## 2 Materials and Methods
### Model Description and Parameterization  
To improve the capability of SCOPE in simulating SIF emission and photosynthesis at the ecosystem level, we assessed how well OCO-2 SIF and flux tower GPP could constrain key uncertain model parameters. The SCOPE model is a 1-D vertical schematization of integrated radiative transfer model (RTM) and energy balance model that enables the simulation of canopy reflectance and fluorescence as well as the heat, carbon, and water fluxes between soil, vegetation, and atmosphere [15; 16]. The radiative transfer and chlorophyll fluorescence routines of the SCOPE model are calculated with the module Fluspect [15], which is based on the vastly used canopy RTM, PROSAIL [56], with the addition of backward and forward fluorescence spectra. The PROSAIL model is a RTM that couples a leaf-level model, PROSPECT [57], with a canopy RTM, SAIL [58]. PROSAIL is perhaps the most commonly used RTM for reflectance and fluorescence applications. The updated version of SCOPE (V1.7) uses a new version of PROSPECT, PROSPECT-D [59], which adds anthocyanins to carotenoids and chlorophylls, the two plant pigments in the current model. The biochemical model in SCOPE is based on [42] and [60] for C3 and C4 plants, respectively. The SCOPE model can simulate fluorescence emission and photosynthesis simultaneously, and more details are provided in previous studies [15; 16].  
SCOPE contains a series of vegetation physiological parameters and requires meteorological data such as incoming solar radiation, wind speed, air temperature, and relative humidity. The LAI and leaf chlorophyll content (Cab) are two important structural and physiological parameters. Given the consistence of SCOPE and PROSAIL in radiation transfer routines, we retrieved the seasonal variations of Cab and LAI using the MODIS reflectance products of band 1 to band 7 and the PROSAIL model. In this study, the genetic algorithm (GA) approach was used to retrieve the structural and physiological parameters. The GA algorithm is a global optimization approach based on an analogy that consists of natural selection and evolutionary genetics [26; 61]. The GA algorithm employs various operations of evolutionary strategies: encoding, fitness evaluation, parent selection, genetic operation, and replacement [61]. Assuming that the best chromosome is a raw fitness, \(f_{best}\), the fitness of the \(i\)-th chromosome (\(f_{i}\)) in the ordered list is conducted using a linear function during the evaluation:  
\[f_{i}=f_{best}-(i-1)\bullet d \tag{1}\]  
where \(d\) is the decrement rate. The average objective value of the population is mapped into the average fitness by Equation (1). The roulette wheel selection is commonly used to implement the proportionate scheme in GA. Giving the chromosome \(x\) with a fitness value \(f(x,t)\), its growth rate \(p_{i}\) can be defined as follows:  
\[p_{i}=\frac{f(x,t)}{F(t)} \tag{2}\]  
where \(F(t)\) is the average fitness of the population. We minimized the following objective function (Equation (3)):  
\[\mathrm{F}_{spec}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(Ref_{i,sim}-Ref_{i,obs})^{2}} \tag{3}\]  
where \(Ref_{i,sim}\) and \(Ref_{i,obs}\) are the \(ith\) simulated and observed reflectance band, respectively, and n is the number of reflectance bands. The prior ranges of the parameters (e.g., Cab, LAI) of the PROSAIL model are given in Table 1.  
The LAI and Cab inverted by the PROSAIL model at Park Falls showed the seasonal patterns that were expected for temperate deciduous forests (Figure 2). The inverted LAI was generally consistent with the MODIS LAI, and the inverted Cab showed a similar seasonal cycle as the LAI.