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Spectral Behaviour of a Coupled Land-Surface and Boundary-Layer System

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Abstract

The temporal spectral response of a coupled land-atmosphere system to daily forcing of net radiation at the land surface is investigated using the analytic approach. The original definition of the problem dates back to an early study by Lettau. The present study builds on the problem and introduces some important additions, with a focus on the propagation of heat flux and temperature waves in both the soil and the atmospheric boundary layer. The study highlights the dependence of the complex amplitude of surface temperature and heat fluxes on the different land-surface parameters, such as friction velocity, evaporative fraction, aerodynamic resistance and vegetation height. Finally, the dependency of surface state variables to the frequency of the forcing is analyzed.

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Abbreviations

λ:

Latent heat of vaporisation at the triple point (2.45 × 106 J kg−1)

λ G :

Penetration depth of the soil heat wave (m)

λ H :

Penetration depth of the sensible heat flux wave (m)

λ s :

Soil thermal conductivity (W m−1K−1)

λ θ :

Penetration depth of the potential temperature wave (m)

λ E(z):

Latent heat flux at height z (W m−2)

λ E(h):

Latent heat flux at the canopy height h (W m−2)

ω :

Angular frequency of the harmonic (rad s−1)

ρ :

Surface air density (1.2 kg m−3)

θ :

Mean potential temperature in the boundary layer (K)

E F :

Evaporative fraction at the land surface (nominal value is 0.6)

C s :

Soil heat capacity (nominal value is 1.42 × 106 J m−3K−1)

C p :

Specific heat capacity of the air at constant pressure (1012 J kg−1 K−1)

d :

Zero-plane displacement (m)

G :

Ground heat flux (W m−2)

h :

Vegetation height (nominal value is 0.5m)

H :

Turbulent (sensible) heat flux of potential temperature \({\overline{{w}'{\theta }'}}\) (Kms−1)

K s :

Soil thermal diffusivity (nominal value is 2.5 × 10−7 m2 s−1)

k :

Von karman’s constant (0.4)

\({r_{a}^{c}}\) :

Canopy aerodynamic resistance (nominal value is 50 s m−1)

R n :

Net radiation at the land surface (nominal peak value is 500W m−2)

T deep :

Deep soil temperature (K)

T s :

Soil temperature (K)

T surf :

Soil surface temperature (K)

T day :

Duration of a day (s)

u * :

Friction velocity at the land surface (nominal value is 0.2m s−1)

z 1 :

Measurement height (nominal value is 2m)

z i :

Boundary-layer height (m)

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Authors and Affiliations

  1. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA

    P. Gentine & D. Entekhabi

  2. Laboratoire de Météorologie Dynamique du CNRS/IPSL, Paris, France

    J. Polcher

Authors
  1. P. Gentine
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  2. D. Entekhabi
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  3. J. Polcher
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Correspondence to P. Gentine.

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Gentine, P., Entekhabi, D. & Polcher, J. Spectral Behaviour of a Coupled Land-Surface and Boundary-Layer System. Boundary-Layer Meteorol 134, 157–180 (2010). https://doi.org/10.1007/s10546-009-9433-z

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