Elucidating large-scale atmospheric controls on Bering Strait throughﬂow variability using a data-constrained ocean model and its adjoint

A regional data-constrained coupled ocean-sea ice general circulation model and its adjoint are used to investigate mechanisms controlling the volume transport variability through Bering Strait during 2002 to 2013. Comprehensive time-resolved sensitivity maps of Bering Strait transport to atmospheric forcing can be accurately computed with the adjoint along the forward model trajectory to identify spatial and temporal scales most relevant to the strait’s transport variability. The simulated Bering Strait transport anomaly is found to be controlled primarily by the wind stress on short time-scales of order 1 month. Spatial decomposition indicates that on monthly time-scales winds over the Bering and the combined Chukchi and East Siberian Seas are the most signiﬁcant drivers. Continental shelf waves and coastally-trapped waves are suggested as the dominant mechanisms for propagating information from the far ﬁeld to the strait. In years with transport extrema, eastward wind stress anomalies in the Arctic sector are found to be the dominant control, with correlation coeﬃcient of 0.94. This implies that atmospheric variability over the Arctic plays a substantial role in determining Bering Strait ﬂow variability. The near-linear response of the transport anomaly to wind stress allows for predictive skill at interannual time-scales, thus potentially enabling skillful prediction of changes at this important Paciﬁc-Arctic gateway, provided that accurate measurements of surface winds in the Arctic can be obtained. The novelty of this work is the use of space and time-resolved adjoint-based sensitivity maps, which enable detailed dynamical, i.e. causal attribution of the impacts of diﬀerent forcings.

Strait volume transport at a time t, J(t) over a period T starting from any given time 275 t − T /2 is defined as: where δJ(t) is the reconstructed transport anomaly, with the symbol added to distin-  Monthly average adjoint sensitivities were computed for all seven atmospheric con-341 trol variables at different monthly-averaged lag times. The largest influence found was 342 related to surface wind stress. Sensitivities with respect to meridional (N) and zonal (E) 343 wind stress ∂J ∂τ N and ∂J ∂τ E are highest at 1-month lag, and both wind stress components 344 contribute significantly to δJ(t) (Fig. 2).

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The largest sensitivities are found in the strait itself, with ∂J ∂τ N being approximately 346 (in magnitude) two times larger than ∂J ∂τ E . This is consistent with previous observation-     that the effect of winds has a short time history (Fig. 3f). Finally, adding the contribu-433 tion from precipitation to δJ (not shown) did not change the correlation significantly. δJ(t) can alternatively be decomposed into its monthly (sub-seasonally), seasonally (12-438 month climatology), and multi-year components (Fig. 4). We calculate this discretely, 439 rather than as a spectral decomposition as our time series is comparatively short. For ity assumption holds and that beyond 36-months this assumption begins to break down.

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There is a very small difference of 1-2% between using only wind stress and using increase, later maximum, later decrease. As in the previous section, we speculate that 486 this degradation is due to non-linear effects of longwave and shortwave absorption in the 487 ocean, such that beyond ∼5 months the linearity assumption for buoyancy flux sensi-488 tivities breaks down. What remains robust is that the sensitivity patterns from the first 489 two months (Fig. 2) capture > 98% of the correlation and ∼ 97% of PEV. Even after 490 a 48 month lag, despite the degradation the PEV is still ≤90%. Overall, the reconstruc-491 tion using only winds yields the highest correlation and PEV.

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The remaining Bering Strait transport residual at sub-seasonal (monthly) time-scale, 493 δJ res , is still well reconstructed (88% of PEV) by the local wind within four months prior, 494 with minimal improvement (∼ 1%) after the first month lag (Fig. 4f). transport anomaly at monthly to multi-year time-scales (Fig 4b,d,f). The degradation 498 in correlation between δJ and δJ f wd (Fig. 3b) is largely due to degradation in the re-499 constructed seasonal cycle (Fig 4d). Despite the degradation, the correlation remains high, 500 with ∼90% of the variance captured at the seasonal time-scale. As the difference in the 501 reconstruction using all forcings and using only wind stresses is small, for the remain-502 der of the analyses we will focus on reconstructions using only wind stress. The convolution restricted to these individual regions (Fig 5b) can be compared 515 with a global convolution (blue curve in Fig. 3    downstream of the strait in the Kelvin wave-propagation sense. The rest of the ocean 537 interior, labeled "rest", generally has a smaller contribution than any of the seven iden-538 tified regions. A hypothesis for the mechanisms that determine these regions will be pre-539 sented in Section 4.

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In the reconstruction of the seasonal cycle (Fig. 6b), while the Bering Sea and the

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In the reconstruction of the interannual time-series (Fig. 6c), the Bering Sea and  The relationship between the extreme years and the regional contribution give in-  Fig. 6 into Pacific and Arctic/Atlantic components. Seasonally (Fig. 7b), 565 the results support the conclusion of Peralta-Ferriz and Woodgate (2017), that the sum-566 mer transport variability is more strongly related to perturbations over the Arctic, al-  Interannually (Fig. 7c), both Pacific and Arctic/Atlantic forcings provide significant con-      The majority of work in this paper has focused on the impacts of wind stress anoma-652 lies on the flow variations through the strait, as that was found to be the greatest driver 653 in the adjoint experiments performed. The method, however, allows us to examine the 654 impact of other forcings as well -e.g., precipitation which is also hypothesized to be a 655 driver of the Bering Strait throughflow variability (Stigebrandt, 1984).  1. Dependence of reconstruction of δJ on the time when J is defined The monthly mean transport J(t i ) for each month t i has large variability with negative values (southward flow) during some months and maximum positive values during other months (Fig. S1a). An important question is whether and how the gradients ∂J ∂Ω k vary when J varies. Intuitively we expect that if there is a dominant linear mechanism controlling the transport, the gradient ∂J ∂Ω k retains the same sign and similar magnitude, independent of the period over which J is defined. For example, if northward wind stress is the dominant controlling mechanism such that ∂J ∂τ N = X, a smaller J is then a result of weaker τ N and a negative J is a result of a reversal of the wind stress (negative τ N ). Thus, J can vary widely and is a result of the variation in τ N , while the physical connection, as captured by ∂J ∂τ N = X, remains the same.
Following this line of argument, we hypothesize that if instead ∂J ∂Ω k is dependent on the time when J is defined (e.g., phase of the seasonal cycle), it is due to J being a highly non- . These constructions as well as the forward anomaly time-series δJ f wd are shown in Fig. S1. Linear fit of scatter plot of these various δJ show that they are different by up to only 3%, depending on the number of lags used in the reconstruction (Fig. S1b,c).
Thus, given that any of the reconstructed δJ [07,09,12] can capture the variability in the forward model δJ f wd (Fig. S1a), that the difference between the these reconstructions is small, and that subsequent analyses show no significant differences in the behavior of how the reconstructions differ from the forward model time-series (Fig. S2), as discussed in the main text, we chose J 09 for all gradients calculations and analyses in this study.
(3) can be used to reconstruct the full anomaly time series, δJ, which can then be decomposed into temporal components associated with interannual, seasonal, and monthly time-scales, as discussed in Section 3. Here we show that by rewriting eqn.
(3), the reconstruction can be approximated as eqn. (4), which allows for more direct connection between the time-scales of the forcing anomalies and the time-scales of the Bering Strait transport anomalies. Our example here is for the reconstruction of the annual mean time series, but the same logic applies to other time-scales.
We first define the annual mean forcing δΩ y for a year t a within the time range [t a , t a +T y ] as, where T y is a time period of 1 year. Based on eqn.
(3), the full reconstruction for the annual δJ y for the same year t a at a specific geographic location [x 1 , x 2 ] for a forcing component k would be as follows, where for clarity we will omit the geographic integrals and location [x 1 , x 2 ] as well as the forcing index k from the equations, but the reader should understand these integrals are still required. Note also that the sensitivity corresponding to the first month ∂J ∂Ω(0) , i.e., where (α − t = 0 mo), also termed the "zero-lag", is the average of sensitivities accumulated between 0-1 month). (3), into annual, seasonal and monthly components, which we refer to as the "exact" method, or using eqn. (4), which we refer to as the "approx" method. Results are summarized in Fig. S3. In general, regardless of the method use, the reconstructed time-series δJ approx and δJ exact capture between 80-97% of the forward signal δJ f wd . Up to 12-month lag, results of the temporal decomposition from the two methods are very similar. Beyond 12-month lags, some difference can be seen with the "exact" method capturing slightly less of the explained variance at seasonal and monthly time-scales (Fig. S3f,i).