AGCIEOC96/TitusSSSII

AGCI Session II: Characterizing and Communicating Scientific Uncertainty

Session Chairs: Dr. Richard H. Moss and Dr. Stephen H. Schneider

July 31 to August 8, 1996

Probabilities in Sea Level Rise Projections

Jim Titus

U. S. Environmental Protection Agency

Washington, DC

Along the Atlantic and Gulf Coasts of the United States, sea level is rising about 3 mm per year or about 1 inch every decade. For people living near the coasts and near sea level, this is significant. The natural consequences of this rise are that ocean beaches are eroding about a meter per year, floods are gradually coming further inland, and water tables are rising.

Though sea level has been changing naturally for thousands of years, what presents the current problem is the interaction between human activity and the consequences of the rise in sea level. In many coastal resorts, beaches are disappearing because houses are being built where the dunes used to be; if the houses weren't there, the dunes could move inland. Beaches are also getting narrower because bulldozers are excavating the coastline, often to build dunes. In many low-lying barrier island areas, whenever it rains at high tide the drainage doesn't work because the third of a meter (one foot) rise in sea level since these communities were built leaves the water table a third of a meter higher, thus slowing the drainage rate. Along estuarine shores like Chesapeake Bay, the natural shoreline is being replaced by walls of concrete, rock and wood. Public access to beach areas is lost, birds can't eat along the shoreline, boats can't land there; in short, much is being lost.

Addressing the consequences of rising sea level depends on factoring in existing sea level rise, how much it will accelerate due to climate change, and how we choose to handle the trade offs between risks and costs.

Addressing these and other consequences of rising sea level depends on factoring in existing sea level rise, how much it will accelerate due to climate change, and how we choose to handle the trade offs between risks and costs. In many cases, we are not yet even dealing with the fact that sea level is rising at all. For example, wetlands protection laws and other U. S. policies are based on the assumption that the sea isn't rising and shores aren't eroding, even though we know that they are.

There are cases where sea level rise is being recognized. Along ocean shores that have not yet been developed, at least half the states in the U. S. have set-back requirements, in many cases, based on current erosion rates. This shows a recognition, at least with regard to new development, that the shores are dynamic. In some cases, there is even a recognition of the acceleration of sea level rise. For example, the Dutch are incorporating accelerating sea level rise into new dike construction plans. San Francisco, Hong Kong, and a few other cities are addressing accelerating sea level rise with regard to newly reclaimed land. The state of Maine has restricted development for any area subject to a one meter (~3-foot) rise in sea level (which was the best estimate when the regulation was put in place).

There are many decisions that are sensitive to future sea level rise. Among them are determining minimum surface elevation for land reclamation, coastal setbacks, the size of urban drain pipes, and the valuation of contingent interests in land for taxation purposes and for the purposes of determining how much to reimburse land owners if their property is "taken" by the government. Decisions such as these often deal with risks versus costs. For example, in building a new urban street drain system, it only costs 1-3 percent more to use the larger pipes that would make the system work well if there is a third of a meter rise in sea level. Current decision makers have to choose whether to spend this extra money now to prevent a possible future problem. Such decisions depend on factors including what discount rates are applied and how likely it is that the sea is going to rise a third of a meter before the system would have to be rebuilt anyway.

Regarding valuation of contingent interests in land, one way to deal with the wetland problem is to create a "rolling easement," in which the government buys an option to take property if sea level rises a certain amount. Essentially, the government is purchasing a contingent property right to ensure that nature can move inland if necessary. In calculating the value of such a rolling easement, we can use a probability distribution regarding sea level rise. In valuing these properties, a court would need expert testimony as to the probability of sea level rise. In general, Titus argues, there is a need to find ways of incorporating sea level rise into rational decision making.

In order to begin doing this, Titus says, it is necessary to calculate a probability distribution for sea level rise. For this reason, Titus brought together many existing models and added what was lacking, which was a way of capturing smaller probability events, such as a deglaciation in Antarctica. The IPCC model assumes no contribution to sea level rise from Antarctica, but most glaciologists believe there is at least a small possibility of such a contribution. Figure 2.16 illustrates how the models used in Titus' study were brought together.

In order to calculate a probability distribution for sea level rise, Titus brought together many existing models and added what was lacking, which was a way of capturing smaller probability events.

It was then necessary to specify probability distributions for all the input parameters. The IPCC and other previous assessments used high, medium and low scenarios, but did not specify probability distributions. This difficult task was accomplished by bringing in a large number of expert contributors. Each expert went "on the record" by name which allowed for probing and disclosing potential biases, etc. Experts were divided into three categories based on their having opinions on: climate parameters, glaciology parameters and precipitation parameters. In addition to the aggregations, each contributor's individual answer on any topic can also be found in the report.

Combining or aggregating their answers was a challenge. How should outlier opinions be used? How should each experts' opinion be weighted? Titus chose to alter the mainstream probability distributions based on outliers' views, and he placed a weight on them, which he chose for each in an ad hoc fashion. There was some discussion on how this should best be accomplished; the view was expressed that it is crucial to understand the underlying reasons for the differences in opinions before choosing if and how to aggregate them.

Combining or aggregating answers was a challenge. How should outlier opinions be used and weighted? Titus chose to alter the mainstream probability distributions based on outliers' views, and he placed a weight on them, which he chose for each in an ad hoc fashion.

The manner in which the EPA authors chose to aggregate the scientists opinions was criticized in editorial comments by Keith, 1996, on the grounds that this may be an inappropriate procedure when an outlier scientist clearly adheres to a different paradigm than the other scientists interviewed. Titus counters that not only would it be wrong to disregard the opinion of a respected scientist simply because it was an outlier, but that the suggested courses of action recommended by Keith do not solve the problem. Keith suggested only reporting nonaggregated results, similar to the approach of Morgan and Keith. That suggestion, however, ignored the practical realities of a modeling study where different groups of experts express opinions on different subsets of parameters. In such a study, there is a vertical aggregation of opinions (combining one expert's opinion of ocean parameters with another's opinion on glacial parameters) as well as the horizontal aggregation involved in specifying a probability distribution based on alternative expert opinions. As a result, Keith's suggestion would have required the reporting of dozens of different probability distributions, for every combination of particular climate modelers with particular glaciologists with particular polar meteorologists. Paté-Cornell suggested that it might have been better for Titus and Narayanan to simply specify composite probability distributions themselves, after duly considering the various reviewer opinions. Titus and Narayanan declined to follow that course, both because the entire objective was to use the experts' opinions, and because such a procedure would undermine the modeling efforts to preserve any functional relations between parameters.

One of the contributions of the Monte Carlo method used in the EPA study was the ways in which the possible correlations between different parameters were dealt with. Even when only one expert is providing probability distributions for different model parameters, care must be taken to avoid unreasonable combinations of parameter values (what might be called the "forbidden parameter space" problem). That is, although each expert scientist may believe that any one parameter has values that fit into a certain probability range, the same scientist might also believe that parts of that probability distribution are impossible or highly unlikely when other parameters take on certain values. In other words, certain combinations of the values of that parameter and the values of other parameters could be forbidden. Thus, a joint probability distribution needs to be constructed from subjective opinions of experts.

The EPA study did attempt to deal with this problem, both by specifying joint probability distributions and by preserving the consistent visions implied by the alternative specifications by various reviewers. In the first case, for example, Titus and Narayanan specifically asked the experts whether particular parameters were correlated. One scientist suggested that the Greenland temperature amplification factor is positively correlated with changes in the rate of deepwater formation (a 1-D ocean model parameter), because deepwater formation drives the Gulf Stream which warms Greenland, and another respondent suggested that there may be a correlation between the dynamic adjustment time of the circumpolar ocean to global warming, and both T2x and the rate of greenhouse gas buildups.

Although each expert scientist may believe that any one parameter has values that fit into a certain probability range, the same scientist might also believe that parts of that probability distribution are impossible or highly unlikely when other parameters take on certain values.

In the second case, Titus and Narayanan attempted to ensure that "internally consistent visions" of the different scientists were maintained, by requiring that each simulation sampled all the climate parameters from the probability distribution specified by one expert, all the glaciological parameters from one expert, etc. For example, although many of the reviewers did not specify a correlation between Greenland amplification and deepwater formation, a correlation across reviewers still existed because those that tended to expect the greatest decline in deepwater formation also projected the least polar amplification.

There was more variation in opinion regarding Greenland warming than global average temperature warming and other parameters. In general, the paleoclimatologists expected more Greenland warming than did the modelers. Regarding forecasts for sea level rise, the answers were similar to those of IPCC. The one exception is that the 1 percent probability on the high end is a few meters of sea level rise in the year 2100, which is higher than the IPCC estimate. This is driven by the possibility of a large warming combined with a surprising level of melting in Antarctica. A one meter rise by 2100 is estimated at about a 50 percent probability in the EPA study.

How important are probabilities? Why not just take our best estimates of each parameter and thus come up with our best answer to a given question? Titus says that probabilities don't really matter, if you have a low discount rate. Take, for example, the case of determining a present value of an interest in land that vests when the sea rises one meter. Using a full probability distribution rather than a median sea level rise estimate, one comes up with a higher monetary value for the land; there is a non-linear valuation function because interest compounding is non-linear.

There is also the question of why the government should have to pay (with tax dollars) for the rolling easements. Why not just tell developers not to develop the coastal zone? In some cases, this is unconstitutional, as explained in Titus (1997). Even if it is legal, it is politically infeasible. For our purposes here, the important point is that these rolling easements cost about 1 percent of the cost of the land whether or not the government or the landowner takes the loss. But whether the true figure is 0.1, 1 or 5 percent depends on probabilities and discount rates, and hence, probability distributions are necessary. A one meter rise would inundate some 18,130 square kilometers or 7,000 square miles of land in the U. S. alone. Titus says that the land use conventions we adopt today will determine whether 100 to 200 years hence our coastal zones look like the Netherlands or pretty much the same as they do today.

References

Keith, D., 1996, When Is It Appropriate to Combine Expert Judgments? An Editorial Essay, Climatic Change, 33(2):139-143.

Titus, J., 1997, Rising Seas, Coastal Erosion, and the Taking Clause, South Carolina Law Review, in press.

The land use conventions we adopt today will determine whether 100 to 200 years hence our coastal zones look like the Netherlands or pretty much the same as they do today.

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