method described above. Second, the multiple estimates were combined using a weighted averaging approach in which each estimate was weighted according to its standard error. In the following discussion, the subscript ic refers to a variable within category c at time i. Suppose that, for a category, K data sets are available; thus, for any year i in the future, K estimates Ŷij, j = 1,2, --- K can be obtained along with their standard errors eij, j = 1,2, --- K. A normalized set of weights is computed as
for j = 1,2…K. The weighted estimate is obtained as
and its standard error as
The 95 percent confidence interval of this weighted estimate is provided as
These calculations were applied for each of the three ice categories, yielding a multi-data averaged estimate and standard error for each.
Third, the global ice mass loss rate for any year i and error were calculated. The global ice mass loss rate was estimated as
and the standard error as
The 95 percent confidence interval of this multi-data averaged global mass loss rate is
The second and third steps were repeated for all of the projection years. The mass loss rates and the interval were subsequently converted to sea-level rates and then cumulatively summed.
RAPID DYNAMIC RESPONSE
Simple extrapolation of existing trends will not capture the effect of rapid dynamic response that begins after the period of observation. The committee calculated the effects of both acceleration and deceleration in ice discharge relative to observed present-day rates, as described below. The term “rapid dynamic response” is defined here as mass changes in a glacier or ice sheet that occur at rates faster than accompanying climatic mass balance and which force glacier or ice sheet conditions further away from equilibrium with climate.
Increases in Dynamic Discharge
To simulate the effect of rapid dynamics, supplementary ice fluxes were added to the loss rates determined by extrapolation. The parameters for the added rapid dynamic response are summarized in Box E.1. The choice of dynamic variations was intended to capture the general magnitude of plausible changes. Although these particular events may not occur, the calculations provide a means to quantitatively estimate the influence of rapid dynamic response on sea-level rise and to translate ranges of plausible future glaciological changes into equivalent sea-level changes.
The range of added rapid dynamic response for each ice source for each projection period is given in Table E.1, and the effect of the simulated rapid dynamic response on the projections, summed for all three sources, is shown in Table E.2. The top rows (“base values”) of Table E.2 show the integrated cumulative sea-level rise from the extrapolation and the low and high values based on uncertainties in the extrapolation. The middle rows of Table E.2 show the effect of additional rapid dynamic response on the projections of sea-level rise. The bottom rows (“percentage effect”) in Table E.2 show the effect of added dynamics expressed as a percentage of total sea-level rise. Rapid dynamic response is not an insignificant factor in future sea-level rise, but according to this simple analysis, it is also not a “wild card” variable that will swamp all other sources if it comes into play.