"The most damaging thing about climate change is that it is change," Caldeira told environmentalresearchweb. "Change is costly. Fast change costs more than slow change. However, most adaptation research has focused on various amounts of warming, or various amounts of sea-level rise, and not on rates of change. My feeling was that we need to be focusing more on rates of change and rates of adaptation, and the rates at which we need to be building new energy systems to avoid very high rates of climate change."

So Caldeira teamed up with colleagues Soheil Shayegh, also at the Carnegie Institution for Science, and Juan Moreno-Cruz of the Georgia Institute of Technology, US, to model adaptation to the rate of sea-level rise rather than a fixed amount. "Sea-level rise – unlike temperature rise – provides a very direct link between natural systems and human systems," said Shayegh. "This helped us compare different adaptation strategies and show which one is more effective."

The resulting model takes into account the rate of sea-level rise, the slope of the land away from the sea, depreciation of the infrastructure being built near the coastline, and the discount rate. Buildings built on the coast tend to generate more revenue but are at greater risk of sea-level rise.

"The optimal investment strategy avoids constructing too near the coast where assets would be shortly lost to sea-level rise, but also avoids constructing too far inland where near-term returns on investment would be expected to be small," writes the team in Environmental Research Letters (ERL). "There is a balance between the loss of the value of an asset through inundation and the loss of value of an asset through depreciation and temporal discounting."

For a sea level rising at 1 cm per year on land with a rise of 1 m per 1 km travelled inland and an economic discount rate of 5%, the optimum location to put up new buildings whose value declines exponentially away from the coast on a length scale of 1 km is 310 m from the coast, according to the model. If the buildings were put up half as far from the shoreline the expected net present value (NPV) of return on this investment would be 14% lower, whilst if they were constructed twice this distance away, the return would be 17% less than the optimum.

"Soheil has shown that the key factors affecting infrastructure in the face of ongoing change are: the rates of change in the physical system, the durability of the built infrastructure, and how much we value near-term profit versus long-term costs," said Caldeira. "The first of these we can affect only by transforming our energy system. The second is a choice: we can decide to build boardwalks near the rising seas, but build marble buildings only further inland. The last of these is a matter of values, both for the individual investor and society as a whole."

For this same scenario, an adaptation model that considered only a fixed amount, say 0.5 m, of sea-level rise might create a buffer zone extending 500 m from the shore. Constructing new assets outside this buffer zone would give a net present value 8% less than the optimal investment at 310 m, once you take the future loss of land due to ongoing sea-level rise into account.

"Soheil [Shayegh] is an expert in mathematical optimization in the context of climate change problems so was able to bring mathematical definition and analytical tools to a problem that I had formulated only informally and verbally," added Caldeira. "The exposition in terms of mathematical optimization is great because, while simplified, it very clearly sets out a series of assumptions and follows those assumptions to their logical conclusion. If you accept the basic assumptions of the analysis, the results follow like a mathematical theorem and are not subject to dispute."

According to Shayegh, the researchers hope their paper will bring new insight into the discussion about adaptation strategies. "We used a very stylized model to highlight the key results," he said. "In reality the adaption problems are more sophisticated, but we believe that our results show the important factors that should be considered when designing a successful adaptation strategy."

Caldeira is keen that others pursue the question of adaptation to rates of change in more depth. "In my group at Carnegie Institution for Science, we do broad-brush research in the hopes that other groups will take up the problems and pursue them in greater detail," he said. "We try to break new ground in the hopes that others will find it a fertile field." Shayegh reckons that a natural extension of the work would be finding the optimal adaptation strategy when rates of change are uncertain.

One thing the researchers didn’t consider is political power. "In the real world, powerful people can marshal societal resources to protect their private interests," Caldeira said. "So wealthy people who own vacation homes on the shore can get society as a whole to subsidize their flood insurance. This kind of thing sets perverse incentives. Future study should take into consideration these sorts of human factors when assessing how we might best respond to ongoing climate change."

The team reported their results in Environmental Research Letters (ERL).

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