CHAPTER
COORDINATORS
COORDINATORS
Stefania Ciliberti
5.1
General introduction to circulation models
5.1.1
Objective, applications and beneficiaries
The main objective of any OOFS is to provide users with the best reliable and easy access information available on the state of the ocean in near real-time. The service is meant for any user, and especially downstream service providers who use the information as an input to their own value added services.
A forecasting system relies on a numerical ocean model and, in many cases, on a data assimilation component able to assimilate the available observations and provide a complete dataset that can be used as initial conditions by the ocean circulation model. The availability of relevant observations is crucial to the success of an OOFS and the development of models and numerical techniques, along with data assimilation schemes that combine all the information taking into account the uncertainties of the observations and models.
The circulation modelling component represents one of the main cores of operational marine monitoring and forecasting systems: it provides an overall description of ocean physical essential variables (i.e. temperature, salinity, currents, sea surface height, etc.) for ocean predictions and for supporting climate studies. Ocean models are able to describe the sea state from global to coastal scales and to predict its variability and evolution in time (from short to mid-term to longterm). This is done by numerically solving a set of partial differential equations, based on an approximated version of the Navier-Stokes equations.
At the beginning of the XX century, Bjerknes (1914) described a practical method that could solve the mathematical dynamic and thermodynamic equations at least for a finite amount of time. He defined two factors that were necessary to make predictions a reality: (1) knowledge of the initial conditions as accurately as possible, and (2) the development of an accurate predictive model. The latter consisted of discretizing the equations and using numerical methods to solve for the time derivative. Based on this approach, the first successful meteorological forecast became operational at the end of the 1960s, while ocean forecasting began in the 1980s; a joint venture between Harvard University and the Naval Postgraduate School in Monterey, both in the United States, completed the first successful forecast of ocean mesoscales in a limited ocean area (see Pinardi et al., 2017, for an overview of the ocean prediction science). Earlier examples of wave forecasting during the second World War responded to the need to know the sea state during landing operations (O'Brien and Johnson, 1947).
During the last decades of the 20th century and the first decades of the 21st century, ocean forecasting has become an operational activity and, thanks to the increase of computing power, today we are able to numerically integrate the governing equations at very high resolution in space and time, to study multi-scale ocean processes, physical properties and their impacts on the climate, and human activities affecting the environment. In modern ocean prediction, stochastic approaches and ensemble estimates complement deterministic solutions, accounting for the different sources of uncertainties (e.g. errors in the initial conditions, in the forcing functions, in the physics of the numerical model, and in the bathymetry) that unavoidably affects the final solution and tends to increase over the forecast period.
To improve the quality of predictions, data assimilation and ensemble techniques are widely used, and their primary scope is to rigorously and systematically combine available observations (in situ and satellite) with numerical ocean models to provide the best estimate of the forecasting cycle. However, in case of very high-resolution nested models and when observation availability is limited, operational systems do not use a data assimilation procedure. When possible, an OOFS system needs to retrieve data observations from a wide variety of observing platforms and systems over the domain of interest for prediction. Satellite based observing systems provide a large source of observational data for an OOFS as well.
An OOFS needs to access information from a numerical weather prediction system in order to provide surface boundary forcing information. The OOFS will also require information on other parameters that influence the ocean such as river outflows, etc. Depending on the domain of interest, the OOFS may also require information about sea ice (see Section 4.2 for the input data and Chapter 6 for understanding sea ice modelling basics). Observations are also used to provide a quantitative understanding of the capacity of the ocean model to make predictions by means of validation and calibration techniques and, consequently, to measure and monitor the accuracy of the forecasting product (see Section 4.5). Routine validation and verification information will tell the OOFS operators when a model is not performing well. The errors identified through validation and verification can be used to set priorities for further development of the OOFS. Despite the enormous improvements reached nowadays by operational forecasting systems ranging from global to coastal scales, much research is still needed to advance in ocean prediction. Developments include access to additional innovative autonomous multi-scale observing technologies observations, both remote and in situ (Le Traon et al., 2019), to new model developments (Fox-Kemper et al., 2019), up to next-generation computational methods and data assimilation schemes supported by the recently expanding applications of machine learning techniques in this field (De MeyFrémaux et al., 2019).
The ultimate purpose for operating an OOFS is the production, preparation, and delivery of operational ocean forecasts to users in forms that meet their needs. There is a growing list of users relying on the products and services from operational ocean forecasting systems. Ocean predictions will continue to produce an increasing number of marine applications and services: e.g. for maritime safety, marine resources, coastal and marine environment (Chapter 11). This is because the new systems allow informed management and emergency decisions to be made based on physical knowledge resolved at unprecedented space and time resolution, with known quality and accuracy.
The emergence of operational organisations for delivering real-time forecasts and analyses will encourage the development of value-added products, including forecasts for extreme weather driven events (such as storm surges), pollution, oil spills, acoustic properties (e.g. the speed of sound), sea ice, ecosystem management, safe offshore activities, search and rescue operations, optimal energy extraction, and maritime safety and transport. In addition, ocean forecast products and services can also be providers of information for aquaculture, fishery research, and regional fishery organisations, contributing to the protection and sustainable management of living marine resources. Availability of predictions on the ocean helps to limit damages in the case of floods, storm surges, heat waves and other dangers associated with sea conditions. Furthermore, detailed and accurate forecasts are also useful to assist decision making to plan long-term strategies aiming at managing the risks associated with the impacts of climate change on the sea and coasts, such as sea level rise and marine heat waves.
A predicted ocean where society has the capacity to understand current and future ocean conditions is one of the proposed seven outcomes of the United Nations Decade of Ocean Sciences for Sustainable Development.
Scope of this chapter is to present all elements that make an OOFS and provides a detailed understanding of the main circulation modelling components. For each component, a comprehensive description is provided in dedicated chapter subsections, including the presentation of some state-of-the-art examples of ocean models currently working in operational frameworks. In addition, basic concepts of data assimilation systems and validation strategies will be presented as well, since an essential part of operating a model is to conduct the necessary validation and verification procedures to maintain a continuous quality control of the system outputs.
5.1.2
Circulation Physics
The physical processes, properties and circulation of the ocean are described numerically by the approximated Navier-Stokes equations (details in Section 5.4.1). The equations allow the spatial and temporal distribution of the temperature, salinity, density, pressure, and currents to be described. Numerical ocean models are the building block of operational oceanography and fundamental for near real time to seasonal to decadal forecasts and climate projections. In operational oceanography, they are used alongside data assimilation techniques to accurately represent the state of the ocean at a particular point in time and space, and to produce the initial condition of the forecasting system.
The governing equations for a real fluid are the Navier-Stokes equations, together with conservation of salt and heat and an equation of state; these equations support fast acoustic modes and involve nonlinearities in many terms that make their solution both difficult and expensive. A series of approximations are made to simplify and yield the “primitive equations”, which are the basis of most general circulation models. The assumptions that are made in ocean models are described in Section 5.4.
Ocean circulation models aim to represent key processes. These include: 1) transport of heat by the ocean; 2) the effect of evaporation, precipitation and runoff on ocean salinity and density; and 3) the role of ocean currents which, along with wind waves and tides, drive ocean mixing and water mass transformation. Ocean circulation models discretize the governing equations on a horizontal and vertical grid (Section 5.4 expands on this). The details of whether processes can be explicitly resolved in models or they must be parameterised depend on the resolution of the grid used to solve the approximate numerical system.
Figure 3.4 (see Chapter 3) shows the order of magnitude of spatial and temporal scales of specific ocean processes. If the model resolves scales of100 km, ocean models should be able to resolve Kelvin and Rossby waves; indeed, the representation of Equatorial dynamics has been shown to be important for forecasting the evolution of El Nino on seasonal timescales (Latif et al., 1994). On shorter timescales but with similar spatial scales, surface tides are key processes to represent. Moving to spatial scales of ~10 km to 100 km, the ocean mesoscale can start to be represented; this scale includes boundary currents and mesoscale eddies (Hewitt et al., 2020). At even finer scales, coastal upwelling, internal tides, and internal waves can be represented. Interactions with bathymetry can be important at the scale of the bathymetry. For example, choke points can determine the exchange between the deep ocean and inland seas, such as the Gibraltar Strait. Horizontal resolution choices are discussed further in Section 5.4.
While a primary consideration is the horizontal scales (Figure 3.4), the choice of vertical resolution and coordinate is also an important consideration. These choices are discussed further in Section 5.4, along with the numerical methods that are employed to solve the equations and some of the parameterisation choices to be made.
The ocean has strong links to other aspects of the Earth system, such as sea ice, which is particularly important for modulating temperature and salinity at high latitudes. Global ocean models include a sea ice component. State-of-the-art sea ice models represent the ice thermodynamics including meltponds and the ice dynamics, with a representation of the ice rheology. Many sea ice models also capture the variations in ice thickness or ice age within a typical ocean grid box. Current status of sea ice modelling and the applicability of models for operational forecasting is discussed in Hunke et al. (2020).
This chapter provides complementary information on the way to set an OOFS, which core is the circulation model. Section 5.3 will provide a list of input data needed for setting up an ocean model, from static datasets such the bathymetry to operational products such atmospheric forcing, to other OOFS for the provisioning of initial/boundary conditions in case of regional/coastal models, to observations used for assimilation and validation. Section 5.4 focuses on the mathematical formulation of the primitive equations, providing some basic information to numerical methods for discretization and numerical integration of such equations. Section 5.5 is devoted to presenting the basic mathematics for the data assimilation schemes commonly used in global and regional OOFS. Section 5.6 deals with ensemble modelling and, finally, Sections 5.7 and 5.8 provide major details on the validation approaches and the OOFS output. The last part of this chapter provides an inventory of OOFS, including multiyear systems, operating at international level, from global to coastal scale.
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