Assessment of JERS-1 SAR for monitoring secondary vegetation in Amazonia: II. Spatial, temporal, and radiometric considerations for operational monitoring

While the role of Synthetic Aperture Radar (SAR) in operational tropical forest monitoring has yet to be defined, it is nevertheless a critical technology for improving our understanding of deforestation and secondary vegetation in the tropics. In order to understand the role of this technology in operational monitoring a systematic evaluation, relative to other existing technologies of its performance is required. In this paper we evaluate the spatial, temporal, and noise constraints of JERS SAR data for mapping and monitoring biomass of secondary vegetation in Rondonia, Brazil. Our results indicate that the variability in stand estimates of biomass is high and that the source of the majority of the variability is not from speckle and the intrinsic texture of the secondary vegetation but likely due to differences in environmental conditions resulting in differential background scattering properties. Multitemporal analysis significantly improves biomass estimates to the point where it is possible to map changes in biomass. Slight reductions in the variability in estimates of normalized radar cross-section greatly improve biomass estimation.


Introduction
Land use within the tropical rain forest biome has a large impact on the net ux of carbon from the biota and is an important component of the global carbon cycle. Conversion of forests to pasture and agriculture results in a net source of biotic CO 2 to the atmosphere, while forest fallow and abandonment into secondary vegetation represent a net sink of biotic CO 2 . The magnitude and timing of these uxes are a function of the extent of the conversion, the fate of the cleared lands, and the carbon stocks of the pre-and post-disturbanc e landscape. Understanding the processes of deforestation and abandonment will improve estimates of the magnitude of the net biotic ux of carbon from the tropics. Accurate, quantitative estimates of deforestation and secondary vegetation extent, rates of deforestation, land abandonment , and forest regeneration are critical for understanding the global carbon cycle. Remote sensing provides the only approach capable of providing this information accurately and timely, over large areas, at a uniform sampling scheme, and repeatedly over time. Optical remote sensing techniques have proven useful for quantifying deforestation and detecting secondary vegetation, but they have been hampered by persistent cloud cover in some regions and by a lack of sensitivity to biomass. There is a clear need for additional techniques to supplement the role of optical sensors for tropical forest monitoring. One most promising alternative to optical is Synthetic Aperture Radar (SAR) because it is not aVected by clouds and oVers some sensitivity to biomass. Ultimately, these two remote sensing tools ought to be working in a synergistic fashion to provide the best characterization of deforestation, abandonment and secondary vegetation.
Numerous studies have focused on the use of remote sensing for mapping the extent, temporal dynamics, age, and biomass of secondary vegetation in the tropics (e.g. Lucas et al. 1993, Mausel et al. 1993, Foody and Curran 1994, Alves and Skole 1996, Steininger 1996, Luckman et al. 1997a,b, 1998, Nelson et al. 2000. Multitemporal Spot XS and Thematic Mapper (TM) data have been used to create maps of secondary growth age (Lucas et al. 1993, Alves and Skole 1996, Steininger 1996, Nelson et al. 2000 and persistence Skole 1996, Nelson et al. 2000 ). Vegetation indices using red and near-infrared re ectance saturate for separating forest secondary vegetation after a few years (Sant'Anna et al. 1995). However, vegetation indices that utilize mid-infrared and near-infrared data (Boyd et al. 1996, Steininger 1996, Nelson et al. 2000 and texture-based classi ers (Palubinskas et al. 1995, Nelson et al. 2000 do not saturate as quickly and are better for detecting secondary vegetation in the tropics. Landsat TM spectral properties diVer among the successional stages of secondary vegetation in the tropics (e.g. Mausel et al. 1993, Moran et al. 1994, Steininger 1996, Sohn et al. 1999. Over time, re ectance properties of secondary vegetation become indistinguishable from those of mature, undisturbed forest (Mausel et al. 1993, Boyd et al. 1996. Results from several studies using Landsat TM data indicate that secondary vegetation stands can be spectrally separated into four to six distinct age classes, with the oldest class remaining distinct from mature forest for # 14-15 years (Boyd et al. 1996, Steininger 1996, Sohn et al. 1999. Neural net classi cation techniques have also been used to map secondary vegetation and estimate stand age with single and two-date Spot XS and Landsat TM spectral and textural data (Kimes et al. 1999, Nelson et al. 2000. C-band radar data are less useful than L-band data for mapping biomass of re-growing forest (Rignot et al. 1997, Saatchi et al. 1997, Yanasse et al. 1997. Single polarization (HH ) L-band radar data have been used successfully to map deforestation and secondary vegetation and estimate ranges of biomass accumulation from radar backscatter (Luckman et al. 1997b(Luckman et al. , 1998 and phase coherence (Luckman et al. 2000). There appears to be a general agreement that radar backscatter increases with increasing biomass and saturates at some biomass level. Estimates of the saturation point of L-band data from tropical forests vary from 40 t haÕ 1 (ImhoV 1995) to 60 t haÕ 1 (Luckman et al. 1997a) . Ranson and Sun (1997 ) and Rignot et al. (1995) have shown that P-band backscatter can estimate biomass for forest stands up to 150 t haÕ 1 (temperate forest) to 200 t haÕ 1 (tropical forest), respectively.
The baseline for an operational forest monitoring system necessitates complete forest inventories as frequently as every 5 years (Ahern et al. 1998). Analysis of Landsat cloud cover metadata indicates that persistent cloud cover in the tropics would severely limit the ability to map annual changes using Landsat data. For example, from 1990 to 1994 less than 50% of the 228 Landsat World Reference System II footprints covering the Brazilian Amazon was covered by a low cloud cover (<20%) Landsat TM image. Clearly, due to persistent cloud coverage, complete optical coverage is diYcult, therefore, attempts at measuring rates of deforestation and secondary vegetation would bene t from SAR imagery, thereby ensuring complete coverage. Numerous studies have demonstrated that SAR data can be used to detect deforestation (e.g. Rignot et al. 1997, Saatchi et al. 1997. A systematic evaluation of errors in estimating deforestation and secondary vegetation relative to estimates derived from optical remote sensing platforms is needed to understand the role of radar in the context of operational forest monitoring. This evaluation should focus on the performance of multidate SAR data for operational forest monitoring. While it is clear that SAR must play an important role in an operational tropical forest monitoring systems (cf. GOFC Strategy Document), the role has yet to be de ned. Knowing the level of performance of SAR for mapping land cover change is critical, especially for regions shrouded by persistent cloud cover where SAR may be the only viable alternative to optical sensors. While several studies have indicated that both optical (e.g. Skole et al. 1994, Steininger 1996 and SAR (Luckman et al. 1997a,b, Curran andKuplich 1999) data can be used to characterize diVerences in secondary vegetation, new research needs to focus on how diVerences in the rates of forest aggradatio n can be quanti ed to improve our understanding of the controls on carbon sequestration across the landscape.
In Salas et al. (2001, this issue) we examined the spatial and temporal variability of mean normalized radar cross-section, called sigma naught (or s°), across a chronosequence of secondary vegetation stands and clearings. In order to evaluate the potential of using multitemporal JERS-1 SAR data for quantifying diVerences in rates of recovery of secondary vegetation, we applied the biomass density retrieval scheme presented by Luckman et al. (1998) and evaluated the sensitivity of using multitemporal JERS-1 SAR data for biomass density estimation. The temporal and spatial stability of the mean stand s°estimates were highly variable due to diVerential eVects of changes in environmental conditions and variability of intrinsic heterogeneity (texture) of the stands. In this paper we develop a series of statistical models to evaluate, in an operational context, what level of changes in biomass density, herein called biomass, one might be able to identify with JERS-1 SAR data for a given con dence level. These models assess the impact of multiple JERS data takes and size of the vegetation secondary vegetation stands on the coeYcient of variation of our biomass estimates. Performance of estimating biomass is evaluated based on the ability to quantify the presence and magnitude of biomass change over time.

Methods
In this section we provide a summary of the methods used in our analysis. Section 2.1 contains a brief description of how the individual secondary vegetation stands were mapped and how their ages were calculated. Sections 2.2-2.5 provide the details of the JERS data pre-processing, extraction of secondary vegetation stand level s°statistics, and the biomass density model used, respectively. Section 2.5 describes the statistical methods and models used. The text provided in these four sections is paraphrased from our companion paper in this special issue, where more details on the image processing methods can be found. Our analysis is based on using multitemporal TM data for mapping age and size of secondary vegetation stands and multitemporal JERS data for generation of s°statistics for a site in Rondonia, Brazil ( gure 1).

T M analysis of secondary vegetation stand age and size
Annual co-registered Landsat TM from 1989 to 1998 were classi ed using an unsupervised (ISODATA) clustering technique, followed by a manual, knowledgebased assignment of the 45 clusters into forest, cleared, natural non-forest, water, cloud, cloud shadow, and secondary vegetation classes. Areas of water, cloud, cloud shadow, and natural non-forest were removed. These 10 classi cations were then combined to create land cover changes map using post-classi cation change detection. Initial analysis of the magnitude of the number of land cover change transitions between 1989 and 1996 and their spatial patterns revealed a highly dynamic landscape. For this study, we segmented the stands of secondary vegetation into two sets of age classes based on whether or not we knew when the areas were initially cleared from forest and how long the area remained as non-forest prior to secondary growth formation. Contiguous areas with the same land cover transition sequence over the 10-year period were identi ed and labelled using an eight-neighbour clump algorithm. A 3×3 low-pass lter was then used to identify edge pixels, which were removed to minimize the impact of mis-registration between the multitemporal SAR data and the TM-based secondary vegetation stand map. All stands smaller than 0.75 ha were subsequently removed from the analysis to minimize the variance of the mean stand s°due to speckle (see discussion below). We estimate the overall accuracy of the stand age maps to range between 72% and 85% (Salas et al. 2001, this issue). The location of the study area and an example of the stand age map are provided in gure 1. Areas that have not been deforested appear tan in the age map in gure 1, with the remaining colours representing various ages, as of 1998, of clearings and secondary vegetation stands.

JERS-1 SAR data pre-processing
We analysed eight L-band (1.275 GHz), HH polarized, SAR from the Japanese Earth Resources Satellite 1 (JERS-1). Table 1 lists the eight level 2.1 products (threelooks with 12.5 m pixels) used for this study. These data were obtained through our participation in NASDA's Global Rain Forest Mapping Project (see Rosenqvist et al. 2000 for details on GRFM). These images were co-registered automatically using image cross-correlation and converted to normalized radar cross-section (s°) values in dB with the following formula: where F is the NASDA provided correction factor ( 68.5 dB for the images nos 1-7 and 68.3 dB for image no. 8). We applied an empirical linear correction, derived from a transect of primary forest, to account a ramp in s°with range (Leckie 1990, Ranson andSun 1994). The range ramp across this transect varied from 0.4 to 1.5 dB (see table 1). While, theoretically, this linear empirical correction may not properly model incidence angle eVects for non-forested areas across the landscape or correct for non-linear eVects of system noise with slant range, we assume that the residual noise correlated with range would be a second order eVect due to the small range in incidence angles across our study area. We then cross-calibrate d these data to normalize their gain diVerences. The cross-calibratio n oVsets (table 1) were derived from mean and coeYcient of variation statistics of s°from 228ha of mature forest.

Extraction of stand s°statistics and con dence limits
Speckle and the intrinsic spatial heterogeneity (texture) of vegetation impacts our ability to accurately estimate the mean s°from stands of secondary vegetation (Rignot and Kwok 1993). The estimate of coeYcient of variation caused by speckle and intrinsic texture can be estimated by: where N is eVective number of looks (ENL) and V t is the variance due to texture (from Luckman et al. 1998), following Oliver (1991, and is calculated as where (SDmÕ 1) is the actual coeYcient of variation (CV ) within the stand. Vieira (1996) estimated N for a single JERS-1 three-look pixel to be 2.8. Using the estimated CV we can estimate the 95% con dence limits in dB by where n is the number of uncorrelated pixels in the stand. Note that (4) ignores all sources of variation except texture and speckle. An improved con dence limit, but still accounting only for texture and speckle, would be 10 log A 1±t 0.05,nÕ 1 CV 1 We used level 2.1 data with a spatial resolution of 12.5 m. However, since JERS resolution is 18 m, there is a signi cant amount of correlation between neighbouring pixels that must be accounted for in calculating our con dence intervals. Using these equations we calculated mean s°with the 95% con dence limits for each of the 182 stands of secondary vegetation. Shimada (1996) estimated N for the NASDA level 2.1 three-look product to be 2.1. The discrepancy with the Vieira estimate could be due to diVerences in the SAR processor used to create the products. If N is closer to 2.1 then our overall con dence limits would be wider than reported here by a factor inversely proportional to the size of the secondary vegetation stand. Luckman et al. (1998) developed a semi-empirical model for estimating biomass density of regenerating forests with JERS-1 radar s°data and asserted that the model is generalizable to other regions in the Amazon. We tested their model for quantifying broad diVerences in biomass of our secondary vegetation stands. Inverting their model to estimate biomass (B) from s°, expressed in linear units, yields

Biomass density model
where a, b, c are constants that were empirically derived from eld data from Tapajos region in Para State in the Amazon. We used the following values a=0.170, b=0.053, and c=2.146 (taken directly from Luckman et al. 1998) for our calculations. Unfortunately, when s°a, the estimate produced by (5), or equivalently by (4), is unde ned, since the model saturates with respect to s°, not biomass density. This situation occurred frequently in all the scenes examined. Unfortunately, the model does not provide a natural or saturated biomass density level, but some value must be speci ed. To provide estimates in these cases, we used which is slightly larger than the largest estimate calculated using (5), or 143.1 t haÕ 1.
Using these equations we then calculated the biomass for all 182 stands of secondary vegetation for each of the JERS images listed in table 1.

Statistical methods and models
Given the availability of multiple, contemporaneous images, con dence limits can be calculated for s°(in linear units), s°(in dB), and biomass in two diVerent ways. First, the full-width (upper minus lower limit) of the 95% con dence limits for s°(in linear units) may be calculated as 2E=2t 0.05,n SD ã n with the corresponding width for s°in dB calculated using (4a). The full-width for biomass may be calculated by substituting s°+E and s° E into (5) or (5a) as appropriate, and taking the diVerence. Note that this procedure speci cally assumes that the all contributions to the variability in s°and biomass, other than those from speckle and texture, are negligible. Alternately, given J scenes, we might consider calculating the full-width of the 95% con dence limits for s°in linear units as 2t 0.05,JÕ 1 times the standard deviation of the J estimates of s°about their arithmetic mean. Con dence limit widths for s°i n dB and biomass may then be calculated as before. This procedure has the advantage that all sources of variation between scenes are accounted for, not just speckle and texture. Substantial diVerences between con dence limits calculated using (6), (4a), and (5a) in turn, and those calculated from the observed temporal variability in the estimates, must be regarded as evidence that speckle and texture are not the major controlling factors in the variability of the estimates. Con dence limits were calculated for both methods using only those 139 stands which were present in all four of the 1996 scenes, since con dence limits based on only two or three scenes would be more variable.
To quantify the contribution of factors other than speckle and texture to the variability in observed s°, we performed a series of x2 tests on the s°from the four 1996 scenes. Since s°(in linear units) for a polygon is estimated as the mean s°for all pixels in the polygon, and since the number of pixels in a polygon is generally large, it follows directly from the Central Limit Theorem that the estimated s°is approximately normally distributed about the true value. The quantity SE2 s°= SD2 n provides an unbiased estimate of the variance of s°, under the null hypothesis that the variance of s°arises from texture and speckle only. Recalling that a sum of squared, normally distributed variables is distributed as chi-squared, we may test the null hypothesis by comparing x2= ae ij to the critical values of x2 for IJ I degrees of freedom. In (8), i indexes I stands or polygons, and j indexes J scenes. Equation (7) is calculated separately for each polygon and scene. Stand area aVects the value of chi-squared through the relationship between stand area and n, which aVects SE2 s°.
In equation (8), each stand is treated as an equally weighted observation. The quantity ŝ ß i , is the least-squares mean of the sß ij values, which minimizes x2. We calculated x2 for all 179 stands that were represented in more than one of the 1996 images combined, and for each stand separately. The combined x2 provides a powerful overall test of whether the observed variation between images could have arisen from texture and speckle alone. The x2 values for each stand individually provide a direct measure of the magnitude of the observed temporal variation relative to the expected temporal variation under the null hypothesis.
Following the results of the x2 tests, we further examined the behaviour of the coeYcient of variation of the biomass predictions, based on the observed intertemporal variability in predicted biomass. We further examined the implications of the magnitude of observed coeYcients of variation for biomass predictions, for the coeYcient of variation of estimates of change.

EVects of factors other than speckle and texture
Con dence limits based on speckle and texture only, and con dence limits based on observed inter-temporal variation, are shown for s°(in linear units), s°(in dB), and biomass in gure 2. First, considering the con dence limits based on speckle and texture alone, it is notable that many stands exceeded the 'worst-case' scenario presented by Luckman et al. (1998, p. 135 ) of full-widths of 1.18 dB. In part, this is because 22% of the stands considered are less than the 1 ha size used by Luckman et al. (1998) in their assessment. The spatial scale of land-clearing and conversion activities is small in this region of Rondonia. Analysis of the distribution of secondary vegetation stands indicates that over 60% of the stands were smaller than 5 ha ( gure 3). On an area-weighted basis, over 45% of the area in secondary vegetation was in stands smaller than 5 ha. Only one stand had estimates of textures variance, calculated using equation (3), higher than the maximum value of 0.2826 reported by Luckman et al. (1998). Regardless of the inter-temporal variability that may or may not be reduced by better signal-to-noise ratio (SNR), texture and speckle impact on con dence limits will be high for a majority of the secondary vegetation stands in this region. Turning to the con dence limits based on observed inter-temporal variability, the diVerence in magnitude of the two sets of con dence limits is striking, regardless what variable is considered. Although the eVect is somewhat exaggerated by the degrees of freedom used for t in (4a) and when evaluating the variability directly, most of the eVect arises from the sheer variability in the images. As shown by Salas et al. (2001, this issue), this inter-temporal variability does not arise from consistent variation from one scene to the next, which could be reduced by a diVerent crosscalibration method. Indeed, despite careful cross-calibration, 125 of 139 stands show Figure 3. Size class distribution of secondary vegetation stands, ranging from 0 to 1 ha to larger than 11 ha. Percentage of each class with respect to total area in secondary vegetation is also plotted. Note that there are many more stands in the smaller range (1-4 ha) than above 8 ha. Approximately 50% of the area in secondary vegetation are in stands less than 5 ha. Stand sizes were calculated from multitemporal TM analysis (see Salas et al. 2001, this issue).
variability exceeding the 1.18 dB threshold identi ed by Luckman et al. (1998) when all sources of variation are considered. In practice, this translates into con dence limits for biomass that approach the range of biomasses calculated using (5) and (5a), or 0-146 t haÕ 1. Con dence limits of such a great magnitude do indicate quite clearly that for many stands the biomass is almost completely undetermined by a single image. The diVerence in magnitude between the variability arising from speckle and texture alone, and the actual variability, is most clearly described by the overall x2 test for all stands using the 1996 data (x2=1897.1, d.f.=506, p<0.001). The ratio of x2 to d.f. indicates that the observed variance among scenes is, on average, 375% of that expected from speckle and texture alone. Clearly, other factors are contributing to the diVerences between scenes for many stands. Accounting for additive temporal eVects that are consistent across scenes reduces x2 somewhat, but not to a practically signi cant degree (x2=1807.7, d.f.=503, p<0.001). Such temporal eVects include any environmental or sensing variations which aVect all stands across a scene in a consistent, additive fashion. Given the relative unimportance of a consistent temporal eVect, we must consider that this extraneous variability arises from some temporally variable factor, such as environmental conditions or sensor calibration, diVerentially interacting with the characteristics of the stands of interest. Seasonal diVerences in surface conditions can in uence s°values diVerently for pastures, secondary forests, and primary forest, with pasture exhibiting a large (>2 dB) seasonal variability, secondary vegetation exhibiting a smaller (~1 dB) variability, and no eVect on primary forests (Hashimoto et al. 1997 ).
Examining the x2 values for individual stands ( gure 4) allows us to gauge the consistency of the extraneous variability, relative to the variability introduced by speckle and texture. It is noteworthy that 76 of 179 stands showed x2 values less than the expected value (equal to the number of scenes in 1996 in which the stand was present, minus one), clearly indicating that the extraneous variability impacts some stands and not others. The lack of clear association between individual-stand x2 values and the least-squares s°value might suggest, at rst, that the extraneous variability is not associated with mean s°, and therefore unrelated to biomass. However, recall that x2 measures variability relative to the variability imposed by speckle and texture, which is correlated with mean s°and biomass. A more careful consideration suggests that the absolute magnitude of the extraneous variability, when it does come into play, is associated with the same factors that govern texture. There is clearly a relationship between texture and stand biomass due to changes in canopy structure during development (Luckman et al. 1997b) . Since mean s°from stands with higher biomass will be less susceptible to variations in environmental condition, such as soil moisture and dielectric properties of sub-canopy vegetation, the magnitude of the extraneous variability may be related to biomass.

CoeYcient of variation of biomass predictions
The parameters used in the biomass model were developed using eld data from Tapajos, and tested with data from Manaus. Likely, the model would have diVerent parameters if it were calibrated for our site in Rondonia because of diVerences in site conditions, soil properties, and species composition. Nevertheless, our results and conclusions would not change because of the non-linear relationship between s°and biomass and, therefore, are intended to be relative.
A useful measure of the variability in predictions of biomass is the coeYcient of variation of the predictions, calculated in a straightforward fashion as the standard deviation of the estimates from each scene, rescaled by their mean. The CV is plotted against the mean predicted biomass for each stand in gure 5. A nuisance feature in developing this relationship between biomass and its CV was the presence of s°v alues for which ŝ ß i a. All stands that had at least one estimate where s°a were omitted from this analysis. Fortunately, most of the stands omitted from this analysis were in the biomass range above which JERS-1 data are regarded as unsuitable for biomass estimation (ImhoV 1995, Luckman et al. 1997b, Curran and Kuplich 1999. The stands for which (5a) was unnecessary all lie within this range. For these stands, it is clear that the CV increases with increasing biomass. The solid curve t to these coeYcients of variation is described by CV(%)=6.4983 ã biomass (9) For example, if the estimated biomass of a stand were 10 t haÕ 1, based on a single scene, we would expect that estimate to have a CV of 20.5%. This implies approximate 95% con dence limits of 6-14 t haÕ 1. By contrast, for a stand with an estimated biomass of 25 t haÕ 1, we would expect a CV of 32.5%, implying 95% con dence limits of approximately 9-41 t haÕ 1. Clearly, stands with small biomass are much better resolved-both in absolute and relative terms -than stands with large biomass.

Single versus multitemporal JERS observations for estimating changes in biomass
To the degree that the variability indicated by gure 5 re ects operational success in quantifying biomass, to what degree of accuracy can we quantify biomass diVerences (either from stand to stand within a scene, or within a stand over time)? If a stand imaged at one time has biomass B 1 , estimated with coeYcient of variation CV 1 , and at a second time has biomass B 2 , estimated with coeYcient of variation CV 2 ,the standard error of the estimate of the diVerence will be and the coeYcient of variation of the estimated diVerence will be The situation when estimating the diVerence between diVerent stands at the same time is directly analogous. Using (11), and the relationship between biomass and its CV from a single scene as given in (9), we can plot the CV we would expect to obtain for the change in biomass of a stand, as a function of its initial biomass and percent growth ( gure 6). Several aspects are immediately apparent. First, if a single scene is used at each time of observation, changes in biomass as large as 30% between the two periods cannot be resolved reliably regardless of the initial biomass of the stand. Second, even considering a 100% change or doubling of biomass, a single scene at each time period provides insuYcient information for a reliable resolution unless the initial biomass of the stand is <10 t haÕ 1. For example, if B 1 =10 t haÕ 1 and B 2 =20 t haÕ 1, the CV of the change is 62%, or 6.2 t haÕ 1. The approximate 95% con dence limits on the change would be 10±12.4 t haÕ 1. In other words, using a single scene at each time period, changes in biomass are unlikely to be well-resolved unless the change is very large, or the stand is nearly bare at one of the two time periods.
Fortunately, it is possible to improve on the resolution by using multitemporal images. If J images are available at each time period, then If we can suggest a target value of CV B 2 Õ B 1 for a given change, then we may estimate the required number of scenes as Using (9) as the relationship between biomass and the CV of its estimate, a solution to (13 ) is shown in gure 7. The target value of CV B 2 Õ B 1 is taken as 50%, which is not an overly restrictive value. It implies approximate 95% con dence limits equal to plus or minus the actual change, or a 39 in 40 chance of obtaining the correct sign on the change. With this rather loose de nition of acceptable accuracy, we see that moderate numbers of additional contemporaneou s scenes at each time period do improve accuracy considerably. For example, with a 44-day repeat cycle, it is possible to obtain eight or nine images in a year. That additional information at each time period would allow identi cation of changes as small as 30% of initial biomass in stands with as little as 17 t haÕ 1, and identi cation of a doubling in biomass up to the saturation point.

Impact of noise on estimating biomass
The variability in our mean s°for our stands was higher than could be accounted for due to texture and speckle alone. Potential sources of this variability include system noise, relative calibration errors, and environmental conditions (primarily surface moisture on vegetation and soil moisture). While estimating contributions of environmental conditions is unlikely with a single polarization instrument like JERS, better estimates of the scattering from vegetation alone may be possible with multipolarization sensors. Therefore, in an attempt to quantify impact of improved SNR (in this sense we consider noise all sources variability not due directly to biomass, including environmental conditions, system noise, calibration oVsets, etc.), we modelled the relative bias, coeYcient of variation, and relative RMSE of estimating biomass with a 1.0 dB versus 0.5 dB normally distributed errors of mean stand s°e stimates. The model rst assumes an actual biomass value and calculates the 'true' s°by inverting equation (5), which was then converted to dB. Based on the 'true' estimate of s°we calculated the probability density from our assumed distribution of s°based on our errors (0.5 or 1.0 dB) and then recalculated biomass from the distribution. Numerical integration was used to estimate the expected value of bias (observed-'true' biomass), variance (observed biomass-average biomass)2, and mean squared error (observed biomass -'true' biomass)2. From these we calculated the relative bias, CV, and relative RMSE as percentages. These steps were repeated across a range of biomass values to create gure 8. The results highlight the interplay between stand biomass and potential errors in estimating biomass. The observed positive bias can be explained by the non-linear (sigmoidal ) relationship between s°a nd biomass. A decrease in overall SNR of 0.5 dB would extend the range of biomass where there is little (<10%) bias, lower CV and lower RMSE. Clearly, any improvement in SNR will have a large impact on improving the success of estimating stand biomass given the sensitivity of these estimates con dence limits over the small dynamic range of s°expected for biomass levels below the saturation point.

Conclusion
A statistical analysis of s°statistics from a series of secondary vegetation stands was presented. These statistics were used to model and assess the impact of spatial and temporal variability in estimating stand biomass and changes in stand biomass with single and multidate JERS SAR data. Many of the secondary vegetation stands in this study had con dence limits due to speckle and texture alone that exceeded the 'worst-case' estimate provided by Luckman et al. (1998). While these diVerences are likely due to the smaller stands in this study, the size class distribution of stands across the landscape in Rondonia indicates that much of the secondary vegetation is contained in these smaller stands (<5 ha). Nevertheless, speckle and texture are not the largest controlling factors on the variability of mean stand s°estimates. Extraneous factors, such as natural noise due to changes in environmental conditions, have the largest impact on the variance of biomass estimates. However, this variability due to these extraneous factors does not impact all stands of secondary vegetation, likely due to the presence of a biomass saturation point. The coeYcient of variation of biomass estimates increases with stand biomass. With single data JERS imagery biomass cannot be estimated for most of the stands in this region of Rondonia. Multitemporal observations improve the accuracy of biomass estimates suYciently to enable identi cation of changes in biomass. Given the non-linear relationship between backscatter and above-groun d biomass, a 0.5 dB reduction in extraneous variability would signi cantly improve biomass estimation, especially for levels below 40-50 t haÕ 1.
While it is clear that estimation of biomass from natural systems, like secondary vegetation in the Amazon, with a single polarization L-band SAR is extremely diYcult, it appears feasible to provide the carbon cycle community information useful for improving our understanding of carbon sequestration in secondary vegetation in Amazonia. Improved techniques for estimating contributions of noise will further enhance this application because we then will be able to quantify stand to stand variability due to environmental conditions.