Study Area
We performed the study in the Dry Chaco region, in Santiago del Estero province, Argentina (Figure 1), between 22°S and 31°S, and between 59°W and 66°W (Kunst et al. 2003). The annual rainfall ranges from 400 mm to 800 mm (Arambarri et al. 2011). The vegetation is composed of forest, shrubland, and grassland (Kunst et al. 2003, Atala et al. 2008, Bravo et al. 2014). The forest canopy is 6 m to 9 m in height and the cover ranges from 15 % to 80 %; it is mainly composed of the evergreen species Aspidosperma quebracho-blanco Schltdl. and the deciduous trees Prosopis spp. L. (Kunst et al. 2003). The shrubland consists of short woody vegetation and an herbaceous layer resulting from excessive logging and grazing; it is mainly composed by Acacia praecox Griseb., Celtis chichape (Wedd.) Miq., and Schinus fasciculatus (Griseb) I.M. Johnst. (Kunst et al. 2003). Nomenclature follows Zuloaga and Morrone (1999). The woody species are 3 m to 5 m in height and the cover ranges from 35 % to 80 % (Atala et al. 2008).
Satellite Data
Time series construction. We used data from MODIS Terra imagery (MOD13Q1) to construct NDVI and EVI time series. We downloaded images from the Oak Ridge National Laboratory Distributed Active Archive Center’s MODIS Land Product Subsets (https://daac.ornl.gov/MODIS/). This product is atmospherically corrected to surface reflectance and has a spatial resolution of 250 m × 250 m, with a temporal resolution of 16 days, resulting in 23 images per year. Since NDVI MODIS Terra dataset has been available from 18 February 2000, we decided to use VI time series that spanned three years before fire events, from 18 February 2000 to the date corresponding to an image prior to each fire event, from August to December 2003.
Fire detection. To detect burned areas, we used the Normalized Burn Ratio (NBR) index (Key and Benson 1999), calculated from Landsat 5 TM images (scenes 229–79 and 229–80 from 12 December 2003, resolution 30 m × 30 m). We downloaded georeferenced and orthorectified images from the US Geological Survey (EarthExplorer; http://earthexplorer.usgs.gov/). In order to validate detected burned areas, we overlapped the MODIS (MCD14L) vector Thermal Anomalies Fire product shapefile (Giglio 2010) with NBR images (Figure 2). This product has a spatial resolution of 1 km ×1 km and a temporal resolution of 6 hr, and was downloaded from NASA FIRMS (National Aeronautics and Space Administration Fire Information for Resource Management System; https://earthdata.nasa.gov/earth-observation-data/near-real-time/firms).
Vegetation map. We used Globcover 2000 vegetation map (Joint Research Centre) to assign vegetation cover to unburned and burned sites. This map is a global vegetation product, has a spatial resolution of 1 km × 1 km (Eva et al. 2002), and incorporates vegetation field data, NDVI data from SPOT VEGETATION (Saint 1994). This NDVI product has a spatial resolution of 1 km × 1 km, with a temporal resolution of 10 days. Besides, Globcover 2000 incorporates ATSR2 (Závody et al. 1994) satellite data to characterize seasonal behavior of forests, JERS-1 (Rosenqvist 1996) radar data to characterize the hydrodynamics of forests, and GTOPO30 topographic data (USGS 2005).
Proposed Criteria and Statistical Methods
As a first step, we proposed to calculate the point-by-point ratio between the VI time series of one pixel of the burned area of interest (TS
b), and the VI time series of one pixel of the unburned area (TS
ub). This unburned area was randomly selected in a buffer area around each burned site (Equation 1; Figure 3, step 1):
$$QV{I_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}} = {{T{S_{\rm{b}}}} \over {T{S_{{\rm{ub}}}}}},$$
(1)
where TS
b is the VI time series of the burned site, and TS
ub is the VI time series of the unburned site
Then, we represented the new time series \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) according to a classical additive statistical model for time series (Morettin and Castro Toloi 1987, Brockwell and Davis 2002), which is presented in Equation 2:
$$QV{I_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}} = M{e_{{\rm{QVI}}}} + {T_{{\rm{QVI}}}} + {S_{{\rm{QVI}}}} + {a_{{\rm{QVI}}}},$$
(2)
where Me
QVI is the arithmetic mean; T
QVI is the tendency component, the function that expresses the rate of change of \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) over time; S
QVI is the seasonality component, the function that expresses the seasonal component of \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\); and a
QVI is the random effect component.
Next, we analyzed the properties of the \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series to test if they met the following proposed criteria. As the first criterion, we proposed that, before the fire, the mean level of photosynthetic activity of the unburned site should not have statistically significant differences from the mean level of photosynthetic activity of the burned site. To detect these unburned sites, we proposed that pre-fire \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series had Me
QVI = 1 (Figure 3, step 2), because if Me was 1, then TS
b and TS
ub had the same mean. To test that Me
QVI = 1, we proposed using μ as an estimator (Efron 1979, Efron and Tibshirani 1986) with a 95 % confidence interval. To break the temporal autocorrelation of the data, the lower and upper limits of Me
QVI were estimated by bootstrapping with replacement (Efron 1979, Efron and Tibshirani 1986), using 1000 iterations and extracting 50 % of the data from each iteration.
As a second criterion, we proposed that the slope of the VI time series of burned and unburned sites should not have statistically significant differences (Figure 3, step 3), because differences in this parameter indicate that the photosynthetic activity of both sites evolved differently in magnitude or direction over time. To test this criterion, we proposed that \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) should exhibit a null T
QVI. To test if T
QVI was null, we proposed using the nonparametric Spearman Rank Correlation Test (Morettin and Castro Toloi 1987, McLeod et al. 1991, Yue et al. 2002).
As a third criterion, we proposed that, in each season of the year, burned and unburned sites should have a mean level of photosynthetic activity without statistically significant differences (Figure 3, step 4), since these differences indicate that burned and unburned sites have a different functional behavior for at least one season of the year. To test this criterion, we proposed that \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) should have a null S
QVI, because the existence of differences between burned and unburned sites in the mean of VI for at least one season of the year would generate a seasonal pattern in the \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series. To test if S
QVI was null, we proposed testing that each season of the year had an arithmetic mean of \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\), without statistically significant differences, by applying the nonparametric Friedman test (Morettin and Castro Toloi 1987, Sutradhar et al. 1995). To implement the test, we used each season as a treatment (four treatments) and the year as a block (three blocks); thus, the Friedman test was implemented using 12 data points. To obtain each data point, we averaged the \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) data corresponding to each season. We used this nonparametric test to avoid the correlation between repetitions, because, in this way, we increased the time lag between replicates of each treatment to one year instead of one data point every 16 days (Franzini and Harvey 1983, Morettin and Castro Toloi 1987, Sutradhar et al. 1995). The \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series that met the three proposed criteria could be considered as a random noise with μ = 1, since the classical additive statistical model assumes that a time series without tendency and seasonality is a random noise (Morettin and Castro Toloi 1987, Brockwell and Davis 2002).
The unburned sites generating \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) that met the three proposed criteria could be considered control sites because they not only had the same vegetation cover as the burned sites, but also the same functional behavior. Figure 4 shows the vegetation structure of actual burned and unburned sites that met the three proposed criteria. Figure 5A shows that the NDVI time series of a burned site and of an unburned site that met the three proposed criteria had the same behavior with occasional differences. And figure 5B shows that the \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) that met the three proposed criteria was centered around 1 and only a few data points were as high as 10 %.
Testing the Performance of the Proposed Method
To test the performance of the method, we assumed that, if it is correct, the pre-fire functional similarity between burned and unburned sites would increase with the increase of met criteria of unburned sites. Therefore, we compared the differences between VI time series of burned sites and VI time series of unburned sites with the same vegetation cover that met three, two, one, and none of the proposed criteria. In addition, we expected that the quality of \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series would increase with the increase of met criteria of unburned sites. Therefore, we compared the width of the confidence interval for \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series that met three, two, one, and none of the proposed criteria. Finally, we expected a decrease in the variability of VI time series of unburned sites with the increase of met criteria, because the VI time series of unburned sites that met the three proposed criteria should be very similar to the VI time series of the burned sites. In turn, VI time series of unburned sites that did not meet the three proposed criteria could be similar or dissimilar to the VI time series of the burned sites.
For this study, we constructed VI time series from forest and shrubland covers using NDVI and EVI data sets (Huete et al. 2002). We used forest and shrubland areas because they are the largest land covers in the region and exhibit VI time series with different inter- and intra-annual behaviors (Clark et al. 2010). We also used NDVI and EVI datasets because they exhibit differences in the range of variation and in the sensitivity to vegetation structure, chlorophyll activity, and soil water status (Huete et al. 2002, Clark et al. 2010, Paruelo et al. 2014), thus providing different types of biological information to select the control sites. We manually selected 20 burned forest sites distributed across seven burned areas, and 20 burned shrubland sites distributed across six burned areas (Figure 1). Each burned site had an area of 250 m × 250 m (1 MODIS pixel). We detected each burned area by visually analyzing the NBR images and the vector Thermal Anomalies Fire product shapefile (Figure 2). All areas were burned in 2003 at different points across an area of 50 000 km2 of the Chaco region. For each burned site, we randomly selected 40 unburned sites with VI time series that met the three proposed criteria and had the same vegetation cover before the fire, 40 that met two criteria, 40 that met one criterion, and 40 that did not meet any criteria. We used a total of 12 840 VI time series for this work: 40 time series of burned sites plus 12800 VI time series of unburned sites (2 plant cover × 20 burned plots × 40 unburned sites per number of met criteria × 4 number of met criteria × 2 vegetation indices = 12 800). Unburned sites were selected from a buffer area of 10 km around each burned site. Unburned site selection and statistical tests were performed automatically using IDL 71 (ITT Visual Information Solutions 2009).
Comparison of Time Series
We measured the pre-fire differences between VI time series of each burned site and unburned sites that met three, two, one, and none of the proposed criteria using two measures: 1) Mean Proportional Difference (MPD; Equation 3), and 2) Mean Square Error (MSE; Equation 4)—the latter being more sensitive to outliers than the former (Lhermitte et al. 2010, Lhermitte et al. 2011). The quality of the \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series generated from the possible control sites was measured using the Width of the Confidence Interval (WCI) of Me
QVI.
$$MPD = {{\sum\nolimits_{i = 0}^{n = 1} {{{{\rm{Abs}}(S{b_i} - Su{b_i})} \over {S{b_i}}}}} \over N},$$
(3)
and
$$MPE = \sqrt {{{\sum\nolimits_{i = 0}^{n = 1} {{{(TS{b_{\rm{i}}} - TSu{b_{\rm{i}}})}^2}}} \over N}} \;,$$
(4)
where TSb
i is the VI value at time i of the burned site time series, TSub
i is the VI value at the i of the unburned site time series, N is the number of observations in the time series, and Abs is the absolute value function.
Data Analysis
We used the nonparametric Kruskal-Wallis test (Sheskin 2004) to compare MPD and MSE differences and WCI of \({\rm{QV}}{{\rm{I}}_{{\rm{T}}{{\rm{S}}_{\rm{b}}}/{\rm{T}}{{\rm{S}}_{{\rm{ub}}}}}}\) time series, using the number of met criteria as treatment. We verified that VI time series variability of unburned sites decreased with the increase of met criteria by unburned sites. For this, we performed an F test for homogeneity of variances to compare the variability of MPD and MSE differences and WCI values obtained for each set of time series (Sheskin 2004), using the number of met criteria as treatment.