Interferometry for Forest Studies
Keywords: Interferometry, Forest, Mapping, Forest Biomass, Forest Height
Several studies have shown the potentialities of repeat-pass interferometry for the extraction of DEMs over temporally stable terrains or for the detection of small terrain movements. The interest in interferometry as a tool to study forests is more recent -. The objective of this paper is 1) to analyse the relations between interferometric data and forest parameters over a well known site, 2) to interpret the underlined physical phenomena using a theoretical model, and 3) to discuss on the influence of environmental and temporal conditions on the results.
Test-sites and Datasets
The reference test site is the Landes forest, located in South-Western France. It is the largest plantation forest in France, constituting nearly one million hectares on flat topography. This artificial forest is almost totally formed of maritime pine (pinus pinaster) and is managed in a consistent fashion, which ensures the canopy to be homogeneous.
The ground data consist in a biomass map which provides information about location and age of more than 50 stands of maritime pine, covering about 20 ha each. The age of these stands ranges between 2 and 50 years, while the corresponding biomass is between 5 and 150 tons / ha. Clear cuts and agricultural fields are also present in the area. Other parameters such as tree densities and dendrometric information are also available. Interferometric data consists of 3 interferometric couples based on ERS-1 SLC images acquired in 1991 and processed by the CNES. The characteristics of the interferometric data are summarized in Table1.
An alternative test-site is chosen in a tropical environment, at Selatan, South Sumatra, Indonesia. This site comprises a mix of primary forest, plantations and deforested areas. Concurrent data consists of a SPOT XS image of the area acquired within one month of the ERS images.
Two tandem (ERS-1/ERS-2) and two 35 days (ERS-1 and ERS-2) interferograms are available over the area. Interferometric data has been processed by CRISP.
Table 1 : Characteristics of available interferometric data.
An accurate interpretation of the phase information contained in the interferometric data would need coherent electromagnetic modeling. Until now, the development of coherent models for such natural medium is very limited. Most of the existing models for radar backscatter of forests are based on the Radiative Transfer Theory which cannot be used to interpret the phase information. However, some insights on the dependency of interferometric data to forest parameters can be derived from the these theoretical models. This section summarizes the four-layer Radiative Transfer (RT) model developed at MIT for the modeling of pine forest  which is used in this study.
The four layers (Fig. 1) include a crown layer, a trunk layer, an understory layer, and a ground interface. Forest canopy and ground surface characteristics are provided by experimental measurements. The Kirchhoff approximation is used to compute the scattering from the ground modeled as a random rough surface. The trunk is modeled as a tilted circular cylinder, branches and needles are modeled as circular cylinders where finite cylinder approximation is applied. The scattering properties of structured pine trees are taken into account in the model by incorporating the branching model  into the phase matrix of the RT equation: the crown is modelled as a 4-scale cluster constituted of trunk, primary branches, secondary branches and needles. The vector radiative transfer equation for the specific intensity in each scattering region is of the form :
where the Stokes vector contains information regarding field intensity and phase relation of the two orthogonal polarisations and is defined as :
In (2), the subscripts h and v represent the horizontal and vertical polarisations, respectively. The bracket < > denotes ensemble averaging over the size and orientation distributions of scatterers and is the free space impedance. The extinction matrix represents the attenuation due to both scattering and absorption, and can be obtained through the optical theorem in terms of forward scattering functions. The phase matrix characterizes the scattering of the Stokes vector from direction into direction. The phase matrix can be formulated in terms of the scattering functions of the randomly distributed discrete scatterers.
Figure 1: Radiative Transfer Approach
The complex degree of coherence of the two co-registered complex image values s1 and s2, is given by:
where is the degree of coherence and the phase difference between the two signals.
Degree of Coherence
Fig. 2 presents the variations of the coherence versus stand age for the 3 interferometric sets. High temporal coherence is obtained for clear cuts and open fields whereas it decreases with stand age.
Figure 2: Variations of the degree of coherence with stand age
Fig. 3 shows the result of theoretical modeling, where different scattering mechanisms at C-band, VV and 23° of incidence are presented.
Figure. 3: Decomposition of scattering mechanisms derived from theory described in 
For clear-cuts and very young stands, the backscattered signal results mainly from the soil contribution. As vegetation grows, this high contribution from the soil is attenuated by the crown layer, and the backscattering from the crown increases. Consequently, three distinct regions can be defined. For very young stands, the soil contribution is dominant in the total signal (region 1), for older stands (3-12 years in the case of the Landes forest), backscattered signal is a sum of ground and crown contributions (region 2), for larger biomasses (> 12 years), most of the backscattered signal comes from the crown layer contribution (region 3).
In terms of degree of coherence, bare surfaces present a high degree of coherence, if they do not undergo any modification in their characteristics (geometry, dielectric, vegetation regrowth) between the two acquisitions. Volume scatterers such as needles or branches are more sensitive to structure variations due to vegetation growth or wind effect. In the case of repeat-pass interferometry, these scatterers have a high probability to move between acquisitions. Thus the volume scattering from vegetation corresponds to a low degree of coherence. The degree of coherence, as a function of forest age or biomass, can be interpreted using the knowledge of the scattering mechanisms as follows. In the region where the soil contribution is dominant (region 1), the degree of coherence is high. On the other hand, the region where most of the backscatter comes from the volume contribution (region 3) shows a low degree of coherence. In the intermediary region (region 2), the degree of coherence decreases with stands age/biomass, with a slope depending on soil/vegetation parameters.
The overall coherence of sets A and C is shown to be lower than coherence of set B. This could be the result of two effects: (a) a decrease of the degree of coherence as a function of time interval between acquisitions as shown in  and (b) a drop of coherence due to the strong precipitation (34 mm) which occured on October 15. Lower coherence of A and C compared to B observed over clear cuts can in addition be explained by changes in the remaining vegetation cover (growth of herbaceous, cleaning of a stand after a cut) or by strong modifications of the roughness state (by harrowing or plough). For long intervals between acquisitions, the degree of coherence obtained over an area can reach the lowest stable values when the time period is sufficient to statistically integrate all possible (non anthropic) temporal changes.
As a consequence, the degree of coherence between two separate acquisitions can be a good discriminator between forests and bare surfaces (or surfaces with low vegetation cover). A comparison with the intensity of the backscattered signal of ERS-1 as forest / non-forest discriminator can be made. At C-band, the intensity of backscattered signal from bare soil surfaces depends on the soil parameters (moisture, roughness). Consequently, bare soil surfaces can present a large range of responses (Fig 4). These possible variations of the soil responses may impede the forest / non-forest discrimination because of the possible confusion between some vegetated and non-vegetated areas. On the contrary, the degree of coherence of a bare surface is in most cases higher than the degree of coherence characterizing forested areas, and this independently of the soil moisture and roughness parameters.
Figure 4: Impact of soil parameters on backscattered intensity
Fig. 5b shows a map of forest / non-forest obtained by thresholding the degree of coherence of A and B interferometric sets (5a for set A). The resulting map is in good agreement with the forest map established from ground data. White areas are ground surfaces which did not change between the two extreme acquisition dates (15 oct / 2 dec). Black areas are forest stands characterized by a low correlation. Areas in grey are fields or stands which correlation state has changed. This could have been caused by plough, harvest (on agricultural fields), growth of herbaceous or cleaning of stands.
Figure 5: Map of (a) coherence of set B
Concerning the study of young forest biomass, in the case of the Landes forest, the characteristics of the underlying ground and vegetation do not differ much from one stand to another, thus reducing the dispersion of the degree of coherence. Inversion of the degree of coherence into young forest biomass for monitoring is then possible.
In the case of the tropical test site, the forest environment is drastically different. The comparison of a tandem and 35 days interval interferogram shows that the latter is useless to discriminate vegetated from non vegetated areas (Fig. 6b-c). In particular, the quick growth of vegetation over former deforested surfaces brings a fast temporal change of target areas. A much shorter time interval is necessary between acquisitions to minimize this effect.
The analysis of the tandem interferogram concurrently to the SPOT image of May 1996 (Fig. 6a) shows that under these environmental conditions, the degree of coherence can be helpful in discriminating heavy vegetated areas (plantations and forests) from sparsely covered surfaces. A more thorough study on the possibilities of discriminating other classes of vegetation (primary forest, different kinds of plantations, deforested areas) using a combination of intensity and interferometric data has been undertaken by CRISP .
Figure 6: (a) SPOT image of the test-site.
Previous studies  have shown the possibility to discriminate forested from non-forested areas in tropical environment using multi-temporal intensity ratio information. A first qualitative comparison between this technique and the use of the degree of coherence of a tandem interferogram shows similar results (Fig. 7). A quantitative analysis of the two algorithms in terms of classification accuracy and effective final resolution is to be undertaken.
Figure 7 (a) Degree of Coherence ERS-1 / ERS-2 96/04/12 -
The interferometric phase shift between forest and ground responses is related to the integrated height of the vegetation scatterers. Thus, penetration of the wave into the medium must be taken into account. Consequently, the interferometric estimated height is an " effective height " function of the real height of the trees and of the penetration depth (Fig. 8).
The Landes forest test-site is well suited to the study aimed at retrieving
the forest height for the following reasons:
Since the phase difference rms decreases with an increase of the degree of coherence, the measurements were extracted from the interferometric set B, which presents the highest overall coherence. The larger baseline of B is also well suited to reducing the rms-height errors .
Figure 8: Determination of canopy height from interferometry
The general topography of the test-site is flat (as a rule, the slope is less than 0.5%). In addition, we chose to restrict the study to a small area around a clear cut which was considered as the ground reference level. The mean value of the phase difference is extracted from each stand and the corresponding height difference is computed. This leads to the interferometric measured heights displayed in Fig. 9.
We can observe on Fig. 9 that the variation of the mean value of the phase difference estimated from interferometry is an increasing function of the stand age. However, discrepancies are observed between the estimated and the actual tree heights.
Figure 9: Estimation of tree height from interferometry
Discrepancies exist between estimated and actual heights, as the measured height is not the height of the top of the trees, but the height of scatterers distributed over a thickness equal to the penetration depth, and is smaller than the actual height. One way to correct these estimated stand heights is to use theoretical modeling to compute the penetration depth of the wave into the medium.
For each stand under study, the penetration depth d defined by:
(where P(z) is the transmitted power at a depth z below the top of the crown layer, and where the conventions are those of Fig. 8 ) is estimated using the modified radiative transfer model described above. In the case of the Landes forest, young stands are characterized by a high density of trees and a thin crown layer. As the trees grow older, the crown becomes thicker, but the tree density decreases as a consequence of thinning practice. As a first approach, the tree crown is modeled as homogeneous layers; a young stand will be represented by a thin slab of homogeneous medium, an older stand will be represented by a thicker slab of homogeneous medium with a lower extinction coefficient, as depicted in Fig. 10.
Figure 10: Variations of penetration depth with tree stand age
In the case of the Landes forest, and for ERS configuration, the resulting penetration depth increases with the age of the trees. A corrected estimated height, sum of the interferometric derived height and of the simulated penetration depth is shown to be a good estimate of the actual height of the trees (Fig. 9).
The remaining errors could be reduced (a) by using interferometric pairs with a larger baseline to reduce rms height dependence on rms phase difference, and (b) by enhancing the overal degree of coherence using interferometric pairs with a smaller time interval.
If the different penetration depths are not available, is should be noted that a classification of relative forest heights is still possible using phase difference information alone. For a given forest, the relation between interferometric height from ERS and real height can be derived once and used (as a look up table) to monitor the forest height variations.
This study has underlined the relations between the interferometric degree of coherence and the forest age (or biomass). Coherence has been shown to be efficient to discriminate forest areas from clear-cuts in a temperate forest environment. For a tropical forest environment, good results are also obtained if the time interval between acquisitions is short enough. In a specific case, the use of phase difference has been undertaken to retrieve forest stands heights. Optimal interferometric pairs with a smaller time interval (tandem acquisitions) and a larger baseline should (a) enhance the use of the degree of coherence to discriminate young forest stands and (b) permit a more quantitative use of the phase difference to extract forest height.
However, some important improvements are to be made:
To process further into the study of the relations between interferometric data and forest parameters, theoretical modeling must be improved to account for coherent interactions.
The work is carried out under CNES/CESBIO Contract n°833/2/95/CNES/171. The interferometric data have been provided by CNES/QTIS. Nicolas Floury receives a grant from CNES and Alcatel Espace.
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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry
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