El October 2007 Tor Håkon Sivertsen



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Discussing some aspects of the concept ‘advective flow’ used in meteorology and agro meteorology

  • El October 2007

  • Tor Håkon Sivertsen

  • Norwegian Institute for Agricultural and Environmental Research


Motivation and intention

  • This concept of ’advection’ is used by meteorologists but it is also used in other fields of science, especially by biologists. It is of importance that the specialists in the different branches of scientific research of environmental phenomena understand each other, therefore I think conceptual discussons is of importance.

  • This discussion contains a specific discussion on ’advection’ and I am advertizing the importance of conceptual discussions generally.





The scientific principle ( an interpretation)

  • We classify natural phenomena (put them into classes and sub-classes) like

  • air, cloud, soil, atmosphere, vegetational cover, canopy, leaf etc.

  • Then we may attach measurable quantities (parameters) to the phenomena, like mass, temperature, energy, leaf area index, momentum etc.





Comments on the WMO-definition of ‘advection’

  • The definition of ‘advection’ is pointing specifically on the way the science of ‘fluid dynamics’ consider fluids, by attaching and defining velocity fields and other measurable quantities (parameters) to the phenomenon, like spatial and temporal coordinates, mass, temperature, energy, momentum etc.

  • Further more this is the world of physics, and we consider mass, energy, momentum conserved in this model of a fluid.

  • This definition is clear connected to meteorological phenomena on the larger spatial scales like the synoptic scale, but below I will use the term on the scale of micro meteorology; evaporation frm a pan evapometer with a surface area of 0.25 m 2 .



A few comments on the basics of traditional fluid dynamics

  • Basically the science of fluid dynamis is considering a micro world of molecules and another macro world connected to parcels of fluids (containing many molecules)

  • In this macro world of parcels of fluid a multitude of phenomena are described quantitatively (using Navier-Stokes equations, the equation of continuity and the ‘laws’ of thermodynamics etc.).

  • Further more the world of the molecules is neatly connected to the macro world of the fluid parcels.

  • The laws of conservation of mass, of energy and momentum are almost valid in this macro world of parcels of fluid.



A few comments on the turbulent flow systems of the atmosphere

  • The flow systems of the atmosphere are basically considered turbulent. It therefore is impossible or meaninglerss to regard the flow systems of the atmosphere as merely consisting of parcels of air. When the resistance of the fluid has to be considered, the flow system usually has to be regarded as consisting of a average flow system ( average velocity field) plus a velocity component giving the deviation from the average flow.

  • A theory of such systems possible to use was originally given by Osborn Reynolds, and this system of equations is called the Reynolds equations.

  • By using the Reynolds equations neither the energy nor the momentum of the flow system may be regarded conserved without adding and defining extra empirical or half empirical parameters





Looking at the energy balance equation close to the surface of the soil ( according to to Thom, 1975)



Looking at the scope of the energy balance equation

  • R n = H + E +S + D + J + A

  • The physical content of the equation is the conservation of energy, but this will always be an approximation, because:

  • .

  • The definition of R n , the net radiation, is an approximation

  • H, vertical turbulent transfer of sensible heat, and E , the vertical turbulent transfer of latent heat, contains empirical coefficients making the fluxes non-linear, etc. etc.

  • D horizontal flux divergence



The advection terms contained in the energy balance equation

  • The ‘advection’ of the fluid flow is contained in the component D, the horizontal flux divergence

  • D n = D H + D E

  • DH= ∫ {∂( c puT)/ ∂x}dz

  • DE= ∫ {∂( c p/ )ue)/ ∂x} dz

  • The limits of integration along the z-axis are the soil surface and some value

  • z R above the surface.













Looking at the energy balance equation close to the surface of the soil ( according to Rosenberg et. al. , 1984)

  • R n = H + E +S + J + A

  • R n net radiation

  • H vertical turbulent transfer of sensible heat

  • E vertical turbulent transfer of latent heat

  • S soil heat flux

  • J physical storage in the canopy

  • A chemical storage in the canopy



Looking at the energy balance equation ( according to Rosenberg et. al. , 1984)

  • R n = H + E +S + J + A

  • This formula is presented and discussed by Rosenberg et al . (1984) prior to a lengthy discussion on advection. In the introduction in the textbook the content of this formula is described like this:

  • ’ Equation (1.1) is applicable on the scale of a single plant or cropped field, exlaining how energy is provided to warm the soil and crop and to evaporate water. The equation is no less valid on the global scale explaining how energy is provided to the continents and oceans where vast quanttities of heat and vapour are given to or extracted from the atmosphere.



Looking at the energy balance equation ( according to Rosenberg et.al. , 1984)

  • R n = H + E +S + J + A

  • But advection is not contained in this formula. It is therefoe valid ( when the parameters are properly defined) for a field situation without advection, and it is valid on the global scale ( with global average values of the different parameters)

  • And advection is never discussed in a formal mathematical manner in this text-book, and only vertical transport is mathematcally discussed for H and E .



The Penman formula of potential evaporation

  • E = a{R n + b(ew(T(z) -e(z))0.27(1+Ur (2)/100) }/(+)

  • E vertical turbulent transfer of latent heat

  •  the latent heat of evaporation

  • Rn net radiation

  • ew(T(z) the saturation vapourpressure of water

  • e(z) the vapour pressure of water in the air

  • Ur (2) the wind measured 2m above the ground, unit km day

  • a is a constant

  • b is a constant



Comments on the Penman formula of potential evaporation

  • The basic physical situation described by the Penman formula is turbulent vertical transfer of water vapour/evaporation from a large surface of fresh water. When looking at a large flat horizontal surface of short cut grass with no alck of water in the soil, coefficients may be determined to describe the potential evaporation from this surface.

  • This fomula contains no advection, because there is no change of any properties/ parameters in the horizontal directions.



Estimation of pan evaporation from weather data (according tp H. Riley)

  • In Norway a pan evaporimeter has been used at Kise Research Station to estimate potential evapotranspiration, Ep ,for agricultural crops. The instrument has a surface of area of 0.25 m 2 and a depth of 60 cm.

  • In Sweden a small evaporimeter designed by S.Anderson has been used in agricultural research. In 1969 Johanson derived an equation relating measurements from Anderson’a evaporimeter to global sort wave radiastion (X) and an advection term (X2 ), the latter being the produuct of average wind speed and the vapour pressure deficit ((ew(T(z) -e(z)); on daily bases.



Estimation of pan evaporation from weather data ( the equation used)

  • The equation operationally used in Norway is further corrected by adding seasonal effects on monthly bases and it looks like this:

  • Ep (mmd-1)=-5.38-0.0594*X1 + 0.1088*X2+1.84* X3 -´0.134*(X3)2

  • The effect of season ( monthly values) are contained in the parameter X3 ,denoting the number of the month, in May X3=5.



Estimation of pan evaporation from weather data ( discussing the content of the equation)

  • The equation contains advection ( the oasis effect) connected to the method for making measurements, but the physical content of this oasis effect is not limited to the second term in the equation.

  • Further more this probability system most certainly contains advection due to weather phenomena like passage of fronts, and such phenomena occur with different frequency in different months of the year.

  • If it is correct that monthly frequency of local weather phenomena are hidden in this equation, this probably limit the adequate use of thed equation far from the place it was tested.







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