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C-SPARC 2008 Summer School 

Dynamics, long-term memory, and trends in the climate system

Lectures and Schedule

Thursday night discussion led by Ted Shepherd.
Introduction to R from Dave Stephenson. A small demo of R from Dave Stephenson.
Commands in R used to do the figures
Data files for the R routines: BELTS_T2.txt, TEMP.TXT, globalmean.txt
To get R source code, go to www.r-project.com.

Syllabus

David Karoly

1. A brief history of detection and attribution of climate change

Covering the paper by Madden and Ramanathan in 1980 that first mentions fingerprints and attribution, to the IPCC assessments in 1990, 1995, 2001 and 2007.

2. At what spatial scale can an anthropogenic influence on climate change be identified?

Discusses identification of an anthropogenic influence on climate at different scales, including down to the single grid box.

3. Detection of a future emerging signal of anthropogenic climate change at the regional scale

Assesses when, where and at what scale a future climate change signal is likely to be able to be detected.

Slava Kharin

1. Fundamentals of statistical methods in climate

The first introductory lecture deals with basic concepts of probability, random variables and distributions. Key concepts in statistical inference, such as estimation and hypothesis testing, are introduced. Two major types of data analysis, exploratory analysis and confirmatory analysis, are outlined.

2. Hypothesis testing

This lecture concentrates on the main ingredients of hypothesis testing. Structure and terminology of a test are introduced. The concept of statistical significance and two types of errors in a statistical test are discussed. Local significance and global (field) significance are defined. The role of auto-correlation in statistical analysis of time series is examined.

3. Climate change detection and attribution

This lecture introduces statistical methods to detect a climate change signal in a noisy background of an incompletely observed climate. These methods are illustrated through recent studies of anthropogenic influence on global temperature and precipitation trends.

Paul Kushner

1. Annular modes and stratosphere-troposphere coupling

This lecture will be organized around the annular modes in the troposphere and stratosphere. I’ll start with a start with a brief description of the observed structure of the annular modes to make the point that in the troposphere the AMs represent a vacillation of the position of the jet stream but in the stratosphere the AMs represent variations in the strength of the polar vortex. I will then discuss theories for stratosphere-troposphere coupling mainly as manifested in annular mode signals but also touching on the Perlwitz & Harnik ideas on wave reflection & absorption. Finally, I will make a connection via fluctuation-dissipation ideas to the atmospheric circulation response to climate change.

2. Atmosphere-ocean coupling and variability

Timescales of the atmosphere/land system. New timescales introduced by coupling to the ocean (thermodynamic/mixed layer timescales, timescales of diffusion and upwelling, timescales of oceanic wind-driven circulation, timescales of tropical variability, and perhaps timescales of external forcing). Characterizing internal variability of the ocean-atmosphere system (Manabe & Stouffer, Dommenget & Latif). Annular modes and annular mode responses in the coupled ocean-atmosphere system.

John Scinocca

1. Simple models of stratospheric variability

This lecture considers the question of what are the essential dynamical ingredients required to account for the observed seasonal and interannual variations of the stratospheric circulation and its inter-hemispheric differences. Much of these dynamics are described by so called “simple models” of the real atmosphere. Here these models will be introduced and used to identify the primary dynamical mechanisms.

2. Stratospheric sudden warmings

This lecture will discuss the dynamics which underlie the phenomenon of stratospheric sudden warmings (SSWs). Building on ideas from the first lecture, two distinct perspectives of stratospheric variability associated with SSWs will be presented: one in which SSWs are viewed as driven by large-amplitude wave forcing events initiated in the troposphere, and the other in which SSWs are viewed as arising from internal nonlinear stratospheric dynamics. The statistical properties of SSWs as understood from models and observations will be reviewed.

3. The “tropical flywheel” as a source of long-term memory

Due to the abeyance of thermal wind balance towards the equator, radiative damping has little impact on tropical stratospheric zonal-mean winds. Anomalies in these low-latitude winds can thus persist on interannual time scales, providing an internal source of interannual mid-latitude stratospheric variability. This mechanism for long-term memory is examined in models and observations.

David Stephenson

1.Statistical modeling

Some basic concepts in statistical modeling such as reasons for using a statistical model, maximum likelihood estimation, model checking, model comparison, etc. Illustrated using linear and generalized linear models. 

2. Introduction to time series modeling

Basic concepts in time series modeling such as additive decomposition, strong and weak stationarity, autocovariance, AR and MA processes.

3. Deterministic and stochastic trend models

Parametric and non-parametric models for deterministic trends. Time series models for stochastic trends: long-range (FARIMA) and non-stationary (ARIMA) processes.

Rich Stolarski

1. Measurement of ozone and the nature of its variability

In this lecture I will talk about the various methods for measuring ozone and their strengths and weaknesses. I will discuss the interpretation of remotely-sensed data and will emphasize issues of maintenance of calibration over long records. I will then discuss the ozone record itself emphasizing spatial and temporal coverage. From this we will develop a picture of how ozone behaves on a variety of time scales from daily variability to seasonal variation to long-term changes.

2. Forcings that cause ozone change: lessons learned from simulation models

In this lecture I will briefly develop the theory of forced ozone change. I will briefly review ozone photochemistry and then will consider a variety of forcings that can perturb the chemistry or the transport of ozone. These will include chlorine and bromine compounds, nitrogen oxides, solar uv, volcanic aerosols, and greenhouse gas cooling of the upper stratosphere. Model simulations will be used as a guide for what to expect in the atmosphere.

3. Time-series regression models and the search for causality of change

In this lecture I will bring together the information on ozone measurements with that on expected forced changes. I will use a time-series regression model to examine questions of detection and estimation of trends, determination of the beginning of recovery, estimation of solar cycle, etc. I will emphasize the importance of estimating uncertainty and the role that measurement uncertainty plays in drawing conclusions.

Betsy Weatherhead

1. Introduction to time series analysis

We know that our data have temporal autocorrelation—now what? The first step in working with environmental time series is to determine what type of autocorrelation exists in the data. This lecture will describe the basic categories of autocorrelation and tools to help identify which ones are in your data. Some discussion will include what the different types of autocorrelation mean about the fundamental processes controlling the climate system.

2. Time scales of change

Natural variability occurs on all levels in the unperturbed environment. Daily, monthly, annual and decadal variability is discussed relative to climate change. How do we know if we have enough data to be representative of longer-term change? Number of years to detect a trend will be discussed under some basic statistical assumptions. However, decadal variability can also limit how quickly a trend can be accurately identified.

3. Attribution of change

What tools do we have to attribute change? Tools for comparing data to model results will be summarized. Clear signatures of change include geographic and seasonal changes. Some statistical tools, including fingerprinting methods exist and will be reviewed. In all cases, scientific judgment and critical statistical interpretation of data are critical to understanding and attributing any change.