2. The Upper Danube Catchment
3.3 The PROMET Biological Model
3.3.3 Biological Processes
3.3.3.1 Model Initialization
When the model run is started, the input parameters that correspond with the different landuse categories and are needed for the calculation of the biological submodels are read from parameter files and stored within the internal GIS structure. All crop specific information, concerning the 27 different landcover categories that are accounted for in the model, is arranged following a strict hierarchy that allows for a clear differentiation between the different landuse types (fig. 3.13). This enables the model to access the correct parameters unmistakeably for each vegetation type from all subroutines. The land cover hierarchy also includes information, if the currently modelled pixel is a vegetated or a non-vegetated surface type. For non-vegetated surface types, the biological submodels are skipped. In PROMET, it also is assumed that no biological activities take place beneath a closed snow cover. The biological routines, with exception of the progress of the phenological stages, consequently do not run if a snow cover is modelled for a proxel at the current time step.
Modelling of Canopy Processes
Figure 3.14: Flowchart of the biological subroutines of PROMET.
The vegetation cover is modelled for two vegetation layers, so that the leaf gas exchange routines have to be called twice for every time step (fig. 3.14). The leaf energy balance is solved subsequently for the sunlit and shaded parts of the leaves of both vegetation layers. Figure 3.14 also illustrates that the actual photosynthesis is a byproduct of the efforts concerned with the determination of the latent heat flux from the leaf. When the leaf energy balance is finally solved, the resulting carbon fixation is passed on to the plant growth routine, where the newly generated biomass is utilized according to the phenological stage of the canopy (see section 3.3.3.6.2).
The biological submodels of PROMET require a set of variables from the preceding model time step. Important parameters for example are the already accumulated biomass, the growth stage that has been reached by the vegetation type of the currently modelled proxel, the overall depth and density of the root system et cetera. When a model run is initialized, this information is not available for the very first time step. The model therefore was equipped with a subroutine that only is called once for the first time step and initializes the most determinant variables of the biological submodels. The initialisation is dynamic to some degree, so that the model run can be started on a user-defined day of the year.
In a first step it is decided, whether the modelled canopy is a perennial type and therefore requires the biological submodel at any time of the year, or if the cover type is of a seasonal kind. The non-perennial crops are discerned into winter and spring crops. If the starting day of the modelled time window lies beyond the vegetation period, the variables are set to zero and 45
Modelling of Canopy Processes
the model run commences without the biological submodels running. If the starting day lies within the vegetation period of the currently modelled canopy type, the explicit initialisation is started.
The determinant that is used to initialise all other important variables is the leaf area index. It is assumed that the annual course of the LAI can generally be structured into four phases (fig. 3.15, left):
− A period, where the leaf area is at its minimum (LAIini),
− a period of increasing leaf area,
− a time of maximum LAI values (LAImax) and
− a time, where the leaf area decreases.
Figure 3.15: Phases of LAI development (left) and LAI curves for selected crops used for the initialization of the first time step.
With a simple function, the green leaf area index is assumed in dependence of the DOY (eqs. 3.28-31). For every crop, a different parameter set is used that modifies the course of the function (fig. 3.15, right). The boundaries of the functions are the days of the year, where the phases of LAI development are changing. While d is the currently modelled day, dincstart is the
day when the leaf area starts to increase, dincend the day when it stagnates, ddecstart the day when
the leaf area starts to decrease again and ddecend marks the completion of the senescent phase.
ini
LAI
LAI
=
dincstartIf d is lower than or d is greaterthan ddecend (Eq. 3.28)
(
)
(
)
[
]
[ k (d dincstart) ini ini inie
LAI
LAI
LAI
LAI
LAI
LAI
⋅
− ⋅ −−
+
⋅
=
1 maxmax ] d If d is greater than
incstart and d is lower
than dincend
(Eq. 3.29)
max
LAI
LAI
=
dincendIf d is greater than and d is lowerthan dincstart
(Eq. 3.30)
( )
[ ]
{ k d ddecstart } (LAI LAIini
ini
e
LAI
LAI
=
+
− 2⋅ − −1 2⋅ max− )If d is greater than ddecstart and d is lower
than ddecend
Modelling of Canopy Processes
For the equations 3.29 and 3.30, k1 and k2 are coefficients that modify the gradient of the LAI
increase and decrease.
This method is considered to provide reasonable initialisation values for the agricultural crops as well as for the natural grasslands in the colline altitudinal belt. However, the different appearances of natural canopies at higher altitudinal vegetation zones are not accounted for in this approach. This would lead to the failure that for example coniferous forests on alpine sites above 1500 m sea level height, where the spruce forest is gradually superseded by dwarf-pines, would be initialized with the same large leaf area that they are supposed to develop in the plain regions of the alpine foreland. To account for this problem, all pixels of the input data set for the Upper Danube Basin that are populated with coniferous trees (see appendix A.8.1) were analysed with respect to their altitude and their annual mean temperature. It was found that a strong correlation of elevation and annual mean temperature exists (r² = 0.96, fig. 3.16, left), so that the annual mean temperature could well be consulted for the differentiation of the altitudinal vegetation zones.
If the observed or interpolated annual mean temperature of a modelled pixel falls below 8 °C, which within the Upper Danube Basin normally is the case for elevations that exceed 600 m a.s.l. (fig. 3.16, left), the determined leaf area values are reduced by a factor that is based on a third-degree polynomial of the annual mean temperature of the preceding model year (fig. 3.16, right, eq. 3.32).
3986
.
0
0524
.
0
0133
.
0
0013
.
0
⋅
3+
⋅
2+
⋅
+
−
=
avg avg avgLAI
T
T
T
R
(Eq. 3.32)Taking the reduction factor into account, the initial leaf area for proxels located at “cold” sites reads (eq. 3.33):
LAI
R LAI
LAI = ⋅ If Tavg is lower than 8 °C (Eq. 3.33)
Figure 3.16: Relation of long-term annual mean temperature and terrain elevation for coniferous sites within the Upper Danube Basin (left) and factor reducing the leaf area of coniferous forest in dependence of the annual mean temperature of the last modelled year (right).
Elevation [m a.s.l.] Annual Mean Temp. [°C] 0 2 4 6 8 10 0 500 1000 1500 2000 2500 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8
Annual Mean Temperature [°C]
R ed uc tion F ac tor [- ] 47
Modelling of Canopy Processes
When the leaf areas for all vegetation categories that either are perennial or in their active growing period are determined, the height of the canopy (hc) is calculated using a cultivar
specific relation of leaf area and plant height (LHrel).
rel
c
LAI
LH
h
=
⋅
(Eq. 3.34)Due to lack of better data for the first model time step, all relevant temperatures like the leaf and soil temperatures are initialised with the air temperature (Ta) as a first guess.
With the help of the LAI development phases (fig. 3.15), the phenological phase is determined according to the DOY. The rate of development (see section 3.3.3.6.1) is supposed of having reached half the amount of the transition to the next growth stage, thus allowing the crop to autonomously commence its phenological development once the model run has started.
As soon as the phenological phase is known, the leaf biomass can be determined by inverting the “LAI-to-leaf-mass-per-area” relationship (eq. 3.35, see section 3.3.3.6.3). The leaf biomass then is extrapolated to the other plant parts that are stem, grain and root using the imported allocation percentages (see section 3.3.3.6.2).
LMA
LAI
B
leaf=
⋅
(Eq. 3.35)For the initialisation of all agricultural vegetation types, the root depth (RD) is assumed as a percentage of the crop specific maximum root depth (RDmax, tab. 3.02), according to the
phenological stage. Natural and perennial canopies are initialized with their specific maximum root depth.
Table 3.02: Initial root depth according to the initial growth stage.
d < dincstart dincstart > d < dincend dincend > d < ddecend d > ddecend
max
3
.
0
RD
RD=
⋅
RD=0.7⋅RD
maxRD=RD
maxRD=0.3⋅RD
max1
2
3
4
0 0.5 1 1.5
Root Length Density [cm/cm³]
So il L ay er 2
)
(
1)(
0.92⋅
− ⋅−=
s s L Le
RLD
(Eq. 3.36)Modelling of Canopy Processes
The distribution of the root density to the soil layers is initialised by an exponential function (eq. 3.36, GEWITZ AND PAGE 1974, ADIKU ET AL.1996). Depending on the soil type, either three or
four soil layers (Ls) exist in the model that can possibly be rooted. The initial root length density
of a soil layer (RLDLs) decreases with increasing soil depth for all vegetation types (fig. 3.17).
Having passed through the initialization process, the model is able to run all biological submodels, starting from any user-defined day of the year. However, it is recommended to compute the model at least one model year in advance, before the results can be considered to be reliable. This spin-up time allows the soil water balance to adjust to the current meteorology and the biological parameters to accommodate to the climatic specifications. All model results and intermediate results presented here were generated with a spin-up phase of at least one model year.