The Atmosphere

In the atmosphere module, potential transpiration, potential soil evaporation, and evaporation from a wet surface are calculated from meteorological and vegetation parameters. Several methods can be chosen depending on the available data and the user’s preferences.

The terms potential evaporation, actual evaporation, and evapotranspiration can lead to some confusion, particularly when using models like VAMPS. In the final version of the model these will be simplified; in the meantime most names and units remain as quoted from the original source.

Potential evaporation

Potential evaporation can be used in VAMPS to determine actual evaporation (or evapotranspiration, depending on the method chosen). Three methods are available:

1. Determine Penman \(E_0\) (open water evaporation) [penman1956N,makkink1957] using reflected radiation, net radiation, relative humidity (used to calculate the vapour pressure deficit), wind speed, temperature, and incoming radiation.

2. Determine Penman \(E_0\) using sun-ratio, relative humidity, wind speed, temperature, and incoming radiation.

3. Using the Makkink formula [makkink1961,commissie1988N] which needs incoming radiation, relative humidity, wind speed, and temperature.

The input file settings for potential evaporation are described in the [pevaporation] section of the Configuration chapter.

Penman open-water evaporation

Penman \(E_0\) is determined via:

\[E_0 = \frac{\Delta R_{no} + \gamma E_a}{\Delta + \gamma}\]

Where:

\(R_{no}\)	net radiation over open water [cm/day]
\(E_a\)	aerodynamic evaporation or drying power of air [cm/day]
\(E_0\)	open water evaporation [cm/day]
\(\Delta\)	slope of the saturation vapour pressure curve
\(\gamma\)	psychrometer ‘constant’ [mbar/°K] (an air pressure of 998 mbar is assumed)

The determination of \(E_a\) follows [3]:

\[E_a = 2.6 \; (e_s - e_a) \; (1 + 0.537 \, u)\]

Where:

\(e_a\)	actual vapour pressure [mbar]
\(e_s\)	vapour pressure at saturation [mbar]
\(u\)	mean daily wind speed at 2 m

VAMPS calculates \(e_s\) and \(e_a\) from relative humidity and dry-bulb temperature using an equation described by [4].

Net radiation over open water is given by:

\[R_{no} = R_s (1 - \alpha) - R_{nl}\]

Where:

\(R_s\)	incoming solar radiation
\(R_{nl}\)	net long-wave radiation
\(\alpha\)	albedo of open water (0.05)

In method 1, \(R_{nl}\) is calculated using incoming and reflected short-wave radiation:

\[R_{nl} = R_s - R_{net} - Rs_{out}\]

Where \(Rs_{out}\) is reflected short-wave radiation and \(R_{net}\) is net radiation.

In method 2, the sun-ratio \(n/N\) is used to calculate \(R_{nl}\):

\[R_{nl} = \frac{86400 \, \sigma T^4 \, (0.56 - 0.248 \sqrt{e}) \, (0.1 + 0.9 \, n/N)}{\lambda}\]

Where:

\(T\)	mean daily air temperature [°K]
\(e\)	mean daily water vapour pressure [kPa]
\(n/N\)	ratio of duration of bright sunshine hours \(n\) to the maximum possible duration of sunshine hours \(N\)
\(\lambda\)	latent heat of vaporisation

Makkink reference evaporation

Makkink [5] reference evaporation is calculated by:

\[\lambda E = C \frac{\Delta}{\Delta + \gamma} R_s\]

Where \(C\) is a constant (usually 0.65) and \(\lambda\), \(E\), \(\Delta\), \(\gamma\), \(R_s\) are as defined above.

Actual evapotranspiration

If you do not want to model an entire canopy (see Plants and Trees) you can estimate actual evapotranspiration using one of three methods:

1. Set actual evapotranspiration equal to potential evaporation.

2. Multiply potential evaporation by a crop factor.

3. Calculate actual evaporation using the Penman–Monteith formula.

The preferred approach is to use the full canopy module, which closely integrates transpiration, interception, and soil evaporation.