Sunday, February 7, 2021

State estimation and observing system design in support of Arctic Ocean Observing

By Patrick Heimbach, Nora Loose, An T. Nguyen, Helen Pillar, and Timothy Smith

 In previous posts Jamie Morison and Mary-Louise Timmermans provided concise overviews of our state of knowledge of the large-scale circulation of the Arctic Ocean (and sea ice). Their discussion reviewed the relationship of ocean circulation changes to dominant modes of atmospheric variability over the last few decades and the interplay between changes in surface atmospheric circulation, freshwater input (river runoff and land ice melt) and redistribution in regulating freshwater buildup in the Beaufort gyre. Deciphering the detailed physical processes underlying regional changes is hampered by the extreme sparsity of in-situ observations in parts of the Arctic, as Jamie noted. Fig. 1 gives an impression of the distribution of most in-situ observational assets between 2002 and 2017. Improved geophysical retrieval algorithms are beginning to enable us to fill certain gaps through satellite remote sensing of altimetry-derived sea surface height (SSH) anomalies from ICESat, ICESat-2, and CryoSat-2 (Armitage et al. 2018), gravimetry-derived ocean bottom pressure (OBP) anomalies from GRACE, GRACE-FO (Peralta-Ferriz et al. 2014), and more recently radiometry-derived sea surface salinity (SSS) from SMOS, Aquarius and SMAP (Fournier et al. 2020). 

Fig. 1: Distribution of in-situ observational assets between 2002 and 2017 used in the Arctic Subpolar gyre sTate Estimate (Nguyen et al. 2021)

Among the questions we may ask are 

  1. how can we take maximum advantage of these sparse observations; 
  2. how do we compare the heterogeneous data streams and disparate variables; and 
  3. can we use quantitative methods to guide the deployment of new observations and/or the design of an “optimized” observing system? 
For example, SSH anomalies, combined with OBP anomalies, carry information about the ocean’s density, mass and circulation changes. Also, hydrographic observations taken at one point imply some knowledge of the surrounding state upstream and downstream (i.e., both backward and forward in time).

Arguably, one answer to these questions is to combine the knowledge reservoir offered by the available, yet incomplete observations with the knowledge reservoir that is encapsulated in the governing equations of motion, rendered in the form of numerical models (including conservation of mass, momentum, heat, and salt, constitutive laws for seawater and sea ice, and subgrid-scale parameterization of unresolved physical processes), but which themselves are subject to “model” uncertainties. The need to deal with sparse data is ubiquitous in the geosciences, fueling significant efforts in the development of inverse methods over many decades (see, e.g., Carrassi et al. 2018 and Wunsch 2019 for concise algorithmic and historical reviews). 

Most common today in the ocean, atmosphere and climate science communities is the notion of data assimilation (DA) as developed for numerical weather prediction (Bauer et al. 2015). Before discussing its role in the context of the planned workshop, it is useful to sketch the process and goal of DA, with the following succinct description given by Kaminski et al (2015): “Ideally, all observational data streams are interpreted simultaneously with the process information provided by the model to yield a consistent picture of the state of the Arctic system that balances all the observational constraints, taking into account the respective uncertainty ranges.” DA more broadly serves different purposes

  1. model calibration (parameter estimation); 
  2. state estimation or reconstruction (interpolation or synthesis); 
  3. model initialization for prediction (extrapolation); and 
  4. observing system design (targeted observation). 
These diverse uses imply the use of different assimilation methods and the need to tackle distinct practical challenges. Here, we will focus on application of DA for reconstructing the time-evolving state of the Arctic over the past decades for the purpose of improved understanding, and the ability to do so more accurately in the future. In addition, we will discuss the related question of how to design a sustained Arctic Ocean observing system that would lead to a better understanding and monitoring of key indices or metrics (to be defined) pertinent to the Arctic Ocean as well as the coupled ocean, atmosphere, marine cryospheric, and biogeochemical system.

Most available Arctic Ocean (and sea-ice) multi-decadal reconstructions available to date are those obtained as part of the global ocean reanalysis efforts. The term “reanalysis” is mostly synonymous to “reconstruction” and derived from the process of “analysis” in the context of numerical weather prediction (e.g., Stammer et al. 2016). Arctic-focused assessments of these global and regional Ocean and sea ice ReAnalysis products (ORAs) have recently been conducted as part of the Polar ORA Intercomparison Project (Polar ORA-IP) under the joint auspices of the CLIVAR Global Synthesis and Observing Panel (GSOP) and the WMO GODAE OceanView program (called OceanPredict since 2021). The two main publications from these are by Chevallier et al. (2016) focusing on Artic sea ice cover, and by Uotila et al. (2018), focusing on Arctic Ocean hydrography and circulation.

It is worth noting that these reanalysis assessments are separate, albeit related to intercomparison efforts that have been previously conducted as part of the Coordinated Ocean-ice Reference Experiments, phase II (CORE-II) under the auspices of the CLIVAR Ocean Model Development Panel (OMDP). This led to Arctic-focused comparisons of simulated  sea ice and solid freshwater (Wang et al. 2016a), liquid freshwater (Wang et al. 2016b), hydrography and fluxes (Ilicak et al. 2016). A new generation of OMDP-led assessments (termed OMIP-2) have recently been conducted with a new atmospheric forcing data set, JRA55-do (Tsujino et al. 2020). Key differences between the Polar ORA-IP and CORE-II/OMIP-2 efforts are (i) CORE-II simulations do not perform any data assimilation; (ii) unlike ORA-IP, all CORE-II simulations use the same atmospheric forcing product and the same set of bulk formulae to compute air-sea fluxes from the atmospheric state over ice-free water; and (iii) unlike most ORA-IP members, CORE-II simulations are free of artificial interior sources or sinks of heat, salt, and momentum (which arise in many of the ORA-IP members from periodic “analysis increments”).

In addition to the global reanalyses, a regional Arctic Subpolar gyre sTate Estimate (ASTE) has recently been produced, supported by NSF, covering the early 21st century, 2002-2017 (Nguyen et al. 2021), which may be considered the northern sibling of the Southern Ocean State Estimate (SOSE; Mazloff et al. 2010).  ASTE seeks to combine all known observational data with the equations of motion encoded in a general circulation model by solving a giant least-squares optimization problem, based on the adjoint infrastructure developed by the ECCO group. It arguably represents the biggest effort undertaken to date with the aim of producing a dedicated Arctic ocean-sea ice estimate. What sets ASTE apart from most reanalysis products is that tracer and momentum tendencies are free of artificial sources or sinks, rendering the product dynamically and kinematically consistent (Wunsch 2019).  Nguyen et al. (2021) provide an initial assessment of the product. Fig. 2 summarizes estimated transports across main Arctic gateways (adapted from Østerhus et al. 2019).

Fig. 2: Time mean volume transports across main Arctic gateways during 2002-2017 (large blue), estimated by ASTE (along with standard deviations based on monthly values). Adapted from Østerhus et al. (2019).

ASTE is openly available to the research community through the Texas Advanced Computing Center (TACC).  The product also provides comprehensive output to conduct accurate budget analyses of tracers, as recommended by Griffies et al. (2016). Access to not only the data itself, but also to capabilities for conducting detailed, sometimes compute-intensive analyses is of increasing importance as the data volume grows. ASTE is exploring a new cloud-based capability enabled through TACC and hosted on Amazon Web Services (AWS) servers, see at Data access and analysis software support specifically tailored for ASTE are based on earlier development of the llcreader package led by R. Abernathey (2019), and enabled through a stack of open-source Python packages: xmitgcm (Abernathey et al. 2019) provides access to the data “on-the-fly” via dask (Dask 2016) in the form of a convenient xarray (Hoyer and Hamman 2017) dataset. Calculations and visualization are made easy for the ASTE grid topology with xgcm (Abernathey et al. 2020) and ECCOv4-py. A dedicated data portal is currently being established at the NSF Arctic Data Center, Enabling such cloud-based analytics capabilities with concurrent access to all available data (in-situ, satellite, and reanalyses/state estimates) represents a step from “Data as a Service” to “Analysis as a Service” (Schnase et al. 2016) and can be another discussion point of the workshop.

A shared desire between reanalysis and state estimation efforts is the ability to derive estimates of time-mean and time-varying ocean mass, heat, salt and freshwater content, transport, divergences, and other derived processes from complete three-dimensional fields of the time-evolving ocean state. Such complete budget analyses provide dynamical insights into the causes and pathways of anomalies propagating throughout the Arctic. They enable quantification of, e.g., the relative role of local forcing (via air-sea fluxes) versus lateral advection, versus diffusive processes (e.g., Buckley et al. 2015). They complement or enhance purely observation-driven estimates, e.g., of time-evolving budgets of Arctic freshwater (Haine et al. 2015; Serreze et al. 2006; Solomon et al. 2021), volume (Østerhus et al. 2019), and heat (Schuckmann et al. 2020; Serreze et al. 2007).

Satisfying the desire to close budgets, however, is a challenging task. Despite the data constraints applied in the ORA-IP members, significant differences exist between the reanalyses for a range of metrics, including transports through key Arctic gateways, regional heat and salt content anomalies, hydrographic vertical profiles, mixed-layer depths, and circulation features. Deciphering the causes of these differences is made difficult by the fact that each reanalysis product is based on (i) a different underlying circulation model, (ii) different atmospheric forcing fields used (mostly atmospheric reanalyses), (iii) a different DA method, (iv) different observations used or different ways in which these observations are ingested (e.g., along-track vs. gridded), and (v) different error estimates (observation, representation and background errors). Overall, a valid expectation is that with increased observational coverage, model skill, and sophistication of the DA schemes, estimates in the ocean state should converge. Therefore, understanding and quantifying the observational needs to reduce the uncertainties among Arctic reanalyses should be an important point of discussion for the workshop. This leads to the issue of how to design an Arctic Ocean observing system. Important aspects for discussions in this regard are (i) what are the design criteria, i.e., what purposes should an observing system serve (e.g., Lee et al. 2019; Smith et al. 2019), and (ii) what quantitative methods exist to support observing system design using simulation-based approaches.

The field of computational science (Rüde et al. 2018) in general and computational oceanography (Haine et al. 2021) in particular, are emerging disciplines developing computational algorithm and physics-based simulation and inverse modeling capabilities to advance scientific discoveries where experimental approaches are severely limited, i.e., too costly, slow, dangerous, or infeasible. These limitations clearly fit the bill of Arctic Ocean observing, given its logistical and technological challenges of sensor design, deployment, and maintenance. A range of algorithms are being developed to support quantitative observing system design, mostly embedded within advanced data assimilation systems. Due to their computational cost and complexity, maturing these algorithms is itself an ongoing area of research, but one that is both highly active and promisingly transformative. It is the subject, among others, of a dedicated activity of the OceanPredict program (Fujii et al. 2019). Recent examples of Arctic and North Atlantic-focused efforts are the quantitative network design studies by Kaminski et al. (2015; 2018), Loose et al. (2020), and Loose and Heimbach (2021). Among the design aspects are the determination of relevant metrics (purpose and objectives of the observing system), determination of observational complementarity versus redundancy, and assessment of data utility as determined from signal-to-noise (or sensitivity-to-noise) ratios of possible acquisitions, along with numerous other practical aspects underlying the design, such as cost or logistical constraints. A workshop that brings together observationalists, modelers, data assimilation experts, and users, offers the prospect of discussing and developing concepts for co-designing a comprehensive yet efficient, targeted Arctic Ocean observing system. Because neither the model, nor the observing network, nor the assimilation systems are free of errors, improving each of these elements is of necessity a symbiotic, iterative process. Related efforts in numerical weather prediction (Bauer et al. 2021) suggest that such an endeavor will take time, resources and willingness to work across disciplines, but will have substantial benefits for the grand challenge of Arctic observing system design.


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