In part, the article states:
Only one thing seems clear so far: without a physical territory, all the Tuvaluans become stateless. There is no general right to a back-up nation or to citizenship of a neighboring country. Those who are already emigrating are not considered refugees...
For a long time legal academics had categorically rejected the notion that a country like Tuvalu could claim damages for its devastated environment -- after all it would be impossible to name the guilty party.
But in the meantime a growing number of lawyers have come to consider such claims legitimate. For example, the State of California's case against major automakers is an indication of the future of climate change in jurisprudence -- even though that case only deals with national, as opposed to international, law.
Some experts now believe changes will have to be made to international law to deal with the impact of climate change.
This is a highly complicated issue. I believe separate international law instruments will need to be adopted to address global issues such as climate change. In spite of the situation, the complexity of the issue will probably mean that this process could be relatively time-consuming both in terms of negotiations and the period of time required until the instrument is ratified.
Such a body of law, almost certainly, won't lead to high penalties against other states, particularly for ex-post-facto situations and matters for which there are few technological alternatives. Otherwise, states simply won't go along with such an approach. No nation is likely to be willing to fundamentally weaken the concept of state sovereignty. Moreover, a precedent that would radically diminish state sovereignty might cause more harm than good if it opens the door for additional serious erosions of state sovereignty.
Nevertheless, I do believe one will see limited protections e.g., an expedited immigration process for "climate change refugees," creation of a global fund for assisting such people/investing in climate change research (e.g., non-fossil fuel-based energy sources, though OPEC states could resist this) and agreed mechanisms for trying to mitigate the consequences of climate change.