Western Boundary Sea Level: A Theory, Rule of Thumb, and Application to Climate Models

Abstract

To better understand coastal sea level variability and changes, a theory that predicts sea levels along a curved western boundary using interior ocean sea level information is proposed. The western boundary sea level at a particular latitude is expressed by the sum of contributions from interior sea levels propagating onto the western boundary by long Rossby waves between that latitude and a higher latitude, and from the western boundary sea level at the higher latitude. This theory is examined by using a linear, reduced gravity model. A comparison between the theory and the model shows good agreement. A simple scaling law (or rule of thumb) derived from the theory provides a measure of the higher-latitude sea level and ocean interior sea level contributions. The theory is then tested using data from 34 climate models in phase 5 of the Coupled Model Intercomparison Project (CMIP5) for dynamic sea level changes between the end of the twentieth and twenty-first centuries. The theory captures the nearly uniform sea level rise from the Labrador Sea to New York City (NYC), with a reduction in the increase of sea level farther south toward the equator, qualitatively consistent with the CMIP5 multimodel ensemble, even though the theory underestimates the equatorward reduction rate. Along the South American east coast, the theory successfully reproduced the spatial pattern of the sea level change. The theory suggests a strong link between a sea level rise hot spot along the northeastern coast of North America and the sea level increase in the Labrador Sea, consistent with the result that rates of NYC sea level rise are highly correlated to those in the Labrador Sea in CMIP5 models.

The Relationship Between U.S. East Coast Sea Level and the Atlantic Meridional Overturning Circulation: A Review

“…Frederikse et al () find that, after being adjusted for local atmospheric (wind and pressure) effects and smoothed on decadal timescales, sea level changes from tide gauges north of Cape Hatteras over 1965–2014 are correlated with upper‐ocean steric height changes in the Labrador Sea and the deep midlatitude North Atlantic intergyre region. This is consistent with the strong relationship between U.S. coastal sea level and Labrador Sea level in the CMIP5 ensemble (Minobe et al, ).…”

“…When shelf bathymetry is included, coastal sea level is still determined by the combination of a poleward reference value, and a weighted integral of interior sea level between that poleward latitude and the latitude of interest. However, the coastal sea level anomaly can be smaller than that predicted in the Minobe et al () configuration: the western pressure signal can all be on the continental slope, with shallower currents causing it to be cancelled out at the coast. Wise et al () find that coastal DSL depends crucially on the strength of the bottom friction and the shelf bathymetry.…”

“…Little et al () specifically tested the ability of an initial condition ensemble of Community Earth System Model simulations to represent interannual U.S. East Coast DSL variability, finding that Community Earth System Model agrees well with observed tide gauge data along the Northeast U.S. coast, but poorly represents the time‐mean and variability of DSL south of Cape Hatteras. The Minobe et al () framework (section ) also exhibits disagreement with CMIP5 US east coast DSL changes south of ~35°N (see their Figure 10). This suggests that large‐scale models might be particularly limited in the South Atlantic Bight.…”

“…Perhaps more important than the spatial pattern in Figure b is the fact that only a small fraction of intermodel DSL variance is explained by differences in AMOC strength change (Figure c). In coastal regions, and in the subpolar gyre, factors unrelated to AMOC strength are principally responsible for the wide spread in 21st century projections of U.S. East Coast DSL rise (Yin et al, , ; Kopp et al, ; Little, Horton, Kopp, Oppenheimer, & Yip, ; Minobe, ).…”

“…Recently, Minobe et al () have addressed coastal DSL onshore of a western boundary current using a reduced gravity, vertical sidewall model. Such a framework bears similarity to that used in other studies of remotely forced coastal sea level variability in western boundary regions (e.g., Hong et al, ; Thompson & Mitchum, ).…”