## Surface and boundarylayer parameterisations

This section briefly reviews the concepts that form the basis for the parameterisation of the boundary layer and surface processes over land in CRCM and its relation with the surface characteristics it employs. The surface parameters are read as input from a land-cover and soil reference dataset. The processes described here and relevant for our study are the surface winds, turbulent vertical flux at the ground, aspects of solar reflection and emitted infrared radiation at the ground, and the surface energy and moisture balance.

The procedures used for the treatment of subgrid-scale vertical transfer processes as well as the land surface processes used in CRCM are those used in GCMII, and most of the material found in this section is described in Boer et al. (1984) and in McFarlane et al. (1992). The source/sink terms of momentum, heat energy, and water vapour at the surface represent effects of turbulent processes that operate at scales which are smaller than those resolved in the CRCM, even with the finest possible resolution of the model. The inclusion of their effects on the resolved scales is nevertheless still necessary. They enter the prognostic equations of the primary atmospheric variables in a parameterised form.

The Reynolds stress due to the vertical exchange of horizontal momentum (¿J enters the prognostic conservation equations as a consequence of vertical momentum flux divergence. This stress has a significant influence on the simulated winds. The first momentum level is often several tens of meters above the modelled surface so that lowest level windspeed may be of limited use. The GCMII physics includes a diagnostic computation of the anemometer-level windspeed according to similarity theory, |pa(Km| = (u*/k) ln where is the anemometer wind speed, is the fric tion velocity, CM is a momentum transfercoefficient, |j?a|= [u2a + v£f2 is the lowest model-level wind speed, z„ is the roughness height for momentum, z is the height above the surface (the anemometer is typically at 10 m), and k is the von Karman constant. The turbulent vertical fluxes and the flux of solar and infrared radiation affect the lowest model level turbulent diffusion of heat and moisture as well as the surface energy balance and hydrology. The treatment of surface processes employs a single layer for heat and a "bucket" model for the soil moisture regime. The surface "ground" prognostic variables are the temperature, Tg, the soil moisture, W, and the snow mass, SM. The surface energy balance equation at the surface can be written as:

where G is the heat flux into the ground, S and FL are respectively the incoming solar and net infrared radiative fluxes at the ground, a is the surface albedo, //y is the sensible heat flux, £.v is the evapotranspiration, L is the latent heat which value depends of the state of the water at the surface, and M represents the energy change associated with the melting of frozen soil moisture and snow. The ground surface temperature over land is computed using the force-restore method and consequently the heat flux into the ground is expressed as in McFarlane et al. (1992):

where (o is the diurnal frequency, and T„ is taken to be a 24-h moving average ofTs. The soil effective heat capacity, C*, is given by the product of the soil heat capacity, Cg, and the exponential damping depth of the diurnal temperature wave, dg = (2Ag/coCg) "', Ag being the soil thermal conductivity.

The model makes use of bulk aerodynamic formulœ for the vertical transfer of heat, moisture and momentum within the constant flux layer. The parameterised fluxes assume that the transfer process is proportional to the local gradient of wind velocity, temperature, and humidity respectively between the surface and the atmosphere multiplied by the wind speed. The general expression for the surface fluxes are the same as used in GCMII (see Boer et al., 1984 and McFarlane et al., 1992):

where y/ is the transported quantity, = [(r,, ry)s, Hs, Ef\, p is the air density, tx and xy are the Renolds stress components at the surface, CF„ = (CM, CHcp, Cgß), where CM is the momentum transfer coefficient, C>/ and CE are the transfer coefficients for sensible heat and for moisture respectively, cp is the specific heat of air, y/a - [{ua, va), Ta, ra], where (wa, va) are the lowest model level air velocity components, and ra are boundary layer temperature and mixing ratio, y/g = [(%, vg), Tg, rg], where (ug, vg) = (0, 0), rg = rml is the saturation mixing ratio at the earth's surface, and ß is the evapotranspiration factor. The transfer coefficients at the surface are functions of the atmospheric stability accounted for a Richardson number dependence, and on the roughness height in the general form

CdhFhQ&b, zjzi)], where Riß is the bulk Richardson number, zL is the lowest prognostic level for momentum, and are neutral drag coefficients.

In this version of the model, the surface moisture flux coefficient is taken to be equal to the ones for heat and momentum

Concerning the surface moisture in the model, soil wetness is expressed by a non-dimensional variable (w = W/Wc), where W is the total soil moisture per unit area including the liquid and solid water phases, and is the water-holding capacity of the soil. The budget equation follows the standard one, i.e., the time evolution of the soil moisture is equal to the liquid precipitation rate plus the melting of snow rate minus the evapo ration rate (EL + Eh\ evaporation and sublimation), minus the runoff (R). The snow mass budget equation is simply equal to the solid precipitation (Ps) minus snow evaporation (Es) minus the melting rate of snow. The evaporation rates must add up to the total evapotranspiration rate, i.e., Es = Et, + E/.• +

The definition of involves an evapotranspiration factor This is an efficiency factor that depends on ground wetness, which is a function of the snow-free evapotranspiration factor where s is a slope factor, and the fractional snow cover.

Generally, the surface albedo, the transfer coefficients, the roughness height, the evapotranspiration factor, the snow masking depth, the soil heat capacity, the soil thermal conductivity and the soil water-holding capacity are functions of the land-cover types and soil characteristics.

The land surface scheme in GCMII uses land-cover characteristics coming from the Wilson and Henderson-Sellers (1985) reference surface data at a resolution of 1° lat x 1° lon. GCMII currently makes use of a set of 22 land-cover categories (apart from open water and sea-ice surfaces) in conjunction with a subset of 9 types of soil data. Table 1 lists the land-cover types and their associated parameter values. Soil types are classified according to their possible combinations of colour (dark, medium, light), and texture (fine, intermediate, coarse). At each model grid square, the most frequently occurring primary (LC1) and secondary (LC2) land-cover and the most frequently occurring soil type as well as their relative proportion are assigned, and respectively, where Once the primary and secondary land-cover are assigned to a grid square, a lookup procedure is used to obtain parameter values needed for the land-surface scheme, namely the soil depth, the evapotranspiration factor, and the snow masking depth. These values are then combined linearly with weights of 2/3 and 1/3 respectively to produce the effective soil depth, the effective evapotranspiration factor, and the effective snow masking depth, at each model grid square. The soil type is used to determine the bare ground colour and texture at each grid square. Then, the resulting soil depth is used in conjunction with the soil texture (determining its porosity) to define the effective water-holding capacity of the soil column, The heat capacity, and thermal conductivity, of the soil are dependent on the soil moisture and on the soil mineral content while the contribution of the air is not taken into account. The proportion of the soil mineral content is derived from the soil texture. The effective heat capacity of the soil, taking into account the contribution due to the snow at the surface, is computed as the weighted average of the snow-free and the snow-covered surface.

The model currently makes use of CDM. The relationship between drag coefficient, measurement height, and surface roughness under statically neutral conditions in the surface layer is given by . The neutral drag coefficient over land, used for either the momentum, heat and moisture transfer are taken from Cressman (1960). The latter is basically a form drag, very coarse in resolution (2.5° x 2.5°), which closely resembles the shape of the large-scale orography.

Type |
Description |
D, |
s |
^mask |

(m) |
(m) | |||

I |
Glacier |
* |
0.25 |
0,01 |

2 |
Inland lake | |||

3 |
Unused | |||

4 |
Evergreen needle leaf tree |
1,5 |
0.25 |
12.0 |

5 |
Evergreen broad leaf tree |
1.5 |
0.25 |
8.0 |

6 |
Deciduous needle leaf tree |
1.5 |
0.25 |
8.0 |

7 |
Deciduous broad leaf tree |
2.0 |
0.25 |
8.0 |

8 |
Tropical broad leaf tree |
2.0 |
0.25 |
8.0 |

9 |
Drought deciduous tree |
1.0 |
0.75 |
4.0 |

10 |
Evergreen broad leaf shrub |
1.0 |
0,50 |
2.0 |

11 |
Dcciduous shrub |
1.0 |
0,50 |
1.0 |

12 |
Thorn shrub |
1,0 |
0.75 |
1.0 |

13 |
Short grass and forbs |
1.0 |
0.75 |
0.1 |

14 |
Long grass |
1.0 |
0.50 |
0,15 |

15 |
Arable |
1.0 |
0.50 |
0.1 |

15 |
Rice |
1.0 |
0.50 |
0.1 |

17 |
Maize |
1.0 |
0.50 |
0.1 |

18 |
Cotton |
1.0 |
0.50 |
0.1 |

19 |
Sugar |
1.0 |
0.50 |
0.1 |

20 |
Irrigated crop |
0.75 |
0.25 |
0.1 |

21 |
Urban |
0.5 |
0.75 |
4.0 |

22 |
Tundra |
0.75 |
0.50 |
0.15 |

23 |
Swamp |
1.0 |
0.25 |
0.01 |

24 |
Desert |
0.5 |
0.75 |
0.01 |

for Glacier Wc is fixed at 200 kg/rrf for Glacier Wc is fixed at 200 kg/rrf

A climatological surface albedo is also assigned to each grid square. It is specified through two spectral intervals, namely the visible band albedo, a'f (0.3 - 0.68 (im), and the near infrared band albedo, a!£ (0.68 - 4 jam), according to a weighted average of the values of the land-cover categories from the Wilson and Henderson-Sellers (1985) dataset. During the course of a simulation, the albedo may be increased due to snow that accumulates over the surface and then reduced as the snow pack ages. Primary and secondary land-cover have their own snow masking depth and the surface is considered as fully covered with snow when snow mass exceeds the effective snow masking depth. Soil types have their own albedo values in the two spectral bands, respectively a'm , and a',:"" = 2a'Jm . During the course of a Simula tion, the values for dry conditions may also be reduced for wet soil conditions, up to 7 % when W = Wc. The resulting spectrally-averaged albedo used in the surface energy balance equation, a, of a partial snow cover surface over land is taken to be the linear combination of the snow-free and the snow-covered albedo values. The weights are determined from the fractional coverage of bare ground, the land-cover and that of the snow mass that has cumulated over the grid square.

This summarizing description of the modelled land-surface process is aimed at emphasizing the close link which exists between the ground-surface prognostic variables of temperature, snow, and moisture, the surface flux of momentum, sensible heat, and moisture as a function of the land-cover and soil types, and the wind speed just above the surface. Modifying the landcover type may have profound effect on the surface fluxes, on the modelled albedo, then on the surface energy and moisture balances, on the surface winds, and consequently on the atmospheric circulation. Thus, the prescription of land-cover and soil types may well be crucial for regional climate simulations at high resolution.

GCMII operates with a resolution typically coarser than 1°, so that representative parameter values are specified by averaging the 1° x 1° data. However, CRCM operates with resolution typically much finer than 1 ° so that representative parameter values are coarser than the mesh size and the problem of "tiling" often arises. In a small country such as Switzerland, only one land-cover and soil type are defined (two at most) so practically no spatial variability are found in the surface parameters. In order to overcome this problem, the reference surface data for use in RCMs must be at a resolution higher than 1°. A few high-resolution datasets do exist, but take into account land-cover and soil categories different from those used in the model; pre-processing of these data is necessary.

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