Agronomy 405/505
Spring 2013
Problem Set 5
Due Tuesday, February 19, 2013.
Assigned February 12, 2013. Updated with Figure 1 February 18, 2013.
1. In the roughness sublayer, a layer of air just above a vegetation canopy, the logarithmic wind
profile that we have discussed in class does not describe the actual wind speed accurately.
The roughness sublayer exists because the uneven distribution of individual canopy elements
(leaves, branches, stems) in space makes the turbulence in this layer different from the rest
of the surface layer. There are many different estimates of roughness sublayer height:
hr = d + 50 zm (Tennekes, 1973)
hr = d + 10 zm (Jacobs and Van Boxel, 1988)
hr = d + 5 zm (Brutsaert, 1984)
hr = 1.5 h (Arya, 1988)
where d is the displacement height, zm is the roughness length for momentum, and h is canopy
height.
(a) Jacobs and Van Boxel (1988) found empirical expressions for the displacment height and
momentum roughness length of maize (corn): d = 0.63 h1.3 and zm = 0.33 (h − d)1.3 .
Compare these two models with the simple models given on page 71 of Campbell and
Norman by plotting the change in d and zm as a function of canopy height. Assume that
a corn canopy reaches a height of 3 m by the end of the growing season.
(b) Compare the models of roughness sublayer height by plotting the change in roughness
sublayer height as a function of corn canopy height over the growing season.
(c) For some distance after a step change in roughness, turbulence in the air near the surface
can not be accurately modeled with the theory discussed in class. For example, the
turbulent quality of the air near the surface downwind of the line separating a corn and
bean field is different than the turbulence in the surface layer in the middle of a large
corn field. After a change in surface roughness, it takes some distance for a surface layer
to develop. Arya (1988) described the growth of a new surface layer with the model:
(hs − d2 )/zm2 = a(x/zm2 )0.8
where hs is the height of the surface layer; d2 and zm2 are the displacement height and
roughness length of the new surface; a = 0.35 to 0.75; and x is the horizontal distance
from the change in roughness. Plot the height of the surface layer as a function of the
1
Figure 1: Illustration for Problems 1c and 1d.
distance from a change in surface roughness from a bean field to a corn field of height
3 m. See Figure 1.
(d) If you wanted to validate the logarithmic wind profile models discussed in class, and you
had three anemometers, how far from the edge of a field of 3 m corn would you place
your anemometers? At what three heights would you place your anemometers? Again,
see Figure 1.
2. 6.1 in Campbell and Norman. The units of your answer should be in kg m−2 day−1 .
3. 6.2 in Campbell and Norman. Assume the total heat flux density will be the sum of the flux
densities produced by latent heat transfer and sensible heat transfer.
4. 6.3 in Campbell and Norman. This problem illustrates an important concept. The heat flux
through each layer is the same as the heat flux through the entire series of layers. Heat
does not “pile up” at any point. In this problem, this means that the heat flux through
your tissue, your clothing, and the boundary layer must all be the same. Note that the
conductances for each layer (your tissue, your clothing, and the boundary layer) are different,
so the temperature between each layer (at your skin and at the surface of your clothing)
must “adapt” to make the heat flux the same through each layer. Only consider sensible heat
transfer in this problem.
5. Read “Putting the Heat on Tropical Animals” at doi:10.1126/science.1159328.
(a) What are ectotherms?
(b) What is an “aseasonal environment?”
(c) An organism would experience a higher “operative temperature” in the sun as opposed
to the shade. Why?
(d) Why may it be that “thermal generalists” appear most commonly in mid–latitudes?
2
6. Read “Dispersal Will Limit Ability of Mammals to Track Climate Change in the Western
Hemisphere” at doi:10.1073/pnas.1116791109.
(a) According to the authors, what is the definition of “dispersal?”
(b) In what region of the Western Hemisphere will species be least likely to be able to track
climate changes? Why?
(c) Which species will be most likely to keep pace with climate change?
(d) Why are land use changes something that must also be considered when predicting the
ability of animals to adapt to climate change?
References
Arya, S. P. (1988), Introduction to Micrometeorology, Academic Press, San Diego, CA.
Brutsaert, W. (1984), Evaporation in the Atmosphere: Theory, History, and Applications, D. Reidel, Boston.
Jacobs, A. F. G., and J. H. Van Boxel (1988), Computational parameter estimation for a maize
crop, Bound. Lay. Meteorol., 42, 265–279.
Tennekes, H. (1973), Logarithmic wind profile, J. Atmos. Sci., 30, 234–238.
3