PollnSar forest studies


Based on forest canopy height inversion theory, the height of ambiguity (HoA) PolInSAR data has an important influence on the final inversion results. HoA reflects the height
change caused by an interference phase change of 2π, with low forests requiring smaller
HoA and taller forests requiring larger HoA; in contrast, multibaseline PolInSAR can effectively solve this problem. Multibaseline PolInSAR has the advantage of more baseline
combinations within the same observation unit relative to single-baseline data. Among
these combinations, the best baseline needs to be selected to invert the forest height. Based
on the RVoG model, the distribution area of the complex coherence within the complex
plane is approximately elliptical; 

accordingly, the baseline that best fits the assumptions
of the RVoG model can be determined among several baseline combinations considering
factors such as the coherence separation, coherence magnitude, and coherence region
shape. In previous studies, we compared the differences in forest height inversion accuracy
between baseline selection methods using the RVoG model and found that the results of
baseline selection via the product of average coherence magnitude and separation (PROD)
method were the most satisfactory [22,23,36,37]. In this study, we used the PROD method
to select baselines (Equation (4)), using the product of coherence separation degree and
average coherence amplitude as the judgment criterion; when the product of the coherence separation degree and coherence amplitude corresponding to the baseline reaches its
maximum value, it is more consistent with the RVoG model hypothesis.
PROD = absγH − γL × absγH + γL (4) 

where γL denotes the complex coherence near the surface.
2.4. Error Source Analysis of Underestimation and Overestimation in the RVoG Model
2.4.1. Analysis of the Error Sources of Overestimation for Low Canopy
The RVoG model relies on polarized interferometric features to estimate forest canopy
height from PolInSAR data. However, temporal decorrelation effects are not considered
in this model, and the contribution of temporal decorrelation has an important impact on
forest parameter estimation in real situations. Therefore, two distinct temporal decorrelation processes can be introduced in the RVoG model: γTV, which denotes the temporal
decorrelation coefficient associated with volume, and γTG, which denotes the temporal
decorrelation coefficient of ground scatter [38,39], as shown in Equation (5):
γ(ω) = e
γvγTV + γTGm(ω)
1 + m(ω)
Remote Sens. 2022, 14, 6145 6 of 27
According to Equation (5), the total temporal decorrelation depends on the groundto–volume magnitude ratio (m(ω)), 

which defines the relationship between the overall
temporal decorrelation and the ground–volume magnitude ratio. Thus, areas of low
vegetation with low forest depression and a high ground-to-volume magnitude ratio tend
to be severely affected by temporal decorrelation. In contrast, taller vegetation areas with
more forest depression and lower ground–to-volume magnitude ratios tend to experience
less impact from temporal decorrelation. When the temporal baseline is relatively short
(less than one hour), the surface scatterers on the ground surface can be assumed to be
constant, i.e., the dielectric constant does not change, and γTG = 1. 

Thus, the most common
temporal decorrelation contribution of forests is wind-induced leaf oscillation.
The distribution of the volume coherence (γv-obv) and the ground phase (ϕ0) in the
unit circle are indicated by red dots in Figure 1 when there is no temporal decorrelation.
Considering the effects of temporal decorrelation, volume coherence is more severely
affected by this issue, especially in the case of low forests. With an increase in the temporal
decorrelation factor of volume scattering (γTV), the volume coherence (γv-obv) shifts to
γvγt-obv in the direction of the center of the unit circle [20,21], causing the ground phase
estimated by the RVoG model also to shift (yellow dots in Figure 2), at which point the
ground phase calculated by the RVoG model is expressed by ϕ0-bias. Figure 2 shows that
the volume and ground phases are misestimated as a result of the effects of temporal
decorrelation, which leads to an increase in phase center height of the volume coherence
and ultimately leading to an overestimation of the forest height.

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