1. Calculating leaf wetness duration in an apple orchard Tor Håkon Sivertsen The Norwegian Crop Research Institute

2. 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 The region is covered by a weather radar The problem of estimating leaf wetness duration is closely connected to plant pathology

3. NORSJØ REGION OF SOUTHERN NORWAY covered by two weather radars

4. The NORSJØ area

7. The system for making measurements 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) There are available hourly recordings of weather radar measurements of precipitation ( pixel area 1x1km)

8. The problem of transferring measurements in the local area We have four agrometeorological stations and 15 sites with fruit farming in the area The measurements of precipitation by radar is connected to each site The measurements at the agro meteorological stations are transferred to the rest of the sites. We are using the hypotheses of turbulent mixing and dry adiabatic processes as a first approximation

9. The problem of calculating/ measuring leaf wetness in an orchard We look at the processes of relevance Precipitation Condensation of water on the leaves Evaporation Dry surface of the leaf

10. Precipitation The amount of precipitation is measured at four sites equipped with agro meteorological stations by using tipping buckets, hourly recordings We also measure precipitation by weather radar i pixel areas of 1x1km, hourly recordings.

11. Condensation 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. While the relative humidity of the air is > 100 % condensation is considered to take place. Measurements of leaf wetness duration at the agro meteorological stations tell us something about the duration of this process in the area.

12. Evaporation In the calculation we are using the parameters ’Storage capacity’ and ’Actual storage of water on the leaf’ These parameters may in the future be modified by our hourly measurements of ’leaf wetness duration’ In the procedure we consider the water balance

13. Calculating Evaporation of intercepted water This process is important and difficult and the approach is connected to the energy balance and the water balance

16. 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?

17. Adiabatic turbulent mixing of air 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(z i )-T(z j )=-(g/c pa )( z i - z j ) g: The acceleration of gravity T(z): The air temperature 2m above the soil surface c pa : The heat capacity of the air at constant pressure z i : The height above sea level of a site denoted by the index ’i’

18. Adiabatic turbulent mixing of air We also know the relative humidity of the air RH(z i ) and the air temperature T(z i ) at the site ‘i’, and we may calculate e w (T(z i )), the saturation vapour pressure and e(z i ), the water vapour pressure of the air. e w (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 p ai α ai = R a T e i α vi = R v T α a : The specific volume of the dry air α v : The specific volume of the water vapour

19. Adiabatic turbulent mixing of air 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’: (T i / T j )·( p i / p j ) κ =1 κ= R a / c p 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’. p i =p ai + e i ρ j = ρ aj + ρ vj In this system the pressure is not measured, we therefore have to put p i equal to some auxiliary value ‘P’ originally.

20. Precipitation Precipitation is measured by weather radar (hourly values) in pixel areas of 1x1km

21. Thank you very much!