Evaluation of Advanced Microwave Sounding Unit Tropical ...rammb.cira.colostate.edu/resources/docs/demuth.pdfTC parameters, including cloud liquid water and rain rate. AMSU-B primarily

282 VOLUME 43J O U R N A L O F A P P L I E D M E T E O R O L O G Y

q 2004 American Meteorological Society

Evaluation of Advanced Microwave Sounding Unit Tropical-Cyclone Intensity and SizeEstimation Algorithms

JULIE L. DEMUTH

Department of Atmospheric Science, Colorado State University, and Cooperative Institute for Research in the Atmosphere,Fort Collins, Colorado

MARK DEMARIA

NOAA/NESDIS, Fort Collins, Colorado

JOHN A. KNAFF

Cooperative Institute for Research in the Atmosphere, Fort Collins, Colorado

THOMAS H. VONDER HAAR

Department of Atmospheric Science, Colorado State University, and Cooperative Institute for Research in the Atmosphere,Fort Collins, Colorado

(Manuscript received 9 October 2002, in final form 18 August 2003)

ABSTRACT

Advanced Microwave Sounding Unit (AMSU) data are used to provide objective estimates of 1-min maximumsustained surface winds, minimum sea level pressure, and the radii of 34-, 50-, and 64-kt (1 kt [ 0.5144 ms21) winds in the northeast, southeast, southwest, and northwest quadrants of tropical cyclones. The algorithmsare derived from AMSU temperature, pressure, and wind retrievals from all tropical cyclones in the Atlanticand east Pacific basins during 1999–2001. National Hurricane Center best-track intensity and operational radiiestimates are used as dependent variables in a multiple-regression approach. The intensity algorithms are eval-uated for the developmental sample using a jackknife procedure and independent cases from the 2002 hurricaneseason. Jackknife results for the maximum winds and minimum sea level pressure estimates are mean absoluteerrors (MAE) of 11.0 kt and 6.7 hPa, respectively, and rmse of 14.1 kt and 9.3 hPa, respectively. For caseswith corresponding reconnaissance data, the MAE are 10.7 kt and 6.1 hPa, and the rmse are 14.9 kt and 9.2hPa. The independent cases for 2002 have errors that are only slightly larger than those from the developmentalsample. Results from the jackknife evaluation of the 34-, 50-, and 64-kt radii show mean errors of 30, 24, and14 n mi, respectively. The results for the independent sample from 2002 are generally comparable to thedevelopmental sample, except for the 64-kt wind radii, which have larger errors. The radii errors for the 2002sample with aircraft reconnaissance data available are all comparable to the errors from the jackknife sample,including the 64-kt radii.

1. Introduction

Upon discontinuation of aircraft reconnaissance in thewestern North Pacific Ocean in 1987, the Atlantic Oceanbecame the only tropical-cyclone basin with routine insitu tropical-cyclone (TC) observations. The worldwidestandard for TC intensity monitoring, especially whenreconnaissance data are not available, is based on amethod developed by Dvorak (1975) and enhanced inthe mid-1980s (Dvorak 1984). The Dvorak technique

Corresponding author address: Mark DeMaria, NOAA/NESDIS/ORA, CIRA/Colorado State University, West Laporte Ave., Fort Col-lins, CO 80523.E-mail: [email protected]

uses visible and IR satellite imagery to observe the cen-tral and banding features of TCs and cloud-top tem-peratures near the eye. Although the methods are aug-mented by a set of empirical rules, interpretations ofTC attributes are subjective and can result in differentintensity estimates of the same storm. The techniquegenerally is successful, but large errors sometimes arepossible. Velden et al. (1998) extended Dvorak’s work,developing an automated version of the IR method—the objective Dvorak technique (ODT)—for which theonly subjectivity is the user’s selection of the storm-center location. Although their rmse is only 8.34 hPa,the ODT is not applicable to tropical depressions (TD)or weak tropical storms (TS), and further limitationsexist when a central dense overcast is present. These

FEBRUARY 2004 283D E M U T H E T A L .

works suggest that it is advantageous to have an alter-native TC intensity estimation technique that is inde-pendent of the Dvorak method.

Operational forecast centers, such as the NationalHurricane Center (NHC), are also required to estimatethe radial extent of 34-, 50-, and 64-kt (1 kt [ 0.5144m s21) surface winds at 6-h intervals. Wind radii ob-servations are obtained from reconnaissance data, shipreports, buoys, or satelliteborne scatterometers, butmany of these data sources have spatial limitations oroccur opportunistically. In their absence, conservativeoverestimates of the wind radii commonly are reportedas symmetric circular and semicircular values whenlarge asymmetries may actually exist. The applicabilityof scatterometers for wind observations has led to asurge in their usage, yet Jones et al. (1999) note manyeffects that degrade the wind retrieval accuracy, espe-cially near the region of peak winds.

Because of the shortcomings of estimating TC inten-sity and wind structure, an alternate method is desiredthat is entirely objective and is applicable to TDs, TSs,and hurricanes. Passive microwave remote sensing issuitable for TC studies because 1) microwaves penetratemost clouds beyond the top layer, a beneficial featurewhen a central dense overcast exists; 2) microwaves areunaffected by hydrometeor contamination, except inheavily precipitating regions; and 3) microwave sensingis not limited to a certain time of day.

Several studies have capitalized on the utility of mi-crowave sensing for tropical cyclone analysis after thepioneering work by Kidder (1979) and Kidder et al.(1978, 1980). Bankert and Tag (2002) describe an ob-jective TC intensity estimation method that uses SpecialSensor Microwave Imager (SSM/I) 85-GHz imageryand derived rain rates. Although their technique showspromise, the rmse is on the order of 20 kt for indepen-dent data. Merrill (1995) used Microwave SoundingUnit (MSU) and Special Sensor Microwave Tempera-ture Sounder (SSM/T) data to estimate TC minimumsea level pressure (MSLP). The primary limitation ofhis technique was the poor horizontal resolution, which,at best, is 110 km for MSU data and 175 km for SSM/T data.

In May of 1998, the MSU’s successor, the AdvancedMicrowave Sounding Unit (AMSU), was launchedaboard the National Oceanic and Atmospheric Admin-istration (NOAA)-15 satellite. The multiplatform AMSUhas more channels (15 on AMSU-A and 5 on AMSU-B) and increased horizontal resolution (48 and 16 kmat nadir for AMSU-A and -B, respectively) relative tothe MSU. AMSU-A primarily is for providing temper-ature soundings, but it also is useful in deriving otherTC parameters, including cloud liquid water and rainrate. AMSU-B primarily is for providing moisturesoundings. For more details of the AMSU instrumentand tropical-cyclone applications, see Kidder and Von-der Haar (1995) and Kidder et al. (2000).

Despite its advantages, one limitation of using AMSU

data for TC analysis is the temporal resolution. TheAMSU instrument passes over the same location a max-imum of 2 times daily. However, the deployment ofthree additional AMSU instruments—aboard NOAA-16(launched in September of 2000), Aqua (May of 2002),and NOAA-17 (June of 2002)—helps to alleviate thisproblem.

The efficacy of the AMSU for TC analysis hasprompted several recent studies. Spencer and Braswell(2001) statistically related six AMSU-derived parame-ters to the maximum winds of Atlantic TCs. Their re-sults, reported as the average error standard deviation,correspond closely with reconnaissance data (9.1 kt) butdegrade markedly (14.6 kt) for cases without aircraftobservations. Similar to Merrill (1995), Brueske andVelden (2003) developed a TC estimation algorithm thatuses 55-GHz AMSU data to estimate MSLP. Their meth-od includes a correction for subsampled upper-tropo-spheric warm anomalies (UTWA) that uses AMSU-Bdata to estimate eye size. However, their retrievals aresensitive to the eye-size parameter, and a version of theiralgorithm is under development in which the eye sizeis determined by other methods.

In this study, a method is described for estimatingTC intensity—measured by 1-min maximum sustainedwinds (MSW) and MSLP—and size (with the wind ra-dii), utilizing AMSU-A data from 1999 to 2001. AMSU-A temperature retrievals are used to determine the geo-potential height and surface pressure fields from thehydrostatic equation, and the gradient wind equation isused to estimate the tangential wind. Parameters fromthese fields are used as input to statistical relationshipsfor estimation of the MSW, MSLP, and azimuthally av-eraged (AA) radii of 34-, 50-, and 64-kt winds. Theasymmetric wind radii are determined by fitting themean wind radii to the sum of an idealized symmetricvortex and an asymmetry factor related to the stormmotion. A jackknifing procedure is used for evaluationof the intensity estimates against NHC postseason best-track (BT) data, and wind radii estimates are evaluatedagainst NHC operational TC forecast advisories. Eval-uations are performed for the entire developmental sam-ple and a subset of the 100 cases with coincident aircraftreconnaissance observations. An independent evalua-tion is performed for cases from the 2002 tropical sea-son.

2. Data

The AMSU-A (hereinafter referred to as AMSU) ra-diances were collected in real time for all storms in theAtlantic and east Pacific basins during the 1999–2001tropical-cyclone seasons. NOAA-15 data were availablefrom 1999 to 2001, and additional data from NOAA-16were collected in 2001. Current and 12-h-old TC po-sition estimates at 6-hourly intervals from the NHC areinterpolated to the time of the most recent AMSU data,which typically is within 6 h of the current storm po-


FIG. 1. A portion of the AMSU swath showing (a) Hurricane Isaac near nadir on 21 Sep 2000 and (b) Hurricane Gert near the 600-kmthreshold of the swath center on 16 Sep 1999.

sition estimate. Although the cross-track-scanningAMSU swaths are nearly 2200 km wide, the samplewas limited to those cases in which the storm center fellwithin 600 km of the swath center. The AMSU data areanalyzed over a domain with a 600-km radius (chosento include the gale radius of the largest Atlantic tropicalcyclones) so that when the storm center falls at or nearthe 600-km threshold there is a small portion of theanalysis domain with no data; this situation is not prob-lematic because the analysis procedure extrapolates datafrom neighboring data points. The maximum resolution(48 km) occurs when the storm is near the center of theAMSU data swath. At 600 km from the swath center,the data resolution is approximately 80 km. Figure 1shows examples of the data coverage for storms nearand 600 km from the center of the AMSU swath.

a. The temperature retrieval

Prior to the temperature retrieval, two corrections tothe NOAA-15 data were made for scan position andviewing angles (Goldberg et al. 2001). For NOAA-16,only the viewing angle correction was applied becausethe scan position correction was negligible for that sat-ellite (M. D. Goldberg 2002, personal communication).After the corrections, the normalized radiances wereused as input to a statistical temperature retrieval (Gold-berg et al. 2001; Knaff et al. 2000), which providestemperature as a function of pressure at 40 levels from1000 to 0.1 hPa. Only the 23 pressure levels between920 and 50 hPa were used, because the 1000-hPa levelgenerally is below the surface in the center of strongTCs, and 50 hPa was assumed to be above the storm

circulation. The cloud liquid water (CLW) also is es-timated from the AMSU-A data as part of the statisticalretrieval algorithm.

Although microwave soundings provide informationbelow the cloud-top layer, utilization in strongly con-vective regions of TCs is problematic because of hy-drometeor attenuation. Because of their relatively largesizes, CLW droplets and ice crystals absorb and scattermicrowave radiation, resulting in anomalously cold re-trieved temperatures and errors in the derived pressurefield. Preliminary investigations of the retrieved fieldsshowed these detrimental effects (Figs. A2a,c,e); thus,two corrections—one for attenuation by CLW and onefor ice scattering—were developed as described in theappendix.

The initial CLW correction was applied to the tem-perature profiles at the AMSU swath points. A two-passdistance-weighted analysis method (Barnes 1964) thenwas applied to interpolate the unevenly spaced temper-ature and CLW data on the swath to an evenly spaced128 3 128 grid with 0.28 grid spacing. This processsmoothes the data, the degree to which is controlled bythe e-folding radius in the Barnes analysis. The mag-nitude of the e-folding radius was chosen based uponthe behavior of the response function and by experi-mentation. Values of 50–150 km were tested, and it wasfound that the minimum value that sufficiently smoothedthe retrieved fields (determined subjectively from con-tour plots) was 100 km, and so this value was used forall of the Barnes analyses. Note, however, that the sta-tistical intensity estimation procedure described in sec-tion 3 was not very sensitive to the choice of the e-folding radius within the range of 75–150 km. After


interpolation of temperature and CLW to the grid, thesecond hydrometeor correction was applied for ice scat-tering (appendix).

b. The wind retrieval

The horizontal wind retrieval assumes hydrostatic andgradient balance. The hydrometeor-corrected tempera-tures at the 23 pressure levels were interpolated to aradial grid and azimuthally averaged, with the TC centerlocated at the origin, so that temperature is a functionof pressure and radius, extending outward 600 km. Sur-face temperature cannot be derived from the AMSU,and so it was obtained from the National Centers forEnvironmental Prediction (NCEP) global analysis clos-est in time to the AMSU swath, though not more than6 h old. The AMSU algorithm is insensitive to the NCEPsurface temperatures, because they are used only as alower boundary condition to derive the surface pressure.Nearly the entire surface pressure gradient comes fromthe temperature structure above the surface through thedownward integration of the hydrostatic equation.

Next, the geopotential height field was derived as afunction of pressure using the hydrostatic equation. Indoing so, additional assumptions were made that 1) tem-perature varies linearly with height between two pres-sure levels, 2) variations in gravity with height can beneglected so that height and geopotential height areequivalent, and 3) virtual temperature effects can beneglected. The last assumption could cause errors of afew hectopascals in the surface pressure, which mighthave been reduced by using AMSU-B moisture profiles.However, the AMSU-B instrument on NOAA-15 wasnot functioning properly, and so the data were not avail-able consistently before 2001. Nevertheless, errors inthe pressure gradient from neglecting virtual tempera-ture effects are proportional to the moisture gradientrather than to the total moisture. The moisture gradienterrors are less than those of the total moisture.

The hydrostatic integration was begun at the surfaceat the outer radius of the domain, where the surfacepressure boundary condition was determined from thesame NCEP analysis used for the surface temperature.This equation was integrated upward to 50 hPa to givethe heights at the AMSU pressure levels at radius r 5600 km. A final assumption then was made that the 50-hPa level is above all perturbations associated with theTC so that the height of this level is constant at all radii.The hydrostatic equation then was integrated downwardfrom 50 to 920 hPa at all radii in the interior of thedomain. With the height and temperature of the 920-hPa level and the surface temperature from NCEP, thehydrostatic equation then was integrated downward tocompute the surface pressure at all points in the domain.Again, assuming a linear variation in temperature withheight between the AMSU pressure levels, the temper-ature and pressure as a function of height were calcu-lated at 1-km intervals from the surface to 20 km, and

the density at each level was calculated with the idealgas equation.

With the pressure p and density r known as a functionof height and r, the wind field was determined assuminggradient balance [(1)], where the radial pressure gradientwas calculated using centered finite differences (withone-sided differences at r 5 0 and 600 km), the Coriolisparameter f was evaluated at the storm center, and V isthe wind speed:

2V 1 ]p1 f V 5 and (1)

r r ]r

22r f r f r ]p

V 5 6 1 . (2)1 2!2 2 r ]r

Sometimes, the radial pressure gradient in (2) is largeand negative, preventing a real solution of the gradientwind equation; for these points, the magnitude of thepressure gradient was reduced until the radicand waspositive, providing a real solution.

An example of the AMSU-retrieved temperature per-turbation and gradient winds for Hurricane Gert isshown in Fig. 2. The anomalies were calculated at eachlevel by subtracting the retrieved temperatures at r 5600 km from the temperature at each radius. The hur-ricane had MSW of 115 kt at this time; however, thecoarse resolution of the AMSU and the smoothing ofthe data resulted in retrieved MSW of approximately 60kt. The retrieved UTWA of approximately 68C also islikely a tempered estimate of the true magnitude.

c. AMSU cases

The temperature, pressure, and gradient winds as afunction of radius and height and the CLW as a functionof latitude and longitude were determined from AMSUdata for all available cases from 1999 to 2001. Casesin which the storm center was within 100 km of a majorlandmass were excluded so that at least one AMSUfootprint in all directions from the storm center was overwater.

Figure 3 summarizes the developmental sample, inwhich the reported intensities are from the NHC besttrack. The distribution of storm intensities in the de-velopmental dataset was representative of climatologi-cal conditions. The sample included 473 cases from 89TCs, of which 247 were from the Atlantic and 226 werefrom the east Pacific. Over two-thirds are at TD (123cases) and TS (199 cases) intensities, and the remainingcases are hurricane strength (151 cases). Of the latter,102 are category-1 or -2 storms (65–95 kt) and 49 arecategory-3 or -4 storms (100–135 kt); there were nocases of category-5 TCs (.135 kt) during an AMSUoverpass. The number of cases for estimating the windradii is reduced, as will be discussed in section 4, leaving129 cases from 31 TCs for the 34-kt wind radii, 92 cases


FIG. 2. Radial–height cross sections for Hurricane Gert on 16 Sep 1999 of AMSU-retrieved (a) temperature anomalies (8C), showing thewarm core at a height of approximately 12 km, and (b) gradient winds (kt), showing that the MSW occur at approximately 175 km fromthe storm center. The data locations for this case are shown in Fig. 1b.

FIG. 3. Histogram of all AMSU cases from 1999 to 2001, binnedby intensity and basin of occurrence.

from 23 TCs for the 50-kt wind radii, and 68 cases from19 TCs for the 64-kt wind radii.

The independent sample from 2002 includes 288 cas-es (143 Atlantic and 145 east Pacific) from 30 TCs, ofwhich 64 cases were within 6 h of reconnaissance. Nine-ty-five cases are TDs, 140 are TSs, and 53 are hurri-canes. Of the latter, 36 are category 1 or 2 and 17 arecategory 3 or higher. For the wind radii estimations,there were 218 cases from 24 TCs for the 34-kt windradii, 120 cases from 16 TCs for the 50-kt wind radii,and 67 cases from 10 TCs for the 64-kt wind radii.

3. Tropical-cyclone intensity estimation

Although the horizontal resolution of the AMSU ismore than 2 times as good as that of the MSU, it stillis too coarse to observe tropical cyclones without sub-sampling problems. The eye diameters of Atlantic trop-ical cyclones range from 8 to over 200 km, but themajority fall between 30 and 60 km (Weatherford andGray 1988). Even if a TC falls near the nadir position,the 48-km resolution is not sufficient to resolve the tightpressure gradient near the radius of maximum wind.However, several parameters can be derived from theAMSU temperature, pressure, and wind retrievals. Asshown in this study, when combined with other param-eters available in real time, these data can be relatedstatistically to NHC-reported MSW and MSLP, provid-ing objective estimates of each. The development ofthese algorithms is explained in this section, followedby an evaluation with the dependent sample and an in-dependent sample from 2002.

a. Methods

Eighteen parameters derived from the AMSU dataand one additional non-AMSU-derived parameter avail-able in real time served as possible estimators of trop-ical-cyclone intensity (Table 1). The parameters relayinformation from various vertical levels about retrievedpressures, winds, temperature anomalies, swath spacing,and cloud liquid water values. The combined 19 param-eters make up the independent variables used as poten-tial estimators of TC intensity through the MSW andMSLP; except for the area-averaged CLW percentage(CLWPER), all AMSU-derived parameters were azi-muthally averaged.


TABLE 1. Potential estimators of tropical cyclone intensity, where r is the radius and z is height.

Potentialintensity

estimators Description

MINPDP0DP3TMAX

Min surface pressure (hPa) at storm centerPressure drop (hPa) at the surface from r 5 600 to 0 kmPressure drop (hPa) at z 5 3 km from r 5 600 to 0 kmMax temperature perturbation (8C), calculated as the temperature at r 5 600 km minus the temperature at each radius

ZMAXSSVMX0RMX0VMX3

Height (km) of max temperature perturbation (TMAX)Resolution (km) of AMSU footprint at storm center (swath spacing)Max wind speed (kt) at the surfaceRadius (km) of max winds at the surfaceMax wind speed (kt) at z 5 3 km

RMX3VBI0VBI3VBI5VBO0

Radius (km) of max winds at z 5 3 kmTangential winds at surface, averaged from r 5 0 to 250 kmTangential winds at z 5 3 km, averaged from r 5 0 to 250 kmTangential winds at z 5 5 km, averaged from r 5 0 to 250 kmTangential winds at surface, averaged from r 5 250 to 500 km

VBO3VBO5CLWAVECLWPERLAT*

Tangential winds at z 5 3 km, averaged from r 5 250 to 500 kmTangential winds at z 5 5 km, averaged from r 5 250 to 500 kmCLW content (mm), averaged from r 5 0 to 100 kmPercentage of area with CLW values .0.5 mm from r 5 0 to 300 kmLat from NHC at storm center, interpolated to AMSU swath time

* LAT is the only parameter not derived from AMSU data.

The dependent data for the TC intensity estimationsare from the NHC BT linearly interpolated to the timeof the AMSU swath. However, the best-track data arenot all ‘‘ground truth’’; the intensity estimates are de-termined from available Dvorak satellite estimates, shipreports, buoy data, land stations, aircraft reconnaissancemeasurements (nearly all of which are from the At-lantic), satellite cloud-track winds, and scatterometerand passive microwave (SSM/I) surface winds. Al-though a developmental dataset consisting entirely ofin situ data is preferable, AMSU and reconnaissancedata were coincident within 6 h only 100 times from1999 to 2001. There is a marginal amount of cases fromwhich to develop a statistical algorithm with 19 potentialestimators, and so, until a larger dataset becomes avail-able, the best-track data are the best alternative for stabledevelopment. The reconnaissance dataset was used fora separate evaluation.

All of the parameters in Table 1 are probably relevantto TC intensity, but the actual significance of each oneis not explicit. Therefore, the relationship between theestimators and the predictands was analyzed with mul-tiple linear regressions. In general, it is not prudent toinclude every possible estimator in the regression equa-tion, because some may not be valuable in estimatingthe predictand or some may be mutually correlated, pro-viding redundant information. The list of potential es-timators was consequently shortened initially by cor-relating each variable against the predictands. If the cor-relation coefficient was less than 0.5, then that variablewas excluded initially.

A backward stepwise regression with a 1% signifi-cance level (a 5 0.01) then was used to select a set ofestimators from the remaining variables. It is possible,though, that some variables removed by the initial cor-

relation step could improve the variance explained: al-though a given variable may not be correlated with theMSW or the MSLP, it may be correlated with the re-siduals of the estimative algorithms. For instance, theAMSU footprint resolution at the storm center (SS) hasno direct physical relationship to TC intensity, but asthe resolution worsens, the intensity is underestimatedby the AMSU data. Thus, there is a relationship betweenSS and the residuals from the backward stepwise re-gression. To avoid excluding these relevant connections,each of the variables removed by the initial correlationwas analyzed against the residuals, and if a relationshipexisted, the variable was added back to the potentialestimator pool. Then the backward stepwise regressionwas reanalyzed, and the variables retained were the finalset used in the algorithms to estimate the MSW and theMSLP.

The intensity estimators selected using the 1999–2001 data were evaluated using a ‘‘storm jackknife’’procedure. The typical jackknife method develops re-gression equations on n 2 1 cases and tests the algo-rithm on the withheld case. However, usually there arenumerous cases from one TC, potentially weighting thedevelopmental dataset and underestimating the error onthe ‘‘independent’’ case. To prevent this bias, all casesfor a given storm were withheld, the algorithms to es-timate the MSW and MSLP were developed with theremaining cases, and then the algorithms were testedindependently on all the withheld cases from that storm.

b. Results

1) DEPENDENT DATA RESULTS

The final regression equation for MSW contains sevenAMSU-derived estimators, explaining 72.3% of the var-


TABLE 2. Regression variables and their corresponding coefficients, normalized coefficients, and p values retained to estimate best-trackreports of MSW (kt) and MSLP (hPa).

Independentvariable

Max sustained winds (kt) R2 5 72.3%

Coef Normalized coef p value

Min sea level pressure (hPa) R2 5 76.5%

Coef Normalized coef p value

MINPDP0TMAXSS

—21.648

2.9960.191

—20.459

0.2040.070

—0.0000.0080.005

0.6231.521

22.77720.145

0.2590.602

20.26920.076

0.0000.0000.0000.001

RMX3VBI5CLWAVECLWPER

20.0204.109

19.55620.222

20.0690.8830.327

20.168

0.0060.0000.0000.000

0.01422.492

212.4990.116

0.07220.76020.297

0.124

0.0020.0000.0000.001

TABLE 3. Comparison of the results for estimations of MSW (kt) and MSLP (hPa) using the AMSU-derived intensity algorithms for thedevelopmental, storm jackknife, and storm jackknife against reconnaissance datasets.

Developmental dataset(n 5 473)

MSW MSLP

Jackknife dataset(n 5 473)

MSW MSLP

Jackknife data againstreconnaissance data

(n 5 100)

MSW MSLP

R2

MAERmseStd dev of residuals

72.3%10.613.513.5

76.5%6.58.88.8

70.2%11.014.114.1

73.9%6.79.39.3

74.3%10.714.913.7

83.1%6.19.29.0

iance (R/2); an additional parameter is retained to explain76.5% of the variance in the MSLP (Table 2).

To compare the coefficients for each estimator, nor-malized coefficients were calculated from nondimen-sional dependent and independent variables calculatedby mean centering and then dividing by the standarddeviation. Each normalized coefficient has a comparablemagnitude for MSW and MSLP, suggesting that the pa-rameters work similarly in estimating each; the signsare opposite, however, because MSW and MSLP areinversely related. The normalized coefficients illustratethat the AMSU-derived tangential wind at a height of5 km from 0 to 250 km (VBI5) is the most influentialparameter in estimating both MSW and MSLP, followedclosely by the pressure drop at the surface (DP0). VBI5probably was selected instead of the comparable vari-ables at 3 km (VBI3) or at the surface (VBI0) becausethe height and wind fields in the domain interior arederived by a downward integration, and noise and errorsaccumulate near the surface. In addition, hydrometeoreffects worsen closer to the surface. As expected, DP0is an influential parameter because the pressure drop isstrongly related to intensity.

The two estimators with lower normalized coeffi-cients, SS and the radius of maximum winds at 3 km(RMX3), were the only ones added back to the estimatorpool by the residual analyses. Although SS is not phys-ically related to TC intensity, it helps to correct forresolution variations by increasing the estimated inten-sity when SS is large. In a similar way, the estimatedintensity decreases as RMX3 increases because theAMSU better resolves larger storms. RMX3 probably

was chosen over the comparable variable at the surface(RMX0) for the same reasons described above for VBI5.

The mean absolute error MAE (rmse) on the devel-opment dataset is 10.6 (13.5) kt for estimating MSWand 6.5 (8.8) hPa for MSLP (Table 3). These statisticsdeteriorate only slightly on the storm jackknife data,suggesting that the artificial skill is minimal. The rmseof 14.1 kt for the MSW estimates is smaller than Bankertand Tag’s (2002) rmse of 19.7 kt. The rmse of the MSLPis 9.3 hPa, which is 1.0 hPa higher than the reportedODT rmse (Velden et al. 1998). However, if one restrictsthe AMSU cases to only Atlantic storms as Velden etal. did, the resultant rmse of 8.2 hPa is comparable totheir findings. The standard deviation of the MSW jack-knife residuals is 14.1 kt, akin to 14.6 kt from Spencerand Braswell (2001). Therefore, the intensity estimationequations developed in this study have errors compa-rable to those from other methods, with the advantagethat they estimate MSW and MSLP for tropical distur-bances of all strengths. However, a homogeneous sam-ple would be necessary for a true comparison of allmethods.

When the storm jackknife estimates were evaluatedonly for the 100 cases with reconnaissance data within6 h, all but one of the statistical measures improves(Table 3). The MSW explained variance increased to74.3%, and the MAE and standard deviation of the re-siduals decreased to 10.7 and 13.7 kt, respectively. How-ever, the rmse increased slightly to 14.9 kt for the air-craft cases, likely signifying that there are a few caseswith large errors, which are skewing the rmse on thissmaller dataset, but that there are many more cases with


FIG. 4. Histogram of residuals (best track minus AMSU estimated)for estimates of MSW (kt) from 1999–2001 storm jackknife data.

FIG. 5. Same as Fig. 4, but for MSLP (hPa).

TABLE 4. Comparison of the results for independent estimationsof MSW (kt) and MSLP (hPa) using the AMSU-derived intensityalgorithms for all 2002 data and only data with reconnaissance.

Best-track cases(n 5 288)

MSW MSLP

Reconnaissancecases (n 5 64)

MSW MSLP

R2

BiasMAERmseStd dev of residuals

69.0%2.2

10.914.113.9

67.5%21.1

7.510.510.4

72.3%24.711.014.313.6

83.4%5.37.0

10.69.2

small errors, keeping the MAE down and raising thecoefficient of determination. For the cases with recon-naissance data, the MSLP explained variance increasedto 83.1%, the MAE (rmse) decreased slightly to 6.1 (9.2)hPa, and the residual standard deviation decreased to9.0 hPa.

The distribution of residuals (Fig. 4) shows that72.5% of the errors fall within 15 kt and only 13% oferrors are more than 20 kt. For the MSLP estimates, theresidual distribution (Fig. 5) shows that 78.4% lie within10 hPa, with only 4.4% exceeding 20 hPa. The fact thatthe maximum wind error exceeded 20 kt in only about13% of the cases is encouraging. Brown and Franklin(2002) showed that the errors in the Dvorak estimatesexceed 20 kt in about 10% of the cases. These resultssuggest that the AMSU can provide intensity estimatesthat are comparable to the Dvorak method but are in-dependent of visible and IR imagery. Because of thisindependence, a method that included both types of datawould likely lead to even more accurate intensity es-timates.

A closer examination of the residuals revealed sixstorms that were underestimated by the AMSU algo-rithm by in excess of 30 kt, with a maximum error of57 kt. One-half of these storms were from HurricaneIris, and another was from Hurricane Juliette. Basedupon their appearance in IR imagery, both were smallstorms. In fact, aircraft data for Iris near the time of itspeak intensity indicated a radius of maximum wind assmall as 8 km. These results indicate that the algorithmdoes not perform well in such cases because of its lim-ited horizontal resolution. The other two underestimatedcases were from Hurricane Lenny, which may have beenill-affected by inaccurate temperature retrievals in andaround the elevated terrain of the Caribbean islands. Inaddition, it appeared that the AMSU footprint locationsoccurred on either side of the warm core associated withthe storm, so that the most intense region was not sam-pled.

There are 14 cases in which the AMSU algorithm

overestimates TC intensity by more than 25 kt, the great-est overestimation being 32.4 kt. These large overesti-mations likely occur for two reasons: 1) when TCs in-tensify rapidly, the warm core appears to increase fasterthan the surface winds, and 2) when TCs lose all con-vection, the warm core is exposed. The latter occursmost often in the east Pacific, which is where 64% ofthe large overestimations occurred. A possible way tocorrect this error would be to use IR data as part of amultisensor algorithm.

2) INDEPENDENT DATA RESULTS

To evaluate further the intensity AMSU estimation,the algorithm developed from the 1999–2001 cases wasrun in real time during the 2002 hurricane season, andresults were compared with the 2002 NHC postseasonbest track. As shown in Table 4, the performance of thealgorithm is robust, with only a slight increase in errorrelative to the developmental dataset. The algorithmsexplain 69.0% of the MSW variance and 67.5% of theMSLP variance. Furthermore, the MAE (rmse) is 10.9(14.1) kt for estimating the MSW and 7.5 (10.5) hPafor estimating the MSLP. When evaluated against onlythe 64 cases from 2002 with reconnaissance data, theresults again are consistent with the developmental da-taset, with 72.3% and 83.4% of the variance explainedfor MSW and MSLP, respectively. In addition, the MAE


TABLE 5. Regression variables and their corresponding coeffi-cients, normalized coefficients, and p values retained to estimate NHCreports of the azimuthally averaged 34-, 50-, and 64-kt wind radii (nmi).

Independentvariable Coef Normalized coef p value

Azimuthally averaged 34-kt wind radii (n mi) R2 5 71.9%MINPVBI5LATBTMSW*

23.78823.135

2.1001.113

20.71820.349

0.3270.501

0.0000.0050.0000.000

Azimuthally averaged 50-kt wind radii (n mi) R2 5 65.9%TMAXVMX0VMX3VBO5CLWPER

9.4611.273

22.0592.2980.620

0.5260.525

20.7720.3000.321

0.0060.0040.0010.0040.002

Azimuthally averaged 65-kt wind radii (n mi) R2 5 80.8%TMAX 6.286 0.623 0.000SSCLWPERBTMSW*

0.4270.2700.217

0.1680.2480.188

0.0050.0100.005

* BTMSW is the best-track estimate of the maximum sustained winds;in real time, the operational estimate will be used.

TABLE 7. Comparison of the results for estimating the asymmetricwind radii (n mi) of 34-, 50-, and 64-kt winds using AMSU-derivedestimates of the azimuthally averaged wind radii with a Rankinevortex model; all quadrants have been combined into one sample.

34-kt asymmetricradii (n 5 129)



R2

MAE(% of avg)RmseBias

58.6%30.2

(27.0%)40.8

23.2

44.0%23.9

(36.1%)34.2

25.2

55.1%14.1

(37.5%)18.7

0.1

TABLE 6. Comparison of the results for estimating the azimuthally averaged 34-, 50-, and 64-kt wind radii (n mi) with AMSU-derivedalgorithms (Dev) for the developmental and storm jackknife datasets (Jack).

34-kt azimuthallyaveraged radii

(n 5 129)

Dev Jack


(n 5 92)

Dev Jack


(n 5 68)

Dev Jack

R2

MAE(% of avg)RmseBias

71.9%21.2

(19.0%)28.3

—

65.4%24.3

(21.7%)31.6

1.0

65.9%17.9

(26.9%)23.3

—

39.3%25.7

(38.7%)32.6

29.9

80.8%8.0

(21.2%)10.1

—

73.7%9.4

(25.0%)11.8

20.1

and rmse of the reconnaissance-only evaluation are verysimilar to the errors of the entire 2002 dataset.

4. Tropical-cyclone wind radii estimation

Similar to the intensity estimation, a statistical pro-cedure that utilizes AMSU-derived parameters was em-ployed to estimate the AA radii of 34-, 50-, and 64-ktwinds. The AMSU-derived AA estimates subsequentlywere used with a simple surface wind model—given asthe sum of a constant vector proportional to TC motionplus a modified Rankine vortex—to make asymmetricestimations of the wind radii in the northeast (NE),southeast (SE), southwest (SW), and northwest (NW)quadrants relative to the TC center, as are reported bythe NHC operational forecast advisories every 6 h. Thedevelopments of the symmetric and asymmetric windradii techniques are described in this section; the formerare cross evaluated with the same storm jackknife pro-cedure used for the intensity evaluation, and the asym-metric estimates were evaluated against the NHC ad-

visories closest in time to the AMSU swath data (witha maximum 3-h difference) for both the developmentaland the 2002 independent datasets.

a. Methods

The NHC operational MSW estimates, as opposed tothe AMSU-estimated MSW, were used to determinewhich wind radii were to be estimated. For example, ifthe operational estimate of the MSW is 65 kt, the 34-,50-, and 64-kt wind radii all are to be estimated, evenif the AMSU estimate is below 65 kt. This method wasused to maintain consistency with the NHC’s reportedTC intensity estimate.

The same 19 parameters used for the intensity esti-mation (Table 1) and the operational estimate of inten-sity itself make up the independent variables (estima-tors) for the AA 34-, 50-, and 64-kt wind radii esti-mations. The dependent variable, reported in nauticalmiles (n mi), is the average of the four wind radii fromthe operational forecast advisories issued every 6 h bythe NHC. The radii closest in time to the AMSU swathwere used with no more than a 3-h difference. Becausethere is no systematic technique analogous to the Dvor-ak method for estimating the wind radii from satellitedata, the wind radii data in the NHC advisories arederived from surface and remotely sensed data and fromaircraft reconnaissance data. As with the best-track data,the majority of the ground-truth data for the wind radiiare not in situ measurements. Unlike the BT intensities,however, there is no postseason analysis of the windradii, suggesting that large errors may be inherent in thedevelopmental dataset. Therefore, the data for devel-


TABLE 8. Comparison of the results, shown by quadrant, for es-timating the asymmetric wind radii (n mi) of 34-, 50-, and 64-ktwinds using AMSU-derived estimates of the azimuthally averagedwind radii with a Rankine vortex model.

NE SE SW NW

34-kt asymmetric wind radiiR2

MAERmseBias

59.5%28.438.4

213.1

66.9%28.939.0

21.8

60.9%30.541.811.5

45.7%32.843.9

29.3


MAERmseBias

33.9%29.241.2

215.8

67.3%21.829.6

22.8

52.8%19.327.0

4.4

26.6%25.437.1

26.8


MAERmseBias

69.0%15.318.9

25.0

59.5%12.017.0

6.3

44.3%14.719.1

3.9

55.5%14.419.6

24.6

oping the wind radii equations were restricted to At-lantic cases west of 558W, which have the best coverageof aircraft reconnaissance, buoys, ships, and island sta-tions. The east Pacific cases that had reconnaissance dataalso were included.

The same four-step statistical method with the samesignificance levels used in developing the intensity es-timation algorithms was used to create three wind radiialgorithms, one each for the AA 34-, 50-, and 64-ktwinds. After the initial correlation (removing those witha coefficient less than 0.5) of each estimator with thepredictand, a backward stepwise regression was em-ployed with the resulting variables (a 5 0.01), followedby an examination of the residuals against the param-eters removed at the outset by the correlation. Again,any parameters showing a relationship with the residualswere added back to the potential estimator pool, and theregression was reanalyzed.

With the AMSU-derived AA wind radii estimates, thewind radii in the NE, SE, SW, and NW quadrants weredetermined by using a modified Rankine vortex (Dep-perman 1947) applied to a polar coordinate system,where the surface wind speed V outside the radius ofMSW rm is given by a simple model,

2xrV(r, u) 5 (V 2 g) 1 g cos(u 2 u ), (3)m 01 2rm

where r is the radius from the TC center, u is the anglemeasured from a direction 908 to the right of the stormheading, Vm is the maximum wind, g is the asymmetryfactor resulting from the storm translational speed(Schwerdt et al. 1979), and x is a unitless, positive num-ber that determines the rate at which the wind speeddecays with radius. Application of (3) to the best-trackMSW and observed wind radii in each quadrant for the1999–2000 sample indicated that the best fit is obtained

when g is 60% of the asymmetry factor from Schwerdt’sequation, and u0 5 0, indicating that the MSW generallyare 908 to the right of the direction of motion.

With u0 and g specified and Vm set to the operationalestimate of MSW, the AMSU-estimated AA wind radiithen were used to determine the two remaining freeparameters, rm and x, by solving (3) for r and applyingan azimuthal average to give

1/x2pr V 2 gm mr 5 du. (4)E [ ]2p V 2 g cos(u 2 u )00

There are three possible scenarios for finding rm andx: 1) when the MSW of a TC is greater than 34 but lessthan 50 kt, providing only an AMSU estimate of theAA 34-kt wind radii; 2) when the MSW is greater than50 but less than 64 kt, resulting in AMSU estimates ofthe AA 50- and 64-kt wind radii; and 3) when the MSWis greater than 64 kt, providing all three AMSU esti-mates of the AA wind radii. The second case is idealin that (4) can be evaluated twice, once each for theAA 34- and 50-kt wind radii, resulting in two equationsfor the two unknowns rm and x. The dilemmas occurwhen the MSW is less than 50 kt, because only themean 34-kt wind radius is known, and when the windis 64 kt or greater, because three average wind radii areavailable.

To remedy these problems, the parameters x and rm

were determined using a variational approach in whicha cost function, C(rm, x), is minimized. The cost functionis given by

2 2(r 2 R ) (r 2 R )34 34 50 50C 5 12 2s s34 50

2 2(r 2 R ) (x 2 x )64 64 c1 1 lx2 2s s64 x

2(r 2 r )m mc1 l , (5)rm 2s rm

where r34 is the average 34-kt wind radius determinedfrom (4), R34 is the 34-kt wind radius from the statisticalalgorithm, s34 is the standard deviation of a sample ofmean 34-kt wind radii (and similar for the 50- and 64-kt wind radii), xc is the climatological value of x, rmc isthe climatological value of rm, and sx and srm are thesample standard deviations of x and rm, respectively.The climatological variables and standard deviationswere determined from NHC operational estimates ofwind radii for all Atlantic storms from 1988 to 2000west of 558W. The standard deviations in (5) are con-stants, but the climatological values of x and rm are afunction of the TC MSW, where rmc decreases and xc

increases for stronger storms.The last two terms on the right side of (5) are ‘‘penalty

terms’’ that prevent the values of x and rm from deviatingtoo far from the climatological values as determined bylx and lrm. Values of 0.1 for both parameters were cho-


FIG. 6. Comparison of AMSU-derived and NHC reports of asym-metric 34- and 50-kt wind radii (n mi) for Tropical Storm Iris (1152UTC 6 Oct 2001), where the arrow denotes direction of storm trans-lation.

sen based upon an analysis of the behavior of the min-imization of (5) for idealized wind profiles. The penaltyterms have only a small influence on the solution exceptin the special cases in which the storm maximum windis very close to one of the wind radii thresholds (34,50, or 64 kt) and the speed of motion is large. In thesecases, the wind radii are zero for a fairly large span ofazimuth for the highest wind threshold, making the az-imuthal mean radius in (4) very small. In the minimi-zation procedure, unrealistic values of x and rm are re-quired to compensate. The penalty terms prevent thisunrealistic solution from being selected.

Once rm and x are known, (3) is used to determinethe radius for any wind speed V at any azimuth u. Thevalue of V is set, depending on which wind radii mag-nitude is sought (e.g., when determining the asymmetric34-kt wind radii, V 5 34), and u is determined by ro-tating the desired geographic direction into the storm-motion relative coordinate system.

b. Results

1) AZIMUTHALLY AVERAGED WIND RADII

The final regressions include from four to five vari-ables (Table 5) that account for approximately 66%–81% of the variations in the 34-, 50-, and 64-kt AAwind radii. The set of estimative parameters varies basedon which wind radius is being approximated. The 50-and 64-kt radii equations have two estimators in com-mon; the 50- and 34-kt radii equations have no commonestimators.

Table 6 shows the error statistics for the wind radiiestimates for the developmental and storm jackknifesamples. For the AA 34- and 64-kt wind radii, the resultsof the jackknife dataset decline modestly, suggestingthat the AMSU-derived algorithms are without artificialskill. However, the 50-kt wind radii are not estimatedas well. There is large scatter (R2 5 39.3%) and a biasof 29.9 n mi, indicating an underestimate of the 50-ktwind radii. It is possible that part of this error is due touncertainties in the NHC estimates of the wind radii;this ambiguity will be resolved once a large enoughreconnaissance dataset is acquired for comparison.However, the lower reliability of the AA 50-kt windradii is less of a problem when the asymmetric windradii are calculated, because the cost function combinesthis information with the AA 34- and 64-kt wind radii.

2) ASYMMETRIC WIND RADII

(i) Dependent data results

The AMSU-derived asymmetric wind radii estimatesgenerally compare well to the NHC asymmetric windradii (Tables 7 and 8), although large differences some-times occurred (the maximum differences are on theorder of 200 n mi for the 34-kt radii, 150 n mi for 50-kt radii, and 90 n mi for 64-kt wind radii). The as-

sumption that the wind field asymmetries are solely theresult of motion may be the cause of such large differ-ences, particularly when a storm is imbedded in an en-vironment that contains strong horizontal wind shear.Once again, without a dataset consisting only of in situobservations, it is difficult to determine whether outliersare due to the statistical estimation or to uncertaintiesin the NHC evaluation data.

To illustrate better the asymmetric wind radii esti-mation, two specific examples are discussed below: 1)a small but highly asymmetric storm that validates wellwith concurrent reconnaissance data and 2) a large stormwithout concurrent aircraft reconnaissance data.

On 1152 UTC 6 October 2001, Tropical Storm Irishad MSW of 55 kt and was moving west-northwest at15 kt. Because Iris was south of the Greater Antilles,reconnaissance data were coincident with this time. Withan intensity so close to the 50-kt wind radii thresholdand a rapid translation speed, 50-kt winds are not ex-pected to encircle the TC; rather, they exist only in theNE and NW quadrants (Fig. 6). Both the AMSU-derivedand NHC radii estimates show this asymmetry verywell, although they differ in magnitude by about 10 nmi.

The case of Hurricane Gert on 1132 UTC 22 Sep-tember 1999 shows how uncertainties in the evaluationdata complicate the assessment of errors. The NHC radiiestimates for this case were almost exactly the same asthose determined from a reconnaissance flight nearly 36h prior. However, between the flight and the time of thiscase, the TC weakened from 95 to 70 kt and the speedof motion increased from 9 to 21 kt. There consequentlywere no 64-kt winds in the NW or SW quadrants fromthe AMSU data, and yet the NHC continued to report64-kt wind radii of 90 and 50 n mi, respectively, inthose quadrants (Fig. 7). Without in situ observations,


FIG. 7. Similar to Fig. 6, but for asymmetric 34-, 50-, and 64-ktwind radii (n mi) for Hurricane Gert (1132 UTC 22 Sep 1999).

TABLE 9. Comparison of the results for independent estimationsof the asymmetric wind radii (n mi) of 34-, 50-, and 64-kt winds for2002 data using AMSU-derived estimates of the azimuthally averagedwind radii with a Rankine vortex model; all quadrants have beenaveraged into one. Results are shown for all cases and for cases inwhich reconnaissance observations were made within 3 h of theAMSU observation.

All cases




R2

MAERmseBias

48.5%35.345.9

216.9

58.5%12.319.2

0.2

15.5%38.048.9

215.5

Reconnaissance cases




R2

MAERmseBias

50.7%37.748.1

215.8

53.1%16.828.4

1.7

60.3%12.316.910.4it is unclear which radii estimates are more accurate in

this case.Despite the uncertainties in the NHC wind radii for

Hurricane Gert, both the AMSU and NHC 34- and 50-kt radii are much larger for Gert than for Iris (Figs. 6and 7). Based upon aircraft data and satellite imagery,Gert was a much larger storm than Iris, indicating thatthe AMSU algorithm can distinguish between storms ofdifferent sizes. In addition, the radius of maximum windis estimated as part of the asymmetric wind radii esti-mation procedure; although these parameters were notevaluated in this study, the values for these Gert andIris examples were 69 and 29 n mi, respectively, againdistinguishing between the large and small storms.

(ii) Independent data results

Table 9 shows the radii error statistics for the 2002independent sample. Comparing Tables 7 and 9 showsthat the errors of the AMSU estimates of the 34- and50-kt asymmetric wind radii for the 2002 independentcases are comparable to the results with the jackknifesample, although the biases are a little larger. For the64-kt radii, the performance for the total 2002 sampledegrades in comparison with the jackknife results, butthe performance for the 2002 sample with reconnais-sance data is comparable. It is possible that the deg-radation of the 64-kt radii estimates for the total 2002sample is partially due to uncertainties in the operationalradii estimates, because this sample includes east Pacificas well as Atlantic storms. The 64-kt wind radii are themost difficult to estimate without aircraft data becausethe satellite winds [Quick Scatterometer (QuikSCAT)and SSM/I] are less valid for higher wind speeds, andgenerally there are fewer in situ data near the stormcenter. When a large enough sample becomes available,the radii algorithm should be rederived and evaluatedusing only those cases that include aircraft reconnais-sance as ground truth. Nevertheless, the general con-

sistency of the radii errors between the jackknife andindependent samples suggests that the performance ofthe algorithm was not overly influenced by the choiceof the developmental sample, and the method providesradii estimates that explain 45%–60% of the variabilityof the NHC operational estimates.

5. Summary and conclusions

This study used AMSU data to estimate two measuresof TC intensity—MSW and MSLP—and wind structurethrough the azimuthally averaged radii of 34-, 50-, and64-kt winds. The physically based part of the algorithmprovides a spatially smoothed view of the tropical cy-clone, which is input to statistical models to provide theintensity and radii estimates. The estimative algorithmswere developed with cases from 1999 to 2001 with acorrelation–multiple-linear-regression-residual analysistechnique, and a storm jackknife evaluation was em-ployed to assess the error characteristics. The azimuth-ally averaged wind radii subsequently were used in con-junction with a simple surface wind model (the sum ofa modified Rankine vortex and a constant vector pro-portional to the storm motion) to estimate the wind radiiin the NE, SE, SW, and NW quadrants. The intensityestimates were evaluated with postseason best-trackanalyses; for the wind radii, evaluation was made withNHC operational forecast advisory estimates. In addi-tion to the jackknife evaluations with the developmentalsample, an evaluation was performed using an inde-pendent sample from the 2002 hurricane season.

In general, the intensity estimates in this study haveerrors comparable to those of the objective Dvorakmethod—with the advantage of providing intensity es-timates for all ranges of storm intensity—and to thosefrom other AMSU-based intensity techniques. An ad-


FIG. A1. The slope of the CLW-vs-temperature-deviation regression vsthe corresponding pressure level, fit with a quadratic curve.

vantage of the current technique, however, is that it alsoprovides estimates of the radii of 34-, 50-, and 64-ktwinds. These radii estimates explain 45%–60% of thevariability of the wind radii in the operational NHCforecast advisories.

Work is under way to extend the intensity and windradii estimation algorithms globally to all other tropicalbasins. Other future work may include enhancing theasymmetric wind estimations by using a nonlinear bal-ance equation to derive the three-dimensional windfield, rather than forcing the maximum wind to be 908to the right of the storm motion, thus accounting forcases in which the tropical cyclone is embedded in anenvironment that contains strong horizontal wind shear.AMSU-B and IR imagery also may be used to determineTC size so that the AMSU-derived estimative param-eters can be scaled accordingly. Last, when a sufficientnumber of AMSU cases with coincident reconnaissancedata exist, the intensity and radii estimative algorithmsmay be redeveloped so that they are based entirely onground truth, making them completely independent ofthe Dvorak method.

Acknowledgments. The authors thank Dr. James Pur-dom for instigating this work and providing initial fund-ing, Dr. Mitch Goldberg for creating the temperatureretrieval, and Dr. Stan Kidder for useful discussions andassistance with data acquisition. This research was par-tially funded by an AMS Graduate Student Fellowship,sponsored by DynCorp, and also by the U.S. WeatherResearch Program, NOAA Grants NA67RJ0152 andNA17RJ1228.

APPENDIX

Development of CLW and Ice Corrections

To represent more accurately the retrieved tropical-cyclone temperature, pressure, and wind fields, a cor-rection for hydrometeor effects in necessary. Modifi-cations for absorption in areas of high CLW content and

scattering by ice were developed, based upon the meth-od described by Linstid (2000).

Both corrections are implemented at 12 pressure lev-els between 350 and 920 hPa (i.e., 350, 400, 430, 475,500, 570, 620, 670, 700, 780, 850, and 920 hPa) atwhich AMSU temperatures are retrieved. As will beseen, the attenuation effects of CLW at the lower pres-sure levels are minimal, so that only a correspondinglyslight adjustment is done. The data used in developingthe correction come from 64 AMSU passes over Atlanticand east Pacific storms from the 1999 tropical season.Despite the 154 total passes over tropical disturbancesthat year, only those are used for which the analysisdomain is completely over the ocean in order to providehomogeneity in the sample.

a. CLW correction

The basis of the CLW correction is to remove theartificial relationship between lower derived tempera-tures and large amounts of CLW by using the temper-ature and CLW data associated with each footprint. Thetemperature data utilized in the correction consist of allAMSU footprints within a 128 3 128 storm-centeredgrid.

At each pressure level, the mean temperature Tmean ofall the swath points is calculated for each storm and isused to find the temperature deviation Tdev at each foot-print i by subtracting the actual temperature T at thatfootprint:

T (i) 5 T 2 T(i).dev mean (A1)

A linear regression then is performed at each of the 12pressure levels, using the data points from all 64 AMSUpasses with the temperature deviations as the dependentvariable and the associated CLW values as the inde-pendent variable. Next, the slopes of the 12 regressionlines are plotted against their corresponding pressurelevel mp, and a quadratic curve is fit to the data (Fig.A1). At 350 hPa, the slope is nearly zero, indicatingthat CLW does not affect temperature because there isless CLW at this level. In contrast, the magnitude of theslope is largest at 920 hPa, representing the decrease intemperature due to the abundance of CLW at this level.

Not all swath points are affected by CLW, and so onlythose with a corresponding CLW value greater than 0.3mm are corrected for attenuation effects. The correctionis given by

T (i) 5 T (i) 1 m CLW(i),corrected original p (A2)

where Tcorrected is the corrected temperature at each foot-print, Toriginal is the uncorrected temperature, and mp isthe slope for a given pressure level.

b. Ice correction

After the CLW correction, the temperature data arecorrected further for scattering by ice crystals with the


FIG. A2. (a), (c), (e) Non-hydrometeor-corrected and (b), (d), (f ) hydrometeor-corrected plots for HurricaneGert (115 kt) from 1148 UTC 17 Sep 1999, showing (a), (b) radial–height cross section of temperatureanomalies (8C), (c), (d) lat 3 lon profile of surface pressure (hPa), and (e), (f ) radial–height profile ofazimuthally averaged gradient wind (kt).


method described by Linstid (2000) with minor modi-fications. Prior to the ice correction, a distance-weightedaveraging method (Barnes 1964) is used to interpolatethe unevenly spaced swath data to an evenly spaced 1283 128 grid with 0.28 grid spacing. It would be preferableto perform the ice correction on the swath data, as withthe CLW correction, because the Barnes analysissmoothes the data. However, the Laplacian method uti-lized by Linstid (2000), described as follows, requiresthat the data be evenly spaced.

At each of the 12 aforementioned pressure levels, themean temperature, unaffected by ice, is calculated byonly using points at which the associated CLW valueis less than 0.2 mm. This constraint is based on theassumption that cloud ice does not occur where thereis little or no CLW. If the temperature at a given gridpoint is less than the mean temperature minus 0.58C,the data point is considered to be too cold because ofice attenuation, and it is flagged to be corrected.

Following Linstid (2000), once all of the points af-fected by ice are flagged at each pressure level, Laplace’sequation [(A3)]—where T is the temperature—is used tofix the corrupted data, because it provides a smooth tem-perature field using uncorrupted data points:

2¹ T 5 0. (A3)

Equation (A3) is solved by iteratively replacing eachflagged data point with the average of its nearest neigh-bors, of which there are four if the point is in the centerof the domain, three if it is on the side, and two if it isin the corner. This correction procedure is continueduntil the temperatures of all the flagged data points con-verge such that the differences in the temperatures be-tween the previous and current iteration are less than0.0058C.

In Fig. A2 are the uncorrected versus the hydrome-teor-corrected plots of the radial–height cross sectionsof temperature anomaly (8C) and azimuthally averagedgradient wind (kt), as well as the horizontal distributionof surface pressure (hPa) of Hurricane Gert when it wasa category-4 storm with an MSW of 115 kt. The cor-rections greatly reduced the large area of low-level coldtemperatures and the large area of surface high pressure.The adjusted wind profile is much more realistic thanthe uncorrected version, with the low-level anticyclonicarea at the storm’s edge removed.

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Documents

Evaluation of Advanced Microwave Sounding Unit Tropical ...rammb.cira.colostate.edu/resources/docs/demuth.pdfTC parameters, including cloud liquid water and rain rate. AMSU-B primarily