The role of storm-relative advection of absolute angular momentum in strengthening of Atlantic tropical cyclones



[1] This study examined absolute angular momentum tendency in Atlantic tropical cyclones. Each advective and torque term in the storm-relative Eulerian absolute angular momentum tendency equation was calculated in a storm relative reference frame using modeled and observational data. 18 storms between 2004 and 2006 were simulated using the hurricane weather research and forecast model. In addition, the storm-relative advection of absolute angular momentum was calculated using reconnaissance aircraft wind data from 12 Atlantic hurricanes which occurred between 2003 and 2007. Through methods of statistical correlation, categorical composition and linear regression, it was found that mid-level horizontal advection of relative angular momentum was most relevant to 12 hour strength change in the modeled tropical cyclones. Mid-level horizontal advection of relative angular momentum was most relevant to intensity change in the observed hurricanes, while mid-level advection of Earth's angular momentum was found to be most closely related to strength change in observed hurricanes.

1. Introduction

[2] The issue of hurricane intensity prediction has been pursued for decades. Despite the rapid proliferation of new techniques in the last two decades, intensity forecast skill for the Atlantic basin has improved little during this time period [DeMaria et al., 2007]. Many authors have presented results that suggest storm relative angular momentum is an important parameter for understanding tropical cyclone (TC) intensity change. These include those by Frank [1977] and Holland [1983] which described the angular momentum budget of TC. Studies by Kepert [2001], Zhang and Yau [2001], and Krishnamurti et al. [2005] analyzed TC angular momentum budgets using numerical models. Other authors suggested that there is a relationship between fluxes of angular momentum and TC intensity change [Molinari and Vollaro, 1989, 1990, 1995].

[3] For the most part, the use of angular momentum as a forecast tool has been limited to observations of the upper levels and outer radii of the TC. The first few generations of the Statistical Hurricane Intensity Prediction Scheme (SHIPS) model used upper level angular momentum flux divergence as a predictor [DeMaria and Kaplan, 1994]. However, wind-derived angular momentum predictors have fallen out of favor in recent years and been replaced by satellite measurements of storm inner-core thermal structure [Guimond et al., 2010]. This study will present an angular momentum driven approach to TC strength-change estimation which has the potential to become a skillful forecast tool based on observations from platforms currently in use.

[4] The following work focuses on analysis of local storm-relative absolute angular momentum tendency in the inner core of Atlantic Tropical Cyclones forecast by the Hurricane Weather Research and Forecast model (HWRF) [Gopalakrishnan et al., 2010]. Along with the results from modeled storms, wind observations taken from aircraft are examined. Given a full array of wind observations from dropsondes, the aircraft flight level and satellite instruments, in principle we can describe major features of the wind field in the inner core of a TC. Unlike model physics, the model dynamics is generally complete. Given adequate initial and boundary conditions a model such as HWRF should in principle be able to handle the transport of angular momentum. The model based component of the present study makes use of assimilated wind observations from aircraft and satellites is therefore able to approximate the true wind field of a TC. A separate analysis of directly observed hurricane wind fields was included in order to strengthen the key conclusion drawn from the HWRF local angular momentum tendency analysis, and to suggest an application to operational hurricane intensity forecasting.

2. Methods

[5] The authors assumed that the storm-center of each modeled storm was located at the minimum surface pressure. The storm-motion was then diagnosed from successive storm-centers. Using these parameters (candr), it is possible to specify a tendency equation for absolute angular momentum in storm-centered cylindrical coordinates. This is expressed

equation image

The total derivative on the L.H.S. is expressed as

equation image

So that the storm-motion c has been subtracted from the environment flow v. The terms on the R.H.S. of equation (1) are the torques on the storm, the first is the pressure torque and the second represents all dissipative drag on the angular momentum of the system. If the advective portion of equation (2) is moved to the R.H.S., then equation (1) becomes a local tendency for the variable uθr + equation image, which is the absolute angular momentum (AAM). Following Holland and Merril [1984], the first term in AAM is the relative angular momentum (RAM), while the second term is Earth's angular momentum (EAM).

[6] In this study, AAM tendency was calculated term by term for the inner 200 km (inner-core) of 18 HWRF forecast TC which occurred in the Atlantic basin between 2004 and 2007. HWRF was run coupled to the Princeton ocean model. (POM) [Blumber and Mellor, 1987] with an interactive inner nest with horizontal resolution of 9 km. The 1 degree Global Forecast System Final global gridded analysis (GFS-FNL) [Kalnay et al., 1996] provided initial and boundary conditions for the outer model nest. Select data was assimilated during a vortex initialization period prior to the start of the forecast phase. These data include GPS sondes and ship and aircraft observations [Gopalakrishnan et al., 2010]. To allow asymmetric features to develop in the modeled TC, 12 hr forecasts were used. It was possible to use shorter or longer lead-times, however it was determined by the authors that realistic wavenumber 1 and 2 structures developed in the modeled TC by no earlier than 12 hours. A sample of 281 12 hour forecasts were gathered from the 18 storms. Model output was interpolated to storm-centered cylindrical coordinates prior to applying equation (1). The storm-motion vector was found by assuming a constant and isotropic translation speed over the 12 hours between validation times. After these post-processing steps, the terms of equation (1) were calculated and examined with respect to the 12 hour strength change calculated from successive forecasts. Strength was calculated as the area-averaged relative angular momentum in the model's 10 meter winds between the radius of maximum winds and the 200 km radius. This definition follows Holland [1983]. 12 Hours was chosen as the interval for calculating strength change because of the results presented by Holland suggest that angular momentum fluxes in the inner-core are most correlated to 12–24 hour intensity changes.

3. Results From Modeled TC

[7] It was assumed that the sample of 12 hr strength change was approximately Gaussian. Values of 12 hr strength change which fell outside the middle half of the sample were considered either strengthening or weakening TC. It was found that the horizontal advection of absolute angular momentum is the most related to 12 hr strength change. This can be shown in two ways. The first is illustrated in Figure 1. Each panel depicts an azimuthally-averaged cross-section of a portion of the storm-relative advection of absolute angular momentum. The horizontal advection has been split into the advection of relative angular momentum (hRAM) (Figure 1a) and of Earth's angular momentum (hEAM) (Figure 1b). Figure 1c depicts vertical advection of relative angular momentum. (vRAM) From left to right is shown the cross-section from the strengthening composite, from the weakening composite, and the difference between the two (strengthening – weakening) with the 90 and 95% confidence interval shown as dashed and solid lines, respectively. Not shown are the terms representing pressure, friction and cloud torques. It is apparent that hRAM shows the largest positive difference between strengthening and weakening storms (m2s−2) at middle levels. This is especially true at levels between 800 and 400 hPa and at radii outside 100 km. There are upper level areas in Figures 1a1c which show larger difference, but all seem to be associated with the average location of the eyewall in the strengthening and weakening composites, rather than a fundamentally different advection regime. The hEAM cross-section shows similar structure. Figure 1c (vRAM) shows a large area where the difference between composites is significant, however the values of vertical advection are greater for weakening storms.

Figure 1.

(a) Azimuthally averaged composite cross-sections of hRAM for (left) strengthening and (middle) weakening storms along with the (right) difference strengthening – weakening. The rightmost panel has the t-test confidence 90 (dotted) and 95% (solid) confidence intervals overlaid. Units are m2s−2. (b) The same as in Figure 1a, but for hEAM. (c) The same as in Figure 1a, but for vRAM.

[8] To further explore the relationship between the advection of AAM and strength change, scatter-plots were created comparing each normalized term from equation (1) with normalized 12 hr strength change. A volume mean of each term was taken for 4 vertical layers within the storm. The best fit was found in the “middle layer” for volume averaged hRAM. This is shown in Figure 2a, along with middle-layer averaged vRAM in Figure 2b. The middle layer is defined between 800 and 500 hPa and between the radius of maximum winds and 200 km radius. Figure 2a shows a correlation of 0.65 between hRAM and strength change. This was the largest value of any AAM tendency term in any layer. The root mean square error of 0.11 and least-square slope of 0.6 were also the best among AAM tendency terms. Not shown is the scatter for hEAM, which showed values nearly as encouraging. Of note in Figure 2b is the negative slope between mid-layer vRAM and strength change. This agrees with the results from the composite cross-section (Figure 1c). The much smaller correlation and higher root mean square error suggest that vRAM is not likely to be as good a predictor of strength change as the horizontal advection terms. The authors wished to explore the relative contribution to strength-change of each of the AAM tendency terms. To this end the following quantity was calculated from the members of the strengthening and weakening groups,

equation image

Where each AAM term has already been volume averaged according to the method which produced the scatter-plots and converted to m2s−1hr−1 and n and m are the number of members in the strengthening and weakening groups. The result of equation (3) then expresses the average contribution to 12 hr strength-change of each AAM term as a percentage. If the term and strength-change are well correlated, then they will on average be of the same sign and the percentage will be more strongly positive. Figure 2c shows the average percent contribution (P) of mid-layer hAAM, mid-layer vRAM, low-layer hAAM, top-layer hAAM and top-layer vRAM. The figure also displays the one-tailed Gaussian limits of 25% of the distribution above and below the mean. Mid-layer hAAM has the highest value of P at 9% with the least uncertainty. As seen with the scatter-plots, the values for vRAM and low-level hAAM are negatively correlated with strength-change. In addition, the low-level hAAM has very wide spread. It is highly likely to observe horizontal advection of AAM in the low levels of a modeled storm which are strongly the same sign as strength-change, strongly the opposite sign and in proportions anywhere from a few to 40%.

Figure 2.

(a) Scatter relation between mid-layer volume averaged hRAM and 12-hr strength-change. Both ordinate and abscissa parameters are normalized. The correlation, root mean square error, least-square slope and mean value of hRAM in the middle-layer are displayed in a table to the lower right. (b) Same as in Figure 2a, but for mid-layer vRAM. (c) Average contribution to 12-hr strength change from select volume-mean AAM terms expressed as a percent. The upper and lower bounds of the boxes are the Gaussian one-tailed limits representing the upper and lower 25% of the sample distribution.

4. Results From Observations

[9] Any predictive parameter derived from a dynamical model forecast, such as the HWRF based advection fields will be limited by the model's forecast and representativeness errors. A predictive parameter derived from observations will have more value, since the observations will represent the true TC with greater accuracy. To determine whether a strong relation exists between horizontal advection of AAM and strength change in observed wind fields, this study examined Atlantic hurricane reconnaissance flight level winds. Wind measurements from reconnaissance aircraft were gathered for 12 mature hurricanes from the years 2003–2007. The data came from the NOAA Hurricane Research Division Surface Wind Analysis System (H*Wind) archive [Powell et al., 1998]. Measurements were restricted to pressures between 650 and 750 hPa. These pressures include most of the flight pattern for most storms. Data came primarily from NOAA's P3 aircraft. If there was no P3 flight available, Air Force C-130 data were used. Wind measurements were interpolated to a cylindrical grid using a cubic spline technique. The given reconnaissance flight estimate of the storm-center location, or the “vortex message” was used as the storm-center location for analysis purposes. Horizontal advection fields were calculated as in equation (2). The resulting analyses were composited using the same technique as used for modeled storms. Strength change was calculated using the estimated surface winds from the current and next available flight.

[10] Figure 3 shows the strengthening and weakening storm composites in a manner similar to Figure 1. Figure 3a shows, from left to right, the composites of hAAM for strengthening, weakening and the difference with the areas enclosed by 90 and 95% confidence intervals. The plan views correspond to the inner-most 200 km at approximately the 700 hPa level. Figure 3b shows the composites for hRAM and Figure 3c shows the hEAM composites. The feature that stands out is the vast difference in strengthening and weakening storms for the advection of Earths angular momentum (Figure 3c). The difference is significant at the 95% level for nearly the entire storm core. The advection of relative angular momentum is significantly greater in strengthening storms primarily in the forward region of the storm and to the right of storm motion. The direction of storm motion coincides with 12 o'clock in these figures.

Figure 3.

(a) Composites of flight-level hAAM from the H*Wind archive. Left to right are strengthening, weakening storms and the difference between the two. The 90 and 95% confidence intervals are overlaid in the rightmost panel. The composite disk is oriented such that direction of storm-motion is at 12 o'clock. (b) Same as in Figure 3a, but for hRAM. (c) Same as in Figure 3a, but for hEAM.

[11] The relationship between mid-level advection of angular momentum and strength-change is quite striking in Figures 13. Does the same relationship exist for intensity change? We would expect that it would, since strength and intensity should be highly correlated for most mature TC. Due to discrete sampling techniques, we would also expect strength to be better represented in a sparsely measured TC than intensity. Therefore the relationship between any skillful predictor of storm strength and intensity change will likely not to be as strong. Figure 4 shows composites of flight-level AAM advection from intensifying and dissipating groups. As before, the largest areas of positive advection are in the forward half of the TC. Unlike in Figure 3, the significant difference is in the fields of hRAM. The storm region in which this is most consistent is to the right of storm motion. For both hRAM and hEAM, significance covers much smaller areas than in the case of strength change composites, and in this case the hEAM composites are only significantly different just behind the storm center.

Figure 4.

(a) Composites of flight-level hAAM from the H*Wind archive. Left to right are intensifying, dissipating storms and the difference between the two. The 90 and 95% confidence intervals are overlaid in the rightmost panel. The composite disk is oriented such that direction of storm-motion is at 12 o'clock. (b) Same as in Figure 4a, but for hRAM. (c) Same as in Figure 4a, but for hEAM.

5. Discussion

[12] Both the modeled and observed storms showed a significant relationship between the storm-relative horizontal advection of absolute angular momentum and TC strength change. If AAM is broken into relative and Earth's components, the HWRF modeled storms showed a more significant relationship between hRAM and strength change, while the aircraft observations showed a more significant relationship between hEAM and strength change. Since the studies of Riehl and Malkus [1961] the middle tropospheric inflows have been a well known feature of the hurricane secondary circulation. The inflow is largest in the planetary boundary layer, but weaker inflow continues through 400 hPa level generally. The inflowing air of the middle troposphere can invite outer angular momentum from greater radii and the results presented here show that this can contribute to TC strengthening and intensification. A clear link between the mid-level advection of angular momentum and TC intensity change has not been established in the literature previously.

[13] The aircraft composites show promise for an operational parameter predicting strength change based on horizontal advection of Earth's angular momentum. The difference between strengthening and weakening storms is significant in nearly the entire core, or out to 200 km radius. This is exactly the area over which operational reconnaissance flights currently sample TC winds in the Atlantic. The prediction of intensity change by a parameter such as horizontal advection of Earth's angular momentum is less compelling from these composites, but given a larger sample of storms, a skillful parameter may be constructed. For example, the storm-relative advection of relative angular momentum values in the region to the right of the storm-motion show promise. It is suggested that such a parameter could be useful in a SHIPS-type statistical dynamical model. The scatter-plot relationships shown in Figure 2 reinforce that the storm-relative horizontal advection of angular momentum could be a useful strength change or intensity change predictor when combined with other skillful predictive parameters.

[14] Currently, work is being completed to include the mid-level horizontal advection of angular momentum from operational model forecasts into a statistical-dynamical intensity prediction model. In addition, other inner-core dynamical fields such as the conversion rate of shear to curvature vorticity, the vertical differential of heating in the complete potential vorticity equation and the conversion of non-divergent to irrotational kinetic energy are being analyzed for their merits as contributing parameters to this model.


[15] The authors would like to thank Mark Powell for technical guidance regarding the H*Wind archive and Vijay Tallapragada and Naomi Surgi for technical assistance with the HWRF datasets. We are also grateful to NASA who funded this work.

[16] The Editor thanks the two anonymous reviewers for their assistance in evaluating this paper.