle of a principal axis.

For anisotropic analyses the principal axis is the base axis from which the offset angles are calculated. Offset angles are 0°, 45°, 90° and 135° clockwise from the base axis (Gamma Design, 1995). The axis of 0° is defined from the north-south axis. The points aligned sufficiently close to one or another of these angles with 22.5° tolerance are included in the anisotropic analysis for that angle.

The main features of a typical variogram are three-fold: (1) range, (2) sill, and (3) nugget effect. Range is the distance at which the variogram reaches its maximum value. Paired samples whose in-between distance is greater than the range is uncorrelated. This means that range is regarded as a measure of the spatial continuity of the investigated variable. Sill, as the upper limit of the variogram which tends to level off at large distances, is a measure of the population variability of the investigated variable generally, the higher the sill, the greater the variability in the population. The nugget effect is exhibited by the apparent jump in the variogram at the origin, a phenomenon that may be attributed to the small-scale variability of the investigated process and/or to measurement errors.

3. Results and Discussion

3.1 Statistics concerning Aggregation sizes
The aggregation processes were based on the 12.5m, 25m, 37.5m, and 50m NDVI resolutions of three different land cover sites. Table 1 summarizes the descriptive statistics relating to the aggregate results. Table1 presents the statistics on the aggregation of the pure grass, mixed grass-shrub and broad forest sites. The statistics, mean, standard deviation, minimum and maximum, of the NDVI data were almost identical to those of the above four resolutions at the pure grass site as listed in Table 1. Meanwhile, The statistics, mean, standard deviation, minimum and maximum, of the NDVI data were different to those of the above four resolutions at the mixed grass-wood and wood sites as listed in Table 1. Comparison revealed the statistics of the aggregated NDVI data in the above four resolutions at the pure grass site display more consistently than those at the mixed grass-shrub and broad forest sites.

3.2 Experimental Variogram
Experimental variograms of the above four resolution NDVI at the three different land cover sites were calculated at same active lag and lag interval. The experimental variograms are isotropic experimental variograms displayed in Fig. 2. Fig. 2(a) displays the experimental variograms of the aggregated NDVI data at the pure grass site in 12.5m, 25m, 37.5m and 50m resolutions. These experimental variogram show that the spatial structures of the above four NDVI resolutions displayed almost identical pattern in isotropic formation. The experimental variograms of the 25 m and 50 m resolutions of the wood site displayed a similar tendency. Moreover, the 12.5 m and 37.5 m resolutions NDVI data exhibit a similar pattern on their variograms, as illustrated in Fig. 2(b). Meanwhile, the four resolutions of NDVI data at the mixed grass-shrub site displayed different tendencies and variations on their experimental variograms, as displayed in Fig. 2(c). These results illustrated that the aggregation size effect on the isotropic spatial structure varies on different land covers in this study area.

The anisotropic formation analysis results illustrated that the experimental variograms of the four resolutions on the pure grass site at 0o, 45o and 135o directions displayed a similar tendency, as presented in Figs. 3(a), (b) and (c). Similar to the isotropic formation analysis Figs. 4(a), (b) and (c) indicated that the experimental variograms at 0o, 45o and 135o directions on the 25 m and 50 m resolutions of the broad forest site displayed a similar tendency. Moreover, on this broad forest site the 12.5 m and 37.5 m resolutions NDVI data exhibit a similar pattern on their variograms at 0o, 45o and 135o directions, as illustrated in Figs. 4(a), (b) and (c). Meanwhile, the four NDVI resolutions data at the mixed grass-shrub site displayed different tendencies and variations on their experimental variograms at 0o, 45o and 135o directions, as displayed in Figs. 5(a), (b) and (c). These results indicated that the aggregation size effect on the anisotropic spatial structure varies on different land covers in this study area.

4. Conclusion
This study has demonstrated isotropic and anisotropic spatial structures in 12.5m, 25m, 37.5m, and 50m resolutions NDVI data from a Spot image at three different 0.1407 km2 land-cover sites that were an almost pure grass, a mixed grass and shrub, and a broad forest within the Yang Ming Shan National Park in Taiwan to evaluate the impact of aggregation on the spatial structure at different land-cover sites. The results indicated that the experimental variograms of the NDVI data in these four different resolutions displayed identical spatial structure in both isotropic and anisotropic directions at the grass site of Yang Ming Shan National Park. At the mixed grass-shrub site of this study area the NDVI experimental variograms in the 12.5m, 25m, 37.5m, and 50m resolutions roughly displayed a similar spatial tendency but different spatial variations. The experimental variograms of NDVI of these four resolutions at the broad-forest site of this study area displayed different spatial patterns and spatial variations in both isotropic and anisotropic directions. The experimental variograms of the broad forest site in the 25 m and 50 m resolutions displayed a similar tendency. Moreover, the 12.5 m and 37.5 m resolutions NDVI data exhibit a similar pattern on their variograms. However, the aggregation effect displayed significantly on the mixed grass-shrub and the broad forest sites in this study.
5. References

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  • Quattrochi, D.A. and J. C. Luvall, 1999,Thermal infrared remote sensing for analysis of landscape ecological processes: methods and applications, 14, Landscape Ecology, pp.577-598.
  • Figure 1. Locations of Study area

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    Figure 2 Experimental variograms of (a) the pure grass site; (b) the broad forest site; (c) the mixed grass-shrub site.

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    Figure 3 Experimental variograms of the grass site at (a) 0°; (b) 45°; (c) 135°.

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    Figure 4 Experimental variograms of the broad forest site at (a) 0°; (b) 45°; (c) 135°.

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    Figure 5 Experimental variograms of the mixed grass-shrub site at (a) 0°; (b) 45°; (c) 135°.