Development of adjoint-based ocean state estimation for the Amundsen and Bellingshausen Seas and ice shelf cavities using MITgcm/ECCO

The Antarctic coastal ocean is impacting sea level rise, deep-ocean circulation, marine ecosystems, and global carbon cycle. To better describe and understand these processes and their variability, it is necessary to combine the sparse available observations with best-possible numerical descriptions of ocean circulation. In particular, high ice-shelf melting rates in the Amundsen Sea have attracted many observational campaigns and we now have some limited oceanographic data that capture seasonal and interannual variability during the past decade. One method to combine observations with numerical models that can maximize the information extracted from the sparse observations is the adjoint method, as developed and implemented for global ocean state estimation by the Estimating the Circulation and Climate of the Ocean (ECCO) project. Here, for the first time, we apply the adjoint-model estimation method to a regional configuration of the Amundsen and Bellingshausen Seas, Antarctica, including explicit representation of sub-ice shelf cavities. We utilize observations available during 2010–2014, including ship-based and seal-tagged CTD measurements, moorings, and satellite sea-ice concentration estimates. After 20 iterations of the adjoint-method minimization algorithm, the cost function, here defined as a sum of weighted model-data difference, is reduced by 65 % relative to the baseline simulation by adjusting initial conditions, atmospheric forcing, and vertical diffusivity. The sea-ice and ocean components of the cost function are reduced by 59 % and 70 %, respectively. Major improvements include better representations of (1) Winter Water (WW) characteristics and (2) intrusions of modified Circumpolar Deep Water (mCDW) towards the Pine Island Glacier. Sensitivity experiments show that ~40 % and ~10 % of improvements in sea ice and ocean state, respectively, can be attributed to the adjustment of air temperature and wind. This study is a preliminary demonstration of adjoint-method optimization with explicit representation of ice-shelf cavity circulation. Despite the 65 % cost reduction, substantial model-data discrepancies remain, in particular with annual and interannual variability observed by moorings in front of the Pine Island Ice Shelf. We list a series of possible causes for these residuals, including limitations of the model, the optimization methodology, and observational sampling. In particular, we hypothesize that that residuals could be further reduced if the model could more accurately represent sea ice concentration and coastal polynyas.

A reduced-order Kalman smoother for (paleo-)ocean state estimation: assessment and application to the LGM

Combining ocean models and proxy data via data assimilation is a powerful means to obtain more reliable estimates of past ocean states, but studies using data assimilation for paleo-ocean state estimation are rare. A few studies used the adjoint method, also called 4D-Var, to estimate the state of the ocean during the Last Glacial Maximum (LGM). The adjoint method, however, requires the adjoint of the model code, which is not easily obtained for most models. The method is computationally very demanding and does not readily provide uncertainty estimates. Here, we present a new and computationally very efficient technique to obtain ocean state estimates. We applied a state reduction approach in conjunction with a finite difference sensitivity-iterative Kalman smoother (FDS-IKS) to estimate spatially varying atmospheric forcing fields and to obtain an equilibrium model simulation in consistency with proxy data. We tested the method in synthetic pseudo-proxy data experiments. The method is capable of very efficiently estimating 16 control variables and reconstructing a target ocean circulation from sea surface temperature (SST) and oxygen isotopic composition of seawater data at LGM coverage. The method is advantageous over the adjoint method regarding that it is very easy to implement, it requires substantially less computing time and provides an uncertainty estimate of the estimated control variables. The computing time, however, depends linearly on the size of the control space limiting the number of control variables that can be estimated. We used the method to investigate the constraint of data outside of the Atlantic Ocean on the Atlantic overturning circulation. Our results indicate that while data from the Pacific or Indian Ocean aid in correctly estimating the Atlantic overturning circulation, they are not as crucial as the Atlantic data. We additionally applied the method to estimate the LGM ocean state constrained by a global SST reconstruction and data on the oxygen isotopic composition of calcite from fossil benthic and planktic foraminifera. The LGM estimate shows a large improvement compared to our first guess, but model-data misfits remain after the optimization due to model errors that cannot be corrected by the control variables. The estimate shows a shallower North Atlantic Deep Water and a weaker Atlantic overturning circulation compared to today in consistency with previous studies. The combination of the FDS-IKS and the state reduction approach is a step forward in making ocean state estimation and data assimilation applicable for complex and computationally expensive models and to models where the adjoint is not available.

Controllability, not chaos, key criterion for ocean state estimation

The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or 4D-VAR) has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – a solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.