Multi-model projections of twenty-first century North Pacific winter wave climate under the IPCC A2 scenario

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 H_S) 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 H_S 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.

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,

$$ {\text{C}}_{\text{YY}} {\text{e}} = \kappa {\text{e}} $$

(1)

$$ {\text{C}}_{\text{ZZ}} {\text{f}} = \lambda {\text{f}} $$

(2)

where C_YY (C_ZZ) 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,

$$ \alpha = {\text{Ye}} $$

(3)

$$ \beta = {\text{Zf}} $$

(4)

carry the variance of the respective EOF modes, so that

$$ \left\langle {\alpha_{\text{i}}^{2} } \right\rangle = \kappa_{\text{i}} $$

(5)

$$ \left\langle {\beta_{\text{j}}^{2} } \right\rangle = \lambda_{\text{j}} $$

(6)

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

$$ {\text{A}} = (\alpha^{\text{t}} \alpha )^{ - 1} (\alpha^{\text{t}} \beta ) $$

(7)

Then

$$ \beta^{*} = \alpha {\text{A}} $$

(8)

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,

$$ {\text{Z}}^{*} = \beta^{*} {\text{f}}^{\text{t}} $$

(9)

The fraction of total hindcast predictand variance accounted for by the regression is then

$$ {\text{R}}^{2} = {\text{Tr}}\left( {{\text{Z}}^{*} {\text{Z}}^{{*{\text{t}}}} } \right) {\text{Tr}}\left( {{\text{ZZ}}^{\text{t}} } \right)^{ - 1} $$

(10)

while

$$ {\text{RI}} = {\text{Tr}}\left( {\beta^{*} \beta^{{*{\text{t}}}} } \right){\text{Tr}}\left( {\beta \beta^{\text{t}} } \right)^{ - 1} $$

(11)

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 (Z^p), the predictor EOF loadings are projected onto the simulated (projected) twenty-first century SLP fields (Y^p) yielding “pseudo-PCs”

$$ {\text{A}}^{\text{p}} = {\text{Y}}^{\text{p}} {\text{e}}^{\text{t}} $$

(12)

for 2001–2099. Then, following from Eqs. 8 and 9,

$$ \beta^{\text{p}} = \alpha^{\text{p}} {\text{A}} $$

(13)

and

$$ {\text{Z}}^{\text{p}} = \beta^{\text{p}} {\text{f}}^{\text{t}} $$

(14)

give the regression-based estimates of future values of the predictand PCs (β^p), and finally of the predicatand (Z^p) by projection onto the predictand loadings (f). The training period means for Z can be then added back to Z^p if desired.

Appendix 2

Supplementary figures related to model CGCM wind speed adjustments and example of resulting changes in wave heights (Figs. 18, 19).

Fig. 18

Ratio of adjusted (reference level) to unadjusted (observation level) CGCM near-surface wind speeds as a function of unadjusted wind speed; CCSM solid black line, CNRM red dashed line, EH4 solid blue line with circles

Fig. 19

Example of wave height changes resulting from wind speed adjustments. Difference in mean November–March EH4 winter average H₉₉ for 1990–1992 (with less without wind speed adjustments) plotted as a function of H₉₉ without adjustment; all locations in the model domain are plotted. The downward adjustments in reference level wind speed (~6–7 % for wind speeds > 10 ms⁻¹; Fig. 18) yield approximately linear (14 %) decreases in H₉₉