Recommended prerequisites for study tracks

General recommended knowledge and skills for you to have before applying to the programme:

Generally, good knowledge of bachelor's degree level physics and mathematical methods are needed as well as practical skills in scientific computing (e.g., Python). In order to successfully pursue Master's studies in the meteorology study track it is recommended that you have the following knowledge and skills before entering to the programme: 

• Physics: At least basic studies of physics (25 cr) is needed. You should be familiar with at least the following:
  
  • Newton’s 2nd law (conservation of momentum)
  • Kinemtics of circular motion. Centrifugal and tangential acceleration.
  • Newton’s law of gravitation
  • Harmonic oscillator
  • Concept of work. Kinetic energy and potential energy.
  • Concept and conservation law of angular momentum
  • Basics of statistical gas theory. Temperature, pressure and entropy as thermodynamical concepts.
  • Basics of electrodynamics and electromagnetism. Electric field, Coulombs law, Maxwell equations
  • Basics of electromagnetic radiation. Black body radiation laws, Electromagnetic wave and its mathematical representation. Refractive index
  • First and second laws of thermodynamics
  • Basic concepts of quantum physics: particle and wave duality, energy of a photon, discrete energy levels and transitions
  • Ideal gas equation of state
• Mathematics
  • Basics of vector algebra, e.g. dot and cross products of vectors, summation of vectors, calculation of the magnitude (modulus) of vectors
  • Complex number arithmetics, including Euler’s formula
  • Differentiation and integration of functions
  • Solving of first- and second-order differential equations
  • Nabla operations
  • Solving sets of linear equations using matrix algebra
  • Stokes’s theorem and Gauss’s divergence theorem
  • Basics of Fourier analysisBasics of vector algebra, e.g. dot and cross products of vectors, summation of vectors, calculation of the magnitude (modulus) of vectors
  • Examples of tasks you should be able to solve (link to be added here)
• Programming and statistics
  • some prior experience of programming and the Unix / Linux environment is desirable. However, be aware that Fortran is widely used in numerical weather prediction and climate models.
  • basic statistical concepts 

Compulsory prerequisite courses for Meteorology study track

In case you have not completed University of Helsinki's courses Introduction to Meteorology and Weather Observations, Atmospheric Thermodynamics, Introduction to Atmospheric Flow Dynamics, Introduction to Climatology and Physical Climatology or equivalent courses during your bachelor's degree, you need to complete them in the beginning of your Master's studies. 

FYS2031 Introduction to Meteorology and Weather Observations (5 cr)
• Meteorology as a field of science: basic concepts, research questions and approaches to solving them
• Structure and composition of the atmosphere
• Basics of atmospheric radiation transfer and the global energy budget
• Overview of global climate and atmospheric general circulation
• Application of basic physical principles to atmosphere: the primitive equations
• Geostrophic balance
• Hydrostatic stability
• Water in the atmosphere and precipitation processes
• Principles of weather predictions
• Climate changes and climate variability
• Classification of clouds
 

FYS2032 Atmospheric thermodynamics (5 cr)
• Thermodynamics of dry air: Ideal gas equation of state, first law of thermodynamics, adiabatic processes, potential energy, entropy, thermodynamic diagrams
• Thermodynamics of moist air: Different ways of expressing the water vapour content of air; virtual temperature; specific heats for moist air, adiabatic processes in undersaturated air.
• Thermodynamics of saturated air: Clausius-Clapeyron equation, pseudo-adiabatic and moist-adiabatic processes
• Hydrostatic balance
• Geopotential
• Hydrostatic stability, air parcel method for studying convection, Brunt-Väisälä frequency, conditional instability, levels of free convection and neutral buoyancy, CAPE
 

FYS2033 Introduction to atmospheric flow dynamics (10 cr)
• Real and apparent forced affecting the motion of an air parcel on a rotating planet
• Vertical distribution of pressure in the atmosphere, as derived from the requirement of hydrostatic balance. The use of pressure as a vertical coordinate. Geopotential.
• Eulerian and Lagrangian frameworks in meteorology.
• Advection.
• Equation of motion in complete vector and component form in spherical coordinates
• Scale analysis of the equation of motion
• Rossby number.
• Continuity equation
• Primitive equations in pressure coordinates
• Baroclinic vs. barotropic atmosphere
• Thermal wind
• Trajectories and streamlines
• Kinematic and adiabatic methods for estimating vertical motion
• Components of the ageostrophic wind: isallobaric, advective, convective, frictional
• Circulation, absolute vorticity and relative vorticity
• Potential vorticity, and consequences of its quasi-conservation
• Vorticity equation
• Stream function and velocity potential
• Secondary circulation in the atmospheric boundary layer.
• Ekman pumping

FYS2034 Introduction to climatology (2 cr)
• The main physical and geographical factors affecting climate
• Global geographical distributions
• Climate classification systems (particularly Köppen’s climate classification)
• Climate in Finland
 

FYS2035 Physical climatology (3 cr)
• Transfer of solar and terrestrial radiation in the atmosphere
• Radiative balance: surface, atmosphere, surface and atmosphere together
• Variation of temperature in soil
• Sensible and latent heat fluxes
• Cycle of water in the surface-atmosphere system
• Energy budgets of surface and atmosphere
• Formation of the vertical temperature distribution in the atmosphere
• The climatic history of Earth
• Energy budget view on climate variability
• Effects of deforestation and desertification on climate

The Atmospheric Chemistry and Aerosol Physics study track is designed for students with a solid background in natural sciences, particularly those with prior knowledge in physics, chemistry, mathematics, or atmospheric/environmental sciences. The track is also open to students from applied science backgrounds who can demonstrate sufficient foundational competence. 

In case you have not completed University of Helsinki's course  (5 cr) or equivalent courses during your bachelor's degree, you need to complete them in the beginning of your Master's studies. It is also recommended that students of this track have studied basics of thermophysics and thermodynamic potentials before entering to the programme or at the beginning of the master's studies, e.g. FYS2001/Basics of Thermophysics (5 cr) and FYS2002/ Thermodynamic Potentials.

Typical student profiles include:

• Bachelor’s graduates in physics or chemistry, with an interest in environmental applications, modelling, or experimental work.
• Students from atmospheric sciences, geophysics, meteorology, or related Earth and environmental sciences.
• Students from applied universities with an engineering background, especially those in environmental engineering, chemical engineering, or applied physics. These students may be required to complete selected prerequisite studies to strengthen their theoretical background.
• Students from mathematics, data science or computer science, who wish to apply computational methods in atmospheric or aerosol research, provided they are willing to supplement their knowledge with basic physical and chemical principles.

Recommended other knowledge before entering to the programme: 

• Physics: basics of physics and principles of mechanics and thermodynamics are particularly important. You should be familiar with at least the following if you focus more in aerosol physics:
  • Newton’s laws
  • Concept of work. Kinetic energy and potential energy
  • Laws of thermodynamics
  • Entropy and free energies as thermodynamic concepts
  • Concept of ideal gas and the ideal gas equation of state
  • Basics of statistical gas theory
  • Basics of electrodynamics and electromagnetism (e.g. electric field, charge, Coulomb’s law)
  • Basics of electromagnetic radiation: black body radiation, refractive index, electromagnetic spectrum
• Chemistry: If you plan to focus more on the atmospheric chemistry,  it is recommended that you have studied first year university studies in Chemistry (min 25 cr). See an example of the content of basis studies, Chemistry, Basic Studies (25 cr) 
• Mathematics
  • Basics of vectors and linear algebra
  • Complex numbers
  • Differentiation and integration of functions
  • First and second degree ordinary and partial differential equations
  • Solving sets of linear equations using matrix algebra
• Programming and statistics
  • some prior experience of programming and statistical analysis of observations
  • basic statistical concepts 

Hydrosphere geophysics has its basis on the theories of classical physics and in advanced high school mathematics and physics. In order to successfully pursue MSc studies in the geophysics of the hydrosphere study track it is recommended that you have the following knowledge and skills before entering to the programme: 

• Physics: principles of mechanics and thermodynamics are particularly important. You should be familiar with at least the following:
  • Principles of mass, momentum and energy conservation
  • Basic knowledge of fluid dynamics
• Mathematics
  • Fundamentals of vectors and linear algebra
  • Complex numbers
  • Differentiation and integration
  • First and second degree ordinary and partial differential equations
• Programming and statistics
  • Ability to demonstrate research results tabularly and graphically  
  • Understanding of standards of scientific writing
  • Basics in programming

In case you have not completed University of Helsinki's courses Basic Course in Oceanography and Basic Course in Hydrology or equivalent courses during your bachelor's degree, you need to complete them in the beginning of your Master's studies.

In order to successfully pursue Master's studies in the biosphere-atmosphere cycles study track it is recommended that you have studied some bachelor's level studies in Forestry and Chemistry. It is also useful to know basics of fluid phenomena. You can also study them in the beginning of your Master's studies. 

Students from various backgrounds can successfully study in this study track. It is required that applicants have at least 60 cr of studies in Physics, Chemistry, Forestry, Biology, Technology or Environmental Sciences.