Approximation methods: Variational methods, WKB approximation; time-indepdndent perturbation theory; time-dependent perturbation theory: Interaction picture, Fermi's golden rule, sudden and adiabatic approximations.

Scattering theory: Transition rates and cross sections, Lippmann-Schwinger equation, scattering amplitude, Green's functions; Born approximation; phase shifts and partial waves.

Second quantization: Fock-space representation for bosons and fermions, representation of many-body operators.

Electron-electron interaction: Hartree and Hartree-Fock approximations; Quasiparticles, Landau-Fermi liquid theory for interaction between quasiparticles, equilibrium properties of normal Fermi liquid, 3He: ideal Fermi liquid, transport of quasiparticles, current density.

Instruments and Measurement Systems: Instrument Response, Measurement Quality, Signal to Noise ratio, Measurement Artifacts, Instrument Response Time, Instrumental Time Resolution, Detection Limit and Sensivity, Sources of Uncertainties, Calibration procedures. Basic statistics, concept of error and uncertainty analysis, Error analysis, probability distribution functions, regression analysis, least square fit, goodness of fit, uncertainties in the fit, propagation of error for a simple linear system.

Introduction to hydrometeorology, hydrologic and bio geochemical cycles, Water vapour in atmosphere, Vertical gradients in atmosphere, Atmospheric Boundary Layer, Surface Energy balances, Sensible heat flux, Latent heat flux, heat budgets, Plant canopy interactions with the atmosphere. Evaporation, evapotranspiration and their measurements, empirical equations, potential evapotranspiration, Global carbon cycling, Leaf energy fluxes, vegetation dynamics, Canopy processes and Canopy resistance.

Unit I:

Unit 1: Structure and variability of Earth's ionosphere

Introduction to neutral upper atmosphere and its interaction with solar radiation: Thermal structure of the atmosphere, Heat balance and temperature profile of thermosphere, Dissociation and diffusive separation and thermospheric composition, Exosphere, Solar radiation at the top of the atmosphere, Attenuation of solar radiation in the atmosphere, thermal effect of radiation, photochemical effects of radiation, Airglow

Overview of Polar Geography and Climate; History of Indian Antarctic programme; Physical
characteristics; weather and climate, ice coring in Antarctica for Paleo-environment studies,
logistics of Antarctic Science, opportunities, Antarctic governance and protection of Antarctic
environment, International linkages.
Ice characteristics and physical oceanography of polar seas; Sea ice: types, physical and
mechanical properties, heat flux, temporal and spatial distribution, melting and freezing processes,

Introduction: definitions and background, variables, wind and flow, turbulent transports; Taylor’s hypothesis and observing techniques, boundary layer depth and structure Mathematical and conceptual tools: Turbulence and its spectrum; spectral gap; mean and turbulent parts; basic statistical methods; rules of averaging; turbulent kinetic energy; kinematic flux, eddy flux; stresses. Governing equations for turbulent flow: methodology, basic equations, simplifications and approximations, equations for mean variables in a turbulent flow.

History of satellite and radar meteorology; Orbits and navigation, Orbit perturbations, Meteorological satellite orbits, Satellite positioning, tracking, and navigation, Space-time sampling, Launch vehicles and profiles; Elements of radiative transfer - Basic quantities, Blackbody radiation, Radiative transfer equation, Gaseous absorption, Scattering, Solar radiation and surface reflection; Meteorological satellite instrumentation - Operational polar orbiting satellites, Operational geostationary satellites, Other satellite instruments, Satellite data archives; Radar - Radar basics, Convent