# Remote Sensing and Bio-Geochemical Modeling of Forest Carbon Storage in Spain
## 2 Modeling Strategy  
To assess forest NPP, a modeling strategy (schematically summarized in Figure 1) that combines two models was applied (for the description of the data involved in the calculation of the different variables, see Section 3.3). The first model was a Monteith-like production efficiency model optimized for the study area [8], which was used to calculate annual forest GPP at 1-km spatial resolution from daily estimates. The model was driven by photosynthetically active radiation (PAR), the fraction of PAR absorbed by the vegetation canopy (\(f_{\text{APAR}}\)), precipitation, and air temperature:  
\[\text{GPP}=\varepsilon_{\text{max}}\sum_{i=1}^{N}\text{PAR}_{i}f_{\text{APAR},i}\varepsilon_{\text{W},i}\varepsilon_{\text{T},i} \tag{1}\]  
where the subindex \(i\) refers to the day of year, while \(N\) is the number of days in the year. The maximum light use efficiency \(\varepsilon_{\text{max}}\) was set as 1.2 g MJ\({}^{-1}\). PAR was calculated as 46% of incident global solar radiation [29]. \(f_{\text{APAR}}\) was computed according to the Roujean and Breon algorithm [30]. Red (\(\rho_{\text{RED}}\)) and near-infrared (\(\rho_{\text{NIR}}\)) reflectances were first calculated from bidirectional reflectance distribution function (BRDF) parameters \(k_{0}\), \(k_{1}\), and \(k_{2}\) for an optimal angular geometry in the solar principal plane. \(f_{\text{APAR}}\) was calculated as a linear function of the renormalized difference vegetation index  
\[\text{RDVI}=(\rho_{\text{NIR}}-\rho_{\text{RED}})/(\rho_{\text{NIR}}+\rho_{ \text{RED}})^{1/2} \tag{2}\]  
\(\varepsilon_{\text{W}}\) is the water stress coefficient (\(C_{\text{WS}}\)) as used in [31] that accounts for short-term water stress  
\[C_{\text{WS}}=(\text{PRE}/\text{PET}+1)/2 \tag{3}\]  
where precipitation (PRE) and potential evapotranspiration (PET, calculated from air temperature and incoming global solar radiation through the Jensen-Haise equation [32]) are accumulated for 60 days. \(\varepsilon_{\text{T}}\) is the TMIN_scalar used in the MOD17 algorithm [33] to account for thermal stress caused by low temperatures: a linear ramp function of daily minimum air temperature with thresholds depending on the vegetation type. The second model was Biome-BGC [15; 16], a bio-geochemical model that, based on daily meteorological data, site information (i.e., soil, vegetation, and site conditions) and parameters describing the ecophysiological features of the vegetation, is able to simulate fluxes and storage of water, carbon, and nitrogen at different spatial scales in terrestrial ecosystems. In particular, Biome-BGC identifies a quasi-equilibrium condition (the so-called climax) with the local ecoclimatic situation, thus quantifying the initial amounts of all carbon and nitrogen pools. Version 4.2 is available at the NumericalTerradynamic Simulation Group (NTSG) website ([[http://www.ntsg.umt.edu/project/biome-bgc.php](http://www.ntsg.umt.edu/project/biome-bgc.php)]([http://www.ntsg.umt.edu/project/biome-bgc.php](http://www.ntsg.umt.edu/project/biome-bgc.php))) and was used together with a set of ecophysiological parameters calibrated for the considered forest types [17]. More information on the use and setup of Biome-BGC in the study area can be found in [19]. NPP is the difference between GPP and \(R_{\mathrm{A}}\), with \(R_{\mathrm{A}}\) equal to the sum of growth (\(R_{\mathrm{G}}\)) and maintenance (\(R_{\mathrm{M}}\)) respirations. Since Biome-BGC assumes that the considered ecosystem is in equilibrium with its surroundings, its outputs must be corrected to account for actual ecosystem conditions. Note that Equation (1) estimates the GPP of all vegetation growing in each pixel. Therefore, it also must be corrected to account only for forest GPP. The correction applied in the present study was based on the distance to climax of the ecosystems concept [34], from which it is deduced that ratios of actual to potential tree cover or GSV are representative of the ecosystem development status or, in other words, its distance to climax [20].