Woodward water-balance model

Woodward uses a water- and energy-balance model to predict vegetation physiognomy and for various locations around the world. Woodward's model estimates available water (AVW) and actual evapotranspiration (AE) to estimate the maximum LAI which can be supported on a site during a typical year (Woodward 1987); other climate information is used to predict the physiognomy of the vegetation which should be present.

The model uses mean monthly temperature (MMT), Absolute minimum temperature (MMINT), monthly temperature range (MTR), monthly precipitation (MPR), monthly solar radiation (MRAD) and monthly relative humidity (MRH) -- to derive the predictions of AVW, evapotranspiration (ET) and physiognomy.

The water balance can be summed up as follows:

Rainfall strikes the vegetation canopy. Some of it is intercepted by the foliage and in hollows of plant stems and by impermeable areas of the ground surface. This is later evaporated away and is not available to the plant;
Some of the water falls through the canopy and eventually percolates into the soil. This water is available to the plant;
Some of the water taken up by the plant is lost via transpiration through the leaves. When transpiration exceeds available water, the plant becomes water stressed.

The net radiation balance can be summed up like this:

Sunlight strikes the canopy. Some of the energy is harvested during photosynthesis. Most of the energy, however, is dissipated by evapotranspiration of water from the plant and the ground surface;
The remainder of the energy is dissipated by convection away from the surface, and by storage into the ground. Soil heat storage is assumed to be a constant proportion of the incoming solar radiation.

Many of the above factors area a function of leaf area index (LAI), such as light attenuation through the canopy, which in turn affects photosynthesis and transpiration rates. Interception (and conversely throughfall) are a function of leaf area index. Evapotranspiration rate is also a function of LAI.

Woodward's model takes the climate information mentioned above and predicts AE (he assumes AE equals potential evapotranspiration) and AVW for odd-numbered values of LAI ranging from 1 to 9. As long as AVW exceeds AE (on an annual basis), the value of LAI can be supported. If AE exceeds AVW, however, the value of LAI cannot be supported.

Annual absolute minimum temperature (AMINT) is the first variable to consider for the prediction of physiognomy, followed by AVW and the distribution of AVW throughout the year. A summary of expected physiognomy based on AMINT in given in the table below:

Temperature	Phenomenon	Physiognomy
> 15°C	Temperature not limiting	Broad-leaved evergreen when rainfall adequate
-1 to 15°C	Chilling	Broad-leaved evergreen when rainfall adequate
-15 to 0°C	Freezing and supercooling	Broad-leaved evergreen
-40 to -15°C	Freezing and supercooling	Broad-leaved evergreen
< -40°C	Freezing and supercooling	Evergreen and deciduous needle-leaved (coniferous)

AVW influences physiognomy by its influence on maximum LAI which can be supported on a site. Typical values of LAI for major vegetation units (biomes) are given in the following table (data from Asner 2003).

Vegetation type	LAI
Crops	0.2-8.7
Desert	0.6-2.8
Forest, boreal deciduous broadleaf	0.6-4.0
Forest, boreal evergreen needleleaf	0.5-6.2
Forest, borea/temperate deciduous needleleaf	0.5-8.5
Forest, temperate deciduous broadleaf	1.1-8.8
Forest, temperate evergreen needleleaf	0.8-11.6
Forest, temperate evergreen broadleaf	0.01-15.0
Forest, tropical deciduous broadleaf	0.6-8.9
Forest, tropical evergreen broadleaf	1.5-8.0
Grasslands	0.3-5.0
Plantations	1.6-18.0
Shrublands	0.4-4.5
Tundra	0.2-5.3
Wetlands	2.5-8.4

Finally, the seasonal distribution of AVW must be considered. There are many drought-deciduous forests which support higher values of LAI than Woodward's model would predict because of abundant rainfall during the growing season. You must interpret these patterns carefully (the necessary information IS provided in the output).

Woodward's model also predicts extremely high LAI for high-latitude regions which in fact have very low LAI. This is a result of the fact that AE is quite low, which leads to a water surplus in Woodward's model, but growing seasons are very short and there is not enough energy for much plant growth. You can control for this by evaluating the temperature criteria listed in Table 1 before carrying out any further analyses.

Using AMINT and annual precipitation (APR) to predict vegetation type, Woodward's water-balance yields the following results (from Woodward and Williams 1987):

AMINT range	Annual precipitation	Vegetation type
≥ 0°C	≥ 600 mm	Evergreen or deciduous broad-leaved forest
≥ 0°C	≥ 600 mm	Deciduous broad-leaved forest
≥ 0°C	< 600 mm	Grassland/shrub
≥ -15°C, < 0°C	≥ 600 mm	Frost-resistant, evergreen broad-leaved forest
≥ -15°C, < 0°C	< 600 mm	Grassland/shrub
≥ -40°C, < -15°C	≥ 600 mm	Deciduous broad-leaved forest
≥ -40°C, < -15°C	< 600 mm	Grassland/shrub
< -40°C	≥ 400 mm	Evergreen or deciduous needle-leaved (conifer) forest
< -40°C	< 400 mm	Tundra (grassland/shrub)

Also, if AMINT is < -40°C, these additional criteria apply:

If the heat sum is < 600 degree days, you have tundra;
For heat sums of 600-950 degree days, you have deciduous conifers;
For heat sums of > 950 degree days, you have evergreen conifers.

Likewise, if AMINT ≥ 0°C, these additional criteria apply:

If AE > APR, you have deciduous broad-leaf forest;
If AE ≤ APR, you have evergreen broad-leaved forest.

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