PREDICTING ATLANTIC BASIN SEASONAL TROPICAL CYCLONE ACTIVITY BY 1 JUNE

William M. Gray
Department of Atmospheric Science
Colorado State University
Fort Collins, CO

Christopher W. Landsea
Department of Atmospheric Science
Colorado State University
Fort Collins, CO

Paul W. Mielke, Jr.
Department of Statistics
Colorado State University
Fort Collins, CO

Kenneth J. Berry
Department of Statistics
Colorado State University
Fort Collins, CO

Weather and Forecasting, Vol. 9, 103-115 (1994)


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ABSTRACT



This is the third in a series of papers describing the potential of the seasonal forecasting of Atlantic basin tropicalcyclone activity. While previous papers describe seasonal prediction from 1 December of the previous year and from 1 August of the current year, this work demonstrates predictability by 1 June, the ``official" beginning of the hurricane season. Through three groupings consisting of 13 separate predictors hindcasts that explain 51% to 72% of the variability as measured by across-validated (o n jackknifed) agreement coefficient are achieved for eight measures of seasonal tropical cyclone activity. The three groupings of independent prediction data include 1) quasi-biennial oscillation (QBO) information from 50 and 30 mb zonal winds (three pre dictors), 2) West African rainfall, sea level pressure, and temperature data (four predictors), and 3) Caribbean Basin and El Niño-Southern Oscillation information including Caribbean 200 mb zonal winds and sea level pressures as well as equatorial Eastern Pacific sea surface temperatures and Southern Oscillation Index values (six predictors). The cross-validation is carried out using least sum of absolute regression that provides an efficient procedure for the maximum agreement measure criterion . Corrected intense hurricane data for the 1950s and 1960s have been incorporated into the forecasts. Comparisons of these 1 June forecast results with forecast results from 1 December of the year previous and 1 August of the current year are also giv en.

1  Introduction

This paper describes an empirically-based Statistical forecasting scheme for seasonal prediction of Atlantic basin tropical cyclone activity by 1 June, the ``official" beginning of the hurricane season. Previous papers by the authors have shown skillful seasonal forecasting by 1 December of the previous year (Gray et al. 1992a) and by 1 August of the current year (Gray et al. 1993). The results presented here builds upon this previous work to provide for improved forecasts utilizing additional predictors that are available by the end of May.

Thirteen variables are arranged into three predictor groupings. The groupings include 1) stratospheric quasi-biennial oscillation (QBO) data, 2) West African surface data, and 3) Caribbean Sea surface data/El Niño-Southern Oscillation (ENSO) data. The stratospheric QBO group is comprised of 50 and 30 mb zonal winds and the vertical wind shear between the two levels extrapolated from May to September near 10N. The West African surface data grouping is composed of previous year August to November Gulf of Guinea rainfall, previous year August to September western Sahelian rainfall, February to May West African sea level pressure gradients, and February to May West African temperature gradients. The Caribbean Basin-ENSO factors include the April to May conditions of the equatorial Eastern Pacific sea surface temperatures (SST) and the standardized Tahiti minus Darwin sea level pressure index (e.g. the Southern Oscillation Index or SOI), the time change of these quantities from January and February to April and May, and the 200 mb zonal wind anomalies (ZWA) and the sea level pressure anomalies (SLPA) within the Caribbean Basin for April and May.

The tropical cyclone-dependent variables include the seasonal total numbers of named storms (NS), hurricanes (H), intense (or major) hurricanes (IH), named storm days (NSD), hurricane days (HD), intense hurricane days (IHD), and hurricane destruction potential (HDP). Definitions of these are contained in Gray et al. (1992a, 1993). Also included is a new parameter of seasonal activity termed the net tropical cyclone activity (NTC), which is defined as


NTC = (%NS + %H + %IH + %NSD + %HD + %IHD)/6

where as each season's percentage values from the long period mean is used for the six measures of seasonal activity. The NTC* is useful as a seasonal tropical cyclone measure because it combines all of the other tropical cyclone parameters into a single, normalized measure of activity. There are many seasons in which a single parameter, such as a number of hurricanes, is not representative of the entire tropical cyclone activity of that yea. For instance, 1977 had 5H, but was otherwise an inact ive year: only 7 HD, 1 IH, an 1 IHD. By contrast, while 1988 also had 5 H, other seasonal parameters indicated an active year: 24HD, 3 IH, and IHD. These are examples of year having an identical parameter yet much different levels of other activity. To ov ercome these difficulties we propose the use of a single index, which is a combination of six measures of tropical cyclone activity.

Note that the 1950-1969 quantities of IH, IHD, HDP, and NTC have been adjusted to reflect a small over estimintation of tropical cyclone intensities as reported by Landsea (1993). These values, which are slightly reduced from previously published data ( Gray et al. 1992a 1993), are identified as IH*, IHD*, HDP*, and NTC*. Table 1 shows the individual yearly values for each dependent variable.

This report will briefly discuss the predictors which have been previously utilized for forecasting as well as a more in depth look at two new predictors, the West African sea level pressure and temperature gradients in the next section. In section 3, analyses of hindcasts based on the years 1950 to 1991 are presented and a comparison with previous results is performed. Finally, implications of the results and possibility of future skill are discussed in section 4.

2  Predictors of Atlantic tropical cyclone activity

2.1  Previously identified predictors

Early work by the lead author (Gray 1984a,b) indicated that Atlantic tropical cyclone activity had a seasonal dependence to pre-1 June values of Caribbean basin SLPA and ZWA as well as to the phase of the stratospheric QBO and whether or not a warm ENSO event was in progress. More recent work also identified previous year rainfall occurring over West Africa as a strong predictor of future tropical cyclone activity (Gray et al. 1992a). What follows is a brief review of these parameters and how they appear to relate to tropical cyclone activity.

Stratospheric quasi-biennial oscillation (QBO). Gray (1984a) and Shapiro (1989) have recognized that the stratospheric QBO apparently modulates Atlantic basin tropical cyclone activity: calm conditions occur during QBO east phases, while enhanced tropical cyclone activity is observed during QBO west phases. More recently, Gray et al. (1992a, 1993) have also utilized the vertical shear between 50 and 30 mb as a predictor of tropical cyclone activity, whereby small amounts of shear increase the numbers of storms and large shear corresponds to decreases. Current research (Gray et al. 1992b, 1993; Knaff 1993) suggests that the physical mechanisms relating tropical convection (and tropical cyclones) to the stratospheric QBO are associated with upper tropospheric to lower stratospheric vertical wind shear in as well as systematic height field differences QBO east phases as well as in the upper troposphere. QBO east phases conditions favor equatorial (0 - 7 latitude) convection over off-equatorial (8 to 18) convection. Conversely, in QBO west phase years upper tropospheric to lower stratospheric vertical wind shear is reduced and the upper tropospheric height fields favor off-equatorial convection. Because of the very regular progression of the QBO cycle, it is possible to make skillful extrapolations of 50 and 30 mb zonal winds by simply knowing the current phase and magnitude of the QBO and projecting the values forward in time using past histories of the QBO as a guide (Gray et al. 1992a). Thus using May data, we make a four month extrapolation to September, the height of the hurricane season, of zonal winds near 10N at 50 mb (U50), 30 mb (U30), and the absolute shear between the two levels ( [U50 - U30] ) at this latitude as shown in Table 2.

West African rainfall. Recently, it has been uncovered that there is a strong concurrent relationship between West Sahel rainfall and Atlantic basin tropical cyclone activity, especially IH activity (Gray 1990, Landsea 1991, Landsea and Gray 1992, Landsea et al. 1992). This association is hypothesized to be due to interannual variations in the upper tropospheric flow patterns (e.g. a wet western Sahel and active tropical cyclone season are both related to easterly ZWA) and in easterly waves intensities (e.g. wet/active conditions also are related to stronger amplitude tropical wave originating over North Africa). Goldenberg and Shapiro (1993) have recently provided more evidence that tropospheric vertical shear is a dominant mechanism connecting the Sahelian monsoon rains and seasonal Atlantic basin tropical cyclones.

In addition to the concurrent relationship, two measures of rainfall in West Africa have been shown to provide a measure of seasonal western Sahel/Atlantic tropical cyclone activity predictability on a multimonth lead (Gray et al. 1992). The first is rainfall that occurs along the Gulf of Guinea coast from August to November of the previous year. It is suggested that the moisture from this rainfall acts to enhance the following summer monsoon through evaporation/evapotranspiration. Thus above normal Gulf of Guinea rainfall allows for greater moisture storage, a later increase in evaporation/evapotranspiration, and an enhanced monsoon trough with more rain in the Sahel. The second predictor is rainfall which occurs in August and September throughout the western Sahel. Because of the strong year-to-year persistence that Sahel rainfall has experienced in the last four decades (Nicholson 1979), the use of previous year Sahel rainfall to forecast next year Sahel rain (and thus Atlantic hurricane activity) has a modest amount of skill. Both the Gulf of Guinea (Rg) and the West Sahel (Rs) rainfall anomalies are shown in Table 2.

Caribbean basin sea level pressure anomalies (SLPA). Stations located throughout the Caribbean basin show an inverse relationship of April to May sea level pressure to subsequent tropical cyclone activity. In general, higher pressure precedes quiet conditions, while lower pressure indicates more activity to come (Ray 1935, Brennan 1935, Shapiro 1982, Gray 1984b). Surface pressure variations are suggested to be associated with interannual fluctuations of the location and/or the intensity of the Intertropical Convergence Zone (ITCZ). Lower pressure would indicate a farther poleward excursion than normal of the ITCZ and/or a stronger ITCZ (more low level convergence and vorticity) favoring tropical cyclone genesis. It is presumed that anomalous conditions occurring in April and May have a tendency to persist through the main months of the hurricane season (August to October). Note that Shapiro (1982) also indicated that although local sea surface temperatures show a degree of predictive ability, they are essential redundant to the information provided by SLPA. Table 2 shows the 1950 to 1992 values of April and May SLPA.

Caribbean basin 200 mb zonal wind anomalies (ZWA). Tropospheric vertical wind shear has long been recognized as a major inhibiting factor for tropical cyclogenesis and intensification (Gray 1968). Because of the circulation regime of the tropical North Atlantic, tropospheric vertical shear is dominated by the variations in the upper troposphere. Thus with the nearly constant tradewind flow (e.g. easterlies) near the surface, 200 mb ZWA adequately specify wind shear: positive anomalies (westerly) indicate enhanced shear and less tropical cyclone activity, while negative anomalies (easterly) indicate reduced shear and more tropical cyclone activity. Similarly to the Caribbean SLPA, the April and May ZWA conditions are useful as a predictor because of their tendency to persist into the heart of the hurricane season. Because of the anomalous circulations forced by ENSO events and the location of the Caribbean stations chosen, the 200 mb ZWA is a good measure of the ENSO effect upon the Caribbean and western North Atlantic (Arkin 1982). Table 2 gives the 1950 to 1992 values of April and May 200 mb ZWA.

El Niño-Southern Oscillation (ENSO). As mentioned earlier, ENSO events cause a large variation in the upper tropospheric circulation over the Caribbean, Gulf of Mexico, and western North Atlantic (Arkin 1982). Gray (1984a) recognized that moderate to strong warm ENSO events reduce the number of Atlantic basin tropical cyclones by creating stronger than normal westerly winds (i.e. more tropospheric vertical wind shear), especially south of 30N (Shapiro 1987). Additionally, Gray et al. (1993) have included the enhancing effects of a moderate to strong cold ENSO events, or La Niñas, toward the predictability of Atlantic basin tropical cyclones. However, while the easterly 200 mb ZWA typically associated with cold ENSO events usually reduce the tropospheric shear and create more favorable conditions for tropical cyclogenesis and intensification, occasionally very strong cold events cause too much easterly shear with height and prevent tropical cyclone activity, such as occurred from June to August, 1988 (Gray 1988). For forecasting the tropical cyclone activity from 1 June, four predictors are being utilized that measure the current magnitude of ENSO and its trend. They are the following: the April and May equatorial Eastern Pacific SST anomalies (the ``Niño 3" region), the change in the SST from January and February to April and May (DSST), the April and May (SOI), and the change in SOI from January and February to April and May (DSOI); see Table 2. These provide an indication of what the ENSO conditions will be like during the key August to October time of maximum tropical cyclone activity. Though there is some redundancy between the SST and SOI data, we find that both are necessary to provide the best hindcasts of the seasonal tropical cyclone activity.

2.2  West African sea level pressure and temperature gradients

In a study of multidecadal changes, Hastenrath (1990) identified significant multidecadal trends of July and August sea level pressure and temperature occurring over West Africa and the adjacent Atlantic waters. In general, over the Atlantic north of 15N and along coastal West Africa pressures tended to increase and temperatures decreased from 1948 to 1983. These changes are attributed to variations in the oceanic ``conveyor belt", which has apparently experienced a slow down in mass and heat transport in the last few decades (Street-Perrott and Perrott 1990). During the same interval, in the interior of West Africa a multidecadal temperature increase and sea level pressure decrease was observed. This is likely being forced as a feedback by the concurrent persistent trend toward lower rainfall amounts throughout the Sahel region. Similarly, modelling work by Druyan and Koster (1989) showed that there existed a reduced sea level pressure gradient along 15N from the West African coast to the interior for `rainy' simulations and an enhanced gradient for `drought' simulations (i.e. their Figure 2) during June and July.

Case study analyses (Lamb 1978, Lamb and Peppler 1992) indicated the sea surface temperature patterns in the Atlantic which lead to Sahel drought or rainy conditions begin to set up months before the height (August) of the Sahel monsoon. Indeed, the Atlantic sea surface temperature anomalies in April and May are a major portion of the UK Meteorological Office's realtime empirical and GCM-based seasonal Sahel forecasts (Folland et al. 1991). Thus the use of adjacent Atlantic temperature fields has already been shown to be useful in a forecasting mode and it is possible that additional use of coastal stations of temperature and pressure would also be of use for Sahel (and thus tropical cyclone activity) seasonal predictions.

In Figure 1, linear correlation coefficient patterns of February to May surface temperatures (top panel) and sea level pressures (bottom panel) versus IHD are displayed. This analysis utilizes individual African and island stations that had a minimum of 15 years of data between 1950 and 1991. Note that in addition to the expected positive temperature/negative pressure correlations along immediate coastal West Africa, a strong pattern of negative temperature/positive pressure correlations occur in interior West Africa south of the Saharan Desert. Thus the use of a difference of the east (interior) and west (coastal) anomalies of temperature and pressure would appear to provide a degree of predictability for upcoming Atlantic tropical cyclone activity (as well as western Sahelian rainfall). A similar use of March and April North African surface temperatures is currently in use for late May realtime forecasting of the Sahel by the UK Meteorological Office (Carson 1992). The interior correlations are partly due to the long-term trend of reduced rainfall for the region as seen in the later months of July and August by Hastenrath (1990). However, most of the signal seen cannot be directly related to rainfall trends. It is suggested here that these pre-season temperature and pressure patterns set up before the onset of the monsoon and act to alter the strength of the monsoon (as seen in the Sahel rainfall). Figure 2 schematically depicts how these pre-season coastal and interior signals can act to alter the Sahel monsoon. A coastal high/cold anomaly coupled with an interior low/warm anomaly forces anomalous surface northeasterlies which weaken the monsoonal southwesterly flow and reduce the Sahel rainfall (and also the Atlantic hurricane activity). Conversely, a coastal low/warm anomaly coupled with an interior high/cold anomaly would lead to anomalous southwesterlies reinforcing the monsoonal flow allowing more Sahelian rainfall and Atlantic tropical cyclone activity. These types of anomalous flow patterns and, implicitly, anomalous moisture fluxes, are precisely those described in the modelling work of Folland et al. (1986).

To use these new predictors quantitatively, indices of temperature and sea level pressure were created. All stations within the coastal and interior regions with the minimum 15 years of data for both temperature and sea level pressure were selected (Figure 3). To make the understanding of the indices as intuitive as possible, the gradients are set up so that positive anomaly values correspond to above normal Sahelian rainfall and Atlantic tropical cyclone activity. Thus, DxT (Tcoastal - Tinterior) is defined as the coastal standardized temperature anomalies minus the interior standardized temperature anomalies and DxP (Pinterior - Tcoastal)is defined as interior standardized sea level pressure anomalies minus coastal standardized sea level pressure anomalies. Figures 4a and 4b showDxT and DxP graphically. To provide for a look at potential predictablity through DxT and DzP, Figure 5 shows the IH* tracks for the 10 seasons from 1950 through 1991 with the largest values of DxT versus those ten seasons with the smallest values of DxT. Figures 6a,b show the same type of information but for DxP. Note the strong modulation of IHD* for both DxT (a 4.8 to 1 ratio).

In summary, the individual effects of the predictors as measured by linear correlation coefficients to various Atlantic basin tropical cyclone measures is shown in Table 3. Note that the strongest predictors are the West African surface data while the weakest tend to be the Caribbean/ENSO data. However, even though the predictors are undoubtedly not independent of one another, the results obtained here (and in Gray et al. 1993) indicate that all predictors utilized contribute useful information toward the predictability of Atlantic tropical cyclone activity. We find that when one predictor is combined with another it can often add skill even though, by itself, it may show only very weak predictive ability.

3  Analyses and Results

The methodology of the statistical procedure have been given in detail in Gray et al. (1992a, 1993). In summary, an objective least sum of absolute deviations (LAD) regression is applied separately to each of the eight predictants (NS, NSD, H, HD, IH*, IHD*, HDP*, NTC*) in a cross-validation mode so that each year of data is independently hindcasted. This provides us with agreement coefficients (a measure of skill) and probabilities of no relationship. For a forecast of an upcoming season, a procedure is performed on all 42 years of the dataset. This leads to a forecast equation in the following form:

                           y = b0 + b1(a1U50 + a2U30 +a [U50 - U30]) 

+ b2( a4Rs + a5Rg + a6DxP + a7 DxT)

+ b3(a8SLPA + a9ZWA+ a10SST

+ allDSST + a12SOI + a13DtSOI),

where y represents one the eight predictants; b0, b1, b2, and b3 represent the LAD regression weights determined from the non-jackknife solution; and a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13 are selected constants for each composite function. The composite function of U50, U30, and [U50 - U30]involves the stratospheric QBO information. Likewise, the composite function of Rs, Rg, DP, and DxT involve the future strength of the western Sahelian monsoon. Lastly, the composite function of SLPA, ZWA, SST, DSST, SOI, and DSOI characterize Caribbean and ENSO information. Note that the use of the groupings (composite functions) effectively reduces the total number of predictors from 13 to 3. Table 3 presents the values determined for the (a's) and (bs).

A step-by-step explication of the methodology for constructing the Atlantic basin tropical cyclone activity annual prediction follows. For any predication the data at hand consist of values for each of the r=13 predictor variables for each of the n=42 yea rs, plus values for each of the eight dependent variable ( number of hurricanes, H) but the same logic applies to the remaining seven dependent variables. The first step in the procedure is to determine cross-validated weights (a's) for each of the 13 in dependent variables. The cross-validated weights should provided high agreement between the predicated values ( ÿ i ) and the observed values (y i ) for i = 1, ..., n = 42. Also, the weights should be obtained in a manner tha t is completely independent of the known information for a particular year (i.e., the 13 independent variables values and the dependent variable value ). This is accomplished though a cross-validation procedure where the hindcast prediction for any year (say, 1964) is based on information obtained from the remaining n - 1 = 41 years, and absolutely no information from 1964 and no information from the dependent variable (H) for 1964. This procedure ensures that the cross-validated estimate of y i ( ÿ i ) is independent of the data for the year being predicated. An iterative procedure is employed to obtain these cross-validated weights. First, an arbitrary set of r=13 weights (a's) is created. This could be (and has been) as simple as setting a 1 = ... = a 13 = 1.0, but it is much more efficient to employ initial values closer to the desired outcomes. For this purpose, the entire n = 42 years are used (not cross validated) in a LAD regression with r = 1 3 predictors and these non-cross-validated LAD regression coefficient become the intial starting weights (a's) are fine-tuned to increase the agreement measure (i.e., decrease the sum of absolute differences ) between the ÿ i and y i values. This is accomplished by incrementing and decrementing each of the 13 cross-validated weights by very small amounts, running another cross-validated weight by small amounts, running another cross-validated analysis after each change, and comparing the predicated ÿ i values with the observed y i values for each of the n = 42 years. A measure of agreement þ is used to determine how close the paired ÿ i and y i values are to one another. When þ = 1, then ÿ i = y i for i = 1, ..., n ( i.e., a set of perfect hindcast). Ths, þ = 1 implies a regression line with a zero intercept and a unit slope, which is a special case of linearity. At some point the process stabilizers and no further improvement in the cross-validated agreement coefficient can be accomplished. This does not mean that the model cannot be improved, simply that the agreement coefficient is stable. At this point in the pr ocess the cross-validated weights (a's) have been determined for each of the 13 independent variables.

At the next step the 13 independent variables are combined into a smaller number of predictors, each of which is a predictive index of some closely related meteorological phenomena; that is, U50 , U30 , and the absolute shear betwe en the two levels [ U50 - U30 ] compose the predictive index of QBO; two indicators of western African rainfall ( Rg and R s and two indicators of western-African pressure and temperature gradient anomalies (< font face=symbol>DxP and DxT compose the predictive index of West African surface data (AFRICA); and Caribbean basin 200-mb zonal wind anomalies (ZWA), and four indicators of the current magnitude of E NSO (SST, DtSST, SOI and D tSOI) compose the predictive index of ENSO. The choice of which independent variables are combined into predictive indices appears to be arbitrary; however, convenient combinations consist of related meteorological phenomena. Next, one final LAD regression equation is constructed. This last analysis of the data is not cross validated, because it will be used to predict a year into the future - that is, year n + 1. The 13 cross-validated weights (a's) based on the final cross-validated analysis are used and all n = 42 years are included. This last analysis yields four LAD regression index weights ( ß's) from a non -cross validated solution, one for eac h of the three predictive indices ( QBO, AFRICA, and ENSO ) plus constant. At this point the regression equation is composed of 13 cross-validated weights (a's) and four LAD regression index weights ( ß's) and is based on all of the n = 42 years.

Finally, the predication of the number of hurricanes for year n + 1 is made. A LAD regression equation is constructed for the observed values of the 13 predictor variables ( U50, U30, Rg, etc. ) for year n + 1, and a non-c ross-validated prediction value ( ÿ ) is made for the number of hurricanes. This entire process is then repeated for the remaining dependent variables, where the (a's) and ( ß's ) will differ for each dependent variable. It is possible to obtai n an improved prediction for a specific dependent variable by constructing a distinct linear ( or nonlinear ) model for each dependent variable. However, this defeats the goal of using a common prediction model for each of the eight indictors of Atlant ic basin tropical cyclone activity.

With this methodology applied to the various predictors described above, we can by 1 June independently hindcast over 60% of the variability (as measured by the agreement coefficient) for all but one (NS) of the 8 dependant variables as seen in Table 5. It is extraordinary that we are able to hindcast as much as 70.3% of the variability in HD, 70.9% in HDP*, and 71.8% in NTC*. This appears to be a very powerful forecast technique. The probability of no hindcast statistical skill in any of these predictant variables is between 10-7 and 10-12. Table 6 gives an example of the year-to-year forecast and verification of intense hurricane days. Some years, such as, 1959, 1960, 1961, an 1977, the forecast missed the number of intense hurricane days by more than 5. However, in most year there was appreciable skill.

4  Discussion

This paper has presented evidence for quite skillful forecast of Atlantic basin tropical cyclone activity by 1 June utilizing information of the future state of the stratospheric QBO, West Africa surface data, and Caribbean/ENSO data. Figure 7 helps to demonstrate the potential skill available in 1 June forecasting by comparing the results of the ten hindcasts for the most tropical cyclone activity versus the results of the ten hindcasts for the quietest tropical cyclone conditions. Note the vast difference in observed IH activity between the active and calm hindcasts. Obviously, if future forecasts are as skillful as the hindcasts suggest themselves to be, then by 1 June, at the ``official" start of the hurricane season in the Atlantic basin, it may be possible to forecast nearly three-quarters of the variability of upcoming tropical cyclone activity by the method described in this paper.

Previous work by the authors have focused upon seasonal forecasting for the Atlantic tropical cyclone activity by 1 December of the previous year, at the end of the previous hurricane season (Gray et al. 1992) and by 1 August of the current year, at the start of the active portion of the hurricane season (Gray et al. 1993). Because of the analyses of Landsea (1993), a reworking of the results of Gray et al. (1992a, 1993) was in order. Table 7 presents the revised constants for 1 December of the previous year and 1 August of the current year f orecasts of IH*, IHD*,HDP*, and NTC*. These revisions resulted in either no change or only a small reduction of hindcast skill. Table 8 details these variations in skill as measured in agreement coefficient for each of the three forecasting starting dates. Note that the current work shows by far the most skill for all eight dependent variables.

Acknowledgments.

The authors wish to thank Richard Taft and William Thorson for their programming and data processing assistance necessary to make this forecast and to John Sheaffer, John Knaff, Pat Fitzpatrick, and Ray Zehr for their providing many beneficial discussions. Barbara Brumit and Laneigh Walters provided expert manuscript assistance. This research was supported primarily by a climate grant from the National Science Foundation and by a special supplementary grant by the NOAA National Weather Service.


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