Detection of external influence on trends of atmospheric storminess and northern oceans wave heights

Abstract

The atmospheric storminess as inferred from geostrophic wind energy and ocean wave heights have increased in boreal winter over the past half century in the high-latitudes of the northern hemisphere (especially the northeast North Atlantic), and have decreased in more southerly northern latitudes. This study shows that these trend patterns contain a detectable response to anthropogenic and natural forcing combined. The effect of external influence is found to be strongest in the winter hemisphere, that is, in the northern hemisphere in January–March and in the southern hemisphere in July–September. However, the simulated response to anthropogenic and natural forcing combined, which was obtained directly from climate models in the case of geostrophic wind energy and indirectly via an empirical downscaling procedure in the case of ocean wave heights, is significantly weaker than the magnitude of the observed changes in these parameters.

Appendices

Appendix A Calculation of the atmospheric storminess index G _t

The atmospheric storminess index G _t is calculated as follows. First, the squared SLP gradient at gridpoint (i, j) is computed as

$$ G^0_t(i,\; j) = {\frac{\left[{\frac{P^0_t(i,\; j) -P^0_t(i-1,\; j)} {\rm cos(\phi_j)}}\right]^2+\left[{\frac{P^0_t(i+1,\; j)-P^0_t(i,\; j)} {\rm cos(\phi_j)}}\right]^2}{2}}+ {\frac{\left[P^0_t(i,\; j) -P^0_t(i,\; j-1)\right]^2+ \left[P^0_t(i,\; j+1)-P^0_t(i,\; j)\right]^2} {2}} $$

(4)

where P ⁰ _t (i, j) denotes the seasonal mean SLP for gridpoint (i, j) in year t, ϕ _j is the latitude of the gridpoint (i, j) and where it is assumed that the grid spacing, in degrees, is equal in both latitude and longitude. Then, the 1961–1990 mean field, $\bar{G}^0(i,\; j),$ is subsequently calculated for each season and subtracted to obtain anomalies of squared seasonal mean SLP gradients:

$$ G_t(i,\; j) = G^0_t(i,\; j) - \bar{G}^0(i,\; j). $$

(5)

The use of the cos(ϕ _j ) weighting above accounts for the dependence of the spherical distance between two neighboring gridpoints on the latitude at which both gridpoints are located (for gridpoints on the equator: ϕ _j  = 0 and cos(ϕ _j ) = 1). This computation is performed for each of the 5° × 5° grid boxes analyzed, and for each season and year. The unit for the resulting squared SLP gradient is (hPa)² per 5° spherical distance.

Appendix B Estimation of internal climate variability

The optimal detection analysis requires knowledge of the internal climate variability. It involves two estimates of the internal variability in this study: $\hat{C}_{\eta_1}$ and $\hat{C}_{\eta_2}.$ Both $\hat{C}_{\eta_1}$ and $\hat{C}_{\eta_2}$ are climate model based estimates of internal climate variability; both are obtained by pooling the variability of the control simulations together with the inter-integration variability of the twentieth-century simulations (after removing the ensemble mean field from each integration in each of the nine ensembles; see Table 1). However, they are based on two non-overlapping periods of the twentieth-century simulations and two non-overlapping ensembles of control simulations.

More specifically, when analyzing the 1955–2004 (or 1958–2001) trends, $\hat{C}_{\eta_1}$ is based on the 41 twentieth-century simulations for the period 1955–2004 (or 1958–2001), while $\hat{C}_{\eta_2}$ is based on the 41 twentieth-century simulations for the period 1900–1949 (or 1900–1943). Accordingly, when analyzing the 1900–1949 trends (see Section 5), $\hat{C}_{\eta_1}$ is based on the 41 twentieth-century simulations for the period 1900–49, while $\hat{C}_{\eta_2}$ is based on the 41 twentieth-century simulations for the period 1955–2004. In the mean time, each of the available control simulations (Table 2) is also divided into non-overlapping 50 or 44-year simulation segments, depending upon whether the detection analysis was of a 50-year period (1955–2004 or 1900–1949) or a 44-year period (1958–2001). For example, the ECHO-G 340-year control simulation can be divided into six non-overlapping 50-year simulation segments, corresponding to years 1–50, 51–100,..., and 251–300, respectively (or seven non-overlapping 44-year segments corresponding to 1–44, 45–88,..., and 265–308; see Table 2). As a result, a total of 86 50-year control simulation segments (or 96 44-year segments) were obtained (Table 2). Half of these control simulation segments are used to obtain $\hat{C}_{\eta_1},$ and the other half, $\hat{C}_{\eta_2}.$ Thus, combining these with information derived from the 41 twentieth-century simulations, we use a total of 84 (= 86/2 + 41) 50-year simulation segments for the detection analysis on the 1955–2004 or 1900–1949 trend pattern. The degree of freedom here is 74 (= 84−9−1), since nine twentieth-century ensemble-mean trend fields and one control ensemble-mean field (here we pool all control simulation segments used into a single large ensemble because some models have short control simulations) were subtracted from the estimated trend patterns before they are used in the detection analysis. Similarly, for the detection analysis on the 1958–2001 trend pattern, a total of 96 non-overlapping 44-year control simulation segments are used (see Table 2); thus the degree of freedom is 79 (= 96/2 + 41−1−9).