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Letters to the Editor

Comment on "Modeling Sensible and Latent Heat Transport in Crop and Residue Canopies" by G.S. Campbell. Agron. J. 95:1388–1392 (2003).

^a College of Sciences, Washington State University, Pullman, WA 99164-3520
^b Blackland Research and Extension Center, Texas Agricultural Experiment Station, 720 E. Blackland Rd., Temple, TX 76502
^c Department of Mechanical Engineering, Washington State University, Pullman, WA 99164-2920
^d Decagon Devices, 950 N.E. Nelson Ct., Pullman, WA 99163

mano{at}wsu.edu

armen{at}brc.tamus.edu

ryanorozco{at}hotmail.com

gaylon{at}decagon.com

Received for publication August 1, 2006.
Dear Editor:

In an article published in Agronomy Journal, Campbell (2003) proposed a set of uncoupled equations to deal with latent and sensible heat flux. The fluxes proposed are enthalpy (H) and isothermal latent heat (E_i) and the new driving forces are equivalent temperature and vapor pressure deficit. In the derivation method, however, there was an error in the mathematical manipulation of one of the equations. The objective of this letter is to correct that error and to show the correct set of uncoupled equations.

Campbell (2003) defined latent heat flux as (Eq. [3] in the original paper)

[1]

where (J mol^–1) is the water latent heat of vaporization, E (mol m^–2 s^–1) is the water vapor flux density, is the air molar density (mol m^–3), K_v (m² s^–1) is the vapor diffusivity, h is relative humidity, e_s (kPa) is the saturation vapor pressure at air temperature, p (kPa) is the atmospheric pressure, and z (m) is distance.

Campbell substituted dT/dz for de_s/dz where is the slope of the saturation vapor pressure function (kPa °C^–1) and T is temperature (°C). He also proposed that since the vapor pressure deficit D (kPa) is defined as D = e_s(1 – h), differentiating and rearranging terms appropriately provides a substitution for the derivative term dh/dz. However, there was an error in the derivation, where Campbell obtained dh/dz = 1/e_s x dD/dz. Substituting in Eq. [1] he obtained (Eq. [4] in the original paper)

[2]

The correct differentiation of D yields = since both e_s and D vary with z. Equation [2] (Eq. [4] in the original paper) therefore becomes

[3]

Equation [3] expresses that the latent heat flux depends on the vapor pressure deficit (or E_i, the second term on the right of the equation) and temperature gradients, without any involvement of h. This correction changes the decoupled Eq. [8] (latent heat flux) and Eq. [9] (sensible heat flux) of Campbell (2003) to the standard Penman–Monteith forms:

[4]

[5]

where s = (K^–1), ^* = and where c_p is the specific heat of air (J mol^–1 K).

Editor's note: Through a series of events, Valipuram S. Manoranjan, Armen R. Kemanian, and Ryan L. Orozco discovered an error in the mathematical manipulation of one of the equations in the article by Campbell (2003). Dr. Kemanian subsequently contacted Dr. Campbell regarding this error and the correct derivation. These authors and Dr. Campbell have jointly prepared this Letter to the Editor. All authors have agreed on the content of the letter so there is no separate reply from Dr. Campbell.

REFERENCES

• Campbell, G.S. 2003. Modeling sensible and latent heat transport in crop and residue canopies.Agron. J. 95:1388–1392.[Abstract/Free Full Text]

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