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  • View in gallery
    Fig. 1.

    The strategy for the use of reverse algorithms within our proposed data assimilation scheme.

  • View in gallery
    Fig. 2.

    The 24-h rainfall ending 1200 UTC 2 October 1995 (a) based on satellite plus rain gauge observations and (b) based on physical initialization.

  • View in gallery
    Fig. 3.

    Assimilated fields of 1000-mb streamlines and 24-h rainfall (mm day−1) preceding (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 4.

    Assimilated streamlines and isotachs (m s−1) at 850 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 5.

    Assimilated streamlines and isotachs (m s−1) at 200 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 6.

    Potential vorticity (10−7 kg−1 m2 s−1 K) at 350-K isentropic surface from the assimilated datasets, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 7.

    Predicted fields of 1000-mb streamlines and 24-h rainfall (mm day−1) preceding (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 8.

    Predicted streamlines and isotachs (m s−1) at 850 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 9.

    Observed and predicted tracks of Opal. Tracks shown here are the official NHC best track and the predicted tracks for two different start times—that is, 1200 UTC 1 October and 0000 UTC 2 October.

  • View in gallery
    Fig. 10.

    Maximum wind speed (kt) at 850 mb for the NHC official best track and that predicted by the FSU model for forecast starting at (a) 1200 UTC 1 October and (b) 0000 UTC 2 October 1995.

  • View in gallery
    Fig. 11.

    Potential vorticity (107 kg−1 m2 s−1 K) at 350-K isentropic surface from the predicted dataset, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

  • View in gallery
    Fig. 12.

    Selected trajectories from assimilated datasets (pressure in tens of millibars).

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Numerical Prediction of Hurricane Opal

T. N. KrishnamurtiDepartment of Meteorology, The Florida State University, Tallahassee, Florida

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Wei HanDepartment of Meteorology, The Florida State University, Tallahassee, Florida

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Bhaskar JhaDepartment of Meteorology, The Florida State University, Tallahassee, Florida

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H. S. BediDepartment of Meteorology, The Florida State University, Tallahassee, Florida

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Abstract

The main theme of this paper is on the intensity forecast of a hurricane (Opal) and interpretation of factors contributing toward it. The paper illustrates the results of assimilation and prediction for Hurricane Opal of 1995 from a very high-resolution global model. The assimilation makes use of a detailed physical initialization that vastly improves the nowcasting skill of rainfall and the model-based outgoing longwave radiation. Some of the interesting aspects of Hurricane Opal’s history occurred between 1200 UTC 1 October 1995 and 1200 UTC 5 October 1995. During this period the storm made landfall over the Florida panhandle. The storm reached maximum wind speed of over 130 kt on 4 October 1995. The intensity issue of Opal has drawn much attention. Issues such as the potential vorticity impact from a middle-latitude trough, the angular momentum of the lower-tropospheric inflow layer, the warm ocean temperature anomalies of the northern Gulf of Mexico, and the possible role of mesoconvective concentric eyewall are discussed in this paper.

The main finding of this study is that a reduction of the gradient of angular momentum occurs above the regions of maximum convective heating. This contributes toward stronger cyclonic spinup of parcels that enter the storm environment from the middle latitudes. Another major contributor is the import of angular momentum along the lower-tropospheric inflow channels of the storm. These channels were found to be open, that is, uncontaminated with a plethora of deep convection and heavy rain. This permitted the high angular momentum to advance toward the storm’s interior thus contributing to its intensification.

Corresponding author address: Dr. T. N. Krishnamurti, Dept. of Meteorology, B-161, The Florida State University, Tallahassee, FL 32306-4520.

Email: tnk@io.met.fsu.edu

Abstract

The main theme of this paper is on the intensity forecast of a hurricane (Opal) and interpretation of factors contributing toward it. The paper illustrates the results of assimilation and prediction for Hurricane Opal of 1995 from a very high-resolution global model. The assimilation makes use of a detailed physical initialization that vastly improves the nowcasting skill of rainfall and the model-based outgoing longwave radiation. Some of the interesting aspects of Hurricane Opal’s history occurred between 1200 UTC 1 October 1995 and 1200 UTC 5 October 1995. During this period the storm made landfall over the Florida panhandle. The storm reached maximum wind speed of over 130 kt on 4 October 1995. The intensity issue of Opal has drawn much attention. Issues such as the potential vorticity impact from a middle-latitude trough, the angular momentum of the lower-tropospheric inflow layer, the warm ocean temperature anomalies of the northern Gulf of Mexico, and the possible role of mesoconvective concentric eyewall are discussed in this paper.

The main finding of this study is that a reduction of the gradient of angular momentum occurs above the regions of maximum convective heating. This contributes toward stronger cyclonic spinup of parcels that enter the storm environment from the middle latitudes. Another major contributor is the import of angular momentum along the lower-tropospheric inflow channels of the storm. These channels were found to be open, that is, uncontaminated with a plethora of deep convection and heavy rain. This permitted the high angular momentum to advance toward the storm’s interior thus contributing to its intensification.

Corresponding author address: Dr. T. N. Krishnamurti, Dept. of Meteorology, B-161, The Florida State University, Tallahassee, FL 32306-4520.

Email: tnk@io.met.fsu.edu

1. Introduction

This paper consists of three parts: (i) data assimilation, (ii) numerical weather prediction of a hurricane with a high-resolution model, and (iii) interpretation of the hurricane’s behavior from model output. The Florida State University (FSU) global spectral model described in our previous studies (Krishnamurti et al. 1991, 1993, 1994) that includes physical initialization to incorporate observed rainfall has been used in this study. The main goal of this study is to explore the predictive capability and interpretation of this assimilation-forecast system on the landfall and intensity changes of Hurricane Opal.

Hurricane Opal formed from an African wave on 10 September 1995 that became a tropical depression on 27 September 1995 located south of the Yucatan peninsula. It became a tropical storm on 30 September near the northern coast of the peninsula, then moved northward from the Bay of Campeche on 2 October when it had acquired hurricane force winds. An upper anticyclone over the Gulf of Mexico and warm sea surface temperatures close to 29°C assisted in a rapid intensification of the hurricane by 4 October when it acquired winds close to 130 kt and a central pressure close to 920 mb. It was designated as a category 4 storm at this stage and was located in the north-central Gulf of Mexico close to 27.5°N, 88.5°W. This storm weakened somewhat as it made landfall around 0000 UTC on 5 October. At the time of landfall the storm had maximum wind speed of around 100 kt and a central pressure of around 942 mb. The storm weakened as it moved through Alabama and Tennessee. Thereafter it moved through the Ohio Valley as an extratropical storm. Further synoptic details on this storm appear in this issue of Monthly Weather Review (Lawrence et al. 1998).

In this study we examine the issue of intensification of Hurricane Opal using the angular momentum–potential vorticity framework. The upper and lower tropospheres are separately addressed. The presence of a middle-latitude upper trough in the vicinity of the hurricane raises interesting questions on parcel motions from the trough region to the hurricane environment. These parcels undergo substantial changes in the potential vorticity (PV) on entering the diabatic environment of the hurricane (a list of acronyms is given in Table 1). A close relationship exists between the PV and the radial gradient of the angular momentum. Storm intensification at the upper levels can occur from a reduction of the PV or of the gradient of angular momentum. A reduction of PV in the upper troposphere above the levels of maximum heating is a most common diabatic feature (Krishnamurti et al. 1997, manuscript submitted to J. Atmos. Sci.). Those diabatic features are described by the complete Ertel’s potential vorticity equation:
i1520-0493-126-5-1347-e1
where
i1520-0493-126-5-1347-e2
Also the angular momentum per unit mass of air is givenby
i1520-0493-126-5-1347-e3
In Eqs. (2) and (3) Vλ and Vr are the tangential and radial velocities, respectively, in local cylindrical frame of reference for a storm-relative coordinate system, and /dt is the diabatic heating rate.
Neglecting the azimuthal variation of Vr, we obtain from Eqs. (2) and (3) the following approximate relationship between the absolute potential vorticity and the angular momentum:
i1520-0493-126-5-1347-e4

Above the level of maximum convective heating that is generally located near the middle troposphere, we have (∂/∂θ)(/dt) < 0. As ζap generally is positive in the Northern Hemisphere, we have at such level ζap(∂/∂θ)(/dt) < 0. In Eq. (1), the contribution of this term will therefore be to reduce PV. Thus parcels transversing such a region above mesoconvective elements would encounter a reduction in PV, that is, ap/dt < 0.

From the relationship (4), we therefore have
i1520-0493-126-5-1347-e5
As for the inflowing parcels dM/dr > 0 and (d/dt)(1/r) > 0, we have
i1520-0493-126-5-1347-eq1
Therefore, from (5) we must have
i1520-0493-126-5-1347-eq2
Thus there is a reduction in the gradient of angular momentum of air parcels under such conditions.

In the context of the angular momentum, parcels moving into the hurricane environment from a middle-latitude trough arrive with a large outer angular momentum. That angular momentum is depleted rapidly because of the pressure torques and the frictional torques of the storm environment. That reduction is somewhat offset if these parcels arrive through regions where the vertical gradient of diabatic heating is negative. This occurs over regions where mesoconvective precipitating elements are present.

The changes in lower-tropospheric angular momentum can be viewed as follows: the lower-tropospheric inflowing air into a hurricane usually follows certain preferred channels. These inflow channels are usually covered by deep convection and heavy rain. The explicit vertical (upward) flux of momentum is usually large, in a high-resolution model, over these mesoconvective precipitating areas. Thus if the inflow channel is cluttered with heavy precipitation, a large fraction of outer large angular momentum of the inflowing air is transported up in these precipitating elements. In the absence of such precipitating elements the inflow channel is uncluttered and a larger fraction of the outer angular momentum reaches the storm’s inner area contributing to the intensification of the storm. These computational aspects are investigated for Hurricane Opal in this study where we show that the intensification appeared to be related to these features.

2. Analysis of Hurricane Opal from assimilated datasets

Following Krishnamurti et al. (1991; 1997), we have assimilated the precipitation and outgoing language radiation (OLR) data using physical initialization within the high-resolution FSU global spectral model, see appendix A for an outline of the model. Figure 1 illustrates schematically the assimilation of “observed” rainfall and OLR using physical initialization. The observed rain-rate estimates are obtained from the analysis of a mix of OLR and SSM/I rainfall and rain gauge observations as described in Gairola and Krishnamurti (1992). The matching of OLR is achieved by restructuring the moisture in the upper troposphere so that the model-calculated OLR matches with the satellite OLR values. This is done in the beginning of physical initialization procedure through an iterative process using a simple structure function for the specific humidity between 500 mb and the top of the model atmosphere. This has been found to greatly improve the initial specification of high and medium clouds, and thus improves the radiation parameterization.

The “observed” rain rates are assimilated continually using a reverse cumulus parameterization algorithm. This is achieved by modifying the specific humidity in the convective column so that the modified moisture convergence in the cumulus parameterization scheme produces rainfall closely matching the observed rain rates. Simultaneously, the specific humidity in the surface layer (lowest model layer) is modified using a reverse similarity algorithm to produce surface fluxes of moisture consistent with the observed rain rates and vertically integrated apparent heat sources and moisture sinks (Q1, Q2), which also undergo adjustment during assimilation.

The final component of physical initialization is the Newtonian relaxation or nudging by which the vorticity, the divergence, and the surface pressure are relaxed to their preassigned future values (ECMWF analysis). The nudging coefficients used for this are shown in Table 2. The divergence and surface pressure are relaxed weakly as compared to the vorticity so as to allow the divergence to evolve more freely consistent with the diabatic heating from assimilation of rainfall. The temperature is not relaxed and is allowed to adjust freely. The physical initialization was performed using the analysis from the European Centre for Medium-Range Weather Forecasts (ECMWF) as the initial input.

The physical initialization yields evolution of model-based diabatic heating, divergence, precipitation, and surface fluxes of moisture consistent with the observed rainfall. Figure 2 shows (a) observed rainfall and (b) the physically initialized rainfall at the resolution T170 (triangular truncation at 170 waves around the globe). The resolution of the SSM/I instrument is around 40 km, whereas the transform grid separation of the T170 model is about 70 km. A close match between the observed and physically initialized rainfall in Fig. 2 portrays the nowcasting skill of physical initialization. The assimilation of rainfall results in mesoconvective scale vertical structure of the rain area (Krishnamurti et al. 1995). This procedure has been shown to have a major impact on numerical weather prediction over the Tropics (Krishnamurti et al. 1994; Treadon 1996.)

We shall next illustrate the assimilated structure of Hurricane Opal. Here we have performed a continuous physical initialization as a data assimilation between 1200 UTC 30 September 1995 and 1200 UTC 5 October. The assimilated motion field at 1000 mb and the 24-h rainfall for 4 days, starting on 2 October, are displayed in Figs. 3a–d. The rainfall is plotted in units of millimeters per day. The heaviest rainfall with amounts of the order of 10 mm day−1 occurred in the 24-h period ending 1200 UTC 4 October and is shown in Fig. 3c. These assimilated rainfall fields are found to be very close to their observed counterparts. One of the most striking aspects about this data is the lack of rainfall along an inflow channel around 10°N, 80°W at 1200 UTC 2 October. That opening (or lack of rain) appears to propagate northward to 20°N between 1 and 2 October. The inflow channel appears to be uncontaminated by deep convection and heavy rain, thus permitting higher angular momentum air to move toward the center of the storm’s circulation at these low levels.

The assimilated 850- and 200-mb wind fields are shown in Figs. 4a–d and 5a–d, respectively. Here we show a sequence of flow fields between 2 and 5 October 1995. In Fig. 4c we note the intensification of the storm by 1200 UTC 4 October with a very clearly defined isotach maximum of around 55 m s−1. This is very close to the reported maximum wind. This analysis was largely accomplished by invoking physical initialization within the continuous assimilation. On day 4 the storm had weakened as it moved inland. The 200-mb flow (Fig. 5) is characterized by an upper anticyclone, whose axis moved somewhat northward over the Gulf of Mexico. Over the northern gulf the eastward passage of a middle-latitude trough was an important feature during the life history of Hurricane Opal. This trough provided the PV maximum that was a crucial element during the history of this storm.

The assimilated potential vorticity (PV) for these 4 days is illustrated in Figs. 6a–d. This figure shows a daily sequence of the PV and the winds on the 350-K isentropic surface. These datasets were obtained by a cubic spline interpolation from the x, y, σ, to the x, y, θ surface at each transform grid point of the spectral model. This roughly depicts an isentropic surface close to the 200-mb surface. The salient feature is a middle-latitude upper trough that arrives to the north of the hurricane by the 4 October 1995. The PV maxima in this trough has values of the order of 10−7 kg−1 m2 s−1 K. This upper trough moved from roughly 105° to 82°W between 3 and 5 October 1996. During this period a rapid interaction of the PV and the storm circulation occurs. Such cases are of a common occurrence. However, these interactions do not always lead to the intensification of a hurricane. As we shall illustrate, the trajectories show that this middle-latitude air with large PV descends to the west of the upper trough and enters the storm circulation. This also leads to an import of high angular momentum into the inner storm area. Storm-relative outflow in the front-right quadrants of storms is often associated with an outward flow of low angular momentum air, where a net convergence of eddy angular momentum occurs. In spite of that well-known scenario, many storms simply do not amplify by this mechanism because the imported angular momentum is generally depleted quickly by pressure and frictional torques. However, in this instance the interaction of the PV with the storms mesoscale diabatic heating provided a different scenario, which is discussed in section 4.

3. The predicted fields

We have superimposed the 24-h total rainfall ending at 24, 48, 72, and 96 h of the forecast period over the 1000-mb predicted streamlines for the corresponding hours in Figs. 7a–d. These are the counterparts of Figs. 3a–d. Here the winds are reduced to 1000 mb by a sigma to pressure coordinate conversion. Over mountainous areas these flows are only qualitative. Over the Gulf of Mexico (the region of interest for this study), the surface pressure is sufficiently close to 1000 mb so that we can infer the surface circulation from these panels. Maximum rainfall amounts of the order 100 mm day−1 are predicted in the vicinity of the storm’s center. A salient feature of the predicted rainfall distribution is the lack of heavy precipitation along the inflow channel to the southeast of the storm. That channel, as in the assimilated fields, remains relatively clear of intense rainfall thus permitting the high angular momentum air to move in, unabated, toward the central heavy rain regions of Opal. Overall the storm circulation at the surface, the track, and the rainfall distributions are reasonably predicted.

To assess the intensity prediction of the forecasts we shall look at the flow field (streamline and isotachs) at 850 mb. Figures 8a–d illustrate these streamline–isotach fields at hours 24, 48, 72, and 96 of the forecast. Perhaps the most important feature of interest is the isotachs at hour 72 when the storm had reached the maximum strength, which is very close to that of the assimilated field at that hour. By hour 96 the storm shows some weakening as the maximum winds reduce to around 40 m s−1. The predicted storm is somewhat stronger than the assimilated one. Overall this forecast could have been still very useful for providing proper guidance on the landfall and the intensity issues. However, more experiments are needed to properly assess the intensity forecast of the model.

Figure 9 illustrates Hurricane Opal’s track based on the best-track data from the National Hurricane Center at Miami and two predicted tracks with two different start times. These two forecasts were initialized at 1200 UTC 1 October and 0000 UTC 2 October 1995, respectively. The initialization at 1200 UTC 1 October was over a 12-h period while that at 0000 UTC 2 October was over a 24-h period. The predicted tracks in both forecasts are quite reasonable; however, the one with the start time at 0000 UTC 2 October is somewhat closer to the best track. The observed (best estimate) and the predicted (at 850 mb) maximum wind speed (m s−1) are shown in Fig. 10. Here also the intensity of the storm for the forecast started at 0000 UTC 2 October is in better agreement with the observed intensity of the storm. The storm in the forecast starting at 1200 UTC 1 October attains its highest intensity about 12 h earlier than the observed highest intensity. This forecast captures the intensification and the weakening of the storm phases quite reasonably. The maximum peak intensity of the storm was noted at around 1200 UTC 4 October. The model predicted intensity is based on 850-mb wind while the best estimates of intensity provided by the National Hurricane Center is for wind at 10 m. For us it was more convenient to extract model results at 850 mb than at 10 m. This is a qualitative comparison since the intensity issue is still one of the most difficult areas in hurricane research and forecasting. There are still some major issues that need to be resolved. There is a discrepancy between the observed and the assimilated intensity during the initial state and the decaying phase of the storm. These require further work on physical initialization, the initial synthetic vortex prescription, and the land surface processes.

The predicted fields of potential vorticity at the 350-K surface are shown in Figs. 11a–d. These predicted fields are quite similar to the observed (assimilated) shown in Fig. 6 earlier. The amplitude of the predicted middle-latitude trough and the maximum values of the PV are slightly larger compared to the assimilated field. The eastward and northward movement of the PV maximum is very well handled by these forecasts.

4. Upper- and lower-tropospheric trajectories entering the storm

Using the velocity components u, υ, σ̇, we have constructed trajectories that terminate near the storms circulation at 850 and 450 mb. Figures 12a–d display some sample trajectories that terminate at these two levels for the assimilated as well as the predicted datasets. The assimilated and the predicted trajectories, shown here, show a close match. The selected lower-tropospheric trajectory ascends from 970 mb (on 1 October) to the 850-mb surface by 5 October (the illustrations identify the pressure level to the closest 10 mb). Over the upper troposphere the selected trajectories originating close to 200 mb descend to 450 mb. We have evaluated the PV budget and angular momentum along these trajectories. Tables 3, 4, 5, and 6 show the coordinates of selected parcels for which these budgets are illustrated. The assimilated and the predicted parcels have nearly the same coordinates. This shows that the large-scale circulations were predicted quite accurately to almost four days. The lower-tropospheric parcels ascend to 850 mb in 4 days. Here again the behavior of the parcels for the assimilated and the forecast datasets are quite similar confirming that the larger-scale forecast in the storm environment is indeed quite reasonable. The agreement shown here between the forecast and assimilation are based on the same resolution in both cases. If the forecast and assimilation are performed at different resolutions, such close agreement may not be possible.

As stated earlier in section 1, above the level of maximum convective heating we have
i1520-0493-126-5-1347-eq3
and therefore
i1520-0493-126-5-1347-eq4
From the analysis of the potential vorticity equation (1), we had shown that the air parcels inflowing into mesoconvective elements above the level of maximum convective heating experience a reduction in PV. As a consequence of relationship (4), there occurs a reduction in the gradient of angular momentum of air parcels under such conditions, that is,
i1520-0493-126-5-1347-eq5

What causes a reduction of the gradient of angular momentum? Frictional torques and pressure torques (pressure field asymmetry around the storm center) are the main contributors to the reduction of angular momentum. If a parcel moves from a point A (away from a storm center) toward a point B (closer to a storm center), conservation of angular momentum would call for unusually large rotational motion at point B. Since that is not always observed, the normal fields of frictional torques and pressure torques inhibit the occurrence of strong winds and intensification. However, if the parcel traverses through a favorable environment where the gradient of angular momentum is reduced, then a spinup and an intensification of a storm can occur. We shall examine this within the framework of Ertel’s potential vorticity equation and ask the question as to what is the contribution to the potential vorticity change from the principal diabatic term, that is, ξ(∂/∂θ)(/dt). That in turn tells us what is the contribution to the gradient of angular momentum, that is, (1/r)(∂M/∂r), from this diabatic effect. Following that, in principle, we can also find out what the change in intensity of the hurricane (i.e., the change in tangential velocity Vλ) is from this diabatic term.

Appendix B of this paper outlines the theoretical aspects of this exercise. This formulation is cast following parcel motion in four dimensions. Given two points, r and r0 + Δr along such a trajectory the change in tangential velocity contributed by the vertical differential of the diabatic heating is expressed by Eq. (9) of appendix B. This equation is
i1520-0493-126-5-1347-e6
Here the variables at the origin point r0 are known. Here ξ(r0) is the absolute vorticity and A = exp[(∂/∂θ)(/dt)(t0, t0 + Δt)] is the exponential of the vertical differential of heating averaged between the time levels t0 and t0 + Δt along the constructed trajectory. Here /dt is assumed to be entirely known from the high-resolution model forecast. All other variables on the right-hand side of the above equation are known from the preconstructed three-dimensional trajectory to which all interpolated relevant information are provided. Here g1 is an integration constant for Eq. (B7) of appendix B. That too is easily determined since Vλ is known at the origin point r0. Thus ΔVλ can be computed for each trajectory segment r0 to r0 + Δr and then from r0 + Δr to r0 + 2Δr and so on. In appendix B we have shown how storm intensification can occur from such a vertical differential of the diabatic heating, which is largely the convective heating in the storms inner rain area for r < 200 km. Computations of the tangential velocity enhancement confirm a spinup of Hurricane Opal from the inclusion of the vertical differential of diabatic heating. Tables 4 and 6 confirm that over the upper troposphere this was the case during the intensification of Hurricane Opal on 4 October 1995. Thus we postulate that a contributor to the intensification of Opal was the interaction of inflowing parcels with the mesoconvective vertical differential heating in the inner rain area. The parcels from the west of the middle-latitude upper trough encountered a descending motion as they moved south and entered the storm environment. These parcels found themselves over and in the vicinity of precipitating regions where the negative vertical gradient of heating led to a substantial reduction of potential vorticity and hence of the gradient of angular momentum.

Tables 3, 4, 5, and 6 carry the following parcel histories in the lower and the upper troposphere: time, position (latitude, longitude, pressure), potential temperature, potential vorticity, angular momentum, angular momentum gradients, pressure torques, frictional torques, tangential velocity, and the precipitation. In Tables 4 and 6, four rows are especially of interest. Here we show (i) the assimilated or the predicted potential vorticity (or the radial gradient of angular momentum) when all of the diabatic (and frictional) terms of the complete PV equation were retained and (ii) when all of the terms of PV except the vertical differential of the convective heating were retained. These entries in time from left to right contain the parcel histories. It is clear from these computations that between hours 60 and 84 parcels experience a significant reduction in PV (and the gradient of angular momentum) from the inclusion of the vertical gradient of convective heating in the complete PV equation. That reduction in the gradient of angular momentum (when the vertical gradient of convective heating is retained in the complete PV equation) leads to a more intense storm (at the vertical levels, where the parcels are moving through). How does this work? There exists a layer above the level of convective heating where the heating decreases faster vertically. In this layer the vertical gradient of heating (<0) is very large, we are capturing this feature by computing the various terms of the isentropic potential vorticity over every single degree of θ surfaces. We have selected a parcel of air that moves through this region where the value of |ζ(∂/∂θ)(/dt)| is near a maximum. It is along these trajectories that one sees a near maximum reduction in the gradient of angular momentum and a spinup in the intensity of Opal. That spinup at one level does communicate to levels below via the hydrostatic thickness—that is, the spinup of the tangential motion via gradient wind balance calls for a lowering of the pressure at the center at that level. That decrease affects the pressure at all levels below that level via hydrostatic column thickness. In Table 6, we have two entries for the model-predicted tangential velocity following the parcel trajectories terminating at 450 mb. The first entry shows the tangential velocity when all of the dynamics and physics of the complete spectral model were retained. The second entry shows the tangential velocity when the heating term (∂/∂θ)(/dt) was dropped for each segment of the trajectory. The computational procedure, however, was different. We calculated ΔVλ based on Eq. (9) of appendix B and subtracted those from the full tangential velocity, to arrive at the last row of tangential velocity that excludes the role of (∂/∂θ)(/dt). These results confirm what is stated in appendix B—that is, a storm intensification can occur via the interaction of the larger-scale flows (i.e., these trajectories) and the mesoconvective scale heating.

For the lower troposphere we present a somewhat different perspective for the storm development. Parcels of air with large angular momentum enter the inner storm area. These lower-tropospheric parcels generally lose some of the angular momentum via frictional and pressure torques. The frictional torques on these parcels arise from the surface frictional stresses at the ocean–atmosphere interface and from the vertical flux of momentum in the shallow and deep convection. Over these convective regions the vertical flux of momentum can lead to a depletion of angular momentum for the inflowing air. However, if the lower-tropospheric inflow channels of a hurricane happen not to be contaminated by deep convection and heavy rain, then there is a stronger possibility that a large proportion of the angular momentum of the outer air will enter the storm interior thus contributing to an intensification of the storm. Tables 3 and 5 convey the parcel histories over the lower troposphere. There are several discrepancies between the assimilated and the predicted quantities shown here. This implies that although the circulations and trajectories appear to be very well predicted, there are internally derived quantities that are not carried equally well. Rapid intensification of the tangential velocity occurs after hour 48 along the trajectory. The rate of drop of angular momentum, as we proceed inward, is slow prior to the occurrence of heavier rain. This is noted for both the assimilated and the predicted cases shown in Tables 3 and 5. We attribute this smaller rate of drop of angular momentum to the absence of explicit vertical flux of momentum in the storm area. Larger vertical fluxes in outer rain areas have been noted in other storms where the storm intensity was weaker. The strong intensity of Opal is attributed to the absence of heavy precipitation and the somewhat uncluttered inflow of outer angular momentum at the lower levels.

5. Concluding remarks

When Hurricane Opal intensified prior to its landfall, various explanations were offered on its strengthening. One of these was that a warm SST anomaly near the central Gulf Coast was a primary factor. It was suggested that the convection in the storm amplified over this region of warm SST leading to an intensification of the storm. The narrowness of this SST region raises the question whether this could be effective in intensifying the storm. Two intensity forecasts were carried out using CPC and LSU SSTs, respectively. The LSU SST field contained a warm anomaly over the northern Gulf of Mexico, whereas the CPC field is smoother and shows a slow cooling of SST toward the northern gulf. Both experiments performed equally well in simulating a reasonable intensity and tracks of Hurricane Opal. Thus we infer that this narrow warm SST from LSU might have enhanced the convection but it did not appear to be crucial for the intensification of Opal. However, the issue of SST may not have been resolved in this study, since we did not resolve features less than 75 km in describing the warm anomalies.

Another attribute for the storm intensification is the presence of a concentric eyewall during the intensification stage. The premise being that an outer eyewall weakens as an inner eyewall develops. This leads to the inflow of air with higher angular momentum to the lower radii of the inner eye thus contributing to storm intensification. At the resolution T170, features such as the inner eyewall are not resolved. The distance of that feature is only around 20 km from the storm’s center of circulation. In spite of that limitation the model does simulate a reasonable history of the storm’s intensity. This could imply that the larger-scale angular momentum controls are capable of describing a reasonable intense storm. Given a finer resolution the same controls may perhaps most likely describe an inner wall as well.

The location of the pathways of the outer angular momentum entering the storm’s inner circulation appears to be a more central issue for the intensity forecast problem. In the upper troposphere the middle latitudes usually carry a PV maximum. Parcels entering a hurricane environment from this region encounter a destruction of PV above the levels of convective heating. That is equivalent to a reduction of the gradient of angular momentum. Thus these parcels exhibit a strong cyclonic spinup as they enter the storm circulation. The other important pathway resides in the lower troposphere. These are the inflow channels close to the rainbands of hurricanes. If these pathways for the outer angular momentum are uncluttered by deep convection then a substantial amount of the angular momentum would be passed to the inner storm area.

Both the track and the intensity forecasts are strong functions of the interaction of the storm’s environmental flows with the details of the storm’s interior convection. The tracks based on steering flows alone are not more than adiabatic forecasts, which are usually very poor beyond the timescales of a few days. We do recognize that the environment that defines the steering is very strongly influenced by the physics of the model. Steering dynamics coexists with the overall model physics, which constantly reshapes it. The intensity issue is an angular momentum issue. Mesoconvective precipitation patterns within the heavy rain areas of a hurricane provide a strong modification of the potential vorticity of the incoming air into the storms inner core. Such changes in potential vorticity produced by the diabatic forcing in the complete Ertel’s potential vorticity equation deserve more detailed studies. Here we show an intimate relationship among the thus modified potential vorticity and the evolution of the gradient of angular momentum of the inflowing air parcels. Those appear to contribute significantly to the storm’s intensity. Further work is needed to clarify these issues in a more general manner.

Acknowledgments

This research was supported by the following grants to The Florida State University: NASA Grant NAG5-1595, ONR Grant N00014-95-1-1132, and NSF Grant ATM 9312537.

REFERENCES

  • Businger, J. A., J. C. Wyngard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationship in the atmospheric surface layer. J. Atmos. Sci.,28, 181–189.

  • Gairola, R. K., and T. N. Krishnamurti, 1992: Rain rates based on SSM/I, OLR and raingauge data sets. J. Meteor. Atmos.,50, 165–174.

  • Harshvardan, and T. G. Corsetti, 1984: Long-wave parameterization for the UCLA/GLAS GCM. NASA Tech. Memo. 86072, 52 pp. [Available from NASA/Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Kanamitsu, M., 1975: On numerical prediction over a global tropical belt. Rep. 75-1, Dept. of Meteorology, The Florida State University, 1–282. [Available from Dept. of Meteorology, The Florida State University, Tallahassee, FL 32306.].

  • ——, K. Tada, K. Kudo, N. Sato, and S. Isa, 1983: Description of the JMA operational spectral model. J. Meteor. Soc. Japan,61, 812–828.

  • Krishnamurti, T. N., S. Low-Nam, and R. Pasch, 1983: Cumulus parameterization and rainfall rates II. Mon. Wea. Rev.,111, 816–828.

  • ——, J. Xue, H. S. Bedi, K. Ingles, and D. Oosterhof, 1991: Physical initialization for numerical weather prediction over the tropics. Tellus,43AB, 53–81.

  • ——, H. S. Bedi, and K. Ingles, 1993: Physical Initialization using SSM/I rain rates. Tellus,45A, 247–269.

  • ——, G. D. Rohaly, and H. S. Bedi, 1994: On the improvement of precipitation forecast skill from physical initialization. Tellus,46A, 598–614.

  • ——, S. K. Bhowmik, D. Oosterhof, G. Rohaly, and N. Surgi, 1995:Mesoscale signatures within the Tropics generated by physical initialization. Mon. Wea. Rev.,123, 2771–2790.

  • ——, H. S. Bedi, G. D. Rohaly, D. K. Oosterhof, R. C. Torres, E. Williford, and N. Surgi, 1997: Physical initialization. Atmos.–Ocean.,35, 369–398.

  • Lacis, A. A., and J. E. Hansen, 1974: A parameterization of the absorption of solar radiation in the earth’s atmosphere. J. Atmos. Sci.,31, 118–133.

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  • Treadon, R. E., 1996: Physical initialization in the NMC Global Data Assimilation System. Meteor. Atmos. Phys.,60, 57–86.

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APPENDIX A

An Outline of the FSU Global Spectral Model

The global model used in this study is identical in all respects to that used in Krishnamurti et al. (1991). The following is an outline of the global model:

(a) Independent variables: (x, y, σ, t).

(b) Dependent variables: vorticity, divergence, surface pressure, vertical velocity, temperature, and humidity.

(c) Horizontal resolution: triangular 170 waves.

(d) Vertical resolution: 15 layers between roughly 50 and 1000 mb.

(e) Semi-implicit time-differencing scheme.

(f) Envelope orography (Wallace et al. 1983).

(g) Centered differences in the vertical for all variables except humidity, which is handled by an upstream differencing scheme.

(h) Fourth-order horizontal diffusion (Kanamitsu et al. 1983).

(i) Kuo-type cumulus parameterization (Krishnamurti et al. 1983).

(j) Shallow convection (Tiedke 1984).

(k) Dry convective adjustment.

(l) Large-scale condensation (Kanamitsu 1975).

(m) Surface fluxes via similarity theory (Businger et al. 1971).

(n) Vertical distribution of fluxes utilizing diffusive formulation where the exchange coefficients are functions of the Richardson number (Louis 1979).

(o) Long- and shortwave radiative fluxes based on a band model (Harshvardan and Corsetti 1984; Lacis and Hansen 1974).

(p) Diurnal cycle.

(q) Parameterization of low, middle, and high clouds based on threshold relative humidity for radiative transfer calculations.

(r) Surface energy balance coupled to the similarity theory (Krishnamurti et al. 1991).

(s) Nonlinear normal mode initialization—five vertical modes.

APPENDIX B

Diabatic Heating and Storm Intensity

The leading diabatic term in the potential vorticity equation has the form
i1520-0493-126-5-1347-eb1
This expression can also be written as
i1520-0493-126-5-1347-eb2
Upon integration of Eq. (B2) from time t0 (when the parcel is at point r0) to time t = t0 + Δt (when the parcel is at point r = r0 + Δr), we obtain
i1520-0493-126-5-1347-eb3
Since ξ = −θ/∂p, where ξ is the absolute vorticity, this can be written as
i1520-0493-126-5-1347-eb4
We assume that (∂θ/∂p)r0(∂θ/∂p)−1r ≈ 1—that is, that stability changes over small distances Δr are small compared to the changes in the absolute vorticity. Stability changes were indeed very small over the troposphere. Let us denote the term
i1520-0493-126-5-1347-eq6
Then Eq. (B4) can be written as
ξrξr0eAΔT
The absolute vorticity ξ is given by
i1520-0493-126-5-1347-eb6
Using the latter expression in Eq. (B5), we obtain
i1520-0493-126-5-1347-eb7
Note that by applying Eq. (B7) at t0, r0 we find g′ = r0Vλ(r0) + f0r20/2. Since
i1520-0493-126-5-1347-eb8
by differentiating Eq. (B7) with respect to r and multiplying by Δr, we obtain
i1520-0493-126-5-1347-eb9

When the heating is strong A = [(∂/∂θ)(/dt)] ≪ 0. When the heating is weak A = [(∂/∂θ)(/dt)] ≈ 0. Let Δr < 0—that is, the parcel is going toward the storm center. Since ξ is essentially positive, the diabatically influenced part of the velocity change δ = ξ(r0)eAΔtΔr/2 is nonpositive. In the case of strong heating, eAΔt → 1, therefore δξ(r0r/2 < 0. Thus, we can conclude that δ(weak heating) < δ(strong heating), resulting in total velocity change ΔVλ(weak heating) < ΔVλ(strong heating), or, in other words, stronger heating leads to larger Vλ—that is, a stronger tangential velocity or a storm intensification.

Fig. 1.
Fig. 1.

The strategy for the use of reverse algorithms within our proposed data assimilation scheme.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 2.
Fig. 2.

The 24-h rainfall ending 1200 UTC 2 October 1995 (a) based on satellite plus rain gauge observations and (b) based on physical initialization.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 3.
Fig. 3.

Assimilated fields of 1000-mb streamlines and 24-h rainfall (mm day−1) preceding (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 4.
Fig. 4.

Assimilated streamlines and isotachs (m s−1) at 850 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 5.
Fig. 5.

Assimilated streamlines and isotachs (m s−1) at 200 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 6.
Fig. 6.

Potential vorticity (10−7 kg−1 m2 s−1 K) at 350-K isentropic surface from the assimilated datasets, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 7.
Fig. 7.

Predicted fields of 1000-mb streamlines and 24-h rainfall (mm day−1) preceding (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 8.
Fig. 8.

Predicted streamlines and isotachs (m s−1) at 850 mb, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 9.
Fig. 9.

Observed and predicted tracks of Opal. Tracks shown here are the official NHC best track and the predicted tracks for two different start times—that is, 1200 UTC 1 October and 0000 UTC 2 October.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 10.
Fig. 10.

Maximum wind speed (kt) at 850 mb for the NHC official best track and that predicted by the FSU model for forecast starting at (a) 1200 UTC 1 October and (b) 0000 UTC 2 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 11.
Fig. 11.

Potential vorticity (107 kg−1 m2 s−1 K) at 350-K isentropic surface from the predicted dataset, for (a) 1200 UTC 2 October 1995, (b) 1200 UTC 3 October 1995, (c) 1200 UTC 4 October 1995, and (d) 1200 UTC 5 October 1995.

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Fig. 12.
Fig. 12.

Selected trajectories from assimilated datasets (pressure in tens of millibars).

Citation: Monthly Weather Review 126, 5; 10.1175/1520-0493(1998)126<1347:NPOHO>2.0.CO;2

Table 1.

List of acronyms.

Table 1.
Table 2.

Nudging coefficients.

Table 2.
Table 3.

Parcel history in storm-relative coordinates (lower–level assimilation case).

Table 3.
Table 4.

Parcel history in storm-relative coordinates (upper-level assimilation case).

Table 4.
Table 5.

Parcel history in storm-relative coordinates (lower-level forecast case).

Table 5.
Table 6.

Parcel history in storm-relative coordinates (upper-level forecast case).

Table 6.
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