Calculating leaf wetness duration in an apple orchard. Tor Håkon Sivertsen The Norwegian Crop Research Institute. The practical context of the problem. We are considering a small region with fruit farming. A few automated agro meteorological stations are placed in the area
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Tor Håkon Sivertsen
The Norwegian Crop Research Institute
NORSJØ REGION OF SOUTHERN NORWAYcovered by two weather radars
Calculating Evaporation orchardof intercepted waterThis process is important and difficult and the approach is connected to the energy balance and the water balance
-How to identify the local weather?
-How to extrapolate measurements when knowing the physical mechanisms?
-What about advection?
-What about modelling?
The procedure for estimating parameter values at a site ‘j’ when knowing the measured parameter values at an
agro meteorological station ‘i’ is connected
to the hypotheses of turbulent adiabatic mixing of parcels of air in the boundary layer close to the ground.
We get the dry adiabatic lapse rate:
T(zi)-T(zj)=-(g/cpa)( zi- zj)
g: The acceleration of gravity
T(z): The air temperature 2m above the soil surface
cpa: The heat capacity of the air at constant pressure
zi: The height above sea level of a site denoted by
the index ’i’
We also know the relative humidity of the air RH(zi) and the air temperature T(zi) at the site ‘i’, and we may calculate ew(T(zi)), the saturation vapour pressure and e(zi), the water vapour pressure of the air.
ew(T(z)): The saturation water vapour pressure at the temperature
e(z): The water vapour pressure of the air at the level ‘z’
We assume that the water vapour in the air and also the dry air may be modelled by the ideal gas law at the site ‘i’ where
paiα ai = RaT
eiα vi = RvT
α a : The specific volume of the dry air
α v : The specific volume of the water vapour
We are using Poisson’s equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site ‘i’ to the site ‘j’:
(Ti/ Tj)·( pi/ pj) κ=1
κ= Ra/ cp
By using the partition of the partial pressures and the partial densities of the air, and using the above formulas we may find the water vapour pressure e(z ) and the saturation pressure of water vapour at the site ‘j’, knowing the thermodynamic properties at the site ‘i’.
pi =pai+ ei
ρj = ρaj+ ρvj
In this system the pressure is not measured, we therefore have to put pi equal to some auxiliary value ‘P’ originally.
Precipitation is measured by weather radar (hourly values) in pixel areas of 1x1km
Thank you very much! orchard