Abstract
A dynamical wave model implemented over the North Pacific Ocean was forced with winds from three coupled global climate models (CGCMs) run under a medium-to-high scenario for greenhouse gas emissions through the twenty-first century. The results are analyzed with respect to changes in upper quantiles of significant wave height (90th and 99th percentile HS) during boreal winter. The three CGCMs produce surprisingly similar patterns of change in winter wave climate during the century, with waves becoming 10–15 % smaller over the lower mid-latitudes of the North Pacific, particularly in the central and western ocean. These decreases are closely associated with decreasing windspeeds along the southern flank of the main core of the westerlies. At higher latitudes, 99th percentile wave heights generally increase, though the patterns of change are less uniform than at lower latitudes. The increased wave heights at high latitudes appear to be due a variety of wind-related factors including both increased windspeeds and changes in the structure of the wind field, these varying from model to model. For one of the CGCMs, a commonly used statistical approach for estimating seasonal quantiles of HS on the basis of seasonal mean sea level pressure (SLP) is used to develop a regression model from 60 years of twentieth century data as a training set, and then applied using twenty-first century SLP data. The statistical model reproduces the general pattern of decreasing twenty-first century wave heights south of ~40 N, but underestimates the magnitude of the changes by ~50–70 %, reflecting relatively weak coupling between sea level pressure and wave heights in the CGCM data and loss of variability in the statistically projected wave heights.
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Acknowledgments
This work was conducted under funding from the California Energy Commission PIER Program through a University of California, California Institute for Energy and Environment (UC-CIEE) Award, No. POCV01-X12 to Scripps Institution of Oceanography (DC, PB, RF) and sub-award 500-09-038 to the Hydrologic Research Center (NG). The authors extend many thanks to Emelia Bainto and Mary Tyree for their valuable assistance with the wave model simulations, and with data acquisition and processing. Thanks as well to three anonymous reviewers whose suggestions helped improve the manuscript.
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Appendices
Appendix 1: PC regression and twenty-first century wave climate projections
Empirical orthogonal functions (EOFs) of the predictor (Y; mean November-March SLP over the North Pacific and surrounding region) and predictand (Z; modeled November–March North Pacific H90 or H99) are obtained from their respective variance-covariance matrices as shown below,
where CYY (CZZ) is the variance-covariance matrix, e(f) is an orthonormal matrix of eigenvectors (or “loadings”) and κ(λ) is a diagonal matrix of eigenvalues for the predictor (predictand) variable. Note that in the notation here Y and Z represent anomalies from their respective means over the training period. The predictor and predictor data for the CCSM analyses are for 1941–2000 (notation referring to the ending year of the winter season). Data up to December 1999 come from the CCSM 20C3M simulations (CGCM for SLP, wave model simulations for wave heights) and for January–March come from the CCSM A2 simulations. An analogous exercise, designed to help evaluate the statistical model regression results derived from CCSM, was conducted using NCEP-RA winds and the wave measures obtained from a historical run of WW3 driven by NCEP-RA winds for the 1948–1999 period.
The EOF PCs, α and β, obtained by projecting the (orthonormal) loadings onto the original data,
carry the variance of the respective EOF modes, so that
where the angle brackets indicate an expectation, κ and λ are eigenvalues and subscripts indicate the EOF mode number.
From this point, linear least-squares regression weights (A) are obtained via
Then
gives hindcast estimates (indicated by the asterisk) of the predictand PCs for the training period, and projection onto the predictand loadings converts these back into full fields in their original units,
The fraction of total hindcast predictand variance accounted for by the regression is then
while
is a “redundancy index” (e.g., WS2001, WS2004), and gives the fraction of EOF-truncated variance retained by the regression.
To make projections (indicated by the super-script “p”) of future wave conditions (Zp), the predictor EOF loadings are projected onto the simulated (projected) twenty-first century SLP fields (Yp) yielding “pseudo-PCs”
for 2001–2099. Then, following from Eqs. 8 and 9,
and
give the regression-based estimates of future values of the predictand PCs (βp), and finally of the predicatand (Zp) by projection onto the predictand loadings (f). The training period means for Z can be then added back to Zp if desired.
Appendix 2
Supplementary figures related to model CGCM wind speed adjustments and example of resulting changes in wave heights (Figs. 18, 19).
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Graham, N.E., Cayan, D.R., Bromirski, P.D. et al. Multi-model projections of twenty-first century North Pacific winter wave climate under the IPCC A2 scenario. Clim Dyn 40, 1335–1360 (2013). https://doi.org/10.1007/s00382-012-1435-8
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DOI: https://doi.org/10.1007/s00382-012-1435-8