Toward reanalysis of the Arctic Climate System – sea ice and ocean reconstruction with data assimilation

Motivation

An Integrative Data Assimilation for the Arctic System (IDAAS) has been recommended for development by a special interagency research program “A Study of Environmental Arctic Change“ (SEARCH, 2005). While existing operational reanalyses assimilate only atmospheric measurements, an IDAAS activity would include non-atmospheric components: sea ice, oceanic, terrestrial geophysical and biogeochemical parameters and human dimensions data. The IDAAS was recommended for development “because recent global reanalyses of the atmosphere have received widespread use by the research community and because they are regarded as one of the major success stories of the past decade in atmospheric research” (SEARCH, 2005). Atmospheric reanalysis products play a major role in the arctic system studies and are used to force sea ice, ocean and terrestrial models, and to analyze the climate system’s variability and to explain and understand the interrelationships of the system’s components and the causes of their change.

Motivated by this success and the major goals and recommendations of SEARCH, we develop an integrated set of assimilation procedures for the ice–ocean system that is able to provide gridded data sets that are physically consistent and constrained to the observations of sea ice and ocean parameters. Building on our past research activities in sea ice and ocean data assimilation, we make some first steps toward the creation of an Arctic Climate System Reanalysis that uses modern four-dimensional variational (4D-Var, adjoint) data assimilation methods. We employ sea ice and ocean models with new data assimilation procedures to maximize the integration of model results with observations and thus attempt to provide the arctic research community with complete and accurate data sets, ultimately for at least the last three decades.

Goals

Our goals are to:

• Develop an integrated set of assimilation procedures for the ice–ocean system that is able to provide gridded data sets that are physically consistent and constrained to match available observations of sea ice and ocean parameters.
• Validate the system performance, assess the quality of the major system products, and provide the community with gridded sea ice and ocean parameters for three approximately seven-year periods characterizing different arctic climate states.
• Investigate arctic system variability and the processes important for causing the observed changes based on the reanalysis products.

Team/instruments/experiences

Polar Science Center team (Lindsay and Zhang) has already accomplished an extensive reanalysis of the ice–ocean system using data assimilation methods for ice concentration and ice velocity (Zhang et al., 2003; Lindsay and Zhang, 2005, 2006) spanning the period 1978–2007. The coupled ice–ocean model they have used is the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS).  However, the assimilation methods were based on optimal interpolation of model results and observations.  These sequential techniques are not entirely consistent with the physics represented in the model.  A more physically consistent method is the 4D-Var approach, which may be used to adjust initial and boundary conditions, or model parameters in a manner that is entirely consistent with the model physics and in a manner that optimizes the fit of the model results with observations (Wunsch, 1996).

International Arctic Research Center and Southern Mississippi University team (Panteleev and Nechaev, respectively) is versed in the application of adjoint methods to the ocean. This group has developed, tested, and used an ocean model (Semi-Implicit Ocean Model; SIOM; Nechaev et al., 2005; Panteleev et al., 2006, see results at http://people.iarc.uaf.edu/~gleb/) that is capable of data assimilation employing the 4D-Var techniques. Unfortunately, this model does not include sea ice dynamics and thermodynamics. It has so far been applied in regional studies of the Arctic marginal seas for ice free periods or in studies that neglect the presence of sea ice (Nechaev et al., 2004, 2005; Panteleev et al., 2006a, 2006b, 2006c).

Proshutinsky and Krishfield from Woods Hole Oceanographic Institution are well experienced in modeling (e.g., Proshutinsky, 1993, 2003a,b; Kowalik and Proshutinsky, 1994; Hakkinen and Proshutinsky, 2003), observational (e.g., Proshutinsky et al., 2004; Krishfield and Perovich, 2005), and integrative studies of the Arctic Ocean climate system (Proshutinsky et al., 1999, 2001, 2002, 2005). Model development and simulations represent a comprehensive level of synthesis because this activity integrates the accomplishments of numerous disciplines (physics, mathematics, atmospheric, oceanic, cryospheric, and related sciences) with observational data, and allows testing of different hypotheses via numerical experiments.

It is through the combination of expertise on the team that we feel significant progress can be made to create a physically consistent reanalysis of the ocean system.  The coupled ice–ocean model group (Zhang and Lindsay) uses conventional methods of sequential assimilation to make a first guess at the state of the ice–ocean system with PIOMAS and provide the surface and lateral boundary conditions to the second group (Nechaev and Panteleev).  This second group determines the 4D-Var optimal solution using SIOM and a large number of ocean observations as constraints.  The third part of our team is responsible for obtaining and processing the hydrographic observations and in interpreting the results.

Approach

The Arctic Ocean is covered by sea-ice year round. Ideally, the data assimilation procedure should take into account ice-ocean interactions and the data assimilation algorithm should be designed for a sea-ice – ocean coupled model system. Development of a 4D-var data assimilation procedure for such coupled ice-ocean system is not straightforward. Strong non-linearity of the sea-ice dynamics complicates development of a stable adjoint model and results in low controllability of the sea-ice model. Effectively, dynamical complexity of these coupled ice-ocean system may limit applicability of 4D-var data assimilation methods for long time period integration intervals. Thus, to avoid such technical problems, we use a set of simplified sub-optimal data assimilation methods described below (see Figure 1).

Pan-Arctic Ice-Ocean Modeling and Assimilation System
The sea-ice data are assimilated by the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS) developed at the Polar Science Center, University of Washington (see Zhang and Rothrock [2001, 2003, 2005]). The PIOMAS is a coupled parallel ocean and sea-ice model with capabilities of assimilating sea ice concentration. It consists of the thickness and enthalpy distribution (TED) sea-ice model developed by Zhang and Rothrock [2001, 2003] and the Parallel Ocean Program (POP) developed at the Los Alamos National Laboratory. The TED sea-ice model is a dynamic thermodynamic model that also explicitly simulates sea-ice ridging. It has 12 categories each for ice thickness, ice enthalpy, and snow. The model employs a teardrop viscous-plastic ice rheology that determines the relationship between ice internal stress and ice deformation  (see Zhang and Rothrock [2005]), a mechanical redistribution function that determines ice ridging (see Thorndike et al. [1975], Rothrock [1979], Hibler, [1980]) and an efficient numerical method to solve the ice motion equation [Zhang and Hibler,1997]). Assimilation of sea ice concentration data from satellites in PIOMAS is based on an assimilation procedure [Lindsay and Zhang, 2006] that "nudges" the model estimate of ice concentration toward the observed concentration in a manner that emphasizes the ice extent and minimizes the effect of observational errors in the interior of the ice pack. This is a relatively simple yet effective assimilation scheme that is computationally affordable for long-term integrations and experiments. In addition to improving the simulated ice edge, comparisons to observed ice thickness measurements in the Arctic indicate that the assimilation of ice data also improves the simulated ice motion and thickness.

Semi-implicit ocean model
Oceanographic observations are assimilated into Semi-Implicit Ocean Model (SIOM) data assimilation system. SIOM is a modification of the C-grid, z-coordinate OGCM (Ocean Global Circulation Model) developed in Laboratoire d'Oceanographie Dynamique et de Climatologie [Madec et al., 1999].  This model was designed specifically for the implementation of 4D-var methods into regional models controlled by fluxes at the open model boundaries and sea surface. The model is semi-implicit both for barotropic and baroclinic modes permitting simulations with relatively large time steps of  approximately  0.1 day [Nechaev et al., 2005, Panteleev et al., 2006a,b]. The tangent linear model was obtained by direct differentiation of the forward model code. The adjoint code of the model was built analytically by transposition of the operator of the tangent linear model, linearized in the vicinity of the given solution of the forward model [Wunsch, 1996]. The details of the SIOM numerical scheme can be found in Nechaev et al. [2005].

Model configurations and assimilating system coupling
The PIOMAS is configured to cover the region north of 43°N with mean horizontal resolution of approximately 22 km (Figure 2). The model is one-way nested to a Global Ice-Ocean Modeling and Assimilation System which consists of similar sea ice and ocean models [Zhang, 2005].  The SIOM was configured for the domain shown in Figure 3. The SIOM’s grid has a horizontal resolution of 75 km. The original version of SIOM does not have sea-ice model, but is able to assimilate the momentum, heat and salt fluxes between ice and ocean. We use this possibility in implementation of a two-step data assimilation algorithm to avoid problems associated with the strong non-linearity of sea-ice dynamics discussed above.

At the first step of the algorithm, we run PIOMAS for the entire Arctic Ocean domain and PIOMAS assimilates sea ice concentration data and simulates sea ice and water dynamics. At the 2^nd step, the SIOM assimilates external forcing provided by PIOMAS output over the SIOM  domain (surface heat, salt and momentum fluxes) and all available hydrographic data (water temperature, salinity, velocity) employing a conventional 4D-var data assimilation procedure that ensures dynamical consistency of the ocean model solution ([Nechaev et al., 2005, Panteleev et al., 2006a,b). To reduce the number of “unknowns” in the 4-Dvar data assimilation procedure, the time variability of the SIOM forcing fields and the functions specifying the open boundary conditions is approximated by piece-wise linear continuous functions of time on 3-day intervals. The final product of the data assimilation system includes reconstructed patterns of circulation and water T&S fields stored at the end of every 10th day of the SIOM integration.

Figure 1. Data flow chart for the data assimilation procedure.

Figure 2. PIOMAS model domain

Figure 3. SIOM model domain

Data sources

PIOMAS is driven by atmospheric forcing applied to the ocean and ice surface and assimilates sea ice concentration and drift.

SIOM uses all available ocean hydrography and current data for assimilation and is forced by data from PIOMAS at the ocean-ice surface. The major sources of data needed for model forcing and assimilation are outlined below.

Atmospheric forcing data
Atmospheric forcing data is needed for both PIOMAS and SIOM. These data are taken from the ERA-40 Reanalysis through 2001 and the ECMWF operational analysis after that.  The fields we need are daily averages of the 10-m wind vector, the 2-m air temperature and humidity, the sea level pressure, and the downwelling long- and shortwave radiative fluxes.  The reason we select the ERA-40/ECMWF products over the NCEP reanalysis is that the downwelling radiative fluxes in the NCEP products are known to have large errors (Serreze et al., 1998).  Previous simulations often have used climatological cloud fractions and parameterized downwelling fluxes, but by using the ERA-40 fluxes we are able to include realistic interannual variability in the radiative fluxes.  The ERA-40 downwelling fluxes compare very well to those measured during SHEBA (Liu et al., 2005). Our analysis of the wind and temperatures of these products show there is no significant jump in their bias after 2001 when compared to NCEP products.  Some inhomogeniety in the products may exist because of atmospheric model changes after 2001, but the changing mix of available observations during the entire reanalysis period also adds unavoidable inhomogeneities in the results.

Surface data
PIOMAS assimilates ice concentration (IC), ice velocity (IV), and wet-ocean sea-surface temperature (SST).  The IC and SST data are obtained from the ERA-40/ECMWF data sets to insure that the air temperature, IC, and SST fields are mutually consistent.  The source data from these fields are: 1) the monthly mean HadISST data set from the UKMO Hadley Centre for 1956-1981; and 2) the weekly NCEP 2D-VAR data for 1982-present (Reynolds et al., 2002). Both data sets are based on satellite and conventional SST/IC observations. The principal reason for the higher quality of these source data sets is the use of a common consensus IC and a common IC-SST relationship in the sea ice margins.  The most recent ECMWF SST fields are from new daily analyses made at NCEP.  The IV are taken from the optimally interpolated ice velocity fields produced by Chuck Fowler and archived as a Polar Pathfinder dataset at NSIDC.  They are derived from buoy, AVHRR, and passive microwave estimates of the ice velocity.

Ocean data
The adjoint data assimilation procedures of SIOM use a variety of ocean data including salinity, temperature, velocity, and sea surface height. The Arctic Ocean hydrographic data is sparse in temporal and spatial coverage.  Recently, the climatology has expanded in two ways. First, historical hydrographic data have been declassified and released by both Russian and western sources in the form of smoothed, three-dimensionally gridded fields for summer and winter [Environmental Working Group Atlas, EWG, 1997, 1998].  This represents a significant advance but unfortunately, the data for these atlases were averaged for the decades of the 1950s, 1960s, 1970s and 1980s, irregardless of climatic regimes. Second, the arctic hydrography database has expanded recently due to an increase in the number of high-latitude cruises and the establishment of several long-term observational sites in key regions of the Arctic Ocean including major ocean boundaries (Bering Strait, Fram Strait, straits of the Canadian Archipelago, and in the central basin such as observations conducted in the vicinity of the North Pole (North Pole Environmental Observatory, NPEO, http://psc.apl.washington.edu/northpole) and in the Western Arctic (Beaufort Gyre Observing System, BGOS, http://www.whoi.edu/beaufortgyre). In addition, there has been at least one major expedition by either icebreaker or submarine into the deep Arctic Ocean nearly every year between 1992 and 2005 (information about existing arctic hydrographic data is posted at the BGOS web site). Figure 4 shows distribution of hydrographic stations in space and time. These monthly gridded data with some spatial and temporal averaging are available at Digital hydrography data archive

Other data include current velocity measured at moorings in the major Arctic Ocean straits and key regions of the deep basins. There are more than 900 months of these observations available just from the Institute of Ocean Sciences, Canada (Greg Holloway, personal communication, see Figure 5) Digital hydrography data archive

Figure 4 Left: T-S station data coverage for 1849-2006. There are 538516 stations in the model domain. Middle: Number of stations by year. Right: Number of stations by month.

Figure 5. Locations of mooring locations with currents data (arrows)

Other sources include the Alfred Wegener Institute, the Polar Science Center, University of Washington, and Ohio State University). Significant amounts of data have already been incorporated into our data archives at WHOI. These data include climatologic information from the EWG atlas and specially selected and gridded T&S data provided by the scientists of the Arctic and Antarctic Research Institute, Russia, for different circulation regimes (http://www.whoi.edu/science/PO/arcticgroup/projects/andrey_project) and for particular years. Completely new data are available from the NPEO and BGOS observing systems. The mooring data from these observatories also includes an upward-looking ADCP at the top mooring float to measure ocean currents in the upper 50-m layer. For 2003/2004 we also collected T&S data in the upper 50-m ocean layer from four ocean buoys. Since 2004 the BGOS archive includes data from a new instrument, the Ice-Tethered Profiler (ITP), which repeatedly samples the properties in the upper 800 m of the ocean at high vertical resolution over long time periods. The instrument, its performance in the field, and examples of the data returned from the system are presented at http://www.whoi.edu/itp.

There also are numerous other sources of data containing water temperature and salinity fields; sea ice thickness, concentration, and drift; sea level; and ocean currents. These data are located in national data archives (NSIDC, ARCSS, NODC) and in local archives of different institutions of the project PIs. Most of the data archives are available publicly via the Internet.    As part of this project we have collect and reprocessed all possible data from a variety of sources for the period 1950-2006 and prepareed these data in a form suitable for assimilation procedures. The pre-processing procedures included: quality control and preliminary data analysis; data unification for data assimilation purposes including low-pass filtering and interpolation to model grids; estimation of typical spatial and temporal scales of variability; and obtaining physically meaningful estimates of the data error variance.