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Diurnal temperature variation in the boundary layer

Definition of the boundary layerDirectly adjacent to the underlying surface layer of the atmosphere within which diurnal variation of various atmospheric parameters (temperature, humidity, wind speed, etc) is well defined is

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Слайд 1Diurnal temperature variation in the boundary layer
The diurnal temperature variation

is defined by the variation of the heat influx to

the earth’s surface during 24 hour period.
During daytime the earth’s surface is getting heat due to solar radiation influx, and its temperature grows up. During night hours it looses energy due to effective radiation and its temperature grows down.
Recall, that the atmosphere does not directly absorb the solar radiation. The air’s own radiation at night hasn’t significant impact on the air temperature.
Therefore, the main reason for temperature variation is the eddy exchange with the underlying surface. This process is responsible for the diurnal temperature variation within whole boundary layer up to 1 - 1,5 km altitude.
Diurnal temperature variation in the boundary layerThe diurnal temperature variation is defined by the variation of the

Слайд 2Definition of the boundary layer
Directly adjacent to the underlying surface

layer of the atmosphere within which diurnal variation of various

atmospheric parameters (temperature, humidity, wind speed, etc) is well defined is called boundary layer of the atmosphere

The height of the boundary layer depends upon static stability of the atmosphere.

Very stable atmosphere

Very unstable atmosphere

In tropics, where the atmosphere can be…

extremely unstable, the top of the boundary layer can reach 3000 m.

Definition of the boundary layerDirectly adjacent to the underlying surface layer of the atmosphere within which diurnal

Слайд 3

Mechanism of the heat spreading up
According to observation, minimal temperatures

are observed near the sunrise or a bit later.






Top of

the boundary layer

As soon as the solar radiation comes to the surface, the latter starts warming.

Due to molecular diffusion, the heat is transferred to the thin layer of air.

Later the heat is transferred upward due to eddy mixing from one layer to that above of it and so on.

Since for the heat transfer up some period of time is needed, there is delay with temperature grow in every following layer

Mechanism of the heat spreading upAccording to observation, minimal temperatures are observed near the sunrise or a

Слайд 4The heat amount, as it spreads up, becomes smaller and

smaller because each layer takes some fraction of heat from

the ascending heat flux. That makes temperature variation at each following layer smaller and smaller too.

Suppose, there are n layers, the lowest of them (adjacent to the surface) is the well known “surface layer”, where the heat flux is quasi- constant, or well call it zero layer (Q0).

The following layers are 1, 2, … n. In every of these layers the heat influx is smaller than in the lower one.
It means that ∆T values will decrease with height.

The heat amount, as it spreads up, becomes smaller and smaller because each layer takes some fraction

Слайд 5An example of the diurnal temperature variation
If we go up,

the amplitude will become smaller, and, at the boundary layer

top, it will be close to zero.
An example of the diurnal temperature variationIf we go up, the amplitude will become smaller, and, at

Слайд 6Diurnal temperature variation at different altitudes
The amplitude of the variation

decreases with height. At the altitude of about 1.5 km

it is 6 – 7 times less than near the surface.
Near the top of the boundary layer the amplitude can be very complicated with 2 or 3 maxima.

Reasons

Observations are not accurate enough.
Fluctuation of eddy intensity.

Near the surface, variation is rather significant. Therefore, comparably small fluctuation of eddy intensity do not seriously distort the diurnal temperature variation rate. At the top of the boundary layer, situation is different. Here, the amplitude is much smaller than at the surface, and even not significant eddy activity fluctuation may result in distortion of the diurnal variation rate.

Diurnal temperature variation at different altitudesThe amplitude of the variation decreases with height. At the altitude of

Слайд 7Cloudiness and wind impact on the diurnal temperature variation
Cloudiness
An increase

of the cloud amount always results in decrease of the

diurnal temperature variation amplitude

Wind

Wind makes the eddy mixing more intensive, and by this way it diminishes the variation amplitude. Along with this, it is associated with temperature advection that also distorts the rate of the variation.




Warm advection

No advection

Cold advection

Starting moment of advection

Cloudiness and wind impact on the diurnal temperature variationCloudinessAn increase of the cloud amount always results in

Слайд 8
Simplified theory of the diurnal temperature variation
Partial differential equation

of the second order

Boundary conditions
At the given boundary conditions, the

solution of the equation will be:
Simplified theory of the diurnal temperature variation Partial differential equation of the second orderBoundary conditionsAt the given

Слайд 9
Amplitude variation with height
Suppose, we took two altitudes z1 and

z2, where the amplitudes are of the same value.
Adopting as

a boundary layer altitude z*, where the amplitude 100 times less than that at the surface, we obtain:

If A0=10°C, A(z*)=0.1°C

Thus, the key role of the amplitude variation with height belongs to K value. On the base of that value, one can calculate the boundary layer altitude

Amplitude variation with heightSuppose, we took two altitudes z1 and z2, where the amplitudes are of the

Слайд 10Here, in the first column is

the molecular heat conductivity coefficient. It shows clearly the role

of the K value in determination of the z* value.
The normal K value is known to be from 1 to 5 m²/s. However, some cases were reported with K>100 m²/s. This kind of a situation is associated with extremely well developed convection, for instance, in tropics. At these cases the diurnal temperature variation can be observed through the whole troposphere.
Here, in the first column			     is the molecular heat conductivity coefficient. It shows

Слайд 11Annual temperature variation
In the Northern Hemisphere maximal temperature is usually

observed in July, and minimal temperature in January or February.
The

annual temperature variation amplitude decreases with height in the same manner as the diurnal one does.
Π1=24 hours is the period of one Earth’s spin.
Π2=24·365.25 hours is the period of annual Earth’s rotation around the Sun.

Assuming normal condition (K=5 m²/s), the annual temperature variation spreads over a layer of about 32 km (whole troposphere and significant part of the stratosphere). We know a little about K value variation with height except the fact that it increases within the surface layer. There are some evidences that it remains almost constant in the boundary layer. As to the free atmosphere, we can judge about it from indirect evidences such as comparison observed and calculated parameters.

Annual temperature variationIn the Northern Hemisphere maximal temperature is usually observed in July, and minimal temperature in

Слайд 12
Rate of heat wave propagation and lag time
We have known:
Air

temperature variation, above else, depends on Earth's surface temperature variation.
The

rate of the heat propagation is a finite value.
The extreme temperatures are to occur the later, the higher altitude is.
Suppose t1 is the time the earth’s surface temperature reaches its maximum; t2 is the respective time for the altitude z.

Lag time

Phase velocity:

In case K=5 m²/s

Rate of heat wave propagation and lag timeWe have known:Air temperature variation, above else, depends on Earth's

Слайд 13Nocturnal temperature decrease
The main reason for nocturnal temperature decrease is

effective radiation. The intensity of the effective radiation, in turn,

depends on the properties of the soil and state of the sky. Significant fall of the temperature occurs at cloudless sky condition.

Effective radiation

Cooling of the surface and adjacent air

Inversion layer formation

Weakening the eddy exchange intensity within the inversion layer

Heat flux decreasing by 3 – 5 times.

Further cooling of the surface and adjacent air

Possibility for a frost formation

Brent’s formula

Nocturnal temperature decreaseThe main reason for nocturnal temperature decrease is effective radiation. The intensity of the effective

Слайд 14Frosts
Temperature fall below 0°C on a positive temperature background is

called FROST.
There are two types of the frosts;
Radiative frosts
Advective frosts
Favorable

conditions for radiative frosts
Low air humidity
Weak wind (1 – 2 m/s)
Cloud free sky
Favorable conditions for advective frost
Low air humidity
Strong cold wind
Small cloud amount

FrostsTemperature fall below 0°C on a positive temperature background is called FROST.There are two types of the

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