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The influence of a depth of a very shallow

cool-pool lake on the nocturnal cooling

Jože Rakovec, Gregor Skok, Rahela Žabkar, Nedjeljka Žagar

Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia and Center of Excellence SPACE‐SI, Ljubljana, Slovenia

ICAM 2013

What is a very shallow CAP lake?

What is a very shallow CAP lake?

What is a very shallow CAP?

• A basin with nearly flat basin floor

• The horizontal extent of the CAP basin is much larger than the vertical extent (ratio > 100:1)

• CAP forms due to the net longwave radiative loss from the uppermost soil layer

Very shallow CAP questions

• How does the CAP thickness (height of the dykes) affect the morning temperatures?

• Influence of humidity of air inside the basin?

• Influence of the free atmosphere humidity?

• Influence of the local scale terrain variation?

Very shallow CAP formation

• The ground starts to cool due to the net longwave radiative loss from the uppermost soil layer

• Air absorbs less energy emitted by the colder ground => air temperature decreases thereby forming a CAP.

• Colder air emits less downward radiation which further reduces the radiation absorbed by the ground – feedback effect

• Differences compared to a “regular” CAP – Not affected by reduced sky view factor

– No large scale (basin scale) katabatic flows

The field experiment • Almost one year of measurement in an orchard in SE Slovenia

Three locations with three levels (0.5 m, 1.75 m and 3m)

An example: Morning of 17. march

• A clear sky night

• Colder closer to the ground – 3oC difference between 3

and 0.5 m

• Colder lower elevation – difference about 4oC

between location 1 and 2 (elevation difference of 3m)

0.5 m 1.75 m

3 m

• A problem: Average winter morning temperatures are not warmest on the location with the highest elevation

• Possible cause: local terrain variation also plays a role

The 5-layer model

• A very simple model was used - similar to the 3-layer mode by Whiteman et al. (2004)

• We added two additional air layers:

100:1 aspect

The 5-layer model

• A set of 3 prognostic equations for temperatures

2ℎ2𝑐𝑝𝜕𝑇2

𝜕𝑡= +2 1 − ′1 𝑇𝑔

4 + ′21 𝑇14 − 22 𝑇2

4 + ′2𝑎𝑡𝑚 𝑇𝑎𝑖𝑟4

1ℎ1𝑐𝑝𝜕𝑇1

𝜕𝑡 = +1 𝑇𝑔

4 − 21 𝑇14 + ′12 𝑇2

4 + ′1 1 − ′2 𝑎𝑡𝑚 𝑇𝑎𝑖𝑟4

𝑔 𝑐𝜕𝑇𝑔

𝜕𝑡= −(g/D)(Tg – TD) − 𝑇𝑔

4 + 1 𝑇14 + 1 − ′1 2 𝑇2

4 + 1 − ′1 1 − ′2 𝑎𝑡𝑚 𝑇𝑎𝑖𝑟4

Radiation emitted by upper air layer which is absorbed by the lower air layer. Due to non-black body spectra of radiation which is emitted/absorbed by air we have to use an “adjusted” emissivity ′1 - in order to get the correct amount of absorbed radiation. The “adjusted” emissivity of air is larger than the black body emissivity of air – by about 50%!!

Heat flow from the ground

Numerical solution

The 5-layer model

• An analytical solution can be found for equilibrium temperatures

• They are strongly depend on emissivity (humidity) of the air layers and the free atmosphere

• We get a colder temperatures in a deeper (thicker) CAP

• Higher humidity of:

– air inside CAP => colder eq. temperatures

– free atmosphere => warmer eq. temperatures

– air inside CAP OR the free atmosphere => bigger difference between deeper and shallower CAP temperatures

Measurement vs. model: Morning of 17. march

• Data: about 4oC colder in a deeper CAP (Dh=3m)

• Model: about 3oC colder in a deeper CAP

• The model cannot explain why average winter morning temperatures are not warmest on the location with the highest elevation

0.5 m 1.75 m

3 m

Conclusions

• A very shallow CAP is somewhat different than “regular” CAP. No effect of sky view factor and large scale katabatic flows

• Measurements: Air cooler at lower elevation by a few degrees

• Measurements: The above is not always true - possible effect of local terrain variations

• The air inside CAP produces a cooling feedback effect – has to be assumed non-constant in the model

• The radiation emitted by air does not have a black body spectra => “adjusted” emissivity

• The model produces realistic results – but not always. The model assumes a totally flat basin bottom.

• In reality due to local variation of terrain there might be some local variation in sky view factor and some local scale katabatic flows.

Figure 8: Tg equilibrium temperature for the nocturnal cooling of ground surface for different values of /𝐷 and for different TD from 273 K to 289 K (in 2 K intervals). Black lines represent ground temperature Tg in deeper CAP and gray lines Tg in shallower CAP.

Figure 9: (a) The dependence of equilibrium T1 and Tg temperatures in a deeper CAP on layer emissivity ′ for three emissivities of the whole atmosphere 𝑎𝑡𝑚. (b) The differences in equilibrium temperatures in the deeper and shallower CAP. The following parameters were used: /𝐷=1 W/Km2, TD= Tair =283 K.