WIMOVAC Macroclimate Module
Introduction
Most models of biological systems require input of data about one or
more environmental factors. These factors are typically key driving parameters that are
significant in determining the results of the simulation but are not directly controlled
by the processes. Models of vegetation growth, for example, typically require information
about solar radiation and temperature as a minimum and may require additional information
about humidity, rainfall, wind, ozone and importantly Ca. As indicated by the
macroclimate section in Figure 1, wimovac can make use of all of these inputs if they are
available.
Light intensity and temperature vary deterministically, because both
follow well-defined cycles of daily and annual periodicity related to solar radiation
inputs to the earth’s atmosphere. Overlaid on top of this essentially deterministic
behavior however, light intensity and temperature at a given site also show a stochastic
variability associated with unpredictable factors such as cloud cover. Consequently most
vegetation models which require an input of macroclimate conditions use a deterministic
model based upon sun-earth geometry to calculate the solar radiation at the top of the
atmosphere and a simplified model of atmospheric attenuation which may contain a
stochastic element that modifies the absorption of light by the atmosphere to reflect
variable cloud cover and atmospheric particulates. This fairly simple approach to
modelling solar radiation has been found to be adequate for a broad range of models
{Monteith, 1991 #1810; Reynolds, 1989 #1837; Reynolds, 1985 #634} and is the approach
adopted in wimovac.
Where vegetation models use humidity and rainfall information this is
usually produced directly from experimental records or from stochastic (gamma
distribution) models based upon long term experimental measurements (>5 years).
Such stochastic models typically use the statistical mean and some
measurement of the variability (coefficient of variation) calculated from the experimental
data to simulate rainfall patterns at various time intervals {Thornley, 1990 #1283}.
Experimental records of rainfall are often in the form of monthly means whilst most
vegetation models require either daily or instantaneous rates of rainfall and stochastic
models of this sort provide a useful tool in bridging this gap in time interval. Although
detailed physical climate models in the form of GCM (global circulation models) exist
which can make predictions about the expected rainfall and humidity for a given site and
time, these are complex and have seldom been linked directly to vegetation models. Most
existing vegetation models are able to make use of the GCM predicted changes to the mean
monthly rainfall and humidity for a site by modifying the monthly mean and variance
parameters to a simpler stochastic model in the appropriate fashion.
Macroclimate Module
The macroclimate (weather) module supplies light, temperature, relative
humidity, rainfall, wind speed and ozone property information. These properties form the
core driving variables needed by the plant and soil modules and can be specified in
wimovac in one of two broadly defined ways. i). Is the simplest and most powerful approach
for long simulation runs and relies on in built simulation models of the climate
properties. For example the light module has a built in model of Sun/Earth geometry,
atmospheric transmissivity and scattering effects on direct/diffuse light.
The light module can consequently be parameterised to simulate incident light for any
given location. This approach has the advantage of being suitable for long term model runs
and provides continuous data at any time interval ii). The second method is typically
useful for short simulation runs in which exact duplication of experimental conditions is
required and relies upon the macroclimate data grid to specify the exact climate
conditions that the models need to be run with. The macroclimate data grid is a
spreadsheet like form available by pressing the weather button on the macroclimate dialog.
When the weather data grid is operational wimovac modules examine the contents of the data
grid and attempt to extract weather information suitable for driving the model. The model
modules look for a specific date and time in the weather data sheet and only use the
corresponding weather conditions if a matching date and time is found. For example if a
model module looks for solar radiation information on an hourly interval and the weather
data grid only contains information on a daily basis the model will receive only one piece
of meteorological (met) data per day. The met data item that is found at the start of the
day in the datasheet will then be used as the basis of all other values for that day until
a new day and a new met data item is found. It is therefore important that the measurement
interval of data entered into the weather data grid reflects the required calculation
interval of the model module that is to use it.
Macroclimate weather outputs. i) Predicted direct, diffuse and
total light on Jday=190, W=52°. ii) Example 30 day temperature profile showing diurnal
patterns of temperature change as well as long term seasonal variations. iii). Stochastic
rainfall model. iv). Predicted sunrise and sunset, W=52°.
Light
The amount of solar radiation striking a surface on Earth is dependent
upon the orientation of the surface relative to the position of the sun and upon
atmospheric transmissivity {Norman, 1980 #1221; Norman, 1989 #1017}. Known relationships
between sun/earth geometry can be used to determine the position of the sun in the sky
from driving variable information about the latitude, year, day of year and time of day
for a given location. The light geometry relationship is expressed in the form of a solar
declination (d ) parameter, which expresses the tilt of the
Earth on its axis relative to the sun (Equation 1), and a solar zenith angle (q ) parameter, which accounts for the angle of the suns rays relative
to the vertical (Equation 2), for a given location and time. Latitude, year, day of year
and time of day are all prerequisite driving variables for any study site that is to be
simulated with the light module in Wimovac.
Wimovac uses information about the position of the sun in the sky
expressed as solar declination (d ) and solar zenith angle (q ) along with information about the solar constant (Is),
which is the amount of extraterrestrial solar radiation falling on a surface perpendicular
to the sun’s rays immediately above the atmosphere, in order to calculate the amount
of extraterrestrial solar radiation modified by absorption and transmissivity effects in
the atmosphere that forms incident direct and diffuse solar radiation at the canopy level
(Equation 3, Equation 4). Atmospheric transmissivity (a ) in
turn is largely determined by altitude (P), cloudiness and the amount of particulates
(pollutants, dust and water vapour) in the air. Details of this approach are given in
{Monteith, 1991 #1810}.
The direct and diffuse solar radiation output properties of the
macroclimate light module are the two main driving variable inputs into the canopy
microclimate and photosynthetic assimilation modules. They largely determine the energy
available to the plant canopy for photosynthesis and are vital for driving plant
evapo/transpiration, soil evaporation and heat fluxes through the energy balance
calculations performed for these structures. The quality of incident solar radiation
expressed as the ratio of direct (Idir) and diffuse (Idiff) light
plays a significant role in determining the nature of canopy light interception, and the
balance of productivity between sunlit and shaded leaves. The model Idir/ Idiff
ratio is strongly influenced by atmospheric transmissivity, altitude and solar zenith
angle for a given study site (Equation 3., Equation 4.).
Equations from {Monteith, 1991 #1810} and {Long, 1991 #1927}.
Parameters and symbols as specified in appendices I & II.
Temperature
The temperature of the climate is largely a function of solar
radiation. For this reason environmental temperatures tend to follow sinusoidal patterns
like those of light intensity. However temperature also partly depends on the quantity of
heat stored in the environment and a simple cosine approximation of temperature related to
solar radiation has proved to be inadequate {Spain, 1992 #1278}. In many biological
simulations, extremes of temperatures are more important than means {Webb, 1975 #1979}.
Wimovac uses the three element approach proposed by Webb et al (1975), to solve this
problem, in which mean daily temperature (Equation 5), daily temperature range (Equation
6) and daily temperature excursion (Equation 7) are calculated in order to express the
importance of temperature extremes as well as the mean. The air temperature at any time of
day can be found with Equation 8 which although strictly empirical has the advantage of
being simple, and easy to parameterise, from limited meteorological data, requiring only
five or more years worth of temperature averages for a given site. The hr
parameter in Equation 8 importantly allows a time offset between the maximum incident
solar radiation and the maximum temperature of simulated days, which reflects the
localised heat capacity of the surroundings.
Equations from Spain (1992){Spain, 1992 #1278}. Parameters and symbols
as specified in appendices I & II.
Humidity
The macroclimate module provides an external property which describes
the average atmospheric relative humidity above the canopy. This property may be set as a
constant in the macroclimate section of the model parameter database base and takes the
form of a single value with the relative humidity expressed on a 0-100 percent scale. The
atmospheric humidity may alternatively be set to one value for dry days and another for
rainy days and can therefore be linked in its behaviour to the rainfall sub-module. The
atmospheric humidity in wimovac has a notable effect on leaf and soil evapo/transpiration
rates and concomitant energy budget/temperature calculations. Some wimovac simulation
modules, particularly those being driven by experimental climate data use vapour pressure
deficit (VPD) rather than relative humidity in their calculations. Where a conversion
between these is required wimovac uses standard data tables of saturated water vapour
content at a specified simulation temperature to make the physically correct conversion
{Jones, 1992 #1954}.
Rainfall
Rainfall is almost invariably a major determinant of yield for most
field crops and an important factor in biomass production in natural vegetative systems.
The growth responses of plants are often a compromise between photosynthesis and
transpiration, with optimisation of water use efficiency being a key aim. The macroclimate
module in wimovac produces an external property which describes the daily precipitation
(rainfall) given in mm day-1. This property may be set as either a constant in
the macroclimate section of the model parameter database which is useful for simple
diagnostic model runs, or by using the built in stochastic rainfall generator.
The variability of rainfall, both in amount, and distribution with
respect to time is an essential component of quantitative studies of irrigation and water
use {Thornley, 1990 #1882}. The simple stochastic rainfall model in wimovac is designed to
account for these two properties of rainfall using only the most commonly available met
station data. The stochastic rainfall model requires three properties to be set for each
month of the year that rainfall is to be simulated for. These are i). Mean monthly
rainfall based upon a 5 or more year average for the site (mm month-1). ii).
Coefficients of variation (CV) between the 5 or more years worth of values for
each month (Cv expresses the degree of spread of the monthly means and is equal
to the standard deviation divided by the mean of the values). iii). Mean number of rainy
days within the calendar month averaged over the 5 or more year period. The stochastic
rainfall model is called once a day and first calculates the probability of rainfall
during that day based upon the mean number of rainy days during the current simulation
month and the number of days in the month (Equation 10).
Equations from {Thornley, 1990 #1882}. Parameters and symbols as
specified in appendices I & II.
The probability that there is no rainfall is given by (1-q). The model
then calculates the effective length of ‘good’ or ‘bad’ periods of
weather (Neff) based upon q and the user inputted coefficient of variation (Cv) for the
simulation month. The mean daily rainfall (r~) can then be calculated as (Equation 11) and
the actual amount of water received (h) on a given rainy day calculated by (Equation 12).
By then generating a pseudo random number in the range zero to one it is possible to
establish stochastically whether it should rain that day. If the random number is greater
than the probability of no rainfall then it should rain and the amount should be h (mm).
If the random number is less than the probability of no rainfall then it should not rain.
Wimovac currently makes the simplifying assumption that all rainfall is
incident upon the soil surface. However at a later date a canopy rainfall
interception/retention model may be added that would allow the effects of canopy water
retention and consequent higher evaporation effects to be explored. A simple water run off
model is included in Wimovac in which excess rainfall falling onto a saturated soil
surface is assumed to runoff the soil surface and is lost to the system.
2.3215 Wind speed
The wind speed properties of the macroclimate module are an important
factor in determining the boundary layer conditions for the energy balance and
evapo/transpiration calculations of canopy and soil surfaces {Monteith, 1991 #1810}. The
macroclimate model contains a property describing the prevailing wind speed at 2m above
the canopy. With the multiple layer canopy model there is an option to attenuate this wind
speed through the canopy profile using either a logarithmic or exponential distribution
{Monteith, 1991 #1810} as expressed in Equation 88, Equation 89 and Equation 90.
Ozone
A relationship between effective ozone exposure, taking into account O3
concentration and stomatal conductance and the maximum rate of carboxylation (Vcmax)
used in the Farquhar model of C3 photosynthesis has been suggested {Martin,
1997 #1980}. An early version of this formulation is built into the leaf photosynthesis
model in wimovac and can be initialised in the leaf ozone section of the model parameters
database.
The leaf ozone model requires that atmospheric ozone concentration
either be set as a constant or more realistically generated dynamically with time. The
atmospheric ozone concentration is therefore a property of the macroclimate module and
consists of a series of sine wave functions similar in nature to the sine wave temperature
functions discussed previously.
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