Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Climate Action

Academic Year 2019/2020

Learning outcomes

At the end of the course the student: - knows the basics of physical climatology; - knows the main statistical methods used in climate analysis; - can use the results of both numerical global climate simulations and regional climate models for future climate scenarios evaluation: - acquires abilities in communication on the subject and becomes familiar with the English terminology used in climatology; - knows how to use scientific literature.

Course contents

The course is organized in two modules delivered by two instructors run in parallel (2+2 hours of each module per week)

Module 1: Prof Michele Brunetti
Module 2: Prof. Erika Brattich

Below the course contents for the two modules:


Module 1

The Global Energy Balance

  • The nature of electromagnetic radiation and the physical laws of radiation
  • Planck’s Law of Blackbody Emission
  • Emission temperature of a planet
  • Greenhouse effect
  • Distribution of insolation
  • The global energy balance (incoming solar radiation, outgoing long-wave radiation, albedo)

Atmospheric Energy Transfer and Climate

  • Selective Absorption and Emission by Atmospheric Gases
  • The Lambert-Bouguet-Beer Law
  • Absorption rate and heating rate
  • Schwarzchild's Equation
  • Heuristic Model of Radiative Equilibrium
  • Radiative-Convective Equilibrium Temperature Profiles

Clouds and radiation

  • The radiative properties of clouds
  • A Simple Model for the Net Radiative Effect of Cloudiness
  • Observed Role of Clouds in the Energy Balance of Earth

The Energy Balance of the Surface

  • The Surface Energy Budget
  • Storage of Heat in the Surface
  • Sensible and Latent Heat Fluxes
  • Variation of Energy Balance Components with Latitude

Aerosols and Climate

  • Aerosol distribution
  • Volcanic Eruptions and Stratospheric Aerosols
  • Anthropogenic Aerosols and Atmospheric Sulfur

The Hydrologic Cycle

  • Water in the climate system
  • Terrestrial branch of the hydrologic cycle
  • Atmospheric branch of the hydrologic cycle
  • Latitudinal distribution of the water balance
  • The concept of evapotranspiration

The General Circulation of the Atmosphere

  • The energy balance of the atmosphere and the general circulation
  • The mean meridional circulation
  • Eddy circulation
  • The meridional transport of energy
  • The meridional transport of moisture
  • Angular momentum balance

The Orbital Parameter Theory of Ice Ages

  • Historical introduction
  • Eccentricity and the Sun-Earth distance
  • Obliquity and insolation
  • The variation of annual mean insolation
  • Orbital parameter evolution
  • Testing the theory
  • The middle pleistocene transition

Geochemical cycles

  • Early evolution of the atmosphere
  • The nitrogen cycle
  • the oxygen cycle
  • the carbon cycle
  • rate of storage and removal of gases in the atmosphere

The Earth Observation

  • The International Geophysical Year and the Global Observation System
  • A brief history of the ground base observation networks with a focus on the Italian network

Proxy Data

  • What proxy data are
  • Documentary reconstructions
  • The delta-O18 isotope ratio
  • Some examples of proxies: Corals, Palynology, Dendroclimatology, Ice cores, Sediments

The Problem of the Data Quality in Climatology

  • The importance of data quality in climatology
  • The example of ground based stations
  • Data error sources (instruments change, instrument and station relocation, solar radiation sheltering, in situ changes, observation rules changes)
  • The metadata
  • Some homogenization techniques

Principal Component Analysis/Empirical Orthogonal Functions (PCA/EOF)

  • What PCA is
  • Diagonalization of the covariance matrix (eigenvalues and eigenvectors)
  • Covariance and correlation matrix
  • Varimax rotation
  • Some example of PCA

Extreme Events Theory

  • General aspects of the extreme events theory
  • Extremal Types Theorem
  • The Generalized Extreme Value (GEV) distribution
  • Above threshold models and the Generalized Pareto distribution

Module 2


  • Components of the climate system
  • Introduction to GCMs.
  • Purpose and limitations of climate modelling
  • Historical development
  • Examples: Simulation of the 20th century to quantify the link between the increases in atmospheric CO2 concentrations and changes in temperature; CO2 emissions permitted for prescribed atmospheric concentration.
  • The structure of the atmosphere
  • Composition of the atmosphere

Climate variability

  • Introduction to climate variability (ENSO, NAO)
  • IPCC scenarios and emissions: Climate variability and weather forecasting

Climate feedback (F) and sensitivity (S)

  • Climate sensitivity and climate feedback: definitions and mathematical derivation.
  • Calculations of F and S due to: Change of S0 by 1%; Change of 1% in planetary albedo; Change of 1% in greenhouse parameter; Stefan Boltzmann feedback; Water vapour feedback; Ice albedo feedback; Cloud feedback; Energy-balance climate model (Budyko-Sellers model).
  • Zero dimensional Energy Balance Model
  • One dimensional Energy Balance Model
  • IPCC radiative forcings
  • Zero dimensional-2 layers model
  • The biogeochemical feedback: the Daisy-world model

Large-scale circulation in the ocean

  • Physical and chemical characteristics of the ocean
  • The “mixed layer”
  • Wind driven circulation
  • Shallow water equations
  • Different types of grids in climate models.
  • ENSO and Southern Oscillation Index
  • Ekman spiral and Ekman transport
  • Sverdrup transport
  • Stommel model
  • Density driven deep thermohaline circulation

Statistics in climate

  • Review of basic probability concepts
  • The Axioms of Probability
  • Conditional probability
  • Independence
  • Persistence as conditional probability
  • Empirical Distributions and Exploratory Data Analysis: robustness and resistance properties
  • Bayes’s Theorem and inference in climate
  • Indicators of position, dispersion and symmetry
  • Parametric Probability Distributions
  • Discrete distributions
  • Continuous distributions
  • Histograms
  • Scatterplots
  • Boxplots
  • Transformations
  • Standardized anomalies
  • Pearson and Spearman rank correlation
  • Lagged correlation
  • Running mean
  • Hypothesis testing: the elements of any hypothesis tests, test levels and p values, one-sided vs. two-sided tests, confidence intervals, error types
  • Parametric and non-parametric hypothesis testing
  • T-test for differences of mean
  • Resampling
  • Bootstrap
  • Mann-Kendall test
  • Elements of statistical forecasting
  • Introduction to use of R programming for statistics in climate


Dennis L. Hartmann: Global Physical Climatology ; Academic Press

Peixoto and Oort: Physics of Climate; American Institute of Physics; 1st edition (February 1, 1992)

Wilks: Statistical Methods in the Atmospheric Sciences, 3rd Edition (2011)

Teaching methods

Frontal lectures

Assessment methods

The final exam is inteded to verify the understanding/comprehension of all phenomenological, mathematical/statistical aspects of the topics dealt during the two modules.

The final exam consist in an oral examination during which the student will be asked generally three questions selected between the two modules.

The exam lasts 45 minutes on average.

Teaching tools

PC and Projector

Office hours

See the website of Michele Brunetti

See the website of Erika Brattich