Evaluation of the Modified Rankine and Holland et al. TC Wind Fields

At the most recent CSTAR Tropical Cyclone wind team conference call, Bryce provided a large set of Holland et al. verification images for 30 different tropical cyclones that impacted the Atlantic basin from 2005-2011 (219 total analyses). The six panel images contain H*Wind analysis, synthetic wind fields using the modified Rankine and the Holland et al. (2010) models, along with three difference plots. All of the images were posted online and feedback was desired.  Before examining the imagery, a brief summary of the wind field models is provided below.


Modified Rankine wind field from the TCM product for Hurricane Rita.

The modified Rankine vortex approach is currently used by the TCMWindTool in GFE to generate a wind field for tropical cyclones from the TCM product.  In the modified Rankine approach, the wind field increases linearly from a value of zero at the center of the storm to a value Vmax at a distance Rmax from the center of the storm.  The tool estimates this distance Rmax to be approximately 31 km from the storm center.  The wind field is estimated to decay exponentially from this distance Rmax to a distance R64, the 64 knot maximum wind radius, then decreasing exponentially to a distance R50, the 50 knot maximum wind radius, and continuing to decease exponentially to a distance R34, the 34 knot maximum wind radius for the tropical cyclone.  Because of this formulation, the wind field is highly sensitive to the R64, R50, and R34 values.  Recent discussions with forecasters at the National Hurricane Center have noted the uncertainty in the four quadrant forecasts of these wind radii.


Holland et al. wind field from the TCM product for Hurricane Rita.

A recently paper, Holland et al. (2010), developed a new parametric approach for modeling the radial profile of winds in hurricanes.  This approach can also generate the interpolated wind speeds from the TCM product, but it is not nearly as sensitive to the maximum wind radii for the various storm quadrants.  A detailed explanation of this method can be found in Holland et al. (2010). The basic equations in the Holland et al. method are shown below. In general, the defined equations used to interpolate the radial wind profile requires the following input:  radius of maximum winds, storm central pressure, maximum surface wind speeds, air density near the radius of maximum winds, and an external estimated pressure and wind speed.  The exponent “x” in Equation 1.1 is developed by anchoring the wind profile to the storm external estimated pressure.  In our analysis, we use the four quadrant 34 knot maximum wind radius to conduct the anchoring.  We make the following approximations, which are not expected to have a large impact on the interpolation error:    Rmax = 31 km    |     ρms = 1.08 kg/m3     |     pms = 1005 hPa (based on Dvorak estimates for 34 knot wind speeds).  Exponent “x” is empirically developed for each quadrant of each storm and the wind field is then calculated for various distances from the storm center out to R34 for each quadrant and each storm.   holland.formulats

A subjective evaluation of the Holland and modified Rankine approaches was undertaken for the 30 storms.  The evaluation was difficult because 219 analysis images were produced, each containing 6 individual panels (example from Rita) , which resulted a large amount of imagery to examine. In order to simplify the process and to efficiently show examples, we opted to select one image from each storm, typically containing the analysis just prior to landfall when the H*Wind analysis was apt to be most reliable because of the inclusion of the dense land observation network and since this is likely the most critical time for these analysis products. We exported a strip of the image for each of the storms at that time and compiled them into a long mosaic of comparison plots for each storm. The full mosaic is shown below along with a table of all of the storms that includes the date and time of the comparison, a link to the comparison image, and a storm track map.

A few generalities were noted in the Holland and modified Rankine approaches:

  1. The four quadrants are easily seen in the modified Rankine imagery which results in a synthetic and unnatural depiction of the wind field.
  2. A large ring of very strong winds in the Holland approach is present in nearly every storm and these winds appear excessively strong.
  3. The ring of strong winds in the Holland model dominates in such a way that no details or differences are shown across the quadrants in the strongest to medium intensity of the wind field. Variations in the wind field across quadrants only appears in the <34kt speeds.
  4. A subjective comparison between the observed H*Wind analysis (left column) and the  modified Rankine and Holland models (center and right columns) notes that the Holland is excessively smoothed and uniform near the center and most often provides a poorer representation of the wind field than the modified Rankine.

A good example of these points is shown in the first storm of the composite, Hurricane Alex, which is shown below.  As the storm approached the Mexican coast to the west, the wind field was asymmetric with the strongest winds analyzed (by H*Wind) across the northern semicircle, with the smallest wind field in the southwest quadrant. While the modified Rankine tried to show this trend, the Holland had an extremely symmetric and strong wind field.


Recent efforts include the examination of a potential hybrid approach to improve the Holland interpolation method. This approach would minimized the systematic errors in the interpolated error over the 219 available analysis times as a function of distance from storm center. I wonder if it would be better to try and correct the modified Rankine model as its initial output appears more realistic as opposed to introducing another model (Holland) with errors and then trying to correct that.

I want to acknowledge Bryce Tyner, Gail Hartfield, Terry Click, and student volunteer Lindsey Anderson for their help with this post.

Composite imagery of the selected comparison image for each tropical cyclone (click on the image to enlarge).
























Table of all of the tropical cyclones examined along with the date and time of the comparison, a link to the comparison image, and a storm track map.


TC Name
Image Date & Time Comparison Image Storm Track Map
Alex 2010|06|30 18Z Link Link
Bertha 2008|07|11 18Z Link Link
Bill 2009|08|22 18Z Link Link
Danielle 2010|08|28 12Z Link N/A
Dennis 2005|07|10 18Z Link Link
Dolly 2008|07|23 12Z Link Link
Earl 2010|09|03 00Z Link Link
Emily 2005|07|18 00Z Link Link
Felix 2007|09|03 18Z Link Link
Florence 2006|09|11 06Z Link Link
Gustav 2008|08|30 18Z Link Link
Hanna 2008|09|02 06Z Link Link
Helene 2006|09|18 18Z Link Link
Ida 2009|11|08 18Z Link Link
Igor 2010|09|20 06Z Link Link
Ike 2008|09|07 12Z Link Link
Irene 2011|08|27 06Z Link Link
Karl 2010|09|17 06Z Link Link
Katia 2011|09|06 18Z Link Link
Katrina 2005|08|29 12Z Link Link
Omar 2008|10|15 18Z Link Link
Ophelia 2005|09|14 18Z Link Link
Paloma 2008|11|08 00Z Link Link
Paula 2010|10|13 06Z Link Link
Richard 2010|10|24 12Z Link N/A
Rina 2011|10|26 12Z Link Link
Rita 2005|09|23 18Z Link Link
Stan 2005|10|04 12Z Link Link
Tomas 2010|10|31 06Z Link Link
Wilma 2005|10|24 06Z Link Link
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One Response to Evaluation of the Modified Rankine and Holland et al. TC Wind Fields

  1. hurricanebob says:

    JB and others,

    Great job displaying the data this way as it is a lot easier to digest. It does appear as though the Modified Rankine method is more representative overall despite it being more “blocky”. I was a bit confused about the hybrid approach that was mentioned. Does that refer to a combination (i.e., averaging) of the Rankine and Holland methods?

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