## Singlecolumn models

Chapter 5 has already provided a few examples of the applications of single-column models. These include assessments of cloud radiative forcing over the sea ice cover (Section 5.6), processes that maintain the low-level Arctic temperature inversion (Section 5.9.2) and the application of a radiative transfer model to a grid array to provide fields of surface radiation fluxes and surface albedo from AVHRR data (the APP-x products, see, for example Figure 5.3).

Another good example is provided by the study of Zhang et al. (2001) who examined how variations in atmospheric thickness (1000 to 500 hPa), mean atmospheric temperature (surface to 10 km) and total atmospheric water vapor content (precipitable water, surface to 10 km) influence the atmospheric downwelling longwave flux at the surface at two sites in Alaska (Barrow and McGrath) during the snowmelt period. Radiation fluxes in this model are computed using a one-dimensional atmospheric radiative transfer model for shortwave and longwave radiation combined with a surface energy balance equation. The radiative transfer model (Stamnes et al., 1988) has routines to include the effects of clouds, Arctic haze, carbon dioxide, water vapor, ozone and snow. Snow optical properties are based on assumed mean grain radii (200 ^m) and snow density (350 kg m-3). The model was driven by twice-daily atmospheric pressure, temperature and water vapor concentrations from rawinsonde observations for the years 1980 through 1991.

Figure 9.1 shows some of the results for Barrow. The most striking feature is the impact of precipitable water on the downwelling longwave radiation. Longwave

Mean atmospheric temperature (°C)

Mean atmospheric temperature (°C)

DLW = a * log(APW) + b a=109.1, b=113.7 r=0.93 . o=+9.7

DLW = a * log(APW) + b a=109.1, b=113.7 r=0.93 . o=+9.7

10 15 20

Precipitable water (kg m"2)

Figure 9.1 Variations of atmospheric downwelling longwave radiation at Barrow with respect to (a) mean atmospheric temperature (surface to 10 km) and (b) precipitable water (surface to 10 km) during the snowmelt period over the years 1980-91. DLW is the downwelling longwave radiation, Tmean is the mean atmospheric temperature and APW is the mean precipitable water. Regression equations are also shown, where a and b in the legend of each panel are the regression constants, r is the correlation coefficient and a is the deviation of downwelling longwave radiation from the regression line. The thin lines are the regression lines while the dashed line is the estimated longwave flux from the Parkinson and Washington (1979) empirical formula, based on the near-surface temperature (using the same scale as for mean atmospheric temperature) (from Zhang et al., 2001, by permission of AMS).

10 15 20

Precipitable water (kg m"2)

Figure 9.1 Variations of atmospheric downwelling longwave radiation at Barrow with respect to (a) mean atmospheric temperature (surface to 10 km) and (b) precipitable water (surface to 10 km) during the snowmelt period over the years 1980-91. DLW is the downwelling longwave radiation, Tmean is the mean atmospheric temperature and APW is the mean precipitable water. Regression equations are also shown, where a and b in the legend of each panel are the regression constants, r is the correlation coefficient and a is the deviation of downwelling longwave radiation from the regression line. The thin lines are the regression lines while the dashed line is the estimated longwave flux from the Parkinson and Washington (1979) empirical formula, based on the near-surface temperature (using the same scale as for mean atmospheric temperature) (from Zhang et al., 2001, by permission of AMS).

Figure 9.2 Schematic of the Bitz et al. (1996) single-column atmosphere-sea ice-upper ocean climate model. Fsw and Folr are incoming shortwave and outgoing longwave radiation, respectively. D is the atmospheric energy flux convergence, Fw the ocean heat flux, Ta the surface air temperature, Ts the sea ice/snow temperature, T\ the temperature at the top of sea ice layer 1, Tb the temperature of the ocean mixed layer and the bottom temperature of the sea ice, h is the thickness of sea ice and hs the thickness of snow (from Bitz et al., 1996, by permission of AMS).

radiation increases logarithmically with an increase in precipitable water. The impact on the downwelling longwave radiation is hence much greater at low precipitable water values. This compares to a linear relationship between the longwave flux and mean atmospheric temperature (and the 1000 to 500 hPa thickness). The conclusion drawn from this modeling study is that the impacts of changes in precipitable water (especially at low values of precipitable water) are much greater than those of temperature. There are a number of empirical formulae to estimate the downwelling longwave flux. Figure 9.1(a) shows the longwave flux estimated from the formula of Parkinson and Washington (1979) based on the near-surface temperature. Compared to results from the radiative transfer model, the Parkinson and Washington formula underestimates the radiation flux when the near-surface temperature is relatively high and overestimates the flux when the near-surface temperature is comparatively low.

We next turn to the study of Bitz et al. (1996). The focus of this effort was to model the low-level natural variability of the Arctic climate system using a single-column energy balance model of the atmosphere, sea ice and upper ocean. Variability was induced by forcing the model with synthetic data, including realistic random perturbations of insolation, the meridional transport of atmospheric energy into the column, cloudiness and snowfall. Figure 9.2 provides a schematic. Conduction of heat through the ice is treated such that the number of ice layers remains fixed while total ice thickness varies (consequently the layer thicknesses vary). The sea ice is modeled as a slab with no leads, with the upper ocean treated as a slab mixed layer.

When the ice surface is snow free, solar radiation penetrates the sea ice, heating its interior and the ocean mixed layer. Surface albedo depends on sea ice thickness and snow thickness. The atmospheric model has 18 layers, and includes heating rates from different atmospheric gases and atmospheric scattering of solar radiation. Clouds are modeled as a single layer. Along with horizontal energy transports, the model includes vertical convective transport of latent and sensible heat, and the radiative effects of ice crystal precipitation.

One of the interesting results from this study is that the volume of perennial sea ice is simulated to vary predominantly on decadal time scales. As assessed from sensitivity studies, variations in ice volume are most sensitive to perturbations in atmospheric forcing not in winter, the period of ice growth, but in late spring, at the onset of melt, pointing to the importance of ice-albedo feedbacks. The model calculations suggest that natural variability in the thermodynamic forcing on Arctic Ocean sea ice volume could (by promoting variations in sea ice export from the Arctic Ocean) lead to freshening of the North Atlantic comparable to that associated with the Great Salinity Anomaly (see Chapter 7).

The ISCCP-D and APP-x surface radiation flux fields outlined in Chapter 5 represent the application of a single-column model to a two-dimensional grid. Another example of this general strategy is the study of Oelke et al. (2003). They simulated the active layer of permafrost over the Arctic terrestrial drainage at a 25 x 25 km resolution using a heat conduction model with phase change developed by Goodrich (1982). Soil is divided into layers with different thermal properties for frozen and thawed soils. Information on the spatial distribution of soil bulk density, and the relative compositions of clay, silt and sand that influence thermal conductivity are taken from existing maps. Soil water content varies with each layer. Initial soil temperatures were chosen according to the permafrost classification of the grid cells based on the International Permafrost Association map (Figure 2.13)

The main model forcings are daily SAT and snow thickness. SAT was based on fields from the NCEP/NCAR reanalysis, adjusted to address better the effects of topography. Snow thickness was obtained by adjusting SSM/I snow water equivalent retrievals by climatological snow densities for different climatic zones (tundra, taiga, prairie, alpine and maritime regions), based on the classification of Sturm etal. (1995) (see Chapter 2). SSM/I cannot detect areas of thin snow. Areas of thin snow were identified through comparisons between the SSM/I fields and NOAA weekly snow charts and given an assumed thickness of 3.0 cm.

Figure 9.3 summarizes results for two grid cells over the period August 31, 1998 through December 31, 2000, which includes two complete freezing and thawing seasons. The first grid cell is at 51° N at 1664 m in southern Siberia, in a region of continuous permafrost with taiga snow. The middle panel depicts the time evolution of the vertical cross section through the soil. Shaded regions in the profiles are where the soil is thawed. Spring and summer thawing occurs from the top down. Autumn/winter freezing is also primarily from the top down. Consequently, from autumn into early winter, one has a frozen surface layer with a thawed layer below. It takes until the middle

750 500 250 0 Ps

750 500 250 0 Ps

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200 400 600

Day (from 31 August 1998)

16065

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 / w 0.37 8! \ 200 400 600 Day (from 31 August 1998) 16666 200 400 600 Day (from 31 August 1998) Figure 9.3 Time series (August 31, 1998 to December 31, 2000) from an active layer thickness model for model grid cells in (a) Siberia and (b) northern Canada. The top panels for each location show surface air temperature (including 31-day running mean), snow height hs (shaded) and snow density ps (thin dashed line). The middle panels show the depth of the thawed layer (shaded regions) and the development of thawing planes (solid line) and freezing planes (dashed lines). The bottom panels show the total thaw depth (with maximum values labeled). Also plotted on the middle and bottom panels by horizonal dash-dotted lines are the boundaries of the major soil layers at 0.3 and 0.8 m depth. Grid cell elevations z, latitude and longitude are also given (from Oelke et al., 2003, by permission of AGU). of winter for the thawed layer at depth to completely re-freeze. This late freeze-up reflects the insulating effects of overlying snow cover. The bottom panel shows the time evolution of the depth of thawed soil. The active layer represents the maximum depth that experiences seasonal thaw (i.e., the maximum value shown in the bottom panel). For the Siberian grid, a fairly deep active layer develops in each year, largest in 2000 with a value of 177 cm. The second grid cell is located in Canada on Prince Patrick Island at 76° N. This is in a much colder climatic zone than for the Siberian example. While the ground is snow covered for a longer period, the snow cover (tundra snow) is thinner due to the scant precipitation. In turn, the active layer depth is shallower. Some idea of the spatial characteristics of the simulated active layer over the Arctic terrestrial drainage is provided in Plate 6. The maximum thaw depth (active layer thickness) is given for 1999, along with the day of the year at which the maximum thaw depth occurred. There is a general decrease with latitude in thaw depth but with minimum values around coastal Greenland and the Canadian Arctic Archipelago. Topographic effects are apparent. The area northwest of Hudson Bay is characterized by high bulk density bedrock areas with high thermal conductivity and hence deeper maximum thaw depths. In general, as latitude increases, the date at which the maximum depth occurs shifts to earlier in the year. This relates to the shorter period of warmth at higher latitudes.
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