Forest biomass and carbon estimation using vegetation indices and leaf area index

Among the consequences of the current dynamics of manmade land use and cover, forest fragmentation results in a large number of isolated fragments of different sizes. Forest provides many environmental services such as carbon sequestration and storage in the form of biomass, demonstrating the crucial role of native forests and the need to develop new methods that estimate forest biomass and carbon by non-destructive methods. This work aimed to develop a methodology to study and estimate the dynamics of forest biomass and carbon stock in successive stages of regeneration in the northwestern region of Rio Grande do Sul, which was the study area. Yearly images from 1985 to 2014 of the Normalized Difference Vegetation Index - NDVI were calculated, and a global regression was archived to obtain the leaf area index (LAI) and estimate the forest biomass. It was possible to observe the good relationship between the increase in LAI as a function of the NDVI, estimating the forest biomass of 61,156 Gg in 2014, where 602 Gg correspond to the initial regeneration stage, 8,287 Gg for the medium stage, and 52,267 Gg for the advanced stage of regeneration. The total estimated carbon for the study area in 2014 was 27,520 Gg CO2 of which 271 Gg were present in the initial stage, 3,729 Gg in the medium stage, and 23,520 Gg in the advanced stage of regeneration.


Introduction
We now experience the "era of secondary vegetation" due to the removal of native vegetation until the end of the twentieth century since the original vegetation is reduced and in the process of adapting to new conditions (Oliveira, 2015). Agriculture, livestock and logging stand out among the main anthropic activities that reduce and modify forests (Santos et al., 2017;Santos e Pontes, 2022;Silva e Moura, 2021;Watrin et al, 2020). These activities have led to an increase in the concentration of greenhouse gases in the atmosphere, generally from emissions from the burning of fossil fuels and changes in land use (Brunes & Couto, 2017;UNFCCC, 2017;Oliveira et al, 2020).
Thus, the importance of carbon fixation is prominent among the various environmental services provided by forests (Lipinski, et al., 2017;Tejada et al, 2020) since they store a large amount of this gas by fixing it in the form of biomass (Roubuste et al, 2022).
In this scenario, the northwestern region of the state of Rio Grande do Sul, has significant remnants of mixed ombrophilous forest (FOM) and deciduous seasonal forest (FED), some protected in public areas and others present in private areas, with high capacity to store biomass and fix carbon dioxide, considering the trend of increasing forest cover in the region (ROSA et al., 2017a;2017B).
According to Madugundu et al. (2008), the data from remote sensing are currently the most reliable for large-scale biomass estimation, still lacking new methodologies for processing these remote sensing data to estimate biomass, obtained through vegetation indices and leaf area index (Mabunda et al, 2021).
According to Galvão et al. (2016), some indeces such as the normalized difference vegetation index (NDVI) (Rouse et al., 1973) and the enhanced vegetation index (EVI) (HUETE el al., 2002) are indices related to pigments (e.g., chlorophyll and carotenoids) and structural parameters of the plant/canopy such as the leaf area, measured by the leaf area index LAI (Silva Junior et al, 2021), respectively. Thus, we can predict that these indices are related to forest succession and regeneration stages before its saturation. The increase in LAI leads to a proportional increase in NDVI values (Knyazikhin et al., 1999;Madugundu et al., 2008), demonstrating that NDVI levels can be indicators of LAI values and, consequently, of vegetation biomass.
According to Albuquerque et al (2019), and as highlighted by Pereira et al (2020), a vegetation index is the integration of two or more spectral bands, in order to highlight vegetation characteristics, biomass, leaf area index between others. Thus, NDVI is widely used in environmental analysis, as it allows studies at different scales, for different areas.
Therefore, the hypothesis of this work is that it is possible to carry out the estimation of aboveground biomass and carbon, through remote sensing data and satellite images, using NDVI and IAF. Therefore, the objective of this study was to develop a methodology to estimate and study the dynamics of forest biomass and carbon stocks in secondary regeneration stages in the northwestern region of Rio Grande do Sul State, in South of Brazil.

Methods
The study area belongs to the Northwest mesoregion of the state of Rio Grande do Sul, covering the microregions of Frederico Westphalen and Três Passos (PessettI e Gomes, 2020), totaling 9,127 km².
Multispectral data were collected at different dates from Landsat 5 and 7 satellites, forming a data time series, encompassing 30 images from 1985 to 2014. Most of the images were obtained in October and November to avoid seasonal effects. The data for the year 1990 was acquired in August, and the data for 1993, 1996, and 1999 were acquired in September. Some images were also obtained from February to April. We used the USGS -Global Visualization Viewer to obtain the images (available at http://earthexplorer.usgs.gov/). The images were acquired with the atmospheric corrections and orthorectification already applied. We sought to select scenes acquired at close dates to avoid forest and illumination seasonal variations. The images were processed using the ENVI software (5.0).
The NDVI was calculated for each year from 1985 to 2014 based on the surface reflectance images. According to Galvão et al. (2016), the NDVI is an index closely related to chlorophyll and carotenoids. Masks were created and applied after calculating the NDVI for each year, leaving only the forest polygons delimited by Rosa (2016). NDVI values were extracted per pixel from these forest areas and measurements per fragment were evaluated to determine the leaf area index (LAI) for each pixel in each year. The empirical model proposed by Knyazikhin et al. was used to estimate the LAI (1999), which relates the NDVI values to LAI values, considering the nonlinear relationship between the variables. The NDVI values found in the study area for the stages studied were adjusted using a known global model.
It was possible to calculate a logistic function to estimate the LAI from the NDVI based on the global data generated by Knyazikhin et al. (1999). Thus, we reached the values of LAI for secondary forest in the three stages of regeneration, initial stage (IS), middle stage (MS), and advanced stage (AS) defined according to CONAMA Resolution nº 33 of 1994 (Brazil, 2021). Subsequently, it was possible to classify and generate the areas of each regeneration stage for the 30 images studied , and estimate the total biomass for all years in each of the forest successions.

Results
To analyze the NDVI, the closer to one, the higher the forest cover (LAI) and the closer to zero the lower the green coverage of the area under study. Negative values refers to water coverage. Thus, although simplistic, the strategy for defining NDVI classes for the different secondary forest successional stages was based on the physical response of the forest, given the nonlinear proportionality that exists between the amount of leaves and the NDVI.
The values of the NDVI in this study ranged from 0.50 to 0.85 in the three successive stages, with IS in the range from 0.5 to 0.6, due to a low canopy vegetation, locally named 'capoeirão' (similar to savanna), vegetation with absence of young trees and shrubs, thus presenting a lower reflectance. The MS was in the range from 0.6 to 0.7, increasing the NDVI due to the presence of tree-sized plants and their greater reflectance. Finally, the NDVI of the AS was superior to 0.7 for all evaluated dates. The adjustment of the LAI intervals as a function of the NDVI to be estimated and the stages was carried out based on known sites in the field.
Forest areas seasonal variations (wintersummer) are clearly represented at all stages of succession given some small variations of the date of image acquisition. Thus, as the forest loses leaves, NDVI presented lower values and as budding occurs, the value tends to increase. This may explain the discrepancy between the smallest and largest values since images such as those from 1999 were obtained in early September. In this period, most of the trees that make the top cover have new leaves and light shades of green, that is, a lower concentration of chlorophyll, which explains the low values of NDVI found. Also due to the period of image acquisition, the position of the sun can cause a great shading of the larger trees, which also explains the NDVI values (due to directional and angular effects).
The values of LAI vary from 1.0 for the IS regeneration to 2.2 when transitioning to the MS, obtaining values of 2.2 to 4.5 and values with LAI superior to 4.5 in the AS regeneration.
In this study, the maximum value obtained was 5.75 of LAI that corresponds to 0.85 of NDVI for the advanced stage of regeneration. The lowest value found was for the initial stage, with a LAI of 1.012. We classified the forests based on the LAI data estimated through the NDVI. This was fundamental to obtain the covered area of each successive stage for our time series (Table 1).
It is possible to observe that the area found in the advanced stage of regeneration in 1999 is not correct since most of it has IS NDVI. This occurs because the image was obtained at the beginning of September, when most of the arboreal plants belonging to this successional stage lost their leaves (seasonal effects). The deciduous and seasonal forests have a lighter green coloration due to shading caused by larger trees and the solar light incidence angle. The same can be observed on other dates, such as 1990 and 1993, when both images were obtained from August to September. Thus, the study demonstrates that images from this period should not be used to estimate biophysical data.
Still, many small isolated fragments in the early stage of regeneration ended up clustering, forming new larger fragments and accumulating a greater forest biomass. The same occurred for fragments in the middle and advanced stage of regeneration, where the junction of these fragments resulted in the formation of large fragments. At this point, it is important to remember that there was no distinction between native and commercial forest and, thus, the measures presented include both types of forests. The amount of biomass was 0.067 Gg/ha in the IS, 0.177 Gg/ha in the MS and 0.38 Gg/ha in the AS of regeneration. In 1985, the total area of initial stage was of 13,641 hectares, totaling 919 Gg of biomass, the area of medium stage was 69,385 ha, totaling 12,297 Gg, and in the advanced stage of 58,890 ha, totaling 22,419 Gg. The evolution of forest fragments in the 30 years and in the three classes of regenerations can be observed in Table 2.
The total biomass found in 2014 was of 602 Gg for the initial stage, 8,287 Gg for the middle stage, and 52,267 Gg for the advanced stage of regeneration, totaling 61,156.50 Gg of forest biomass in secondary succession. In 1985, the total biomass was 35,636 Gg, almost half of the total biomass in 2014, demonstrating an increase of about 41.7%. As it was possible to observe an increase in the area in hectares of the succession stages, it is also possible to observe an increase in biomass and carbon, related to the increase in the LAI. The values obtained for 1999 were excluded because they were very different from the other years. Therefore, an average was generated between the values of 1998 and 2000 (due to the absence of an adequate image).
Analyzing the data obtained, it was possible to generate an average of the last five years studied, which served to dilute the error caused by satellite images, resulting in an average value of 60,199.20 Gg of forest biomass, clearly demonstrating an increase in biomass in the study area.
The initial stage of regeneration did not have much presence in 1985 and 2014, when the total biomass was composed of the middle stage of regeneration, with few fragments in advanced stage, which were generally concentrated in three protected areas found in the study area, two indigenous reserves and a state park (Figure 1). There was a confusion of reflectance and shading in 1999 because the leaves of the fragments of the advanced regeneration had fallen, since the period of the image collection was in September, and the fragments were characterized as an initial stage. It is possible to observe a large evolution of the dynamics of forest fragments for 2014, especially for the advanced stage of regeneration ( Figure 2).  The study area has three preserved remnants of native Atlantic Forest, very significant in terms of biomass, being the Parque Estadual do Turvo and the Guarita and Nonoai Indigenous Reserves, which have a high carbon stock and a great potential for expansion of advanced biomass according to data found in the temporal study carried out.
It is possible to emphasize that there was a great evolution of biomass in the study area, proving the consolidation of areas. Very small forest fragments ended up joining with larger fragments or were simply increasing due to the abandonment of the areas surrounding them. With the evolution of technology, these areas were no longer mechanizable, and therefore became an early stage shrubbery forest, thus evolving to medium and advanced stage of regeneration. Examining the fragments spatial distribution it is noticed that most of them are located in areas close to the areas of permanent preservation of rivers, lakes, and springs, as well as on land unsuitable for mechanized farming.
Another relevant question for this study is the quantification of carbon present in forest biomass, where carbon constitutes 45% of the estimated biomass (Table 3). The amount of carbon was 0.030 Gg/ha in the IS, 0.079 Gg/ha in the MS, and 0.171 Gg/ha in the AS of regeneration. The total estimated carbon for the study area in 2014 was 27,520 Gg CO2, of which 271 Gg were present in the initial stage, 3,729 Gg in the middle stage, and 23,520 Gg in the advanced stage. It is possible to observe that the carbon present in this study had a significant increase from 1985 to 2014, especially in the advanced stage, which doubled in less than 30 years.
Before the beginning of colonization, the study area was fully covered by native forests, belonging to the Atlantic Forest biome, with FOM and FED forest typologies. Colonization opened up spaces for agriculture, livestock, and housing, modifying the land use, where only a few forest fragments remained, resulting in large emissions of CO2 to the atmosphere. As technological evolution occurred, areas impossible to be mechanized were abandoned, regenerated their initial formations. Thus, it is possible to observe that the abandoned or otherwise evolving areas of the fragments still have a great capacity to store the CO2 present in the atmosphere, which helps to reduce this gas and positively add to the context of climate change.
In turn, the three large areas present in the study (Guarita and Nonoai Indigenous Reserves and Parque Estadual do Turvo) have a high stock of biomass and carbon, which are very important and should be treated with greater attention. Incentive programs such as REDD can be installed to further increase the potential of these areas in mitigating and storing carbon.
It is possible to observe a trend from 2012, where biomass and carbon began to increase, coinciding with the enactment of Law 12,651, which provides for native vegetation, where the suppression of new areas of native vegetation for other purposes is prohibited. With the growing concern about climate change and large CO2 emissions to the atmosphere, the stock of CO2 in plants tends to only increase, until the vegetation reaches the stage of primary forests and stagnates the growth and mitigation, becoming a forest with great importance of carbon stock. Therefore, we can conclude that in 30 years of study (1985 to 2014), there was an increase of 11,486 Gg of carbon that corresponds to 42,119 Gg of CO2 removed from the atmosphere.

Discussion
Estimates based on remote sensing data and the size of the fragments can be evaluated through vegetation indices since these depict vegetative vigor and leaf cover in the area under study and did not reach the saturation. Therefore, in this study, the forest biomass and carbon for each successive stage was estimated throughout the northwestern region of Rio Grande do Sul, through the NDVI and LAI, adjusting a global model with local bases, using remote sensing data.
In studies carried out by Luz et al (2022), vegetation indices related to caatinga vegetation showed a positive and significant correlation with aboveground biomass values estimated by allometric equations. Furthermore, Pedreira Junior et al (2020) analyzed the biophysical parameters of the surface in different uses and occupations in Cuiabá. The sites with the highest amount of plant biomass (DV) had the highest values of NDVI and radiation balance, in addition to the lowest values of surface albedo and surface temperature. Such studies agree to our results, considering the use of NDVI stratus.
According to Madugundu et al. (2008), the NDVI presents a strong relationship with the LAI and the global model generated by Knyazikhin et al. (1999) allowed the adjustment of a logistic regression, and from it, the estimation of the LAI. From this equation adjustment and the NDVIs calculated for each image, it was possible to calibrate the LAI model according to NDVI levels. The generated model behaved very well for the adjustment of the NDVI values found, where we obtained 30 samples of LAI with model significance (p-value) inferior to 0.0001 and R2 0.99. As the NDVI values increased, it was possible to observe an increase in the LAI estimate.
According to studies carried out by Caruzzo and Rocha (2000), the estimate of the accumulated LAI in a pasture region was 2.63, while for a forest region, it was 4.97, thus demonstrating that the LAI increases from the initial stage known as shrubbery forests, to the advanced stage, a mature forest.
According to Breunig et al. (2015), in studies conducted in the Parque Estadual do Turvo, the LAI from January to December ranged from 6.5 in the summer to 3.4 in the winter. The values were the lowest in September, reaching 3.4, demonstrating large oscillations when plants lose leaves and chlorophyll decreases, which leads to a decrease in the absorption of electromagnetic radiation by pigments and incurs an increase in reflectance in the visible spectral range. This fact reaffirms the care that must occur when selecting the date when the images are obtained. Furthermore, one should be careful with the geometry of illumination during the winter, which leads to changes in reflectance and, consequently, in the value of NDVI and biophysical parameters calculated in sequence (Breunig et la., 2015).
The studies conducted by Rosa (2016) demonstrate a trend of a greater density of rural population in the 1980s and earlier, due to which there was an advance of anthropic occupation over native forest areas, causing forest suppression and fragmentation (in part associated with the government's agricultural expansion policy). As the rural exodus increased (for various reasons), the labor force in the countryside decreased and areas of difficult cultivation or access were abandoned and/or occupied by cultivated forests. Thus, there was a high emergence of new forest fragments, which are at an early stage of development.
Another important highlight is the development of rich snippets over the next 30 years. Such areas ranged widely and remained constant only from in 2007, later coinciding with the creation of a new Forest Code, Law 12,651 of May 25th, 2012) (BRASIL, 2012), in which the extraction activity began to be more precisely controlled, leading the people to a greater awareness of preserving and adding value to the forest. As result a tendency to stabilize the decline of the forest fragments, thus, resulting in an increase in forest biomass and carbon.
According to the studies carried out by Costa and Lameira (2022), who studied the characterization of the NDVI through Pléiades images in two forest areas, one managed and the other secondary forest. Regarding the minimum and maximum reflectance data found by the authors in the two study areas, the NDVI was higher in the secondary forest, indicating a value of approximately 0.736 and 0.849 respectively with an average of 0.790.
According to Madugundu et al. (2008), when an increase in LAI occurs, there is also a proportional (nonlinear) increase in NDVI values, demonstrating that NDVI levels are good indicators of LAI values, and that as the leaf area (LAI) increases, there is an increase in accumulated biomass. The same occurred with this study. As the NDVI increased, an increase in leaf area occurred, demonstrating the difference in the succession stages and causing an increase in forest biomass according to the succession stage.
In studies conducted by Goswami et al. (2015), all NDVI relationships with the LAI and biomass demonstrated strong exponential relationships, with R2 ≥ 0.7 indicating that NDVI saturates to estimate higher values of biomass and LAI. On the other hand, the strong linear relationship between LAI and biomass suggests that there is no saturation in the measurement of biomass and LAI. R2 was superior to 0.7 for this study, indicating that there will be NDVI saturation at some point, but there will be no LAI and biomass saturation. The strong relationship observed between NDVI and LAI with the biomass found in this study is similar to studies conducted in other ecosystems such eucalyptus plantations (Berger, et al. 2019) and the high arctic tundra (Walker et al., 2003).
According to studies conducted by Boelman et al. (2003), the greener the leaf area, the higher the LAI and photosynthetically active radiation (PAR), and the higher the NDVI values, which was also observed in this study. Piazza et al. (2016) proved that all the sample units studied when mapping the early forest remnants are represented by inhomogeneous vegetation. The initial regeneration classes presented the highest digital number values along the spectrum due to the more regular structuring of the canopies. The opposite was found for the advanced vegetation classes, where there is a greater irregularity of the canopies, and thus a greater influence caused by shade. This study conducted by Piazza et al. (2016) demonstrated the similarity of the succession stages in spectral terms, once again emphasizing the importance of care, such as the date of acquisition of images, due to the difficulty of classifying heterogeneity through images.
The methodology proposed by this study demonstrated the possibility of using remote sensing data spectral response to estimate biomass and carbon. However, it should be noted that biomass estimation based on remote sensing encompasses several factors, such as image quality and pixel size, data saturation, biophysical environments, extracted remote sensing variables, and the algorithm variables that may affect the estimation (Luther et al., 2006). Thus, the results archived required care and more validation procedures.
The use of remote sensing as a tool for environmental analysis, such as the survey of vegetation cover, can facilitate environmental control for researchers for the monitoring of vegetation cover, associating the use of technologies aimed at planning and environmental control (PEREIRA et al, 2020).

Conclusion
An indirect empirical estimation model was applied, where the classification was performed according to the leaf area index adjusted by the NDVI to calibrate the biomass stock estimates. Due to this fact, the model estimated more exact values, closer to the real ones.
It is possible to estimate the forest biomass and carbon stock for the entire northwest region of the state of RS, in primary and secondary forests, in the three stages of regeneration, using the proposed methodology.
According to the methodology, the forest biomass in 2014 in the northwestern region of the state of Rio Grande do Sul was 61,156 Gg, divided into three stages of initial (602 GG), medium (8,287 Gg), and advanced regeneration (52,267 Gg).
The estimated carbon stock for the study area in 2014 was 27,520 Gg, which were also estimated according to the succession stage, initial (271 Gg), medium (3,729 Gg), and advanced (23,520 Gg).
Therefore, according to the methodology developed in this study, considered the most realistic and conserved, we can conclude that there was an increase of 11,486 GG of carbon that corresponds to 42,119 Gg of CO2 removed from the atmosphere in the study area in 30 years of study (1985 to 2014).