H = H t + H b
where Ht = exp (b0 + b1x1
+ b2x2 + b3x3 + b4x4)
and where the b's are coefficients on the predictors x.
The four predictors include (1) a 1-month forward extrapolation of the
30 mb zonal winds at 10N (a measure of the QBO phase), (2) Jun-Jul average
rainfall anomalies (expressed in standard deviations) for the West Sahel
region in Africa, (3) the past Aug-through-Nov average rainfall standardized
anomalies in the Gulf of Guinea region, and (4) the Southern Oscillation
Index (SOI) averaged over June and July. The direction of the relationships
are as highlighted in Gray's predictions: positive correlations with the
rainfalls, with the 30 mb zonal wind, as well as with the SOI.
We also use a Poisson regression to estimate the number of intense hurricanes
(3 or more on the Saffir/Simpson scale), as detailed in Elsner and Schmertmann
(1993):
I = exp (g0 + g1x1 + g2x2 + g3x3 + g4x4)
The predictors used to forecasts intense hurricanes are identical
to those used to predict tropical-only hurricanes except that the 50 mb
zonal wind is used instead of the SOI, providing a more complete description
of the QBO state. This set of predictors is changed slightly from that
used in the longer-lead forecast for the 1996 storm season shown in the
December 1995 issue of this Bulletin because it was determined, based on
statistical tests, that the shear parameter used in the early December
forecast model adds nothing significant to the early August model. The
December 1993 issue of this Bulletin briefly summarizes the reasoning behind
the beneficial use of the Poisson as compared to ordinary multiple linear
regression, particularly for relatively infrequently occurring events such
as intense hurricanes.
Both the hurricane and intense hurricane models have been skill-evaluated
using a hold-one-out cross-validation strategy. The correlation between
actual and predicted number of hurricanes is 0.65 with a mean absolute
error of 1.51 storms. For the number of intense hurricanes the correlation
between actual and predicted is 084, with mean absolute error 0.74 storms.
Forecast methodology for sub-basin activity
In addition to basin-wide activity we are now predicting activity in four
sub-basins of the Atlantic including the Caribbean Sea, the Gulf of Mexico,
the Southeast U.S. Coast (Cape Hatteras south to Key West) and the Northeast
U.S. coast (Cape Hatteras north to the Canadian border) (Lehmiller et al.
1996). We use logistic regression to predict hurricane landfalls along
the Northeast and Southeast coasts and the presence or absence of intense
hurricanes in the Gulf and Caribbean. As with the approach taken for basin-wide
activity, we express the sub-basin forecasts in terms of probabilities.
Logistic regression is a statistical model used to predict events in a
yes/no framework by estimating coefficients for several predictor variables.
Here we use a maximum likelihood technique to obtain the coefficients.
A logical regression can be expressed as
where the a's are the coefficients on the p predictors x.
Predictors for these models include those used for basin-wide activity,
with the addition of several others. For example, vertical shear is computed
from July averaged winds at Cape Hatteras and Miami using 00 and 12 UTC
rawinsonde observations. The shear is the Euclidean distance between the
700 and 200 mb wind components:
[ (u700-u200)2 + (v700-v200)2
]. Additionally, we use sea level pressures (SLPs) averaged over four locations
along the U.S. East Coast including Miami, Charleston, Cape Hatteras and
Boston, and sea surface temperature anomalies averaged from April through
June in the North Atlantic and the tropical Atlantic and Caribbean (Gray
et al. 1996) and the zonal wind anomaly from upper tropospheric (12 km)
zonal winds averaged over June and July (Gray et al. 1996).
Prediction error for the logistic models expressed as a cross-validated
accuracy ratio ranges from 81.4% (compared with a climatology of 58.1%)
for the U.S. Southeast coastal hurricane landfall model, to 78.3% (climatology
of 52.2%) for the Gulf of Mexico intense hurricane model, to 82.6% (climatology
of 52.2) for the Caribbean intense hurricane model. Forecast accuracy for
the U.S. Northeast coastal landfall model is not significantly better than
climatology.
Predictions for the 1996 Atlantic Hurricane Season
Some of the predictor data for the statistical models was obtained from
Dr. Chris Landsea on August 7. The predictor variables and regression coefficients
for the number of tropical-only hurricanes and the number of intense hurricanes,
estimated from the 1950-95 data, are shown in Table 1 and the resulting
forecast probabilities are shown in Tables 2 and 3.
The forecasts indicate a near average 1996 hurricane season with a better
than 70% chance of observing less than 2 intense hurricanes in addition
to Bertha (which reached intense hurricane strength in July). Moreover,
there is a better than 65% chance of observing between 3 and 6 hurricanes
from August onward (i.e. in addition to the two tropical cyclones that
reached hurricane strength before the beginning of August). The models
indicate a 40% chance of observing at least one more (following July) intense
Caribbean hurricane this year, and reflect only a slim likelihood of an
East Coast hurricane landfall in addition to Bertha. Despite the expectation
of a near average season, Table 3 indicates that the forecast probabilities
for East Coast hurricane landfall are lower than the climatological probabilities.
Table 1. Model specifications for total Atlantic hurri-cane activity. See text for more detail about the nature and timing of the predictors.
Coeff: | Coeff: | ||
1996 | Tropical | Intense | |
Predictor Term | Value | Hurric. | Hurric. |
constant | ----- | 1.036 | 1.117 |
50mb zonal wind | -20 m/s | ----- | 0.021 |
30mb zonal wind | -33 m/s | 0.014 | 0.013 |
western Sahel rainfall | -0.60 sd | 0.369 | 0.410 |
Gulf of Guinea rainfall | 0.10 sd | 0.670 | 0.428 |
SOI | 1.30 sd | 0.163 | ----- |
Table 2. Atlantic hurricane activity probabilities for 1996.
H refers to hurricanes, I intense hurricanes. The expected value of H for
the balance of the 1996 season is 4.5, and the expected value of I is 1.1.
Number | ||||||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9+ | |||||||||||
H | 0.011 | 0.050 | 0.112 | 0.169 | 0.190 | 0.171 | 0.128 | 0.082 | 0.046 | <0.040 | ||||||||||
I | 0.344 | 0.367 | 0.196 | 0.070 | 0.019 | 0.004 | 0.001 | 0.000 | 0.000 | 0.000 |
Table 3. Probabilities of a hurricane landfall along the Southeast and Northeast coasts and the probabilities of the presence or absence of an intense hurricane in the Gulf and Caribbean for 1996. H denotes hurricanes, I intense hurricanes. The asterisk indicates that the model has statistically significant forecast skill, given the present sample size of events.
Climatological | |||
Sub-basin | Probability | Probability | |
H | SE Coast | 0.088 | 0.488 |
H | NE Coast | 0.010 | 0.152 |
I | Gulf | 0.130 | 0.478 |
I | Caribbean | 0.400 | 0.478 |
Acknowledgments: Partial support for this work came from the Risk
Prediction Initiative (RPI) of the Bermuda Biological Station for Research
(BBSR).
References
Elsner, J.B. and C.P. Schmertmann, 1993: Improving extended-range
seasonal predictions of intense Atlantic hurricane activity. Wea. Forecasting,
8, 345-351.
Elsner, J.B., G.S. Lehmiller and T.B. Kimberlain, 1996: Objective classification
of Atlantic basin hurricanes. J. Climate, 9, accepted.
Gray, W.M., C.W. Landsea, P.W. Mielke, and K.J. Berry, 1993: Predicting
Atlantic seasonal tropical cyclone activity by 1 August. Wea. Forecasting,
8, 73-86.
Hess, J.C., J.B. Elsner and N.E. LaSeur, 1995: Improving seasonal
hurricane predictions for the Atlantic Basin. Wea. Forecasting, 10, 425-432.
Lehmiller, G.S., T.B. Kimberlain and J.B. Elsner, 1997: Seasonal prediction
models for North Atlantic basin hurricane location. Mon. Wea. Rev., 125,
submitted.