NASA/TM-2012-216310

Dual-Doppler Feasibility Study

Lisa L. Huddleston

Applied Meteorology Unit

Kennedy Space Center, Florida

April 2012
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NASA/TM-20 12-21631 0

Dual-Doppler Feasibility Study

Lisa L. Huddleston

Applied Meteorology Unit

Kennedy Space Center, Florida

National Aeronautics and

Space Administration

Kennedy Space Center

Kennedy Space Center, FL 32899-0001
I

I

l

April 2012

Acknowledgements

The author thanks Mr. William Roeder, Mr. Todd McNamara, and Mr. Jon Saul of the 45th Weather

Squadron for their technical guidance on this project. Ln addition, thanks go to Mr. Dave Sharp and Mr.

Matt Volkmer of the National Weather Service in Melbourne, Fla. for their assistance in understanding

the NOAA products available for dual-Doppler analysis and in obtaining the specifications for the WSR880 radar. Finally, the author would like to thank Ms. Winnie Crawford ofthe Applied Meteorology Unit

and Dr. Frank Merceret of the KSC Weather Office for their participation in extensive discussions of the

subject matter included in this report and for their editorial expertise.

Available from:

NASA Center for AeroSpace Lnformation

7121 Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

This report is also available in electronic form at

http://science.ksc.nasa.govlamul
Executive Summary

When two or more Doppler weather radar systems are monitoring the same region, the Doppler

velocities can be combined to form a three-dimensional (3-0) wind vector field thus providing for a more

intuitive analysis of the wind field. A real-time display of the 3-D winds can assist forecasters in

predicting the onset of convection and severe weather. The data can also be used to initialize local

numerical weather prediction models. Two operational Doppler Radar systems are in the vicinity of

Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS); these systems are

operated by the 45th Space Wing (45 SW) and the National Weather Service Melbourne, Fla. (NWS

MLB). Dual-Doppler applications were considered by the 45 SW in choosing the site for the new radar.

Accordingly, the 45th Weather Squadron (45 WS), NWS MLB and the National Aeronautics and Space

Administration tasked the Applied Meteorology Unit (AMU) to investigate the feasibility of establishing

dual-Doppler capability using the two existing systems. This study investigated technical, hardware, and

software requirements necessary to enable the establishment of a dual-Doppler capability.

Review of the available literature pertaining to the dual-Doppler technique and consultation with

experts revealed that the physical locations and resulting beam crossing angles of the 45 SW and NWS

MLB radars make them ideally suited for a dual-Doppler capability. The dual-Doppler equations were

derived to facilitate complete understanding of dual-Doppler synthesis; to determine the technical

information requirements; and to determine the components of wind velocity from the equation of

continuity and radial velocity data collected by the two Doppler radars. Analysis confirmed the suitability

of the existing systems to provide the desired capability. In addition, it is possible that both 45 SW radar

data and Terminal Doppler Weather Radar data from Orlando International Airport could be used to

alleviate any radar geometry issues at the NWS MLB radar, such as the "cone of silence" or beam

blockage. In the event of a radar outage at one of the sites, the multi-radar algorithms would provide

continuing coverage ofthe area through use ofthe data from the remaining operational radar sites.

There are several options to collect, edit, synthesize and display dual-Doppler data sets. These options

include commercial packages available for purchase and a variety of freeware packages available from

the National Center for Atmospheric Research (NCAR) for processing raw radar data. However,

evaluation of the freeware packages revealed that they do not have sufficient documentation and

configuration control to be certified for 45 SW use. Additionally, a TI data line must be installed/leased

from the NWS MLB office and CCAFS to enable the receipt of NWS MLB raw radar data to use in the

dual-Doppler synthesis. Integration ofthe TI data line into the Eastern Range infrastructure that will meet

the security requirements necessary for 45 SW use is time-consuming and costly.

Overall evaluation indicates that establishment of the dual-Doppler capability using the existing

operational radar systems is desirable and feasible with no technical concerns. Installation of such a

system represents a significant enhancement to forecasting capabilities at the 45 WS and at NWS MLB.

However, data security and cost considerations must be evaluated in light of current budgetary

constraints. In any case, gaining the dual-Doppler capability will provide opportunities for better

visualization ofthe wind field and better forecasting of the onset of convection and severe weather events

to support space launch operations at KSC and CCAFS.

4
--------------

Table of Contents

Executive Summary 4

List of Figures 6

List of Tables 6

I. Introduction 7

2. Principles of Dual-Doppler Radar Measurements 8

2.1 Dual-Doppler Equation Derivations 8

2.2 Dual-Doppler Area Geometry 9

Hardware and Software 14

3. Summary and Conclusions 16

3.1 Dual-Doppler Analysis Feasibility 16

3.2 45 WS Interests 16

3.3 NWS MLB Interests 16

3.4 Future Work 17

Appendix 18

References 23

5
List of Figures

Figure 1. Orientation ofthe 45 SW radar and the NWS MLB radars with respect to KSC and CCAFS. 7

Figure 2. The geometry ofthe radial distance (R) between radars and a point in space. The target point

ofthe radars is at P(x, y, z). Radar 1 is at point (XI, yI, ZI) and radar 2 is at point (X2, Y2, Z2). Adapted from

Figure 9.3 in Doviak and Zrnic (1993) 8

Figure 3. The typical beam geometry for a single radar. Adapted from Figure 6.2 in Rinehart (2004) 9

Figure 4. a) The beam crossing angle between the 45 SW and NWS MLB radars for launch complexes

17A (67.9°) and b) 41 (52.2°) on CCAFS. The yellow pins show the locations ofthe radars. The red lines

labeled R] and R2 are analogous to the similarly labeled lines in Figure 2 10

Figure 5. a) Area AI that shows the dual-Doppler lobes as stippled areas bounded by B= 30° (1[/6 rad)

(Figure la in Davies-Jones 1979), and b) Area A2, shown as a stippled area that lies within distance R of

both radars (Figure 1b in Davies-Jones 1979) 11

Figure 6. Same as Figure 4 except for the 45 SW and NWS MLB radars, where a) is area AI and b) is

area A2. The yellow pins show the locations ofthe radars. The white circles in a) are the dual-Doppler

lobes within which the angles subtended by the radials from the radars lie between 30° and 150°. The

intersecting area between the two circles along the radar baseline is not part ofthe dual-Doppler area

because the beam crossing angles in this area are < 30° or> 150°. The white outline in b) shows area A2,

the outline of points that lie within a distance of 46.1 NM (85.3 km) of each radar. 12

Figure 7. The intersection of areas Al and A2 for the 45 SW and NWS MLB radars. The yellow pins

show the locations ofthe radars 13

Figure 8. An example of an NDOP Display for strong northerly winter monsoon flow over China near

Hong Kong, colliding with easterlies over the sea. The "+" points show regions where the minimum

crossing angle between radars was met, but there were no weather targets, so a wind could not be

calculated. The green and gray contours indicate ~300 m (~1000 ft) elevation intervals (Vaisala IRISTM

Product and Display Manual 2006) 15

Table 1.

List of Tables

Technical specifications for the NWS MLB WSR-88D and 45 SW Radtec 43/250 radars.... 12

6
_ .._

1. Introduction

When two or more Doppler weather radar systems are monitoring the same region, the Doppler

velocities can be combined to form a three-dimensional (3-D) wind vector field. Such a wind field allows

a more intuitive analysis of the 3-D winds, especially for users with little or no experience in deciphering

Doppler velocities (Bousquet 2004). A real-time display of the wind field can assist forecasters in

predicting the onset of convection and severe weather. The data can also be used to initialize local

numerical weather models. Two Doppler radars are in the vicinity of Kennedy Space Center (KSC) and

Cape Canaveral Air Force Station (CCAFS): the 45th Space Wing (45 SW) RadTec 43/250 radar and the

National Weather Service (NWS) office in Melbourne, Fla. (MLB) Weather Surveillance Radar - 1988

Doppler (WSR-88D) radar. The orientation of these radars with KSC and CCAFS are shown in Figure 1.

The 45th Weather Squadron (45 WS), NWS MLB and National Aeronautics and Space Administration

(NASA) customers tasked the Applied Meteorology Unit (AMU) to investigate the feasibility of

establishing dual-Doppler capability using these two systems. This task summarizes a literature review

and consultation with experts to determine technical, hardware, and software requirements necessary to

create a dual-Doppler capability. The AMU also investigated cost considerations and viable alternatives.

Developing a dual-Doppler capability can provide a real-time horizontal wind field display to assist

45 WS and NWS forecasters in predicting the onset of convection and severe weather events. These data

can also be used to initialize a local mesoscale numerical weather prediction model. in addition, data

combined from two or more radars mitigate radar geometry problems such as the cone of silence and

beam blockage. (Lakshmanan et al. 2007)

Figure 1. Orientation of the 45 SW radar and the NWS MLB radars

with respect to KSC and CCAFS.

7
2. Principles of Dual-Doppler Radar Measurements

With traditional single Doppler radar, only the radial component of the wind field can be measured.

When two or more Doppler radars are surveying an area, the Doppler velocities can be combined to

estimate the 3-D wind field. Each individual radar system scans according to its own particular strategy

and time, therefore the velocities from each radar must be merged to a common coordinate system and

reference time before wind synthesis can occur (Friedrich and Hagen 2004).

The main objective of multiple-Doppler analyses, which combine observations collected by several

neighboring Doppler radars to construct the 3-D wind field, is to ease the interpretation of airflow and to

provide detailed information on the kinematics of observed storms that even a non-radar specialist can

easily understand. Knowledge of storm kinematic structure can provide interesting insights on the storm

dynamics through revealing mesoscale wind features that would be difficult to ascertain from just the

radial velocity field. Another unique benefit of dual- or multiple-Doppler wind synthesis is to provide

information on the structure ofthe vertical motion field (Bousquet, et al. 2008).

2.1 Dual-Doppler Equation Derivations

The AMU derived the dual-Doppler equations to facilitate complete understanding of dual-Doppler

synthesis, to determine the technical information requirements, and to determine how to find the three

components of wind velocity from the continuity equation and radial velocity data from two Doppler

radars (Armijo 1969). The derivations are available in the Appendix of this report for the interested

reader. The dual-Doppler equations were compiled from a combination ofthe methods of Armijo (1969),

Obrien (1970), Lhermitte and Miller (1970) and Carey (2005). The geometry of the radial distance

between two radars and a point in space is shown in Figure 2. The typical beam geometry for a single

radar is shown in Figure 3.

z

. R2 ",." ",

Radar 2 ."."

(x2, Y2' Z2)

, R1

"

Y

"

"

Figure 2. The geometry of the radial distance (R) between radars and a point in space. The

target point ofthe radars is at P(x, y, z). Radar 1 is at point (x" YI, z,) and radar 2 is at point

(X2, Y2, Z2). Adapted from Figure 9.3 in Doviak and Zrnic (1993).

8
tilrcet

a= elevation ancle ofradar

• =azimuth ancJe of radar

..................... _-

Vrslna

:

Figure 3. The typical beam geometry for a single radar. Adapted from

Figure 6.2 in Rinehart (2004).

2.2 Dual-Doppler Area Geometry

When planning a dual-Doppler capability, the specific area of interest must be studied to determine if

the locations of the radars will allow an accurate wind field calculation. Dual-Doppler coverage depends

on

• The minimum spatial resolution needed to resolve the weather phenomena of interest,

• The largest acceptable error in horizontal velocity, and

• The distance between the radars (Davies-Jones 1979).

• The orientation ofthe radars relative to the area for which dual-Doppler coverage is desired.

2.2.1 Optimal vs. Actual Arrangement of Radars

To begin the analysis, unit vectors of the two radial velocities intersect an angle, (Davies-Jones

1979, Friedrich and Hagen 2004). Using the schematic in Figure 2 as an example, is the angle between

R) and R2 at P. The error variances, (J~ and (J;, of u- and v- wind components are related to the Doppler

mean velocity error variances ofthe two individual radars, (Jf and (Ji, by (Davies-Jones 1979):

(J2 + (J2

; =csc

2 fl.

(J) + (J2

The optimal that will provide the most accurate wind synthesis is 90° (Beck 2004). Experience at

the National Severe Storms Laboratory (NSSL) has shown that a of 30° and::; 150° is adequate for

accurate wind synthesis (Davies-Jones 1979). Outside of this range, a large component of both beams is

oriented in the same direction. This will cause large errors in the velocity components derived from the

dual-Doppler wind synthesis. The calculated beam crossing angle between the 45 SW and the NWS MLB

radars for launch complexes 17A (Figure 4a) and 41 (Figure 4b) on CCAFS are 67.9° and 52.2°,

respectively, both within the 30° to 150° range recommended by Davies-Jones (1979).

9
Figure 4. a) The beam crossing angle between the 45 SW and NWS MLB radars for launch complexes

17A (67.9°) and b) 41 (52.2') on CCAFS. The yellow pins show the locations ofthe radars. The red lines

labeled R1 and R2 are analogous to the similarly labeled lines in Figure 2.

The spatial resolution of the dual-Doppler coverage area is related to the baseline, or horizontal

distance between two radars. Davies-Jones (1979) and Friedrich and Hagen (2004) proposed that the

optimal distance between two radars would range between 23.2 NM (43 kIn) and 43.7 NM (81 kIn).

Examination of Figure 3 shows that the baseline between the 45 SW and NWS MLB radars is 23 NM

(42.6 km), at the low end of the optimal separation distance. The beam crossing angles over KSC and

CCAFS and the baseline of the 45 SW and NWS MLB radars makes them ideally suited for a dualDoppler capability. A critical element of site location is the technical trade-off between velocity

component accuracy and spatial resolution (Davies-Jones, 1979). This placement was considered by the

45 WS during the original 45 SW radar site location determination.

2.2.2 Dual-Doppler Area for 45 SW and NWS-MLB Radars

The next step in the analysis is to calculate the total coverage area of the dual-Doppler analysis.

Davies-Jones (1979) and Friedrich and Hagen (2004) show that the total coverage area is the intersection

of the area (AI) defmed by the upper limits on velocity error variance (Figure Sa) and the area (A2)

defined by the maximum range of the radars (Figure 5b). The area AI is made up of two circular areas

called dual-Doppler lobes. In the formula for AI (Davies-Jones 1979) shown in Figure Sa, d is half of the

baseline (23 NM/2 = 11.5 NM) and is the minimum beam crossing angle in radians (n/6 rad or 30°). In

the formula for A2 in Figure 5b, R is the maximum range from any point in area AI to either ofthe radars.

R for the 45 SW and NWS MLB radar pair is given by (Davies-Jones 1979)

2*d*csc~ = 2*(11.51 NM)*csc(300) = 46.1 NM (85.3 km).

Area A2 is the maximum area that can be covered by two radars at an elevation angle of 0'. With

increasing elevation, area A2 decreases (Friedrich and Hagen 2004, Davies-Jones 1979). The dualDoppler coverage area is defined as the area common to both AI and A2 (Davies-Jones 1979):

AI2 (;3,R) =AI (/3)(1 A2(R)

10
y

----~'----+---____,i1¥_----... X

A,(P)= 2(d csc flY (Jr - 2/l +sin 2/l)

a b

y

Figure 5. a) Area AI that shows the dual-Doppler lobes as stippled areas bounded by p= 30° (1t/6 rad)

(Figure 1a in Davies-Jones 1979), and b) Area A2, shown as a stippled area that lies within distance R of

both radars (Figure 1b in Davies-Jones 1979).

In a dual-Doppler analysis, the resolution of the resulting merged data is defined as s = R1tNI80,

where is the half power beam width in degrees of the radars (Davies-Jones 1979). The technical

specifications for the NWS MLB WSR-88D and the 45 SW Radtec 43/250 radars are shown in Table 1.

Using these values, the resolution ofthe 45 SW and NWS MLB radar pair is

s = (46.1 NM)*1t*(0.95°)/180 = 0.76 NM (1.41 kIn).

Using the formula for AI shown in Figure 5a, the coverage area AI of the radar pair is 3,140.2 NM2

(10,770.7 km2). Area AI for the 45 SW and NWS MLB radars is shown in Figure 6a. The maximum area

that can be covered by the radar pair at an elevation angle of 0° is calculated using the formula for area A2

shown in Figure 5b. This area is shown in Figure 6b and is 4,565.6 NM2 (15,659.7 km2). The size of area

A I fits into the size of area A2 and is shown in Figure 7. Therefore the area common to both AI and A2 for

the 45 SW and NWS MLB radar pair is 3,140.2 NM2 (10,770.7 km2

). However, the maximum area that

can be covered by a radar pair decreases with increasing elevation angle (Davies-Jones 1979, Friedrich

and Hagen 2004).

11
---------------------------------------------------

Table 1. Technical specifications for the NWS MLB WSR-88D and 45 SW

Radtec 43/250 radars.

Parameter NWS-MLB WSR-88D 45 SW Radtec 43/250

(Salazar et al. 2009) (Short 2008)

Wavelength 10.5 cm 5.32cm

Frequency S-band, 2.7 - 3.0 GHz C-band, 5.6 - 5.65 GHz

Peak Power 750 kW 250 kW

Antenna diameter 8.5 m 4.3 m

Beam width 0.95' 0.95'

Rotation Rate 6 rpm 6 rpm

PRF 318 - 1304 S·1 200 - 2000 s·,

Pulse Length 1.57 and 4.7 Jls 0.4 to 16.7 Jls

Gain 45.5 dB 44 dB

Latitude 28.1131 N 28.3938 N

Longitude 80.6541 W 80.9510 W

Figure 6. Same as Figure 4 except for the 45 SW and NWS MLB radars, where a) is area A, and

b) is area A2• The yellow pins show the locations of the radars. The white circles in a) are the

dual-Doppler lobes within which the angles subtended by the radials from the radars lie between

30° and 150°. The intersecting area between the two circles along the radar baseline is not part of

the dual-Doppler area because the beam crossing angles in this area are < 30° or > 150°. The

white outline in b) shows area A2, the outline of points that lie within a distance of 46.1 NM (85.3

km) of each radar.

12
13

Figure 7. The intersection of areas AI and A2 for the 45 SW and

NWS MLB radars. The yellow pins show the locations of the

radars.
Hardware and Software

There are several options to collect, edit, synthesize and display dual-Doppler data sets. The 45 SW

currently uses the Interactive Radar Information System (IRISTM) software package by Vaisala to display

their radar data. The lRlSTM software has an add-on product, called NDOP, that provides capability for

Dual-Doppler wind fields based on radial wind inputs from two Doppler radars that can ingest WSR-88D

data. Ingesting WSR-88D data also provides the opportunity to eliminate the cone ofsilence, an important

issue for thunderstorms approaching from the southwest (a frequent trajectory in the summer). The

license includes the ability to make mosaics, or composites, of radar products from multiple sites. The list

cost is $16,000. This is a one-time cost for an add-on license to the existing IRIS software used by the 45

SW. An example of an fRlSTM NDOP product display is shown in Figure 8. Also a variety of freeware

packages are available from the National Center for Atmospheric Research (NCAR) for processing raw

radar data, but these packages do not have the thorough documentation and stringent configuration

control needed in order to be certified for 45 SW use.

Regardless of software choice, a T1 data line must be installed between the Morrell Operations

Center (MOC) on CCAFS and NWS MLB to enable the receipt of NWS MLB raw radar data needed for

the dual-Doppler synthesis. This line, with additional costs, could also be used to send the 45 SW radar

data to NWS MLB. In this case, NWS MLB can use the multi-sensor, multi-radar processing options via

the Warning Decision Support System Integrated Information (WDSS-II) system for viewing the dualDoppler radar data and then pass this information back to the 45 SW. The AMU could then create a way

to view the dual-Doppler data using Meteorological Interactive Data Display System (MIDDS),

Advanced Weather Interactive Processing System (AWIPS), or other display techniques. Due to the

proprietary nature of the vendor costs of installing and maintaining the T1 line, performing drawing and

configuration changes, and assuring information security functions, only a lower bound on the cost could

be obtained from the 45 SW. The cost and time estimate given was a minimum of $150,000 and 6 to 12

months for this project. A monthly maintenance cost ofthe T1 line was estimated to be $1000.

14
15

Figure 8. An example of an NDOP Display for strong northerly

winter monsoon flow over China near Hong Kong, colliding with

easterlies over the sea. The "+" points show regions where the

minimum crossing angle between radars was met, but there were

no weather targets, so a wind could not be calculated. The green

and gray contours indicate ~300 m (~1000 ft) elevation intervals

(Vaisala IRISTM Product and Display Manual 2006).
3. Summary and Conclusions

This study investigated technical, hardware, and software requirements necessary to enable the

establishment of a dual-Doppler capability using the 45 SW Doppler and the NWS MLB WSR-88D

radars. Use of these two Doppler radars to provide a 3-D display of the wind field will help forecasters to

better predict the onset of convection and severe weather in support of space launch operations at KSC

and CCAFS. The data can also be used to initialize a local mesoscale numerical weather prediction model

to improve forecast output.

3.1 Dual-Doppler Analysis Feasibility

Evaluation ofthe physical locations and resulting beam crossing angles ofthe 45 SW and NWS MLB

radars make them ideally suited for a dual-Doppler capability. The AMU derived the dual-Doppler

equations to facilitate complete understanding of dual-Doppler synthesis, to determine the technical

information requirements, and to determine how to find the three components of wind velocity from the

equation of continuity and radial velocity data collected by two Doppler weather radars.

There are several options to collect, edit, synthesize and display dual-Doppler data sets. In addition to

the commercially available Vaisala NDOP package available for purchase, there are a variety of freeware

packages available including WDSS-II software available via license from the University of Oklahoma

and from NCAR for processing raw radar data. Unfortunately, the freeware packages do not have

sufficient documentation and configuration control to be certified for 45 SW use. In any case, a TI data

line must be installed between the MOC and NWS MLB to enable the receipt of NWS MLB raw radar

data to use in the dual-Doppler synthesis. The installation of a TI data line that will meet the security

requirements necessary for 45 SW use is time-consuming and costly.

3.2 45 WS Interests

Possible applications for utilization of dual-Doppler data by the 45 WS are as follows. Note that due

to the distance ofthe NWS MLB radar from sites on KSC/CCAFS, the beam altitude ofthe lowest beam

may be too high to see some ofthe low level features suggested below:

• Easier visualization of wind fields for launch operation, pre-launch operations, wind

warnings and wind forecasting.

• Easier detection ofthreatening convective winds.

• Better detection of convergence lines for forecasting convection initiation.

• Detection of low level helicity for severe weather prediction.

• Detection of winds near offshore for possible improved wind warnings.

• Initiation ofshort forecast local numerical models, especially the wind field over the

ocean that is currently not measured well.

• Replacement of lost inland wind tower data to support 21 5t Century Spaceport or Air

Force Smart Operations 21 st Century (AFSO-21) initiative.

3.3 NWS MLB Interests

NWS MLB agrees that the siting of the two radars is ideal for use of dual-Doppler techniques at

KSC and CCAFS. Once the 45 SW and NWS MLB radar data co-exist, NWS MLB can use the multisensor, multi-radar processing options via the Warning Decision Support System Integrated Information

(WDSS-lI) system for viewing. The WDSS-ll is the second generation of a system of tools for the

analysis, diagnosis and visualization of remotely sensed weather data. WDSS-ll has the capability to

merge multiple-radar data into four-dimensional grids including Terminal Doppler Weather Radar

(TDWR) data. It is possible that both 45 SW radar data and TDWR data from Orlando International

Airport could be used to alleviate radar geometry issues at the NWS MLB radar, such as the cone of

silence or beam blockage. In addition, in the event of a radar outage at one of the sites, the multi-radar

16
algorithms would provide continuing coverage of the area through use of the data from the remaining

operational radar sites.

3.4 Future Work

Accurate near-term forecasting of convective activity and severe storms is of continuing interest to

all customers. As has been described, dual-Doppler capability can provide significant improvement to that

forecasting capability. To illustrate the level of improvement that may be achieved, the AMU suggests the

dual-Doppler data be subjected to a proof-of-concept activity by which wind data is validated to provide

baseline confidence. Specifically, dual-Doppler data can be compared to balloon and/or wind profile data

to evaluate and quantifY the observed accuracy. These proof-of -concept evaluations could be performed

on a variety of "typical" days including a summer day and a winter day when no convection or frontal

zones are present and the normal sea breeze location is known. Once the data is validated and the

capability has been confirmed, merged scans from the existing radars during known periods of convective

activity and storms, such as that observed Oct 9 -10, 2011 (Columbus Day Storm) can be analyzed to

determine ifthe dual-Doppler capability would have aided in the near-term forecasting.

17
Appendix

Derivation of the Dual-Doppler Equations

The following derivations were compiled from Armijo (1969), Obrien (1970), Lhermitte and Miller

(1970) and Carey (2005). Before the Doppler radar data can be used to perform dual-Doppler wind

retrieval, they must be converted from polar to Cartesian coordinates as follows (Goh and Holt 2004).

Referencing Figure 2, the distance between the target and radar 1 is:

(A-I)

The distance between the target and radar 2 is:

(A-2)

Squaring equations A-I and A-2 above and taking the derivative ofthe squared radial velocities with

respect to time will allow the distances to be converted to velocities that can then be solved to find the

horizontal wind components:

R,2 =(x-x,Y +(y- yy +(Z_ZI)2

~=~-~Y+(Y-~Y+~-~Y

2R dRI =2(x _ x ) dx + 2(y _ Y ) dy + 2(z - z , dt ) dt I dt ) dt

(A-3)

(A-4)

(A-5)

(A-6)

(A-8)

2R dR2 =2(x _ x ) dx + 2(y _ Y ) dy + 2(z _ Z ) dz

2 dt 2 dt 2 dt 2 dt

Divide equation A-5 by 2RI and substitute VI for dR, , u for dx , v for dy , and w + VI for dz to get:

dt dt dt dt

T/ (x - XI) (y - yJ ( V ) (z - z) ) Y 1 =U +v + w+ ( (A-7) R, R, R,

Divide equation A-6 by 2R2 and substitute V2 for dR2 , u for dx, v for dy , and w + VI for dz to get: dt dt dt dt

V

2 =U (x-x2) +v (y- Y2) +(w+V;)(Z-Z2)

R2 R2 R2

Referencing Error! Reference source not found., write equations A-7 and A-8 in terms ofthe radars'

elevation (a) and azimuth (B) angles using the radar geometry as follows (Note: m denotes a generic radar

number).

(x-xm)=cosa sin'" (Y-Yn,)=cosa cos'" and (z-zm)=sinam. R m 'f'm' R m 'f'm' m m Rm

Using the above substitutions, equation A-7 becomes:

=ucosal sin¢I +vcosa)cos¢I +(w+V,)sinal .

Equation A-8 becomes:

V2 =ucosa2sin ¢2 + vcosa2 COS¢2 + (w + V; )sin a 2 .

(A-9)

(A-IO)

18
Solve equation A-9 for v:

v=secaJsec¢, (-ucosa, sin¢J -(w+Vt)sina, +VJ ).

Substitute equation A-II into equation A-I 0:

Vz = u cosaz sin¢z + (secal sec¢l (- ucosa, sin ¢J - (w + V, )sin a, + VI))

*cosazcos¢z +(w+V,)sinaz'

Expand equation A-12 and multiply both sides of equation A-12 by cos ~,:

Vz cos¢, = ucosazsin¢z COS¢I - ucosal sin¢J secal sec¢, cosaz cos¢z COS¢I

-(w + Vt)sinaJseca, sec¢1 cosaz cos¢z cos¢, + secal sec¢1 cosaz cos¢z cos¢J

+ (w + VJsinaz cos¢,.

Simplify equation A-l3:

Vzcos¢J =ucosazsin¢zcos¢, -usin¢,cos¢zcosaz

-(w + Vt)tana, cosaz cos¢z + seca, cosaz cos¢z

+ (w + Vt)sin a z cos¢J

Solve equation A-14 for u:

ucosaz(sin¢, cos¢z - sin¢z cos¢.)= seca, cosaz cos¢z

- VZ COS¢I - (w + VJtana, cosaz cos¢z + (w + VJsinazCOS¢l

sec a J cos a z cos ¢z Vz cos ¢J U = - ----,---=-------''--'---------.,..

cos a z(sin ¢J cos ¢z - sin ¢z cos ¢I) cos a z(sin ¢I cos ¢z - sin ¢z cos ¢J)

(w + Vt)tana, cosaz cos¢z (w + Vt)sinaz cos¢, ---'------,------'--'------'--------"------'--"--.,..+----+------''"'-----''----'--'-----.,..

cos a z(sin ¢J cos ¢z - sin ¢z cos ¢I ) cos a z(sin ¢1 cos ¢z - sin ¢z cos ¢I )

1 [~ cos¢z V zcos¢,]

u = (sin¢l cos¢z - sin¢z cos¢,) cosa, - cosaz

_(w + V

t

{ cos¢z tanal - COS¢l tanaz ].

t (sin ¢, cos ¢z - sin ¢z cos ¢J)

(A-II)

(A-12)

(A-l3)

(A-14)

(A-15)

(A-16)

(A-17)

Substitute the trigonometric identity sin(u - v) = sin u cos v - cos u sin v in the denominator of equation

A-17 (Lhermitte and Miller 1970):

u =. 1 [~ cos¢z _ VZCOS¢I ] _(w + V

t

{ cos¢z ta~a, -cos¢J tanaz ]. (A-18)

sm(¢J -¢z) cosa, cosaz t sm(¢, -¢z)

Solve for v by repeating the above steps. Solve equation A-I 0 for u:

u = secaz csc¢z(-vcosaz cos¢z -(w+ V,)sinaz +Vz).

19

(A-19)
Substitute equation A-19 into equation A-9:

= [seca2CSC¢2 (- vcos a2 cos ¢2 - (w + )sin a 2 +V2 )]cosa, sin ¢I

+ vcosa1 cos¢, + (w + VI )sin a,.

Expand equation A-20 and multiply both sides of equation A-12 by sin ~2:

sin ¢2 = -vcosa2COS¢2 cosal sin ¢I seca2CSC¢2 sin ¢2 + vcosal COS¢I sin ¢2

- (w + VI )sin a 2 seca2CSC¢2 cosa, sin ¢I sin ¢2 + V2 seca2CSC¢2 cos a l sin ¢, sin ¢2

+ (w + VI )sin a, sin ¢2'

Simplify equation A-21:

sin ¢2 =-v cos ¢2 cos a 1 sin ¢l + v cos a l cos ¢, sin ¢2

- (w + VI )tan a2 cos a, sin ¢, + V2 sec a2 cos a, sin ¢I

+ (w + VI)sina, sin¢2'

Solve equation A-22 for v:

v cos a 1(cos ¢2 sin ¢, - sin ¢2 cos ¢,) = V2 sec a 2 cos a l sin ¢l

- VI sin ¢2 - (w + VI )tan a2 cos a, sin ¢l + (w + VI )sin a, sin ¢2

V2 sec a 2 cos a, sin ¢I sin ¢2 V= ------,.----'----------'--=------------,-

cos a l (sin ¢, cos ¢2 - sin ¢2 cos ¢I) cos a, (sin ¢, cos ¢2 - sin ¢2 cos ¢,)

(w + VI )tan a2cos at sin ¢I (w + Vt )sin a 1sin fJ2 --'---;----'-"'-----=------'----'-'-----,-+---;.------'-'---------'------'---"-------,-

cos a l (sin ¢l cos ¢2 - sin ¢2 cos ¢I) cos a 1(sin ¢, cos ¢2 - sin ¢2 cos ¢,)

I [V2sin¢1 ~sin¢2] v = (sin ¢l cos ¢2 - sin ¢2 cos ¢I) cos a 2 - cos a,

_(w + VI { sin ¢, tan a2 - sin ¢2 tan a, ].

t (sin ¢I cos ¢2 - sin ¢2 cos ¢,)

(A-20)

(A-21)

(A-22)

(A-23)

(A-24)

(A-25)

(A-27)

Substitute the trigonometric identity sin(u - v) = sin u cos v - cos u sin v in the denominator of equation

A-25 (Lhermitte and Miller 1970):

v = 1 [V2 sin ¢I _ V,sin ¢2 ] _(w + V { sin ¢I tan a 2 - sin ¢2 tan al ] • (A-26)

sin(¢, -¢2) cosa2 cosal It sin(¢, -¢2)

Now there are two equations, A-18 and A-26, with four unknowns: u, v, w, and VI' Therefore, equations

A-18 and A-26 must be supplemented with the equation of continuity:

ap + a(pu) + a(pv) + a(Pw) = O.

at ax ay az

Expand equation A-27 to get:

ap au ap av ap aw ap -+p-+u-+p-+v-+p-+w-=O

at ax ax ay ay az az (A-28)

20
Assume density, p, is constant at a particular level, z, and simplify equation A-28:

ou Ov Ow op p-+p-+p-+w-=O.

Ox Oy oz oz

Rearrange equation A-29:

pOw +wop =_[pou +pOv). OZ OZ ox Oy

Substitute o(PW) = p Ow + w op into equation A-30:

oz oz oz

o(pw) =_[p ou + pOv).

oz ox Oy

Now, equation A-31 can be integrated from one level to the next for each level:

rbO(pw) =_rb[p ou + p Ov) Ja oz Ja ox Oy

(PW)b - (pwt = _[p[OU + Ov) liz _p[OU + Ov) liz]. ox Oyb ox Oya

(A-29)

(A-30)

(A-31 )

(A-32)

(A-33)

(A-34)

Equation A-33 can be solved for vertical velocity, w, at every height by first assuming w=o at the surface

and then iterating until the mean difference between the horizontal and vertical divergence is less than

some predetermined threshold.

Finally, Vt can be estimated by using standard Vt-Z relationships (Doviak et at. 1976):

V, ~2.65Z0114[ )"[ms·']

The IRIS NDOP software estimates Vt using the following relationships (IRIS 2006):

Above the melting level (snow and graupel): = 0.8Z006 [ms-l

]

Below the melting level (rain): = 2.70Z0 1l[ms-I

]

21

(A-35)

(A-36)
List of Acronyms

45 SW 45th Space Wing NCAR National Center for Atmospheric

45 WS 45th Weather Squadron Research

AMU Applied Meteorology Unit NDOP IRIS product that calculates dualDoppler wind fields based on

AWIPS Advanced Weather Interactive radial wind inputs from two

Processing System Doppler radars

CCAFS Cape Canaveral Air Force Station NM Nautical Mile

IRISTM Interactive Radar Information NSSL National Severe Storms

System Laboratory

KSC Kennedy Space Center NWS National Weather Service

MIDDS Meteorological Interactive Data TDWR Terminal Doppler Weather Radar

Display System WDSS-II Warning Decision Support

MLB Melbourne, Fla. - 3 letter System Integrated Information

identifier WSR-88D Weather Surveillance Radar -

MOC Morrell Operations Center 1988 Doppler

NASA National Aeronautics and Space

Administration

22
References

Armijo, L., 1969: A Theory for the Determination of Wind and Precipitation Velocities with Doppler

Radars, J. Atmos. Sci., 26, 570-575.

Beck, 1., 2004: High-Resolution Dual-Doppler Analyses ofthe 29 May 2001 Kress, TX, Cyclic Supercell.

Masters Thesis, Texas Tech University, 109 pp.

Bousquet, 0., P. Tabary, and J. Parent du Chatelet, 2008: Operational Multiple-Doppler Wind Retrieval

Inferred from Long-Range Radial Velocity Measurements, J. Appl. Meteor., 47, 2929-2945.

Carey, L., 2005: Houston Advanced Research Center, Texas Environmental Research Consortium. Final

Progress Report for the Deployment of the C-band Radars to DFW and HGB for the 2005 Ozone

Season, 47 pp.

Davies-Jones, R., 1979: Dual-Doppler Radar Coverage Area as a Function of Measurement Accuracy and

Spatial Resolution,J. Appl. Meteor., 18,1229-1233.

Doviak, R. and D. Zrnic, 1993: Doppler Radar and Weather Observations, 2nd Ed., Academic Press, San

Diego, CA, 562 pp.

Doviak, R., P. Ray, R. Strauch and L. Miller, 1976: Error Estimation in Wind Fields Derived from DualDoppler Radar Measurement, J. Appl. Meteor., 15, 868-878.

Friedrich, K. and M. Hagen, 2004: On the Use of Advanced Doppler Radar Techniques to Determine

Horizontal Wind Fields for Operational Weather Surveillance, Meteorol. Appl., 11, 155-171.

Goh, Y. and A. Holt, 2004: Analysis of Three-dimensional Wind Fields from Two Operational Doppler

Radars, Proceedings of ERAD 2004 (European Conference on Radar in Meteorology and

Hydrology), Visby, Sweden, Sept. 6-10,2004,35-40.

IRIS Product and Display Manual, Configuring IRIS Products NDOP, Vaisala Corp., January 2006, pp.

3-46 to 3-54.

Lakshmanan, V., T. Smith, G. Stumpf, and K. Hondl, 2007: The Warning Decision Support SystemIntegrated Information, Wea. Forecasting, 22,596-612.

Lhermitte, R. and L. Miller, 1970: Doppler Radar Methodology for the Observation of Convective

Storms. 14th Con! on Radar Meteor., Tuscon, AZ, Amer. Meteor. Soc., 133-138.

Obrien, J., 1970: Alternative Solutions to the Classical Vertical Velocity Problem, J. Appl. Meteor., 9,

197-203.

Rinehart, R., 2004: Radarfor Meteorologists, 4th Ed., Rinehart Publications, Columbia, MO, 482 pp.

Salazar, J., A. Hopf, R. Contreras, B. Philips, E. Knapp, D. McLaughlin, J. Brotzge, and K. Brewster,

2009: Coverage Comparison of Short Range Radar Networks vs. Conventional Weather Radars: Case

Study in the Northwestern United States. Proc. Geoscience and Remote Sensing Symp., IGARSS'09,

Vol. 2, Cape Town, South Africa, IEEE, 964-967.

Short, D., 2008: Radar Scan Strategies for the Patrick Air Force Base Weather Surveillance Radar, Model

74C, Replacement. NASA Contractor Report CR-2008-214745, Kennedy Space Center, FL, 28 pp.

[Available from ENSCO, Inc., 1980 N. Atlantic Ave., Suite 830, Cocoa Beach, FL, 32931 and online

at http://science.ksc.nasa.gov/amu/final.html.]

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NOTICE

Mention of a copyrighted, trademarked or proprietary product, service, or document does not constitute

endorsement thereof by the author, the AMU, the National Aeronautics and Space Administration, or the

United States Government. Any such mention is solely for the purpose of fully informing the reader of

the resources used to conduct the work reported herein.

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