# Can I estimate leaf temperature from air temperature? What other information would be required?

Physiological measurements such as respiration rate and assimilation rate depend on temperature.

Most papers report tissue temperature (e.g. leaf temperature for leaf measurements), although some report air temperature.

My goal is to compare measurements in the literature. I use leaf temperature at time of measurement to adjust the rates to a common temperature. Currently, I assume that if leaf temperature is not available, it is the same as air temperature. (This is often assumed in papers where the leaf temperature was not measured).

Is there a way to estimate the difference between air temperature and leaf temperature? I can get fairly good estimates of other physiological traits (e.g. leaf thickness, albedo, stomatal conductance) as well as climate data (e.g. humidity, soil moisture content).

My model is:

$T_{leaf} = T_a + X + \epsilon$

And I currently assume X = 0 in my calculations

Is there a better way to estimate X?

Under what conditions would X < 0? X > 0?

• I am not a plant physiologist but it seems very odd to me that people are just assuming that Tleaf = Ta without proving it. Surely there must be some old reference somewhere...
– nico
Jun 15, 2012 at 7:02
• @nico perhaps because the error of measurement is >= than the error introduced by this assumption (e.g. if the delta-T is ~1-2C the error might be on the order of 10%). If there is a reference, I haven't seen it cited, and this assumption is made ~ 10% of the time - usually in older papers before thermocouples on the leaf surface at the time of measurement were integrated into standard equipment.
– Abe
Jun 19, 2012 at 4:43
• surely, but at some point someone must have started to use thermocouples on leaves... and didn't they check the relation of their leaf measures to Ta? I understand that you cannot generalize that to all plants/conditions, but at least knowing whether the initial assumption is correct would be good. Unfortunately, as I said, I cannot help you with that, my test subject do not have the same temperature as the ambient (and if they have something has gone terribly wrong... :D)
– nico
Jun 19, 2012 at 5:49
• Leaf temperature is a function of air temp, water vapor pressure deficit, net radiation, stomatal conductance, and boundary layer conductance, among other things. Most of these change significantly within the course of a day (or more often), and consequently, so will the offset between leaf and air temp. There are some energy balance models that would be appropriate for estimating this offset (which I'll dig up if I get a chance). Jun 22, 2012 at 5:22

One way to do this is to use the "humid operative temperature" equation, or something similar. A variant of this equation, specifically for estimating leaf temperature, is derived using a leaf energy balance equation in chapter 14.1 of the Environmental Biophysics book (cited below).

I'll let you look up the actual equation since I'm not sure how to do math symbols here. But, in addition to air temperature, you will need to know a few pieces of information:

1. Vapor pressure deficit - calculated from humidity and temperature.
2. Incoming radiation - Measured, or you could model this using time of day, latitude, etc.
3. Emissivity of your leaves - you can probably look this up for your species or a similar one.
4. Windspeed
5. Characteristic dimension of leaves - measure, or look up a value for your species (Use this with windspeed to calculate boundary layer heat conductance).
6. Leaf vapor conductance - a combination of stomatal and boundary layer conductance to water vapor. You must know something about where the stomata are on your leaf (both sides or one side), but you can often look this value up for a given species.
7. A few other constants that are easy to look up.

That's about it - its a somewhat hairy calculation, but if you have standard weather data and a little knowledge of the plants you are estimating the leaf temperature of, it should be manageable.

This equation and other relevant info are in this book:

• Campbell, G.S. and Norman, J.M. An Introduction to Environmental Biophysics. Springer Science, 1998