2.1. Description of the Lowland Savanna Ecosystem
This study is conducted within the lowland areas of Belize (
Figure 1A), which comprise approximately 1754 km
2 of savanna landscape [
36] (
Figure 1B). These areas are the most northern Neotropical savannas [
37], which represent the second most extensive savanna vegetation formation within the America Neotropics [
38]. In this analysis, we focus on mapping the aboveground woody biomass (AGWB) of woody savannas, which are recognized for their importance in carbon sequestration due to the presence of pine trees [
39]. Pine (
Pinus caribaea var.
hondurensis) forms low density wood clusters (10%–~65% canopy cover) within the savanna landscape, while other woody vegetation, such as Palms (
Acoelorrhaphe wrightii) and shrubs (
Byrsonima crassifolia), are often evident and usually scattered through the grass landscape [
40].
Figure 1.
(A) Belize in the region of Central America; (B) footprints of the ALOS PALSAR and the national ecosystems map based on UNESCO classes; and (C,D) the lowland savanna areas in the ALOS PALSAR scenes; light grey areas indicate the extent of protected areas with lowland savannas; RBCMA stands for Rio Bravo Conservation and Management Area.
Figure 1.
(A) Belize in the region of Central America; (B) footprints of the ALOS PALSAR and the national ecosystems map based on UNESCO classes; and (C,D) the lowland savanna areas in the ALOS PALSAR scenes; light grey areas indicate the extent of protected areas with lowland savannas; RBCMA stands for Rio Bravo Conservation and Management Area.
The national ecosystems map of Belize classifies the lowland savannas into three UNESCO classes (
Figure 1C and
Figure 1D). Here, we examine the: (1) short-grass savannas with dense trees or shrubs (UNESCO code: VA2a (1/2)) (
Figure 2A,C); and (2) short-grass savannas with scattered trees and/or shrubs (UNESCO code: VA2a (1) (2)) (
Figure 2B,D). Pine woodlands occur in both of these vegetation zones, and the local density of the tree cover in relation to other shrubs and grasses has until now been interpreted qualitatively as the basis for allocating most savanna land into one or the other of these classes [
41]. The climate in Belize is subtropical to tropical with an average annual precipitation of around 1500 mm in the northern parts of the country and 3800 mm in the south. In
Figure 3, the annual mean precipitation is shown per month using data collected in three weather stations of the Belize National Meteorological Service and a rainfall monitoring product, which is based on derived data from the Global Precipitation Climatology Centre (GPCC).
Figure 2.
Representative photographs of lowland savanna areas with dense trees or shrubs (VA2a (1/2)) (A,C); and sparse trees and/or shrubs (VA2a (1) (2)) (B,D).
Figure 2.
Representative photographs of lowland savanna areas with dense trees or shrubs (VA2a (1/2)) (A,C); and sparse trees and/or shrubs (VA2a (1) (2)) (B,D).
Figure 3.
Illustrating the wet and dry seasonality in Belize; two major precipitation spikes are observed in June and October, while September also appears to be a rainy month.
Figure 3.
Illustrating the wet and dry seasonality in Belize; two major precipitation spikes are observed in June and October, while September also appears to be a rainy month.
2.2. ALOS PALSAR Data
Two fine beam dual polarization (FBD) ALOS PALSAR datasets (Level 1.0) covering approximately 55% (933.46 km2) of the lowland savanna ecosystem in Belize were collected during the wet season in September, 2008 (
Figure 1B, I,II). The radar data that were used in this study included only the horizontal-vertical polarization (HV), because of their sensitivity to biomass found for the same areas used in this study in [
42,
43]. The HV data were pre-processed at Aberystwyth University from raw data to single look complex (SLC) images using the Modular SAR processor in GAMMA software, while a calibration factor of −58.30 decibels (dB) was used. Subsequently, the SLC images were multi-looked and geo-coded to precision images (PRI) using the differential interferometry geocoding module (DIFF and GEO), which is also included in GAMMA. The resulting four look images (pixel spacing ≈ 13 m) were further processed to reduce speckle by aggregating neighbourhoods of adjacent pixels (2 × 2) and arithmetically averaging the radar intensity at the power domain [
42,
43]. The final radar product has a pixel-spacing of 26 m, and data represent the normalized radar cross-section (
), where dB is decibels. The total extent of the lowland savanna has been mapped by previous projects [
36], and that map is used to constrain the biomass mapping from the ALOS data to within the savanna extents.
The total study area is 933.46 km
2 (
Figure 1, C,D) and is comprised of approximately 345 km
2 of lowland savannas with sparse trees or shrubs (VA2a (1/2) (51% of total VA2a (1/2)) and 588 km
2 of lowland savannas with dense trees or shrubs (VA2a (1) (2) (58% of total VA2a (1) (2)).
Although the ALOS PALSAR data were acquired during the wet season, the rainfall estimates of the Tropical Rainfall Measurement Mission (Product 3B42V7) for the radar data acquisition dates (+/− three days) within the study area shows that the mean rainfall is very low in both ALOS PALSAR images (~15 mm/day for Image I and ~9 mm/day for Image II). When comparing these mean precipitation estimates to the mean dry season gauged precipitation data acquired in the two weather stations falling within the ALOS PALSAR image extents (
Figure 3), we have more confidence for using this ALOS PALSAR imagery, which was collected during the wet season for AGWB estimation.
2.3. Biomass Mapping Using ALOS PALSAR and Semi-Empirical Modelling
Biomass mapping was achieved by adapting a forward parametric model, which is based on a semi-empirical water cloud model (WCM) [
42,
43,
44] to derive a mathematical relationship between the backscattered intensity of the radar signal (
), where
pp corresponds to emitted and received polarization of the radar signal and the biomass (AGWB) calculated from ground surveys of 6,457 trees collected over 32.6 hectares of savanna woodlands throughout Belize.
In the WCM, the AGWB is represented as a relatively homogeneous aboveground volume, which consists of canopy components and air [
42,
44]; the canopy components are assumed to be relatively homogeneous spherical scatterers, which mimic a water cloud. Mathematically, the parametric forward model describing the WCM usually takes the form of Equation (1) to perform fitting, non-linear least squares regression and calculation of the empirical coefficients
,
and γ, which are dependent on the structure of the woodlands. The regression equation is then re-arranged to estimate biomass as shown in Equation (2) [
42].
In Equation (2),
represents the total backscattered intensity of the radar signal collected by ALOS PALSAR,
is the fraction of the total backscattered intensity due to radar-vegetation interaction and
is due to bare soil interaction.
Using this WCM (Equation (1)), an AGWB training dataset, which was collected on the ground in four different years, 2006, 2011, 2012 and 2013 (
Table 1), and the ALOS PALSAR imagery (HV polarization), Michelakis
et al. in [
42] undertook non-linear regression analysis to show that the HV intensity of the radar backscatter can be predicted in relation to the AGWB with an
R2 = 0.92 (
Figure 4A).
Figure 4.
(
A) The non-linear regression model fitted (solid line) using the training dataset from
Table 1 and ALOS PALSAR HV imagery; and (
B) the histogram of both aboveground woody biomass (AGWB) datasets (training and external validation); note the zero AGWB points in scatterplot (A), which were collected on the ground using a global navigation satellite system (GNSS) device on areas with no woody vegetation to sample the backscatter in these areas.
Figure 4.
(
A) The non-linear regression model fitted (solid line) using the training dataset from
Table 1 and ALOS PALSAR HV imagery; and (
B) the histogram of both aboveground woody biomass (AGWB) datasets (training and external validation); note the zero AGWB points in scatterplot (A), which were collected on the ground using a global navigation satellite system (GNSS) device on areas with no woody vegetation to sample the backscatter in these areas.
Table 1.
Training and external validation AGWB datasets that were used in the non-linear regression fitting and the validation of the WCM; these datasets are described in [
42].
Table 1.
Training and external validation AGWB datasets that were used in the non-linear regression fitting and the validation of the WCM; these datasets are described in [42].
| | AGWB (tha−1) | Density (Trees ha−1) | BA (m2 ha−1) |
---|
Datasets | Plot size (ha) | Range | Mean | St. Dev. | Range | Mean | SD | Range | Mean | St. Dev. |
---|
Training | 32 × 1 | 0–101.6 | 47.3 | 37.1 | 0–680 | 155 | 171.7 | 0–15.3 | 6.15 | 5.0 |
6 × 0.1 |
Validation | 38 × 0.1 | 1–72 | 39.5 | 19.4 | 20–350 | 145 | 75.1 | 0–11.0 | 5.7 | 2.6 |
Although the satellite data were collected in 2008, the slow growth rate of Caribbean pine, even in better sites in Belize as recorded by [
45] (0.4 cm ≤ dbh ≤ 1 cm), allows us to use these field measurements in the development of the WCM. The semi-empirical model fitted in this study is shown in Equation (3). Using an external validation dataset (
Table 1), AGWB estimates were assessed demonstrating that AGWB can be predicted on the ground with a root mean squared error (RMSE) ~ 13.5 tha
−1, while 80% of the AGWB estimates were found to have an error of less than 20 tha
−1 [
42].
To assess the uncertainty of the AGWB map created using the ALOS PALSAR data and the semi-empirical WCM, an evaluation of the estimation accuracy was conducted using the validation dataset (
Table 1) for the lower biomass range (
i.e., ≤75 tha
−1) and the training dataset (
Table 1) for the higher biomass range (
i.e., ≥75 tha
−1). The training dataset was used for estimating uncertainty in the higher biomass range due to the lack of high biomass observations in the validation dataset. The relative root mean squared error (RRMSE) was separately calculated for seven biomass classes with 15 tha
−1 intervals (
i.e., 0–15, 15–30, 30–45, 45–60, 60–75, 75–90 and 90–105 tha
−1) using Equation (4).
here RMSE and
AGWB are the root mean squared error and the mean observed AGWB within each biomass class.
A concern with the mathematical formulation in Equation (2) is that negative or infinite values of biomass can be predicted [
46,
47,
48]. To constrain estimates to realistic values, any cells with infinite values were assigned the highest value of biomass actually measured in the field (101.65 tha
−1), whilst any cells with negative estimates of biomass were assigned a value of zero. No previous field studies conducted in savanna woodlands in Belize by [
45,
49,
50,
51,
52] have measured AGWB in these savanna woodlands above 101.65 tha
−1, so we feel confident using this value as our realistic upper limit for this case study.
Although a recent study from [
53] has shown that parametric forward models show higher errors than other approaches, there are five reasons that a semi-empirical WCM is employed in this study: (1) The semi-empirical model is grounded in the physical basis of how the backscattered intensity of the radar is expected to interact with vegetation targets in contrast to more statistically driven approaches, such as backward models; (2) the use of non-parametric models, such as machine learning algorithms, could not be implemented in this research, because of the lack of the significant data amounts that are needed (for example, [
54] used more than 50 data samples for biomass mapping using decision trees classifiers); (3) the WCM accounts for the low canopy cover nature of the savanna woodlands (10%–65%) by using a weighting area fill factor
in the vegetation backscatter [
53]; (4) the WCM varies as it interacts with vegetation of different biomass and supplements and extends upon previous quantitative analysis of radar backscatter as a surrogate measure of biomass [
42,
44]; and (5) the biomass estimation results can be comparable to future research using methods that are based on other forward models in contrast to solely statistical approaches.
2.4. Deriving Ground-Based Estimates of AGWB for Two Protected Areas
We used the inverted WCM (Equation (2)) described in the previous section and the ALOS PALSAR data covering two of the country’s largest savanna woodlands (Rio Bravo Conservation and Management Area (RBCMA) and Deep River protected area) to estimate the mean AGWB for the whole protected area extent and compared these with AGWB estimates calculated from previously published data [
50,
52]. These two protected areas are both over 10,000 ha and are typical locations and extents for sub-national scale UN-REDD+ projects [
17].
In RBCMA, Brown
et al. in [
52] estimated mean carbon stock of 13.1 tCha
−1 for approximately 10,000 ha of savanna by developing new allometric equations, which predicted biomass carbon using tree attributes as independent variables that could be easily measured from aerial images. To develop the allometric equations, Brown
et al. used an extensive ground dataset, which was collected by the destructive sampling of 51 pine trees, and then 77 image sample plots were used in three-dimensional very high spatial resolution aerial imagery to assist with the remote measurement of the tree attributes, which were used to estimate carbon stocks. To convert the carbon stock estimation by Brown
et al. to biomass, we multiplied by a factor of two [
55] (carbon is 50% of biomass), calculating a mean AGWB of 26.2 tha
−1 for RBCMA. In Deep River (DR), to estimate AGWB for approximately 3500 ha of savanna woodlands (31.60 tha
−1), we used 62 circular sample plots (0.1 ha), which were not used during the WCM training, and only 18 out of the 62 were used in the external validation of the WCM, in the denser woodland areas originally collected by [
50] to support plans for sustainable timber extraction (
Table 2).
Table 2.
Summary of the plots that were collected in the denser woodland areas of Deep River (DR).
Table 2.
Summary of the plots that were collected in the denser woodland areas of Deep River (DR).
| | AGWB (t ha−1) | Density (Trees ha−1) | BA (m2 ha−1) |
---|
Data | Plot size (ha) | Range | Mean | SD | Range | Mean | SD | Range | Mean | SD |
DR | 62 × 0.1 | 2.25–76.19 | 31.60 | 17.78 | 20–350 | 121 | 70.40 | 0.5–11.25 | 6.15 | 2.54 |
To derive the mean AGWB value for both RBCMA and DR, for each tree, the AGWB was estimated using the allometric equations (Equations (5) and (6)) developed by [
52] in RBCMA, where dbh is the diameter at breast height (1.3 m) and biomass is dry aboveground woody biomass in kilograms. More than 30% (2190 trees) of the field data measurements that are used in this study were collected within RBCMA, and more than 95% of the tree dbh measurements are within the range sampled by [
52] (1–52.4 cm). The AGWB ha
−1 was estimated for each 0.1 ha sample plot by summing the AGWB of individual trees and multiplying the sum by a factor of 10 to extrapolate to the hectare.
Having obtained these “ground truth” estimates of mean AGWB ha
−1 for both protected areas, we then multiplied these up by the area of the RBCMA and the denser woodland areas of DR and compared these totals to those obtained by using a GIS to aggregate cells from the 100-m biomass map within the boundaries of the RBCMA and DR, respectively.
2.5. Classification of Savannas by Protection and Management Type
Approximately 25% of the lowland savannas in Belize are under some form of protection [
36] and have been characterized as Category Ia, II, IV or VI, according to the International Union for Conservation of Nature (IUCN) classification system [
56]. Using information acquired from land managers and published management plans [
50,
57,
58,
59,
60], we examined the influence of land management in various protected savanna woodlands by comparing the biomass quantities predicted by our model. In unprotected savanna woodlands, the possibility of a management plan cannot be excluded. However, it was not possible to acquire management information for these savannas woodlands; thus, the unprotected areas are considered as not managed in this study. To allow the influence of both passive and active management to be explored, as well as the binary “protected-unprotected” dichotomy, we subdivided the study area into three protection and management groups using the information acquired by managers and the published management plans.
Approximately 40 km
2 of savanna woodlands found within the RBCMA and in the Bladen nature reserve were characterized as highly protected and passively managed areas (henceforth, PRPM). These areas have been managed mostly to promote biodiversity [
57,
58,
59,
60], while they have been classified as “strict nature reserve, Ia” and “habitat/species management area, IV” by the IUCN. Similarly, some 118 km
2 of savanna woodlands found in the Manatee and DR forest reserves were grouped as protected and actively managed (PRAM) areas, where timber is extracted sustainably [
50], and both have been classified as “protected area with sustainable use of natural resources, VI” by the IUCN. Further areas, totalling approximately 595 km
2 of savanna woodlands, with no protection designations, were identified as unprotected (UPR) areas. The remaining 185 km
2 of protected areas for which we could not obtain reliable information about their management were not included in this analysis. Using GIS, we then overlaid the new biomass map upon the three forest management groups and calculated the biomass in mean AGWB ha
−1 for each of the three areas.
2.6. Comparing the New Mapping with National Level Carbon Stock Maps from Pantropical Data Sets
To conduct a comparison with our local biomass map (Michelakis biomass estimates henceforth MBE
100), two national-level carbon stock maps were acquired for Belize. These were the pantropical national-level carbon stock dataset (Baccini biomass estimates, henceforth BBE
500) produced by [
17] and the benchmark national carbon data (Saatchi biomass estimates, henceforth SBE
1000) produced by [
18]. Both datasets are stored in a single tagged image format file (*.tiff) representing the aboveground carbon density of aboveground live woody vegetation. These gridded values were predicted using data collected by a range of EO sensors, such as the ICESAT GLAS, MODIS and the Shuttle Radar Topography Mission (SRTM) in non-parametric spatial modelling processes. Baccini
et al. used in [
17] the RandomForests algorithm to produce the BBE
500 product, and Saatchi
et al. in [
18] used the Maximum Entropy (MaxEnt) modelling algorithm for the SBE
1000 product [
18]. The BBE
500 data were downloaded from the Woods Hole Research Centre (WHRC) website [
61] with a pixel size of 463.31 m × 463.31 m, and the SBE
1000 data were downloaded by [
62] with a pixel size of 910.89 m × 910.89 m.
To enable a cell-by-cell comparison between MBE
100, BBE
500 and SBE
1000 at the 500-m and 1000-m scale using ANOVA and to produce percentage difference maps, we reduced the resolution of the MBE
100 data to 500 m and 1000 m, and the BBE
500 data from [
61] to 1000 m (
Table 3). We compared MBE
100 to both BBE
500 and BBE
1000, to enable, in the first instance, a more direct comparison to the pantropical national carbon stock, using the spatial resolution defined by Baccini
et al., and at the former instance, to compare all three carbon maps at the coarser resolution (
i.e., 1000 m defined by Saatchi
et al.). The data meaning for each reduced resolution pixel is the arithmetic mean of all the increased resolution pixel values, which were contained within the extent of each new reduced resolution pixel. To assess the differences between our local biomass estimates and these national carbon stock estimates, within the boundaries of our study area, we aggregated and averaged the grid values of our MBE
100 data set using a window size of 5 × 5 and 10 × 10 to create reduced resolution rasters (MBE
500, and MBE
1000, respectively).
Table 3.
Local and pantropical datasets used for comparison and summary of the data and methods used to derive the biomass maps; MBE, Michelakis biomass estimates; BBE, Baccini biomass estimates; SBE, Saatchi biomass estimates.
Table 3.
Local and pantropical datasets used for comparison and summary of the data and methods used to derive the biomass maps; MBE, Michelakis biomass estimates; BBE, Baccini biomass estimates; SBE, Saatchi biomass estimates.
Biomass map | EO data used | Algorithm | Pixel size (m) | Reduced resolution (m) | Compared to |
---|
MBE100 | ALOS PALSAR | Semi-empirical water cloud model | 100 | 500 | BBE500 BBE1000 SBE1000 |
1000 |
BBE500 | ICESAT GLAS MODIS Bidirectional Reflectance Distribution Function BDRF SRTM | RandomForests | 500 | 1000 | MBE500 |
SBE1000 |
SBE1000 | ICESAT GLAS MODIS LAI/NDVI/Vegetation Continuous Fields VCT SRTM QUICKSAT | MaxEnt | 1000 | - | MBE1000 |
BBE1000 |
To perform AGWB comparisons between our reduced resolution AGWB estimates and BBE500 and SBE1000 estimates, we calculated the percentage differences (Equation (7)) per pixel and per protected areas (i.e., DR and RBCMA). To assess the difference between mean biomass estimations for the whole protected areas, percentage errors were calculated (Equation (8)).
In Equation (7), AGWB
1 and AGWB
2 refer to (1) the AGWB values in each individual pixel of the compared datasets (e.g., MBE
500 vs. BBE
500) or (2) the mean AGWB values derived using all biomass pixels of the compared datasets within the extent of a protected area. In Equation (8), AGWB
reference corresponds to the locally derived mean AGWB value for the woody savannas using field data in DR (
Table 2) or to the derived mean AGWB calculated by [
52] in BCMA. In Equation (8), AGWB
estimated refers to the AGWB estimates based on the MBE, BBE and SBE maps.