Classification 3.4.1
For a uniform land cover class on flat terrain the backscatter level γ0 has a mean 0
and a stochastic variation depending on speckle and textural characteristics. This is usually described with a probability density function, which is used in classification procedures or biophysical parameter estimation procedures. In case there is a significant incidence angle range between near and far range and the incidence angle effects cannot be ignored, this is usually described by a modulation of 0
as 0
= 0
(θi). When, in addition, slope effects cannot be ignored the modulation can be
described as 0
= 0(θi,αr,αaz). This modulation is class and polarisation dependant
and can be modelled as described in the previous two sections. Several approaches to handle slope effects can be followed. Since the polarisation, incidence angle and the two slope angles are known, the only unknown is the land cover class. Land cover class in this context should be understood in its relation to its slope modulating behaviour. With respect to the theory introduced three fundamentally different situations exist:
(i) The terrain is flat. For example, a coastal plain with many different wetland classes falls in this category. In this case a single-model for slope modulation, any model, or no model at all, would be adequate.
Chapter 3
(ii) The terrain has significant slopes, but all land cover on the slopes has the same modulating behaviour. Land cover on flat parts of the area may have different behaviour. In this case a single-model would still be adequate. Often, in case of densely forested terrain, this is Model 1.
(iii) The terrain has significant slopes, but not all land cover on slopes has the same modulating behaviour, just like the situation in the Rupununi as described above. In this case only a multi-model approach would be appropriate.
Situations 1 and 2 can be handled straightforward. Situation 3 is more complicated and can be handled in two different ways. Suppose the objective is to make a land cover map and for each class a slope modulation model has been determined (cf. the procedure outlined in Section 3.3). Then, in case probabilistic classification methods are used, such as Markov Random Field classification, the classification can be done directly. Therefore, in this case, in principal, there is no need to remove slope effects from the image. However, the difficulty is that the slope correction models are based on samples of the relevant land cover classes, which are very hard to delineate on the original image because of the slope effects (as in Figure 3.3A). It would be much easier to make this delineation on the transformed image (as in Figure 3.3C) but this image cannot be made before all slope modulation models are determined. The strength of the methodology proposed in this paper is that the slope modulation is described as a two-step approach. After the first step, i.e. the normalization N1 (or
N2), slope effects are mitigated strongly and, for some classes, even absent (as in
Figure 3.3B). The first step is easy to apply, and samples for the development of the models for the second step of the slope modulation (M1 or M2) can be obtained much
easier.
When the slope modulation models are determined the land cover classification can be made. To remove the slope effects from the radar image itself the following approach based on stratification in feature space is suggested. All land cover classes that occur on flat terrain only, such as wetland classes, can be ignored. The remaining classes should have a low degree of overlap in feature space. This is best done after application of Model 1, since it reduces the size of land cover clusters in feature space. Note that the alternative, i.e. Model 2, may give much less reduction (as shown in Section 3). For the example shown in Figure 3.3C the flat savannahs could be ignored and a boundary in HH-HV feature space was drawn between the forest cluster and the woodland cluster. A simple approach would be to apply Model 3 for forest for all pixels that lie on the forest side of this boundary and to apply Model 3 for woodland for pixels at the other side of the boundary. Since there is a small overlap in feature space (i.e. after applying Model 1), and to avoid the introduction of artefacts, a transition zone was designed with a width of ±0.35 dB. In this transition zone a weighted mixture of Model 3 for woodland and Model 3 for forest was applied. In case such stratification cannot be made (e.g. when the overlap
Multi-model slope correction of SAR images in complex terrain
56
is too high) the feature space could be extended (e.g. with an optical image). In case all slope modulations can be removed from the image, the classification can be made in a much simpler way.
For the Fiji test area a simpler stratification procedure was applied based on the HVHH backscatter ratio only. This stratification, at exactly the same levels for the transition zone, would also be appropriate for the Rupununi case.
In summary, there are two classification approaches. (a) No removal of slope effects using class statistics modulated by models of the type N1M1(θi,αr,αaz) or
global removal of slope effects with a single-model such as Model 1 (or N1) using
class statistics modulated by models of the type M1(θi,αr,αaz). (b) Multi-model slope
effect removal (when this is possible) using class statistics derived from the multi- model transformed image, which have little or none dependence on the angles θi, αr,
αa. The latter method is somewhat different because the image transformation
procedures may introduce artefacts but, on the other hand, subtle landscape ecological patterns that would otherwise be obscured by slope effects may now became visible. This actually is the case in Figure 3.3C, where patterns in the woodlands landscape become more pronounced. Both multi-model methods give considerable improvement over the single-model method. In a follow-on paper this will be addressed explicitly and these two multi-model methods will be compared.
Biomass estimation 3.4.2
Another type of application of the multi-model approach is the improvement of biomass estimation. A simple example will be given first. Suppose the HV backscatter level is used to estimate biomass, for example as described for PALSAR by Mitchard et al. (2009). When a single-model is used to account for slope effects Model 1 may be the most appropriate choice, since it is near perfect for closed forest. Only a multi-model approach can account for all slope effects the landscape comprises both closed and open types of forest. This is illustrated in Figure 3.3D where the difference between the single-model and multi-model HV images are shown. This difference, only prominent in the woodlands, is the remaining error present in the HV backscatter level. Next, suppose that the same relationship between biomass and HV backscatter exist as given by Mitchard et al. (2009; Figure 3.2), i.e. an approximately 1.34 dB backscatter increase when biomass level doubles. Then, using Eq. 3.11b, on the facing slope, the biomass would be overestimated by 21.6% at a +25° range steepness angle (for a 0° azimuth steepness angle). On the back slope the underestimation is 39.7% at a -25° range steepness angle (at 0° azimuth steepness angle). For example, when the biomass is 50 ton/ha the single- model estimation could deviate between approximately 30 and 60 ton/ha. Similar effects may occur for any open forest type where the relation between backscatter level and biomass is linear. When biomass levels go up, and consequently the canopy closes, the relation is less steep, or even may become ‘saturated’, the errors are less or absent. At the same time Model 3 would become more similar or identical to
Chapter 3
Model 1. In other words, for the single-model approach, in the biomass range where backscatter is most sensitive to biomass variation, the largest errors occur. For P- band this would be at a higher biomass range (Hoekman & Quiriones 2000). Carbon monitoring systems focus on accurate estimation of biomass change, rather than elimination of small systematic errors. In this context it is important to note that the overestimation in range at facing slopes reduces when biomass increases, because the forest becomes a more ‘pure’ volume scatterer. Consequently, the biomass increase is underestimated for the single-model approach. Vice-versa, biomass increase on back slopes is overestimated. A simple technique to quantify how well single or multi-model approaches eliminate slope effects is to compare images taken from different directions (see also Goering et al. 1995). For PALSAR this could be observations from ascending and descending mode (nearly East and West looking at Equator). These should be near identical for all land cover types on steep slopes.