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Species distribution modeling aimed at forecasting the spread of invasive species under projected global warming offers land managers an important tool for assessing future ecological risk and for prioritizing management actions. The current study applies Bayesian inference and newly available geostatistical tools to forecast global range expansion for the ecosystem altering invasive climbing fern Lygodium microphyllum. The presented modeling framework emphasizes the need to account for spatial processes at both the individual and aggregate levels, the necessity of modeling non-linear responses to environmental gradients, and the explanatory power of biotic covariates. Results indicate that L. microphyllum will undergo global range expansion in concert with anthropogenic global warming and that the species is likely temperature and dispersal limited. Predictions are undertaken for current and future climate conditions assuming both limited and unlimited dispersal scenarios.

Tornadoes are capable of catastrophic destruction and mass casualties, but there are yet no estimates of how sensitive the number of casualties are to changes in the number of people in harm's way or to changes in tornado energy. Here the relationship between tornado casualties (deaths and injuries), population, and energy dissipation is quantified using the economic concept of “elasticity.” Records of casualties from individual tornadoes over the period 2007–2015 are fit to a regression model. The coefficient on the population term (population elasticity) indicates that a doubling in population increases the casualty rate by 21% [(17, 24)%, 95% credible interval]. The coefficient on the energy term (energy elasticity) indicates that a doubling in energy dissipation leads to a 33% [(30, 35)%, 95% credible interval] increase in the casualty rate. The difference in elasticity values show that on average, changes in energy dissipation have been relatively more important in explaining tornado casualties than changes in population. Assuming no changes in warning effectiveness or mitigation efforts, these elasticity estimates can be used to project changes in casualties given the known population trends and possible trends in tornado activity.

Tropical cyclones, with their nearshore high wind speeds and deep storm surges, frequently strike the United States Gulf of Mexico coastline influencing millions of people and disrupting offshore economic activities. The combined risk of occurrence of tropical cyclone nearshore wind speeds and storm surges are assessed at 22 coastal cities throughout the United States Gulf of Mexico. The models used are extreme value copulas fitted with margins defined by the generalized Pareto distribution or combinations of weibull, gamma, lognormal, or normal distributions. The statistical relationships between the nearshore wind speed and storm surge are provided for each coastal city prior to the copula model runs using Spearman Rank correlations. The strongest significant relationship between the nearshore wind speed and storm surge exists at Shell Beach, LA (ρ=0.67) followed by South Padre Island, TX (ρ=0.64). The extreme value Archimedean copula models for each city then provide return periods for specific nearshore wind speed and storm surge pairs. Of the 22 cities considered, Bay St. Louis, MS has the shortest return period for a tropical cyclone with at least a 50 ms−1 nearshore wind speed and a three meter surge (19.5 years, 17.1?23.5). 90% confidence intervals are created by recalculating the return periods for a fixed set of wind speeds and surge levels using one hundred samples of the model parameters. The results of this study can be utilized by policy managers and government officials concerned with coastal populations and economic activity in the Gulf of Mexico.

Identification and inventory of wetlands are essential components of natural resource management. To be effective in these endeavors, it is critical that the process used to detect and document wetlands be time efficient, accurate, and repeatable as new environmental information becomes available. Approaches dependent on aerial photographic interpretation of land cover by individual human analysts necessitate hours of assessment, introduce human error, and fail to include the best available soils and hydrologic data. The goal of the current study is to apply hierarchical modeling and Bayesian inference to predict the probability of wetland presence as a continuous gradient with the explicit consideration of spatial structure. The presented spatial statistical model can evaluate 100 km 2 at a 50 x 50 meter resolution in approximately 50 minutes while simultaneously incorporating ancillary data and accounting for latent spatial processes. Model results demonstrate an ability to consistently capture wetlands identified through aerial interpretation with greater than 90 % accuracy (scaled Brier Score) and to identify wetland extents, ecotones, and hydrologic connections not identified through use of other modeling and mapping techniques. The provided model is reasonably robust to changes in resolution, areal extents between 100 km 2 and 300 km 2, and region-specific physical conditions.

Climate influences on hurricane intensification are investigated by averaging hourly intensification rates over the period 1975–2014 in 8° × 8° latitude–longitude grid cells. The statistical effects of hurricane intensity and sea-surface temperature (SST), along with the climatic effects of El Niño–Southern Oscillation (ENSO), the North Atlantic Oscillation (NAO) and the Madden–Julian Oscillation (MJO), are quantified using a Bayesian hierarchical model fit to the averaged data. As expected, stronger hurricanes tend to have higher intensification rates, especially over the warmest waters. Of the three climate variables considered, the NAO has the largest effect on intensification rates after controlling for intensity and SST. The model shows an average increase in intensification rates of 0.18 [0.06, 0.31] m s−1 h−1 (95 % credible interval) for every 1 standard deviation decrease in the NAO index. Weak trade winds associated with the negative phase of the NAO might result in less vertical wind shear and thus higher mean intensification rates.

The statistical relationship between elevation roughness and tornado activity is quantified using a spatial model that controls for the effect of population on the availability of reports. Across a large portion of the central Great Plains the model shows that areas with uniform elevation tend to have more tornadoes on average than areas with variable elevation. The effect amounts to a 2.3% [(1.6%, 3.0%) = 95% credible interval] increase in the rate of a tornado occurrence per meter of decrease in elevation roughness, defined as the highest minus the lowest elevation locally. The effect remains unchanged if the model is fit to the data starting with the year 1995. The effect strengthens for the set of intense tornadoes and is stronger using an alternative definition of roughness. The elevation-roughness effect appears to be strongest over Kansas, but it is statistically significant over a broad domain that extends from Texas to South Dakota. The research is important for developing a local climatological description of tornado occurrence rates across the tornado-prone region of the Great Plains.

The destructive impact tornadoes have on communities has sparked interest in predicting the risk of impacts on seasonal time scales. Here, the authors demonstrate how to build statistical models for predicting tornado rates. They test the models with tornado counts accumulated over a 45-year period aggregated to counties in the State of Oklahoma and to cells in a latitude/longitude grid across a large portion of south central United States. The spatial model provides a fit to the counts, which includes terms for the spatial correlation and the population effect. A space-time model not only provides a similar fit to annual counts but also includes a term for a time-varying climate factor. This work contributes to methods for forecasting severe convective storms on the seasonal time scale.

The authors analyze the historical record of tornado reports in the United States and find evidence for changes in tornado climatology possibly related to global warming. They do this by examining the annual number of days with many tornadoes and the ratio of these days to days with at least one tornado and by examining the annual proportion of tornadoes occurring on days with many tornadoes. Additional evidence of a changing tornado climate is presented by considering tornadoes in geographic clusters and by analyzing the density of tornadoes within the clusters. There is a consistent decrease in the number of days with at least one tornado at the same time as an increase in the number of days with many tornadoes. These changes are interpreted as an increasing proportion of tornadoes occurring on days with many tornadoes. Coincident with these temporal changes are increases in tornado density as defined by the number of tornadoes per area. Trends are insensitive to the begin year of the analysis. The bottom line is that the risk of big tornado days featuring densely concentrated tornado outbreaks is on the rise. The results are broadly consistent with numerical modeling studies that project increases in convective energy within the tornado environment.

Data from some recent tornado damage assessments are used to compute the percentage of damage path area by enhanced Fujita (EF) rating and to estimate kinetic energy. Only a small fraction of the damage area gets the highest damage rating, and this fraction is lower than a model used by the U.S. Nuclear Regulatory Commission. However, estimates of kinetic energy derived from a characteristic wind speed for each EF rating and the fraction of area with that rating match kinetic energy estimates using the model percentages. On average, the higher the EF rating, the larger the kinetic energy, but there is large variability in the relationship. The average total kinetic energy over the EF1 tornadoes examined in the study is 0.61 TJ, which compares with an average of 2.37 TJ, 40.1 TJ, 36.5 TJ, and 50.4 TJ for the EF2, EF3, EF4, and EF5 tornadoes, respectively. The most energetic tornado examined had a maximum damage rating of EF3.

The authors define a spatio-statistical response of hurricane frequency to the solar cycle. Previous research indicates reduced (increased) hurricane intensities and frequency in the western (eastern) tropical Atlantic. However, no formal quantitative relationship has been spatially established between hurricane frequency and solar activity. The authors use a Bayesian hierarchical space–time model, an increasingly popular approach due to its advantage in facilitating regression modeling of space–time phenomena in the context of large data sets. Regional hurricane frequency over the period 1866–2010 is examined in response to September sunspot number (SSN) while controlling for other relevant climate factors. The response features a 13 % reduction in probability of annual hurricane occurrence for southeastern Cuba, the southern Bahama islands, Haiti, and Jamaica when the SSN is 80 sunspots. In contrast, hurricane risk in regions of the southeastern Atlantic is predicted to increase by 73 % when the SSN is 160 sunspots. The model can be ported to explore other relationships over contiguous space.

Consideration of climate-related impacts on coasts is important to ensure readiness for disaster response. Local risk of storm surge and strong winds from hurricanes affecting Galveston, Texas, is quantified using a bivariate copula model fit to observed data. The model uses a two-dimensional Archimedean copula. Parametric uncertainty (5th and 95th percentiles) is quantified using a Monte Carlo procedure. The annual probability of a hurricane producing winds of at least 50 ms−1 and a surge of at least 4 m is 1.7 percent with a 95 percent confidence interval of (1.33, 1.78) percent. The methodology can be extended to include inland flooding and can be applied elsewhere with available information.

A statistical model for the intensity of the strongest hurricanes has been developed and a new methodology introduced for estimating the sensitivity of the strongest hurricanes to changes in sea surface temperature. Here, the authors use this methodology on observed hurricanes and hurricanes generated from two global climate models (GCMs). Hurricanes over the North Atlantic Ocean during the period 1981–2010 show a sensitivity of 7.9 ± 1.19 m s−1 K−1 (standard error; SE) when over seas warmer than 25°C. In contrast, hurricanes over the same region and period generated from the GFDL High Resolution Atmospheric Model (HiRAM) show a significantly lower sensitivity with the highest at 1.8 ± 0.42 m s−1 K−1 (SE). Similar weaker sensitivity is found using hurricanes generated from the Florida State University Center for Ocean–Atmospheric Prediction Studies (FSU-COAPS) model with the highest at 2.9 ± 2.64 m s−1 K−1 (SE). A statistical refinement of HiRAM-generated hurricane intensities heightens the sensitivity to a maximum of 6.9 ± 3.33 m s−1 K−1 (SE), but the increase is offset by additional uncertainty associated with the refinement. Results suggest that the caution that should be exercised when interpreting GCM scenarios of future hurricane intensity stems from the low sensitivity of limiting GCM-generated hurricane intensity to ocean temperature.

The authors illustrate a statistical point process model that uses the spatial occurrence of nonviolent tornadoes to predict the distribution of the rare, violent tornadoes that occur during springtime across the US central Great Plains. The average rate of nonviolent tornadoes is 55 per 104 km2 per 62 years which compares with an average rate of only 1.5 violent tornadoes per 104 km2 over the same period (less than 3 %). Violent tornado report density peaks at 2.6 per 104 km2 (62 yr) in the city but is only 0.7 per 104 km2 in the countryside. The risk of a violent tornado is higher by a factor of 1.5, on average, in the vicinity of less violent tornadoes after accounting for the population bias. The model for the occurrence rate of violent tornadoes indicates that rates are lower by 10.3 (3.6, 16.5) % (95 % CI) for every 1 km increase in distance from the nearest nonviolent tornado, controlling for distance from the nearest city. Model significance and the distance-from-nearest nonviolent tornado parameter are not sensitive to population threshold or the definition of a violent tornado. The authors show that the model is useful for generating a catalogue of touchdown points that can be used as a component to a tornado catastrophe model.

This paper estimates local tornado risk from records of past events using statistical models. First, a spatial model is fit to the tornado counts aggregated in counties with terms that control for changes in observational practices over time. Results provide a long-term view of risk that delineates the main tornado corridors in the United States where the expected annual rate exceeds two tornadoes per 10,000 square km. A few counties in the Texas Panhandle and central Kansas have annual rates that exceed four tornadoes per 10,000 square km. Refitting the model after removing the least damaging tornadoes from the data (EF0) produces a similar map but with the greatest tornado risk shifted south and eastward. Second, a space-time model is fit to the counts aggregated in raster cells with terms that control for changes in climate factors. Results provide a short-term view of risk. The short-term view identifies the shift of tornado activity away from the Ohio Valley under El Ni\~no conditions and away from the Southeast under positive North Atlantic oscillation conditions. The combined predictor effects on the local rates is quantified by fitting the model after leaving out the year to be predicted from the data. The models provide state-of-the-art views of tornado risk that can be used by government agencies, the insurance industry, and the general public.

The authors demonstrate a statistical model for the time it takes a manuscript to be accepted for publication. The manuscript received and accepted dates from published manuscripts with the term “hurricane” in the title are obtained from the American Meteorological Society's online publication search feature. The time to acceptance as the difference in days between these two dates is modeled using a Bayesian approach. Assuming an article picked at random gets published, draws from the posterior distribution of the modeled time-to-acceptance parameter indicate about a 12% chance that it will spend more than 210 days (7 months) in review. The model can be adapted to fit similar data obtained using other search criteria.

Models that predict annual U.S. hurricane activity assume a Poisson distribution for the counts. Here the authors show that this assumption applied to Florida hurricanes leads to a forecast that underpredicts both the number of years without hurricanes and the number of years with three or more hurricanes. The underdispersion in forecast counts arises from a tendency for hurricanes to arrive in groups along this part of the coastline. The authors then develop an extension to their earlier statistical model that assumes that the rate of hurricane clusters follows a Poisson distribution with cluster size capped at two hurricanes. Hindcasts from the cluster model better fit the distribution of Florida hurricanes conditional on the climate covariates including the North Atlantic Oscillation and Southern Oscillation index. Results are similar to models that parameterize the extra-Poisson variation in the observed counts, including the negative binomial and the Poisson inverse Gaussian models. The authors argue, however, that the cluster model is physically consistent with the way Florida hurricanes tend to arrive in groups.

The strongest hurricanes over the North Atlantic Ocean are getting stronger, with the increase related to rising ocean temperature. Here, the authors develop a procedure for estimating future wind losses from hurricanes and apply it to Eglin Air Force Base along the northern coast of Florida. The method combines models of the statistical distributions for extreme wind speed and average sea surface temperature over the Gulf of Mexico with dynamical models for tropical cyclone wind fields and damage losses. Results show that the 1-in-100-yr hurricane from the twentieth century picked at random to occur in the year 2100 would result in wind damage that is 36% [(13%, 76%) = 90% confidence interval] greater solely as a consequence of the projected warmer waters in the Gulf of Mexico. The method can be applied elsewhere along the coast with modeling assumptions modified for regional conditions.

The authors demonstrate a spatial framework for studying hurricane climatology. The framework consists of a spatial tessellation of the hurricane basin using equal-area hexagons. The hexagons are efficient at covering hurricane tracks and provide a scaffolding to combine attribute data from tropical cyclones with spatial climate data. The framework’s utility is demonstrated using examples from recent hurricane seasons. Seasons that have similar tracks are quantitatively assessed and grouped. Regional cyclone frequency and intensity variations are mapped. A geographically-weighted regression of cyclone intensity on sea-surface temperature emphasizes the importance of a warm ocean in the intensification of cyclones over regions where the heat content is greatest. The largest differences between model predictions and observations occur near the coast. The authors suggest the framework is ideally suited for comparing tropical cyclones generated from different numerical simulations.

Hurricane winds present a significant hazard for coastal infrastructure. An estimate of the local risk of extreme wind speeds is made using a new method that combines historical hurricane records with a deterministic wind field model. The method is applied to Santa Rosa Island located in the northwestern panhandle region of Florida, USA. Firstly, a hurricane track is created for a landfall location on the island that represents the worst-case scenario for Eglin Air Force Base (EAFB). The track is based on averaging the paths of historical hurricanes in the vicinity of the landfall location. Secondly, an extreme-value statistical model is used to estimate 100-year wind speeds at locations along the average track based again on historical hurricanes in the vicinity of the track locations. Thirdly, the 100-year wind speeds together with information about hurricane size and forward speed are used as input to the HAZUS hurricane wind field model to produce a wind swath across EAFB. Results show a 100-year hurricane wind gust on Santa Rosa Island of 58 (±5) m s−1 (90% CI). A 100-year wind gust at the same location based on a 105-year simulation of hurricanes is lower at 55 m s−1, but within the 90% confidence limits. Based on structural damage functions and building stock data for the region, the 100-year hurricane wind swath results in $574 million total loss to residential and commercial buildings, not including military infrastructure, with 25% of all buildings receiving at least some damage. This methodology may be applied to other coastal areas and adapted to predict extreme winds and their impacts under climate variability and change.

The authors show that historical property damage losses from US hurricanes contain climate signals. The methodology is based on a statistical model that combines a specification for the number of loss events with a specification for the amount of loss per event. Separate models are developed for annual and extreme losses. A Markov chain Monte Carlo procedure is used to generate posterior samples from the models. Results indicate the chance of at least one loss event increases when the springtime north–south surface pressure gradient over the North Atlantic is weaker than normal, the Atlantic ocean is warmer than normal, El Nino is absent, and sunspots are few. However, given at least one loss event, the magnitude of the loss per annum is related only to ocean temperature. The 50-year return level for a loss event is largest under a scenario featuring a warm Atlantic Ocean, a weak North Atlantic surface pressure gradient, El Nino, and few sunspots. The work provides a framework for anticipating hurricane losses on seasonal and multi-year time scales.

A statistical procedure for estimating the risk of strong winds from hurricanes is demonstrated and applied to several major cities in Florida. The procedure, called the hurricane risk calculator, provides an estimate of wind risk over different length periods and can be applied to any location experiencing this hazard. Results show that the city of Miami can expect to see hurricane winds blowing at 50 m s−1 [45.5–54.5 m s−1 is the 90% confidence interval (CI)] or stronger, on average, once every 12 yr. In comparison, the city of Pensacola can expect to see hurricane winds of 50 m s−1 (46.9–53.1 m s−1, 90% CI) or stronger once every 24 yr. A quantile regression is applied to hurricane wind speeds in the vicinity of Florida. Results show that the strongest hurricanes are getting stronger as a consequence of higher offshore intensification rates.

Interest in hurricane risk usually focuses on landfalling events of the highest intensity, which cause a disproportionate amount of hurricane-related damage. Yet assessing the long-term risk of the most intense landfalling events is problematic because there are comparatively few of them in the historical record. For this reason, return periods of the most intense storms are usually estimated by first fitting standard probability distribution functions to records of lower-intensity events and then using such fits to estimate the high-intensity tails of the distributions. Here the authors attempt a modest improvement over this technique by making use of the much larger set of open-ocean hurricane records and postulating that hurricanes make landfall during a random stage of their open-ocean lifetime. After testing the validity of this assumption, an expression is derived for the probability density of maximum winds. The probability functions so derived are then used to estimate hurricane return periods for several highly populated regions, and these are compared with return periods calculated both from historical data and from a set of synthetic storms generated using a recently published downscaling technique. The resulting return-period distributions compare well to those estimated from extreme-value theory with parameter fitting using a peaks-over-threshold model, but they are valid over the whole range of hurricane wind speeds.

Wind speeds from tropical cyclones (TCs) occurring near the USA are modeled with climate variables (covariates) using quantile regression. The influences of Atlantic sea-surface temperature (SST), the Pacific El Nino, and the North Atlantic oscillation (NAO) on near-coastal TC intensity are in the direction anticipated from previous studies using Poisson regression on cyclone counts and are, in general, strongest for higher intensity quantiles. The influence of solar activity, a new covariate, peaks near the median intensity level, but the relationship switches sign for the highest quantiles. An advantage of the quantile regression approach over a traditional parametric extreme value model is that it allows easier interpretation of model coefficients (parameters) with respect to changes to the covariates since coefficients vary as a function of quantile. It is proven mathematically that parameters of the Generalized Pareto Distribution (GPD) for extreme events can be used to estimate regression coefficients for the extreme quantiles. The mathematical relationship is demonstrated empirically using the subset of TC intensities exceeding 96 kt (49 m/s). Copyright © 2008 Royal Meteorological Society

Atlantic tropical cyclones are getting stronger on average, with a 30-year trend that has been related to an increase in ocean temperatures over the Atlantic Ocean and elsewhere. Over the rest of the tropics, however, possible trends in tropical cyclone intensity are less obvious, owing to the unreliability and incompleteness of the observational record and to a restricted focus, in previous trend analyses, on changes in average intensity. Here we overcome these two limitations by examining trends in the upper quantiles of per-cyclone maximum wind speeds (that is, the maximum intensities that cyclones achieve during their lifetimes), estimated from homogeneous data derived from an archive of satellite records. We find significant upward trends for wind speed quantiles above the 70th percentile, with trends as high as 0.3 +/- 0.09 m s(-1) yr(-1) (s.e.) for the strongest cyclones. We note separate upward trends in the estimated lifetime-maximum wind speeds of the very strongest tropical cyclones (99th percentile) over each ocean basin, with the largest increase at this quantile occurring over the North Atlantic, although not all basins show statistically significant increases. Our results are qualitatively consistent with the hypothesis that as the seas warm, the ocean has more energy to convert to tropical cyclone wind.

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. Here a statistical algorithm is developed to predict North Atlantic hurricane activity out to 5 yr. 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 multiseasonal 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.

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 analog (Hurricane Ivan of 2004) to be 54 m s−1 (105 kt) for a return period of 318 yr based on 11 events over 3500 yr. 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−1 (141 kt), with a lower bound on the 95% confidence interval of 64 m s−1 (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−1.

The interannual variability in typhoon landfalls over China is investigated using historical and modern records. For the purpose of substantiating and elaborating upon the claim of north to south variation in tropical cyclone activity over China, a north-to-south anti-correlation in yearly activity is confirmed in the historical cyclone records. When cyclone activity over the province of Guangdong is high (low), it tends to be low (high) over the province of Fujian. A similar spatial variation is identified in the modern records using a factor analysis model, which delineates typhoon activity over the southern provinces of Guangdong and Hainan from the activity over the northern provinces of Fujian, Taiwan, Zhejiang, Shanghai, Jiangsu, and Shandong. A landfall index of typhoon activity representing the degree to which each year follows this pattern of activity is used to identify correlated climate variables. A useful statistical regression model that includes sea-level pressure differences between Mongolia and western China and sea-surface temperature (SST) over the northwestern Pacific Ocean during the summer explains 26% of the interannual variability of the landfall index. It is suggested that a stronger than normal north-south pressure gradient increases the surface easterly wind flow over northern China; this, coupled with lower SST over the Pacific, favors typhoons taking a more westerly track toward southern China.

The rarity of severe coastal hurricanes implies that empirical estimates of extreme wind speed return levels will be unreliable. Here climatology models derived from extreme value theory are estimated using data from the best-track [Hurricane Database (HURDAT)] record. The occurrence of a hurricane above a specified threshold intensity level is assumed to follow a Poisson distribution, and the distribution of the maximum wind is assumed to follow a generalized Pareto distribution. The likelihood function is the product of the generalized Pareto probabilities for each wind speed estimate. A geographic region encompassing the entire U.S. coast vulnerable to Atlantic hurricanes is of primary interest, but the Gulf Coast, Florida, and the East Coast regions are also considered. Model parameters are first estimated using a maximum likelihood (ML) procedure. Results estimate the 100-yr return level for the entire coast at 157 kt (±10 kt), but at 117 kt (±4 kt) for the East Coast region (1 kt = 0.514 m s−1). Highest wind speed return levels are noted along the Gulf Coast from Texas to Alabama. The study also examines how the extreme wind return levels change depending on climate conditions including El Niño–Southern Oscillation, the Atlantic Multidecadal Oscillation, the North Atlantic Oscillation, and global temperature. The mean 5-yr return level during La Niña (El Niño) conditions is 125 (116) kt, but is 140 (164) kt for the 100-yr return level. This indicates that La Niña years are the most active for the occurrence of strong hurricanes, but that extreme hurricanes are more likely during El Niño years. Although El Niño inhibits hurricane formation in part through wind shear, the accompanying cooler lower stratosphere appears to increase the potential intensity of hurricanes that do form. To take advantage of older, less reliable data, the models are reformulated using Bayesian methods. Gibbs sampling is used to integrate the prior over the likelihood to obtain the posterior distributions for the model parameters conditional on global temperature. Higher temperatures are conditionally associated with more strong hurricanes and higher return levels for the strongest hurricane winds. Results compare favorably with an ML approach as well as with recent modeling and observational studies. The maximum possible near-coastal wind speed is estimated to be 208 kt (183 kt) using the Bayesian (ML) approach.

The authors build on their efforts to understand and predict coastal hurricane activity by developing statistical seasonal forecast models that can be used operationally. The modeling strategy uses May–June averaged values representing the North Atlantic Oscillation (NAO), the Southern Oscillation index (SOI), and the Atlantic multidecadal oscillation to predict the probabilities of observing U.S. hurricanes in the months ahead (July–November). The models are developed using a Bayesian approach and make use of data that extend back to 1851 with the earlier hurricane counts (prior to 1899) treated as less certain relative to the later counts. Out-of-sample hindcast skill is assessed using the mean-squared prediction error within a hold-one-out cross-validation exercise. Skill levels are compared to climatology. Predictions show skill above climatology, especially using the NAO + SOI and the NAO-only models. When the springtime NAO values are below normal, there is a heightened risk of U.S. hurricane activity relative to climatology. The preliminary NAO value for 2005 is −0.565 standard deviations so the NAO-only model predicts a 13% increase over climatology of observing three or more U.S. hurricanes.

The power dissipation of Atlantic tropical cyclones has risen dramatically during the last decades and the increase is correlated with an increase in the underlying sea surface temperature (SST) at low (decadal) frequencies. Because of the large positive correlation between global mean surface air temperature (GT) and Atlantic SST it has been speculated that increases in the power dissipation might, in part, be related to human activity. Here we investigate the question of the relationship between GT and hurricane power dissipation directly using statistical analysis and show that after removing the effect of SST, the correlation between GT and hurricane power dissipation is negative. This suggests that the positive influence of global temperature on Atlantic hurricanes appears to be limited to an indirect connection with tropical Atlantic SST. We also show that the relationship between hurricane power dissipation and Atlantic SST is significant at the high-frequency time scales. El Nino–Southern Oscillat...

Advances in hurricane climate science allow forecasts of seasonal landfall activity to be made. The authors begin with a review of the forecast methods available in the literature. They then reformulate the methods using a Bayesian probabilistic approach. This allows a direct comparison to be made while focusing on a single hindcast of the 2004 season over Florida. The models, including climatology, are estimated using Gibbs sampling. Diagnostic checks verify convergence and efficient mixing of the samples from each of the models. A below average sea level pressure gradient over the eastern North Atlantic Ocean during May and June in combination with an above average tropospheric-averaged wind index associated, in part, with a strengthening of the Bermuda high pressure during July resulted in an above average probability of at least one Florida hurricane. The relatively high hindcast probabilities for 2004 were in marked contrast to the most recent 50-yr empirical probabilities for Florida, but fell short in anticipating the unprecedented level of activity that ensued. Similar results are obtained from hindcasts of total U.S. hurricane activity for 2004.

A hierarchical Bayesian strategy for modeling annual U.S. hurricane counts from the period 1851-2000 is illustrated. The approach is based on a separation of the reliable twentieth-century records from the less precise nineteenth-century records and makes use of Poisson regression. The work extends a recent climatological analysis of U.S. hurricanes by including predictors (covariates) in the form of indices for the El Nino-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO). Model integration is achieved through a Markov chain Monte Carlo algorithm. A Bayesian strategy that uses only hurricane counts from the twentieth century together with noninformative priors compares favorably to a traditional (frequentist) approach and confirms a statistical relationship between climate patterns and coastal hurricane activity. Coinciding La Nina and negative NAO conditions significantly increase the probability of a U.S. hurricane. Hurricane counts from the nineteenth century are bootstrapped to obtain informative priors on the model parameters. The earlier records, though less reliable, allow for a more precise description of U.S. hurricane activity. This translates to a greater certainty in the authors' belief about the effects of ENSO and NAO on coastal hurricane activity. Similar conclusions are drawn when annual U.S. hurricane counts are disaggregated into regional counts. Contingent on the availability of values for the covariates, the models can be used to make predictive inferences about the hurricane season.

Time series of annual hurricane counts are examined using a changepoint analysis. The approach simulates posterior distributions of the Poisson-rate parameter using Gibbs sampling. A posterior distribution is a distribution of a parameter conditional on the data. The analysis is first performed on the annual series of major North Atlantic hurricane counts from the twentieth century. Results show significant shifts in hurricane rates during the middle 1940s, the middle 1960s, and at 1995, consistent with earlier published results. The analysis is then applied to U.S. hurricane activity. Results show no abrupt changes in overall coastal hurricane rates during the twentieth century. In contrast, the record of Florida hurricanes indicates downward shifts during the early 1950s and the late 1960s. The shifts result from fewer hurricanes passing through the Bahamas and the western Caribbean Sea. No significant rate shifts are noted along either the Gulf or East Coasts. Climate influences on coastal hurricane activity are then examined. Results show a significant reduction in U.S. hurricane activity

A space–time count process model is explained and applied to annual North Atlantic hurricane activity. The model uses the best-track data set of historical hurricane positions and intensities, together with climate variables, to determine local space–time coefficients of a right-truncated Poisson process. The truncated Poisson space–time autoregressive (TPSTAR) model is motivated by first examining a time-series model for the entire domain. Then a Poisson generalized linear model is considered that uses grid boxes within the domain and adds offset factors for latitude and longitude. A natural extension is then made that includes instantaneous local and autoregressive coupling between the grids. A final version of the model is found by backward selection of the predictors based on values of Bayesian and Akiake information criteria. The final model has five nearest neighbours and statistically significant couplings. Hindcasts are performed on the hurricane seasons from 1994 to 1997. Results show that, on average, model forecast probabilities are larger in regions in which hurricanes occurred. Quantitative skill assessment indicates some useful skill above climatology—currently the default leading candidate. The TPSTAR model could be a valuable guidance product when issuing seasonal hurricane forecasts. Copyright © 2002 Royal Meteorological Society.

The authors develop and apply a model that uses hurricane-experience data in counties along the U.S. hurricane coast to give annual exceedence probabilities to maximum tropical cyclone wind events. The model uses a maximum likelihood estimator to determine a linear regression for the scale and shape parameters of the Weibull distribution for maximum wind speed. Model simulations provide quantiles for the probabilities at prescribed hurricane intensities. When the model is run in the raw climatological mode, median probabilities compare favorably with probabilities from the National Hurricane Center’s risk analysis program “HURISK” model. When the model is run in the conditional climatological mode, covariate information in the form of regression equations for the distributional parameters allows probabilities to be estimated that are conditioned on climate factors. Changes to annual hurricane probabilities with respect to a combined effect of a La Nina event and a negative phase of the North Atla...

All hurricanes are different. Statistics helps you characterize hurricanes from the typical to the extreme. In this chapter, we provide an introduction to classical (or frequentist) statistics. To get the most out of it, we again encourage you to open an R session and type in the code as you read along. Descriptive statistics are used to summarize your data. The mean and the variance are good examples. So is correlation. Data can be a set of weather records or output from a global climate model. Descriptive statistics provide answers to questions like does Jamaica experience more hurricanes than Puerto Rico? In Chapter 2, you learned some functions for summarizing your data, let us review. Recall that the data set H.txt is a list of hurricane counts by year making landfall in the United States (excluding Hawaii). To input the data and save them as a data object, type . . . > H = read. Table ("H.txt", header=TRUE) . . . Make sure the data file is located in your working directory. To check your working directory, type getwd (). Sometimes all you need are a few summary statistics from your data. You can obtain the mean and variance by typing . . . > mean (H$All); var (H$All) [1] 1.69375 [1] 2.10059 . . . Recall that the semicolon acts as a return so you can place multiple functions on the same text line. The sample mean is a measure of the central tendency and the sample variance is a measure of the spread. These are called the first-and second-moment statistics. Like all statistics, they are random variables. A random variable can be thought of as a quantity whose value is not fixed; it changes depending on the values in your sample. If you consider the number of hurricanes over a different sample of years, the sample mean will almost certainly be different. Same with the variance. The sample mean provides an estimate of the population mean (the mean over all past and future years).

In this chapter, we focus on Bayesian modeling. Information about past hurricanes is available from instruments and written accounts. Written accounts are generally less precise than instrumental observations, which tend to become even more precise as technology advances. Here we show you how to build Bayesian models that make use of the available information while accounting for differences in levels of precision. We begin with a model for U.S. hurricane frequency and finish with a space–time model for basin-wide occurrences. We start with a model for predicting U.S. hurricane activity over the next three decades. The model is useful as a benchmark for climate change studies. The methodology was originally presented in Elsner and Bossak (2001) based on the formalism given in Epstein (1985). As you have seen throughout this book, the arrival of hurricanes on the coast is usefully considered a stochastic process, where the annual counts are described reasonably well by a Poisson distribution. The Poisson distribution is a limiting form of the binomial distribution with no upper bound on the number of occurrences and where the parameter λ characterizes the rate process. Knowledge of λ allows you to make statements about future hurricane frequency. Since the process is stochastic, your statements will be given in terms of probabilities (see Chapter 7). For example, the probability of ĥ hurricanes occurring over the next T years (e.g., 1, 5, 20, etc.) is . . . f (ĥ |λ,T) = exp(−λT) (λT)h/h! for h = 0,1,. . . , λ>0, and T > 0 (12.1) . . . The hat notation is used to indicate future values. The parameter λ and statistic T appear in the formula as a product, which is the mean and variance of the distribution. Knowledge about λ can come from historical written archives and instrumental records. It is logical for you to want to use as much of this information as possible before inferring something about future activity. This requires you to treat λ as a parameter that can be any positive real number, rather than as a fixed constant. One form for expressing your judgment about the values λ can take is through the gamma distribution.

Classical statistics involves ways to test hypotheses and estimate confidence intervals. Bayesian statistics involves methods to calculate probabilities associated with your hypotheses. The result is a posterior distribution that combines information from your data with prior beliefs. The term “Bayesian” comes from Bayes’s theorem—a single formula for obtaining the posterior distribution. It is the cornerstone of modern statistical methods. In this chapter we introduce Bayesian statistics. We begin by considering the problem of learning about the population proportion (percentage) of all hurricanes that make landfall. We then consider the problem of estimating how many days it takes your manuscript to get accepted for publication. Again, we encourage you to follow along by typing the code into your R console. Models that have skill at forecasting hurricane counts are more relevant to society if they include an estimate of the proportion that make landfall. Before examining the data, you hold a belief about the value of this proportion. You model your belief in terms of a prior distribution. Then after examining some data, you update your belief about the proportion by computing the posterior distribution (Albert, 2009). This setting allows you to predict the likely outcomes of a new sample taken from the population, for example, the proportion of landfalls for next year. The use of the pronoun “you” focuses attention on the Bayesian viewpoint that probabilities do not exist but are how much you personally believe that something is true. Said another way, probabilities are subjective and based on all the relevant information available to you. Here you think of a population consisting of past and future hurricanes in the North Atlantic. Then let π represent the proportion of this population that hit the United States at hurricane intensity. The value of π is unknown. You are interested in learning about what the value of π could be. Bayesian statistics requires that you represent your belief about the uncertainty in this percentage with a probability distribution. The distribution reflects your subjective prior opinion about plausible values of π. Before you examine a sample of hurricanes, you think about what the value of π might be.

Graphs and maps help you reason with data. They also help you communicate results. A good graph gives you the most information in the shortest time, with the least ink in the smallest space (Tufte, 1997). In this chapter, we show you how to make graphs and maps using R. A good strategy is to follow along with an open session, typing (or copying) the code as you read. Before you begin make sure you have the following data sets available in your workspace. Do this by typing . . . > SOI = read.table("SOI.txt", header=TRUE) > NAO = read.table("NAO.txt", header=TRUE) > SST = read.table("SST.txt", header=TRUE) > A = read.table("ATL.txt", header=TRUE) > US = read.table("H.txt", header=TRUE) . . . Not all the code is shown but all is available on our Web site. It is easy to make a graph. Here we provide guidance to help you make informative graphs. It is a tutorial on how to create publishable figures from your data. In R you have several choices. With the standard (base) graphics environment, you can produce a variety of plots with fine details. Most of the figures in this book use the standard graphics environment. The grid graphics environment is even more flexible. It allows you to design complex layouts with nested graphs where scaling is maintained upon resizing. The lattice and ggplot2 packages use grid graphics to create more specialized graphing functions and methods. The spplot function for example is plot method built with grid graphics that you will use to create maps. The ggplot2 package is an implementation of the grammar of graphics combining advantages from the standard and lattice graphic environments. It is worth the effort to learn. We begin with the standard graphics environment. A box plot is a graph of the five-number summary. The summary function applied to data produces the sample mean along with five other statistics including the minimum, the first quartile value, the median, the third quartile value, and the maximum. The box plot graphs these numbers. This is done using the boxplot function.

A cluster is a group of the same or similar events close together. Clusters arise in hurricane origin locations, tracks, and landfalls. In this chapter, we look at how to analyze and model clusters. We divide the chapter into methods for time, space, and feature clustering. Of the three feature clustering is best known to climatologists. We begin by showing you how to detect and model time clusters. Consecutive hurricanes originating in the same area often take similar paths. This grouping, or clustering, increases the potential for multiple landfalls above what you expect from random events. A statistical model for landfall probability captures clustering through covariates like the North Atlantic Oscillation (NAO), which relates a steering mechanism (position and strength of the subtropical high pressure) to coastal hurricane activity. But there could be additional time correlation not related to the covariates. A model that does not account for this extra variation will underestimate the potential for multiple hits in a season. Following Jagger and Elsner (2006), you consider three coastal regions including the Gulf Coast, Florida, and the East Coast (Fig. 6.2). Regions are large enough to capture enough hurricanes, but not too large as to include many non-coastal strikes. Here you use hourly position and intensity data described in Chapter 6. For each hurricane, you note its wind speed maximum within each region. If the maximum wind exceeds 33 m s−1, then you count it as a hurricane for the region. A tropical cyclone that affects more than one region at hurricane intensity is counted in each region. Because of this, the sum of the regional counts is larger than the total count. Begin by loading annual.RData. These data were assembled in Chapter 6. Subset the data for years starting with 1866. . . . > load("annual.RData") > dat = subset(annual, Year >= 1866) . . . The covariate Southern Oscillation Index (SOI) data begins in 1866 . Next, extract all hurricane counts for the Gulf coast, Florida, and East coast regions. . . . > cts = dat[, c("G.1", "F.1", "E.1")] . . .

This book is about hurricanes, climate, and statistics. These topics may not seem related. Hurricanes are violent winds and flooding rains, climate is about weather conditions from the past, and statistics is about numbers. But what if you wanted to estimate the probability of winds exceeding 60 ms−1 in Florida next year. The answer involves all three, hurricanes (fastest winds), climate (weather of the past), and statistics (probability). This book teaches you how to answer these questions in a rigorous and scientific way. We begin here with a short description of the topics and a few notes on what this book is about. A hurricane is an area of low air pressure over the warm tropical ocean. The low pressure creates showers and thunderstorms that start the winds rotating. The rotation helps to develop new thunderstorms. A tropical storm forms when the rotating winds exceed 17 ms−1 and a hurricane when they exceed 33 ms−1. Once formed, the winds continue to blow despite friction by an in-up-and-out circulation that imports heat at high temperature from the ocean and exports heat at lower temperature in the upper troposphere (near 16 km), which is similar to the way a steam engine converts thermal energy to mechanical motion. In short, a hurricane is powered by moisture and heat. Strong winds are a hurricane’s defining characteristic. Wind is caused by the change in air pressure between two locations. In the center 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 difference causes the air to move from the outside inward toward the center. 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 counter clockwise direction toward the region of lowest pressure.

Strong hurricanes, such as Camille in 1969, Andrew in 1992, and Katrina in 2005, cause catastrophic damage. It is important to have an estimate of when the next big one will occur. You also want to know what influences the strongest hurricanes and whether they are getting stronger as the earth warms. This chapter shows you how to model hurricane intensity. The data are basinwide lifetime highest intensities for individual tropical cyclones over the North Atlantic and county-level hurricane wind intervals. We begin by considering trends using the method of quantile regression and then examine extreme-value models for estimating return periods. We also look at modeling cyclone winds when the values are given by category, and use Miami-Dade County as an example. Here you consider cyclones above tropical storm intensity (≥ 17 m s−1) during the period 1967–2010, inclusive. The period is long enough to see changes but not too long that it includes intensity estimates before satellite observations. We use “intensity” and “strength” synonymously to mean the fastest wind inside the cyclone. Consider the set of events defined by the location and wind speed at which a tropical cyclone first reaches its lifetime maximum intensity (see Chapter 5). The data are in the file LMI.txt. Import and list the values in 10 columns of the first 6 rows of the data frame by typing . . . > LMI.df = read.table("LMI.txt", header=TRUE) > round(head(LMI.df)[c(1, 5:9, 12, 16)], 1). . . The data set is described in Chapter 6. Here your interest is the smoothed intensity estimate at the time of lifetime maximum (WmaxS). First, convert the wind speeds from the operational units of knots to the SI units of meter per second. . . . > LMI.df$WmaxS = LMI.df$WmaxS * .5144 . . . Next, determine the quartiles (0.25 and 0.75 quantiles) of the wind speed distribution. The quartiles divide the cumulative distribution function (CDF) into three equal-sized subsets. . . . > quantile(LMI.df$WmaxS, c(.25, .75)) 25% 75% 25.5 46.0 . . . You find that 25 percent of the cyclones have a lifetime maximum wind speed less than 26 m s−1 and 75 percent have a maximum wind speed less than 46ms−1, so that 50 percent of all cyclones have a maximum wind speed between 26 and 46 m s−1 (interquartile range–IQR).

In this chapter, we consider time series models. A time series is an ordered sequence of numbers with respect to time. In climatology, you encounter time-series data in a format given by . . . {h}Tt=1 = {h1,h2,. . . ,hT} (10.1) . . . where the time t is over a given season, month, week, or day and T is the time series length. The aim is to understand the underlying physical processes that produced the series. A trend is an example. Often by simply looking at a time series plot, you can pick out a trend that tells you that the process generating the data is changing. A single time series gives you a sample from the process. Yet under the ergodic hypothesis, a single time series of infinite length contains the same information (loosely speaking) as the collection of all possible series of finite length. In this case, you can use your series to learn about the nature of the process. This is analogous to spatial interpolation encountered in Chapter 9, where the variogram was computed under the assumption that the rainfall field is stationary. Here we consider a selection of techniques and models for time series data. We begin by showing you how to overlay plots as a tool for exploratory analysis. This is done to compare the variation between two series qualitatively. We demonstrate large variation in hurricane counts arising from a constant rate process. We then show techniques for smoothing. We continue with a change-point model and techniques for decomposing a continuous-valued series. We conclude with a unique way to create a network graph from a time series of counts and suggest a new definition of a climate anomaly. A plot showing your variables on a common time axis is an informative exploratory graph. Values from two different series are scaled to have the same relative range so the covariation in the variables can be compared visually. Here you do this with hurricane counts and sea-surface temperature (SST). Begin by loading annual.RData. These data were assembled in Chapter 6.

Here in Part II, we focus on statistical models for understanding and predicting hurricane climate. This chapter shows you how to model hurricane occurrence. This is done using the annual count of hurricanes making landfall in the United States. We also consider the occurrence of hurricanes across the basin and by origin. We begin with exploratory analysis and then show you how to model counts with Poisson regression. Issues of model fit, interpretation, and prediction are considered in turn. The topic of how to assess forecast skill is examined including how to perform cross-validation. Alternatives to the Poisson regression model are considered. Logistic regression and receiver operating characteristics (ROCS) are also covered. You use the data set US.txt which contains a list of tropical cyclone counts by year (see Chapter 2). The counts indicate the number of hurricanes hitting in the United States (excluding Hawaii). Input the data, save them as a data frame object, and print out the first six lines by typing . . . > H = read.table("US.txt", header=TRUE) > head(H) . . . The columns include year Year, number of U.S. hurricanes All, number of major U.S. hurricanes MUS, number of U.S. Gulf coast hurricanes G, number of Florida hurricanes FL, and number of East coast hurricanes E. Save the total number of years in the record as n and the average number hurricanes per year as rate. . . . > n = length(H$Year); rate = mean(H$All) > n; rate [1] 160 [1] 1.69 . . . The average number of U.S. hurricanes is 1.69 per year over these 160 years. First plot a time series and a distribution of the annual counts. Together, the two plots provide a nice summary of the information in your data relevant to any modeling effort. . . . > par(las=1) > layout(matrix(c(1, 2), 1, 2, byrow=TRUE), + widths=c(3/5, 2/5)) > plot(H$Year, H$All, type="h", xlab="Year", + ylab="Hurricane Count") > grid() > mtext("a", side=3, line=1, adj=0, cex=1.1) > barplot(table(H$All), xlab="Hurricane Count", + ylab="Number of Years", main="") > mtext("b", side=3, line=1, adj=0, cex=1.1) . . . The layout function divides the plot page into rows and columns as specified in the matrix function (first argument).

Hurricane data originate from careful analysis of past storms by operational meteorologists. The data include estimates of the hurricane position and intensity at 6-hourly intervals. Information related to landfall time, local wind speeds, damages, and deaths, as well as cyclone size, are included. The data are archived by season. Some effort is needed to make the data useful for hurricane climate studies. In this chapter, we describe the data sets used throughout this book. We show you a work flow that includes importing, interpolating, smoothing, and adding attributes. We also show you how to create subsets of the data. Code in this chapter is more complicated and it can take longer to run. You can skip this material on first reading and continue with model building in Chapter 7. You can return here when you have an updated version of the data that includes the most recent years. Most statistical models in this book use the best-track data. Here we describe these data and provide original source material. We also explain how to smooth and interpolate them. Interpolations are needed for regional hurricane analyses. The best-track data set contains the 6-hourly center locations and intensities of all known tropical cyclones across the North Atlantic basin, including the Gulf of Mexico and Caribbean Sea. The data set is called HURDAT for HURricane DATa. It is maintained by the U.S. National Oceanic and Atmospheric Administration (NOAA) at the National Hurricane Center (NHC). Center locations are given in geographic coordinates (in tenths of degrees) and the intensities, representing the one-minute near-surface (∼10 m) wind speeds, are given in knots (1 kt = .5144 m s−1) and the minimum central pressures are given in millibars (1 mb = 1 hPa). The data are provided in 6-hourly intervals starting at 00 UTC (Universal Time Coordinate). The version of HURDAT file used here contains cyclones over the period 1851 through 2010 inclusive. Information on the history and origin of these data is found in Jarvinen et al (1984). The file has a logical structure that makes it easy to read with a FORTRAN program. Each cyclone contains a header record, a series of data records, and a trailer record.

Hurricanes are nature's most destructive storms and they are becoming more powerful as the globe warms. Hurricane Climatology explains how to analyze and model hurricane data to better understand and predict present and future hurricane activity. It uses the open-source and now widely used R software for statistical computing to create a tutorial-style manual for independent study, review, and reference. The text is written around the code that when copied will reproduce the graphs, tables, and maps. The approach is different from other books that use R. It focuses on a single topic and explains how to make use of R to better understand the topic. The book is organized into two parts, the first of which provides material on software, statistics, and data. The second part presents methods and models used in hurricane climate research.

In this chapter, we show some broader applications of our models and methods. We focus on impact models. Hurricanes are capable of generating large financial losses. We begin with a model that estimates extreme losses conditional on climate covariates. We then describe a method for quantifying the relative change in potential losses over the decades. Financial losses from hurricanes are to some extent directly related to fluctuations in climate. Environmental factors influence the frequency and intensity of hurricanes at the coast as detailed throughout this book (see for example Chapters 7 and 8). So, it is not surprising that these same environmental signals appear in estimates of losses. Here loss is the economic damage associated with a hurricane’s direct impact. A normalization procedure adjusts the loss estimate from a past hurricane to what it would be if the same cyclone struck in a recent year by accounting for inflation and changes in wealth and population over the intervening time, plus a factor to account for changes in the number of housing units exceeding population growth. The method produces loss estimates that can be compared over time (Pielke et al. 2008). Here you focus on losses exceeding one billion ($ U.S.) that have been adjusted to 2005. The loss data are available in Losses.txt in JAGS format (see Chapter 9). Input the data by typing . . . > source("Losses.txt"). . . The log-transformed loss amounts are in the column labeled ‘y’. The annual number of loss events are in the column labeled ‘L’. The data cover the period 1900–2007. More details about these data are given in Jagger et al. (2011). You begin by plotting a time series of the number of losses and a histogram of total loss per event. . . . > layout(matrix(c(1, 2), 1, 2, byrow=TRUE), + widths=c(3/5, 2/5)) > plot(1900:2007, L, type="h", xlab="Year", + ylab="Number of Loss Events") > grid() > mtext("a", side=3, line=1, adj=0, cex=1.1) > hist(y, xlab="Loss Amount ($ log)", + ylab="Frequency", main="") > mtext("b", side=3, line=1, adj=0, cex=1.1) . . .

In Chapter 7, annual counts were used to create rate models, and in Chapter 8, lifetime maximum winds were used to create intensity models. In this chapter, we show you how to use cyclone track data together with climate field data to create spatial models. Spatial models make use of location information in data. Geographic coordinates locate the hurricane’s center on the surface of the earth and wind speed provides an attribute. Spatial models make use of location separate from attributes. Given a common spatial framework, these models can accommodate climate data including indices (e.g., North Atlantic Oscillation) and fields (e.g., sea-surface temperature). Here, we show you how to create a spatial framework for combining hurricane data with climate data. The method tessellates the basin with hexagons and populates them with local cyclone and climate information (Elsner et al., 2012). In Chapter 5, you learned how to create a spatial data frame using functions from the sp package (Bivand et al., 2008). Let us review. Here you are interested in wind speeds along the entire track for all tropical storms and hurricanes during the 2005 North Atlantic season. You begin by creating a data frame from the best.use.RData file, where you subset on year and wind speed and convert the speed to meters per second. . . . > load("best.use.RData") > W.df = subset(best.use, Yr==2005 & WmaxS >= 34 + & Type=="*") > W.df$WmaxS = W.df$WmaxS * .5144 . . . The asterisk for Type indicates a tropical cyclone as opposed to a tropical wave or extratropical cyclone. The number of rows in your data frame is the total number of cyclone hours (3,010), and you save this by typing . . . > ch = nrow(W.df) . . . Next, assign the lon and lat columns as spatial coordinates using the coordinates function (sp). Finally, make a copy of your data frame, keeping only the spatial coordinates and the wind speed columns.

[1] The strongest hurricanes are getting stronger as the oceans heat up especially over the North Atlantic. Sensitivity of hurricane intensity to ocean heating is an important variable for understanding what hurricanes might be like in the future, but reliable estimates are not possible with short time-series records. Studies using paired values of intensity and sea-surface temperature (SST) are also limited because most pairs represent hurricanes in an environment less than thermodynamically optimal. Here we overcome these limitations using spatial grids and a model for the limiting hurricane intensity by region and estimate the sensitivity to be 7.9 ± 1.19 m s− K−1 (s.e.) for hurricanes over seas hotter than 25°C across the North Atlantic. Results indicate the potential for stronger hurricanes during the 21st century as oceans continue to warm over this part of the world.