Implementation of a Mesh Movement Scheme in a Multiply Nested Ocean Model and Its Application to Air±Sea Interaction Studies
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AUGUST 1999 ROWLEY AND GINIS 1879 Implementation of a Mesh Movement Scheme in a Multiply Nested Ocean Model and Its Application to Air±Sea Interaction Studies C. ROWLEY AND I. GINIS Graduate School of Oceanography, University of Rhode Island, Narragansett, Rhode Island (Manuscript received 30 January 1998, in ®nal form 1 September 1998) ABSTRACT A mesh movement scheme is implemented in a multiply nested primitive equation ocean model. Mesh move- ment can be speci®ed or determined in the course of the model run so as to follow an evolving oceanic feature, such as a wave front or propagating eddy, or atmospheric forcing, such as a tropical cyclone. Mass, heat, and momentum are conserved during the movement. The mesh movement scheme is tested in idealized and realistic con®gurations of the model. The idealized tests include simulations in which the moving meshes follow a propagating equatorial Kelvin wave, a dipole, or move across an existing mesoscale eddy. The tests demonstrate that the solutions in the ®ne-mesh region of the nested meshes reproduce well the equivalent solutions from uniform ®ne-mesh models. The model is applied for simulations of the ocean response to tropical cyclones, in which the moving meshes maintain high resolution near the cyclone center. The solution in the inner meshes reproduces very well the uniform ®ne-mesh simulation, in particular the sea surface temperature. It demonstrates that the moving meshes do not degrade the solution, even with the application of strong winds and the generation of energetic surface currents and near-inertial gravity waves. The mesh movement scheme is also successfully applied for a real-case simulation of the ocean response to Typhoon Roy (1988) in the western North Paci®c. For this experiment, the model is initialized using the ®elds from a general circulation model (GCM) multiyear spinup integration of the large-scale circulation in the tropical Paci®c Ocean. The nested-mesh solution shows no dif®culty simulating the interaction of the storm-induced currents with the existing background circulation. 1. Introduction with permanently ®xed ®ne-grid meshes may not be adequate. Moving tropical cyclones are one example of Nested-mesh numerical models have in recent years this type of phenomenon. Meteorologists have for some become useful research and operational tools for sim- time recognized that simulations of tropical cyclone dy- ulating mesoscale meteorological and oceanic phenom- namics require very high resolution to better resolve the ena in the large-scale environment. The important ad- storm inner-core structure. Because tropical cyclones vantage of a multiply nested mesh arrangement is that usually travel thousands of kilometers, it is not com- it allows improved horizontal resolution in a limited putationally ef®cient to use ®ne-grid resolution over the region without requiring a ®ne grid resolution through- entire area of the storm track. Instead, movable multiply out the entire model domain. Therefore the model do- nested mesh con®gurations are used for hurricane pre- main to be resolved with higher resolution is kept to a dictions. Atmospheric models with this capability have minimum, greatly reducing computer memory and been in use for the last few decades (e.g., Harrison 1973; speed requirements, and allowing better resolution than Ley and Elsberry 1976; Jones 1977). For example, the would otherwise be possible. of®cial operational hurricane prediction model for the For many geophysical applications, however, our in- National Weather Service developed at the National terest is not so much in a limited region as it is in a Oceanic and Atmospheric Administration (NOAA) particular process. Moving weather systems, propagat- Geophysical Fluid Dynamics Laboratory (GFDL; Ku- ing waves, and oceanic mesoscale eddies represent clas- rihara et al. 1998) is based on the movable nested-mesh ses of phenomena for which a nested mesh con®guration framework. It provides the means to translate the ®nest- scale meshes with the moving hurricane, thus placing the ®ne resolution exactly where it is needed, in the vicinity of the storm center. Corresponding author address: Dr. Clark Rowley, Graduate School of Oceanography, University of Rhode Island, Narragansett, RI Proper simulation of tropical cyclones calls for the 02882. use of fully coupled atmosphere±ocean models. Recent E-mail: [email protected] numerical studies using coupled hurricane±ocean mod- q 1999 American Meteorological Society 1880 MONTHLY WEATHER REVIEW VOLUME 127 els (e.g., Khain and Ginis 1991; Bender et al. 1993a; 3) the formulation of the mesh nesting algorithm allows Schade and Emanuel 1999; Falkovich et al. 1995) have ¯exibility in deciding the number of meshes and the demonstrated that interaction with the ocean has an im- ratios of grid resolutions between adjacent meshes. If portant impact on storm intensity. This is because trop- the grid ratio is made to be unity, the model simply ical cyclones moving over the ocean produce signi®cant reduces to a single mesh con®guration and can be used changes in the sea surface temperature (SST). Obser- as a large-scale general circulation model (GCM). vational and numerical studies have shown that the SST In the next sections of this paper, the formulation of may decrease up to 68C underneath a tropical cyclone the movement scheme is presented, as well as various as a result of the strong wind forcing (e.g., see the review simulations designed to test the method and to dem- article of Ginis 1995). This amount of cooling can sig- onstrate its utility for certain types of geophysical prob- ni®cantly reduce the heat and moisture ¯uxes at the sea lems. A brief outline of the model physics and a de- surface, which play an important role in storm evolution. scription of the mesh nesting technique are presented In developing a coupled tropical cyclone±ocean mod- in section 2, and a detailed discussion of the mesh move- el, the same issue of computational ef®ciency applies ment method in section 3. In section 4 results from to the ocean component of the coupled system: high idealized cases used to test the mesh movement tech- horizontal resolution is needed only in the region within nique are described. Section 5 presents realistic simu- several radii of the maximum wind. Therefore, a mov- lations that demonstrate the application of the movable able nested-mesh con®guration is also highly desirable nested-mesh method to simulations of the ocean re- for ef®cient modeling of the ocean response to tropical sponse to tropical cyclone forcing. We conclude with a cyclone forcing. This capability is especially important summary discussion in section 6. for coupled tropical cyclone±ocean simulations in the eastern and western Paci®c, because it is not compu- 2. Nested mesh ocean model tationally practical to use a single very high resolution mesh over the entire Paci®c Ocean. However, all of the A brief outline of the model physics and numerics is few recently developed nested-mesh ocean models uti- included here for clarity, with a review of the key prin- lize mesh con®gurations that are ®xed in time and space ciples of the mesh nesting technique. For a full descrip- (e.g., Spall and Holland 1991; Oey and Chen 1992; Fox tion of the model the reader is referred to Ginis et al. and Maskell 1995; Ginis et al. 1998) and, therefore, are (1998). not very suitable for simulations of the ocean response to a moving storm. a. Model physics and numerics The purpose of this paper is to present the imple- mentation of a mesh movement scheme in a nested-mesh The model is based on a primitive equation multi- primitive equation ocean model, and the results of its layered formulation in spherical coordinates. The mixed rigorous testing in idealized and realistic ocean settings. layer is treated as a turbulent boundary layer that ex- The model is designed to allow the inner meshes of changes momentum and heat with the atmosphere at its ®ner resolution to follow moving oceanic or atmospher- surface, and with the thermocline by entrainment at its ic features. It employs a mesh movement technique orig- base. It is well mixed due to turbulent mixing and is inally proposed by Kurihara et al. (1979) and success- vertically homogeneous in density. The strati®ed ther- fully applied for many years in the GFDL hurricane mocline below is divided into an arbitrary number of prediction model (Kurihara et al. 1998). Although the numerical layers, according to a sigma coordinate sys- movement scheme has been implemented in the model tem originally proposed by Gent and Cane (1989). The with the coupled tropical cyclone±ocean application in essence of the sigma coordinate is to keep the ratio of mind, we envision its use in a variety of studies that the layer depths below the mixed layer equal to a pre- focus on moving mesoscale ocean and coupled air±sea scribed value. With this vertical coordinate, the layer variability. depths are rearranged at each time step in the course of The mesh movement scheme is implemented here in the model integration. As a result, mass ¯uxes are in- the nested-mesh ocean circulation model recently de- troduced across the layer interfaces. The mass ¯uxes veloped by Ginis et al. (1998). A distinguishing char- are calculated diagnostically, along with their accom- acteristic of their model is the method by which regions panying ¯uxes of momentum, heat, and salt. of ®ne resolution are embedded into a more coarsely The effects of horizontal diffusion of momentum, resolved domain. The model employs a two-way inter- heat, and salt are estimated by the Smagorinsky non- active nesting technique and includes the following fea- linear viscosity scheme (Smagorinsky 1963). The ver- tures: 1) the interface where the two integration domains tical diffusion processes include three major mecha- dynamically interact with each other is separated from nisms of vertical turbulent mixing in the upper ocean, the change in resolution at the mesh interface; 2) the that is, wind stirring, shear instability, and convective interaction at the dynamical interface is expressed in the overturning.