Enrollment in the 3rd study year.

Completed 2nd year course Introduction to Meteorology, or equivalent

Passed problem-solving written examination and seminar work is a prerequisite for the theoretical part of the examination.

Conservation law: Momentum equations on the sphere. Conservation of mass. Conservation of energy. Scale analysis and simplification of the momentum equations. Scale analysis of the thermodynamic equation. Adiabatic processes. Potential temperature and static stability.

Derivation of the conservations laws in the system with the pressure vertical coordinate. Comparison of the height and pressure vertical corrdinate systems.

Flow dynamics on synoptic scales: Solutions for stationary and balanced winds. Diagnosis of vertical velocity. Surface pressure tendency.

Wind shear and thermal wind. Weather maps. Polar front. Baroclinic and barotropic atmosphere. Definition of circulation and vorticity. Bjerkness circulation theorem. Vorticity equation in height and pressure systems and its scale analysis. Simplification of the vorticity equation for synoptic scales. Conservation of absolute vorticity. Observed properties of synoptic motions in midlatitudes.

Perturbation method for Navier-Stokes equations: Method of linear pertubations applied to momentum and vorticity equations. Helmholtz theorem. Kinematics of synoptic flow. F-plane and beta-plane. Phase and group velocity, wave dispersion. Rossby waves.

Phase and group velocity of Rossby waves. Application to weather maps.

Quasi-geostrophic theory: quasi-geostrophic approximations. Quasi-geostrophic vorticity equation. Quasi-geostrophic geopotential forecasting. Quasi-geostrophic omega equation. Ageostrophic wind. Hydrodnamic instability.

Barotropic and baroclinic instability. Two-layer model of baroclinic instability, its construction and solutions for instability development.

Vertical motions in baroclinic model. Develoment and life cycle of midlatitude cyclone. Energetics of baroclinic waves. Eady and Sutcliff models for baroclinic development.

J.E. Martin: Mid-Latitude Atmospheric Dynamics. J. Wiley & Sons, Ltd.
J.R. Holton: An introduction to dynamic meteorology. Academic Press.
H.B. Bluestein: Synoptic-Dynamic Meteorology in Midlatitudes, Volumes I,II. Oxford University Press.

Systematic introduction of Navier-Stokes equation for atmospheric motions on synoptic scales in the midlatitudes. Basic analytical solutions for stationary and time-dependent synoptic-scale motions. Quasi-geostrophic theory and analytical solutions for the baroclinic development. Analysis of weather maps in

process in midlatitudes.

Knowledge and understanding: Knowledge of conservation laws applied to the atmosphere. Understanding of the multi-scale nature of atmospheric processes and methods for the simplification of the Navier-Stokes equations. Knowledge of the baroclinic instability process and application of the linear wave solutions methods to complex equation systems.

Understanding of differences between analytical soltuions and real state presented on weather maps.

Application: Students will learn to recognize,

define, and solve problems in atmospheric dynamics on synoptic scales as well as to

recognize and discuss differences between theoretical solutions and real atmopsheric motions.

Reflection: The course builds systematic understadning of atmospheric dynamics on synoptic scales. Students are trained to recognize and analyze weather map based on underlying physical laws.

Transferable skills: Scale analysis. Systematic application of the linearization method and analytical wave solutions of the systems of non- linear partical differential equation.

Lectures, tutorials, discussion and training by using daily weather maps, homeworks and consultations.

2 written tests (mid-term and end-term) applied towards the problem-solving examination, problem-solving examination,
seminar presentation, theoretical examination
Grades: 1-5 (fail), 6-10 (pass) (inagreement with the Statutes of the Univesity of Ljubljana)

Žagar, N., M. Žagar, J. Cedilnik. G. Gregoric and J. Rakovec, 2006: Validation of mesoscale low- level winds obtained by dynamical downscaling of ERA40 over complex terrain. Tellus, 58A, str. 445-455.
Žagar, N., G. Skok and J. Tribbia, 2011: Climatology of the ITCZ derived from ERA Interim reanalyses. J. Geophys. Res., 116, D15103, doi:10.1029/2011JD015695.
Žagar, N., K. Terasaki and H. Tanaka, 2012: Impact of the vertical discretization of analysis data on
the estimates of atmospheric inertio-gravity energy. Mon. Wea. Rev., 140, 2297-2307.

Žagar, N., L. Isaksen, D. Tan and J. Tribbia, 2013: Balance properties of the short-range forecast errors in the ECMWF 4D-Var ensemble. Q. J. R. Meteorol. Soc., 139, 1229-1238. DOI: 10.1002/qj.2033