FY00 radar report - University Corporation for Atmospheric Research · Radar Activities FY00 Year-End Report Submitted by The National Center For Atmospheric Research Deliverable

Remote Sensing of Turbulence:

Radar Activities

FY00 Year-End Report

Submitted by

The National Center For Atmospheric Research

Deliverable 00.7.3.E3

1

Introduction

In FY00, NCAR was given Technical Direction by the FAA’s Aviation Weather Research

Program Office to perform research related to the detection of atmospheric turbulence by remote

sensing devices. Specifically, the research has been focused on two tasks: the development of an

improved turbulence detection algorithm for the WSR-88D radar network and the investigation

of turbulence detection algorithms for Doppler lidars. This year-end report discusses the efforts

in the WSR-88D area; a separate report discusses the lidar work.

Typically, the measurables that can be used to infer turbulence intensities from Doppler

radars and lidars are the first three moments of the Doppler spectrum. For a given pulse volume,

the zeroth moment provides the total power (or reflectivity) of the returned signal, the first

moment is the reflectivity-weighted average radial velocity, and the second moment (square of

the spectrum width) is related to the spread of the reflectivity-weighted radial velocities of

reflectors within the pulse volume. The turbulence detection methods that can be employed with

these measurables can be classified into first moment, second moment and combined first and

second moment algorithms.

Two types of first moment algorithms are applicable to the detection of atmospheric

turbulence. The first is based on the velocity structure function, a commonly-used description of

turbulent fields formed by averaging the squared difference between velocities measured at

points separated by a prescribed displacement. By fitting the structure function derived from the

turbulent component of measured first moments to theoretical curves, information about the

magnitude and scale of turbulence can, at least in principle, be extracted. Unfortunately, second

moments computed from measured radial velocities have proven to be very sensitive to errors in

the data, so a robust implementation will require careful control of data quality. The

development and testing of a structure function algorithm has not been a focus of the FY00 work,

but it will certainly merit further attention in FY01.

2

A second and simpler first moment algorithm makes use of the local variance of the

measured radial velocities. While such a method does not use the spatial statistics of the radial

velocities in a sophisticated way as the structure function algorithm does, it does detect

fluctuations in the wind field on a larger scale than that contained in a single pulse volume and so

may be a useful complement to a second moment algorithm. Variants are available which

operate on the turbulent component of the measured radial velocities obtained by removing local

trends (i.e., removing the ambient wind field). It seems reasonable to expect that an algorithm

based on both measured second moments and the variance of the measured first moments would

be only minimally impacted by uncertainty in the value of the turbulence outer length scale.

Second moment algorithms are based on theoretical relationships between the statistical

properties of the turbulent wind field, the ambient wind field, and the measured second moment.

The existing WSR-88D turbulence detection algorithm is a second moment algorithm. Both the

structure function and second moment methods may be used to estimate the eddy dissipation rate,

a commonly-used measure of turbulence intensity. A combined first and second moment

algorithm could produce an estimate of the variance of the “true” (i.e., not influenced by the radar

pulse volume weighting) radial velocities. The zeroth moment can be used for data quality

control. Specifically, it is well known that the pulse-pair algorithm which generates the first and

second moments is problematic at low signal to noise (SNR) levels.

As part of the ongoing NCAR research, fundamental aspects of the second moment and

structure function methodologies are being investigated. This work has shed some light on

existing theory and, in some cases, provided new theoretical and practical results. Several papers

are under preparation to disclose these results to the scientific community. Drafts of two papers

related to turbulence detection using Doppler radars were included with the FY98 report; they

continue to be refined. In addition, the papers “Simulation of Three Dimensional Turbulent

Velocity Fields” (Journal of Applied Meteorology, in press) and “Coherent Doppler Lidar Signal

Spectrum with Wind Turbulence” (Applied Optics, Vol. 38, pp. 7456-7466) were included with

last year’s FY99 report.

3

As part of the Aviation Safety Program (AvSP), NASA is also heavily involved in a

turbulence research program. The Turbulence Detection work area is investigating the use of

airborne Doppler radars and lidars to detect atmospheric turbulence. NASA supports NCAR in

this work and hence a good deal of leveraging has occurred. Specifically, NCAR has developed

a radar simulation software package that has been used to investigate various practical aspects of

the problem. Although this simulation code has not be run using parameters for the WSR-88D

radar, it has provided insight into the problem of turbulence detection and has been used to

develop a hazard algorithm for airborne Doppler radar which may be adapted for use with

ground-based radar data in FY01. Furthermore, the algorithm that has been developed for the

NASA airborne radar employs a method for averaging the Doppler spectra prior to computing the

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investigated as a potential future processing algorithm for the WSR-88D system. Its

implementation would, of course, require real-time processing of the Doppler spectra, which is

currently unavailable in the WSR-88D radars.

4

The Detection of Turbulence Via the WSR-88D WeatherRadar

The current WSR-88D turbulence algorithm is a second-moment algorithm which attempts

to account for the filtering of the reflectors’ radial velocities by the radar’s illumination function,

the motion of the reflectors (typically hydrometeors), and the magnitude of measured reflectivity.

Unfortunately, the current implementation of this algorithm does not produce operationally

useful turbulence information. NCAR’s analysis has revealed a number of problems which

reduce the operational utility of the current WSR-88D algorithm: (a) it ignores the need for

averaging of the measured second moments, (b) the imperfect response of the hydrometeors is

incorrectly handled, (c) it makes use of an a priori choice of the turbulence outer length scale,

(d) it uses insufficient quality control of the raw second moments, (e) the resolution of the

layered composite product is too coarse, (f) the use of the maximum value of the unaveraged and

non-quality-controlled spectral widths in the layer composite (with only 4 km x 4 km horizontal

resolution) produces over-estimates of the turbulence, (g) it uses of a number of assumptions in

the algorithm (e.g., isotropy and form of the energy spectra), and (h) it does not account for other

broadening mechanisms besides turbulence in the second moments. These problems were

described and discussed in some detail in the FY98 year-end report.

Last year’s FY99 report presented an analysis of the RAPS92 Mile High Radar and T-28

aircraft data, including eddy dissipation rate (EDR) estimates derived from high-rate true

airspeed and vertical accelerometer sensors, which suggested that the performance of the

turbulence detection algorithm could be greatly improved by (a) using a higher resolution product

(2 km discs instead of the layer composite product’s parallelepipeds), (b) using the reflectivity

field for quality control of the raw second moments, (c) extracting the median of the derived

turbulence estimates from the second moments measured within the disc, and (d) omitting any

attempt to account for the response of the hydrometeors. In this report we present a similar

analysis of data collected in the June, 1999 NASA Turbulence Characterization and Detection

(TCAD) field program near Greeley, Colorado. The primary goal of these analyses is to

5

determine whether an improved turbulence detection algorithm for the WSR-88D radar is

feasible. At the current time, this feasibility analysis only considers the infrastructure of the

current (or near-term) radar system, i.e., changes that can be implemented as a software

modification. Longer-term algorithm concepts (e.g., spectral processing and averaging) are

under investigation as part of the NASA Aviation Safety Program.

Second Moment Analysis

Even for the case of perfect point reflectors, the radar-measured second moment is a

function of both the turbulent and ambient components of the wind field. Since the large-scale

ambient winds are not usually a danger to aviation safety, it may be desirable to remove the

effects of such winds on the second moment so that it reflects only the turbulent wind field. In

last year’s FY99 report, an analysis of the effect of a linear wind field on the measured second

moments was presented. In FY00, that work was extended to derive formulas which account for

this effect when spectra are averaged over several pulse volumes. The results of this work will be

included in the paper, “The Detection of Atmospheric Turbulence from Doppler radars: A

Review, Critical Analysis and Extension,” an early draft of which was included with the FY98

report. Unfortunately, the complete linear wind field cannot be recovered from radial velocities

obtained from a single radar, so only a portion of its broadening effect on the measured second

moments can be removed in practice. Calculations using simulated turbulent wind fields suggest

that this effect will usually be small for single pulse volumes, and the adjustment of measured

second moments has not yet been incorporated into the NCAR turbulence algorithm.

Nevertheless, a more complete study of this issue should be performed in FY01.

Field Data Analysis

The primary effort in FY00 was in the analysis of the 1999 TCAD field program data for

the purposes of refining and verifying the NCAR turbulence algorithm. The Turbulence

Characterization and Detection (TCAD) field program was conducted near Greeley, Colorado

from 2 June to 25 June 1999. It was funded by NASA, the AlliedSignal Corporation and the

6

Rockwell-Collins Corporation; the National Center for Atmospheric Research was also a major

participant. The goal of the TCAD field program was to obtain radar measurements of

turbulence within or near convective clouds in conjunction with in-situ turbulence measurements

for the purposes of (a) obtaining a data base to facilitate the development and testing of radar

turbulence detection algorithms, (b) identifying correlations between observable cloud properties

that exist within turbulent regions, and (c) obtaining truth data for comparisons to cloud-scale

numerical simulations and turbulence characterization studies. Data were collected by three

aircraft, two ground-based Doppler radars, and the NCAR Mobile Cross-chain Loran Sounding

System (CLASS) sounding van. Of these, the data analyzed in this report includes in-situ data

collected from the South Dakota School of Mines and Technology T-28 research aircraft,

airborne radar data collected from the Rockwell-Collins Corporation Sabreliner, and ground-

based radar data from the Colorado State University CHILL radar. (For more information on the

TCAD field program, see the website http://www.rap.ucar.edu/projects/nasa_turb/turb.html and

the links contained therein.)

Two different analyses of the TCAD field program data are presented below. The first

illustrates the correlation between an aircraft-derived measure of turbulence and the airborne and

ground-based radar-measured second moments via a set of overlays. Instead of deriving an eddy

dissipation rate estimate from the T-28 aircraft vertical acceleration time series, as was done for

the analysis presented in last year’s FY99 report, the variance of the vertical acceleration over 2

km paths is used here as the metric of aircraft turbulence. This quantity is arguably more directly

related to the rapidly-changing accelerations of the aircraft which are most likely to cause injury;

furthermore, it may be shown (using appropriate assumptions on the turbulent wind field) that it

is proportional to the variance of the true wind field, the constant of proportionality being a

function of the aircraft type, weight, and flight conditions. In processing the aircraft data, the

variance of the vertical accelerations over 2 km flight paths centered at each point in the raw 20

Hz time series was calculated, and the median over one-second intervals was then used to

resample the data to 1 Hz.

7

The plots on the following pages overlay the variance of the T-28 vertical accelerations

computed over 2 km flight paths onto the radar second moment and other fields for the airborne

(Rockwell-Collins) radar for five cases of interest on June 5 and 12. The moments displayed on

the airborne radar plots were produced by a new spectral processing algorithm developed as part

of the NASA efforts. This algorithm, the NCAR Efficient Spectral Processing Algorithm

(NESPA), is a significant improvement over the standard pulse-pair processing algorithm.

Besides generating the standard three Doppler moments, this algorithm also produces a

“confidence” value for each moment. Confidence values near one indicate that, roughly

speaking, the corresponding second moment values are likely to be correct, while confidences

near zero indicate poor-quality second moments. Figure 1 illustrates the NESPA second

moment with an overlay of the local variance of vertical acceleration from the T-28 aircraft over

2 km flight paths from a six-minute flight segment centered at the time of the radar scan. Blank

(white) patches in the radar second moment plot indicate zero confidence for those data. Figure

2 illustrates the NESPA second moment confidences for the data in Figure 1. Four other cases

are presented similarly in Figures 3 and 4, Figures 5 and 6, Figures 7 and 8, and Figures 9 and 10.

Some of these cases seem to exhibit a clear correlation between the aircraft values and the

second moments from both radars, but there are also some notable exceptions. These may be

partly due to inaccuracies or inconsistencies in the positions and times recorded by the T-28 and

Sabreliner. Alternately, they could be due to the lack of isotropy in an active thunderstorm, along

with the fact that the radar measures only the radial velocities of the reflectors, while it is largely

the vertical winds which are responsible for the T-28’s vertical acceleration. Furthermore, these

cases are a random sample and may not be indicative of the usual behavior of either the radar or

the aircraft. Nevertheless, these overlays do strongly suggest that the radar second moments can

frequently be used to predict the aircraft response, especially where high-quality data is available.

8

Nes

pa S

econ

d M

omen

t (m

/s)2

0

5

10

15

20

25

Local Variance over 2 km of Aircraft Vertical Acceleration (m/s2)20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

15 20 25 30 35 40 45 50

50

55

60

65

70

75

80

x displacement from CHILL (km west−east), range lines in km

y di

spla

cem

ent f

rom

CH

ILL

(km

sou

th−

nort

h)

06/05 20:54:51, Rockwell Radar (Frame: 10), South Dakota T−28 (1 s median)(14.16 km, 47.69 km, 15663 feet above CHILL), Heading: 82.35o

510

1520

2530

35

Figure 1 NESPA-derived second moments from the airborne radar with an overlay of therunning-variance of vertical acceleration from the T-28 aircraft.

9

Nes

pa C

onfid

ence

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


15 20 25 30 35 40 45 50

50

55

60

65

70

75

80


y di

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rom

CH

ILL

(km

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510

1520

2530

35

Figure 2 NESPA confidences for the data in Figure 1.

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Nes

pa S

econ

d M

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t (m

/s)2

0

5

10

15

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25


15 20 25 30 35 40 45

70

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80

85

90

95

100

105


y di

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CH

ILL

(km

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h)


5

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30

35

Figure 3 NESPA-derived second moments with overlaid aircraft acceleration variances.

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Nes

pa C

onfid

ence

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


15 20 25 30 35 40 45

70

75

80

85

90

95

100

105


y di

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rom

CH

ILL

(km

sou

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h)


5

10

15

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25

30

35

Figure 4 Second moment confidences for the data in Figure 3.

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Nes

pa S

econ

d M

omen

t (m

/s)2

0

5

10

15

20

25


5 10 15 20 25 30 35

0

5

10

15

20

25

30


y di

spla

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rom

CH

ILL

(km

sou

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h)


5

10

15

20

25

30

35

Figure 5 NESPA second moments with overlaid aircraft acceleration variances.

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Nes

pa C

onfid

ence

0

0.1

0.2

0.3

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0.5

0.6

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5 10 15 20 25 30 35

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(km

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14

Nes

pa S

econ

d M

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t (m

/s)2

0

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−30 −25 −20 −15 −10 −5 0 5

5

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30

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y di

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rom

CH

ILL

(km

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5

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30

35

Figure 7 NESPA-derived second moments with overlaid aircraft acceleration variances.

15

Nes

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0

0.1

0.2

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−30 −25 −20 −15 −10 −5 0 5

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Nes

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/s)2

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−35 −30 −25 −20 −15 −10 −5

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y di

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ent f

rom

CH

ILL

(km

sou

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nort

h)

06/12 00:24:42, Rockwell Radar (Frame: 5), South Dakota T−28 (1 s median)(−2.22 km, 6.43 km, 12300 feet above CHILL), Heading: 265.34o

5

10

15

20

25

30

35

Figure 9 NESPA second moments with aircraft acceleration variances overlaid.

17

Nes

pa C

onfid

ence

0

0.1

0.2

0.3

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0.6

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−35 −30 −25 −20 −15 −10 −5

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y di

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(km

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06/12 00:24:42, Rockwell Radar (Frame: 5), South Dakota T−28 (1 s median)(−2.22 km, 6.43 km, 12300 feet above CHILL), Heading: 265.34o

5

10

15

20

25

30

35


18

The plots on the following pages are similar to those preceding, except that overlays of the

T-28 track onto the ground-based (CHILL) radar fields are now presented. In addition to the

second moment field, the reflectivity and radial velocity fields are also displayed. The second

moment field has been median-filtered over range x azimuth “blocks” chosen to be roughly 4 km

x 4 km; thus, blocks near the radar contain many more points than those further away. “Bad”

data points for each field appear as blank (white) patches. The three times and regions of space

displayed correspond to those of Figures 5, 7, and 9. Perhaps because of the relatively large

distance from the radar, the CHILL radar data for the cases presented in Figures 1 and 3

contained a large proportion of bad values and thus did not allow for a meaningful comparison

with either the T-28 aircraft data or the airborne radar data; they are therefore not presented here.

As was true for the airborne radar comparison, the second moments from the ground-based

CHILL radar appear to show good correlation with the local variance of the aircraft vertical

acceleration displayed in the aircraft track overlays. An exception occurs about one minute along

the aircraft track in Figure 14; however, it may be ascribed to either the fact that the aircraft was

turning there, causing a variation in vertical acceleration not due to turbulence, or to the close

proximity to the radar and resulting poor quality of the measured second moments there.

19

CH

ILL

rada

r m

edia

n−fil

tere

d se

cond

mom

ent (

m2 /s

2 )0

1

2

3

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5 10 15 20 25 30 35

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x displacement from CHILL (km west−east)

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ILL

(km

sou

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nort

h)

12−Jun−1999 00:15:38, CHILL MOM2 (6.60 deg); 00:13:33−00:19:33, T−28 Acc. Variance

Local variance over 2 km path of T−28 vertical acceleration (g2)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 1333

− 19

33

Figure 11 Median-filtered second moments from the CHILL radar with an overlay of the runningvariance of vertical acceleration from the T-28 aircraft. The time and spatial limits of the plotwere chosen to correspond to those of Figure 5.

20

CH

ILL

rada

r un

filte

red

refle

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ity (

dBZ

)

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(km

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h)12−Jun−1999 00:15:38, CHILL DBZ (6.60 deg); 00:13:33−00:19:33, T−28 Acc. Variance


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 1333

− 19

33

Figure 12 CHILL reflectivity (unfiltered) for the case shown in Figure 11.

21

CH

ILL

rada

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red

radi

al v

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m/s

)

−20

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−10

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ILL

(km

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h)12−Jun−1999 00:15:38, CHILL VEL (6.60 deg); 00:13:33−00:19:33, T−28 Acc. Variance


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 1333

− 19

33

Figure 13 CHILL radial velocities (unfiltered) for the case shown in Figure 11.

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CH

ILL

rada

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mom

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m2 /s

2 )

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y di

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(km

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h)12−Jun−1999 00:21:45, CHILL MOM2 (12.60 deg); 00:19:58−00:25:58, T−28 Acc. Variance


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 19

58

− 25

58


23

CH

ILL

rada

r un

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refle

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dBZ

)

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−30 −25 −20 −15 −10 −5 0 5

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 19

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− 25

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CH

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m/s

)

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 19

58

− 25

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25

CH

ILL

rada

r m

edia

n−fil

tere

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cond

mom

ent (

m2 /s

2 )

0

1

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−35 −30 −25 −20 −15 −10 −5

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y di

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rom

CH

ILL

(km

sou

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nort

h)12−Jun−1999 00:24:39, CHILL MOM2 (7.40 deg); 00:21:42−00:27:42, T−28 Acc. Variance


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 21

42

− 27

42


26

CH

ILL

rada

r un

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refle

ctiv

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dBZ

)

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 21

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m/s

)

−20

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

− 21

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28

As previously mentioned, one of the significant problems with the existing WSR-88D

algorithm is using un-averaged spectra to produce the second moments. There are two main

reasons that averaging of the second moments is required: (a) turbulence is a random process and

hence the only pertinent information about it must be obtained via statistical methods, (b)

individual Doppler spectra (and hence second moments) are contaminated by so-called phase

noise (due to the interaction of the phases between different scatterers in the pulse volume) and

(c) the spectra are contaminated by receiver noise; spectral or moment averaging is required to

reduce these effects. The averaging of spectra prior to computing second moments is far

preferable to averaging moments obtained from the contaminated spectra. Unfortunately, for the

WSR-88D system (in its current form), averaging moments is all that is available. The NCAR

turbulence algorithm implementation presented in last year’s FY99 year-end report satisfied this

requirement by making use of the median radar-measured second moment obtained from a disc

or sphere centered at a point of interest, or the nearest parallelepiped on a predetermined grid,

scaling it by a theoretical quantity dependent on the distance from the radar and the estimated

turbulence outer length scale to obtain an eddy dissipation rate (EDR) estimate. For comparison

with the turbulence derived from the T-28 aircraft, a “point of interest” is the closest point on the

radar scan cone at each comparison time. Of these volumes, the disc was deemed the most

satisfactory; this conclusion was based not only on the demonstrated empirical correlation with

the aircraft measurements, but also on the fact that both parallelepipeds and spheres include

points from different altitudes, and therefore different strata of turbulence and varied times due to

the radar’s scanning. Equally important, the disc method (i.e., using points from a single

elevation scan) would be the most straightforward method from an implementation viewpoint.

For this reason, only discs were used in this year’s analysis.

Several radar-derived quantities were extracted from discs at the various aircraft

positions: second moments, eddy dissipation rates computed by dividing each second moment by

a range-dependent theoretical factor, and the variance of the radial velocities. Two different

methods were used to average the second moments and eddy dissipation rates. The first was to

simply take the median of those values corresponding to reflectivities between 20 and 65 dBZ, a

29

strategy that was shown to work well for the RAPS92 data in last year’s FY99 report. The

second was to take a confidence-weighted average of all the values. The confidence value used

for this purpose was derived from the reflectivity via a function which increases linearly from 0.4

to 1 between 10 and 30 dBZ, remains at 1 between 30 and 50 dBZ, decreases linearly from 1 to

0.4 between 50 and 70 dBZ, and is zero for all other values. The rationale for this approach is

that second moments derived from regions having moderately high reflectivity are likely to have

the highest quality, and therefore should be assigned the highest weights. On the other hand,

other values should not be thrown out entirely, but should simply be weighted less depending on

how far away they are from the ideal range. The form of the function was chosen somewhat

arbitrarily based on the results from last year’s FY99 report, which suggested that second

moments for measurements having reflectivities between 20 and 65 dBZ are of relatively high

quality. This confidence-based methodology, a fuzzy logic approach, is the beginning of the

development of a fuzzy turbulence detection algorithm for the WSR-88D system.

Two additional filters were used in the comparison of the aircraft and radar-derived

quantities. First, only those aircraft data which were recorded within 90 seconds of a radar scan

were used for comparisons. Second, data points were eliminated when the number of “good”

(reflectivity between 20 and 65 dBZ) radar measurements within the disc fell below a certain

threshold (80, 140 or 200 points). This strategy eliminates comparisons for which the radar data

is of low quality. Similar results are obtained by restricting the allowable range of aircraft

positions from the radar as was done last year; both of these strategies ensure that only radar data

in regions of high-reflectivity and relatively dense measurements are used. Indeed, an analysis of

the TCAD field program’s CHILL radar data shows that 2 km-radius discs containing 80 or more

valid points have ranges distributed between 5 and 75 km from the radar, 2 km discs containing

140 or more points range from 5 to 37 km, and 2 km discs containing 200 or more points lie

almost exclusively between 12 and 25 km.

The scatter plots on the following pages illustrate the correlation between the second

moments, eddy dissipation rates or variance of radial velocities derived using 2 km-radius discs

from the CHILL radar with the variance of the T-28 aircraft’s vertical acceleration over 2 km

30

flight paths using data collected on June 5, 9, 10, 11, 12, 14, 17, 18 and 20, 1999. An analysis

was also performed for 1 km-radius discs, but the higher resolution was offset by the fact that

many fewer radar points could be averaged, causing greater scatter in the results, and so those

plots are not presented here. Note that for the highest quality data (largest number of good data

points in the disc), the radar second moments and derived eddy dissipation rates show excellent

correlation with the variance of the T-28 aircraft’s vertical acceleration. That the second moment

correlates as well as the derived eddy dissipation rates may be due to the fact that the range to the

radar is quite restricted for these data and hence the factors used to convert second moments to

eddy dissipation rates do not vary greatly. However, despite the excellent correlation, it would

be desirable to reduce the scatter around the best-fit line.

Figure 20, Figure 21and Figure 22 show the comparison between the median value of

CHILL radar second moments over a 2 km disc versus the variance of T-28 vertical acceleration

over a 2 km path. The number of points within the disc is restricted to greater than 80, 140 and

200 points, respectively. The correlation coefficients for these three cases are 0.26, 0.61 and

0.87, respectively. The last value is quite good; however, the data points for this case represent

only measurements taken fairly close to the radar.

Figure 23, Figure 24, and Figure 25 show a comparison between the median values of the

NCAR algorithm EDR estimate calculated over a 2 km-radius disc and length scale of 500 m

versus the variance of T-28 vertical acceleration over a 2 km path. The number of points within

the disc is restricted to greater than 80, 140 and 200 points, respectively. The correlation

coefficients for these three cases are 0.36, 0.70 and 0.87, respectively. As with the previous

figures, the correlationsespecially the last oneare very good. Figure 26, Figure 27 and

Figure 28 illustrate these comparisons for a length scale of 3000 m. The correlation values are

0.40, 0.72 and 0.86. Comparing these values as well as the slope of the best-fit line and variance

of the residuals with those from the 500 m length scale cases, it can be seen that the numbers are

very similar, implying that the NCAR turbulence algorithm is relatively insensitive to the length

scalea fortuitous result. This insensitivity to outer length scale was also observed in the

31

analysis presented in last year’s report, when EDR values from the NCAR turbulence algorithm

were compared to EDR estimates from the T-28 aircraft.

Figure 29, Figure 30 and Figure 31 illustrate a similar set of cases to those shown in Figure

20, Figure 21, and Figure 22 except that a “confidence-weighted average” is used in place of

median values. The confidences used in the weighted averages were simply derived from the

reflectivity values as described abovelow confidence was assigned to very low and very high

reflectivity measurements, while mid-range reflectivities received high confidence values. The

correlation coefficients for these scatter plots are 0.29, 0.63, and 0.85, respectivelyvalues

which are commensurate with those for the corresponding cases presented above for median

values. Figure 32, Figure 33, and Figure 34 are the same as Figure 23, Figure 24 and Figure 25,

except that again confidence-weighted average are used instead of median values. The results are

again similar, yielding correlation coefficients of 0.36, 0.70, and 0.76.

Finally, the last three plots, Figure 35, Figure 36 and Figure 37 illustrate a comparison

between the variance of the CHILL radar-measured radial velocities over a 2 km disc and the

variance of the aircraft vertical accelerations over 2 km flight paths. The correlations (0.39, 0.58,

and 0.50, respectively) are less than the values obtained using median or confidence-weighted

average second moments. However, the second moment and the variance of the first moment

should respond to different scales of the turbulence, and a careful combination of the two values

using principles of fuzzy logic may provide better turbulence information than either value alone.

32

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

Variance of T−28 acceleration over 2 km path (g2)

Rad

ar m

edia

n se

cond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )

CHILL/T−28, 5−20 June 1999: TFS < 90 s, pts > 80

ρ = 0.25978σ2 = 8.0478fit slope = 20.8458# points = 2972

Figure 20 Scatter plot of the median value of CHILL radar second moments over a 2 km-radiusdisc versus the variance of the T-28 aircraft vertical acceleration over a 2 km path. The numberof points in the disc are restricted to being greater than 80.

33

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25


Rad

ar m

edia

n se

cond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )




34

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25


Rad

ar m

edia

n se

cond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )




35

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 5

00 m

(m

4/3 /s

2 )CHILL/T−28, 5−20 June 1999: TFS < 90 s, pts > 80


Figure 23 Scatter plot of the median value of the NCAR turbulence algorithm’s EDR estimateover a 2 km-radius disc versus the variance of the T-28 aircraft vertical acceleration over a 2 kmpath. The length scale for the NCAR algorithm is 500 m. The number of points in the disc isrestricted to more than 80 points.

36

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 5

00 m

(m

4/3 /s




37

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 5

00 m

(m

4/3 /s




38

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 3

000

m (

m4/

3 /s2 )



Figure 26 Same as Figure 23, with a length scale of 3000 m.

39

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 3

000

m (

m4/

3 /s2 )




40

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

med

ian

ED

R fr

om 2

km

dis

c, L

= 3

000

m (

m4/

3 /s2 )




41

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25


Rad

ar C

WA

sec

ond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )



Figure 29 Confidence-weighted averages of second moments over a 2 km-radius disc comparedto the variance of the T-28 aircraft vertical acceleration over a 2 km path. The number of pointsin the disc is restricted to greater than 80 points.

42

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25


Rad

ar C

WA

sec

ond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )



Figure 30 Same as Figure 29, with the number of points restricted to greater than 140 points.

43

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25


Rad

ar C

WA

sec

ond

mom

ent f

rom

2 k

m d

isc

(m2 /s

2 )



Figure 31 Same as Figure 29, with the number of points restricted to greater than 200.

44

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

CW

A E

DR

from

2 k

m d

isc,

L =

500

m (

m4/

3 /s2 )



Figure 32 Same as Figure 23, using a confidence-weighted average over the 2 km-radius discinstead of a median value.

45

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

CW

A E

DR

from

2 k

m d

isc,

L =

500

m (

m4/

3 /s2 )




46

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25


NC

AR

CW

A E

DR

from

2 k

m d

isc,

L =

500

m (

m4/

3 /s2 )




47

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

45

50


Var

ianc

e of

rad

ial v

eloc

ities

in 2

km

dis

c (m

2 /s2 )



Figure 35 The variance of radar-measured radial velocities over a 2 km-radius disc versus thevariance of the T-28 aircraft vertical accelerations over a 2 km path. The number of points in thedisc are restricted to greater than 80.

48

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

45

50


Var

ianc

e of

rad

ial v

eloc

ities

in 2

km

dis

c (m

2 /s2 )



Figure 36 Same as Figure 35, using at least 140 points in the disc.

49

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

45

50


Var

ianc

e of

rad

ial v

eloc

ities

in 2

km

dis

c (m

2 /s2 )



Figure 37 Same as Figure 35, using at least 200 points in the disc.

50

Future WorkThe analyses presented in this report have illustrated both encouraging results and the

need for further work. The radar activities for FY01 will again be focussed on the WSR-88D

turbulence detection algorithm development. The work will involve both the use of simulations

and the continued analysis of the RAPS92 and 1999 TCAD datasets.

Simulation software developed for the NASA Aviation Safety Program provides an ideal

testbed for further development and verification of the NCAR turbulence algorithm. In addition

to simulating radar measurements of a wind field, aircraft flights through the same wind field can

also be simulated. In addition, important issues related to spectral and moment averaging can be

investigated.

Both the RAPS92 Mile High radar and T-28 aircraft data used in last year’s FY99 report

and the 1999 TCAD field program data described in the present report require further analysis.

In both cases, the radar data should be edited and converted into a Matlab-readable format with

less loss of precision in the data values, spatial locations, and timestamps than is accorded by the

current “uf2mdv” software. In addition, the high-rate T-28 aircraft data from RAPS92 should be

filtered in the same manner as the TCAD data was to obtain the variance of the vertical

acceleration over 2 km paths, and both in-situ datasets should be used to derive eddy dissipation

rates for further comparison with the radar values. Many other variations of the data processing

are possible, including removal of trends before variances are calculated in both the aircraft

vertical accelerations and radar radial velocities, and these should be tried. The structure

function method should also be implemented and tested. Finally, principles of fuzzy logic should

be used to combine the results of the first and second moment methods with appropriate

confidences to obtain a final turbulence value.

Documents

FY00 radar report - University Corporation for Atmospheric Research · Radar Activities FY00 Year-End Report Submitted by The National Center For Atmospheric Research Deliverable