Stein Valley Study Site

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Project
Short Title of Project Brief Outline of Project

Estimating Forest Patterns and Structures from Airborne Digital Remote Sensing Imagery. Using semivariograms and related geostatistical proceedures to develop and test a methodology for automated estimation of forest structural parameters from high-resolution digital images.

Project
Short Title of Project	Brief Outline of Project
Estimating Forest Patterns and Structures from Airborne Digital Remote Sensing Imagery.	Using semivariograms and related geostatistical proceedures to develop and test a methodology for automated estimation of forest structural parameters from high-resolution digital images.

Geostatistics

The study of geostatistics is based on the principle of the regionalized variable which has properties intermediate between a truly random variable and a completely deterministic variable (Matheron, 1963). Many features that have geographic distributions show this type of relationship (Evans, 1972; Oliver and Webster, 1986; Curran, 1988; Woodcock, Strahler and Jupp, 1988), for example, pixel digital numbers (DN) in forested environments. In these environments, there is local spatial dependence expressed in the distribution of DN changes. This property is referred to as spatial auto-correlation, which means that the closer two variables are to each other in space the more likely they are to be related. The problem with variables that exhibit this property is the way in which the change is expressed. The change in the variable is so complex that it cannot be described adequately by any deterministic function (Oliver and Webster, 1986; Davis, 1986; Woodcock, Strahler and Jupp, 1988).

The theory of geostatistics and the concept of the regionalized variable make it possible to define the criteria for an appropriate spatial resolution (Curran, 1988; Atkinson, 1993). More importantly, geostatistical theory can define the nature of the variance in models of ground scenes to actual spatial variation within images (Woodcock, Strahler and Jupp, 1988). The geostatistical measure that describes the rate of change of the regionalized variable is known as the semivariance. Semivariance is measured for a specific orientation and gives a measure of the degree of spatial dependence of the variable along this orientation. The variable measured can be any continuously varying property, for example, elevation, water content, or organic matter. If the spacing between variables along a line is some distance D, the semivariance can be estimated for distances that are multiples of D

where X_i is a measure of the regionalized variable taken at location X sub i and X_i+h is another measurement of the same variable taken at h intervals away. The equation, therefore, represents the sum of the squared differences between pairs of points separated by the distance h. The number of points is n, so the number of comparisons between pairs of points is n-h (Davis, 1986).

The usual way to represent the relationship between semivariance and distance is in the form of a semivariogram, where semivariance is the Y axis and h (distance) is represented on the X axis. Semivariance can be displayed graphically along any orientation. For example, if there was a specific orientation to the data, the semivariance can be measured with respect to that orientation. It is also possible to measure the semivariance with respect to every orientation (referred to as direction 0 or omnidirectional).

Texture is a measure of spatial context and is, therefore, a spatial characteristic of a data set rather than a spectral property. Current digital approaches to image classification have no means of incorporating this important property. In the study being conducted at Simon Fraser University, new methods for measuring and incorporating this type of data as a means of measuring forest stand structure to aid in forest stand classification.

Study Area and Data

Located west of the town of Lytton, BC, the Stein Valley is one of the study sites use in this research. The Stein Valley is a steep-sided valley with the most steeply sloping area occurring within the area of overlap of the three flight-lines. The imagery presented on this page was acquired in the early fall (some of the deciduous vegetation is changing colour). The Stein Valley has a number of physical attributes that make data collection difficult. The valley in the area of overlap is oriented almost exactly east-west resulting in north and south facing slopes. This fact not only controls the distribution of trees in the area (due to different insolation conditions) but the time of day that images are acquired. Slope steepness also causes localized tilt displacement. This type of distortion causes difficulties when the data sets are registered for processing.

The fall data set used in this preliminary study was acquired in the mid-afternoon. Given the time of day, and the season, valuable imagery was lost as it was in shade. The southern facing slope is in full sun while the northern facing slope is in shade. Unfortunately the southern facing slope has a sparse pine forest that is unsuitable for texture analysis. The north facing slope has an old growth Douglas-Fir stand that may be suitable but is in shade. There were, however, several good, usable, datasets acquired during this imaging session.

The data were acquired using 24 mm lenses. The reason for using these lenses is that they allow the acquisition of data with a resolution that approaches orbital satellite data. In this area the angular field of view of these lenses, 121.9° (2 arctan ((Length²+Width²)½/(2 focal length))= 121.9° a super wide angle lense), results in a lot of radial distortion (Figure 3). This causes difficulty when the data are registered. This is primarily because the optical centre of the images are not the same. If the data were acquired with longer focal length lenses the radial distortion would be less.

The three composite figures show how semivariance was measured from the Stein Valley data sets.

The first procedure was to scan the imagery and enhance the contrast using a linear contrast stretch with five percent saturation on the tails of the data.
Select images where the center of the frames are coincident.
Register the images. Select the highest altitude data and register the other altitudes to this data set. Although this is not the optimal procedure for this type of study it is the simplest procedure and is adequate for preliminary analysis. While this procedure does not remove all distortions, it does make distortions present in the original data set similar in all data sets.
Select and extract a transect from all data sets.
Process the data using an exponential variogram model.

Stein Valley, 2500 ft. Altitude
Figure 1. Image of study site 1. Transect is indicated by the white line.
			Figure 1a. Spectral responce along transect from bottom to top of image.
			Figure 1b. Semivariogram modeled for transect at 2500 ft altitude. An exponential model was fitted to the data from the transect. The range is 6.53 and the sill =220.

Stein Valley, 1500 ft. Altitude
Figure 2. Image of study site 1. Transect is indicated by the white line. Figure 2a. 1500 ft image registered to the 2500 foot image.
			Figure 2b. Spectral responce along transect from bottom to top of image.
			Figure 2c. Semivariogram modeled for transect at 1500 ft altitude. An exponential model was fitted to the data from the transect. The range is 6.06 and the sill =630.

Stein Valley, 500 ft. Altitude
Figure 3. Image of study site 1. Transect is indicated by the white line. Figure 3a. 500 ft image registered to the 2500 foot image.
			Figure 3b. Spectral responce along transect from bottom to top of image.
			Figure 3c. Semivariogram modeled for transect at 500 ft altitude. An exponential model was fitted to the data from the transect. The range is 3.06 and the sill =950.

Preliminary Results

The preliminary results of this study are very positive. The results from the geostatistical analysis indicate that the range values seem to be stabilizing at around 6 to 10 metres as the semivariance decreases from 950 at 500 feet to 220 at 2500 feet in altitude. This result indicates that spatial structures in this environment can be adequately characterized by 6 to 10 metre pixels.

In order to deal with some of the difficulties encountered with these data several changes must be made. More attention needs to be placed on the amount of structural control exhibited by the area of interest. In the case of the Stein Valley time of day is important due to the aspect of the valley and longer focal length lenses will be experimented with to lessen radial distortion making registration easier.

References

Atkinson, P.M., 1993. The Effect of Spatial Resolution on the Experimental Variogram of Airborne MSS Imagery. International Journal of Remote Sensing. 14:1005- 1011.

Curran, P., 1988; The semivariogram in remote sensing: an introduction, Remote Sensing of Environment, Vol. 24, pp. 493-507.

Davis, J.C., 1986. Statistics and Data Analysis in Geology, Second Edition. (John Wiley and Sons: New York).

Evans, I.S., 1972. General Geomophometry, Derivatives of Altitude, and Descriptive Statistics, Chorley, R.J. (Ed.) Spatial Analysis in Geomorphology. (Methuen & Co. Ltd.:London.): 17-90.

Matheron, G., 1963; Principles of geostatistics, Economic Geology, Vol. 58, pp. 1246-1266.

Oliver, M.A. and Webster, R. 1986. Semi-Variograms For Modeling The Spatial Pattern of Landform and Soil Properties. Earth Surface Processes and Landforms. 11: 491-504.

Woodcock, C., A. Strahler, and D. Jupp, 1988a; The Use of Variograms in Remote Sensing: I. Scene Models and Simulated Images, Remote Sensing of Environment, Vol. 25, pp. 323-348.

FRBC Funded Research