ORCHIDEE Development Section


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 \(dt\).