Skip to main content
Springer Nature Link
Log in

The Temperature–Humidity Covariance in the Marine Surface Layer: A One-dimensional Analytical Model

  • Original Paper
  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

An analytical model that predicts how much of the temperature–humidity covariance within the marine atmospheric surface layer (ASL) originates just above the ASL and just near the surface is proposed and tested using observations from the Risø Air Sea Experiment (RASEX). The model is based on a simplified budget for the two-scalar covariance that retains three basic terms: production, dissipation, and vertical transport. Standard second-order closure formulations are employed for the triple moments and the dissipation terms, and the canonical mixing length for the closure model is assumed linear with height (z) from the surface. Despite the poor performance of the gradient–diffusion closure in reproducing the measured triple moment, the overall covariance model was shown to be sufficiently robust to these assumptions. One of the main findings from the analytical treatment is the origin of the asymmetry in how the top and bottom boundary conditions affect the two-scalar covariance in the ASL. The analytical model reveals that ‘bottom-up’ boundary-condition variations scale with \(z^{-\sqrt{a}}\) , while ‘top-down’ variations scale with \(z^{\sqrt{a}}\) , where a is a constant that can be derived from similarity and closure constants. The genesis of this asymmetry stems from the flux-transport term but is modulated by the dissipation, and persists even in the absence of any inhomogeneity in the local production function. It is shown that the local production function acts to adjust the relative proportions of these two boundary conditions with weights that vary with the Obukhov length. The findings here do not provide ‘finality’ to the discussions on the covariance between humidity and temperature or the role of entrainment in modulating the turbulence within the ASL. Rather, they are intended to guide new hypotheses about interpretations of existing field data and identify needs for future field and numerical experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  • Andreas EL, Hill RJ, Gosz JR, Moore DI, Otto WD and Sarma AD (1998). Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity. Boundary-Layer Meteorol 86: 379–408

    Article  Google Scholar 

  • Asanuma J and Brutsaert W (1999). Turbulence variance characteristics of temperature and humidity in the unstable atmospheric surface layer above a variable pine forest. Water Resour Res 35: 515–521

    Article  Google Scholar 

  • Asanuma J, Tamagawa I, Ishikawa H, Ma Y, Hayashi T, Qi Y and Wang J (2007). Spectral similarity between scalars at very low frequencies in the unstable atmospheric surface layer over the Tibetan plateau. Boundary-Layer Meteorol 122: 85–103

    Article  Google Scholar 

  • Assouline S, Tyler S, Tanny J, Cohen S, Bou-Zeid E, Parlange MB, Katul GG (2007) Evaporation from three water bodies of different sizes and climates: measurements and scaling analysis. Adv Water Resour (to appear)

  • Choi T, Kim J, Lee H, Hong J, Asanuma J, Ishikawa H, Gao Z, Wang J and Koike T (2004). Turbulent exchange of heat, water vapour and momentum over a Tibetan praire by eddy covariance and flux-variance measurements. J Geophys Res Atmos 109(D21): D21106

    Article  Google Scholar 

  • Coulman CE (1980). Correlation between velocity, temperature and humidity fluctuations in the air above land and ocean. Boundary-Layer Meteorol 19: 403–420

    Article  Google Scholar 

  • Cullen NJ, Steffen K and Blanken PD (2007). Nonstationarity of turbulent heat fluxes at Summit. Greenland. Boundary-Layer Meteorol 122: 439–455

    Article  Google Scholar 

  • Bink NI, Kroon LJM and Bruin HAR (1991). Fluxes in the surface layer under advective conditions. In: Schmugge, TJ and Andre, JC (eds) Workshop on land surface evaporation measurement and parameterization, pp 157–169. Springer-Verlag, New York

    Google Scholar 

  • Kroon LJJM, Bruin HAR and Hurk JJM (1999). On the temperature–humidity correlation and similarity. Boundary-Layer Meteorol 93: 453–468

    Article  Google Scholar 

  • Dias N and Brutsaert W (1996). Similarity of scalars under stable conditions. Boundary-Layer Meteorol 80: 355–373

    Article  Google Scholar 

  • Donaldson C (1973). Construction of a dynamic model of the production of atmospheric turbulence and the dispersal of atmospheric pollutants. In: Haugen, D (eds) Workshop on micrometeorology, pp 313–392. American Meteorological Society, Boston

    Google Scholar 

  • Friehe C, LaRue J, Champagne F and Gibson C (1975). Effects of temperature and humidity fluctuations on the optical refractive index in the marine boundary layer. J Opt Soc Am 65: 1502–1511

    Article  Google Scholar 

  • Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, UK 316 pp

  • Hill RJ (1989). Implications of Monin–Obukbov similarity theory for scalar quantities. J Atmos Sci 46: 2236–2244

    Article  Google Scholar 

  • Högström U (1990). Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J Atmos Sci 47: 1949–1972

    Article  Google Scholar 

  • Högström U, Hunt JCR and Smedman AS (2002). Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103: 101–124

    Article  Google Scholar 

  • Højstrup J, Edson JB, Hare JE, Courtney MS, Sanderhoff P (1995) The RASEX 1994 experiments Risø-R-788. Risø National Laboratory, DK4000 Roskilde, Denmark

  • Hsieh CI and Katul GG (1997). Dissipation methods, Taylor’s hypothesis and stability correction functions in the atmospheric surface layer. J Geophys Res Atmos 102(D14): 16391–16405

    Article  Google Scholar 

  • Juang J-Y, Katul GG, Siqueira MB, Stoy PC, Palmroth S, McCarthy HR, Kim H-S, Oren R (2006) Modeling nighttime ecosystem respiration from measured CO2 concentration and air temperature profiles using inverse methods. J Geophys Res 111, D08S05. DOI:10.1029/2005JD005976

  • Kaimal JC and Gaynor JE (1991). Another look at the sonic anemometry. Boundary-Layer Meteorol 56: 401–410

    Article  Google Scholar 

  • Katul GG and Hsieh C-I (1999). A note on the flux-variance similarity relationship for heat and water vapour in the unstable atmospheric surface layer. Boundary-Layer Meteorol 90: 327–338

    Article  Google Scholar 

  • Katul GG and Parlange MB (1994). On the active role of temperature in surface layer turbulence. J Atmos Sci 51: 2181–2195

    Article  Google Scholar 

  • Katul GG, Goltz SM, Hsieh C-I, Cheng Y, Mowry F and Sigmon J (1995). Estimation of surface heat and momentum fluxes using the flux-variance method above uniform and non-uniform terrain. Boundary-Layer Meteorol 74: 237–260

    Article  Google Scholar 

  • Katul GG, Hsieh C-I, Oren R, Ellsworth D and Phillips N (1996). Latent and sensible heat flux predictions from a uniform pine forest using surface renewal and flux-variance methods. Boundary-Layer Meteorol 80: 249–282

    Google Scholar 

  • King JC and Anderson PS (1994). Heat and water-vapor fluxes and scalar roughness lengths over an Antarctic ice shelf. Boundary-Layer Meteorol 69: 101–121

    Article  Google Scholar 

  • Kroon LJM and Bruin HAR (1995). The Crau field experiment: turbulent exchange in the surface layer under conditions of strong local advection. J Hydrol 166: 327–351

    Article  Google Scholar 

  • Kustas W, Blanford J, Stannard D, Daughtry C, Nichols W and Weltz M (1994). Local energy flux estimates for unstable conditions using variance data in semiarid rangelands. Water Resour Res 30: 1351–1361

    Article  Google Scholar 

  • Lamaud E and Irvine M (2006). Temperature–humidity dissimilarity and heat-to-water-vapour transport efficiency above and within a pine forest canopy: the role of the Bowen ratio. Boundary-Layer Meteorol 120(1): 87–109

    Article  Google Scholar 

  • Lang A, McNaughton KG, Fazu C, Bradley E and Ohtaki E (1983). Inequality of eddy transfer-coefficients for vertical transport of sensible and latent heats during advective inversions. Boundary-Layer Meteorol 25: 25–41

    Article  Google Scholar 

  • Liu XH, Tsukamoto O, Oikawa T and Ohtaki E (1998). A study of correlations of scalar quantities in the atmospheric surface layer. Boundary-Layer Meteorol 87: 499–508

    Article  Google Scholar 

  • Mahrt L (1991). Boundary-layer moisture regimes. Quart J Roy Meteorol Soc 117: 151–176

    Article  Google Scholar 

  • Mahrt L, Vickers D, Edson J, Sun J, Højstrup J, Hare J and Wilczak J (1998). Heat flux in the coastal zone. Boundary-Layer Meteorol 86: 421–446

    Article  Google Scholar 

  • Mahrt L, Vickers D, Edson J, Wilczak J, Hare J and Højstrup J (2001a). Vertical structure of turbulence in offshore flow during RASEX. Boundary-Layer Meteorol 180: 265–279

    Google Scholar 

  • Mahrt L, Vickers D and Sun J (2001b). Spatial variations of surface moisture flux from aircraft data. Adv Water Resour 24: 1133–1141

    Article  Google Scholar 

  • McNaughton KG and Brunet Y (2002). Townsend’s hypothesis, coherent structures and Monin–Obukhov Similarity. Boundary-Layer Meteorol 102: 161–175

    Article  Google Scholar 

  • McNaughton KG and Laubach J (1998). Unsteadiness as a cause of non-equality of eddy diffusivities for heat and vapour at the base of an advection inversion. Boundary-Layer Meteorol 88: 479–504

    Article  Google Scholar 

  • McNaughton KG and Laubach J (2000). Power spectra and cospectra for wind and scalars in a disturbed surface layer at the base of an advective inversion. Boundary-Layer Meteorol 96: 143–185

    Article  Google Scholar 

  • Moeng CH and Wyngaard JC (1984). Statistics of conservative scalars in the convective boundary layer. J Atmos Sci 41: 3161–3169

    Article  Google Scholar 

  • Moriwaki R and Kanda M (2006). Local and global similarity in turbulent transfer of heat, water vapour and CO2 in the dynamic convective sublayer over a suburban area. Boundary-Layer Meteorol 120: 163–179

    Article  Google Scholar 

  • Nagata K and Komori S (2001). The difference in turbulent diffusion between active and passive scalars in stable thermal stratification. J Fluid Mech 430: 361–380

    Article  Google Scholar 

  • Padro J (1993). An investigation of flux-variance methods and universal functions applied to three land-use types in unstable conditions. Boundary-Layer Meteorol 66: 413–425

    Article  Google Scholar 

  • Papaioannou G, Jacovides C and Kerkides P (1989). Atmospheric stability effects on eddy transfer coefficients and on Penman’s evaporation estimates. Water Resour Manag 3: 315–322

    Article  Google Scholar 

  • Phelp GT and Pond S (1971). Spectra of temperature and humidity fluctuations and of humidity fluxes and sensible heat flux in a marine boundary-layer. J Atmos Sci 28: 918–928

    Article  Google Scholar 

  • Piper M, Wyngaard JC, Snyder WH and Lawson R (1995). Top-down, bottom-up diffusion experiments in a water convection tank. J Atmos Sci 52: 3607–3619

    Article  Google Scholar 

  • Roth M and Oke T (1995). Relative efficiencies of turbulent transfer of heat, mass, momentum over a patchy urban surface. J Atmos Sci 52: 1863–1874

    Article  Google Scholar 

  • Schotanus P, Nieuwstadt FTM and De Bruin HAR (1983). Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary-Layer Meteorol 26: 81–93

    Article  Google Scholar 

  • Sempreviva AM and Gryning SE (2000). Mixing height over water and its role on the correlation between temperature and humidity fluctuations in the unstable surface layer. Boundary-Layer Meteorol 97: 273–291

    Article  Google Scholar 

  • Sempreviva AM and Højstrup J (1998). Transport of temperature and humidity variance and covariance in the marine surface layer. Boundary-Layer Meteorol 87: 233–253

    Article  Google Scholar 

  • Sjoblom A and Smedman AS (2003). Vertical structure in the marine atmospheric boundary layer and its implication for the inertial dissipation method. Boundary-Layer Meteorol 109: 1–25

    Article  Google Scholar 

  • Sorbjan Z (1989). Structure of the atmospheric boundary layer. Prentice Hall, Englewood Cliff, NJ,, 317 pp

    Google Scholar 

  • Steinfeld G, Letzel MO, Raasch S, Kanda M and Inagaki A (2007). Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study. Boundary-Layer Meteorol 123(1): 77–98

    Article  Google Scholar 

  • Stull R (1988) An introduction to boundary layer meteorology. Kluwer Academic Press, 666 pp

  • Tillman JE (1972). The indirect determination of stability, heat and momentum fluxes in the atmospheric boundary layer from simple scalar variables during dry unstable conditions. J Appl Meteorol 11: 783–792

    Article  Google Scholar 

  • Verma S, Rosenberg B and Blad BL (1978). Turbulent exchange coefficients for sensible heat and water vapour under advective conditions. J Appl Meteorol 17: 303–338

    Article  Google Scholar 

  • Warhaft Z (1976). Heat and moisture fluxes in the stratified boundary layer. Quart J Roy Meteorol Soc 102: 703–706

    Article  Google Scholar 

  • Weaver HJ (1990). Temperature and humidity flux–variances relations determined by one-dimensional eddy-correlation. Boundary-Layer Meteorol 53: 77–91

    Article  Google Scholar 

  • Wesley ML (1976). Combined effect of temperature and humidity fluctuations on refractive index. J Appl Meteorol 15: 43–49

    Article  Google Scholar 

  • Wesley ML (1988). Use of variance techniques to measure dry air-surface exchange rates. Boundary-Layer Meteorol 44: 13–31

    Article  Google Scholar 

  • Williams CA, Scanlon TM and Albertson JD (2007). Influence of surface heterogeneity on scalar dissimilarity in the roughness sublayer. Boundary-Layer Meteorol 122: 149–165

    Article  Google Scholar 

  • Wyngaard JC and Brost RA (1984). The top-down and bottom-up diffusion of scalar in the convective boundary-layer. J Atmos Sci 41: 102–112

    Article  Google Scholar 

  • Wyngaard JC, Pennel WT, Lenschow DH and LeMone MA (1978). The temperature–humidity covariance budget in the convective boundary-layer. J Atmos Sci 58: 35–47

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nicholas School of the Environment and Earth Sciences, Duke University, Box 90328, Durham, NC, 27708-0328, USA

    Gabriel G. Katul

  2. Department of Civil and Environmental Engineering, Duke University, Durham, NC, 27708-0328, USA

    Gabriel G. Katul

  3. Department of Wind Energy, Risø National Laboratory, Technical University of Denmark, 4000, Roskilde, Denmark

    Anna M. Sempreviva

  4. Institute of Atmospheric Sciences and Climate, ISAC-CNR, Area di Ricerca CNR, Roma Tor Vergata, Via Fosso del Cavaliere 10, 00133, Rome, Italy

    Anna M. Sempreviva

  5. CNR – Institute of Atmosphere Sciences and Climate Section of Lecce, Lecces, Italy

    Daniela Cava

Authors
  1. Gabriel G. Katul
    View author publications

    Search author on:PubMed Google Scholar

  2. Anna M. Sempreviva
    View author publications

    Search author on:PubMed Google Scholar

  3. Daniela Cava
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Gabriel G. Katul.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Katul, G.G., Sempreviva, A.M. & Cava, D. The Temperature–Humidity Covariance in the Marine Surface Layer: A One-dimensional Analytical Model. Boundary-Layer Meteorol 126, 263–278 (2008). https://doi.org/10.1007/s10546-007-9236-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-007-9236-z

Keywords

Profiles

  1. Gabriel G. Katul View author profile
  2. Daniela Cava View author profile