Albedo Computation

Fractioning for bare soil, vegetation and snow

The land surface in ORCHIDEE is represented by 13 plant functional types (PFTs), including bare soil (PFT1), that can co-exist in any grid cell. The PFT distribution is described by yearly PFT maps, defining the maximum possible fraction of each vegetation type at each pixel ($frac_\mathsf{max,pft}$), so that $$frac_\mathsf{veg} = \sum_\mathsf{pft=1}^{13} frac_\mathsf{max,pft} \leq 1$$ The rest fraction of this distribution (if present) is considered as non-biological fraction (e.g. ice, permanent snow, etc.): $$frac_\mathsf{nobio} = 1 - \sum_\mathsf{pft=1}^{13} frac_\mathsf{max,pft}$$ The actual vegetation fractions for each vegetated PFT (PFT2-PFT13) are calculated at each time step as an exponention function of the simulated leaf area index (LAI): $$frac_\mathsf{pft} = (1-\exp(-\mathsf{LAI}_\mathsf{pft})) \cdot frac_\mathsf{max,pft}$$ The bare soil fraction (PFT1) then can be found as: $$frac_\mathsf{bs} = \sum_\mathsf{pft=1}^{13} frac_\mathsf{max,pft} - \sum_\mathsf{pft=2}^{13} frac_\mathsf{pft}$$ The fraction of snow on vegetated surfaces is calculated in the explicit snow scheme from the simulated snow depth ($d_\mathsf{snow}$) and snow density ($\rho_\mathsf{snow}$) as: $$frac_\mathsf{snow,veg} = \tanh{\frac{50 \cdot d_\mathsf{snow}}{0.025 \cdot \rho_\mathsf{snow}}}$$ Whereas the fraction of snow on non-biological surfaces is calculated using simulated snow mass ($m_\mathsf{snow}$ in kg/m²) and two fixed parameters — critical snow depth ($d_\mathsf{snow,cri}$) and snow density ($\rho_\mathsf{snow,cri}$): $$frac_\mathsf{snow,nobio} = \min\left(1,\frac{\max(0,m_\mathsf{snow})}{\max(0,m_\mathsf{snow}) + d_\mathsf{snow,cri} \cdot \rho_\mathsf{snow,cri}}\right)$$

Albedo parametrization

The overall albedo for the land surface is calculated by parameterizing the albedo coefficients for each land surface compartment (bare soil, vegetation types, non-biological surace, plus the snow cover for any of the land surface type): $$albedo = frac_\mathsf{veg} \left[ (1-frac_\mathsf{snow,veg}) \cdot alb_\mathsf{veg} + frac_\mathsf{snow,veg} \cdot alb_\mathsf{snow,veg} \right] +$$ $$+ frac_\mathsf{nobio} \left[ (1-frac_\mathsf{snow,nobio}) \cdot alb_\mathsf{nobio} + frac_\mathsf{snow,nobio} \cdot alb_\mathsf{snow,nobio} ) \right]$$ Where the vegetation albedo ($alb_\mathsf{veg}$) is defined as the superposition of the preset albedo coefficients for bare soil ($alb_\mathsf{bs}$) and leaf albedo for each vegetation type ($alb_\mathsf{leaf}$), weighted by their fractions: $$alb_\mathsf{veg} = frac_\mathsf{bs} \cdot alb_\mathsf{bs} + \sum_{\mathsf{pft}=2}^{13} frac_\mathsf{pft} \cdot alb_\mathsf{leaf,pft}$$ The snow albedo is parameterized for each vegetation type with the two coefficients — aged snow albedo ($alb_\mathsf{snow,aged}$), describing the minimum snow albedo value for dirty old snow, and snow albedo decay rate ($alb_\mathsf{snow,dec}$), used to calculate the snow albedo as the function of the simulated snow age ($age_\mathsf{snow}$): $$alb_\mathsf{snow,veg} = \frac{\sum\limits_{\mathsf{pft}=1}^{13} frac_\mathsf{max,pft} \cdot \left[ alb_\mathsf{snow,aged,pft} + alb_\mathsf{snow,dec,pft} \cdot \exp(-age_\mathsf{snow} / tcst_\mathsf{snow}) \right] }{\sum\limits_{\mathsf{pft}=1}^{13} frac_\mathsf{max,pft}}$$ Where $tcst_\mathsf{snow}$ is the time constant of the albedo decay of snow. The snow albedo for non-biological surfaces is calculated using the same principle with the coefficients for bare soil (PFT1): $$alb_\mathsf{snow,nobio} = alb_\mathsf{snow,aged,1} + alb_\mathsf{snow,dec,1} \cdot \exp(-age_\mathsf{snow} / tcst_\mathsf{snow})$$ Finally, the two additional parameters are used in controlling the snow age evolution — the maximum period of snow aging ($age_\mathsf{snow,max}$) and the transformation time constant for snow ($trans_\mathsf{snow}$), both used in calculating the snow age at each time step of the model simulations: $$age_\mathsf{snow,i+1} = (age_\mathsf{snow,i} + (1-age_\mathsf{snow,i} / age_\mathsf{snow,max}) \cdot dt ) \cdot \exp (-precip_\mathsf{snow} / trans_\mathsf{snow} )$$ Where $precip_\mathsf{snow}$ is the snow precipitation content falled during the time interval $dt$.