Wave climate on the southwestern coast of Lake Michigan: Perspectives from wave directionality

TL;DR

The paper tackles how to quantify and interpret directional wave climate along the southwestern Lake Michigan coast. It introduces Directional Wave Entropy (DWE) and applies it to 1979–2023 hindcast data from 26 WIS stations, focusing on four representative sites to dissect inter- and intra-annual patterns and directional extreme waves. The results reveal a persistent bi-directional climate with northern and southern components, stronger northern extremes, and clear seasonal modulation, with spatial variability linked to shoreline geometry and fetch. These findings have practical implications for coastal design, morphology management, and shoreline planning in freshwater lake systems, while also delineating the limitations of the DWE approach and opportunities for extension to wind directionality and more complex coastal configurations.

Abstract

Wave directionality plays a critical role in shaping coastal conditions and influencing local livelihoods, underscoring the importance of conducting detailed analyses. This study examines directional wave climate along the southwestern coast of Lake Michigan from 1979 to 2023 using the Directional Wave Entropy (DWE). Directionality was characterized in terms of inter-annual trends, monthly patterns, spatial variation, and extreme wave conditions. Overall, results exhibited a strong bi-directionality, with dominant northern and southern wave systems along the coast of our study site. A few annual trends for the inter-annual wave climate were observed, and there is a clear seasonal variation such that bi-directionality increases in the summer and winter seasons. As for spatial variation of wave directionality, all locations in the study sites presented a bi-directional wave climate. The two dominant directions of wave directionality: northern and southern mean significant wave heights were also characterized in all locations of study sites as 0.566 and 0.563 meters. Furthermore, the extreme wave heights in the northern direction are significantly greater than the extreme waves in the southern direction. In summary, these findings suggest the importance of wave directionality on coastal structural design and coastal morphology management along the coast of our study site.

Figures (12)

• Figure 1: Study Sites. (a) the location of Lake Michigan in the United States. (b) Lake Michigan bathymetry and WIS stations. The 490 WIS stations are marked as dark dots, and the white diamond marks the deepest point of Lake Michigan. (c) study sites in Wisconsin area. Four major cities (PW-Port Washington, MIL-Milwaukee Harbor, WP-Wind Point, and KEN-Kenosha Harbor) are marked with dark triangles. The four stations for four cities are marked with colored stars, aligned with their corresponding station IDs. The interval of the bathymetry contour is 10 meters under IGLD1984.
• Figure 2: Characterization of two typical wave directionalities: uni- and bi-directionality. (a) and (b) are schematics of height-direction distribution and wave rose for bi-directionality, respectively. (c) and (d) are schematics of height-direction and wave rose for uni-directionality, respectively. The shoreline orientation is marked as a black dash line, while the characterizations of northern wave and southern waves are marked with red frames, respectively. The green arrows $P_1$ and $P_2$ represent the averaged waves for the northern and southern components. $\theta$ is the angle between these two averaged wave components.
• Figure 3: Wave rose maps and DWE at four selected locations. (a) PW-Port Washington, (b) MIL-Milwaukee Harbor, (c) WP-Wind Point, and (d) KEN-Kenosha Harbor with their corresponding directional wave entropy. The black dashed lines represent the shoreline orientation and red frames indicate the selected directional bins.
• Figure 4: Directional-time wave height spectrum from 1979 to 2021 at the following locations : (a) PW-Port Washington, (b) MIL-Milwaukee Harbor, (c) WP-Wind Point, and (d) KEN-Kenosha Harbor.
• Figure 5: Inter-annual patterns of wave directionality. (a) – (d) are the inter-annual wave height difference between for northern wave and total wave at four major cities (PW-Port Washington, MH-Milwaukee Harbor, WP-Wind Point, KH-Kenosha Harbor), respectively, (e) – (h) are the inter-annual wave height differences between southern waves and total waves at four major cities, respectively, and (i) to (l) are the inter-annual directional wave entropy at four major cities, respectively.