A hurricane track density function and empirical orthogonal function approach to predicting seasonal hurricane activity in the Atlantic Basin Elinor Keith April 17, 2007 Abstract

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A hurricane track density function and empirical orthogonal function approach to predicting seasonal hurricane activity in the Atlantic Basin

Elinor Keith

April 17, 2007

Seasonal hurricane forecasts are continuing to develop skill, although they are still subject to large uncertainties. This study uses a hurricane track density function (HTDF) and empirical orthogonal functions (EOFs) to help find variables to predict seasonal Atlantic hurricane and tropical storm activity, with an emphasis on US landfalling hurricanes. Correlations on time scales ranging from intraseasonal, such as the Madden-Julian Oscillation (MJO), to multidecadal, such as the Atlantic multidecadal Oscillation (AMO) are tested against historic data.


Many climatic factors are used in predicting the strength of a hurricane season. One of the most cited is the multidecadal cycle, which affects key factors in hurricane development such as SSTs and wind shear. Since 1995 the Atlantic has been in its active multidecadal mode, as shown by the increase in storms from the 1970-1994 period and the 1995-2000 period (Goldenberg, S. B., Landsea, C. W., Mestas-Nunez, A. M., and Gray, W. M., 2001.)

Another important factor is El Niño-Southern Oscillation (ENSO). During La Niña (cooler than normal eastern tropical Pacific SSTs), convection over the Pacific is reduced. This in turn leads to more easterly upper tropospheric winds over the Atlantic and reduced vertical wind shear (VWS; Gray, W. M., 1984). VWS over the main development region (MDR) between 10°N-20°N from Africa to the Americas can significantly reduce hurricane activity (Gray, W. M., 1990). Gray (1984) found that there were an average of 10.9 hurricane days during El Niño years and 23.2 hurricane days during non-El Niño years. Out of the 54 major hurricanes which made landfall over the US from 1900-76, only four happened during the 16 strong to moderate El Niño years. There was an average of 0.25 major hurricane strikes in El Niño years during 1900-83, compared to 0.74 in non-El Niño years.

Chelliah and Bell (2004) studied both the Tropical Multidecadal Mode (TMM), which corresponds to this multidecadal signal, and ENSO. They found the TMM to be even more important than ENSO in determining the upper tropospheric winds. TMM and ENSO combined accounted for 70-80% of the variance of the 200 hPa velocity anomalies between 30S-30N. TMM was found to represent 50-60% of the overall variability, with ENSO contributing 22-24%. Negative TMM and La Niña conditions both tend to reduce shear over the tropical Atlantic.

The negative-phase TMM (an active multidecadal mode) is also associated with anomalous upper-level divergence and increased rainfall over Africa (Chelliah, M. and Bell, G. D., 2004). The plentiful African rainfall is in turn associated with increased Atlantic hurricane activity and, in particular, greater landfall of intense hurricanes in the US, especially over Florida (Gray, W. M., 1990).

Atlantic SSTs are another extremely important factor, since hurricanes are essentially heat engines deriving their power from the warmth and moisture of the ocean surface. Negative TMM is associated with anomalously warm Atlantic SSTs (Chelliah, M. and Bell, G. D., 2004).

One of the most widely used seasonal hurricane forecasts, that of Dr. William Gray at Colorado State University, uses 6 parameters as early indicators of an active Atlantic hurricane season in their April predictions: (1) February upper tropospheric (200 hPa) easterlies over Equatorial East Brazil, indicating ENSO-neutral or La Niña conditions, (2) February-March 200 hPa northerlies over the southern Indian Ocean, indicating that the South Indian Convergence Zone is shifted to the northeast, (3) high February sea level pressure (SLP) over the Southeast Pacific Ocean, indicating a strong Southern Oscillation Index and stronger trade winds over the Pacific, which lead to increased upwelling along South America and La Niña conditions, (4) high SSTs in the off the northwest coast of Europe, indicating that later in the year there will be a strong Thermohaline Circulation (THC), a weaker subtropical high, and reduced trade winds, which implies weaker upwelling in the tropical Atlantic, bringing higher SSTs, (5) high 500 hPa geopotential height over the Greenland-Iceland-Norwegian Sea from the previous November, linked with a negative Arctic Oscillation (AO) and North Atlantic Oscillation (NAO) and, in the long term, strong THC as in 4, and (6) low SLP over the Gulf of Mexico during the previous September-November, which is generally positive during the final year of El Niño conditions, and therefore indicates a coming switch to La Niña conditions. In addition to these factors, they find analog years with similar oceanic and atmospheric conditions (Klotzbach, P. J. and Gray, W. M., 2006).

The hurricane and tropical storm data come from the “best-track” database (HURDAT), maintained by NOAA's National Hurricane Center (NHC). This data set contains 6-hourly storm locations for all tropical storms and hurricanes between 1851-2005. Because of large uncertainties in the earlier data, the analysis was limited to data from 1944-2005, when airplanes were used to help track storms. Landfalling hurricanes in the US are listed in the record along with their category at landfall and the state in which it occurred.

The HTDF is based on the cyclone track density function of Anderson and Gyakum (1989), and is a way of converting track data from discrete storms into a regular grid in time and space. The cyclone track density field, C(x, t), is defined as:



when and

otherwise, .

The variable xj is defined as the jth cyclone observation taken at time tj, and the grid point being estimated is at position x and time t. vj is the cyclone’s windspeed, in knots. W(Δx, Δt) is a weighting function for the interpolation; in this paper, Sx is set to 16/π and St to 36/π (Anderson, J. R. and Gyakum, J. R., 1989; Xie, L., Yan, T. Z., Pietrafesa, L. J., Morrison, J. M., and Karl, T., 2005).

In this EOF analysis, the data were interpolated onto a 1°x 1° grid between 20°N-42°N and 60°W-100°W. Gridpoints over land, the Great Lakes, and the Pacific are removed. The 63 years of data 1944-2006 were computed using a daily time resolution within the 183-day hurricane season (June 1-November 30).

The EOF is a form of PCA described in Lorenz (1956) and is commonly used in meteorological and oceanic data analysis (Richman, M. B. and Lamb, P. J., 1985; Xie, L., Yan, T. Z., Pietrafesa, L. J., Morrison, J. M., and Karl, T., 2005) and, like any form of factor analysis, seeks to represent a set of variables in terms of a smaller set of hypothetical (and, in this case, orthogonal) variables (Kim, J.-O. and Mueller, C. W., 1978). In this case, the EOFs are computed via Singular Value Decomposition (SVD). Should each of the largest eigenvectors correspond to a physical factor, that factor might make a valuable predictor of hurricane activity.

Richman and Lamb (1985) asserted the importance of factor rotation in order to generate more robust spatial patterns. To address this, VARIMAX rotation was used but made an insignificant difference. (The Pearson correlation between the unrotated and rotated top three EOF patterns were 0.97, 0.996, and -0.997, respectively.)

Cross-correlations between these EOF time series and a large set of monthly atmospheric and oceanic indices were computed. Indices that either showed significant, prolonged correlation with one or more of the EOF time series or were discussed in the literature were deemed worth further exploration.

Figure 1 shows the percent variance accounted for by the largest 20 EOFs. The top 3 EOF patterns account for 65% of the variance, and after them the percent variance explained by each EOF drops below 10% and levels off a little, making it a decent cut-off point for an exploratory study.

The EOF patterns and time series are shown in Figure 1.

Figure 2 shows the spatial loading patterns and reconstructed time series for the top 3 EOFs. The loading pattern of EOF 1 is positive everywhere (which is common for the first EOF pattern) and is maximized in the western Atlantic near Bermuda. It should correlate well with total Atlantic activity as well as landfall counts in the southeast and northeastern US. Indeed, during the five years with the highest values in EOF 1, 55 hurricanes occurred over the entire Atlantic, versus only 18 in the 5 lowest years.

EOF 2 is maximal over the Gulf of Mexico, with smaller negative values in the northern Atlantic, sugguesting that it distinguishes years with a strong easterly steering flow, when tropical cyclone are more likely to be driven westward towards the US coastline, from those with weak steering flow. EOF 3 has a more complicated pattern. It is positive along the east coast of Florida, over the Bahamas, and negative in the Gulf of Mexico and in the central north Atlantic.

Figures 3 -5 show a selection of the cross-correlations of the HTDF EOFs with common climate indices, which exhibit a range of time scales from 40-50 days in the case of the Madden-Julian Oscillation (Figure 3) to several months (Western Hemisphere Warm Pool, Figure 4) to several years (Atlantic Multidecadal Oscillation, Figure 5.) All of these indices show significant correlation at a lead time that would be useful in a seasonal hurricane forecasting.


The HTDF/EOF approach is useful in taking a dataset which is highly variable in space and time and gridding it, reducing its dimensions, and separating the larger signals from noise so that it is easier to work with. The EOF time series also provide a benefit over simple hurricane counts as they have a higher temporal density and are not limited to integers. The HTDFs and EOFs are extremely useful as tools of exploratory data analysis, despite their empirical nature.



AMO Index is available from the Climate Prediction Center (CPC) at http://www.cdc.noaa.gov/ClimateIndices/List/ and is based on Enfield, et al (2001)

MJO Index available from the CPC at http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_mjo_index/proj_norm_order.ascii

WHWP is available from CPC and AOML at http://www.cdc.noaa.gov/ClimateIndices/List/ and climatology is from Wang and Enfield (2001)
Data analysis was done in FORTRAN and R (R Development Core Team, 2006).


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