## Materials and Methods
### LST, NDVI Climate Data Records, and SPEI Dataset  
Here, three LST CDRs are considered. The first LST dataset was developed at Princeton University (PU) [31; 32] and consists of hourly data defined on a global high-resolution grid (\(0.5^{\circ}\)) for a period spanning from January 1979 to December 2009. This all-sky LST dataset relies on information from the High-Resolution Infrared Radiation Sounder (HIRS) retrieved LST merged through a Bayesian postprocessing methodology with the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) LST with the aim of filling unobserved estimates of satellite retrievals. The dataset was comprehensively validated with in situ LST observations [31]. In order to provide appropriate consistency between datasets, the authors [31] used a unitary emissivity to retrieve satellite and reanalyzed LSTs. The merged variable therefore represents a surface brightness temperature. However, the term LST that is used for this variable by the dataset authors is kept here. The remaining two LST CDRs used in this work are developed at CM-SAF (in a joint effort with the EUMESTAT SAF on Land Surface Analysis, LSA-SAF) and are derived from the geostationary MFG and MSG satellites using the so-called Physical Mono-Window (PMW) and Statistical Mono-Window (SMW) algorithms [10; 33]. The first algorithm is based on radiative transfer simulations inverting the radiative transfer equation and Planck's distribution [10; 52; 53], whereas the latter relies on the linear relationship between LST and top of atmosphere brightness temperatures and consists on linearizing the radiative transfer equation while maintaining an explicit dependency on surface emissivity [10]. Both datasets rely on observations of a single channel in the thermal infra-red window, so that the same algorithm can be used for both MFG and MSG. The two CDRs are provided in a regular latitude and longitude grid with spatial resolution of \(0.05^{\circ}\) with the geographical coverage detailed in Section 2.1. CM-SAF PMW and SMW LST CDRs cover the period ranging from January 1991 to December 2015, and the monthly diurnal cycle is used in this work. These datasets consist of satellite data alone,and therefore it is worth stressing that they are clear-sky estimates and that, in this case, a map of variable emissivities [54] is used. The CM-SAF LST products were compared [55] in terms of: (1) precision and accuracy against more than 50,000 in-situ LST measurements and showed errors below 1 K for the monthly CDRs; and (2) decadal stability against ERA-Interim skin temperatures and the Moderate Resolution Imaging Spectroradiometer (MODIS) LST where errors were below 0.8 K.  
The Moderate Resolution Imaging Spectroradiometer (MODIS) NDVI used in this study was processed and produced by the NASA/Goddard Space Flight Center's Global Inventory Modelling and Mapping Studies (GIMMS) Group [56]. This NDVI CDR, consisting of 8 km spatial resolution and bi-monthly temporal resolution values, starts in January 1982 and is the longest and most complete NDVI record available. The multi-scalar drought index SPEI used in this study, from the Consejo Superior de Investigaciones Cientificas (CSIC, Spain; [[http://spei.csic.es/index.html](http://spei.csic.es/index.html)]([http://spei.csic.es/index.html](http://spei.csic.es/index.html))) [23; 24; 57], relies on Climate Research Unit (CRU) TS 3.23 datasets of temperature and precipitation [58] and is based on a normalization of the simple water balance developed by [PERSON] [59]. This monthly global dataset covers the period ranging from January 1901 to December 2015 with a spatial resolution of 0.5\({}^{\circ}\), and as a multi-scale character with available time-scales between 1 and 48 months.