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.
A graphical
representation
of an
interpretation
of the
scientific
principle used
in meteorology
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.
The definition of the concept
of ‘advection’ given by WMO
The transfer of air mass properties by the
velocity field of the atmosphere
(International meteorological vocabulary WMO-No. 182-1992)
Comments on the WMOdefinition
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)
R n = H + E +S + D + J + A
R n net radiation
H vertical turbulent transfer of sensible heat
E vertical turbulent transfer of latent heat
S soil heat flux
D horizontal flux divergence
J physical storage in the canopy
A chemical storage in the canopy
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.
Definition of ‘advection’
connected to agro meteorology
‘Rosenberg et. al.(1984)
is defining advection in the
textbook ‘Microclimate’ ‘The Biological Environment’
in the following manner:
”We will use the term advection as synonymous with
the transport of energy or mass in the horozontal
direction. We are most concerned with the transport
of latent heat from one field to anotheror from one
region to another,namely, heat that is used to
evaporate water.”
Discussing ‘advection’ on
larger temporal and spatial
scales
This textbook ‘Microclimate’ also
contains a discussion on local and
global advection and regional or
large scale advection.
The cloth-line effect and the
oasis effect
In Rosenberg 1t. Al, (1984), these effects
are described in the following manner:
When air is horizontally transferred from
areas where sensible heat has been
generated through crops, a clothline effect
exists.
( The crop is getting drier)
The oasis effect
When advected enerrgy is drawn from the air
an oasis effect exists. The air is being cooled
when evaporation takes place. And when
water supply is unlimited, the
evapotranspiration is very great.
The passage of a frontal system
close to the ground
The passages of a frontal systems, a cold front
or a warm front, reaching down to the
ground level , typically are situations with
advection close to the ground. A site on the
ground will get another type of air mass
covering the area, and the horizontal
transport of air has to be taken into account.
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.
Proposal of a specific
definition of ‘advection’ for
practical use
‘Advection’ may be regarded as a net
horizontal turbulent transfer of energy ,
mass and particles by the flow of air.
It is difficult to measure directly the
advective transport in any system.