Patrick Heimbach's Group

The overarching theme of our research rests on the recognition that many elements of the present climate remain poorly sampled by observations, preventing a quantitative mechanistic understanding of climate variability and change over the past decades. Yet, such understanding is an essential prerequisite for attempting predictions with quantified uncertainties. Of particular interest are climate processes in polar regions. Rigorous mathematical methods and computational tools play a central role in that they are enabling advances in climate science that are not otherwise possible.


Within the “Estimating the Circulation and Climate of the Ocean” (ECCO) project we are concerned, through application of optimal estimation & control methods, with synthesizing most of the available oceanographic observations of diverse types into a coherent framework of a state-of-the-art ocean general circulation MITgcm, to produce a best-possible estimate of the time-evolving global ocean circulation. In contrast to many data assimilation systems, ECCO is quasi-unique in putting a premium on exact dynamical and kinematical consistency over climate-relevant periods (here decades) to enable closed global budget analyses. Primary applications are the study of meridional mass and associated heat transport variability in the Atlantic, and the three- dimensional partitioning of sea-level change contributions.



In collaboration with colleagues at JPL, we are developing a next-generation estimation system which incorporates more Earth system components to represent as many as possible physical constraints, in particular the development of a coupled ocean/sea-ice/land-ice system. A regional effort targeting the Arctic and Atlantic subpolar gyre is designed to address the question of what drives inter-annual sea ice variability and its decline in recent decades. The prospect of a seasonally ice-free Arctic is prompting various government agencies to study its societal and economic impacts. Basic understanding of the physical drivers remain insufficient, both because of a lack of observations and insufficient representation of important processes in models.



The potential role of ocean circulation in promoting dynamic changes of the Greenland and Antarctic ice sheets, with serious societal implications of sea level change, is a fascinating subject. It brings together relevant processes acting over a vast range of scales. On the fluid side, they comprise (i) boundary-layer dynamics at the ice-ocean interface, (ii) localized circulation in Antarctica’s sub-ice shelf cavities or Greenland’s outlet glacier fjords, (iii) exchange processes between the fjords/cavities, the continental shelf and the ocean interior, (iv) large-scale coupled atmosphere-ocean circulation which is responsible for the variability of heat delivery to the ice sheet’s margins, and (v) global mass redistributions through changes in the gravity field and lithosphere.

We are contributing to the US CLIVAR working group on Greenland Ice Sheet-Ocean Interactions (GRISO) to establish what are the most urgent observational, theoretical, and modeling requirements to fill the gaps in our understanding. Since observations around Greenland are very challenging to obtain, and novel observational technologies remain elusive, we work closely with colleagues at WHOI to complement observations by modeling work of some of the processes described. In collaboration with colleagues at AWI (Germany), BAS (UK) and JPL (USA), we have also begun a rigorous study to invert melt rates under Pine Island Glacier and Ice Shelf (which is exhibiting the largest changes in West Antarctica) from available hydrographic and remote sensing measurements.



Is there a basis for decadal predictability in the climate system? If so, what processes may be responsible? If not, what sets inherent limits for predictability? Which observations may extend the predictability horizon?

Answers to these questions are crucial for successful prediction. Despite attempts to develop decadal prediction systems of the climate over the North Atlantic, evidence in support for predictive skill on those time scales remains elusive. A powerful framework for studying linear predictability is that of transient amplification in dynamical systems which exhibit non-normal behavior (most fluids). It enables calculation of singular vectors which point to patterns of maximum growth of a chosennorm, or, equivalently, to patterns of maximum uncertainty growth. This approach is successfully being applied in numerical weather prediction, but remains little used in climate research, in part because of the computational hurdles (solving generalized eigenvalue problems of combined tangent linear and adjoint forms of general circulation models). Rigorous application in the context of full-fledged GCM’s for which derivative code is available enables the study of predictability limits due to intrinsic oceanic variability, and can be used for targeted observations to extend the predictability horizon. For this work we collaborate with Laure Zanna (now at Oxford) and Eli Tziperman (Harvard).



Closely related to state and parameter estimation, uncertainty quantification and predictability is the theme of optimal observing system design in the context of climate science. Among the vexing problems are the fact that the ocean remains seriously under-sampled even with the present observing system, with near-absence of abyssal observations, and the long time scales inherent in the climate problem which requires sustaining observing systems over many decades to be really useful to future researchers. State estimation systems offer ways of quantifying the impact of observing systems on relevant climate metrics. We are promoting efforts to explore these systems within the U.S. AMOC science team and the Global Ocean Observing System (GOOS) study group on a Deep Ocean Observing System for climate monitoring.



For a potential international greenhouse gas (GHG) emissions treaty to be credible, independent “top-down” monitoring capabilities seem indispensable to verify estimates obtained from “bottom- up” reporting approaches. Conceptually not unlike the ocean state estimation problem, the backbone of such a system would comprise a coupled model of atmospheric and oceanic tracer transport, to- gether with a coupled biogeochemical and hydrology model of the atmosphere, land, and ocean. The need for a coupled approach comes from the large “background” natural variability, e.g., from air-sea carbon fluxes. Forced by best-estimate dynamical states of the atmosphere and ocean, the model is fed with emissions (e.g., from “bottom-up” approaches) to provide an initial guess of GHG distribution. Optimal estimation of (or inversion for) GHG emissions (here, adjustment of the initial-guess emissions) is performed through fitting the model to available satellite and in-situ tracer concentration observations and related quantities. Along with these, posterior uncertainties in the estimated emissions are inferred, given prior uncertainties in the observations, the reported emis- sions, and the model. The existence of a comprehensive estimation infrastructure would also enable quantitative design studies of required observational capabilities to reduce posterior uncertainties in the emission estimates. The basis for a system that we envision in a recent MIT Joint Program Report  is the availability of adjoint versions of the transport and biogeochemical model components.



Adjoint methods to solve deterministic inverse problems are at the heart of much of our work. For the complex models considered, automatic or algorithmic differentiation has been essential to generate the required efficient, up-to-date adjoint model code. We are also pursuing adjoint code development for new geophysical applications.