Quantile Regression for Trend Analysis

Introduction
Quantile regression extends ordinary least-squares regression to quantiles of the response variable. Ordinary regression is a model for the conditional mean, where the mean is conditional on the value of the explanatory variable. Likewise, quantile regression is a model for the conditional quantiles. For trend analysis the explanatory variable is time. Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. The quantiles mark a set of ordered data into equal-sized data subsets.

The software is downloaded from the internet and installed on a computer. A data set from the internet is imported into a software session. An exploratory plot of the data is created to visualize the trends. A quantile regression model is run on the data to quantify the trends and determine their statistical significance.

Equipment

1. Computer running Macintosh, Linux/Unix, or Windows
2. Internet connection
3. R for statistical computing (http://www.r-project.org/) [1]
Time Needed
Approximately 20 minutes.

Procedure
1. Download and install R.
Tip: Only the base directory is needed.

2. Click on the icon to start R. With Linux/Unix, type the letter R from a command window.

3. Read the data into an R session by typing on the command line:
StormMax=read.csv("http://myweb.fsu.edu/jelsner/
extspace/extremedatasince1899.csv",T)
Caution: Type it all on a single line. The quotes must be bidirectional.

4. Subset the cyclones by basin and by year after 1977 (satellite era) by typing:
StormMaxBasin=subset(StormMax,Region=="Basin")
StormMaxBasin=subset(StormMaxBasin,Yr>1977)
5. Make the columns of the data set available by name by typing:
attach(StormMaxBasin)
6. Create an exploratory plot of the annual lifetime maximum wind speed (intensity) as a function of year by typing:
x=boxplot(Wmax~as.factor(Yr),plot=F)
boxplot(Wmax~as.factor(Yr),ylim=c(35,175),
xlab="Year",ylab="Intensity (kt)")
xx=1:32
abline(lm(x$stats[5,]~xx),col="red")
abline(lm(x$stats[4,]~xx),col="blue")
abline(lm(x$stats[3,]~xx),col="green")
7. Install and load the quantreg package developed by Roger Koenker [2]. Then print the reference citation.
install.packages("quantreg")
library(quantreg)
citation("quantreg")
8. Summarize the results of the quantile regression model at the upper quantiles 0.75, 0.9, and 0.95.
summary(rq(Wmax~Yr,tau=c(0.75,0.9,0.95)),se="iid")
Tip: The standard errors (se= argument) can be estimated using other methods, type ?summary.rq
9. Plot the model results.
model=rq(Wmax~Yr,tau=seq(0.2,0.8,0.1))
plot(summary(model,alpha=0.05,se="iid"),
parm=2,pch=19,cex=1.2,mar=c(5,5,4,2)+0.1,
ylab="Trend (kt/yr)",xlab="Quantile")
Troubleshooting

Make sure there is permission on the computer to install software.

Make sure the commands are typed exactly as shown with bidirectional double quotes.

If copy/paste is used, make sure to change the quotations to bidirectional.

Anticipated Results
The exploratory plot should verify the lack of trend in the median lifetime maximum intensity. It should show a tendency for the strongest cyclones (higher quantiles) to get stronger over time. The statistical significance of the trends is assessed with a quantile regression model and the results are plotted.

References

[1] R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org (2006).

[2] Koenker, R. quantreg: Quantile Regression. R package version 4.10. http://www.r-project.org (2007)

Acknowledgments
Thanks go to all involved with the R project for statistical computing. Special thanks go to Thomas Jagger for his statistical help. The work is supported by the U.S. National Science Foundation, Risk Prediction Initiative of the Bermuda Institute for Ocean Studies, and the Florida Catastrophic Storm Risk Management Center of Florida State University.

Physical Geography of Hurricanes

Named after a Caribbean god of maleficence, the hurricane is an awesome, yet deadly and destructive natural phenomenon of the Earth's occasionally tumultuous atmosphere. Labeled a typhoon in the Pacific Ocean west of the International Dateline and a cyclone over the Bay of Bengal and Arabian Sea, a hurricane is powered by the heat and moisture of the tropics rather than temperature differences across latitudes, as is the case for the more common extratropical cyclone.

A hurricane begins as an area of low air pressure over warm ocean waters (at least 27 degrees Centigrade down to 50 meters below the sea surface). As a result of atmospheric instability, the area of low pressure features numerous showers and thunderstorms that, over several days, organize the winds into a counterclockwise (clockwise in the Southern Hemisphere) swirl. The swirl in turn organizes the existing thunderstorms and helps new thunderstorms develop. The swirl then becomes a tropical storm when the circulating wind speeds, estimated at 10 meters above the ocean, exceed 17 meters per second (averaged over a one-minute time interval).

When the wind speeds reach 33 meters per second or more the tropical storm is called a hurricane. Once formed, the hurricane winds are maintained by the import of heat from the ocean at high temperature and the export of heat at lower temperature in the upper troposphere (near 16 kilometers) similar to the way a steam engine converts thermal energy to mechanical motion.

On average 50 hurricanes occur worldwide each year. Hurricanes develop during the time of the year when the ocean temperatures are hottest. Over the North Atlantic (including the Gulf of Mexico and Caribbean Sea) this includes the months of June through November with a sharp peak from late August through the middle of September when the direct rays of the summer sun have had the largest impact on sea temperature. Worldwide, May is the least active month for hurricanes, while September is the most active.

Hurricanes vary widely in intensity as measured by their fastest moving winds. Hurricane intensities are grouped into five categories (Saffir-Simpson scale) with the weakest category-one winds blowing at most 42 meters per second and the strongest category-five winds exceeding speeds of 69 meters per second. Three category five hurricanes hit the United States during the 20th century including the Florida Keys Hurricane in 1935, Hurricane Camille in 1969, and Hurricane Andrew in 1992.

Hurricanes also vary considerably in size (spatial extent) with the smallest hurricanes measuring only a few hundred kilometers in radius (measured from the eye center to the outermost closed line of constant surface pressure) and the largest exceeding a thousand kilometers or more.

Strong winds are the defining characteristic of a hurricane. Wind is caused by the change in air pressure between two different locations. In the eye of a hurricane the air pressure, which is the weight of a column of air from the surface to the top of the atmosphere, is quite low compared with the air pressure outside the hurricane. This pressure difference causes the air to move from the outside of the hurricane inward toward the center of the hurricane.

By a combination of friction as the air rubs on the ocean below and the spin of the Earth as it rotates on its axis, the air does not move directly inward but rather spirals in a counterclockwise direction toward the region of lowest pressure. The vertical component of the Earth's spin is too weak to support a spiral within about 5 degrees of latitude from the Equator so hurricanes do not develop there.

To a first approximation, the pressure difference between the eye and the surrounding air determines the speed of the wind. Since the pressure outside the hurricane is roughly uniform, a hurricane's central pressure is another measure of a hurricane's intensity. The lower the central pressure the more intense the hurricane. Pressures inside the most intense hurricanes are among the lowest that occur anywhere on the Earth's surface at sea level.

In the largest and most intense hurricanes (like Hurricane Katrina in 2005), the strongest winds are located in the eyewall that surrounds the nearly calm eye. If the hurricane is stationary (spinning, but with no forward motion) the field of winds is shaped like a torus, with a calm center and the fastest winds forming a ring around the center. Concentric rings of incrementally weaker winds are analyzed outward from the core of strongest winds.

The distance from the center of the hurricane to the location of the hurricane's strongest winds is called the radius of maximum winds. In well-developed hurricanes, the radius of maximum winds is found at the inner edge of the eyewall. This distance varies considerably from hurricane to hurricane and, due to cycles of eyewall replacement, even from day to day for a particular storm.

While the wind just above the ocean surface spirals anticlockwise toward the center, the air at high altitudes blows outward in a clockwise spiral. This outward flowing air produces thin cirrus (feathery) clouds that extend great distances (thousands of kilometers) from the center of circulation and the presence of these clouds may be the first sign that a hurricane is approaching.

Hurricanes are steered by large-scale wind streams in the atmosphere above the surface and by the increasing component of the Earth's spin away from the equator. In the deep tropics these forces push a hurricane slightly north of due west (in the Northern Hemisphere). Once north of about 23 degrees of latitude a hurricane tends to take a more northwestward track then eventually northeastward at still higher latitudes. This creates the parabolic shaped track often observed on maps of historical hurricanes. Local fluctuations in the magnitude and direction of steering can result in tracks that deviate significantly from this pattern.

Landfall occurs when the hurricane center crosses a coastline. Because the fastest winds are located in the eyewall it is possible for a hurricane's fastest winds to be over land even if landfall does not occur. Similarly it is possible for a hurricane to make landfall and have its fastest winds remain out at sea. Fortunately, the winds slacken quickly after the hurricane moves over land. Hurricanes made landfall in the United States at an average rate of five every three years during the 20th century.

Winds blowing overland from a hurricane destroy poorly constructed buildings and mobile homes. Debris such as signs, roofing material, and small items left outside become flying projectiles adding to the destructive power of the wind.

Besides the destructive power of the winds, hurricane damage results from two other causes: flooding from torrential rainfall and storm surge. Rainfall is the quantity of water, expressed in millimeters, that falls from the hurricane in a specified area and time interval. Hurricanes derive energy from the ocean by evaporating the water into the air that then gets converted back to liquid water through condensation inside thunderstorm clouds. The water falls from the clouds as rain, and the stronger the hurricane thunderstorms, the greater the amount of rain and thus the greater the potential for flooding.

The amount of rainfall deposited overland from a hurricane depends on many complicated factors including hurricane intensity, forward speed, and the underlying topography. The rainfall of a hurricane can intensify when the strong winds carry the moisture up a mountainside. Antecedent moisture conditions also play a role in whether and to what extent flooding will occur from a hurricane. Freshwater flooding from hurricanes can be a serious danger even hundreds of kilometers from point of landfall.

Bands of showers and thunderstorms that spiral inward toward the hurricane center are the first sensible weather experienced as a hurricane approaches. High wind gusts and heavy downpours occur in the individual rain bands, with relatively calm weather occurring between the bands. Brief tornadoes can form in the rain bands especially as the hurricane crosses the coastline.

Storm surge is ocean water that is pushed toward the shore by the force of the winds moving around the storm. Over the open ocean, the water can flow in all directions (including downward) away from the storm. Strong winds blowing across the ocean surface creates a stress that forces the water levels to increase downwind and decrease upwind. This wind set-up is inversely proportional to ocean depth so over the deep ocean away from land the water level rises are minimal. However, when the hurricane approaches shallow water, there is no room for the water to flow underneath so it rises and gets pushed by the wind as a surge, much like a plow pushes the snow from the roadway.

The advancing surge can increase the water level five meters or more above sea level. In addition, wind-driven waves are superimposed on the storm surge. The total water level can cause severe surge impacts in coastal areas, particularly when the storm surge coincides with the normal high tide.

Slope of the continental shelf also determines the level of surge in a particular area. A shallow slope will allow a greater surge. With a steeper continental shelf coastal areas will not experience as much surge inundation, although large breaking waves can still present major problems. The low pressure in the middle of the storm causes a smaller part of the storm surge.

The pressure in the eye is significantly lower than the surrounding atmosphere, so the atmosphere pressure causes the water in the eye to rise like sucking a drink up a straw. This pressure effect will cause the water level in the open ocean to rise in regions of low pressure and fall in regions of high pressure. In general, for a one-hectopascal drop in surface pressure there is a one-centimeter rise in water level. In short, the cause of storm surge is the combined effect of low air pressure and persistent winds blowing over the water surface.

Hurricanes are tracked with satellites, radar, and specially equipped aircraft reconnaissance flights. Ocean buoys and ships also provide storm information. Successful experiments with remotely piloted drone aircraft (aerosonde) suggest they might be used to help forecast the intensity and track of future hurricanes.

Because of their potential for death and destruction, the U.S. National Hurricane Center issues watches and warnings for hurricanes threatening the United States a few days before a landfall. A hurricane watch means that hurricane conditions in specific coastal areas are possible within 36 hours. A hurricane warning means that hurricane winds associated with a hurricane are expected in a specified coastal area within 24 hours. A hurricane warning can remain in effect when dangerously high water or a combination of dangerously high water and exceptionally high waves continue, even though winds may be less than hurricane intensity.

Hurricane activity, on time scales of seasons and longer, responds to variations in climate. To a first order, greater ocean warmth and relatively calm winds enhance the potential for hurricanes. The strength and position of the subtropical high-pressure zone determines the steering currents, which is important for predicting landfall probabilities. Many catastrophe models that project future damage losses from hurricanes now include this information.

Increases in ocean temperature will raise a hurricane's potential intensity, all else being equal. However, corresponding increases in atmospheric wind shear--in which winds at different altitudes blow in different directions tear apart the developing hurricane--could counter this tendency by dispersing the hurricane's heat. A recent study based on a set of homogenized satellite-derived wind speeds indicates the strongest hurricanes are getting stronger worldwide. Modeling studies indicate that rainfall from hurricanes may get heavier in the future. However, more research is needed to better understand this important issue.

Quantile regression and extreme hurricane winds

Coastal tropical cyclones (TCs) pose a serious threat to society and the economy. Strong winds, heavy rainfall, and storm surge kill people and destroy property. The destructive power of the most intense TCs can rival that of earthquakes. The rarity of intense TCs implies that empirical estimates of their return periods will be unreliable. Fortunately extreme value theory provides parametric models for rare events and a justification for extrapolating to intensity levels that are greater than what has been observed. We developed an extreme value model for US hurricane intensity based on the method of peaks over thresholds using data over the period 1899-2006 (Jagger and Elsner 2006) and showed how the models can be used to assess the probability of extremely intense hurricanes controlling for climate factors.

Quantile regression offers another way to model extreme TC events that has yet to be examined. Quantile regression, introduced by Koenker and Bassett (1978), extends the ordinary least squares regression model to conditional quantiles (e.g., 90th percentile) of the response variable. It can be considered a semi-parametric technique because it relies on non-parametric quantiles, but uses parameters to assess the relationship between the quantile and the covariates.

Ordinarily we think of parametric models as more informative, with nonparametric models useful for an initial look at the data. A parametric model involves more stringent assumptions, but it is usually a good idea to start with stronger assumptions and back off toward weaker assumptions when necessary. However, parametric models are generally more sensitive to outlying data points, which can be problematic for extreme value models. Also, with parametric models care must be given to the form of the distribution. A drawback of parametric models is that the parameters can be more difficult to interpret physically. It is this difficulty in interpreting the parameters of the extreme value models with respect to issues of climate's influence on TC activity that prompted the present work. It is our contention that extreme value models are valuable for quantifying the probability of high winds from TCs conditional on climate covariates, but that quantile regression can be quite useful as an exploratory tool.

Use R for climate research (Part 1: Introduction)

Climate research is greatly facilitated with access to a powerful environment for statistical computing. R is an open-source statistical environment modeled after S and S-Plus. The S language was developed in the late 1980s at AT&T labs. The R project was started by Robert Gentleman and Ross Ihaka of the Statistics Department of the University of Auckland in 1995. It now has a large audience. It's currently maintained by the R core-development team; an international group of volunteer developers. Learn how to download and get started using R for climate research with this video tutorial.

United States and Caribbean tropical cyclone activity related to the solar cycle

The recent increase in the power of Atlantic tropical cyclones is attributable to greater oceanic warmth in part due to anthropogenic increases in radiative forcing from greenhouse gases. However solar activity can influence a hurricane's power as well through changes in upper tropospheric temperature. Here we report on a finding that annual U.S hurricane counts are significantly related to solar activity. The relationship results from relatively more intense tropical cyclones over the Caribbean when sunspot numbers are low. The finding is in accord with the heat-engine theory of hurricanes that predicts a reduction in the maximum potential intensity with a warming in the layer above the hurricane. An active sun warms the lower stratosphere through ozone absorption of additional ultraviolet (UV) radiation. Since the dissipation of the hurricane's energy occurs through ocean mixing and atmospheric transport, tropical cyclones can act to amplify a relatively small change in the sun's output appreciably altering the climate. Results from this study have serious implications for life and property throughout the Caribbean, Mexico, and portions of the United States. The paper is currently under review for publication.

A hurricane network

Relationships of hurricanes affecting the United States can be examined using the methods of network analysis. Network analysis has been used in a variety of fields to examine relational data, but has yet to be used in the study of hurricane climatology. A single hurricane can affect more than one coastal region. This can happen when the regions are small relative to the hurricane size, when the hurricane comes onshore near regional boundaries, and when the hurricane makes multiple landfalls. Thus we suggest a network that links coastal locations (termed nodes) with particular hurricanes (termed links). The topology of the network can then be examined using local and global metrics. Certain regions of the coast (like Louisiana) may have high occurrence rates, but not high values of connectivity. Regions with the highest values of connectivity should include Florida and North Carolina. Virginia which has a relatively low occurrence rate is well-positioned in the network having a relatively high value of "betweenness". Conditional networks can be constructed based on below and above average values of important climate variables. Significant differences in the connectivity of the network are likely for different phases of ENSO.

Five year model of Atlantic hurricanes

Hurricanes cause drastic social problems as well as generate huge economic losses. A reliable forecast of the level of hurricane activity covering the next several seasons has the potential to mitigate against such losses through improvements in preparedness and insurance mechanisms. We develop a statistical model to predict North Atlantic hurricane activity out to five years. The algorithm has two components, a time series model to forecast average hurricane-season Atlantic sea surface temperature (SST), and a regression model to forecast the hurricane rate given the predicted SST value. The algorithm uses Monte Carlo sampling to generate distributions for the predicted SST and model coefficients. For a given forecast year, a predicted hurricane count is conditional on a sampled predicted value of Atlantic SST. Thus forecasts are samples of hurricane counts for each future year. Model skill is evaluated over the period (1997--2005) and compared against climatology, persistence, and other seasonal forecasts issued during this time period. Results indicate that the algorithm will likely improve on earlier efforts and perhaps carry enough skill to be useful in the long-term management of hurricane risk. Read more.

In the eye of the storm

Storm World: Hurricanes, Politics, and the Battle Over Global Warming
by Chris Mooney
Harcourt: July 2007. 392 pp. $26

[An edited version published in Nature, v448, 648, August 9, 2007]

Chris Mooney’s follow-up to his The Republican War on Science (Basic Books, 2005) is a reconnaissance flight into the turbulent debate on a possible link between hurricane activity and global warming. The flight log is compelling enough for Hollywood. It records a clash between the empiricist climate scientist William Gray (think Ian McKellen) at Colorado State University (in a red state) and the theoretician Kerry Emanuel (think Tom Hanks) at the Massachusetts Institute of Technology (in a blue state). Journalist Mooney has a scriptwriter’s flair for pitting his protagonists against each other and dishing the historical and methodological back story in vivid prose: “If we’re really making the deadliest storms on Earth still deadlier, it will represent one of humanity’s all-time greatest foot-shooting episodes.”

The debate swirls about the cause of the recent upswing in severe hurricanes, especially over the Atlantic where evidence for a change is most compelling (here). There is no question that warmer tropical oceans will increase the potential intensity of tropical cyclones (all else being equal), but for Gray the causal chain ends with the ocean. “Nobody knows how the atmosphere works,” he says, feeling that it is far too complicated to be captured by a computer. Emanuel, on the other hand, adds a further link to the chain, placing the blame on human meddling with the composition of the atmosphere (aerosols and greenhouse gases). Having challenged Gray and his colleagues on their forecast methods, it's clear why it took someone with Emanuel's stature (Time Magazine) to spar with him on the climate-change issue.

Just a month before hurricane Katrina’s devastating strike on America’s south coast on 29 August 2005, Emanuel published a paper in this journal (Nature 436, 686–688; 2005) that ignited a scientific debate by linking storm strength to ocean temperatures. It also triggered a maelstrom of media coverage that resulted in the US National Oceanic and Atmospheric Administration (NOAA) closing ranks and claiming unequivocally that the increase in Atlantic hurricane activity since 1995 could be attributed solely to an ocean cycle unrelated to greenhouse warming. Mooney is at his best when describing the political tempest. By allowing what Emanuel calls the “party line” while discouraging dissenters, NOAA was, in Mooney’s words, “gaming the release of information and trying to shift the debate in their favored direction.”

Mooney revisits his call, propounded in his earlier book and in subsequent newspaper columns, for scientists to do a better job of communicating science to the public and media. He urges researchers to stop pretending that they are nothing but objective “fact machines” and to instead give more general interpretations of their results and put them into a broader context.

Drawing on scientific conferences and on interviews with hurricane and climate scientists during 2006, Mooney covers plenty of ground, from heat engines and synoptic meteorology to computer modeling, and all without equations. At times it feels hurried, US-centric and somewhat uneven, jumping between history, science and politics. But Mooney presents an accurate account of the clash between two of the most prominent climate scientists today. He is a good writer — “Scientists, like hurricanes, do extraordinary things at high wind speeds” — and his stories are consistently about people, giving the book a wide appeal.

In the end he gives us a clear picture of what the hurricane–climate change debate is about and where it might go next (sensitivity). As there are no answers, Mooney provides none. Not surprisingly, Chris takes a liking to Bill, but cannot recommend his view that global warming has nothing to do with hurricane activity. I also detected a commentary about storm climatologists for which science sometimes plays second fiddle to entertaining sound bites.

While the inner-core dynamics are well resolved in Storm World, a hurricane needs its outer rain bands and there are many scientists contributing to the whirlwind surrounding what is arguably the most important climate debate in history. Neither side is completely wrong and both would do well to study the full breadth of literature.

Storm World is a great summer read. The story continues however with more answers likely in the sequel.

Summary: Summit on Hurricanes and Climate Change

An International Summit on Hurricanes and Climate Change was held May 27-30, 2007 at the Aldemar Knossos Royal Village in Hersonissos, Crete. It was hosted by Aegean Conferences and supported by the Bermuda Institute for Ocean Sciences (BIOS) Risk Prediction Initiative and by the U.S. National Science Foundation. It was organized by myself and Richard Murnane (BIOS). There were 77 participants from at least 18 countries with a mix of academics and stakeholders (insurance and risk modelers). The purpose was to gather leading researchers in the field of tropical cyclone climate for sustained discussions on the state of the science and to elevate the discourse above the fray. In this spirit, it was appropriate to convene at the birth place of the Socratic method.

Traditionally tropical cyclones are analyzed as a passive response to climate forcing: the hurricane as a product of its environment. A warm ocean provides sustenance, a calm atmosphere nurturing, and a subtropical high pressure cell forward direction. An increase in oceanic heat will raise a hurricane's potential intensity, yet an increase in shearing winds could counter by dispersing the heat in a fledgling storm. This perspective is useful for identifying the mechanisms responsible for making some seasons active while others inactive. In this regard it was argued that data modeling is superior to data analysis (trend lines, etc) as it avoids cherry-picking the evidence and provides a framework for making use of older, less reliable data.

For example, a Poisson distribution is useful for modeling tropical storm counts over time. The benefit of this approach is that it provides a context that is consistent with the nature of underlying physical processes, analogous to the way the laws of physics provide a context for studying meteorology. It was shown that smoothing (filtering) the count data introduces low frequency patterns that may not be significant and that a data model of Atlantic hurricanes indicates a recent upswing in the number of strongest hurricanes with little multidecadal variation. The figure above shows annual hurricane rates using a data model of basin-wide Atlantic hurricane counts. Results are shown for different categories of hurricane intensity. Note that for each year the model provides a distribution on the estimated annual rate as indicated by a box plot. The model also provides a distribution for the number of rate changes over the 63-year period (1943-2005). Note the absence of a multidecadal pattern.

Although the question of whether we can ascribe a change in tropical cyclone intensity to anthropogenic climate change (attribution) is still open, it was argued based on data models for extreme winds that the difference in U.S. hurricane intensity between globally warm and cool years is consistent in sign and magnitude with theory and simulations. In this regard it was noted that the discrepancy between numerical model results and observations is likely due to a reliance on data analysis rather than data models.

The collective role that hurricanes play in changing the climate was a point of emphasis at the Summit. In the Atlantic, heat and moisture transport out of the tropics by an ensemble of hurricanes moving poleward in a given season was shown to have a detectable influence on the baroclinic activity at high latitudes the following winter which in turn influences the preferred hurricane track type (recurving or straight-moving) during the subsequent hurricane season. Thus a communication between the tropics and the middle latitudes on the biennial time scale is accomplished through tropical cyclone track changes and middle latitude baroclinicity. Also, the relationship between global warming and ENSO was explained in terms of warming rather than warmth. A warming planet is associated with more El Nino events which on the biennial time scale leads to cooling. These are intriguing hypotheses about climate change and tropical cyclones that merit further investigation. It was also shown that super typhoons in the western North Pacific need a deep ocean mixed layer for rapid intensification only in regions where the sub surface water temperatures are marginally supportive of tropical cyclone intensification. It was demonstrated that high aerosol concentrations lead to an enhancement of the ice/water cloud microphysics leading to the invigoration of the convection inside a tropical cyclone.

Another important theme of the Summit was paleotempestology. Paleotempestology is the study of prehistoric storms from geological and biological evidence. For instance, coastal wetlands and lakes are subject to overwash processes during hurricane strikes when barrier sand dunes are overtopped by storm surge. The assumption is that during landfall the waves and wind-driven storm surge reach high enough over the barrier to deposit sand in the lake. In a sediment core taken from the lake bottom, a sand layer will appear distinct from the fine organic mud that accumulates slowly under normal conditions. Sediment cores taken from the northeastern Caribbean show more sand layers during the second half of the Little Ice Age when sea temperatures near Puerto Rico were a few degrees C cooler than today provides some evidence that today's warmth is not needed for increased storminess. Not surprisingly intervals of more hurricanes correspond with periods of fewer El Nino events. Sedimentary ridges in Australia left behind by ancient tropical cyclones indicate that activity from the last century under represents the continent's stormy past. Proxy techniques based on oxygen isotopes from tree rings and cave deposits also show promise for studying prehistoric tropical cyclone events.

It was mentioned that a spatially limited set of proxies or historical records is not able to resolve changes in overall activity from changes in local activity due to shifts in tracks. While the northeastern Caribbean region is in the direct path of today's hurricanes, was it always? The answer is important as more hurricanes locally could mean changes in steering rather than changes in abundance. Proxy data from the U.S. Gulf coast show a pattern of frequent hurricanes between 3800 and 1000 years ago followed by relatively few hurricanes during the most recent millennium which is explained in terms of the position of the subtropical North Atlantic High. Moreover it was shown that recent increases in typhoon intensities affecting Korea can be explained by an eastward shift in the subtropical North Pacific High allowing the storms to recurve over the warmer waters of the Kuroshio Current rather than the colder subsurface waters of the Yellow Sea. In order to understand how climate influences local changes in tropical cyclone activity, more research is needed to identify factors influencing tropical cyclone tracks.

Results from various high resolution numerical models, including a 20 km-mesh model, were consistent in showing stronger tropical cyclones in a warmer future. Most models indicate an overall decrease in the number of storms, attributable in one study to greater atmospheric stability and a decrease in the vertical mass flux. Not all models agree on the change in individual basin numbers with some models showing an increase in the Atlantic and others a decrease. It was shown that models without tropical cyclones need to remove the oceanic heat in the tropics through stronger trade winds. It was noted that models may be better at identifying changes to the large-scale genesis fields and that models still do not have the resolution to be useful to society. Climate model projections can be downscaled to construct tropical cyclone climatologies using a method that combines rejection sampling of genesis points with simple physical models for storm motion and winds. A few presentations focused on the perception and politics of tropical cyclone risk in a changing climate.

The summit was a success. All sessions were plenary and attendance averaged greater than 90%. There were 4 days of talks with each day broken into an early and late morning session of 4 to 5 speakers each. Coffee, tea, soft drinks, and snacks were served during the poster session between the oral sessions. The posters were available for viewing during the entire summit. Lunch was served on the beach after the late morning session followed by free time. In the evening participants and their company were treated to a full course meal at a local restaurant. Wednesday afternoon featured a tour of the Minoan Palace of Knossos near the city of Heraklion. The Summit concluded with a gala dinner featuring traditional Greek and Cretan music and dancing. Invited speakers were provided full accommodations. Travel awards were given to six students and two additional participants. The conference proceedings will be published by Springer as an edited volume in 2008.

Hourly Atlantic hurricane data

In the absence of higher temporally resolved information on historical hurricanes, we develop a set of hourly-interpolated track values that can be used for hurricane climate studies. A spline interpolation is used to obtain locations and wind speeds at 1-hr intervals from the 6-hr values for all tropical cyclones in NOAA's dataset. The data set is augmented with a set of storm intensification and heading estimates based on a Savitzky-Golay filter. The data are available here.

Limitation of risk models in a changing climate

Hurricane risk models used by the insurance industry rely on a catalog of storms that represent the historical data in some way or another. While useful for estimating aggregate portfolio losses from a hypothetical worse case scenario, these catalogs are not easily suited for anticipating losses based on a changing climate. At the core of the catalog is a set of synthetic storms and a way to assign a probability to each. But each synthetic storm in the catalog is a composite of size, track, and intensity so it is difficult to estimate risk at a particular point location. Additionally, it is important to consider how climate influences hurricane risk, but it is not obvious how to condition the multidimensional storm event on climate. Perhaps most importantly, the assigned return rates are empirically driven in that the rates are not connected parametrically to a theoretical distribution. This leads to lower confidence in the estimated rates.

We propose an alternative approach for anticipating losses that produces predict expected wind speed distributions at any location. The parametric distributions which give tighter confidence intervals can be naturally conditioned on preseason climate variables. More importantly this approach could allow the reinsurance industry to examine which coastal regions are most sensitive to the changing climate. For example, with increasing Atlantic sea-surface temperatures is it realistic to expect that the risk of hurricane damage will increase everywhere? The answer to this question has implications for insurance rates and societal vulnerability.

2005 Atlantic hurricane season in motion

Watch the record-setting season in motion.

Better risk models

Important advances are being made to understand and predict hurricane activity. On the seasonal time scale, and to a first order, we know that a warm ocean fuels storm genesis, a calm atmosphere allows storms to intensify, and the position and strength of the subtropical high pressure region paves the tracks for storms that do form. The next generation of risk modelers should incorporate this science into their assessments.

We at the Hurricane Climate Institute at Florida State University (FSU) have made important contributions to this science. We have developed techniques for predicting seasonal hurricane activity (Elsner et al. 1998; 1999; Jagger et al. 2001; 2002), have quantified the statistical association between the North Atlantic oscillation (NAO) and hurricane activity (Elsner et al. 2001; Elsner 2003; Elsner and Jagger 2006), and have demonstrated the utility of Bayesian methods for handling incomplete and missing data (Elsner and Bossak 2001; Elsner et al. 2004; Elsner and Jagger 2004). Our approach is to build models from the available data.

Data models help us understand and predict relationships beyond that accessible with statistical descriptions because they provide a safeguard against cherry-picking the evidence. Data models help us unravel the nuances of climate on hurricanes. Standard meteorological procedures like filtering, trend lines, and empirical orthogonal functions are not up to this task. Data models provide us a context that is consistent with the nature of underlying climate processes, similar to the way the laws of physics provide a context for studying meteorology. In short, data modeling is a scientific way to understanding how the climate works given the available evidence. At issue for risk assessment is how extreme coastal hurricane activity is conditional on climate patterns.

The next big improvement in risk modeling will likely come with data models that assess regional hurricane activity using historical data and numerical prediction output. Indeed, we now successfully model hurricane counts (Elsner and Jagger 2006) and hurricane intensities (Jagger and Elsner 2006) in regions along the coastal United States. Moreover we demonstrate statistical skill in predicting the expected annual insured loss conditional on the state of the NAO and Atlantic ocean temperatures (Jagger et al. 2007).

With our help this science is incorporated in risk models from Accurate Environmental Forecasting (AEF). However, more work is needed to add spatial information and regional predictors. Global predictors include leading modes of variability such as the NAO as well as variables that track the El Nino. Regional predictors like sea temperatures in the Gulf of Mexico and the Caribbean Sea, surface air pressures over Bermuda, and rainfall/soil moisture indicators over eastern North America and western Europe should be considered.

As a consequence of incomplete data and the existence of alternative scientific theories (e.g., climate change versus natural variability), probabilistic risk assessment requires some degree of expert judgment. One approach is to use Bayesian statistics another is to use expert opinion in formal elicitation. Elicitation is practiced in analyzing earthquakes and other geological hazards. Although the physics of climate is better understood than certain geological processes, there remains a sufficient lack of understanding with regard to hurricane risk to cause divergence among researchers.

Formal methods are available for eliciting expert judgment. One method involves a panel of experts who debate and explain the merits of evidence and argument. This approach is based on the assumption that group judgments can improve the validity of forecasts. In any case, the procedures will provide information about the relative risk that is agreeable to the panel. This is done by Risk Management Solutions (RMS) resulting in updates to their hurricane risk assessments that reflects, to some degree, expert opinions about future hurricane activity.

To improve these efforts evidence models should be used to ensure that the experts give credible witness to the data. For example, it is inconsistent for an expert to believe that the most likely number of U.S. hurricanes over the next 5 years will be 10 while at the same time believing there is a 40% chance that the number will be less than 3. The data simply do not conform to this type of distribution.

Averaging expert opinion will not necessarily give a consistent estimate of the hurricane rate either and the method does not account for the uncertainty inherent in the numbers provided by the experts. Moreover, there is some agreement on increased hurricane activity over the basin as a whole for the next few years, but much less agreement on what that means for citizens living along the U.S. coast. This differential in uncertainty also needs to be quantified and incorporated.

As mentioned, a data model can help. One model is to assume that each of the N-year totals from the experts is Poisson with a parameter equal to rate times N. This generates separate estimates for each expert. Another model is to assume that the observed counts have a negative binomial distribution. More work is needed, but future risk models will certainly benefit by utilizing the latest hurricane climate science.

Disclosure: I acknowledge discussions with Thomas H. Jagger on this topic. My financial support comes from the U.S. National Science Foundation and the Risk Prediction Institute of the Bermuda Institute of Ocean Sciences. These opinions are mine and do not necessarily reflect those of the funding agencies. I worked previously under contract with AEF. Currently I have no financial interest in a risk modeling or insurance company.

Comparing hurricane return levels using historical and geological records

Hurricane return levels estimated using historical and geological information are quantitatively compared for Lake Shelby, Alabama. The minimum return level of overwash events recorded in sediment cores is estimated using a modern analogue (Hurricane Ivan of 2004) to be 54 m/s (105 kt) for a return period of 318 years based on 11 events over 3500 years. The expected return level of rare hurricanes in the observed records (1851-2005) at this location and for this return period is estimated using a parametric statistical model and a maximum likelihood procedure to be 73 m/s (141 kt) with a lower bound on the 95% confidence interval of 64 m/s (124 kt). Results are not significantly different if data are taken from the shorter 1880-2005 period. Thus the estimated sensitivity of Lake Shelby to overwash events is consistent with the historical record given the model. In fact, assuming the past is similar to the present the sensitivity of the site to overwash events as estimated from the model is likely more accurately set at 64 m/s. Read more.

U.S. hurricanes and the North Atlantic oscillation

One thing I find surprising about the debate on climate change and hurricanes is the lack of discussion on the North Atlantic oscillation (NAO). Some in politics and insurance suggest greater attention be placed on understanding future hurricane activity as it relates to the United States. We've published 13 scientific papers on this topic since 2001 (here). The research identifies and elucidates the role of the NAO in portending hurricane tracks across the Atlantic Ocean. A weak NAO phase tends to favor tracks that parallel lines of latitude. In contrast a strong NAO phase tends to favor tracks that cross latitudes (hurricanes that, in general, get steered away from the U.S. coast). We speculate the reason for this is related to the position and strength of the subtropical high pressure system.

Interestingly, the NAO was in a positive phase for much of the 1970s and 1980s with historic highs in the early 1990s and speculation about a link to global warming has been made. Osborn et al. (1999) show that the NAO from the 1960s to early 1990s is outside the range of earlier variability in the instrumental record and also outside the range of variability simulated using UK Hadley Centre's numerical model. Thus with greater warmth and perhaps more Atlantic hurricanes it is possible that the threat to the United States as defined by the probability of a strike will remain relatively constant rather than increase.

In fact there is some evidence for this in the historical record of U.S. hurricane counts which show no long term trend but a tendency for a smaller ratio of landfall counts to basin-wide counts. The differential influence of improvements in observing technologies on landfall and total counts tends to confound attempts to understand this tendency as noted in Elsner and Kara (1999). Moreover, conditional on the phase of the NAO, there are statistically significant positive relationships between Atlantic sea-surface temperature (SST) and both U.S. hurricane counts (Elsner and Jagger 2006) and insured losses (Jagger et al. 2007).

Hurricane evidence

The debate on hurricanes and climate change can sometimes devolve into issues of data reliability. Unfortunately some of what is said about these issues is nonsense, or worse, self serving. As one example, during the middle 1990's, the high priest of NOAA's best-track data argued vehemently that the hurricane intensities during the 1950's and '60s were biased upward. I checked with my colleague Noel LaSeur, who flew into these early storms, and he said "If anything, we underestimated the intensity" suggesting a possible downward bias. Noel is correct. With this light, the intensity of the hurricanes of 2004 & 2005 is not that unusual against the backdrop of the formidable mid century hurricanes. Enthusiasts and partisans should not be tinkering with these data. Moreover, while it stands to reason (a priori) that the historical information will be less precise than data collected today with modern technologies, to ignore these earlier records is scientifically indefensible. Inspired by Edward Tufte recommendations for truth-telling in graphical presentations (Visual Explanations, Graphics Press, 1997), I suggest that one way to enforce data standards is to insist that the original, unprocessed data be posted alongside the manipulated data, and that the manipulators and their methods be identified.

Hurricanes and climate change

The World Meteorological Organization has just released their consensus statement on tropical cyclones and climate change which mentions that because of the rapid advances being made in this area findings may be soon superceded by new results. Please consider joining us for the First International Summit on Hurricanes and Climate Change to hear all about the latest discoveries.

Atlantic hurricanes and global warming

The power of Atlantic tropical cyclones has risen rather dramatically and the increase is correlated with an increase in the late summer/early fall sea-surface temperature over the North Atlantic. A debate concerns the nature of these increases with some studies attributing them to a natural climate fluctuation, known as the Atlantic Multidecadal Oscillation (AMO), and others suggesting climate change related in part to anthropogenic increases in radiative forcing from greenhouse-gases. Here I apply tests for causality using the global mean near-surface air temperature (GT) and Atlantic sea-surface temperature (SST) records during the Atlantic hurricane season and find that GT is useful in predicting Atlantic SST, but not the other way around. Thus I concluded that GT "causes" SST providing evidence in support of the climate change hypothesis.

Forecast model of U.S. hurricanes 6 months in advance

Hurricanes are a serious social and economic threat to the
United States. Hurricane Katrina is a grim reminder of this fact.
Recent advances allow skillful forecasts of the U.S. hurricane
threat at (or near) the start of the Atlantic hurricane season.
Skillful forecasts of hurricane landfalls at longer lead times
(forecast horizons) for the complete hurricane season would greatly
benefit risk managers and others interested in acting on these
forecasts. Here we show a model that provides a 6-month forecast
horizon for annual hurricane counts along the U.S. coastline during
the June through November hurricane season. Forecast skill exceeds
that of climatology. The long-lead skill is linked to the
persistence of Atlantic sea-surface temperatures and to
teleconnections between North Atlantic sea-level pressures and
precipitation variability over North America and Europe. The model
is developed using Bayesian regression and therefore incorporates
the full set of Atlantic hurricane data extending back to 1851.

[with R.J. Murnane and T.H. Jagger]

Return periods for Hurricane Katrina

Hurricane Katrina is the most destructive natural disaster in U.S. history. The relative infrequency of severe coastal hurricanes implies that empirical probability estimates of the next big one will be unreliable. Here we use an extreme-value model and show that a hurricane of Katrina's intensity or stronger can be expected to occur, on average, once every 21 years somewhere along the Gulf coast and once every 14 years somewhere along the entire coast from Texas to Maine. The model predicts a 100-year return level of 83 m/s (186 mph) during globally warm years and 75 m/s (168 mph) during globally cool years. The magnitude of this difference is consistent with models predicting an increase in hurricane intensity with increasing greenhouse warming.

[with T.H. Jagger & A.A. Tsonis]