The methods and results of this paper suggest that measurements of X-band phase-height are potentially an indicator of tropical-forest structure and AGB change. The efficacy of using X-band in tropical forests with interferometry will be discussed below, as well as the use of phase-height from InSAR. Future improvements to the study described here follow.
4.1. X-Band Interferometry for Tropical-Forest Structure and Biomass
It has long been thought that X-band signals would not penetrate the tropical forest sufficiently to sense AGB much above 30 Mg-ha
]. Because interferometry involves phase, it has been suggested that interferometry, even at higher frequencies, has more of a “height perception” [34
]. A simple way to envision the gains by using phase is to imagine that the forest is a nearly impenetrable layer. If radar only sees the top few cm, say, power measurements will be the same if that impenetrable layer is displaced vertically by a few meters. However, if the nearly impenetrable layer is raised by 1 m, the InSAR phase-height will change by 1 m. InSAR is sensitive to the spatial origins of the return radiation, and this is the big difference between interferometry and traditional power-based radar. The origins of return radiation—whether from InSAR or LiDAR [35
]—bear on AGB estimation. In fact, the X-band signal does appear to penetrate, yielding a vertical diversity of returns. Although not used in this paper, X-band coherence should decrease as plot AGB goes up, if there is penetration. Coherence was shown to decrease with increasing AGB for a subset of the plots in this study [10
Signals attenuate more at higher frequencies principally because the absorption by water increases with frequency [36
]. However, as frequency goes up, the ability of the signal to penetrate holes in the medium increases. Thus modeling suggests that an X-band signal appears to be able to penetrate 50 cm holes e.g., [37
], even though it may be severely attenuated by vegetation in its path. The inspection of TanDEM-X data suggests that the tropical-forest signal at X-band is consistent with hard, attenuating targets and significant gaps, allowing more penetration than previously suspected [38
4.2. Using Phase-Height to Measure Tropical Forest Dynamics
The time evolution of phase-height was chosen for AGB-rate estimation. It was chosen because phase-height is close to the radar-power-averaged mean canopy height, which, in turn, is plausibly connected to profiles of the density of scatterers, as detailed in Section 2.3
. Phase-height was chosen in part because the median 1.3-m RMS scatter about a linear or logistic model is smaller than errors attained using other height metrics with InSAR alone, as detailed below.
Phase-height is one of two observations from interfermetric SAR. Coherence, the normalized amplitude of the InSAR cross correlation in (1), is the other. Coherence has been used along with phase-height in simple models—e.g., Random Volume Over Ground (RVOG)—to estimate forest height, extinction, and underlying topography [7
]. Forest height RMS’s of RVOG height about LiDAR had values of 2 m in boreal forests, 2–4 m in tropical forests when used in conjunction with LiDAR, and >5 m for InSAR alone in tropical forests [42
]. In [17
], 3–4 m RMS’s for forest height were demonstrated with (3.5 m) and without (4.3 m) LiDAR in temperate forests. TanDEM-X phase-height, in addition to its correspondence with MCH and density profiles, produces lower RMS’s than most of the height estimates arrived at by modeling. This study investigated a monitoring scenario with the temporal frequency of Figure 5
, and therefore focused on “InSAR-only” phase-height rate monitoring, which motivated the focus on the high-performing phase-height for dense temporal measurements. This work initiates a thorough understanding of phase-height for change measurements, and begins to ask whether that might lead to approaches for monitoring dynamics that are complementary to model approaches such as RVOG. The RVOG performance might be improved if there were more frequent HV (horizontal send, vertical receive) polarization data, and simultaneous, baseline acquisitions. The RVOG attempts to date with TanDEM-X have used only the dominant HH and VV signals at one baseline per epoch, and this could be part of the reason for the poorer performance. It could also be that the RVOG model best estimates structure for more penetrating frequencies, such as L-band, for which ground returns will contribute more polarimetric diversity, and thereby lower the errors on height estimates.
4.3. The Performance of Phase-Height and AGB Rate and Future Enhancements
All estimates of the performance of phase-height and AGB rates for measuring slow change are based on a 3.2 year observing period, with 32 observations, as in Figure 5
. An indication of the phase-height rate performance is the array of formal error bars in Figure 7
. Recall that these errors result from phase-height errors, which had an added component to account for unmodeled scatter. The average formal error is 0.27 m-yr
with a standard deviation of 0.15 m-yr
. The scatter of phase-height rate about the
line in Figure 6
provides another approach to assessing phase-height rate error. The 1.2-m-yr
scatter of InSAR phase-height rates about LiDAR RH90 rates can be interpreted as the 1-yr error in phase-height rate (assuming LiDAR errors are much smaller than those of InSAR). Assuming a time interval
dependence of the rate error estimate, an error estimate of 0.21 m-yr
is derived for a 3.2-yr interval, which is of the order of the formal error bar based on the phase-height fit alone. Similarly, the performance of AGB-rates from the array of error bars in Figure 10
is indicated by the average error of 1.9 Mg-ha
with a standard deviation of 2.2 Mg-ha
. From an average phase-height rate error of 0.27 m-yr
, with an average conversion factor of 7, an AGB-rate error estimate of about 1.9 Mg-ha
results, equal to the rate error above. A source of systematic error in the phase-height rate is in the correction derived from the two buildings. The correction of 0.45 m-yr
was the average of 0.5 and 0.4 m-yr
of the two buildings. A phase-height systematic error of about 0.05 m-yr
can be assumed in the phase-height rate, which, multiplied by the average conversion factor of 7, gives a possible AGB-rate systematic error of ≈0.4 Mg-ha
. In the future, many buildings or ground control points could be sought to drive this error lower.
The AGB-rate error of 1.9 Mg-ha
is based on the scatter about a linear or logistic phase-height fit and does not account for important systematic errors in the conversion from phase-height rate, including model assumptions in (10)–(12). The largest systematic effect in AGB-rate is the choice of
in (11). The green curve in Figure 10
argues for a higher
to bring the low-AGB red points closer. The study which generated the green line did not use the same plots as in this study, nor was it done at the same general epoch. Other studies mentioned in Section 3.4.2
. A range of 1–2 seems plausible. The black curve of Figure 9
, based on cleared areas in this study, suggests a 30% increase in the conversion factor, and hence all AGB-rates. In general, there are many alternatives to the treatment of the conversion factor in (10). The density function, for example, in (11) could be some other function of
and not a power law at all. Differential fieldwork, on so-called “permanent plots” with tagged trees, could suggest other functional forms for
, including values for
. The scatter of the red points about the dashed line of Figure 9
is 0.3 Mg-ha
, which, when multiplied by the average phase-height rate (from Table 1
) of 0.5 m-yr
yields a 0.15 Mg-ha
systematic effect. This scatter is in part due to the error in measured AGB of 25% [24
]. In looking up a plot’s AGB/
, a 25% error will be made in the AGB argument of (13). This translates to a 15–25% error in AGB/
Another source of systematic error is the treatment of the square-bracket term in (12). It was assigned an average value of 0.85, with a standard deviation of 0.05, based on modeling attenuation and a random volume. Using this value of 0.85 therefore constitutes a 6% systematic error. The permanent-plot fieldwork could help to model this term as a function of AGB, and apply the functional form of the term without having to resort to just an average value.
Most systematic errors would take the form of overall scale factors. Given that all the systematic effects (except for assignment of ) cause <1 Mg-ha-yr errors, the AGB-rate error from the error bars or LiDAR comparison of ≈2 Mg-ha-yr quoted here is plausible, but probably an underestimate by 1–2 Mg-ha-yr.
The best indicator of the error is a comparison to field estimates of change, as mentioned repeatedly. In fieldwork done in 2010 and 2013, there were a few plots repeated, but not tagged, so AGB errors were about 25%, as noted above, and therefore too large to be an indicator of truth AGB-rate. We never intended to re-measure the 2010 plots and that is why they were not marked. The comparison to external reports mentioned just below Table 2
shows that all approaches, in Tapajós, Costa Rica, and Panama, get the same order of secondary-forest and primary-forest change [19
Estimates of the performance of phase-height for measuring jumps, or abrupt disturbance, entail errors in the epoch of the event and the magnitude of the phase-height change. From Figure 5
and Monte Carlo error analysis, the epoch and magnitude of disturbance can be determined with about 1 month and 2 m accuracy, respectively. All of the 8 jump events, 2 of which are shown in Figure 5
, were seen in Landsat images, with temporal resolution of about 1 year. The ability to establish a 1-month window for clearing events seems a strength of phase-height measurements, and will be of considerable use to REDD+ mitigation activities.
On the data acquisition side, an improvement could be to use the same
for each epoch. The model calculations leading to Figure 4
suggest that even with extremely asymmetric radar power profiles, only a 0.6 m difference arises between MCH and InSAR phase-height. This 0.6 m could be contributing to the RMS phase-height scatters in 5, but it seems unlikely as the MCH-
comparison was a worst-case result for the volume calculation of (7). It is also possible that pathological asymmetries could result from adding ground contributions to the model in (7). In one variant of the analysis, extremely large height ambiguities of 250 m were removed without appreciable difference in phase-height rate. It does appear that phase-heights from similar
exhibited some clumping in plots like those of Figure 5
. If, in the future, all
s were the same, this worst-case RMS contribution would drop to 0.1 m for the phase-height scatter.
Although the revisit intervals and accuracy of current TanDEM-X measurements is sufficient to detect the epochs of observed jumps to within about a month, the error estimates above for measuring growth or gradual degradation of 2–4 Mg-ha-yr or more apply to a 3.2 year period. The average ratio of the magnitude of estimated AGB slope to slope error bar is 2.9. Assuming a time-span error dependence again, almost a factor of two accuracy would be lost in going to a 2-yr delivery period. This factor of two could probably be recouped by using 1 ha sample instead of 0.25 ha of this study.