Peter G. Black and Eric Uhlhorn
NOAA/OAR/AOML/ Hurricane Research Division

Jimmy Franklin and Richard Knobb
NOAA/NWS/NCEP/ OAR (Tropical Prediction Center)

Alan S. Goldstein
NOAA/OMAO/ Aircraft Operations Center

Ivan Popstefanija and Mark Goodberlet
ProSensing, Inc.

Extreme Wind SFMR Algorithm Adjustment, 2005

The NOAA WP-3D flights into Hurricanes Katrina and Rita provided the first opportunity to confirm the ability of the pod-mounted production version of the SFMR to measure extreme surface wind speeds, i.e. surface wind speeds in excess of 120 kt. In addition, these flights provided the opportunity to check instrument performance at moderate hurricane wind speeds as well. The previous version of the SFMR flown for years on the P3 aircraft, known as the HRD SFMR, as well as the production version of the SFMR, known as the AOC SFMR, had suggested the possibility that the existing algorithm might underestimate extreme winds over 120 kt, as well as the possibility that there was a 2-5 kt high bias at moderate hurricane winds. The earlier measurements were somewhat equivocal due to relatively high electronic signal to noise ratios in the HRD instrument and to the large scatter in GPS surface wind measurements. With the vertical averaging inherent in the WL150 method for surface wind estimation (Franklin, NHC- referred to as JF method), the advent in 2005 of the new UBLOX GPS sondes (allowing measurements to the surface in high winds with twice the vertical resolution of the previous sondes) and the reduction in the SFMR instrument noise figure by an order of magnitude (Goodberlet, ProSensing, Inc)- the accuracy of the extreme wind SFMR emissivity measurements and accuracy of the GPS 'ground truth' This has resulted in the confirmation of the extreme wind underestimate suggested by the earlier measurements.

Fig. 1 shows the apparent 'roll-off' in SFMR winds compared to dropsonde WL150 estimated surface winds using JF method above 110 kt based on the 2004 data. Fig 2 shows the same behavior for Hurricane Katrina in 2005. These figures compute the 10m surface wind from its relation to the mean boundary layer wind in the lowest 150 m of the atmosphere as suggested by Jimmy Franklin (Jimmy), NHC. The SFMR winds are 10s averages. As can be noted in these two figures, the scatter plots also suggest that the SFMR values are biased high compared to the JIMMY WL150 estimates of the surface wind by about 5 kt.

The SFMR algorithm was therefore modified to take this roll-off into account and more accurately estimate extreme winds, while at the same time eliminating the SFMR high bias. This modification was undertaken following the CAT 5 Katrina flight on 28 Aug, and implemented on the NOAA P3s on 22 Sept, the day after the CAT 5 flight in Rita. A lookup table was provided to NHC forecasters on Sept 21 to adjust extreme peak winds from reported values using the old SFMR algorithm to corrected values using the new algorithm adjustment.

Subsequent to the completion of the Rita flights on Sept 23, the entire SFMR algorithm was re- examined. First the JIMMY relation between actually measured 10m winds from GPS sondes and the WL150 mean boundary layer wind was checked by combining all the dropsonde data from both 2004 and 2005. Previously, using only 2004 data, the relation between 10m GPS winds and WL150 winds suggested a slope of 0.88, somewhat larger than the 0.83 JIMMY value derived from sondes during 1997-1999. Using only the 2005 data, a value of 0.84 was obtained. However, when the 2004 and 2005 data are combined (Fig. 3), one sees that the mean slope is 0.86. The exact value of the slope in this relation depends rather critically on the distribution of data points at the high wind end, which varied considerably in the year-to-year subsets of observations. Our conclusion is that the 0.86 value with a standard deviation of 0.11, obtained from the combined 2004 and 2005 data sets, is well within the range of uncertainty of the original 0.83 value proposed by JIMMY. Hence this value will be retained and the SFMR emissivity values tuned to the original JIMMY WL150 algorithm. Fig 4 illustrates the effect of this choice by showing that there is little descernable difference between the least squares regression line and the line of perfect agreement between the actual GPS 10m winds and the JIMMY WL150 estimate of the surface winds. At most, a 3% difference can be seen at the high wind end above 100 kt, which if significant would result in a 3-5 kt low bias. However, given the inherent scatter in the surface values of ?7kt, this difference is not statistically significant with the present 2004-05 data set.

Figure 1. HRD SFMR surface winds vs. GPS sonde JIMMY WL150 estimated surface winds from 2004 hurricane flights.

Figure 2. Pod-mounted production SFMR surface winds derived from original algorithm vs GPS sonde JIMMY WL150 GPS estimated surface winds for three NOAA P3 flights in Hurricane Katrina, 2005.

Figure 3. Surface 10m wind observed by GPS sonde as a function of the mean boundary layer mean wind in the lowest 150 m layer using GPS sondes from 2004-05.

Figure 4. Surface 10m wind observed by GPS sonde as a function of the JIMMY-estimated 10m surface wind from the WL150 mean wind using GPS sondes from 2004-05.

Given this result, the relation between the JIMMYWL150 surface wind estimate and the excess emissivity (above zero wind ocean emissivity) measured by the SFMR is now examined using the data from Katrina and Rita in 2005 when the new production SFMR unit was in use. Instead of using a quadratic fit to excess emissivity vs wind speed as was done with the pre-2005 data sets, it was noticed that once the entire data set for 2005 was examined as a whole, including the two CAT5 cases, Katrina on 8/28 and Rita on 9/21, that a linear trend in the data was evident above hurricane force winds (64 kt).

Thus, a piece-wise curve was fit to the data (Fig. 5), where a quadratic fit is retained for lower wind speeds and a linear fit was choosen for the high winds. A solution was sought to objectively determine the break-point such that the slopes of the two pieces would match and the sum of the squares of the resulting differences would be minimized. A curve fitting program was run over a range of trial breakpoints (from 40-80 kt), and a value found that produced the mininmum error (rms) in the fit. This value is 64.5 kt.

Based on this result, it appears that over the entire range of hurricane force winds (i.e. > 64 kt), the emissivity/windspeed relationship may in fact be linear, as opposed to the quadratic behavior previously employed. One can see that the effect of the new fit is to remove the observed small (< 5kt) high bias in the mid range of wind speeds, i.e. 50-100 kt. At the same time the high-wind linear fit also corrects the low bias at extreme winds, i.e. > 115 kt, that had been interpreted incorrectly as a high wind 'roll-off'. Further, it can be concluded that the slight high wind bias in the mid-range was due to the erroneous choice of a quadratic algorithm extending to high winds and not due the choice of regression coefficient between WL150 mean winds and true surface winds.

That the breakpoint is right at the definition of a hurricane is completely coincidental. What may be physically significant, however, is the fact that this is also very near the point where a number of scientists are suggesting that sea surface drag (and the nature of air/sea momentum transfer) is profoundly modified (Powell, 2003; Donelan, 2004). Remember, though, that nadir emissivity at C-band is not related to drag or stress (roughness), but to surface wave energy dissipation (wave breaking).

What this result may mean, is that at the same point where the surface drag is reduced, and therefore wind momentum and energy transfer to the surface waves is diminished, the surface wave energy dissipation rate is also reduced relative to lower winds (i.e. the quadratic behavior dissappears) since the wave field is not continuing to absorb the energy as it does at the lower winds. This in turn may be saying that these two processes are related.

The old and new curves are compared to GPS 10m surface wind measurements in Fig. 6, and provides a measure of the scatter in real world surface wind measurements relative to the SFMR observations of excess emissivity.

Figure 5. Old and new model functions of excess emissivity averaged over 10s time interval vs GPS dropsonde JIMMY WL150 estimated surface wind speed for Hurricanes Katrina and Rita, 2005.

Figure 6. Old and new model functions of excess emissivity averaged over 10s time interval vs GPS dropsonde measured 10m surface wind speed for Hurricanes Katrina and Rita, 2005.

The SFMR 10 m winds computed from the SFMR emissivity with the new algorithm are now plotted vs the JIMMY WL150 surface wind estimate from the GPS dropsondes in 2005 (Fig. 7), and for the entire 2004-05 data set in Fig. 8. Fig. 9 shows the relation between the SFMR 10-m winds using the new algorithm and the measured GPS sonde 10m winds.

Figure 7. Pod-mounted production SFMR surface winds derived from new algorithm vs GPS dropsonde JIMMY WL150 surface winds for four NOAA P3 flights in Hurricane Katrina, 2005 and three flights in Hurricane Rita. This data set contains two CAT 5 flights: Katrina on 28 Aug and Rita on 21 Sept. The blue points are from Katrina at landfall on Aug 29.

Figure 8. Same as Fig. 7, except new algorithm applied to entire 2004 and 2005 data set.

Figure 9. Same as Fig. 8, except vs GPS sonde observed 10m surface wind for 2004 and 2005.

Last modified: October 17, 2005