MODES - Modal view of atmospheric circulation
Spherical harmonics have been used extensively for representing many geophysical quantities over the globe. They are useful for the decomposition of global circulation data because they are eigensolutions of the global barotropic vorticity equation involving the Laplace operator on the sphere. Furthermore, spherical harmonics are used as basis functions for the numerical discretization of dynamical terms of the global prognostic equations for numerical weather prediction (NWP) in some of the major global NWP models (e.g. ECMWF). A scale-dependent distribution of atmospheric kinetic energy at a given horizontal level is readily produced from spherical harmonics as a function of the global wave number. It is however often more desirable to represent ﬂow patterns not only of the horizontal velocity components but also of the associated mass-ﬁeld variables as functions of longitude, latitude and height. Our picture of the atmosphere is that of a vibrating system with many modes of oscillations, like a musical instrument. Hence, it is desirable to have some vector functions to represent simultaneously both the wind ﬁeld and the mass ﬁeld corresponding to the various modes. Such modes are provided by the eigensolutions of the primitive equations linearized around a simple reference state of rest, and they are known as normal modes. A daily updated web site with modal decompositions of ECMWF deterministic forecasts is here.
This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 28015, ERC StG MODES.