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Resumo -O objetivo deste trabalho foi avaliar a redução do vigor vegetativo da cobertura vegetal do Pampa do Brasil e do Uruguai, por meio da identificação de tendências negativas em séries temporais de imagens. Utilizaram-se séries temporais de imagens de NDVI/EVI do sensor Modis, de 2000 a 2011; imagens de índices de umidade do solo do "climate forecast system reanalysis"; e dados de precipitação pluvial de estações meteorológicas. O estudo quantificou tendências lineares e não lineares nas séries de NDVI e EVI, em áreas de campos. Na tendência monotônica de Mann-Kendall, a 5% de probabilidade, 81,9% da área total estudada foi significativa com o NDVI, e 74,8%, com o EVI; no entanto, o EVI apresentou contraste superior na estimativa dos parâmetros. Os resultados mostraram maior sinal negativo a oeste, com valores médios de R 2 >0,15, r<-0,3 e τ <-0,15 na tendência dos índices de vegetação, e tendência decrescente para NDVI, EVI e precipitação pluvial, com menores valores médios de umidade do solo. A tendência negativa dos índices de vegetação, relacionada à combinação da ocorrência de deficit hídrico em solos rasos com o sobrepastoreio, indica alterações no padrão de cobertura vegetal do Pampa, com redução do vigor vegetativo.Termos para indexação: campos nativos, EVI, Modis, NDVI, séries temporais. Temporal trends of vegetation indices on Pampa grasslands in Brazil and UruguayAbstract -The objective of this work was to evaluate the reduction in the vegetative vigor of Pampa vegetation cover in Brazil and Uruguay, by identifying negative trends in images time series. The following were used: time series of NDVI/EVI images from the Modis sensor, from 2000 to 2011; images from soil moisture indices from the climate forecast system reanalysis; and precipitation data from meteorological stations. The study quantified linear and nonlinear trends in the NDVI and EVI series in grassland areas. With the MannKendall monotonic trend, at 5% probability, 81.9% of the total area studied was significant with NDVI, and 74.8% with EVI; however, EVI showed superior contrast in the estimation of parameters. The results showed: highest negative signal in the west, with average values of R 2 >0.15, r<-0.3, and τ <-0.15 in the tendency of the vegetation indices; and decreasing tendency for NDVI, EVI, and rainfall, with lower mean soil moisture values. The negative trend of the vegetation indices, related to the combination of drought occurrence in surface soils with excessive grazing, indicates changes in the pattern of Pampa vegetation cover, with reduction in vegetative vigor.

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The present study aimed to characterize the dynamics of NDVI and meteorological conditions, relating both to the annual dynamics of biomass accumulation in natural pastures of the Pampa biome as a way of subsidizing growth modeling. Forage accumulation rate data from a long-term experiment, NDVI data from the MODIS images, and meteorological data measured at the surface were used. We verify that the agrometeorological element associated to the accumulation of forage in the natural grasslands is different according to the season, which is typical of the subtropical climate. Winter is the critical season for livestock production due to the lower forage accumulation rate and lower

We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered complex and ends with a persistence diagram. This procedure is stable (at least to certain types of perturbations of the input). This justifies the use of the diagram as a signature of the input, and the use of features derived from it in statistics and machine learning. However, these computations also produce other information of great interest to practitioners that is unfortunately unstable. For example, each point in the diagram corresponds to a simplex whose addition in the filtration results in the birth of the corresponding persistent homology class, but this correspondence is unstable. In addition, the persistence diagram is not stable with respect to other procedures that are employed in practice, such as thresholding a point cloud by density. We recast these problems as real-valued functions which are discontinuous but measurable, and then observe that convolving such a function with a suitable function produces a Lipschitz function. The resulting stable function can be estimated by perturbing the input and averaging the output. We illustrate this approach with a number of examples, including a stable localization of a persistent homology generator from brain imaging data.