Dear Annu temperature lapse rate is small over forested areas than over bare land. The wind flows over forested area is more turbulent than flows over bare land. The higher mixing create small lapse rate.
I just want to know Tsurface will also reduce due to plants and hence Tair too...
Tsurface -Tair is changing but both factors have been reduced.
But as pointed by Philbert, Turbulence may cause the small lapse rate over forested area. But at the same time the buoyancy is higher over bare land due to more heating.
The mechanisms involved in controlling the distribution of temperature in the atmospheric surface layer with plants are very complex and they are still not completely understood. They include radiation transfer, convective mixing, the leaf energy budget dependent on the stomatal resistance and the storage of water in the soil and in the root system.
One of the best discussions of the related topics is presented in the following text
The most important element in this biophysical system is the highly nonlinear formula for the stomatal resistance.
It is evident that there are significant memory effects to be expected and that we still have to perform some work before building the realistic mathematical models of the atmospheric surface layer with plants. I suspect that the mixing of temperature and moisture in such a layer is governed by the fractional order diffusion equation. This fact is definitely important for the dynamics of the turbulence in the surface layer with plants.
To answer your question--How important are plants to control the gradient in temperature from land to atmosphere? Turbulence and roughness are insignificant factors. The importance is divided into two categories--what allows the plants to exist where they are, and what do the plant contribute directly to control the transfer of heat from the land to the atmosphere.
If you use the vegetation in the mountains of Oman near Salalah as your study area, as I have at http://www.ecoseeds.com/cool.html and at MIT Prof. Elfatih Eltahir http://web.mit.edu/eltahir/www2/dhofar/content/fdi.htm, that is the planet's best example area to study the effects of vegetation on climate.
So why do the forests grow only in the mountains of Salalah and nowhere else on the Arabian peninsula?
They insulate the soil, and that does not allow the heat of the sun to get stored by barren sands, which goes very deep into barren soils during the day. They also act as insulators, and you could calculate a "R" factor for each kind of plant, for its individual insulating value. I measured this effect in the Mojave Desert with a single native grass plants, image attached.
Around the plant, the soil surface was 128 deg. F. , and the air temp. was 90 deg. F., but under the grass plant it was 2 degrees cooler!
Then the other important insulating effect of vegetation, is that by dropping the air temp., then you change the dew point, so then rain clouds and rain can occur, like the vegetation in the mountains of Salalah create their own climate and rain is produced each summer, by changing the dew point so clouds can form.
Then bacteria are the last puzzle piece, the cloud producing bacteria that live on the tree leaves, that help create the rain clouds. Like on the trees in Salalah, or in the California Sierras and Coast ranges, or the trees growing in the Western Ghat sacred forests, or the trees in Southeast Asian forest.
You can have heat-maiden moisture going overhead, like before the summer monsoon starts, or over most of Arabia all summer, high humidity with high temperatures in the atmosphere.
What you need to break and release that heat, is vegetation with the Pseudomonas bacteria, so the vegetation can lower the dew point, and rain clouds form to release the bacteria to produce rainfall, and the atmospheric heat is dissipated, as is experienced each summer with the monsoon rain.
Then, you need to factor in atmospheric dust as a atmospheric heat trapping and heat transfer agent. Clear air by itself is a very good insulator, just like pure water cannot transfer electricity very well.
But add only 20-40 micrograms per cubic meter of dust to the air, and that dust acts as a very good heat trapper. And the dust works against the vegetation wanting to lower the dew point, and instead raises the dew point to impossible levels for rain clouds or rain to exist.
The ecological restoration of arid barren lands, about one billion acres worldwide, with the original native vegetation and native trees, will be the ultimate solution to planetary global warming. It is NOT going to be these ridiculous climate engineering solutions, like those written about in the May/June MIT Technology Review "The Growing Case for Geoengineering" by James Temple, pages 28-33.
Global warming is NOT going be solved by salting the oceans with iron to feed the plankton, or by burying CO2 in old mines, or by shooting up space umbrellas to cover the planet, or any of those other insane geoengineering solutions that are being proposed. Global warming will be solved by replanting the barren hot arid lands, so that they are insulated with the original native vegetation, to keep the heat from getting into the atmosphere in the first place.
If we have to fix things, why not try the most environmentally safe solution first? Your question that you ask here, is at the heart of a solution to global warming-- How important are plants to control the gradient in temperature from land to atmosphere?