While computational models of global climate show remarkable qualitative agreement, they also differ widely in their sensitivity to projected increases in greenhouse gases. They are all based on general circulation models of the atmosphere and ocean, but they often differ in detail in the way they account for observed climate. These differences become more apparent when the models are forced away from their present equilibrium.
These are the rises in global average temperature predicted by the main worldwide climate models as the amount of carbon dioxide in the atmosphere is doubled over the period of a century. Charles Jackson of UTIG and his group are attempting to quantify the uncertainties within the models that produce the spread in the predictions. (click for larger image)
Source: UN Intergovernmental Panel on Climate Change report 2001.
"There is enough variability among the predictions of these models to make it worthwhile to try to pin down and reduce the sources of uncertainty," says Research Associate Charles S. Jackson, a climatologist at The University of Texas Institute for Geophysics (UTIG) in Austin. "Model predictions of future climate provide an embarrassing range of possibilities. Moreover, models are currently incapable of reproducing some of the most volatile episodes of climate change that are well documented in the geologic record.
"Both these facts underscore the importance of identifying sources of modeling uncertainty. Some spring from the ways models represent physical processes. But others could be related to processes that the models may be missing altogether," Jackson says. With less uncertainty, he notes, the formulation of better policies to mitigate adverse effects of climate change will be less controversial and more scientifically defensible.
Jackson and his group are interested in problems that arise all along the axis of time. "The earth's climate is influenced by everything from the brief periodic El Niño episodes in the Pacific to the planet's orbital wobbles, over tens and hundreds of thousands of years," he says. In all its studies, the group takes advantage of UTIG's strength in the development and application of efficient algorithms for searching through and evaluating the ways in which model formulations match observational data.
Jackson's collaborators include UTIG Director Paul Stoffa and Professor Mrinal K. Sen, who pioneered the group's methods in estimating modeling uncertainties through stochastic (random or nondeterministic) "inverse modeling." The work of Sen and Stoffa focuses primarily on inverse modeling of the solid earth, working backward from the seismic data to infer the structure of the earth's crust and interior. Because there are multiple consistent interpretations of the seismic data, a statistical approach is required to quantify the uncertainties in any one particular interpretation. "The same methods can be applied to climate models and climate data," Jackson says.
Jackson works closely with colleague Rob Scott (the two are leading UTIG's climate research), with Zong-Liang Yang in the UT Department of Geological Sciences, and with UTIG postdoctoral researchers Faming Wang and Christina Holland. Youlong Xia, a postdoctoral researcher until 2003 (now at Princeton) and Qiaozhen Mu (now at the University of Montana) also worked with the group. In addition to funding for specific projects from the National Science Foundation (NSF), the group's activities receive support under a grant from the G. Unger Vetlesen Foundation.
A fascinating project, just now getting under way, teams the UTIG climate group with a distinguished colleague, Senior Research Scientist Frederick Taylor, Jr., of UTIG. Taylor is a geologist and paleoclimatologist with special expertise in the analysis of corals. He has documented the temperature history in the Western Pacific Warm Pool region, an area that is critical to the earth's climate and weather, by drilling and analyzing cores from living and fossil corals. These corals, which come from New Caledonia, Vanuatu, the Solomon Islands, and Papua New Guinea, contain a subseasonal record of climate during 100- to 200-year time segments thousands of years ago.
"Fred finds sea surface temperatures precisely recorded in the isotopic composition of calcium carbonate in the annual growth bands of the coral," Jackson says, "and we will use those data to learn something of the history of sea-surface temperature fluctuations that occur in association with ENSO phenomena." ENSO stands for El Niño/Southern Oscillation, the periodic pattern of tropical ocean surface warming and tropospheric wind shifts that affects climate worldwide. The coral data provide a unique perspective on how this leading mode of variability for the climate system is sensitive to changes in global climate. "Currently models have no agreement on what will happen to ENSO fluctuations in a world with more greenhouse gases," Jackson says. "Our approach is to understand the mechanisms for past changes in ENSO as a check on our understanding of what mechanisms may be important to future changes."
A second project deals not with seasonal change known in the present but abrupt changes that took place in the past. One of the most significant recent discoveries in climate research is the documentation of repeated periods of abrupt warming during the last Ice Age. Ice cores drilled in Greenland and sediment cores from the North Atlantic document a series of large flips between warm and cold climate between 80,000 and 10,000 years ago. These were double-digit swings (about 15 degrees Celsius), representing 60 percent of the total temperature change between glacial and interglacial climate.
"This information turned upside down our notion that climate only evolves gradually in pace with changes in the earth's orbital geometry," Jackson says. Some of these swings may have taken place over just a few years, rather than millennia--changes apparently much more abrupt and potentially punishing to the world environment than anything that has affected humanity over the past 10,000 years. "We don't understand fully the mechanisms of abrupt climate change, and our models neglect or minimize this extreme natural variability," Jackson says.
The abrupt climate change project is a three-year study by Jackson and collaborators Olivier Marchal of the Woods Hole Oceanographic Institute and Thomas Stocker of the University of Bern, Switzerland. The team is assessing the relative influence of rapid glacial melting on major changes in ocean currents, a mechanism sometimes invoked to explain the sudden changes. "We want to test the adequacy of theories that have been put forth to explain the sequence of abrupt climate change events in the North Atlantic. Our experimental design is unique as it allows the data to constrain what needs to occur in the model. Secondary data sources may then be used to evaluate the relative success or failure of any particular theory."
Most recently, Jackson, Sen, and collaborator Gabriel Huerta of the University of New Mexico Statistics Department, with funding from NSF, have begun to assess uncertainties related to model predictions of global warming. They want to determine how uncertainty in parameters affecting clouds, convection, and radiation affect a typical climate model's sensitivity to increases in atmospheric concentration of carbon dioxide. Accounting for sources of climate modeling uncertainty is currently a high priority for climate change research. "The need for policy makers to make informed decisions is placing added pressure on scientists to formulate better ways to account for uncertainty in the conclusions they infer from models," Jackson says. "This exercise also yields insights into fundamental properties of the climate system and the set of balances that maintain climate and its stability."
The primary tools for studying the physics of the climate system and for predicting future climate or simulating past climate are three-dimensional climate models (see sidebar). These models are large and complex, like the complex and interacting components of the real earth system that they represent, and it is difficult to formally separate the effects of individual processes. "Currently, the few methods that exist for assessing the strengths and weaknesses of models are not sophisticated enough," Jackson says.
Climate models follow the exchanges of energy between the sun and the various components of the climate system: atmosphere, oceans, land surface, and cryosphere [snow and sea ice]. The processes that govern these exchanges take place in the natural world on a broad spectrum of space and time scales. They range from microphysical events (the nucleation of raindrops on micron-size aerosols) through diurnal and seasonal cycles to long-term changes beyond the scope of most models (e.g., entire ice ages).
Climate models are best at keeping track of the large-scale exchanges of energy that take place within and among the fluid motions of the atmosphere and oceans. Global models resolve processes taking place on scales down to just one or two degrees of latitude or longitude, but many significant processes take place on smaller spatial scales that are not resolved in the models. Most important among these microphysical processes are the hydrological: those that govern cloud formation and rainout. To incorporate such processes, models use "parameterizations"--formulas that estimate the effects on the larger scales of the "subgrid-scale" physics. All parameterizations include parameters (think of them as knobs to turn and tweak) that provide flexibility so the model may be coaxed into better agreement with what we actually observe in nature.
The choice of values for these parameters inevitably introduces some arbitrariness into the modeling process, since the parameters often do not correspond directly to quantities physically measurable in nature. The arbitrary choices can and do lead to differences in the models' sensitivities to external forcings, such as their estimates of the degree of warming that will take place due to a doubling of greenhouse gases. Current climate research focuses on the task of understanding the way nature maintains energy balances within the climate system and on the equally difficult task of correctly representing these processes within computer simulations of climate.
Since the 1990s, the climate science community has organized a number of model intercomparison projects, in which a group of global models is given the task of reproducing observed climate or simulating climate states preserved in geologic history (paleoclimate), with similar inputs (forcings) and experimental designs. "These have been useful in quantifying a consensus and range of behaviors," Jackson says, "but it is important to remember that when models are tuned toward the mean of what is observed, they may no longer be fully representative of the realistic range of probable outcomes."
If we seek predictions that are optimum with respect to the combined uncertainty in the observations and model physics, Jackson says, "We need to identify a range of model configurations that are consistent with observational constraints."
Climate model responses to inputs depend nonlinearly on combined changes in model parameters, and the main limitation to quantifying modeling uncertainties has been the computational cost of evaluating the uncertainty associated with any given choice of parameter values or any given combination of parameters. The most accurate ways of estimating parameter interdependencies and uncertainties are probabilistic statistical analyses requiring hundreds to thousands of costly model runs per parameter under investigation.
The term "Bayesian" refers to the Rev. Thomas Bayes (1702-1761), a British mathematician and Presbyterian minister who formulated a special case of what is now known as Bayes's theorem. The French mathematician Pierre Simon de Laplace (1749-1827) independently rediscovered and extended Bayes's work in 1774, with greater clarity and generality, After more than a century of relative neglect, Bayesian ideas were most fully expounded in the 1930s by another English mathematician and physical scientist, Sir Harold Jeffreys, FRS (1891-1989).
Bayesian inference is an approach to statistics in which all forms of uncertainty are expressed in terms of conditional probabilities. While there has been much philosophical argument over Bayesian approaches, they have proved their immense practical merit since the rise of the computational sciences, which enabled Bayesian statistics to be used in more and more sophisticated ways.
Simply, given a belief or hypothesis (h) and evidence for or against it (e), we can write the probability of the hypothesis being true altogether as P(h) and the probability of the hypothesis being true given the evidence as P(h|e). From Bayes's theorem we deduce
P(h|e) ∝ [P(e|h) X P(h)]
In this proportion, P(h) is a "first guess" at the actual value, which we may assign on the basis of total ignorance or on the basis of any evidence we already have; it is called the "prior" probability of the hypothesis being true. P(e|h) is the likelihood or conditional probability for the evidence, and P(h|e) is called the "posterior" probability, the probability that the hypothesis is true given the evidence.
We may take as our "hypothesis" a complex, three-dimensional climate model containing many parameters (a vector m) and as our "evidence" the changing data, d, which can come from a new run of the model and which may incorporate new outside evidence (actual measurements or observations of the parameters). Using this information, Jackson and his group can take data from "forward" runs of the model and use the Bayesian inverse modeling tools to make inferences about the forcings or properties of the climate system. These would be difficult to obtain otherwise, since the quantities or processes of interest in the model are only indirectly or nonlinearly related to observed weather and climate data.
To unravel the tangled effects of each of the parameters, Jackson employs the Sen-Stoffa method, Bayesian stochastic inversion (see sidebar), and a sampling algorithm called multiple very fast simulated annealing (VFSA) to search through parameter space. "One of the virtues of our approach," Jackson says, "is that our implementation with multiple VFSA enables us to reduce the total number of model runs needed to obtain good statistics. Without multiple VFSA, most of the problems we are interested in solving would be intractable. The combination of these advanced stochastic sampling algorithms with TACC's high-performance resources provides unparalleled opportunities to make major advances toward answering these difficult questions."
Bayesian stochastic inversion asks, given the observed data, what is the probability that a given set of model parameters will reproduce the observations as a prediction? Jackson, Sen, and Stoffa tested the method on a simplified climate model and were able to quantify the relative influence on overall model outcomes of uncertainty in multiple nonlinearly related model parameters. More importantly, they were able to demonstrate that Bayesian stochastic inversion using multiple VFSA was one to two orders of magnitude more efficient than the Metropolis/Gibbs sampler, a more common algorithm for statistical sampling, against which the multiple VFSA algorithm was tested.
The level of agreement between climate model predictions and observations depends sensitively on choices of model parameter values. Each point in these plots represents a different model configuration for a single value of Parameter 3 as the other two parameters are varied.* The parameterizations come from climate model representations of the energetics of cloud evolution over time. More negative scores indicate better agreement of the model with observational data, but the multiple minima (areas that are the same color) show that the observations provide nonunique constraints for these sources of uncertainty in model physics. Charles Jackson and postdoctoral fellow Qiaozhen Mu collaborated in this study, which has been submitted to Geophysical Research Letters.
*Parameter 1 is the initial mass flux in downwelling regions of a cloud and Parameter 2 is the rate at which convective clouds consume available potential energy. Parameter 3 specifies the relative humidity at which clouds form within the model.
The more parameters that were included in the test, the more efficient VFSA proved to be. In one comparison, for example, VFSA converged on an answer after 2100 model runs, while the Metropolis/Gibbs analysis required 23,000. Jackson, Sen, and Stoffa published the work in July 2004 (An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions, Journal of Climate 17: 2828-2841).
"Our Bayesian stochastic inversion procedures constitute an infrastructure for letting observational data guide modelers to those model configurations that warrant further exploration," Jackson says.
Jackson and his group will be moving their climate research from Lonestar onto a new machine to be shared among UTIG, the Astronomy Department, and the Bureau of Economic Geology. The machine, called Wrangler, is located at TACC and consists of 128 Dell two-processor nodes with a total of 512 gigabytes of memory and 6.6 terabytes of disk storage. The processors are 3.2 GHz EM64T Xeon chips, each of which can address the entire 4 gigabytes of memory per node. Both Myrinet and Infiniband interconnects will be available to various node subsets. In addition, the memory subsystem ("frontside bus") runs at 800 MHz, making memory access faster than on other machines. "The rapid access and 64-bit arithmetic are ideal for the codes that we are using," Jackson says, "and we will be collaborating with TACC's HPC Systems group to get our codes up and running on Wrangler this spring."
Jackson believes that his group's activities will result in an important advance: much better understanding of the contributions and weightings of the many interacting processes represented in climate models. "Because our statistical analyses are independent of the model intercomparison work, they can serve as a check on and a complement to the results of that work," he says. "We're hoping that our findings will be of benefit to the entire climate modeling community, whether the topic is paleoclimate or current or future climate and whether the time scales are measured in decades or centuries or longer."
Research Feature - February 23, 2005