A RetroSearch Logo

Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Search Query:

Showing content from https://link.springer.com/doi/10.1007/s10546-013-9823-0 below:

Large-Eddy Atmosphere–Land-Surface Modelling over Heterogeneous Surfaces: Model Development and Comparison with Measurements

Abstract

A model is developed for the large-eddy simulation (LES) of heterogeneous atmosphere and land-surface processes. This couples a LES model with a land-surface scheme. New developments are made to the land-surface scheme to ensure the adequate representation of atmosphere–land-surface transfers on the large-eddy scale. These include, (1) a multi-layer canopy scheme; (2) a method for flux estimates consistent with the large-eddy subgrid closure; and (3) an appropriate soil-layer configuration. The model is then applied to a heterogeneous region with 60-m horizontal resolution and the results are compared with ground-based and airborne measurements. The simulated sensible and latent heat fluxes are found to agree well with the eddy-correlation measurements. Good agreement is also found in the modelled and observed net radiation, ground heat flux, soil temperature and moisture. Based on the model results, we study the patterns of the sensible and latent heat fluxes, how such patterns come into existence, and how large eddies propagate and destroy land-surface signals in the atmosphere. Near the surface, the flux and land-use patterns are found to be closely correlated. In the lower boundary layer, small eddies bearing land-surface signals organize and develop into larger eddies, which carry the signals to considerably higher levels. As a result, the instantaneous flux patterns appear to be unrelated to the land-use patterns, but on average, the correlation between them is significant and persistent up to about 650 m. For a given land-surface type, the scatter of the fluxes amounts to several hundred W \(\text{ m }^{-2}\), due to (1) large-eddy randomness; (2) rapid large-eddy and surface feedback; and (3) local advection related to surface heterogeneity.

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

Access this article Subscribe and save

Springer+ Basic

€34.99 /Month

Subscribe now Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. References

Download references

Acknowledgments

This work is supported by the DFG Transregional Cooperative Research Centre 32 “Patterns in Soil-Vegetation-Atmosphere-Systems: Monitoring, Modelling and Data Assimilation”. We thank Bruno Neininger (MetAir) for performing and processing of the aircraft measurements, Heiner Geiss (Juelich Research Center), Martin Lennefer, Dirk Schüttemeyer, Stefan Kollet (University Bonn) who supported the micrometeorological measurements, Gerritt Maschwitz for launching the radiosondes.

Author information Authors and Affiliations

  1. Institute for Geophysics and Meteorology, University of Cologne, Cologne, Germany

    Yaping Shao, Shaofeng Liu, Jan H. Schween & Susanne Crewell

Authors
  1. Yaping Shao
  2. Shaofeng Liu
  3. Jan H. Schween
  4. Susanne Crewell
Corresponding author

Correspondence to Yaping Shao.

Appendix: Canopy Temperature Scheme Appendix: Canopy Temperature Scheme

The equation for canopy temperature, \(T_\mathrm{c}\), can be written as

$$\begin{aligned} c_\mathrm{vg} \frac{\partial T_\mathrm{c} }{\partial t}=-{\vec {\nabla }}\cdot \vec {R}-\alpha _\mathrm{t} \varepsilon \sigma T_\mathrm{c}^4 -\rho c_\mathrm{p} S_\mathrm{T} -\rho LS_q \end{aligned}$$

(26)

where \(c_\mathrm{vg}\) is the volumetric vegetation heat capacity (J m\(^{-3}\) s\(^{-1}\)), i.e., the energy required to increase the temperature of vegetation per unit (air) volume, \(\alpha _\mathrm{t}\) is the vegetation area density (total area per unit volume), \(\varepsilon \) is vegetation emissivity, \(\rho \) is air density, \(c_\mathrm{p}\) is air specific heat at constant pressure, \(L\) is the latent heat of vaporization of water, \(S_\mathrm{T}\) and \(S_\mathrm{q}\) are as given in Eqs. 7 and 8, \(\vec {R}\) is net radiation flux. Suppose net radiation is horizontally homogeneous, then, Eq. 26 becomes

$$\begin{aligned} c_\mathrm{vg} \frac{\partial T_\mathrm{c} }{\partial t}=-\frac{\partial R_\mathrm{n} }{\partial z}-\alpha _\mathrm{t} \varepsilon \sigma T_\mathrm{c}^4 -\rho c_\mathrm{p} S_\mathrm{T} -\rho LS_q , \end{aligned}$$

(27)

where \(R_\mathrm{n}\) is the vertical component of the net radiation. For simplicity, we divide the radiation spectrum into the shortwave (solar) and longwave (terrestrial) bands. Then, as illustrated in Fig. 12, \(R_\mathrm{n}\) for any given level can be expressed as

$$\begin{aligned} R_\mathrm{n} =(R_{\mathrm{s}\uparrow } -R_{\mathrm{s}\downarrow } )+(R_{\mathrm{l}\uparrow } -R_{\mathrm{l}\downarrow } ). \end{aligned}$$

(28)

In general, radiation passing through a vegetation layer of thickness, d\(s\), is scattered and absorbed by leaves. The dependence of \(R\) on \(s\) can be expressed as

$$\begin{aligned} \text{ d }R=-kR\text{ d }s, \end{aligned}$$

(29)

where \(k\) is the canopy extinction coefficient. It therefore follows that

$$\begin{aligned} -\frac{\partial R_\mathrm{n} }{\partial z}=k_\mathrm{s} (R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow } )+k_\mathrm{l} (R_{\mathrm{l}\uparrow } +R_{\mathrm{l}\downarrow } ), \end{aligned}$$

(30)

noting that \(\text{ d }R_\downarrow =-kR_\downarrow \text{ d }s\), \(\text{ d }s = -\text{ d }z\), and therefore,

$$\begin{aligned} \frac{\partial R_\uparrow }{\partial z}&= -kR_\uparrow ,\end{aligned}$$

(31a)

$$\begin{aligned} \frac{\partial R_\downarrow }{\partial z}&= kR_\downarrow . \end{aligned}$$

(31b)

In Eq. 30, \(k_\mathrm{s}\) and \(k_\mathrm{l}\) are respectively the extinction coefficients for shortwave and longwave radiation. It follows that Eq. 27 becomes

$$\begin{aligned} c_\mathrm{vg} \frac{\partial T_\mathrm{c} }{\partial t}=k_\mathrm{s} (R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow } )+k_\mathrm{l} (R_{\mathrm{l}\uparrow } +R_{\mathrm{l}\downarrow } )-\alpha _\mathrm{t} \varepsilon \sigma T_\mathrm{c}^4 -\rho c_\mathrm{p} S_\mathrm{T} -\rho LS_q. \end{aligned}$$

(32)

Suppose \(c_\mathrm{vg}\) is small, then the canopy temperature can be determined from the following diagnostic equation

$$\begin{aligned} \alpha _\mathrm{t} \varepsilon \sigma {T_\mathrm{c}^{4}} =k_\mathrm{s} (R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow } )+k_\mathrm{l} (R_{\mathrm{l}\uparrow } +R_{\mathrm{l}\downarrow } )-\rho c_\mathrm{p} S_\mathrm{T} -\rho LS_{q}. \end{aligned}$$

(33)

The treatment of the radiation fluxes is straightforward. Suppose the shortwave flux at the top of the canopy, \(h\), is \(R_\mathrm{sh}\). Then, the fraction of the shortwave radiation entering the canopy is \((1-a_\mathrm{vg})R_\mathrm{sh}\) and the fraction reaching the surface is

$$\begin{aligned} R_\mathrm{s0} =(1-a_\mathrm{vg} )R_\mathrm{sh} \exp \left( -\int \limits _0^h {k_\mathrm{s} } \text{ d }z\right) . \end{aligned}$$

(34)

where \(a_\mathrm{vg}\) is vegetation albedo. Thus, for a level \(z\),

$$\begin{aligned} R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow }&= a_{0} (1-a_\mathrm{vg} )R_\mathrm{sh} \exp \left( -\int \limits _0^h {k_\mathrm{s} \text{ d }z}\right) \cdot \exp \left( -\int \limits _0^z {k_\mathrm{s} \text{ d }z}\right) \nonumber \\&+\,(1-a_\mathrm{vg} )R_\mathrm{sh} \exp \left( -\int \limits _z^h {k_\mathrm{s} \text{ d }z}\right) \end{aligned}$$

(35)

or

$$\begin{aligned} R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow } =(1 - a_\mathrm{vg})R_\mathrm{sh} \left[ {a_{0} \exp \left( -{\int \limits _{0}^{h}} {k_\mathrm{s} dz} -\int \limits _0^z {k_\mathrm{s} \text{ d }z}\right) +\exp \left( -{\int \limits _{z}^{h}} {k_\mathrm{s} \text{ d }z}\right) } \right] . \end{aligned}$$

(36)

where \(a_0\) is surface albedo. Suppose the atmospheric longwave radiation at the top of the canopy is \(R_\mathrm{lh}\) and the ground surface temperature is \(T_{0}\). Further, suppose the canopy layer between \(z\) and \(h\) is divided into \(I_\mathrm{a}\) layers, and the vegetation layer between 0 and \(z\) is divided into \(I_\mathrm{b}\) layers, each of \(\delta \)z thick (Fig. 12). Then

$$\begin{aligned} R_{\mathrm{s}\uparrow } +R_{\mathrm{s}\downarrow }&= \varepsilon \sigma T_0^4 \exp \left( -\int \limits _0^z {k_\mathrm{l} \text{ d }z} \right) +R_\mathrm{lh} \exp \left( -\int \limits _z^h {k_\mathrm{l} \text{ d }z}\right) \nonumber \\&+\sum _{i=1}^{I_\mathrm{b}} {r(z_i )}\exp \left( -\int \limits _{zi}^z {k_\mathrm{l} \text{ d }z}\right) +\sum _{i=1}^{I_\mathrm{a} } {r(z_i)}\exp \left( -\int \limits _z^{z_i } {k_\mathrm{l} \text{ d }z}\right) \end{aligned}$$

(37)

with

$$\begin{aligned} r(z_i )=\frac{1}{2}\alpha _{t} (z_i )\varepsilon \sigma {T_\mathrm{c}^{4}} (z_{i} )\delta z \end{aligned}$$

(38)

where \(\alpha _\mathrm{t} (z_i )\)is the vegetation area density at level \(z_{i}\).

Fig. 12

Schematic illustration of radiation transfer through vegetation canopy

About this article Cite this article

Shao, Y., Liu, S., Schween, J.H. et al. Large-Eddy Atmosphere–Land-Surface Modelling over Heterogeneous Surfaces: Model Development and Comparison with Measurements. Boundary-Layer Meteorol 148, 333–356 (2013). https://doi.org/10.1007/s10546-013-9823-0

Download citation

Keywords

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4