Plants and Trees
Although VAMPS has been designed to support a multi-layer canopy, this option is untested and has been disabled in the current version. At present only one canopy layer is supported.
At the base of the canopy module lies the Penman–Monteith equation [2]:
Where:
\(\rho\) |
density of air |
\(C_p\) |
specific heat of air |
\(\delta e\) |
vapour pressure deficit |
\(\gamma\) |
psychrometric constant |
\(\Delta\) |
slope of the saturation vapour pressure curve |
\(r_s\) |
canopy resistance |
\(r_a\) |
aerodynamic resistance |
The program separates wet and dry periods. Evaporation from the wet canopy is calculated using the Penman–Monteith equation with \(r_s = 0\). During these periods transpiration (and hence root extraction) is assumed to be zero.
The amount of net radiation available is determined either via a simple fraction or via an equation by [6] linking the leaf area profile to absorbed radiation.
This module combines evaporation, transpiration, and interception, and VAMPS works best when it is used.
Interception
Interception of precipitation can comprise a large part of the water balance in forested catchments. Interception is defined as [7]:
… the amount of rainfall retained by the vegetation and evaporated without dripping off or running down the stem. At some point after precipitation ceases, all of the intercepted water will be evaporated…
Note that losses in the litter layer are not included. The balance between precipitation, evaporation, and canopy storage [8] determines the amount of rainfall interception.
How interception losses are calculated is mostly determined by the available data. The Rutter model [8] needs hourly input, while some of its parameters should be determined using 5-minute values. Daily values are most commonly available, so developing equations for daily values is practical [9]. Gash [1] developed an analytical variant of the Rutter model for use with daily data, assuming one storm per day.
The input file settings for interception are described in the
[interception] section of Configuration.
Gash’s method
For daily input data the method described by [1] is preferred. Gash’s model is based on the numerical model of [8] but can be applied to daily measurements assuming one storm per day. [10] tested both models on the same dataset and found comparable results.
The amount of water needed to completely saturate the canopy, \(P'\), is:
Interception losses for storms smaller than \(P'\):
Interception losses for storms larger than \(P'\):
Where:
\(\overline{R}\) |
average precipitation [mm/d] |
\(\overline{E}\) |
average evaporation during storms [mm/d] |
\(S\) |
storage capacity of the canopy [mm] |
\(p\) |
free throughfall coefficient |
\(p_{Tr}\) |
stemflow coefficient |
\(P\) |
precipitation [mm/d] |
\(E_i\) |
interception loss [mm] |
VAMPS can calculate the ratio \(\overline{E}/\overline{R}\) from the Penman–Monteith equation or use a fixed value (generally preferable, as Penman–Monteith with \(R_s = 0\) is not very accurate during storms due to advective energy).
VAMPS also allows the parameters \(S\), \(p\), and \(p_{Tr}\) to be linked to the Leaf Area Index (LAI) using the method of [11].
A version of the Gash model adapted for sub-daily time-steps is also available, in which the canopy storage \(S\) is reduced by the actual canopy storage at each time-step. Tests show that results from this adapted version and the standard daily version differ by no more than 2 %.
Calder regression model
[12] presented a simple regression model for interception loss that can adequately describe interception of forests in the UK:
Where:
\(E_i\) |
interception loss [mm/d] |
\(P\) |
precipitation [mm/d] |
\(\gamma\) |
maximum interception loss per day [mm] |
\(\delta\) |
fitting parameter |
Interception as a fraction of LAI
Where:
\(E_i\) |
interception loss [mm/d] |
\(P\) |
precipitation [mm/d] |
\(\text{laifrac}\) |
interception fraction (approximately equal to canopy storage per unit LAI) |
\(LAI\) |
leaf area index |
This method describes total interception well but fails on a storm-by-storm basis (used in the TOPOG model [13]). It is well suited for applications in which the canopy changes in time.
Rutter’s model
[8] developed a numerical interception model based on canopy storage. Hourly (preferably 5-minute) meteorological data are required:
Where:
\(t\) |
time-step [hour] |
\(C\) |
amount of water in the canopy |
\(P\) |
gross precipitation [mm/h] |
\(p\) |
free throughfall coefficient |
\(p_{Tr}\) |
proportion of water discharged via stem flow |
\(S\) |
canopy storage capacity [mm] |
\(E_c\) |
evaporation rate from wet canopy [mm/h] |
\(D_r\) |
drainage speed from storage in canopy [mm/h] |
The model is rather insensitive to both \(S\) and \(p\) [14].