The assimilation scheme

The purpose of the present study is thus twofold: to introduce an assimilation scheme for land surface models that uses a quantity related to vegetation productivity; and to assess the impact of derived surface properties on the simulated climate. If there is a significant impact, this can be taken as an indication that assimilation of surface variables in addition to atmospheric variables could be used to improve GCM simulations. Since in the modelling framework used here, this requires the inclusion of an active biosphere within the surface model, the degree of the impact can also be taken as an indication of the importance of vegetation feedback to climate.

This preliminary setup preceding a full assimilation of atmospheric and surface variables within a GCM follows the lower part of Fig. 1. fAPAR is chosen as a critical parameter that controls primary productivity and transpiration, one that at the same time can be derived rather accurately from the contrast between the red and near-infrared reflectances measured from space [Asrar et al., 1994; Goel and Qin, 1994].

The assimilation is performed by a parameter re-estimation of the BETHY scheme, in which three key parameters are modified (see below). Those parameters have earlier been identified to as those to which the carbon and moisture balance are most sensitive [Knorr, 1997; Knorr, 2000]. This fAPAR assimilation scheme consists of four steps:

1. Global monthly fields of fAPAR are derived from NOAA-11/AVHRR data at 1 degree resolution after rigorous screening of cloudy and unfavorable angular conditions.

2. The BETHY scheme is driven with mean climate data to compute both land-surface carbon and water exchanges and fAPAR for 12 months at 1 degree spatial resolution.

3. Satellite derived and model predicted values of fAPAR are compared.

4. Model parameters x1...xn are modified until a cost function, J, reaches its minimum:

This minimisation is carried out separately for each grid point.

The cost function, J, accounts for the difference between monthly satellite derived fAPAR, fm, and model computed fAPAR, g„„ scaled by the assumed error variance of fAPAR, a2f. An additional term is used to increase J when the model parameters, x„ deviate from the standard values, y„ assumed to represent a priori knowledge, with error variance of a2y,j for the values y,.

The three model parameters chosen as xi...x3 are: xt=wmax, representing water limitation (wmax is the bucket size, i.e. the maximum amount of plant-available soil moisture), x2=T^ representing temperature limitation (T^ is the leaf onset and shedding temperature, cf. Eq. 4), and x3=fc, representing other, residual limitations that typically have longer times scales than decades, such as human land use or nutrient availability (fc is the vegetated cover fraction, cf. Eq. 5). J is then minimised by modifying xi to x3 at each grid cell, rerunning the model each time for the six-year simulation period, with the first three years neglected as spinup (see above). The parameters, their assumed error variances and their allowed value ranges are listed in Table 1. The constrained minimisation technique used is the downhill simplex method j{xr..x „)= 2,1-5-L + 2/—2

[Press et al., 1992], which, compared to gradient methods, is extremely robust against abrupt changes in J(xi...x„).

Table 1, Measured quantities and model parameters used in the assimilation scheme, together

General symbol

in model

quantity/ parameter










radiometric measure

monthly fAPAR

indicative of vegetation



bucket size




water limitation


leaf onset/ shedding




temperature limitation




vegetation fractional




other limitations


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