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Calculating leaf wetness duration in an apple orchard
Tor Haringkon Sivertsen
The Norwegian Crop Research Institute
The practical context of the problem
bull We are considering a small region with fruit farming
bull A few automated agro meteorological stations are placed in the area
bull The region is covered by a weather radarbull The problem of estimating leaf wetness
duration is closely connected to plant pathology
NORSJOslash REGION OF SOUTHERN NORWAY
covered by two weather radars
The NORSJOslash
area
The system for making measurements
bull There are a few automated agro meteorological stations in the area measuring air temperature precipitation relative humidity of the air global radiation wind velocity (2m) and leaf wetness duration (hourly recordings)
bull There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The practical context of the problem
bull We are considering a small region with fruit farming
bull A few automated agro meteorological stations are placed in the area
bull The region is covered by a weather radarbull The problem of estimating leaf wetness
duration is closely connected to plant pathology
NORSJOslash REGION OF SOUTHERN NORWAY
covered by two weather radars
The NORSJOslash
area
The system for making measurements
bull There are a few automated agro meteorological stations in the area measuring air temperature precipitation relative humidity of the air global radiation wind velocity (2m) and leaf wetness duration (hourly recordings)
bull There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
NORSJOslash REGION OF SOUTHERN NORWAY
covered by two weather radars
The NORSJOslash
area
The system for making measurements
bull There are a few automated agro meteorological stations in the area measuring air temperature precipitation relative humidity of the air global radiation wind velocity (2m) and leaf wetness duration (hourly recordings)
bull There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The NORSJOslash
area
The system for making measurements
bull There are a few automated agro meteorological stations in the area measuring air temperature precipitation relative humidity of the air global radiation wind velocity (2m) and leaf wetness duration (hourly recordings)
bull There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The system for making measurements
bull There are a few automated agro meteorological stations in the area measuring air temperature precipitation relative humidity of the air global radiation wind velocity (2m) and leaf wetness duration (hourly recordings)
bull There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The problem of transferring measurements in the local areabull We have four agrometeorological stations and 15
sites with fruit farming in the areabull The measurements of precipitation by radar is
connected to each sitebull The measurements at the agro meteorological
stations are transferred to the rest of the sitesbull We are using the hypotheses of turbulent mixing
and dry adiabatic processes as a first approximation
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The problem of calculating measuring leaf wetness in an orchard
bull We look at the processes of relevance
bull Precipitation
bull Condensation of water on the leaves
bull Evaporation
bull Dry surface of the leaf
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Precipitation
bull The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets hourly recordings
bull We also measure precipitation by weather radar i pixel areas of 1x1km hourly recordings
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Condensationbull Using the (transferred) mesurements of
temperature and relative humidity of the air as well as the knowledge of the altitude above sea level the relative humidity of the air at each site is estimated
bull While the relative humidity of the air is gt 100 condensation is considered to take place
bull Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Evaporation
bull In the calculation we are using the parameters rsquoStorage capacityrsquo and rsquoActual storage of water on the leafrsquo
bull These parameters may in the future be modified by our hourly measurements of rsquoleaf wetness durationrsquo
bull In the procedure we consider the water balance
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Calculating Evaporationof intercepted water
This process is important and difficult and the approach is connected to the energy balance and the water balance
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
The general problem of local weather
-How to identify the local weather
-How to extrapolate measurements when knowing the physical
mechanisms
-What about advection
-What about modelling
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Adiabatic turbulent mixing of air
The procedure for estimating parameter values at a site lsquojrsquo when knowing the measured parameter values at an
agro meteorological station lsquoirsquo 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)=-(gcpa)( 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 rsquoirsquo
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Adiabatic turbulent mixing of air
We also know the relative humidity of the air RH(zi) and the air temperature
T(zi) at the site lsquoirsquo 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 lsquozrsquo
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 lsquoirsquo 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
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Adiabatic turbulent mixing of airWe are using Poissonrsquos equation to calculate the change of total pressure in (an adiabatic process of turbulent mixing of air parcels) from the site lsquoirsquo to the site lsquojrsquo
(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 lsquojrsquo knowing the thermodynamic properties at the site lsquoirsquo
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 lsquoPrsquo originally
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Precipitation
Precipitation is measured by weather radar (hourly values)
in pixel areas of 1x1km
Thank you very much
Thank you very much
