MIT Model

The main advantage of a simpler climate model such as the MIT model is that it allows one to not only estimate the change in sea-level resulting from a reference climate change transient scenario similar to the IPCC's IS92A (Houghton et al. (1996)), but it also allows an assessment of how various assumptions about the emissions of greenhouse gases and the uncertainty in key parameters in the climate model affect the estimate. The scenarios which are used in this study are characterized by a three letter code (Prinn et al. (1997)):

• The first letter represents high, standard and low estimates for the increase in emissions of greenhouse gases.
• The middle letter gives an indication of the rate of warming. By taking lower/higher values for the aerosol optical depth and the oceanic heat uptake, the rate of warming will be faster/slower than for the reference case.
• The last letter gives the sensitivity of the model to greenhouse forcing. By tuning the cloud feedback, higher and lower sensitivities than the reference case can be obtained.

The HHH scenario combines high emissions, a strong rate of warming and a large climate sensitivity, it therefore exhibits the largest warming of the runs, globally +5.5^oC degrees by 2100. The LLL scenario has the smallest warming, +1^oC degrees in 2100. The reference scenario, which mimics the IPCC's IS92a scenario, and which was used to derive the melting and runoff at the time of carbon dioxide doubling in the preceeding section, has a global average increase in temperature of +2.5^oC by 2100. The scenarios are considered as being equally probable, and the results obtained by driving the snowpack model with this input data can be regarded as a first estimate of the range of uncertainty in the contribution of Greenland and Antarctica to sea-level change in the 21^st century.

The evolution from 1990 to 2100 of the individual contributions to the mass balance of the Greenland ice sheet, as estimated by the snowpack model for the REF, HHH and LLL scenarios, is shown in Fig.4.

  

Figure: Time evolution from 1990 to 2100 of the amount of snowfall, rainfall, evaporation, melting, freezing and runoff over the Greenland ice sheet. Units are 10¹² kg a^-1. MIT model. Solid line: REF, dahed line: HHH, dash-dotted line: LLL scenarios.

Snow- and rainfall increase steadily over the next century, and the rate of increase is closely linked to rate of warming of the atmosphere, as shown by the differences between the three curves. As noted previously, this does not however mean that temperature changes control the increase in precipitation, the latter is determined by the modifications in atmospheric circulation which are associated with the changes in temperature. The slow changes in summer air temperatures have an important impact on the evolution of melting and runoff, these quantities do not increase beyond their 1990 values until 2050 in the REF scenario, increase most rapidly between 2030 and 2070 in the HHH scenario and do not show any visible change in the LLL run. This delay is closely linked to the role of oceanic convection which limits the heating of the ocean surface in high latitudes, thereby increasing the time the atmosphere takes to adjust to the changes in forcing in transient simulations. Note that the warming predicted for the Arctic is still larger than the global average because of the ice-albedo feedback effect. The refreezing of rainfall and meltwater remains an important component of the mass balance throughout the integrations, but the capacity of the snow cover to refreeze liquid water diminishes as the warming accelerates and more meltwater is produced. The ratio of melting/freezing in the HHH run is $\sim$ 4 at the start of the integration and increases to $\sim$ 6 by 2100. These changes are closely linked to the density structure of the snow cover in the ablation region: Once the newly deposited snow of the previous winter is melted away and bare ice is exposed, the capacity to refreeze water is lost until new snow is deposited, the meltwater contributes therefore rapidly to the total runoff. The albedo of bare ice is set to a constant value and the melting becomes largely independent of the surface air temperature once ice is exposed, which explains why runoff in the HHH scenario levels off after 2070. Refreezing does however retain an important role in delaying the formation of runoff in areas which were previously not exposed to melting: The small amounts of rain- or meltwater which are added at the surface in the summer immediately refreeze in the snowpack to form superimposed ice layers, thereby delaying the onset of runoff.

  

Figure: Evolution from 1990 to 2100 of the amount of snowfall, rainfall, evaporation, melting, freezing and runoff over the Antarctic ice sheet. Units are 10¹² kg a^-1. MIT model. Solid line: REF, dahed line: HHH, dash-dotted line: LLL scenarios.

The equivalent projections for the Antarctic ice sheet are shown in Fig.5. The most striking difference to Greenland is the amount of refreezing taking place. The very cold winter temperatures combined with large negative values in the energy balance lead to firn temperatures which are much colder than on Greenland, and which represent a sufficient storage of energy to refreeze any meltwater which percolates into the snowpack during the summer. With the exception of the HHH scenario which does show substantial melting taking place in Antarctica by the end of the 21^st century, runoff remains a negligible quantity in the REF and LLL scenarios. Note that most of the melting occurs on the Antarctic Peninsula, an area characterized by strong topographic gradients. It is far from certain that the 40 km grid which was used is sufficiently fine to capture the changes in mass balance in that region adequately.

  

Figure 6: Individual contribution to sea level change from Greenland, in cm. Reference transient scenario, MIT model.

The impact on the sea-level of the changes in the individual components which form the mass balance are shown as an example for the case of the REF scenario and Greenland in Fig.6. Changes in rainfall and evaporation contribute almost equally but in opposite directions to the sea level change, both effects are also very small. The increase in accumulation is balanced by the increase in melting, and the net sea level change is very small. This is to a certain extent also the case for the other six scenarios, shown in Fig.7; the +1.7 cm increase in sea-level from Greenland associated with the HHH run is the result of a 4.2 cm rise due to increased runoff and of a 2.5 cm drop due to increased accumulation. As the climatic forcing strengthens, increasingly large changes in accumulation and ablation are to a large degree offsetting each other, giving the impression that the mass balance of the Greenland ice sheet is relatively insensitive to changes in climate when in fact the amount of meltwater runoff has doubled or tripled by 2100. The contribution of Greenland to sea-level rise can nevertheless be expected to be in the -0.5 - +1.7  cm range by 2100.

  

Figure 7: Sea level rise induced by the change in mass balance for 7 transient runs for the Greenland (left) and the Antarctic ice sheet (right), MIT model. Units are cm.

It is worth noting that the dominant factor in determining the range of uncertainty in the prediction of sea-level rise is not the rate of increase in emissions of greenhouse gases, but the assumption made about two climate model parameters: the aerosol optical depth and the deep ocean heat uptake. The latter factor is particularly important in high latitudes. The runs which have a low ocean heat uptake (middle letter H) exhibit a larger sea level rise than those with high heat uptake (middle letter L). By mixing the water column and transporting heat from the surface to the deep ocean, convective overturning in high latitudes is the main mechanism which delays the warming of the atmosphere. In a simplifying assumption, oceanic heat uptake is modeled as a diffusive process below the mixed layer ocean model which is coupled to the MIT atmospheric model for the transient runs (Sokolov and Stone (1998)).

The situation in Antarctica is dominated by the increase in accumulation. The small increase in snowfall in the LLL scenario leads to a 2.6 cm decrease in sea-level. The substantial increase in runoff observed during the last 20 years of the HHH integration is sufficient to begin a reversal of the downward trend in sea-level. This leads to a range of uncertainty of -6.2 - -2.6  cm for Antarctica.

The scaling applied to the precipitation field in Antarctica, which reduces current total accumulation to the observed value, has an important impact on the estimates of sea-level rise, without it, the decrease in the level of the oceans would be in the -12.2 - -4.3 cm range.

The combined effects of Greenland and Antarctica on sea-level changes predicted by the MIT/snowpack model is summarized in Table 4 and is in the -4.5 - -2.7  cm range. This is a surprisingly small range of uncertainty when considering the large spread in temperature changes associated with the various scenarios, but it follows logically from the offsetting effects of the two ice sheets.

 

Table: Sea-level change predicted by the MIT model for the REF, HHH, LLL scenarios and the snowpack (SP), Positive Degree-Day (PDD) and Linear models (LM). Left-hand column: Greenland, Middle column: Antarctica, Right-hand column: Net sea-level change. Units are cm

	Greenland			Antarctica			Net
	SP	PDD	LM	SP	PDD	LM	SP	PDD	LM
REF	0.2	0.1	0.3	-4.3	0.4	2.6	-4.1	0.5	2.9
HHH	1.7	2.0	2.8	-6.2	24.6	6.5	-4.5	26.6	9.3
LLL	-0.1	-0.1	0.0	-2.6	-1.1	1.1	-2.7	-1.2	1.1

The estimates of runoff derived with the three melt models for Greenland were all within a reasonable range of observations for the current climate. It is therefore particularly interesting to observe how they respond to the range of forcing provided by the HHH - LLL scenarios. The evolution of the runoff from the Greenland ice sheet is shown as the left-hand column of Fig.8, the changes in sea-level in 2100 are summarized as the first three columns of Table 4. The three models are generally in good agreement over a broad range of forcing. The discrepancy which occurs during the last 20-30 years of the HHH integration does however point to a limitation of the degree-day model and to the crucial role of the albedo parameterization in detemining melting. Beyond a certain threshold which is reached once ice outcrops during the ablation season, increasing temperatures will no longer have much impact on the rate of meltwater formation in the snowpack model (they have an indirect effect through the sensible and latent heat fluxes), the amount of runoff predicted by the degree-day model will however continue to increase. The linear model predicts a slightly larger amount of runoff in all scenarios and suffers from the same flaw as the degree-day model, most likely because the range of temperatures over which the model was originally calibrated has been exceeded by the end of the HHH run.

  

Figure: Evolution of the runoff from 1990 to 2100. Left column: Greenland, Right column: Antarctica. MIT climate model. Snowpack Model: solid line, Degree-Day Model: dashed line, Linear Model: dash-dotted line. Top panels: REF, Middle panels: HHH, Lower panels: LLL. Units are 10¹² kg a^-1

The equivalent results for Antarctica are shown in the right-hand column of Fig.8 and are summarized as the central three columns of Table 4, they do not have the consistency of the results presented for Greenland. The temperature based methods, and the degree-day method in particular, are much more sensitive to the changes in climate which are taking place. This is in large part due to their inability to refreeze large amounts of meltwater (refreezing in the snowpack model reduces the amount of runoff by 615 ^. 10¹² kg a^-1 in the HHH scenario in 2100 and offsets a large part of the increase in rainfall and melting) and to the fact that they were not calibrated to the conditions prevailing in that part of the world.