3.2.1.9 Propiedades mecánicas

By definition, trend analysis is the practice of finding a pattern within collected information. It often relies on a set of statistical techniques that deals with time series data. Time series data refer to data in a series of particular periods or intervals. This discussion focusses specifically on time series analysis of Earth observation data to reveal land surface dynamics and highlight the magnitude of these dynamics within defined monitoring periods (Kuenzer, Dech & Wagner 2015; Lasaponara & Lanorte 2012). In the past, time series analysis was complicated and limited to a small number of expert users, relying on coarse resolution data (Kuenzer, Dech & Wagner 2015). The release of several satellite data archives has led to free access to a large volume of imagery ideal for time series analysis (Lasaponara & Lanorte 2012; Wulder & Masek 2012). This is complemented by the availability of new open source tools and novel techniques

for time series analysis (Kuenzer, Dech & Wagner 2015). This section reviews some of the products and methods applied in trend analysis involving remotely sensed data.

2.6.1 Remotely sensed data available for time series analysis

Accurate estimation of trends depends on the quality of the sensed data, the statistical method used, the length of the time series, as well as the temporal and spatial resolution of the data (Sulkava et al. 2007). Moreover, very few sensors have captured data that span several decades available for time series analysis.

Two of the sensors that have produced the longest available time series of data are the advanced very high-resolution radiometer (AVHRR) sensors, operated by the National Oceanic and Atmospheric Administration (NOAA) that offers coarse resolution daily coverage since 1978. The Landsat archive, operational since 1972, includes Landsat 4 MSS (MultiSpectral Scanner), Landsat 5 TM (Thematic Mapper), Landsat 7 ETM+ (Enhanced Thematic Mapper Plus), and Landsat 8 OLI (Operational Land Imager) consisting of medium resolution imagery at 16-day intervals (Kuenzer, Dech & Wagner 2015; Wulder et al. 2018).

Since the early 2000s, the moderate resolution imaging spectroradiometer (MODIS) sensor (Justice et al. 1998), and the European Environmental Satellite (ENVISAT) sensors, advanced along-track scanning radiometer (AATSR) and medium resolution imaging spectrometer (MERIS) have provided access to coarse and medium resolution data. MODIS was launched on the Terra satellite in 1999 and on the Aqua satellite in 2002, whereas the sensors on board ENVISAT have collected data from 2002 to April 2012. More recently, the European Space Agency (ESA) Sentinel series provides many new multi-sensor options for time series analysis, with global coverage and provided on a free and open basis. The compatibility of Sentinel 2 with Landsat allows measurements from Sentinel 2 to be integrated with Landsat, thereby allowing the Landsat and Sentinel 2 archive to be used for time series analysis in combination (Wulder et al. 2018).

Selected SPOT (Satellite Pour l’Observation de la Terre) VEGETATION data from 1998 onwards at one-kilometre resolution are also available at a daily interval, while higher resolution SPOT multispectral data was made available as part of the SPOT World Heritage Programme (Kuenzer, Dech & Wagner 2015). Lasaponara & Lanorte (2012) comment on the high cost of multispectral SPOT data, which has been prohibitive in assessing its value for time series analysis.

2.6.2 Trend analysis techniques and examples

Temporal vegetation information have been derived from time series of normalised difference vegetation index (NDVI) data since the early 1980s (Malingreau 1986; Tucker, Justice & Prince 1986) and many methods for extracting seasonality and trends have been developed since. For instance, time series satellite data (Forkel et al. 2013; Zhu et al. 2016) have recently been used to quantify changing trends in ecosystem productivity linked to land cover classes and can provide a continuous view of ecosystem dynamics (Kennedy et al. 2014). Trend analysis is not limited to NDVI but can be applied to time series of other satellite-derived data, such as land surface temperature or snow cover (Kuenzer, Dech & Wagner 2015).

All trend estimation methods have limitations that may be more or less critical, depending on the application. Estimation of trends from time series data differs substantially depending on analysed satellite dataset, the corresponding spatio-temporal resolution and the applied statistical method (Forkel et al. 2013). Fensholt et al. (2012) attested that both linear and non- linear development in the time series value, e.g. NDVI, could be detected from time series data. Linear development can be derived using the Pearson Product–moment linear correlation test and Theil-Sen median slope trend analysis (Sen 1968; Theil 1950). However, care must be taken when using linear regression analysis for estimating trends in time series data, as spatial and temporal autocorrelation can violate statistical assumptions, such as the independence of observations (De Beurs & Henebry 2010). Accordingly, De Beurs & Henebry (2010) suggested the application of temporal autocorrelation structures or the use of the non-parametric Mann- Kendall monotonic test for non-linear development, while Neeti & Eastman (2011) proposed using spatial autocorrelation as contextual evidence in the testing of trends based on a modification of the Mann‐Kendall statistic, as implemented in IDRISI. The additional contextual information reinforced evidence of neighbouring pixels with similar trends, whereas spurious trends would be removed.

Many studies have calculated trends based on annual time steps, using regression analysis (Eklundh & Olsson 2003), either from annually or seasonally aggregated values, or extracted annual values. Röder et al. (2008) acquired a time series of Landsat data consisting of a single image per year and was able to retrospectively assess rangeland processes and interpret the linear trends in relation to land use practices and previous management interventions. Annual aggregation eliminates the seasonal cycle in a satellite parameter, such as the NDVI time series, removing the seasonal correlation structure that could hamper trend analysis. However, the annual aggregation of time series data reduces the temporal resolution and time series length, which is critical for assessing the statistical significance of the observed trend.

Various methods have been developed to estimate and subtract the seasonal cycle or by modelling the seasonal signal (De Jong et al. 2011; Verbesselt et al. 2010a; Verbesselt et al. 2010b) thereby providing access to the full temporal resolution. Verbesselt et al. (2011) demonstrated that break detection for additive seasonal trend (BFAST) could detect and characterise spatial and temporal changes within the trend component of satellite image time series. BFAST employs the seasonal trend decomposition method (STL) based on a locally weighted regression smoother (LOESS) (Cleveland et al. 1990). Abrupt changes that were not associated with trend or seasonal components of the time series could be identified (Verbesselt et al. 2010b) using BFAST. Method STM (trend estimation based on a season-trend model) described by Forkel et al. (2013) uses this method implemented specifically for remotely sensed data. Method AAT (Forkel et al. 2013) was designed to estimate trends and trend changes based on an annual aggregated time series, with breakpoints estimated using the method of Bai & Perron (2003) and Zeileis et al. (2003). The Mann-Kendall trend test (Mann 1945) was applied to determine significance of trends. To enable detection of long-term trend changes, the observation periods of 48 monthly observations are recommended, while time series segment of a length smaller than eight years are not considered trends (Forkel et al. 2013). Kuenzer et al. (2014) suggested that the residuals, the remainder of the time series after trend and seasonal components were removed, could be relevant for management of natural resources, such as plant disease, fires or natural hazards.

Overall, De Jong et al. (2011) found that trend estimates from the different methods resulted in similar general spatial patterns of the major regional greening and browning trends, but noted substantial spatial pattern variations in areas with weak trends. Vogelmann et al. (2016) advised that gradual changes were best characterised and monitored using time series analysis. Wessels, Van den Bergh & Scholes (2012) identified abrupt changes that were correlated with land cover change and hypothesised error. Similarly, Fensholt et al. (2015) found that patterns of diverging NDVI metric trends could also be used to evaluate the impacts of environmental changes related to land cover change, thereby detecting changes in ecosystem functioning over time. Forkel et al. (2013) developed trend estimation methods specifically applicable to remote sensing data, implemented in R statistical software (R Core Team 2017) package greenbrown (Forkel & Wutzler 2015).