Snow parameterization in GCMs

Richard Essery

4.4.1 Introduction

General circulation models (GCMs) are three-dimensional numerical models of the global climate system; an introductory review of their use in climate modeling is given by McGuffie and Henderson-Sellers (1997). The atmospheric component of a GCM may be coupled to an ocean model or run with prescribed sea-surface temperatures and sea-ice extents to provide surface boundary conditions over oceans. Land-surface models, used to supply boundary conditions over land, have to take account of the influences of snow cover on interactions between the surface and the atmosphere because the unique properties of snow, discussed in Chapter 2, can present marked and rapidly varying modifications in the characteristics of the land surface. The large contrast in albedo between snow-covered and snow-free land, in particular, is often cited as providing a possible positive feedback mechanism for climate change; reduced snow cover in a warmer climate will tend to increase the absorption of shortwave radiation at the surface, reinforcing the warming. This simple interpretation neglects other feedbacks involving changes in snow cover: the surface temperature of snow-covered land cannot exceed 0 °C, limiting the outgoing longwave radiation and giving a negative feedback; systematic changes in cloud cover resulting from changes in snow cover could lead to positive or negative feedbacks; and warming could lead to increased snow cover in cold regions where snowfall is currently limited by moisture supply rather than by temperature.

In comparison with satellite observations of snow cover on continental scales, Frei et al. (2003) found that 15 GCMs participating in the second phase of the atmospheric model intercomparison project gave better results than the 27 GCMs in the first phase (Frei and Robinson, 1998), although consistent model biases remained over Eurasia. Cess etal. (1991) investigated snow-climate feedbacks by comparing results from 17 GCMs and Randall et al. (1994) analysed results from 14 of the GCMs in more depth. Pairs of perpetual-April simulations were carried out with fixed sea-ice and homogeneous perturbations of ±2 °C in sea-surface temperatures. Dividing resulting differences in global-mean surface temperature between simulations by differences in global-mean net radiation at the top of the atmosphere gives a climate sensitivity parameter for each GCM. A second sensitivity parameter was calculated from simulations where the snow cover was fixed, rather than allowed to respond to the perturbations. The ratio of these two parameters is interpreted as a measure of snow feedback, with values of greater than one indicating positive feedbacks. The 17 GCMs produced results, shown in Fig. 4.8, ranging from weak negative to strong positive feedbacks. More recently, Hall and Qu (2006) investigated the strength of snow albedo feedbacks in simulations of climate change by 17 GCMs for the Intergovernmental Panel on Climate Change fourth assessment report and, again, found a wide range in results. Differences in GCM snow feedback results are not solely due to differences in their representations of snow processes, but improved representations will allow greater confidence in predictions of climate change.

Figure 4.8. Snow feedback parameters from Cess et al. (1991) for 17 GCMs.
Figure 4.9. A global land mask with a typical GCM resolution of 2.5° latitude by 3.75° longitude.

The temporal and spatial resolutions of GCMs are strongly constrained by computational cost, particularly when investigating long-term changes in climate; the standard configuration of the HadAM3 climate model (Pope et al., 2000), for example, has a horizontal resolution of 2.5° latitude by 3.75° longitude (Fig. 4.9), 19 vertical levels in the atmosphere and a 30 min timestep. The complexity with which physical processes can be represented is also limited, and processes on scales too small to be resolved by GCM grids have to be "parameterized" in terms of resolved quantities. Sophisticated snow-physics models, such as CROCUS (Brun et al., 1989), SNTHERM (Jordan, 1991), and SNOWPACK (Bartelt and Lehning, 2002), are not suitable for use in GCMs, which ideally need snow models that are not computationally demanding, represent processes averaged over GCM grid scales rather than at a point, and are applicable in the widely varying environments in which snow cover occurs. Nevertheless, the insight gained from detailed snow models has been useful in the development of GCM snow models; many of the more sophisticated GCM schemes have adopted features of the Anderson (1976) model, for example. Detailed models have also been implemented in GCMs to study their impact on short simulations (Brun et al., 1997) and used to assess the importance of individual processes in simpler parameterizations (Loth and Graf, 1998a,b; Pomeroy etal., 1998).

An extensive list of snow models, developed for a range of applications, has been given in Section 4.2. Acronyms and references for a small selection of models that will be used to illustrate the discussion in this section are given in the table below, drawn from descriptions of GCMs, GCM land-surface schemes and snow models developed for use in GCMs.


Best approximation of surface exchange

Slater etal. (1998)


Biosphere-atmosphere transfer scheme

Yang etal. (1997)


Canadian land-surface scheme

Verseghy (1991) Verseghy et al.



Community land model

Oleson et al. (2004)


Goddard Institute for Space Studies

Hansen etal. (1983)


Goddard Institute for Space Studies

Lynch-Stieglitz (1994)


Interactions between soil, biosphere and

Douville etal. (1995a, b)



Met Office surface exchange scheme

Cox et al. (1999) Essery (1997a,



Max-Planck-Institut für Meteorologie

Loth et al. (1993) Loth and Graf



Simple biosphere

Sellers etal. (1996)

4.4.2 Thermal and hydraulic properties of snow

Changes in density and porosity due to compaction, crystal metamorphosis, and freezing of meltwater or rain cause the thermal and hydraulic properties of snow to vary with time (Sections 2.2-2.4). GCMs generally neglect snow hydrology and often simply adopt constant values for the density, heat capacity, and thermal conductivity of snow, but some more sophisticated parameterizations have been introduced.

fe 200

Figure 4.10. Snow density as a function of age from parameterizations used by

CLASS (—), GISS94 (■ ■ ■) and BATS (---), and the fixed value used by GISS83

and MOSES (-----). Snow is assumed to be melting for GISS94 and BATS, and the snow mass is set to 100 kg m-3 for GISS94.

CLASS and ISBA use compaction parameterizations in which the density of snow increases with time after snowfall. Given snow density ps at time t, the density at time t + At is calculated as

Ps(t + At) = [ps(t) - Pmax] exp ^- — J + pmax, where pmax is the maximum permitted snow density and t p is a time constant. BASE, BATS, GISS94, and MPI use similar parameterizations but with increasing compaction rates at higher temperatures. In both BASE and GISS94, the densifi-cation rate is given by dp1__0.5psgM_

for snow mass M (kg m-2), snow temperature Ts (K) and gravitational acceleration g (m s-2). CLM uses the more sophisticated scheme of Anderson (1976), which has separate rates for compaction due to overburden, metamorphosis, and melting. Results from these parameterizations are shown in Figure 4.10.

In all models with a variable snow density, the density is recalculated after snowfall as a weighted average of the new and old snow densities. Fresh snow density is usually set to a constant value (100 kg m-3 in BASE, BATS, CLASS, and ISBA, 150 kg m-3 in GISS94), but is parameterized as a function of air temperature or wet bulb temperature in some models; CLM, for example, follows Anderson (1976) in setting



200 400

Snow density (kg m~3)

Figure 4.11. Thermal conductivity as a function of snow density from parameter-

izations used by CLASS (—), GISS94 (■ ■ ■), ISBA (---) and MPI (-----), and fixed values used by GISS83 (+) and MOSES (♦).

for air temperature T (°C), with the limits that pfresh is between 50 and 169 kg m-3.

The specific heat capacity of snow can be simply calculated as the sum of the heat capacities of the ice, water, and air mass fractions (Section 2.3), but transport of heat in snow is a complicated process involving conduction, advection, phase changes, and radiation (Section 2.3). Several empirical relationships have been proposed that give effective thermal conductivities for snow as functions of density (Anderson, 1976; Yen, 1981; Sturm etal., 1997). Figure 4.11 compares parameterizations (cf. Fig. 2.10). GISS83 and MOSES, both of which assume a fixed snow density of 250 kg m-3, and use fixed values of thermal conductivity. BASE, CLASS, GISS94, and MPI all use a quadratic function but choose different values for the parameters a1 and b1. CLM uses a different quadratic function keff = ka + (7.75 X 10-5ps + 1.105 X 10-6ps2) (ki - ka), from Jordan (1991), where kair and kice are the conductivities of air and ice. ISBA uses a power-law relationship where pe is the density of water.

GCMs have mostly neglected the complexities of snow hydrology discussed in Section 2.4, instead draining meltwater instantaneously. As a simple improvement, keff = a1 + &1p.

GISS94 allows a snow layer to retain up to 5.5% of its mass as liquid water, excess water draining through the bottom of the layer. MPI parameterizes this capacity as a function of density, decreasing from a maximum of 10% to 3% for densities of 200 kg m-3 and greater. Liquid water may freeze within the snow in both of these models and CLASS.

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