January 2014

NASA/TM–2014-218152

NASA AVOSS Fast-Time Wake Prediction 

Models: User’s Guide

Nash'at N. Ahmad and Randal L. VanValkenburg

Langley Research Center, Hampton, Virginia

Matthew Pruis

NorthWest Research Associates, Inc., Redmond, Washington
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January 2014

NASA/TM–2014-218152

NASA AVOSS Fast-Time Wake Prediction 

Models: User’s Guide

Nash'at N. Ahmad and Randal L. VanValkenburg

Langley Research Center, Hampton, Virginia

Matthew Pruis

NorthWest Research Associates, Inc., Redmond, Washington
Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076-1320

443-757-5802

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an 

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and Space Administration. 
iiL

Contents

List of Acronyms, Abbreviations, and Symbols............................................................................................ i

Introduction ..................................................................................................................................................1

Software Distribution....................................................................................................................................2

Model Input/Output Filename Convention.................................................................................................. 3

Model Input File Formats.............................................................................................................................. 4

Case Input File (cases.i)............................................................................................................................. 4

Aircraft Parameters Input File (YYYY_MO_DY_HRMNSC.ADATA) ............................................................ 4

Temperature/Theta Profile (YYYY_MO_DY_HRMNSC.TDATA)................................................................. 5

Crosswind Profile (YYYY_MO_DY_HRMNSC.UDATA)................................................................................ 6

Eddy Dissipation Rate Profile (YYYY_MO_DY_HRMNSC.QDATA) ............................................................. 6

Lidar Data File Format...................................................................................................................................7

Lidar Data File (YYYY_MO_DY_HRMNSC.cwp).......................................................................................... 7

Model Output File Format ............................................................................................................................ 8

Model Output File Format (e.g., YYYY_MO_DY_HRMNSC.apa34) ........................................................... 8

Model Output File Example (e.g., YYYY_MO_DY_HRMNSC.apa34) ......................................................... 9

Memphis Field Experiment (1995).............................................................................................................. 10

Data Processed for Fast‐Time Wake Models.......................................................................................... 10

Evaluation of Fast‐Time Models using the Memphis 1995 Data ................................................................ 13

Example from the Memphis 1995 Dataset................................................................................................. 15

List of Contributors .....................................................................................................................................17

Acknowledgment........................................................................................................................................17

References ..................................................................................................................................................17
iY

List of Acronyms, Abbreviations, and Symbols

AGL    Above Ground Level

APA    AVOSS Prediction Algorithm

ATM    Air Traffic Management

ATPG    Atmospheric Turbulence Profile Generator

ASOS    Automated Surface Observations System

AVOSS    Aircraft VOrtex Spacing System

AWAS    AVOSS Winds Analysis System

b0     Initial vortex pair separation (m)

B     Wingspan (m)

CW    Continuous Wave Lidar

EDR    Eddy Dissipation Rate (m2

/s

3

)

   Eddy Dissipation Rate (m2

/s

3

)

0     Initial vortex circulation (m2

/s)

IGE    In‐Ground Effect

Lidar    LIght Detection And Ranging

MEM    Memphis International Airport, Memphis, Tennessee

NASA    National Aeronautics and Space Administration

NGE    Near‐Ground Effect

OGE    Out‐of‐Ground Effect

PL     Pulsed Lidar

     Air density (kg/m3)

RASS    Radio Acoustic Sounding System

SAO    Surface Aerodrome Observations

     Potential Temperature/Theta (K)

TASS    Terminal Area Simulation System

TDAWP   TASS Driven Algorithms for Wake Prediction

TDP    Abbreviation used for the TDAWP model

U     Airspeed (m/s)

V0     Initial vortex pair descent velocity (m/s)

W     Landing weight of the aircraft (kg)

y0     Initial position of the vortex pair with respect to the runway centerline (m)

z0     Initial vortex height AGL (m)
1 

Introduction

The National Aeronautics and Space Administration (NASA) is developing fast‐time wake transport

and decay models to safely enhance the capacity of the National Airspace System (NAS).  These models

are empirical algorithms used for real‐time predictions of wake transport and decay based on aircraft

parameters and ambient weather conditions.    The aircraft dependent parameters include the initial

vortex descent velocity (V0) and the vortex pair separation distance (b0).    The atmospheric initial

conditions include vertical profiles of temperature or potential temperature (), eddy dissipation rate

(EDR), and crosswind.    The model output consists of time history of vortex circulation strength and

position.  The fast‐time wake models can be used for the systems level design of advanced air traffic

management (ATM) concepts that safely increase the capacity of the NAS.  It is also envisioned that at

some later stage of maturity, these models could be used operationally, not only within the terminal

airspace but also as onboard tools to support concepts such as dynamic separation of aircraft.

NASA’s first fast‐time wake transport and decay model was developed by Greene (1986).  In the late

1990s, under NASA’s Aircraft Vortex Spacing System (AVOSS) project, significant advances were made in

wake vortex modeling based on the data from field experiments and large eddy simulations.  The initial

versions of the AVOSS Wake Vortex Prediction Algorithm (APA) were developed during the AVOSS

program and demonstrated in the AVOSS demo at the Dallas/Ft. Worth (Hinton 2001).  The APA model

computes the out‐of‐ground‐effect (OGE) decay and descent based on Sarpkaya (Sarpkaya 2000;

Sarpkaya et al. 2001).  The model has an algorithm for enhanced rate of decay during the ground effect

developed by Proctor et al. (2000).    The scheme to compute lateral vortex transport is based on the

vertical profile of crosswind (Robins and Delisi 2002), and the in‐ground‐effect (IGE) transport accounts

for vortex spreading and rebound (Robins et al. 2002).  The code development of APA is described in

Robins and Delisi (2002).

NASA has also developed the TASS (Terminal Area Simulation System) Derived Algorithms for Wake

Prediction (TDAWP) model.  In the TDAWP model, the Sarpkaya component is replaced with algorithms

developed from parametric studies using a Large Eddy Simulation (LES) model.   The TDAWP model is

described in Proctor et al. (2006) and Proctor and Hamilton (2009).  The current version of the TDAWP

model includes the effect of the crosswind shear gradient on transport.    The TDAWP model is also

denoted by TDP.

The current distribution includes the latest versions of the APA (3.4) and the TDP (2.1) models.  This

User’s Guide provides detailed information on the model inputs, file formats, and the model output.  An

example of a model run is also provided.  A brief description of the Memphis 1995 Wake Vortex Dataset

is also provided.   Additional questions regarding this software distribution can be directed to Nashat

Ahmad (nashat.n.ahmad@nasa.gov) or Randy VanValkenburg (randal.l.vanvalkenburg@nasa.gov).

 
2 

Software Distribution

NASA’s AVOSS Fast‐Time Wake Prediction software distribution is given below:

avoss/ 

| 

`--bin/ 

| | 

| +-- apa34.exe

| | 

| `-- tdp21.exe

| 

`--doc/ 

| `-- APA-UsersGuide.pdf

| 

`--etc/ 

| `-- cases.i

| 

`--mem/ Memphis 1995 Wake Vortex Dataset

| | 

| +-- ADATA/ aircraft information and initial vortex location

| | 

| +-- QDATA/ vertical profiles of eddy dissipation rate

| | 

| +-- TDATA/ vertical profiles of potential temperature

| | 

| +-- UDATA/ vertical profiles of crosswinds

| | 

| +-- UPROXY/ vertical profiles of proxy crosswinds

| | 

| +-- CWP/ lidar data for port vortex

| | 

| `-- CWS/ lidar data for starboard vortex

| 

`--run/ 

 | 

 +-- cases.i list of cases to run

 | 

 +-- 1995-08-10-230029.apa34 APA3.4 output

 | 

 +-- 1995-08-10-230029.tdp21 TDP2.1 output

 | 

 +-- 1995-08-10-230029.tplt Potential Temperature() input

 | 

 +-- 1995-08-10-230029.qplt Eddy Dissipation Rate() input

 | 

 `-- 1995-08-10-230029.uplt Crosswinds input

 
3 

Model Input/Output Filename Convention

The file names are chosen to give a unique identifier for each case and model run.    The unique

identifier has the form:

YYYY_MO_DY_HRMNSC 

where,

YYYY =   Four digit year

MO    =   Two digit month

DY    =   Two digit day

HRMNSC =   Six digit HourMinuteSeconds

Example:

2003_09_19_181019 has the following associated input files:

2003_09_19_181019.ADATA    Initial Vortex Location & Aircraft Parameters

2003_09_19_181019.TDATA    Vertical Profile of Temperature or Theta

2003_09_19_181019.UDATA    Vertical Profile of Crosswind

2003_09_19_181019.QDATA    Vertical Profile of Eddy Dissipation Rate

The model output is written to (depending on the model used):

2003_09_19_181019.apa34    APA3.4 output

2003_09_19_181019.tdp21    TDP2.1 output
4 

Model Input File Formats

Case Input File (cases.i)

The first six lines list the paths to input files.  Line number 7 has the total number of cases (maximum

number of cases = 5000) in the file and the type of lidar.  The lidar type is not used in fast‐time models –

it is used by plotting and validation routines.  The rest of the file lists the unique identifiers for each case.  

The path names should have a maximum length of 132 characters.

CASE FILE (cases.i)

/home/nnahmad/apa-models/data/MEM1995/ADATA/ 

/home/nnahmad/apa-models/data/MEM1995/QDATA/ 

/home/nnahmad/apa-models/data/MEM1995/TDATA/ 

/home/nnahmad/apa-models/data/MEM1995/UDATA/ 

/home/nnahmad/apa-models/data/MEM1995/CWP/ 

/home/nnahmad/apa-models/data/MEM1995/CWS/

2 0 ! total number of cases to run/lidar type

1995-08-06-230412 

1995-08-06-232159 

Aircraft Parameters Input File (YYYY_MO_DY_HRMNSC.ADATA)

The first 11 lines of this file contain the header information.  After the header lines, the file contains

the initial vortex location and the aircraft data:  Initial lateral location of the vortex (y0), initial height of

the vortex (z0), initial descent velocity (V0), and the separation distance (b0) of the vortex pair.  The units

are MKS.

AIRCRAFT PARAMETERS FILE (YYYY_MO_DY_HRMNSC.ADATA)

# Location: MEM, 18L_TANG 

# Run Number: 1026 

# A/C Type: AT43 

# Wing span* (m): 24.6 

# Weight* (kg): 13940 

# ACspeed* (m/s): 63.4 

# Air Density* (kg/m3): 1.2 

# This file was created on 22-Mar-2012 12:42:37 Pacific Time 

# File created by Matt Pruis, NWRA, matt@nwra.com 

# *If data not provided with original data set, then default values used. 

# Data File Format: yo (m),zo (m),Vo (m/s), bo (m) 

5.2895, 90.03, 0.76635, 19.321
5 

Temperature/Theta Profile (YYYY_MO_DY_HRMNSC.TDATA)

The first 11 lines in this file contain header information.  The first line after the header information

gives the total number of data points in the file.    If negative, then the file contains potential

temperatures, otherwise the data are temperatures.    The rest of the file has two columns: the first

column lists the AGL height in meters and the second column lists the potential temperature in K or

temperature in C.    If the user inputs a temperature profile, then it is converted by the model to

potential temperature ().

At least three data points are required in the initial profile and the points should extend above and

below the heights of vortex descent trajectory.    If the input potential temperature profile contains

regions of unstable stratification, then those values are set to zero (neutral stratification) within both

the APA and TDP codes.    Observations from various field sensors as well as simulation data from

mesoscale models (Ahmad et al. 2013) can be used to generate the vertical temperature/potential

temperature profiles.  It should be noted that the fast‐time wake models use potential temperature in

model calculations.

TEMPERATURE PROFILE DATA (YYYY_MO_DY_HRMNSC.TDATA)

# Location: MEM, 18L_TANG 

# Run Number: 1026 

# A/C Type: AT43 

# Potential modifications from original data include: 

# (1) extrapolation above and below profile (with N=0 in these regions) 

# (2) removal of unstable regions that are not attached to ground 

# (with N=0 in these regions) 

# This file was created on 22-Mar-2012 12:42:37 Pacific Time 

# File created by Matt Pruis, NWRA, matt@nwra.com 

# Data File Format (1st line): number of points (-ve indicates theta) 

# Data File Format (remainder of file): z (m) potential temperature (K) 

-120 

0, 303.98 

5, 303.98 

10, 304.04 and so on.....

 
6 

Crosswind Profile (YYYY_MO_DY_HRMNSC.UDATA)

Similar in format to the xxx.TDATA file, but contains crosswinds (m/s).    Heights are in meters.  

Crosswind profiles can be generated from the lidar data or estimated from the wake vortex trajectory

(Pruis et al. 2011).

CROSSWIND PROFILE DATA (YYYY_MO_DY_HRMNSC.UDATA)

# Location: MEM, 18L_TANG 

# Run Number: 1026 

# A/C Type: AT43 

# Potential modifications from original data include: 

# (1) extrapolation above and below profile (with U constant in these regions)

# This file was created on 22-Mar-2012 12:42:37 Pacific Time 

# File created by Matt Pruis, NWRA, matt@nwra.com 

# Data File Format (1st line): number of data points 

# Data File Format (remainder of file): z (m) Crosswind (m/s) 

120 

0, 2.124 

10, 2.074 and so on.....

Eddy Dissipation Rate Profile (YYYY_MO_DY_HRMNSC.QDATA)

Similar in format to the xxx.TDATA file, but contains the eddy dissipation rates (m2/s

3

).  Heights are

in meters.  Given two observations of EDR, the vertical EDR profile can be generated using atmospheric

boundary layer similarity theory (Han et al. 2000).  EDR profiles can also be estimated from lidar data

(Pruis et al. 2013).  Input EDR values less than 10‐7

m2/s

3 are set to 10‐7

m2/s

3 within the models.

EDDY DISSIPATION RATE DATA (YYYY_MO_DY_HRMNSC.QDATA)

# Location: MEM, 18L_TANG 

# Run Number: 1026 

# A/C Type: AT43 

# Potential modifications from original data include: 

# (1) extrapolation above and below profile (with EDR constant in these regions)

# This file was created on 22-Mar-2012 12:42:37 Pacific Time 

# File created by Matt Pruis, NWRA, matt@nwra.com 

# Data File Format (1st line): number of data points 

# Data File Format (remainder of file): z (m) EDR (m2/s3) 

120 

0, 0.0026156 

5, 0.0026156 

15, 0.002405 

20, 0.0023001 

30, 0.0020895 and so on.....
7 

Lidar Data File Format

Lidar Data File (YYYY_MO_DY_HRMNSC.cwp)

For each case there are two lidar data files: one each for the port and the starboard vortices.  The

filename conventions are as follows:

2003_09_19_181019.cwp     Continuous Wave Lidar Port Vortex Data

2003_09_19_181019.cws     Continuous Wave Lidar Starboard Vortex Data

2003_09_19_181019.plp     Pulsed Lidar Port Vortex Data

2003_09_19_181019.pls     Pulsed Lidar Starboard Vortex Data

In most of the field experiments only one type of lidar was used and therefore a particular dataset

will have either CW or PL files.  In the Denver 2003 Field Experiment (Dougherty et al. 2004) both CW

and PL lidars were deployed.

The first six lines in the lidar data files contain the header information.  Missing data points in the

files are marked by a -9999.  Please note that it is not uncommon for the lidar files to contain points

that include valid times and vortex positions, but for which the circulation cannot be calculated due to

missing or invalid data values.    Consequently for a given vortex, the plots of circulation may display

fewer discrete points than do the corresponding plots of lateral transport or altitude.

LIDAR DATA FILE (YYYY_MO_DY_HRMNSC.cwp)

# Location: MEM, 18L_TANG 

# Run Number: 1026 

# A/C Type: AT43 

# This file was created on 22-Mar-2012 12:42:38 Pacific Time 

# File created by Matt Pruis, NWRA, matt@nwra.com 

# Data File Format: time_p(s), y_pos_p(m), z_pos_p(m), Circ_p(m2/s) 

21 

8.88, 5, 87, 125.9091 

11.4, 8.3, 84.7, 158.1455 

13.6, 18.4, 92.5, -9999 

15.57, 20.5, 83.2, 123.7773 and so on.....
8 

Model Output File Format

Model Output File Format (e.g., YYYY_MO_DY_HRMNSC.apa34)

The model output files are currently written in Tecplot® format.  The model output file gives the

time history of position (lateral distance and altitude) and circulation strength of both the port and

starboard vortices.  The output variables are listed in Table 1.

Table 1:  Fast‐Time Wake Model Output

column # variable description

1 time Time (seconds) 

2 yp Lateral position of port vortex (m) 

3 zp Altitude of port vortex (m) 

4 gp Circulation of port vortex (m2/s) 

5 ys Lateral position of starboard vortex (m) 

6 zs Altitude of starboard vortex (m) 

7 gs Circulation of starboard vortex (m2/s) 

The output filename extension is based on the model type:

2003_09_19_181019.apa34     APA3.4 output

2003_09_19_181019.tdp21     TDP2.1 output

In addition to the model output, for each run the environmental initial conditions are also written to

files for plotting purposes:

2003_09_19_181019.uplt     Crosswinds

2003_09_19_181019.qplt     EDR

2003_09_19_181019.tplt     Theta/Temperature

 
9 

Model Output File Example (e.g., YYYY_MO_DY_HRMNSC.apa34)

An example of a model output file is shown below:

MODEL OUTPUT (YYYY_MO_DY_HRMNSC.apa34)

TITLE="APA 3.4" 

VARIABLES = "Time(s)", "Yp(m)", "Zp(m)", "Gp(m^2/s)", "Ys(m)", "Zs(m)", "Gs(m^2/s)" 

ZONE T="31", I= 1097 

 0.000 8.356 41.821 63.793 25.164 41.821 63.793 

 0.100 8.300 41.761 63.738 25.108 41.761 63.738 

 0.200 8.243 41.700 63.683 25.051 41.700 63.683 

 0.300 8.187 41.640 63.627 24.995 41.640 63.627 

 0.400 8.130 41.580 63.572 24.938 41.580 63.572 

 0.500 8.074 41.520 63.517 24.882 41.520 63.517 

 0.600 8.017 41.460 63.461 24.825 41.460 63.461 

 0.700 7.960 41.399 63.406 24.768 41.399 63.406 

 0.800 7.904 41.339 63.351 24.712 41.339 63.351 

 0.900 7.847 41.279 63.296 24.655 41.279 63.296 

 1.000 7.790 41.220 63.241 24.598 41.220 63.241 

 1.100 7.734 41.160 63.186 24.542 41.160 63.186 

 1.200 7.677 41.100 63.131 24.485 41.100 63.131 

 1.300 7.620 41.040 63.076 24.428 41.040 63.076 

 1.400 7.563 40.980 63.021 24.371 40.980 63.021 

 1.500 7.507 40.921 62.966 24.315 40.921 62.966 

 1.600 7.450 40.861 62.912 24.258 40.861 62.912 

 1.700 7.393 40.802 62.857 24.201 40.802 62.857 

 1.800 7.336 40.742 62.802 24.144 40.742 62.802 

 1.900 7.279 40.683 62.748 24.087 40.683 62.748 

 2.000 7.222 40.623 62.693 24.030 40.623 62.693 

 and so on.....
10 

Memphis Field Experiment (1995)

A comprehensive field experiment to measure wake vortices and the associated ambient

meteorological conditions was conducted at the Memphis International Airport in Memphis, Tennessee

from August 6 through August 29, 1995 (Zak 1995; Campbell, et al. 1997).    The experiment was

sponsored under NASA Langley Research Center’s Aircraft Vortex Spacing System (AVOSS) project

(Hinton 1995; Perry et al. 1997).  The wake data were collected using a continuous wave lidar (Figure 1).  

The meteorological sensors included radiosondes, sodars, a wind profiler, one 150ft high meteorological

tower, a Radio Acoustic Sounding System (RASS), and NASA Langley’s OV‐10 research aircraft.    The

radiosondes were used to measure winds and temperature measurements (10s averages) at 50m

vertical resolution.    The OV‐10 aircraft was flown at selected times and took measurements of

temperature and winds at a sample rate of 10Hz.  Temperature (5min averages) was measured using

RASS every 30min at 14 vertical levels from 127m to 1492m.  The 150ft (45.7m) meteorological tower

was equipped with a large array of sensor systems.  Winds, temperature and moisture were measured

from the tower at 5m, 10m, 20m, 30m, and 42m heights.    Turbulence quantities (turbulence kinetic

energy and eddy dissipation rate) were estimated from wind measurements at 5m and 40m heights.  

Rain rate, soil temperature, soil moisture, barometric pressure, and incoming and outgoing solar

radiation also were measured by the sensors deployed on the meteorological tower.    Standard

meteorological data such as atmospheric pressure, temperature, moisture, cloud cover, visibility, etc.

were obtained from the National Weather Service’s Surface Aerodrome Observations (SAO) and the

Automated Surface Observations System (ASOS).

Data Processed for Fast‐Time Wake Models

Aircraft Data

The aircraft data used by the fast‐time wake prediction models include the initial position (offset) of

the vortex pair with respect to the runway centerline (y0), the initial height of the vortices (z0), the initial

vortex descent rate (V0) and the initial separation of vortices (b0).

The initial position (offset) of the vortex pair with respect to the runway centerline y0 was estimated

using an average of the first few data points for each landing.  The initial height of the vortices z0 was

estimated from backward extrapolation of the altitude trajectory in time.  The initial separation distance

between the vortices b0 was estimated assuming an elliptical wing loading,

b B

4 0



 (1) 

where B is the wingspan of the aircraft.  The initial vortex descent rate was estimated from the aircraft

weight, aircraft speed, air density, and the initial vortex separation b0,

2

0

0 2 Ub

gW V

  (2) 

where g (=9.81m/s2) is the acceleration due to gravity,  is the air density  ‐ which was assumed to be

1.2kg/m3 for all the landings, U is the reported airspeed, and W is the reported landing weight of the

aircraft.

Types of aircraft observed at different measurement sites are listed in Table 2 and a graphical

presentation of aircraft distribution is shown in Figures 1‐2.  The Armory site was located south of the

airport, while the TANG, Tchulahoma, and Threshold sites were all located at the north end of the

airport.
11 

Crosswinds and Headwinds

The profiles of the mean crosswind and headwind were generated by the AVOSS Winds Analysis

System (AWAS) using an optimal estimation of data fusion from several different wind sensors including

two Doppler radars, the meteorological tower, and the SODAR.  There are some known deficiencies in

the AWAS profiles which are discussed in detail by Dasey et al. (1998).  In the current distribution, only

the crosswinds are included.

Eddy Dissipation Rate

EDR profiles were estimated using the two sonic anemometers on the meteorological tower and

extrapolating to heights using atmospheric boundary layer similarity theory (Han et al. 2000).    The

profiles were generated using the atmospheric turbulence profile generator (ATPG) code which

implements the algorithms described in Han et al. (2000).  Turbulence profiles were extrapolated to the

ground (z = 0) and to a height above the observed vortices with a constant EDR value whenever the

measured profiles did not extend to those heights.

Stratification

Temperature profiles were estimated using a fusion of the RASS and temperature sensors on the

ASOS and the meteorological tower.    The temperature profiles were converted to potential

temperatures using the dry adiabatic lapse rate.  The highest temperature measurement on the tower

was at approximately 43m AGL and the lowest observation of the RASS was at 127m.    A known

deficiency in the profiles is a frequent mismatch in these two temperatures, leading to unrealistic

gradients in the temperature profile within this region.    This can sometimes lead to highly unstable

persistent regions that are not attached to the ground.    The potential temperature profiles were

therefore pre‐processed to remove these unstable regions by making the potential temperature

constant in these regions.

Table 2:  Aircraft Observed at different Measurement Sites

Aircraft Type Armory TANG Tchulahoma Threshold Total 

AT42 1 1 - - 2 

B727 86 1 3 24 114 

B737 3 - - - 3 

B757 5 2 1 - 8 

BA31 - - 2 - 2 

DC10 25 - - 2 27 

DC9 57 19 6 3 85 

EA30 11 - - - 11 

EA31 9 - - 1 10 

EA32 15 7 2 1 25 

FK10 5 2 - - 7 

MD11 - - - 1 1 

SF34 2 - 8 - 10 

Total 219 32 22 32 305 
12 

      

Figure 1:   Distribution of the aircraft types in the MEM dataset is shown in the left panel.   A B757

landing in the background of the NASA lidar van is shown in the right panel.

Figure 2:  Distribution of the lidar data by aircraft category and location.  The Armory site was located

south of the airport, while the TANG, Tchulahoma, and Threshold sites were all located at the north

end of the airport.
13 

Evaluation of Fast‐Time Models using the Memphis 1995 Data

Several evaluations of NASA’s fast‐time models have been conducted in the past (Proctor and

Hamilton 2009; Pruis and Delisi 2011a; Feigh et al. 2012).    Under a NASA Research Announcement

(Enabling Super‐Dense Operations by Advancing the State of the Art of Fast‐Time Wake Vortex

Modeling), the NorthWest Research Associates (NWRA) was tasked to conduct an independent

evaluation of NASA’s fast‐time models over a three year period.    This evaluation concluded that in

general the errors in model circulation predictions had a mean root mean square error on the order of

0.20 to 0.30 (0 is the initial wake circulation), the vertical transport errors were on the order of 0.5b0

and the lateral transport errors were on the order of b0 (Pruis and Delisi 2011b).    NWRA also

demonstrated that the lateral transport errors can be reduced to as low as 0.5b0 if more accurate

crosswind initial conditions (e.g., by using proxy crosswinds as initial conditions) were provided to the

fast‐time models (Pruis et al. 2011).

In this section the current distribution of the fast‐time models are evaluated using the continuous

wave lidar observations from the Memphis 1995 field experiment.  The accuracy of predictions for the

two models was quantified in terms of root mean square error (Errorrms), mean absolute error (Errormae),

and Bias:

       

     

n

i

obs

i

apa

i

n

i

obs

i

apa

mae i

n

i

obs

i

apa

rms i x x

n

x x Bias

n

x x Error

n

Error

1 1 1

2 1

;

1

;

1

 (3) 

The prediction errors in TDP2.1, and APA3.4 for all Memphis cases are given in Table 3.  The errors in

TDP2.1 and APA3.4 categorized approximately by phase (OGE, NGE, and IGE) are given in Tables 4‐6.  

Proxy crosswinds were not used in this evaluation.

For the Memphis data, the groupings of the landings were based on the measurement site where the

observations were obtained.  The OGE observations are the measurements obtained at the 36R_Armory

site, where the mean initial vortex height was 180m.   The NGE observations were obtained from the

18L_TANG site where the mean initial observations, were at a height of 99m.  The IGE data came from

two different lidar locations; the 27_Tchulahoma and the 27_Threshold data.  The mean height of the

initial vortex observation for these two sites was 36m.  In dimensional space, the combined different

phases of vortex trajectory (OGE, NGE and IGE) are defined as follows:

75 IGE

75 130 NGE

130 OGE

 

  

 

z m

m z m

z m

o

o

o

 (4) 

Table 3:  Memphis: All 305 Cases

Model 

Circulation 

(normalized by 0) 

Lateral Transport 

(normalized by b0) 

Altitude 

(normalized by b0) 

rmse mae bias rmse mae bias rmse mae bias 

TDP2.1 0.26 0.22 0.02 1.01 0.83 0.09 0.52 0.44 0.07 

APA3.4 0.24 0.21 -0.05 0.97 0.80 0.10 0.54 0.46 0.14 
14 

Table 4:  Memphis OGE: 219 Cases

Model 

Circulation 

(normalized by 0) 

Lateral Transport 

(normalized by b0) 

Altitude 

(normalized by b0) 

rmse mae bias rmse mae bias rmse mae bias 

TDP2.1 0.25 0.21 0.03 1.06 0.87 0.16 0.58 0.50 0.06 

APA3.4 0.23 0.20 -0.04 1.02 0.83 0.18 0.60 0.51 0.15 

Table 5:  Memphis (NGE): 32 Cases

Model 

Circulation 

(normalized by 0) 

Lateral Transport 

(normalized by b0) 

Altitude 

(normalized by b0) 

rmse mae bias rmse mae bias rmse mae bias 

TDP2.1 0.25 0.21 -0.02 1.05 0.86 -0.32 0.46 0.39 0.12 

APA3.4 0.25 0.21 -0.12 1.04 0.86 -0.33 0.47 0.39 0.18 

Table 6:  Memphis (IGE): 54 Cases

Model 

Circulation 

(normalized by 0) 

Lateral Transport 

(normalized by b0) 

Altitude 

(normalized by b0) 

rmse mae bias rmse mae bias rmse mae bias 

TDP2.1 0.31 0.26 0.02 0.67 0.58 0.02 0.23 0.20 0.06 

APA3.4 0.31 0.26 -0.05 0.67 0.57 0.01 0.22 0.20 0.02 
15 

Example from the Memphis 1995 Dataset

An example case is given in the run/ directory of the distribution.    The directory, contains the

following cases.i file:

cases.i

/home/nnahmad/apa-models/avoss/mem/ADATA/ 

/home/nnahmad/apa-models/avoss/mem/QDATA/ 

/home/nnahmad/apa-models/avoss/mem/TDATA/ 

/home/nnahmad/apa-models/avoss/mem/UPROXY/ 

/home/nnahmad/apa-models/avoss/mem/CWP/ 

/home/nnahmad/apa-models/avoss/mem/CWS/ 

1 0 

 1995-08-10-230029

The user needs to edit the first six lines to reflect the location of the input files.  In this case, the

proxy crosswinds were used.  The number of cases is 1 and the lidar flag is set to 0 for the CW lidar.  The

lidar flag is not used by the fast‐time models and is used only by post‐processing routines.  After editing

the cases.i file, the fast‐time models tdp21.exe and, apa34.exe can be invoked.  Figure 3 shows

the environmental initial conditions as well as the *.ADATA file for this case.  The output of APA3.4 and

TDP2.1 is compared with the CW lidar data in Figures 4‐5.

Environmental Initial Conditions ADATA File

# Location: MEM, 36R_Armory 

# Run Number: 1108 

# A/C Type: DC93 

# Wing span* (m): 28.5 

# Weight* (kg): 46653 

# ACspeed* (m/s): 78.1 

# Air Density* (kg/m3): 1.2 

# File was created on 22-Mar-2012 

# File created by Matt Pruis, NWRA 

# 

# yo (m),zo (m),Vo (m/s), bo (m) 

 17.301, 218.589, 1.5512, 22.384

Figure 3:    The environmental initial conditions (crosswind, eddy dissipation rate, and potential

temperature are plotted in the left panel.  The ADATA file for this example case is given in the right

panel.
16 

         

Figure 4:  The circulation strength (m2

/s) predicted by APA3.4 and TDP2.1 are plotted along with the

lidar data in the left panel.    The right panel shows the comparison of vortex descent with lidar

observations.

         

Figure 5:    The vortex trajectories predicted by APA3.4 and TDP2.1 are plotted along with the lidar

data.
17 

List of Contributors

The following individuals (listed in alphabetical order) have contributed in the development and or

evaluation of one or more components of the NASA AVOSS Fast‐Time Wake Models:

 Ahmad, N.N.    (NASA Langley)

 Bagwell, D.R.    (NASA Langley)

 Delisi, D.P.     (NorthWest Research Associates)

 Greene, G.C.    (NASA Langley/FAA)

 Hamilton, D.W.    (NASA Langley)

 Hinton, D.A.    (NASA Langley)

 Johnson, E.J.    (NASA Langley)

 Lai, D.Y.     (NorthWest Research Associates)

 Proctor, F.H.    (NASA Langley)

 Pruis, M.J.     (NorthWest Research Associates)

 Robins, R.E.     (NorthWest Research Associates)

 Rutishauser, D.K.    (NASA Langley)

 Sarpkaya, T.    (Naval Postgraduate School)

 Switzer, G.F.    (Analytical Services and Materials)

 VanValkenburg, R.L.  (NASA Langley)

Acknowledgment

Many thanks to Fred Proctor and Neil O’Connor for reviewing this document and for their helpful

comments and suggestions.

References

Ahmad, N.N., F.H. Proctor, R.L. VanValkenburg, M.J. Pruis, F. Limon Duparcmeur, “Mesoscale

Simulation Data for Initializing Fast‐Time Wake Transport and Decay Models,” AIAA Paper 2013‐0429.

Campbell, S.D., et al., “Wake Vortex Field Measurement Program at Memphis, TN Data Guide”,

Lincoln Laboratory, Massachusetts Institute of Technology.  Project Report NASA/L‐2. 1997.

Dasey, T.J., R.E. Cole, R.M. Heinrichs, M.P. Matthew, and G.H. Perras, “Aircraft Vortex Spacing System

(AVOSS) Initial 1997 System Deployment at Dallas/Ft. Worth (DFW) Airport,” Lincoln Laboratory,

Massachusetts Institute of Technology, Project Report NASA/L‐3, 1998.

Dougherty, R.P., F.Y. Wang, E.R. Booth, M.E. Watts, N. Fenichel, R.E. D’Errico, “Aircraft Wake Vortex

Measurements at Denver International Airport,” AIAA Paper 2004‐2880.
18 

Feigh, K.M., L. Sankar, V. Manivannan, “Statistical Determination of Vertical Resolution Requirements

for Real‐Time Wake‐Vortex Prediction”, Journal of Aircraft, Vol. 49, 2012, pp. 822‐835.

Green, G.C., “An Approximate Model of Vortex Decay in the Atmosphere”, Journal of Aircraft, Vol. 23,

1986, pp. 566‐573.

Hinton, D.A., “Aircraft Vortex Spacing System (AVOSS) Conceptual Design”, NASA‐TM‐110184, 1995.

Hinton, D.A., “Description of Selected Algorithms and Implementation Details of a Concept‐

Demonstration Aircraft Vortex Spacing System (AVOSS),” NASA TM‐2001‐211027.

Han, J., S.P. Arya, S. Shen, Y. Lin, “An Estimation of Turbulent Kinetic Energy and Energy Dissipation

Rate Based on Atmospheric Boundary Layer Similarity Theory”, NASA‐CR‐2000‐210298. 2000.

Perry, R.B., D.A. Hinton, and R.A. Stuever, “NASA Wake Vortex Research for Aircraft Spacing,” AIAA

Paper 1997‐0057.

Proctor, F.H., Hamilton, D.W. and Han, J., “Wake Vortex Transport and Decay in Ground Effect:

Vortex Linking with the Ground,” AIAA‐2000‐0757.

Proctor, F.H., D.W. Hamilton, G.F. Switzer, “TASS Driven Algorithms for Wake Prediction,” AIAA Paper

2006‐1073.

Proctor, F.H., “Evaluation of Fast‐Time Wake Vortex Prediction Models,” AIAA Paper 2009‐0344.

Pruis, M.J., D.P. Delisi, N.N. Ahmad, F.H. Proctor, “Atmospheric Turbulence Estimates from a Pulsed

Lidar,” AIAA Paper 2013‐0512.

Pruis, M.J., D.P. Delisi, N.N. Ahmad, “Comparisons of Crosswind Velocity Profile Estimates Used in

Fast‐Time Wake Vortex Prediction Models,” AIAA Paper 2011‐1002.

Pruis, M.J., D.P. Delisi, “Assessment of Fast‐Time Wake Vortex Prediction Models using Pulsed and

Continuous Wave Lidar Observations at Several Different Airports,” 2011a, AIAA Paper 2011‐3035.

Pruis, M.J., D.P. Delisi, “Assessment of the Capabilities of Six Deterministic Fast‐time Wake Vortex

Prediction Models,” NorthWest Research Associates Report NWRA‐12‐RS443.

Robins, R.E., and D.P. Delisi, “NWRA AVOSS Wake Vortex Prediction Algorithm Version 3.1.1,” NASA

CR 2002‐211746.

Robins, R.E., Delisi, D.P., and Greene, G.C., “Algorithm for Prediction of Trailing Vortex Evolution,”

Journal of Aircraft, Vol. 38, 2001, pp. 911‐917.

Sarpkaya, T., “New Model for Vortex Decay in the Atmosphere,” Journal of Aircraft, Vol. 37, 2000, pp.

53‐61.

Sarpkaya, T., R.E. Robins, and D.P. Delisi, “Wake‐Vortex Eddy‐Dissipation Model Predictions

Compared with Observations,” Journal of Aircraft, Vol. 38, 2001, pp. 687‐ 692.
19 

Zak, J.A., “Cases of Interesting Meteorological Conditions during Wake Vortex Measurements at

Memphis, Tennessee during August 1995”, Vigyan Interim Report for NASA Contract NAS1‐19341. 1996.
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NASA AVOSS Fast-Time Wake Prediction Models: User’s Guide 

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Ahmad, Nash'at N.; VanValkenburg, Randal L.; Pruis, Matthew

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conditions. The aircraft dependent parameters include the initial vortex descent velocity and the vortex pair separation 

distance. The atmospheric initial conditions include vertical profiles of temperature or potential temperature, eddy dissipation 

rate, and crosswind. The current distribution includes the latest versions of the APA (3.4) and the TDP (2.1) models. 

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model run and a brief description of the Memphis 1995 Wake Vortex Dataset is also provided. 

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