Climate Change

Apply the Stefan-Boltzmann law to calculate the effective temperature of the Earth, treating it as a black-body and ignoring the atmosphere.

Quantify the magnitude of the greenhouse effect by comparing the Earth's actual average surface temperature to its effective black-body temperature.

Relate the molecular structure of key greenhouse gases (e.g., H₂O, CO₂, CH₄) to their ability to absorb infrared radiation, and rank these gases by their contribution to the total greenhouse effect.

Calculate the Earth's surface temperature using a simple one-layer atmospheric model.

Define radiative forcing (ΔF) and calculate the forcing for a doubling of atmospheric CO2 using the standard logarithmic approximation.

Derive the hydrostatic equilibrium equation and use it to explain the vertical pressure structure of the atmosphere.

Derive the barometric formula to show how atmospheric pressure decreases exponentially with altitude in an isothermal atmosphere.

Derive the dry adiabatic lapse rate from the first law of thermodynamics and the hydrostatic equilibrium equation.

Define optical depth and apply the Beer-Lambert law to calculate the attenuation of radiation through a simplified atmospheric layer.

Synthesize the concepts of optical depth and atmospheric structure to explain why greenhouse gas absorption and emission occur in distinct layers.

Using a representative plot of Earth's outgoing longwave radiation (OLR) spectrum, estimate the fraction of total energy that escapes through the primary atmospheric window and explain its significance.

Analyze how increasing greenhouse gas concentrations alters the outgoing longwave radiation spectrum.

Formulate a simple mathematical expression for a climate feedback loop, and use it to calculate the final temperature change for a given initial forcing and feedback factor.

Explain the thermodynamic basis of the Clausius-Clapeyron relation and its application to atmospheric water vapor.

Using the Clausius-Clapeyron relation, perform a back-of-the-envelope calculation to estimate the magnitude of the water vapor feedback.

Incorporate a temperature-dependent albedo into a simple energy balance model to quantify the strength of the ice-albedo feedback.

Using the concept of the lapse rate, perform a back-of-the-envelope calculation to demonstrate how a warmer, moister atmosphere creates a negative feedback.

Perform a simple calculation to illustrate how a cloud's altitude and optical depth determine whether its net effect on the Earth's energy balance is one of warming or cooling.

Define Equilibrium Climate Sensitivity (ECS) and calculate its value using a simple energy balance model that incorporates a feedback parameter.

Estimate the order of magnitude of the Earth's major carbon reservoirs (atmosphere, oceans, land biosphere, and lithosphere).

Compare the magnitudes of the main natural fluxes of carbon (e.g., photosynthesis/respiration, ocean-atmosphere exchange) with anthropogenic emissions.

Perform a 'back-of-the-envelope' calculation of global CO2 emissions from fossil fuel combustion using energy consumption data.

Describe the methodologies and uncertainties involved in estimating carbon emissions from land-use change.

Analyze the partitioning of anthropogenic CO2 emissions between the atmosphere, ocean, and land biosphere sinks, using data from the Global Carbon Budget.

Model the decay of an atmospheric CO2 pulse using a multi-box model to understand its long residence time.

Critically assess the statistical adjustments (e.g., for time-of-observation bias, station moves, and urban heat island effects) used in the construction of global temperature datasets.

Estimate the trend in a global mean temperature time series, implementing statistical tests that account for autocorrelation and natural variability signals (e.g., ENSO).

Analyze the methods and data used to quantify global mean sea-level rise, including satellite altimetry and tide gauges, and evaluate the major sources of uncertainty.

Analyze the methods and data used to quantify global glacier mass balance, including satellite gravimetry and in-situ measurements, and evaluate their associated uncertainties.

Describe the physical basis of a key climate proxy, such as the relationship between oxygen isotope ratios (δ¹⁸O) in ice cores and local temperature.

Evaluate the statistical methodologies for paleoclimate reconstruction, focusing on the challenges of proxy calibration (e.g., non-stationarity) and uncertainty quantification.

Formulate the multiple linear regression model used in optimal fingerprinting, specifying the dependent and independent variables used to separate anthropogenic and natural climate signals.

Analyze the IPCC's formal system for evaluating and communicating uncertainty in its attribution statements.

Evaluate the argument that recent warming is primarily caused by natural forcings, with a focus on solar activity.

Describe the basic architecture of a General Circulation Model (GCM), distinguishing between resolved physical processes and parameterized processes (e.g., clouds).

Explain the methods used to validate climate models, including hindcasting against historical and paleoclimatic data, and the use of multi-model ensembles (e.g., CMIP).

Distinguish between a climate 'projection' (a response to a given emission scenario) and a weather 'forecast' (an initial value problem), and explain why this distinction is critical when evaluating model skill.

Critically assess the argument that models are unreliable because they are 'tuned' to match past observations, considering the trade-offs between model fidelity and complexity.