# Monitoring and Forecasting the Impact of the 2018 Summer Heatwave on Vegetation
## 2 Material and Methods
### Satellite Derived Observations  
Two satellite products from the Copernicus Global Land Service project are used in this study, the Surface Soil Moisture (SSM) and the Leaf Area Index (LAI) derived from SPOT-VGT (prior to 2014) and PROBA-V (from 2014 onward). The SSM product is derived from the Advanced Scatterometer (ASCAT), an active C-band microwave sensor on board the European MetOp polar-orbiting satellite (METOP-A&B). Information on soil moisture comes from ASCAT radar backscatter coefficients using a methodology developed at the Vienna University of Technology (TU-Wien) based on a change detection approach originally developed for the active microwave instrument flown on-board the European satellites ERS-1 and ERS-2 [66; 67]. The recursive form on an exponential filter [68] is applied to the soil moisture product to estimate the Soil Wetness Index (SWI) using a timescale parameter, T, varying between 1 day and 100 days. T implicitly takes many physical parameters into account, it can be considered as a surrogate parameter for all the processes affecting the temporal dynamics of soil moisture, such as the thickness of the soil layer, soil hydraulic properties, evaporation, run-off and vertical gradient of soil properties (texture, density). T represents the time scale of soil moisture variation, in units of day. A high value of T describes a deeper soil layer (assuming that the soil diffusivity is constant) [69]. While giving a general rule on how to translate a given T-value to a certain soil depth is currently not possible since this depends strongly on the application and the soil composition of the area of interest, in this study, following work from [18; 33] SWI-001 (i.e. T = 1 day, the smallest T value available) is used as a proxy for SSM [69]. The result for the top soil moisture content (<5 cm) is expressed as a degree of saturation and ranges between 0 (dry) and 100 (saturated). It is a global product at 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) spatial resolution available daily from 2007. As in [7], pixels whose average altitude exceeds 1500 m above sea level as well as pixels with urban land cover fractions larger than 15% were discarded as those conditions may affect the retrieval of soil moisture from space. SSM product has to be transformed into the model-equivalent surface soil moisture for data assimilation purposes and in order to address possible misspecification of physiographic model parameters (like field capacity and wilting point). As in [18] and [33] in LDAS-Monde, the linear rescaling approach described in [70] (using the first two moments of the cumulative distribution function, CDF) has been used in this study; it is a linear rescaling that enables a correction of the differences in the mean and variance of the distribution. The first two moments, \(a\) the intercept and \(b\) the slope are as follow:  
\[a=\overline{SSM_{m}}-b\times\overline{SSM_{o}} \tag{1}\]  
\[b=\frac{\sigma_{m}}{\sigma_{o}} \tag{2}\]  
where \(\overline{SSM_{m}}(\sigma_{m})\) and \(\overline{SSM_{o}}(\sigma_{0})\) correspond to the model and observation means (standard deviations), respectively. The authors of [33; 71] discussed the importance of allowing for seasonal variability in the CDF matching. \(a\) and \(b\) parameters vary spatially and were derived on a monthly basis by using a three-month moving window after screening for presence of ice and urban areas over (i) January 2008 to October 2018 when using ERA5 as atmospheric forcing and (ii) April 2016 to December 2018 when using IFS HRES as atmospheric forcing. LAI, defined as one-sided area of green elements of the canopy per unit horizontal ground area is observable from space and quantifies the thickness of the vegetation cover. Several LAI collections/versions are available from the CGLS project from 1999. They are retrieved from the SPOT-VGT (from 1999 to 2014) and then from PROBA-V (from 2014 to present) satellite data according to the methodology proposed by [72].