Physics, Second Cycle
1. year
Course director:
Hours per week – 1. semester:

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

Content (Syllabus outline)

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.

Objectives and competences

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.

Intended learning outcomes

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.

Learning and teaching methods

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
Project work presentation, theoretical examination

Lecturer's references

SKOK, Gregor, BACMEISTER, Julio T., TRIBBIA, Joe. Analysis of tropical cyclone precipitation using an object-based algorithm. Journal of climate, ISSN 0894-8755, 2013, vol. 26, iss. 8, str. 2563-2579.
SKOK, Gregor, HLADNIK, Veronika. Verification of gridded wind forecasts in complex alpine terrain: a new wind verification methodology based on the neighborhood approach. Monthly weather review, ISSN 0027-0644, 2018, vol. 146, no. 1, str. 63-75.

SKOK, Gregor, ROBERTS, Nigel. Estimating the displacement in precipitation forecasts using the Fractions Skill Score. Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 2018, vol. 144, iss. 711, str. 414-425.

CEGLAR, Andrej, HONZAK, Luka, ŽAGAR, Nedjeljka, SKOK, Gregor, ŽABKAR, Rahela, RAKOVEC, Jože. Evaluation of precipitation in the ENSEMBLES regional climate models over the complex orography of Slovenia.

International journal of climatology, ISSN 0899-8418, 2015, vol. 35, iss. 9, str. 2574-2591.
ŽABKAR, Rahela, HONZAK, Luka, SKOK, Gregor, FORKEL, R., RAKOVEC, Jože, CEGLAR, Andrej, ŽAGAR, Nedjeljka. Evaluation of the high resolution WRF-Chem (v3.4.1) air quality forecast and its comparison with statistical ozone predictions. Geoscientific model development, ISSN 1991-959X, 2015, vol. 8, no. 7, str. 2119-2137.