Vol.:(0123456789) 1 3 Modeling Earth Systems and Environment https://doi.org/10.1007/s40808-019-00614-x ORIGINAL ARTICLE Mathematical modeling and use of orbital products in the environmental degradation of the Araripe Forest in the Brazilian Northeast Dimas de Barros Santiago 1  · Washington Luiz Félix Correia Filho 2  · José Francisco de Oliveira‑Júnior 2,3  · Carlos Antonio da Silva Junior 4 Received: 19 February 2019 / Accepted: 10 June 2019 © Springer Nature Switzerland AG 2019 Abstract Vegetation cover is indispensable in the process of inhibiting environmental degradation. In the Northeast of Brazil, especially in the Araripe Nacional Forest (FLONA), this problem is related to the removal of vegetation for industrial and domestic use, in addition to the expansion of livestock. Thus, the objective of this work was to evaluate the environmental degradation in the area of FLONA from orbital products via remote sensing with the aid of mathematical modeling. For this, two orbital images of the orbit 65, point 217 were used for processing and obtaining the variables: (1st) July 7, 2003 from TM/Land- sat-5 and (2nd) July 15, 2018 from OLI/Landsat-8. In mathematical modeling, the multiple linear regression (MRL) model was applied to the orbital products: land surface temperature (LST), normalized burn ratio (NBR), Normalized Diference Moisture Index, Normalized Diference Water Index (NDWI) to estimate the Soil Adjusted Vegetation Index (SAVI) and hence to predict the Normalized Diference Vegetation Index (NDVI). All the processing to obtain the results was carried out in the software R version 3.4-1. O NDVI pointed out a signifcant increase of 72.05% in dense vegetation, from 158.33 to 272.40 km 2 . However, vegetation is more likely to sufer from stress due to the increase in LST at 5 °C, which increased from 17.5 to 25.0 °C, reaching its highest value of 42 °C in July 2011. The MRL results indicated that the models have an excellent predictive capacity in the estimation of degradation, with R 2 value greater than 92% of the explained variance. In addition, the MAE and root mean square error were less than 0.03 for both models. The models pointed out that SAVI, NBR and NDWI are responsible for the variability of NDVI in environmental degradation of FLONA. Highlight for the theoretical- conceptual model that can be applied to any semi-arid and highly-sensitive region to changes in the rainfall pattern. Keywords Vegetal cover · Orbital products · Use and occupation of the soil Introduction The vegetation has an indispensable role in several pro- cesses of protection and fxation of the soil, for example, the increase of porosity and permeability and in the min- imization of the impact of raindrops to which it prevents the surface runof (Miatto et al. 2016; Labrière et al. 2015; Bélanger et al. 2017). In a macroscale analysis, the type of vegetation present in forests is essential in the process of absorbing greenhouse gases (GHG), such as CO 2 , the most abundant in the atmosphere and one of the main responsi- ble for the intensifcation of climate change (Ribeiro et al. 2013). In addition, this type of vegetation contributes to the maintenance of soil moisture and fertility by the presence of organic matter. All factors cited previously to minimize the * Dimas de Barros Santiago dimas.barros91@gmail.com 1 Postgraduate Program in Meteorology, Unidade Acadêmica de Ciências (UACA), Federal University of Campina Grande (UFCG), Campina Grande, Paraíba 58428-830, Brazil 2 Institute of Atmospheric Sciences (ICAT), Federal University of Alagoas (UFAL), Maceió, Alagoas 57072-260, Brazil 3 Postgraduate Program in Biosystems Engineering (PGEB), Federal Fluminense University (UFF), Niterói, Rio de Janeiro 24220-900, Brazil 4 Department of Geography, State University of Mato Grosso (UNEMAT), Sinop, Mato Grosso 78555-000, Brazil