Understanding Relative Sea Level Rise

Relative sea level rise refers to the change in the average sea level experienced at a specific location on the coast. It is determined by the combination of global mean sea level changes and local vertical land motion (uplift or subsidence).

Analyzing Scenarios for Relative Sea Level Change

Relative sea level rise occurs when the sea surface elevation increases compared to the land surface elevation. Let's examine the given scenarios:

• Scenario 1: Sea level rises while the land surface subsides at a slower rate.

  In this case, both factors contribute to relative sea level rise. Mathematically, if $SL_{rise}$ is the rate of sea level rise and $L_{subsidence}$ is the rate of land subsidence, and $SL_{rise} > L_{subsidence}$, the relative sea level change is positive ($SL_{rise} - L_{subsidence} > 0$).

• Scenario 2: Sea level remains stationary while the land surface subsides.

  Land subsidence directly causes the sea level to appear higher relative to the land. Mathematically, if the sea level change is 0 and $L_{subsidence} > 0$, the relative sea level change is positive ($0 + L_{subsidence} > 0$).

• Scenario 3: Sea level rises while the land surface rises at a faster rate.

  Here, the land is gaining elevation relative to the sea. Let $SL_{rise}$ be the rate of sea level rise and $L_{uplift}$ be the rate of land uplift. If $L_{uplift} > SL_{rise}$, the relative sea level change is negative ($SL_{rise} - L_{uplift} < 0$). This results in a relative sea level fall, not rise.

• Scenario 4: Sea level falls while the land surface subsides at a faster rate.

  The land is sinking faster than the sea level is dropping, leading to an overall rise relative to the land. Mathematically, if $SL_{fall}$ is the rate of sea level fall (a negative value, e.g., $-SL_{fall\_rate}$) and $L_{subsidence}$ is the rate of land subsidence, and $L_{subsidence} > SL_{fall\_rate}$, the relative sea level change is positive ($-SL_{fall\_rate} + L_{subsidence} > 0$).

Conclusion

Based on the analysis, the scenario where the sea level rises while the land surface rises at a faster rate is the only one that does not result in a relative sea level rise. Instead, it causes a relative sea level fall.