Using multi-platform 4D-Var data assimilation to improve modeling of Adriatic Sea dynamics
Introduction
Recent advances in computing power, developments in ocean data assimilation (hereafter DA) techniques, improvements in satellite radiometer resolution and increased number of locally available observations (i.e. coastal HF radars, ADCPs and CTD mooring/cruises, coastal buoys), have allowed for substantial advances in objective and dynamically consistent mapping of the ocean state (Dobricic and Pinardi, 2008, Li et al., 2008). The Four-Dimensional Variational (4D-Var) DA technique (Courtier et al., 1994, Courtier, 1997) is the most advanced version of the variational schemes, with its usage becoming more prevalent in ocean research (Weaver et al., 2003, Moore et al., 2009, Moore et al., 2011a, Moore et al., 2011b, Usui et al., 2015).
There are many benefits of using 4D-Var DA over simpler methods like 3D-Var, optimal interpolation, or the simplest nudging techniques (Powell et al., 2008, Powell et al., 2012, Moore et al., 2009, Moore et al., 2011a, Moore et al., 2011b, Matthews et al., 2012, Powell, 2017). The notable feature of 4D-Var DA is its capability to ingest observations at their exact time and location, together with their time-evolving error covariance matrix (Weaver and Courtier, 2001). This feature retains temporal information that would otherwise be lost through averaging, thus enhancing our ability to simulate rapidly changing coastal ocean dynamics, as occurs during severe and abrupt winter storms that are associated with extreme cooling processes (Janeković et al., 2014).
By definition, variational methods aim to minimize model to data discrepancy () and changes to the model background (associated model part of the cost function - ) at the same time during each DA cycle, usually referred to as total cost function (Eq. (1)). This is achieved by adjusting the control parameters for initial and boundary conditions, and atmospheric forcing fields: where x is state vector (i.e. free surface, currents or tracer), represents deviation of x from its background, D is the normalized background error covariance matrix, R is the normalized observational error matrix and represents the mismatch between the Tangent Linear model mapped to the observations () and the innovation vector d (defined as difference between observations and the model equivalent of the observations computed from the background circulation). The goal of minimization is to find optimal perturbation (), such as to minimize J with respect to the deviation of the state vector from its background (Eq. (2)): One of the challenges in this approach is to very closely proximate the D matrix, which in our case was done by using correlation modeling via a generalized diffusion equation (Weaver and Courtier, 2001). These methods rely on the linear variational approach (Tangent Linear model and the Adjoint model) that limits spatial and temporal scales specific to the modeled region. In high resolution coastal applications, nonlinearity of the system increases with smaller spatial and temporal scales which can be of order of 100 m in space and seconds in time. Consequently, this can pose significant computational burdens. Despite the demanding computational requirements, 4D-Var has also been successfully applied in highly dynamical, regional coastal seas (Janeković et al., 2013, Iermano et al., 2015, Souza et al., 2015, Kerry et al., 2016, Sperrevik et al., 2017).
The scope of the study is the Adriatic Sea, the 800 × 200 km northernmost extension of the Mediterranean Sea, connected to the adjacent Ionian Sea through the Otranto Strait (Fig. 1). The Adriatic bathymetry exhibits a shallow (80 m) and wide northern Adriatic shelf, gently increasing in depth towards the middle Adriatic depressions of approx. 250 m (Jabuka Pit, JP in Fig. 1), being separated from the 1200 m deep and circular Southern Adriatic Pit (SAP) by the 170 m deep Palagruža Sill (PS in Fig. 1). General circulation of the Adriatic is cyclonic, with Eastern Adriatic Current (EAC) flowing along the eastern perimeter of the sea and transporting saline Levantine Intermediate Water (LIW, Zore-Armanda, 1963), while the Western Adriatic Current (WAC) transports fresher surface water having its origin in the northern Adriatic (Orlić et al., 1992, Artegiani et al., 1997).
Although the northern Adriatic is shallow and its bathymetry mostly flat, its circulation is particularly challenging to reproduce. This is because of: (1) the influence of large rivers, of which the largest is the Po River with an annual mean flux of approx. 1500 m3/s (Raicich, 1994, Vilibić et al., 2016); and (2) extreme forcing during winters when across-basin, cold, and dry bora winds blow downslope along the coastal mountains and extensively cool the shallow sea (Grisogono and Belušić, 2009). Heat losses during such periods may reach 2000 W/m2 (Janeković et al., 2014). The consequence is the generation of extremely dense and cold waters (1030.0 kg/m3 and 5–7 °C during extreme episodes, e.g. 2012) (Mihanović et al., 2013, Janeković et al., 2014) which sink to form a bottom density current (Nof, 1983) and fill the middle Adriatic depressions (Artegiani and Salusti, 1987, Vilibić and Supić, 2005) and the Southern Adriatic Pit (Querin et al., 2016). Conversely, during the summer season, sea surface temperatures can reach as high as 30°C with sharp thermocline located at 20 m depth. Additionally, the effect of tides can be important in the northern Adriatic, particularly in narrow channels (Janeković and Kuzmić, 2005).
In this study, we present a year-long reanalysis of the Adriatic dynamics carried out by using 4D-Var DA, formulated on the physical-space statistical analysis system algorithm (PSAS) (Moore et al., 2011b). In this system, applied minimization procedures that estimate optimal analysis increments are defined in the observation space, in contrast to the primal definition and full model space (I4D-Var).
The motivation for the study was to (a) quantify the usefulness of 4D-Var DA in such a dynamic environment due to linear constraints inherent inside Tangent Linear and Adjoint models, (b) quantify how long the improvements achieved by DA persist in the model, and (c) quantify the improvements in reproducing the ocean state, i.e. to reach the best ocean state description in relation to different observing platforms used in the Adriatic Sea.
The structure of the paper is as follows: the modeling system setup is described in Section 2; multi-platform observations assimilated in our numerical experiments in Section 3; Section 4 is an assessment of the results and a verification using the independent dataset; and Section 5 contains the discussion and summarizes the major conclusions.
Section snippets
Numerical model setup and experiments
ROMS was used as a base ocean model in the DA experiment. ROMS is three-dimensional, free surface, bathymetry following s-coordinate model solving set of the Reynolds-Averaged Navier–Stokes equations with finite difference approximation and a time splitting approach (Shchepetkin and McWilliams, 2005, Shchepetkin and McWilliams, 2009).
The standard set of daily averaged lateral boundary conditions (free surface, temperature, salinity and velocity) were interpolated from the wider Adriatic
Observations
The observational period ranged from 1 October 2014 to 30 September 2015, with more than 15 million, high-resolution observations used in the DA, most of which were sea surface temperatures (SST) measured by satellite radiometers and surface ocean currents measured with high-frequency (HF) radars. In addition, the following in situ data has been used for the DA: (1) vertical temperature and salinity profiles from various ocean platforms (Argo profiling floats, shipborne yo-yo profiler,
Cost function
During the year-long DA experiment, applied model minimization procedure reduced observation-to-model discrepancy scaled with appropriate observation error covariance matrix ( inside the cost function J in Eq. (1), Fig. 3a) and at the same time penalizing mismatch with the model background ( in the Eq. (1) and Fig. 3b; for details see Broquet et al., 2011, Moore et al., 2009, Moore et al., 2011a, Moore et al., 2011b). Overall, the mismatch between the model and the observations () was
Discussion and conclusions
Until now, reproducing the dynamics of the Adriatic at high resolution has been predominantly achieved by ocean models forced by mesoscale atmospheric models (e.g. Bergamasco et al., 1999, Beg Paklar et al., 2001) or coupled atmosphere-ocean models (e.g., Loglisci et al., 2004, Pullen et al., 2006, Pullen et al., 2007, Ličer et al., 2016), some of them using a simple bias correction for improving the model performance (e.g. Benetazzo et al., 2014).
To improve the model dynamics, we implemented a
CRediT authorship contribution statement
I. Janeković: Conceptualization, Methodology, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. H. Mihanović: Data curation, Formal analysis, Investigation, Writing - review & editing. I. Vilibić: Data curation, Formal analysis, Investigation, Writing - review & editing, Funding acquisition. B. Grčić: Software, Investigation, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This project has been supported by Croatian Science Foundation under the Grants ADAM-ADRIA (IP-2013-11-5928), ADIOS (IP-2016-06-1955), and SCOOL (IP-2014-09-5747). Some observational data were acquired within FP7 PERSEUS-ADREX and EUROFLEETS2 ESAW (Grant No. 312762) projects. Numerical simulations were made possible using HPC infrastructure through ECMWF project “PSAS Data Assimilation for the Adriatic Sea using Regional Ocean Modeling System (ROMS)” and Pawsey Supercomputer Centre, Australia.
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