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NASA CA — 167664

COMPARATIVE ANALYSISOF

OPERATIONAL FORECASTSvs

ACTUAL WEATHER C,ONOITIONSIN

AIRLINE FLIGHT RLANNING

93 7?7^SEP 1; s--

VOLUME 111 ^,RECEIVEDN NASA Sri FACIL1T►/CV 9R,INlN

N^Ol^9̂ Sl b1^^2^'^^

PRC SPEASDIVISION OF PRC PLANNING ANO ECONOMICS, INCORPORATED

PREPARED FORNATIONAL AMRONAUTICS AND SPACE ADMINISTRATION)

(NASA-CR-167864) COMPARATIVE ANALYSIS CF N85-35536OPEFATIONPL FORECASTS VFPSUS ACTUAL W0THXkLCONDITIONS IN AIRLINE FLIGHT PLANNING, JvVOLUME 3 (PRC Planninq and Economics, Inc.) Unclas96 p HC A05 /MF A01 CSCL ('4b ;3/47 26884

P4"A LEWIS RZBEAACN CENTIERCONTRACT NAS 3-22748

I

I meow No. 2. Odwrnmant Accao.on Nn. 3. A emoven q 'I CAta" Ne.NASA CR-Wlb»

a, me sr10 Susetne I Report OatsComparative Analysis of Operational Forecasts vs. actual

April 196:

6. PVtorm ,ng Orgena st on CodeWeather Canditions in Airline Flight Planning - Volume III

.'. Ir:ff10►1e1 & FWforming Orgemration Aeport NoJohn F. Koit:

10. Wort unit yo.9. f*fornwne Orgen,tatWn Noma mid AddTe

PRZ apeas - Division of M ? lanninq b Economics, Inc. If. Contract or Ghent No1003 New Hyda Park Road1_%ka Success, yew York 11042

NAS 3-Z""48

17. TvPa of Report and 2wiod ^ovwed

Coneraeeot deport12. Sooesonny Agsnev yams and Aoorws

National Aeronautics and Space AdministrationWashington, D.C. 20346

Ia Soonuv„q AVe^cv Cape

19. Suopemenury Notre

?roject Manager, labor: Steinberg, Aircraft ?repulsion Divtsion, NASA LewisRasurch Canter, Cleveland, Ohio 44133

16. Atswect

A study was cocAucted on the impact of more timely and accurate weather data on airl4ne fli;htplanning with the emphasis on fuel savings.

This volume of the report discusses :he results

of Task I1I of the flur aa;or tasks : eluded in the study. Task III cexpsred flight plansdeveloped on the Suitland forecast wick actaal data observed by the aircraft Viand averagedover l0 degree segments). The results shoved that the average difference bet-dean the forecastand observed :tad speed was 9 kcs. without considering direction, and :he average differenceloche component of the forecast wind parallel to the direction of the observed wind •das 13kits. - both indicating that the Suitland forecast underestimates the wind speeds. The Root!lean Square ,LMS) vector error was 30.1 kts. The average absolute difference in directionbacween the forecast and observed wind was .'6 degrees and the temperature difference was Jdegrees Centigrade. These results indicate that the forecast model as well as the verifyinganalysis used to develop comparison flight planr in Tasks I and LI was a limiting factor andchat : he average potential fuel savings or penal q are up to 3.6 percent depending on thedirection of 'light.

17. Key Words (Suapated by Autnor1s11 18. Oisvibu..on Statement

Aircraft fuel savings:teacherFlighc planning

.torch Atlantic track syscam

19. SeeurIty paswf, ;of tfns report? :0, Secunty C-4mif. (of tfus oopi 21. No. of D ow1 22 °ryceUnclassified Unclassified 94

For Sale tly the Nat(onai Tectlmcal information Service, 3pringfleld. Virginia 22161

4ASA -C•16f- ( Rr. 10-73)

^!'{i SPEAS

TABLE OF CONTENTS

PageNumber

1. INTRODUCTION ........................................... 1

2. SUMMARY ................................................ 2

2.1 Magnitude of Forecast Differences ................. 42.2 Sign of of Forecast Differences ................... 5

3. ANALYSIS METHODOLOGY ................................... 8

3 .1 Data Sources ...................................... 83 .2 Data Normalization ................................ 10

4. FINDINGS ............................................... 174.1 BLUE Airlines Findings ............................ 174.2 Supplemental BLUE Airlines Findings ............... 234.3 RED Airlines Findings.... ... . .................... 254.4 Supplemental RED Airlines Findings ................ 29

i

APPENDIX A - FINDINGS BY REGION, DIRECTION OF FLIGHT ANDAIRLINE

Pf'O SPEAS

1. INTRODUCTION

PRC Speas, assisted by David R. Bornemann Associates, Inc., has conducted

analyses of flight plan data for the National Aeronautics and Space

Administration-Lewis Research Center under Contract #NAS3-22748.

The objective of these analyses was to assess the potential improvements

in fuel savings which may be possible from improved meteorological

data. Flight plans calculated from prescribed input parameters and

meteorological data sets were used as quantitative indicators of differ-

ences in fuel burn and other relevant parameters. Flight plan data were

provided through the cooperation of two airlines which will be referred

to as "BLUE Airlines" and "RED Airlines" throughout this report in order

to itaintain anonymity.

The work program under this contract was divided into four tasks. This

volume of the final report presents the findings of Task III which

involved comparisons of actual flight plan winds and temperatures from an

operational forecast with the actual winds and temperatures observed by

flights equipped with an Aircraft Integrated Data System (AIDS).

Subsequent sections of this volume describe the analysis methodology and

the results for Task III.

1.

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2.

2. SUMMARY

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The Task III analysis compared actual wind and temperature observations

taken by AIDS equipped aircraft during eight months of 1979 with data

from the flight plans used by those flights. The flight plans were based

`. upon the NWS forecasts valid near the time the flights operated and were

G computed on the RED or BLUE Airlines flight planning systems. Flight

3 "plans for flights of the other airlines that use the BLUE Airlines system

were also ir..luded in this analysis.

The objective of the Task III analysis was to determine differences that

existed between the forecast winds and temperatures and those actually

observed by the aircraft. In Task I, differences were determined

(measured by fuel burn, flight time and air miles) between the forecast

and the actual as represented by the NWS forecast and analysis models,

after the data were subjected to the editing, smoothing, and other

adjustments inherent in the model.

The key findings in Task III were:

•

Based on analysis of 2,430 flight segments when the flight planwinds and temperatures based upon the NWS forecast were comparedto actual data observed by the aircraft and averaged over 10 degreesegments, difference between the forecast and observed wind speedwas 9 kts., the direction difference averaged 26 degrees and theaverage temperature difference was 3°C. The average difference inthe component of the forecast wind parallel to the direction of the

i

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observed wind was 13 kts. The Root Mean Square (RMS) vector errorwas 30.1 kts. When the wind is always from the direction withmaximum impact on the direction of flight a 13 kt. error results infuel burn and time penalties of up to 15 minutes and 2,835 kg (932gal.) of fuel for the average B747 flight. lhese flight segmentswere from operational routes which were not minimum fuel tracks andmay not have been in the area of maximum wind and thus actual errorsmay be larger.

• Although BLUE and RED Airlines data agreed that the absolute valueof the average temperature errors was 3°C, BLUE found the temper-atures warmer than forecast while RED found them colder thanforecast. Similarly, BLUE found the wind direction forecast errortoward decreasing azimuthal directions while RED found errors towardincreasing azimuth eastbound and decreasing westbound, indicatingthat weather data interpolation errors probably exist in one or bothflight planning systems.

Computer programs were developed to extract the wind and temperature data

from the flight plans and AIDS tapes, reduce them to comparable flight

segments, and produce statistics on the differences between the forecast

and actual winds and temperatures. While the flight plan winds and

temperatures were normally already available as averages'of ten degree

longitude segments, the AIDS observations were typically spaced at 200 km

intervals and averages for 10 degree segments had to be developed.

A cubic spline function was used to represent the AIDS flight's wind

direction, speed, temperature and latitude as a continuous function of

longitude along the flight path. The discrete values of these parameters

were then determined for each five degree meridional crossing - i.e.,

50W, 45W, 40W, 35W, etc. Average values for the ten degree segment

were then determined weighting the midpoint twice the weight of each

endpoint.

3.

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Segment data were checked for matches of month, day, flight number,

origin, destination position and flight level. Segments for which the

AIDS flight did not match the operational flight plan were discarded.

2.1 MAGNITUDE OF FORECAST DIFFERENCES

Matching data from AIDS flights and flight plans were found for 2,430

segments distributed regionally as follows:

SLUE RED

Airlines Airlines

Eastbound North Atlantic 394 358

Westbound North Atlantic 696 736

Eastbound Polar 4 79

Westbound Polar 13 109

Eastbound Mid-Atlantic 9

Westbound Mid-Atlantic 32

Differences between the flight plans and AIDS data per flight segment,

and thus between the forecast and the observed, are summarized below:

SLUE RED

Airlines Airlines

Average Algebraic Difference

Wind Direction -5 deg +1 deg

Wind Speed -9 kts -5 kts

Temperature -2°C +1°C

Average of Absolute Values of Differences

Wind Direction 29 deg 20 deg

Wind Speed 14 kts 13 kts

Temperature 3°C °C3

Average Difference in Component of 16 kts S kts

Forecast Wind Parallel to Observed Wind

RMS Vector Error 33 kts 24 kts

4.

pro sPEAs

5.

Using data from Task I on average North Atlantic flight times and fuel

burns, it was determined that if the wind were always from the direction

with maximum impact on the direction of flight this error results in fuel

burn and time penalties of up to 15 minutes and 2,835 kg of fuel for a

8747 flight. This fuel burn penalty, or potential savings, amounts to

3.6 percent of the fuel burn for the flight.

Since the criteria for matching AIDS flights and flight plans resulted

in some 70 to 80 percent of segments being rejected, a supplemental j

analysis was conducted with relaxed criteria to expand the size of the

sample. In this second run segments with flight level differences of

plus or minus 2,000 feet between the flight plan and AIDS data were nut

j

rejected. This resulted in a sample of 1,788 BLUE Airlines segments and

1,282 RED Airlines segments for a total of 3,070 segments. Even though

the sample increased by 72 percent the average forecast error only

changed by 0.5 degrees on wind direction, 0.2 kts. on speed, and 0.34°Ca

on temperature, leading to the conclusion that the original sample was

large enough to be representative of the real world even though many data

had to be rejected.

2.2 SIGN OF FORECAST DIFFERENCES

Since the average algebraic differences between the forecast values and

the observed values were determined by subtracting the observed value

from the forecast value, the algebraic sign of the differences provided

further data on the forecast errors.

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For the North Atlantic region the means of the algebraic differences

between the operational flight plan and the AIDS data were:

Temperature Wind Speed

( C) Direction (deg) kts

BLUE Airline

Eastbound -2.28 -5.35 -8.27Westbound -2.53 -4.17 -8.97

RED Airline

Eastbound +1.97 +1.94 -6.39Westbound +1.69 -2.04 -4.24

For both airlines the average wind speed differences were always nega-

tive, meaning the AIDS winds were stronger and implying that wind speeds

were underestimated which confirms the findings of the other tasks in

this study.

Negative temperature differences mean temperatures were warmer than

forecast and the findings on temperature were somewhat incongruous.

Even though both airlines' data agreed that the temperature forecasts

were in error by approximately 3 0C, the BLUE Airlines data showed the

temperatures warmer than forecast while the RED data implied temperatures

were colder than forecast (positive differences). Regarding wind

direction, negative differences mean the forecast wind is from a lower

azimuthal direction than the actual wind, or in other words, considering

6.

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that tl-io average wind direction should be from 270 degrees, negative

differences suggest actual winds more northwesterly than forecast

and positive differences suggest actual winds more southwesterly than

forecast. On wind direction, the BLUE Airlines differences were always

negative while the RED Airlines differences (for the larger North

Atlantic sample) were positive eastbound and negative westbound. No

information available to PRC Speas suggests an explanation for these

latter two incongruous findings and it is suspected that they are the

result of features peculiar to the weather data interpolation techniques

in use by the RED or BLUE Airlines or both.

7.

PrC SPEAS

3. ANALYSIS METHODOLOGY

The objective of Task III was to determine differences that existed

between actual winds and temperatures and those derived from the National

Weather Service forecasts by airline flight planning systems. In Task I

airline flight plans were used to determine differences that existed

be*ween the forecast and the verifying analysis as depicted by the

NWS models, the Seven Level Primitive Equation Model and the Flattery

Analysis Model, but this approach could not detect anomalies that may

have been introduced by the flight planning systems or the NWS forecast

model. Here, the forecast winds and temperatures from operational flight

plans were compared directly to winds and temperatures observed by AIDS

equipped aircraft and the results may represent the most accurate measure

to date of the differences between expected wind/ temperature fields and

those actually encountered.

3.1 DATA SOURCES

The data included in Task III were collected for NASA during 1979 by

eight international airlines. Flight plans and AIDS data were collected

from the seven airlines that use the BLUE Airlines flight planning

system, and from RED Airlines. AIDS automatically collected on-board the

aircraft and stored on magnetic tape, readings of position, altitude,

temperature, wind velocity and time. Since AIDS was coupled to the

8.

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9.

Inertial Navigation System (INS) and other on-board computers, the data

gathered by AIDS were extremely accurate.

Data collected by the airlines using the BLUE system were collected

during the first four months of 1979 and for August through November.

Data from RED Airlines flights were collected for the same months except

that July was included and November was not. However, no RED AIDS data

were available for January, February and March. Therefore, the analysis

of RED Airlines data was based on the five months - April, July, August,

September and October.

Data were collected by the eight airlines for some 250 days by some 80

AIDS equipped aircraft. Since most of the airlines were principally

North Atlantic operators, most of the AIDS data were for the North

Atlantic, Middle Atlantic, Caribbean or Polar regions. However, some

data were collected by flights through the Mid East or Far East.

u

Flight plans for RED Airlines AIDS equipped flights were collected for

NASA on magnetic tape throughout the year. Copies of all BLUE Airlines

flight plans produced on the BLUE flight planning system were also

collected. Raw AIDS data from the various airlines were collected,

quality controlled and reformatted by a government agency as part of a

global weather experiment.

PrC SPEAS

10.

3.2 DATA NORMALIZATION

NASA specified that the Task III analysis should compare flight plan

segments of 10 degrees of longitude with corresponding AIDS segments.

Therefore, the principal data reduction task was the normalization of the

flight plan and AIDS data in to common 10 degree segments.

i

For most off-airways segments flight plan data were already presented

in 10 degree segments. For these segments the forecast winds and

temperatures could be read directly from the RED Airlines flight plans

and derived from the wind data on the BLUE Airlines plans. These winds

and temperatures represent the average values for the 10 degree segment

as determined by the respective flictht planning system. Since each of

these airlines use a different algorithm for interpolation between data

points, it is not likely that both would develop identical winds and

temperatures for any given segments. The values they do develop,

however, must be considered to be reasonably representative of the

average segment winds and temperatures determined from the NWS forecast,

and represent the techniques which are used by many of world's airlines.

For airways segments identified on the flight plans by navigational aids

or other checkpoints, 10 degree longitude segments were not clearly

defined. Latitudes and longitudes locati ng airways checkpoints were

not included on many of the flight plans making it impossible to define a

10 degree segment on airways. It may have been possible with manual

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11.

intervention in the otherwise automated analysis process to define

airways segments of approximately 10 degrees of longitude. However, due

to such things as multiple use of the same checkpoint identification in

different parts of the world and the highly variable length of airways

segments, this analysis would have been very difficult and would have

added little additional data since most of the segments were off airways.

Normalizimi the AIDS data to 10 degree segments was a more complex

problem. AIDS data could not be compared directly, since AIDS reporting

points did not coincide with flight plan checkpoints. Although both sets

of data followed the same track (or else the flight was rejected as a

mismatch), the AIDS data were captured every 13 or 14 minutes at random

positions along the route. On a typical North Atlantic flight, there

would be about 20 AIDS observations between SOW and 1OW longitude. By

contrast, the corresponding flight plan would include only six or seven

checkpoints, normally at ten degree meridians and whole degrees of

latitude. Before any meaningful data comparisons could be made, it was

necessary to develop a technique to "map" the'AIDS observations onto the

flight plan checkpoints.

After considering linear and geographic interpolation schemes similar to

those used in the RED, BLUE and other airline flight planning systems it

was decided that the AIDS wind direction, speed, temperature and latitude

should be represented as continuous functions of longitude along the

prc SPEAS

12.

e

flight path and representative segment values determined from these

functions.

An interpolation technique was therefore required to develop simulated

AIDS data at the flight plan positions, i.e., ten degree meridians and

whole degrees of latitude, for purposes of comparison. Normal curve fit

routines, such as multiple regression or Box-Jenkins techniques, were not

deemed suitable for this purpose; these techniques are generally used to

forecast or extrapolate data outside the range of observations; however,

this task required careful interpolation of data between observations.

The Polynominal approximation is considered to be the best technique for

this purpose.

The AIDS data elements of interest (temperature, wind speed, and wind

direction) all have the property that they are "continuous", i.e.,

are gradually changing over time (or distance) and do not have discon-

tinuities or gaps in the data. Temperatures, wind velocities and

directions change gradually and do not Jump from one value to another.

For this type of data, cubic polynominals have been found to produce the

best interpolations; cubic polynominals produce a continuously varying

curve, or "spline", through the data observations in such a way as to

minimize errors in curvature. This technique has been previously

applied to meteorological conditions.

prc sPEAsfi .

13.

This "cubic spline" technique was applied to all AIDS flights with

tiat least 14 data reports, and for which a corresponding flight plan

existed. Longitude was used as the independent variable in the spline

develo;nent process, so that data (temperature, east-west and north-south

component of the wind) could be derived for any longitude. These data

were computed For every five degrees of longitude, and then a "1-2-1"

weighting technique was applied to calculate the average value for a

given ten degree segment so as to correspond to the segments on the

flight plan. (The 1-2-1 weights are simply Romberg integration with two

sub-intervals.) For example, the calculation of the average temperature

for a segment from 30W to 40W longitude was based on single weighting of

the derived temperatures at 30W and 40W combined with a double weighting

of the 35W temperature.

The following table of wind speeds and temperature, based on AIDS data

for a trans-Atlantic flight, demonstrates the cubic spline technique:

F

PrO SPEAS

z;

14.

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WIND SPEED (KTS) TEMPERATURE (-°C)

Spline AIDS Lat/Long AIDS S line

-- 34 44N/80W 47 --

62 45,59 75W 47,47 47

93 65,86 46N/70W 47,48 48

102 110 65W 48 47

68 95 49N/60W 46 4356 60 55W 42 43

52 -- 51N/50W 50,56 50

100 80,110 45W 56 56

91 112 52N/40W 55,57 55

76 9,79 35W 58 57

53 70 53N/30W 57,59 57

45 51,46 25W 59 59

65 49 54N/20W 57,51 57

64 66,63 15W 50 50,51

84 72 55N/1OW 47,49 47

107 87,119 5W 53 49

100 107 54N/OW 54 53

These derived spline values were then subjected to the 1-2-1 weighting

techniques to produce the following segment averages:

44N/80W to 46N/70W 64 kts, -47°

46N/70W to 49N/60W 92 kts, -460

49N/60W to 51N/50W 58 kts, -45°

51N/50W to 52N/40W 86 kts, -540

52N/40W to 53N/30W 74 kts, -570

53N/30W to 54N/20W 52 kts, -590

54N/20W to 55N/10W 70 kts, -510

rrO SPEAS

15.

These calculated segment averages were then compared to the corresponding

values on the computer flight plan. In accordance with standard meteoro-

logical practice, all calculatirns involving wind were performed on the

scalar components of a given wind velocity; these scalar components were

then recombined to produce the appropriate wind vector.

Having resolved the AIDS data into 10 degree segments, it was then

necessary to match AIDS segments with the appropriate flight plans

and verify that the routes, flight levels, and forecast times were

comparable.

The BLUE Airlines flight plans were collected by copying the outgoing

queue of all flight plans produced by the system and periodically dumping

the queue onto magnetic tape. Thus, these tapes included many plans that

were not relevant to this analysis which had to be removed from the data

during preliminary processing. A more significant problem resulted from

the presence of more than one flight plan for the same flight. When

several flight plans existed for the same flight number and date the

plan that the aircraft actually followed had to be determined first by

comparing the plans to the AIDS route. Of course, in some case the

aircraft actually followed a route other than the one in any of thet

plans. In these cases data were salvaged for that portion of the route

which did match.

prc sFFAs

16.

A similar procedure was followed for the RED Airlines data. However, in

this case only plans from AIDS flights were included on the tape.

Having matched operational airline flight plans and AIDS flights a final

check on flight level and routing was made. Flight plan segments with

flight levels or checkpoints that did not match the AIDS data were

discarded initially. However, when it was determined that a large number

of segments was rejected, a second run was made which retained all flight e

plan segments whose flight levels were within plus or minus 2,000 feet of

the AIDS flight levels.

Pr'O SPEAS

17.

4. FINDINGS

****************

The results of the comparisons between the AIDS data and the corre-

sponding flight plan segments based on the operational forecast are

presented in this section. Results from plans developed by the BLUE and

RED systems are presented separately as are findings by region and

direction of flight.

4.1 BLUE AIRLINES FINDINGS

In the initial run, matching data from AIDS flights and BLUE flight plans

were found for 1,148 segments. Data for approximately 11,000 AIDS

segments were collected by the seven airlines using the BLUE Airline

flight planning system. Therefore, matching data were found for some 10

percent of the segments.

Based upon a sampling of the data it was determined that about 16 percent

of the segments could not be matched because the AIDS flight levels or

routings were not the same as the planned routings or flight levels. The

remaining 74 percent of AIDS segments could not be matched to flight plan

segments because a corresponding flight plan could not be found. It was

eventually determined that the BLUE flight planning system output queue

was not dumped onto the magnetic tape frequently enough and flight plans

were lost during 24 to 48 hour periods. It is estimated that this

r.rC SPEAS

resulted in the loss of up to 50 percent of the otherwise valid segment

comparisons,

The regional and directional distribution of the 1,148 valid segment

comparisons was as follows:

North Atlantic Eastbound 394

North Atlantic Westbound 696

Polar Eastbound 4

Polar Westbound 13

Mid-Atlantic Eastbound 9

Mid-Atlantic Westbound 32

As in Tasks I and II, the results of the segment comparisons were

presented in the form of histograms which depict the number of occur-

rences of a given temperature or wind difference between the flight plan

segments. and the AIDS derived segments. These data are included in

Appendix A to this volume of the report for both BLUE and RED Airlines

results. The data in the Appendix present the findings by direction of

flight and region, and include the algebraic mean of the differences as

well as the variance, standard deviation and 90 percent confidence limits

for the temperature difference, the wind direction difference and the

wind speed difference, the difference in speed between the component of

the forecast wind parallel to the actual wind and the actual wind, the

similar difference for the component perpendicular to the actual wind

18.

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19.

i(the cross-component), and the magnitude of the vector difference. The

RMS of the Vector Error is also -included for each region, airline and

direction of flight group at the end of Appendix A.

Figure 4-1 summarizes the BLUE Airlines results by region and direction

of flight. The results are presented in several forms so that they

may be meaningful to the widest audience. It was believed that, tradi-

tionally, pilots and others concerned with flight planning refer to wind

"forecast error" as the differences between the forecast and observed

wind, as defined by the differences between the two scalar quantities

wind directions and wind speed. Thu,, if the forecast wind were 290

degrees at 100 kts. and the observed wind were 270 degrees at 120 kts.,

one would say the "forecast error" was 20 degrees and 20 kts. Using this

definition of "forecast error" the mean forecast error for all segments

was found to be 28.5 degrees and 13.8 kts for the wind and 2.9°C for the

temperature.

Results according to the above definition are identified in Figure 4-1 as

the "Algebraic Differences" which include the algebraic sign of the

average differences between the forecast value and the observed value,

and the "Absolute Value of Differences" which eliminate the sign or

directional nature of the differences.

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Using data from Task I on average North Atlantic flight times and fuel

burns, it was determined that if the wind were always from the direction

with maximum impact on the direction of flight this error results in fuel

burn and time penalties of up to 15 minutes and 2,835 kg of fuel for a

8747 flight. This fuel burn penalty, or potential savings, amounts to

3.6 percent of the fuel burn for the flight.

u

However, this finding may be misleading if taken out of context because,

in reality, elimination of the forecast error would result in a new route

selection for the flight on the improved forecast which would maximize

the savings. In this analysis the route is the same on the AIDS observed

weather as on the forecast weather.

White the presentation of "forecast errors" as defined above will be

meaningful to some, if not most readers, it is not mathematically correct

since the wind is a vector and one cannot refer to the independently

determined differences (or error) between the scalar components as the

difference between the vectors. Therefore, in order that the results

presented here may be related to other mathematically sound forecast

verification data that may be more meaningful to meteorologists, the

other quantities presented in Figure 4-1 were determined.

It is interesting to consider the meaning of the findings regarding the

mean of the algebraic differences. Reference to Figure 4-1 shows that

1-4 `C SPEAS

22.

for both directions, and for nearly all combinations of region and

forecast parameter especially on the North Atlantic where there is

a substantially higher number of observations, all of the means are

negative. Since these differences are obtained by subtracting the AIDS

derived value from the flight plan value, the negative numbers mean

that the AIDS values were larger, on the average. Since the AIDS data

represent the actual and the flight plans represent the forecast, these

data show that wind speeds are higher than forecast (again confirming the

findings from the other tasks) and temperatures are warmer than forecast

on the average. Regarding wind direction, negative differences mean the

forecast wind is from a lower azimuthal direction than the actual wind,

or in other words, considering that the average wind direction should

be from 270 degrees, negative differences suggest actual winds more

northwesterly than forecast.

4.2 SUPPLEMENTAL BLUE AIRLINES FINDINGS

Since so many segments were rejected because a corresponding flight

plan could not be fjund in the BLUE Airlines data, it was decided that j

the analysis would be rerun with a relaxation of the criteria for

matching segments. It was assumed that, if a substantially higher

number of segments could be included in the sample without changing the

result significantly, the sample was large enough in the first place to

represent the real world and the loss of some of the BLUE Airlines data

did not distort the findings.

,Cf C SPEAS

23.

For the reanalysis run the requirement that segment flight levels match

was changed to a requirement that the AIDS flight segment be within plus

or minus 2,000 feet of the flight plan segment. A match was still

required on the beginning and end points of the segment. Under these

conditions matches were found for 1,788 segments distributed as follows:


North Atlantic Westbound 1,142

Polar Eastbound 4

Polar Westbound 14

Mid-Atlantic Eastbound 12

Mid-Atlantic Westbound 35

A summary of the mean of the differences of the absolute values is

presented in Figure 4-2 for each region and direction along with the

differences between these data and the data from Figure 4-1 which used

the more stringent flight level matching criterion.

The differences of 0.5 degrees on wind direction, 0.2 kts. for wind

speed, and 0.3 0C for temperature are negligible.

As might be expected when more comparisons from different flight levels

are included, the averages of the algebraic differences also changed, but

by relatively small amounts. For the North Atlantic region, each of the

forecast parameters had larger negative differences with the larger

r'I'C.' SPEAS

q

f^

24.

Figure 4-2f

{

TASK III RESULTSSEGMENT FORECAST ERRORS

BLUE AIRLINE DATAr

MEAN OF THE ABSOLUTE VALUES OF DIFFERENCES BETWEEN FORECAST FLIGHT PLANSEGMENTS AND AIDS DERIVED SEGMENTS i

(RELAXED FLIGHT LEVEL MATCHING CRITERION) i

WIND TEMPERATURE

Direction (deg) Speed kts

Eastbound North Atlantic 22.8 15.5 3.4

Westbound North Atlantic 30.7 13.3 3.2

Eastbound Polar 0 0 0

Westbound Polar 42.6 15.7 2.4

Eastbound Mid Atlantic 48.8 13.5 2.4

Westbound Mid Atlantic 54 9.4 1.5

All Segments 29.0 14.0 3.2

^9.

DIFFERENCES BETWEEN ABOVE VALUES AND MATCHED FLIGHT LEVEL VALUES(FIG. 4-2 DATA MINUS FIG. 4-1 DATA)


o Westbound North Atlantic 0.9 0.3 0.2

Eastbound Polar 0 0 0s


N Eastbound Mid Atlantic 9.1 0.9 0.3

Westbound Mid Atlantic 2.8 0 0


Source: PRC Speas Analysis of SLUE Airline data.

pro SPEAS

number of observations, implying that the forecast errors were larger,

which would be expected when different flight levels are compared.

4.3 RED AIRLINES FINDINGS

Matching AIDS data and flight plan data were found for 575 segments which

were included in the statistical analysis. This represents 22 percent of

the AIDS derived segments.

A sample of six day's data was reviewed manually to determine why no

matching segments were found for the remaining 78 percent of AIDS

segments. Based on this sample:

• 28 percent were airways segments;

• 16 percent were at different flight levels;

• 5 percent had different flight numbers and could not be identifiedpositively with the AIDS flight;

• 7 percent were on a different route;

s 22 percent had no corresponding operational flight plan for the samedate and flight number. (The possibility that these flight planshad the wrong flight date was checked but the flights did not existon the preceding or following day either.)

The regional and directional distribution of the 575 segment comparisons

was as follows:

25.

Pf C SPEAS

26.



Polar Eastbound 36

Polar Westbound 47

The RED Airlines results are summarized in Figure 4-3. As with the BLUE

Airlines results, more detailed data are included in Appendix A.

The forecast errors indicated by the RED Airlines data are quite similar

to those from the BLUE Airlines data. The average segment temperature

error is almost identical at 3°C. The wind speed error is slightly

smaller at 12.9 knots. However, the average wind direction error is

nearly ten degrees less at 19.6 degrees. The RMS of the vector error for

the RED data was 24.0 and the magnitude of the vector'difference was 20.2

kts.

While the data in Figure 4-3 confirm that the magnitude of the forecast

errors are comparable to those found in the analysis of the BLUE Airlines

data, consideration of the algebraic differences shows some inconsistency

between the findings for the two airlines.

The negative wind speed differences imply that actual wind speeds are

normally higher than forecast - a finding consistent with the BLUE

Airlines data and with the findings throughout the other tasks in this

study. The predominantly positive temperature differences imply actual

1

^ro SPEps

27.

OMtn 10010 O T N OJIQ NU- NNM O O Nt N

C7 tp N V' co O MOL N 01 O q' v N N N Q1 Ny I I t N N N 1 .-1 NN 1Gl34 ¢

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3mot' W W IJ—

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W Op ++ a7UT] L u L W Z W Z~.' OZ UW v N 7 w ai 7 U W U W W W Wtr L GJ J..1 W i. N +.1 Z Z Z Z p = ^.a, •1- o. ea H •1- o. Ia w o w o wC p V7 i O p N i C y = Cl. I— U- WW C. O'OO O •a Ô G w 0$ Iwi0 Z.w..C7 c L^ E V7 C c W U W U C7 p V1

33F^ Q 33F0-• O O E C

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2s.

temperatures colder than forecast and, as discussed earlier, positive

wind direction differences mean winds from a lower azimuthal heading or

more southwesterly than forecast while negative differences denote winds

more northwesterly than forecast, or from a higher azimuthal heading.

These data suggest two incongruous conclusions. First, even though

both RED and BLUE agree that the average segment temperature forecast is

in error by VC, one airline consistently finds the forecast temper-

atures too warm while the other finds them too cold. Second, wind

direction forecast errors tend to be dependent on the direction of

flight, according to the RED Airlines data.

Since the average direction errors are so small, the second conclusion

may be merely a statistical quirk. If it is not, it cannot be explained

by any information that was available to PRC Speas and it is suspected y

that it is the result of the weather data interpolation scheme used by

RED Airlines. Similarly, tnere is no explanation for the BLUE Airlines'

tendency toward larger and more northwesterly wind direction errors and

it too must be the result of an inherent feature in the flight planning

system.

Regarding the temperature errors, no explanation can be offered for the

inconsistency and these must certainly be the result of the flight

planning system's processing algorithm.

r,rCi SPEAS

29.

4.4 SUPPLEMENTAL RED AIRLINES FINDINGS

Although the supplemental run was conducted primarily because of the lost

BLUE Airlines data, the RED data were also included in the rerun with the

relaxed flight level criterion.

In the rerun 707 additional matching segments were found bringing the

total to .1,282. These segments were distributed geographically as

follows:



Polar Eastbound 79

Polar Westbound 109

The results of the analysis with the supplemental data are summarized in

Figure 4-4.

As with the BLUE Airlines data, the 120 percent increase in the number of

segments compared did not change the results appreciably. The average

wind direction error changed by 1.9 degrees, the speed changed by 0.4

kts. and the temperature changed by 0.4°C.

rrC saeAs

30.

Figure 4-4

TASK III RESULTSSEGMENT FORECAST ERRORS

RED AIRLINE DATA

MEAN OF THE ABSOLUTE VALUES OF DIFFERENCES BETWEEN FORECAST FLIGHT PLANSEGMENTS AND AIDS DERIVED SEGMENTS

(RELAXED FLIGHT LEVEL MATCHING CRITERION)

Eastbound North Atlantic

Westbound North Atlantic

Eastbound Polar

Westbound Polar

All Segments

WIND TEMPERATURE

Direction (deg) Speed (kts)

16 16.4 3.6

22.8 12.0 3.4

22.0 10.5 2.8

30.1 13.6 3.3

21.5 13.3 3.4

i

DIFFERENCES BETWEEN ABOVE VALUES AND MATCHED FLIGHT LEVEL VALUES(FIG. 4-4 DATA MINUS FIG. 4-3 DATA)


Westbound North Atlantic 1.1 0.5 0.4

Eastbound Polar 0.3 1.9 0



Source: PRC Speas Analysis of RED Airline data.

aSPEAS y

t'_

APPENDIX A

FINDINGS BY REGION, DIRECTION OF FLIGHT, AND AIRLINE

SPEAS 3

80 ; A-1

78 I7674

72 I70

68 * I

66 * I64

62 I

60 I

58 * I

56 I

54 * I

52 e I50 »

48464442*40};^r

38 zxi

3634

32 z*ax

30 irks

28 ^m^•26 atc^^Tr24aa#af22rv^^20#8 iri?: iiE

18 ^^ a-0f#? 49E16

14 #xix:^F^' E

12 i2' ?F #• ir 9E it ?F xx

10 3 bx f £i $Y$F.#

B # fs?F"x}g ?Fa &xdE

6 uatr:zY*x*

4 » ;r:x x=awe

Z iE?.^'.F ?E ?F ?:.?fi3?53E ?F #iE :x ii if ?^ i

-----+----+----+--------- .----+---------+--- ---------------+-30 -20 -10 0 +10 +20 +30

NUMBER OF OCCURRENCES BY DIFFERENCE

Temperature Difference in Degress Centigrade

Operational Segments MINUS AIDS Derived Segments

MEAN = -2.27664975.VARIANCE - 9.91585072MEAN (ABSOLUTE DIF.)= 2.99746193STANDARD DEVIATION = 3.1489443890% CONFIDENCE LIMITS -7.45666326 TO 2.90336376

TOTAL OCCURRENCES = 394

CARRIER: BLUE DIRECTION: East pound REGION: North AtlanticSPEAS

A2

76 j7472

68666#626058565#5250#B |#6##424038 .

3432 .a

28 $| )262; ,..,

\2 .a,21816 ! ,-,,,#g e a s .22m , w wa,. - «w§

, eaaw,eaa,ww .# . leaeaeaww#,eal,2ela#,w#waaaa#weawew#

_.+..+ -- .. --. -- — -------------------------- \ ,.q -6o -o 0 qo a0 a0 } /

R2Q OF OCCURRENCES A DIFFERENCE \

Wind Direction Difference in Degrees : \

Operational Segments Rq s AIDS Derived Segments i%

MAN =.5-327288 \VARIANCE _ 1076.98468 tRAN (ABSOLUTE DI J= 22.0228426 *STANDARD DEVIATION = 32.8174447 \9$ CONFIDENCE LIMITS -932483 TO 482399 :}mzL«G9@CES = ##

G9«E: E3 DIRECTION: cab_d REGION: North Atlantic j

s AS

A-3

# #art#x#^###rtY##^:^##^

+----+° --+----+----+----+-----+----+----+----+----+----+----+-90 -6o -30 0 +30 +6o +90


Wind Speed Difference in Knots


MEAN = -8.27226463VARIANCE = 351.0989MEAN (ABSOLUTE DIF.)= 15.3053435STANDARD DEVIATION = 18.737633390% CONFIDENCE LIMITS -39.0956714 TO 22.5511421TOTAL OCCURRENCES = 393

CARRIER: BLUE DIRECTION: Eastbound REGION: North Atlantic

8078767472

6866646260585654525048464442403836343230282624222018161412108642

SPEAS

80

A-47876

74I

72 I7068666462

60 I58

56 I54

52 I50484644

42 I*

40 I*

32 I*

36 I*

34 I*

32 I*

30 I*28 * I*

26 **I***

24 **I***

22 ******

16 * *********

14 ***********

12 *s^***********10 * ****************

8 * ******************

6 * *******************

q * * ************************2 *** * * ***********************************

-90 -60 -30 0 +30 +60 +90

NUMBER OF OCCURRENCES BY DTFFERENCE

Cross—Component Difference in Knots


MEAN = -4.39694656VARIANCE = 478.081619MEAN (ABSOLUTE DIF.)= 15.8676845STANDARD DEVIATION = 21.865071690% CONM- ENCE LIMITS -40.3649993 TO 31.5711062TOTAL OCCURRENCES = 393


>^Ea.

A-5

f^

807876

70686664626058565452504846444240383634323028262422201816141210

8642

fII

^ I

iYYYN^Y

-90 -60 -30 0 +30 +60 +90


Parallel-Component Difference in Knots




SPEAS

807876

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36

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36

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262422201u1614121086

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2

-90 -60 -30 0 +30 +60 +90


Magn7.tude of 4ector Difference in Knots


MEAN = 26.2213741VARIANCE = 445.902648MEAN (ABSOLUTE DIF.)_ 26.2213741STANDARD DEVIATION = 21.116407190% CONFIDENCE LIMITS -8 .51511563 TO 60.9578637TOTAL OCCURRENCES = 393


A-6

i

„^ x

i

{SPEAS

139116 1114 I112 I110 I108 t106 I104 I102 t100 '+ I98 ++ 196 toot

-- -A--------------"m92 +'+I90 +'•I88 +" I86 "'+I84 a.f.

82 Alto'80 "f # l

78 ... ► •76 A+++"74 ...ff

72 ++"'70 of, of

68 of ..

66 ita,o

64 off ##

62 #++"60 *foil

58 ..raf

56 tilt+54 eee.e

52 a.f sct

50J8 of eau#46 aeff.af

4442 .a#ff r:r

40 ...fffsa

38 ftfaf#t#

36 ...r.f.t

34 lassttlt

32 .efa.s.a

30 fta..f t.

28 lH Oaf O ♦26 .ra.tafaa

24 st #..f arfr

22 fr.f #.f tr.

20 #.afaesef.

18 saf..ff.a.

16 .aassasata

14 fa.tff rfff#

12 ls.s.lsaffs

10 ffa.s.attaf.g .#alaat.ataaa6 ..tat.aaff.afty s tara.a.aaf ea #t..

2 s .leaf r..fct.sa.t

+----+----+----+----+----+----+----+----+--30 -20 -10 0 +10

A-7

-+----+----++20 +30




14EAN _ -2.53448276VARIANCE = 7.70283393MEAN (ABSOLUTE DIF.)= 2.96551724STANDARD DEVIATION = 2.7753979890t CONFIDENCE LIMITS -7.10001243 TO 2.03104692TOTAL OCCURRENCES = 696 SPEAS

CARRIER: BLUE DIRECTION: Westbound REGION: North Atlantic

80 I A-8

78

76 I

74 I

72 i

70 I

68 I66

64 I

62 I60

58 i56

54 i

52 I50;

48 #

46 ;#44;#

42 *i#

40 ^I*

38 {^'*36*34rx #

32 ';x

30 x„#?r#28?tx# ^x? ae

24 Esx 4^?b##Y

22 zy#r: s?: s•? err#

18 N ##} ^3 ^Y F f?.YX?

12 a#r, rxt r?^f;#? a c'} Y . #

8 R #x# ii :i •%Jr##ti$?f ?i$tJ#'.:•l: i R• ?F ^E

4 #ir # # #!f#?:#4r}i?fx?rx3'r#i'r##^?#####?P r'T U.?C # •k ?i !Ex iE !F #?t

2 #kir i•??•?'i;{?}rtii:^.a ii rlii?iz#fr#^'?i3'r y # rL##•Jt.#irk##?F##•n ?e #a^ xrx #?f#}?E it 3?4# i!?: iF ?: ii#1'J

+-------------------+----+----+----+----+----+----+-----------90 -60 -30 0 +30 +60 +90


Wind Direction Difference in Degrees


MEAN = -4.16522989VARIANCE - 2226.48276MEAN (ABSOLUTE DIF.)= 29.8146552STANDARD DEVIATION = 47.185620290% CONFIDENCE LIMITS —81. 7855752 TO 73.4551154TOTAL OCCURRENCES = 696

CARRIER: SLUE DIRECTION: Westbound REGION: North AtlanticSPEAS

80 A-9

78 * ;7674

72 * ;

70 # ;

68 *%1

66 `%f1

64 =rf{

62 % .iyr 160

58 %%1

56 r%154

52 ^;x

50 riai%1*

48 x

46

44 %n%c

42

38

36 s%%% f•%?34_=;:n

32r%% Y. i% Y Y x

28L%_ Y Y%%% Y Y ]a

24

22 % 4 4;:% Y % xy.r %iF !F

16 #i:%#%j•#%f %•a•%F

14 ^' % •rY' }•i' Y Y.Y. _ T .^ 35 Y. ^. Y. S .T.

10 xr ^xza#rrsx%%

YIi ssx_. s..xy. .. ,^;^ y.ys

x xa$--ir xiix ti%

'2 L1Ki X•%%%x'JC'%Fn F'i: t: :t T'F%FT'.^SFn '::'T'%% rF ^: ^:

+ — + + - — + + + + ^ + + — + — + — +

-90 -60 -30 0 +30 +60 +90




MEAN o -8.96839081VARIANCE = 211.024863MEAN (ABSOLUTE DIF.)_ 12.9827586STANDARD DEVIATION = 14.526694890% CONFIDENCE LIMITS -32.8648039 TO 14.9280222TOTAL OCCURRENCES o 696


SPEAS

78

A-10

76 I

74 I

72 I

70 *I*

68 *I*66 *I*64 #I*

62 *I*

60 *I*58 #*I*

56 *#I*

54 #*I*

52 # #*I*

50 if **I*

48 * #*I*

4b *##*I*

44 **#*I*

42 *##*I***

40 *#**I***38 *###*I ****

36 *wi* I *###

34 **#**I*#**

32 **********

30 ****#**###*

28 n^^nxx^^nxT

26 ******######

24 *****#****#*

22 **********#*

20 >t##********#

18 *********#***

16 *#****#**^F***

14 * *##**#***#*#* #

12 * ***************#

10 *******##***#*****g * # **************#***##

6 * #**#****###***###******

4 ** ******#*#*#***********ix* ***

2 * if ** **#***#******#*#****##***********#* if

-90 -60 -30 0 +30 +60 +90


Cross-Component Difference in Knots

Operationai Segments MINUS AIDS Derived Segments

MEAN = -2.97844828VARIANCE = 307.702122MEAN (ABSOLU'rE DIF.)= 13.2284483STANDARD DEVIATION = 17.541440190% CUNFIUENCE LIMITS -31 .8341173 TO 25.8772208TOTAL OCCURRENCES = 69b


SPFAS

80

A-11

78767472

70 #I

68 #I

66 ## I

64 ## I

62 *# I

60 *# I

58

** I56

54 # ## I

525048

46 # ####

44

# ####

42 ######

40 #######

38

########

36

#########

34 #########

32

#########

30 YYY YiiY YYY

28

##########26

24 # ###########

22

# ###########

20 ## ############

18 ###############

16

###############

14 ###############

12 ## ###############

10

##################

8

## ####################6

4 ################################2 ####################################### #

-90 -6o -30 0 +30 +60 +90






SPEAS

A-12II *I

I **

I **I **

I ****

-90 -60 -30 0 +30 +60 +90


Magnitude of Vector Difference in Knots


8078767472706866646260585654525048464442403836343230282624222018161412108642

MEAN =VARIANCEMEAN (ABSOLUTE DIF.)=STANDARD DEVIATION =90% CONFIDENCE LIMITSTOTAL OCCURRENCES =

CARRIER: BLUE DIRECTION: West!

24.908046509.08637324.90804622.5629425

-12.2079944 To 62.0240863696

bound REGION: North Atlantic

SPEAS

80

A-137876

74

I

72

{

68

{

66 I

64626058

56 {

54525048464442403836343230282624222018161412

10 i

i6 i4 i2

--------------------------------------------------------------30 -20 -10 0 +10 +20 +30




MEANVARIANCEMEAN (ABSOLUTE DIF.)=STANDARD DEVIATION =90% CONFIDENCE LIMITSTOTAL OCCURRENCES =

CARRIER: BLUE DIRECTION: East

3.51.51.87082869

-4.0775132 TO

2.07751324

bound REGION: PolarSPEAS

A-148078767472706866646260585654525048464442403836343230282624222018161412108642 ^ la

-------------------------------- -----------------------------90 -6o -30 0 +30 +60 +90




MEAN = 69VARIANCE = 12245.5MEAN ( ABSOLUTE DIF.)= 109STANDARD DEVIATION = 110.65938790% CONFIDENCE LIMITS -113 . 034692 TO 251.034692TOTAL OCCURRENCES = 4

CARRIER: BLUE DIRECTION: Eastbound REGION: PolarSAEAS

A-15807876747270686664626058565452504846444240383634323028262422201816141210

54

si

i

iIii

2 a 1*+----+----+----+----+----+----+----+----+----+----+----+----+

-go -60 -30 0. +30 +60 +90




MEAN = -18VARIANCE = 256.5MEAN (ABSOLUTE DIF.)= 19.5STANDARD DEVIATION = 16.015617490% CONFIDENCE LIMITS -44.3456906 TO 8.34569062TOTAL OCCURRENCES = 4

CARRIER: BLUE DIRECTION: Eastbound REGION: PolarSPEAS

8 f76 I74 I

72 I

70 I68 I

66

64 I

62 {60 I

58 I

56 I

54 I

52 I

50 I

48 I

46 I

44 I

42 I

40 I

38 I36 I

34 I

32 I

30 I

28 {

26 {

24 I

22 I

20 I

18 I

16 i

14 I

12 I10 I

8 i

6 I

4 I

2 **

-90 -60 -30 0 +30 +60 +90




MEAN = -5VARIANCE = 164MEAN (ABSOLUTE DIF.)= 8.5STANDARD DEVIATION = 12.806248590% CONFIvENCE LIMITS -26.0662788 TO 16.0662788TOTAL OCCURRENCES = 4

CARRIER: BLUE DIRECTION: Eastbound REGION: Polar

A-16

SPEAS

807876747270686664626058565452504846444240383634323028262422201816141210

864 i2

-90 -60 -30 0 +30 +60 +90

NUMBER OF

BY DIFFERENCE



MEAN = -34.25VARIANCE = 138.6875MEAN (ABSOLUTE DIF.)= 34.25STANDARD DEVIATION = 11.776565790% CONFLUENCE LIMITS -53.6224506 TO -14.8775494TOTAL OCCURRENCES = 4


A-17

I

,I

SPEAS

807876747270686664626058565452504846444240383634323028262422201816141210864

A-18

2 1 **i---+----+----+----+----+-- -+---+----4----+----+--- t----+

-90 -60 -30 0 +30 +60 +90


Magnicude or Vecror Difference in Knots


MEAN = 35.5VARIANCE = 213.25MEAN (ABSOLUTE DIF.)= 35.5STANDARD DEVIATION = 14.603081990% CONMENCE LIMITS 11.4779303 TO 59.5220697TOTAL OCCURRENCES = 4


SPEAS

A-19 jL^

7876

I I727068 {

64

j60ji

56 ji 54 {

{ 52 {

I4846 I

1i 44 I4 2240 j

3 8I36 {34 I

F 32 I30

is 28 I26 {

{

22

20 {

6 1816 {14 {12 {18

I

42 ar,^ta^ n

+----+----+----+----+----+----+----+----+----+----+----+----+-30 -20 -10 0 +10 +20 +30



Operational Segments MINUS AIDS Derived Segmentsl

MEAN = —1.69230769VARIANCE 3.13609468MEAN (ABSOLUTE DIF.)- 2.15384615STANDARD DEVIATION o 1.7709022290% CONFIDENCE LIMITS -4.60544185 TO 1.22082646TOTAL OCCURRENCES = 13

CARRIER: BLUE DIRECTION: Westbound REGION: PolarSPEOS

A-20807876747270686664626058565452504846444240383634323028262422201816141210

8

J

i

64 {

----- ----------+----+----+----+-_.-------+--------------+------90 -60 -30 0 +30 +60 +90




MEAN = - 17.9230769VARIANCE = 2589.76332MEAN (ABSOLUTE DIF.)= 43.3076923STANDARD DEVIATION = 50.889717290 0A CONFIDENCE LIMITS - 101.636662 TO 65.7905079TOTAL OCCURRENCES = 13

CARRIER: BLUE DIRECTION: Westbound REGION: Polar;PEAS

iAd

A-71807876747270686664626058565452504846444240383634323028262422201816141210

6

I

IiI

I

I

4 I

+----+---------4'----+ — —••+--------------+---------+--.. --------90 -60 -30 0 +30 +60 +90




MEAN = -11. 3846154VARIANCE - 337.159764MEA14 (ABSOLUTE DIF.)- 16.3076923STANDARD DEVIATION = 18.361910790 00 CONFIDENCE LIMITS -41.5899585 TO 18.8207277TOTAL OCCURRENCES = 13

CARRIER: BLUE DIRECTION: Westbound REGION: Polarrfif 0Srens

78

A-22

76 I

74 I

72 I

70 I

68 I

66 I

64 I

62 I

60 I

58 I

56 I

54 I

52 I

50 I

48 I

46 I

44 I

42 I

40 I38 I

36 I

34 I

32 I

30 I

28 I

26 I

24 I

22 I

20 I

18 I

16 I

14 j

12 I

10 I

8 I

6 I

4 I

2 • * * al* ^a*

-90 -6o -30 0 +30 +60 +90




MF.i+N = -8.69230769

VARIANCE = 250.366864MEAN (ABSOLUTE DIF.)= 15.4615385STANDARD DEVIATION = 15.822985390% CONFLUENCE LIMITS -34.7211186 TO 17 .3365032TOTAL OCCURRENCES = 13

CARRIER: BLUE DIRECTION: Westbound REGION: Polar

Pf'C SPEAS

80 I A-2378

76 {

74 {

72 I

70 I

68 I

66 I

64 I

6;P, I

60 I

58 I56 I

54 I

52 I

50 I

48 I

46 I

44 I

42 I

40 I

38 I

36 I

34 I

32 I

30 i

28 I26

24 I

22 I

20 i

16 I

16 {

14 I

12 I

10 I

8 I

6 I4 *I

2 * * I*i----+----+----i-- ^- -+----a-------+------a----+---+

-90 -60 -30 0 +30 +60 +90


Parallel—Component Difference in Knots


MEAN = —19.769230°VARIANCE = 275.869823MEAN (ABSOLUTE DIF.)= 20.0769231STANDARD DEVIATION = 16.60S- _ K90% CUNFIUENCE LIMITS -47.0915777 TO 7.5531161TOTAL OCCURRENCES = 13


PS`C SPEAS

A-2478 I76 I

74 I

72 I

70 I68

66 I64 I

62 I

60 I

58 I

56 I

54 {

52 I50 I

48 I

4b I

44 {

42 I

40 I38

36 {

34 I

32 I30 I

28 I

26 I

24 I

22 I

20 I

16 {

16 I

14 I

12 I

10 I6 j

4 I

2 I* ***

-90 -60 -30 0 +30 +60 +90




MEAN = 26.5384615VARIANCE = 257.171598MEAN (ABSOLUTE DIF.)= 26.5384615STANDARD DEVIATION = 16.036570690% CUNFIUENCE LIMITS .158302828 TO 52.9186203TOTAL OCCURRENCES = 13

CARRIER: BLUR DIRECTION: Westbound REGION: Polar

I

4

SPEAS

A-268078767472706866646260585654525048464442

40

38363432

2826242220

1816141210

i

i

i

8642 * ^^+

+----+----+r---+----+----+----+--"-+---------+----+----+----+-30 -20 -10 0 +10 +20 +30




MEAN = .444444444VARIANCE = 10.0246914MEAN (ABSOLUTE DIF.)= 2.66666667STANDARD DEVIATION = 3.166179390% CONFIDENCE LIMITS -4.76392051 TO 5.6528094TOTAL OCCURRENCES = 9

CARRIE',f: BLUE DIRECTION: Eastbound REGION: Middle Atlantic,crc SPEAS

A-26807876747270686664626058565452504846444240383634323028262422201816141210

8642 f F

+-- - - +- - - - + -- - - +- - - - +- - - - +-- - - +- - - - +- - - - +- - - - +- - - - +- - - - +- - - - +-90 -60 -30 0 +30 +6o +90




MEAN = - 13VARIANCE = 6440.0000111EAN (ABSOLUTE DIF.)= 57.8888889STANDARD DEVIATION = 80.249610690% CONFIDENCE LIMITS - 145.01061 TO 119.01061TOTAL OCCURRENCES = 9

CARRIER: BLUE DIRECTION: Eastbound REGION: Middle AtlanticSPEAS

}

i

i

i

Y.

So I A-2/

78 I767472706866

64 I6260585654

52 I5048

46 I444240

38 I363432

30 I2826

24 I2220

18 I16141210

8 I6

4 i

2 n

+----+----+----+----+----+----+----+----+----+----+----a-----+-90 -6o -30 0 +30 +60 +90




MEAN = -14.4444444VARIANCE = 21.1358025MEAN (ABSOLUTE DIF.)= 14.4444444STANDARD DEVIATION = 4.5973690990% CONFIDENCE LIMITS -22.0071166 TO -6.8817723TOTAL OCCURRENCES = 9

CARRIER: BLUE DIRECTION: Eastbound REGION: Middle Atlantic-7- SPEAS

78 i76

74 I

72 I

70 I

68 I

66 I

64 I

62 I

60 I

58 I

56 I54 I

52 I

50 I

48 I

46 I

44 I

42 I

40 I

38 I

36 I

34 I

32 I

30 I

28 I

26 I

24 I

22 I

20 I

18 I

16 I

14 I

12 I

10 I

8 I

6 I

4 I

2 * *^t

-90 -6o -30 0 +30 +60 +90





CARRIER: BLUE DIRECTION: Eastbound REGION: Middle Atlantic

A-28

.'J y SPEAS

80 I

76 I74

72 I

70 I

68 I

62 I

60 I

k 58 I

56 I54

n

48 I

44

t 42 I

r 40

F

?6 j

34 I

32 I

30 I282624

22 I20

18 I

16 I

10 j

8 I

6 I4

u 2

—90 —60 —30 0 +30 +60 +90


f, Parallel-Component Difference in KnotsK


} MEAN = -17.75VARIANCE = 42.6875MEAN (ABSOLUTE DIF.)= 17.75STANDARD DEVIATION = 6.5335671890% CONFIWENCE LIMITS -28.497718 TO -7.00228199TOTAL OCCURRENCES = 4


A-29

f" ^ SPEAS

i

80 I A-30

76 1

72 I

68 I

66 !

64 I

60 I

94 I

52 I

48 I

44 I

40 j

38 I

36 I

34 I

32 I30

28 I

26 !

24 I

22 I20

18 I

16 I14

12 I10

8 I

6 I4

2 I * ***

-90 -60 -30 0 +30 +60 +90




MEAN = 22VARIANCE = 61MEAN (ABSOLUTE DIF.)= 22STANDARD DEVIATION = 7.8102496890% CONFIDENCE LIMITS 9.15213928 TO 34.8478607TOTAL OCCURRENCES = 4


W1 :SPEAS

I

} A-3178I

767472

68 I1666462605856545250484644424038 i

3634

32

30 i28

26

2422201816141210

864r2}*rx^

+----+----+----+----+----+----+----+----+----+----+----+----+-30 -20 -10 0 +10 +20 +30



O.nerational Segments MINUS AIDS Derived Segments

MEAN = -1.03125VARIANCE - 3.03027344MEAN (ABSOLUTE DIF.)= 1. 146875 .STANDARD DEVIATION = 1.74076806900A CONFIDENCE LIMITS -3.89481346 TO 1.83231346TOTAL OCCURRENCES = 32

CARRIER: BLUE DIRECTION: Westbound REGION: Middle Atlantic`".. SPEAS

A-32SO7876747270686664626058565452504846444240383634323028262422201816141210864'Z 'Ff Y T S jF Y It i X 5 ft' F ^t'X ^I »

----------+---------+--------------+-------------------------

-90 -6o -30 0 +30 +60 +90




MEAN = .9375VARIANCE = 5783.5586MEAN (ABSOLUTE DIF.)= 56.75STANDARD DEVIATION = 76.049711490 00 CONFIDENCE LIMITS -124.164275 TO 126.039275TOTAL OCCURRENCES = 32

CARRIER: BLUE DIRECTION: WestboOnd REGION: Middle Atlantic„i- : SPEFS

i78 A-33

76 I74 I

7o j I

68 I66 I6462 I

58 t

54 I52 I5048 I46 I44 I42 I4038 I36 I34 I32 I30 I28 I26 I24 I22 I20 I18 I16 I1412 I10

8 I6 * I*4 j(.x* r!i x2 X Y. Yt ft J ^! R

------------------- ...._ -_+---------+-------------- •_---+_-----90 -6o -30 0 +30 +60 +90

NUMBER OF OC.CURRENCES BY DIFFERENCE



MEAN = -5VARIANCE = 129.625MEAN (ABSOLUTE DIF.)= 9.4375STANDARD DEVIATION = 11.385297690° CONFIDENCE LIMITS -23.7288145 TO 13.7288145TOTAL OCCURRENCES = 32

CARRIER: BLUE DIRECTION: Westbound REGION: Middle Atlanticr . SPEAS

80

78 I

76 I74

72 I

70 I

68 I

66 I64

62 I

60 I

58 I

56 I

54 I

52 I

50 I484b

44

42 I

40

38 I

36 I

34 I

30 I2826

24 I

22 I

20 I

18 I

16 I

14

12 I

10 I

8 I

6 I

4 ^r I #

-90 -6o -30 0 +30 +60 +90




MEAN = 0VARIANCE = 173.909091MEAN (ABSOLUTE DIF .) = 11.8181818STANDARD DEVIATION = 13.187459690% CONMENCE LIMITS -221.6933711 TO 21.6933711TOTAL OCCURRENCES = 22

CARRIER: BLUE DIRECTION: Westbound REGION: Middle Atlantic

A-34

:i' , SPEAS

8078 A-35

76 I74 I

72 I70 I

68 1

66 I64 I

62 I

60 I58 I

56 I

54 I

52 I

50 I48

46 I

44 I42 I

40 I

38 I

36 I

34 I

32 I

30 I

28 I

26 I

24 I

22 I

20 I18 I

16 I

14 I

12 I

10 I8 I

6 I

4 * I

2 * ** **•*******

-go -60 -30 0 +30 +60 +90


Parallel—Component Difference in Knots


MEAN = —10.4545455VARIANCE = 137.520661MEAN (ABSOLUTE DIF.)= 12.9090909STANDARD DEVIATION = 11.726920490% CONFT)ENCE LIMITS -29.7453295 TO 8.83623856TOTAL OCCURRENCES = 22

1


I + SPEAS

8078767472706866646260585654525048464442403d363432Sri

=dI26

24 i2220

18 I16141210

8 I64

2 I** **

-90 -60 -30 0 +30 +60 +90


Magnitude or Vector Difference in Knots


MEAN = 18.4545455VARIANCE = 71.5206612MEAN (ABSOLUTE DIF.)= 18.4545455STANDARD DEVIATION = 8.456988990% CONFIDENCE LIMITS 4.54279871 TO 32.3662922TOTAL OCCURRENCES = 22


A-36

.J,

'j

i • .y SPEAS

Operational Segments MINUS AIDS Derived SegmentsA-37

RMS or Vector Error = 33.6669438TOTAL OCCURRENCES = 393



RMS of Vector Error = 33.607992TOTAL OCCURRENCES = 69b


k Operational Segments MINUS AIDS Derived Segments

RMS of Vector Error = 38.3861955TOTAL, OCCURRENCES = 4



RMS of Vector Error = 31.0074433TOTAL OCCURRENCES = 13


Operational Segw'its MINUS AIDS Derived Segments

RMS of Vector Error = 23.3452351

s^TOTAL OCCURRENCES = 4


r

kk Operational Segments MINUS AIDS Derived Segments

RMS of Vector Frror = 20.30002244 TOTAL OCCURRENCES = 22

':ARRIER: BLUE DIRECTION: Westbound REGION: Middle Atlantic

• . SPEAS

i

80

A-38

787674727068

66

164

62 a

6058565u

52 l

48

I4644

42

i

40 l

38363432

30

I

28 l

262422

20 x^ e^

1816

14 sus=^^«

12 x=e=:tai

10 'Xe=}axax

8 a=ar. ai'r^ws

6

4 Y ^.°l. lr'Y aLlr' 9C .1 «mot.

2.+ - + Y + -+ - -i. + 1 +..- + ..+ +

-30 -20 -10 0 +10 +2D +30




MEANVARIANCEMEAN (ABSOLUTE DIF.)-STANDARD DEVIATION =90a CONFIDENCE LIMITSTOTAL OCCURRENCES =

1.9634146312.57183233.073170733.54567797

-3.86922563 TO 7.79605489164

CARRIER: RED DIRECTION: Eastbound REGION: North Atlantic

: sP=Fs

80 A-39787674727068 =666462605856545250484644424038 I36 I34 13230282624222018 i16_14^12 ntu*10 % a c•x

8czxa^

6 Ykx ;:.4 Fifl[lS: Y. i•J^t Y'/^ni •̂• Y ••r^•e

2i4# ^'^?E # ?E?ti##if 3k*#?i 2FY i4 N:"r ?Ex :r . ?E !: ".

-- - - - +-- - - --- - - -- - - - -- -- - +- - - - +- - - - -- - - - -- - - - -- - - - -- - - - -- - - - + .-90 -6o -30 0 +30 +60 +90




MEAN 1.93939394VARIANCE = 321.911479MEAN (ABSOLUTE DIF.)= 13.4545455STANDARD DEVIATION = 17.941891790% CONFIDENCE LIMITS -27.575018 TO 31.4538058TOTAL OCCURRENCES = 165


I" SPEAS

4

p

9

80 ; A-40 j

78 {7674 I72 I70686664 ; jl

626058 I ij565452 I50 I48 I4644424038 I3634 I3230 I28

2624222018 I1614 x x x

12 a n110 r. Efi 3 TY^

64 'F:' 1P XfXY.^.G Y1. Y. {'X X:: ^: It F2{'Li

--------------------- - —+ + Y +-- ------------------90 -60 -30 0 +30 +60 +90


Wind Speed Difference in knots

Operational Segments MINUS AIDS Derived ;,egments


CARRIER: RED DIRECTION: Eastbound REGION: North Atlantic'.. SPEAS

7876

74 {

72 I

70 168

66 I

64 I

60 {5856

54 I

52 I

50 I

48 I4b4442

40 I

38 {

36 I34

32 I

30 I

28 I26

24

22 I

20 I

lb I

16 **I14 ***i #

12 *****

6 ********* * **

4 *a*********** * ****

2 * **************************** **

-90 -60 -30 0 +30 +60 +90




MEAN = 3.35757576VARIANCE = 380.944868MEAN (ABSOLUTE DIF.)= 14.8121212STANDARD DEVIATION = 19.51780990% CONFIDENCE LIMITS -28.74922 TO 35.4643716TOTAL OCCURRENCES = 165


A-41

saeas

t^ 54 Y" .J v ^""

76

A-42

74 I72 I70 I6866 I64

6260 I58 I56 I54 I52 I50 I484644 I42403b I

36 I34 I32 I30 I282624 i2220 I1816 * I14i12**I10 *****

+---+---+---i----+-- ^---- i-- t---+-----°---+•----+----+-90 -60 -30 0 +30 +60 +90






:i+ a SPEAS

J

80 I A-43 178

76 I

72 I

68 j

66 i

64 I

58 I

52 { i

50 I

48 I

46 I44

42 I

40 {

38 I

36 {

34 {32

30 I

28 {

26 {

24 {

22 I201d

16 I a^

14 I **

12 I ****

10 I **a*

g I *^t:t**** a

—90 —6o —30 0 +30 +60 +90




MEAN = 23.9515152VARIANCE = 240.288559MEAN (ABSOLUTE DIF.)= 23.9515152STANDARD DEVIATION = 15.501243890% CONFIDENCE LIMITS —1.54803086 TO 49.4510612TOTAL OCCURRENCES = 165

CARRIER: RED DIRECTION:- Eastbound REGION: North Atlantic

( '^ SPEAS a

80

A-44

78767472706866646260

l

5856545250 ; x484644 +f42 ; *^40 ; "•38^x36 ;xf34 ; nT

3230 vix xk2826 xt*24 `**22'

20 + u#

18 :K•e;aeu

1412 Fig cox-rxz.s>

8 1Y"K FIf :]:, ^: TT Y3l'•^

6 ^: 1.:• it•'T T'T 'RY F^''X'4 $$?i %'%ir'^iF fr#^kux

rc i^'Z *

--------------------------------------------------------------30 -20 -10 0 +10 +20 +30




MEAN = 1.6941896VARIANCE = 13.0746757MEAN (ABSOLUTE DIF.)= 3.04587156STANDARD DEVIATION = 3.6158921190% CONFIDENCE LI14ITS -4.25395292

TO 7.64233213TOTAL OCCURRENCES = 327

CARRIER: RED DIRECTION: Westbound REGION: North AtlanticSPEAS

80 } A-46

78 I

76 }

74 i u

72 i70

68 I

66 I

64 }62

60 I

58 i

56 I

54 I52 }

50 }48

46 I

44 I

42 }40

38 I

36 I

34 }

32 I30

28 }

26 ;#

24 I#

22 F# #

20 sit###

18 #it ith#

16 # E> r>.•# #

14 ## # ## it #i

12 #iti # ii##ti###

10 # ##7## Fi iYii #i # #

8 # .x it#^S###^#ie#it #it itS# s

6 # #it it#±it #itf##3i #i4 ii## # xx

2 # ## ### g #i#it#s riit it iF #?: :{###-##i:###-#?i#?i##i: # se# # # # it iF#

+---------+----+---------+----+---------+----+----+----------

-90 -6o -30 0 +30 +60 +90


Mind Direction Difference in Degrees


MEAN = -2.03669725VARIANCE - 1142.64086MEAN (ABSOLUTE DIF.)= 21.706422STANDARD DEVIATION = 33.802971190% CONFIDENCE LIMITS -57.6425848 TO 53.5691903TOTAL OCCURRENCES - 327

CARRIER: RED DIRECTION: Westbound REGION: North AtlanticSPEAS

80 1 A-46

78 {76

74 {72

68 j666462

60 {

58 {

56 {54

52 {

50 I

48 {46444240

38 i

36 {34

32 i

30 F i

28 *„ it

26 iE {f tf {i# x

2 4 1TR y'^l f

22 ff g tf f}

20 tfsffff a

16 It

12 x=tfaf f^eae^

10 s faf:#+ o-y:rl}f

3 ;ffsf}fa v ^^

6 iC^}Yif if •.Y'{f :t i^iffNR'.-1 if tf

14 Z'^}^:'^}'K'1FY11

ii

A-47

n

ov8

76 {74 I72 I70 I68 {66 I64 I62 I60 I58 I56 I54 I52 I50 I48 I4b I44 I42 I40 I38 I36 I*34 I*32 I*

30 'I*28 #* { r^r

26 **I**24 # **I**22 ^t***20**a*

14*********

12 * ******x***

g r* * *********6^sn ** *apt**

-go -6O -30 0 +30 +60 +90




MEAN = -3.11009174VARIANCE = 210.948125MEAN (ABSOLUTE DIF.)= 11.3363914STANDARD DEVIATION = 14.524053390; CONFIuENCE LIMITS -27.0021595 TO 20.781976TOTAL OCCURRENCES = 327

CARRIER: RED DIRECTION: Westbound REsION: North Atlantic

SPEAS

807876747270686664626058565452504846444240

38

*I3634323028262422

20 ********

18 **********

16

14

*********** *12

10 ************* *

8

*************

6

* ****************

4

******************** *2

-90 -60 -30 0 +30 +60 +90


A-48


• Operational Segments 14INUS AIDS Derived Segments

MEAN = 7.55045872VARIANCE = 217.091491MEAN (ABSOLUTE DIF.)= 12.8470948STANDARD DEVIATION = 14.734024990% CONFIDENCE LIMITS -31.7879298TOTAL, OCCURRENCES = 327

TO 16.6870123

CARRIER: RED DIRECTION: Westbound REGION: North Atlantic

f ': SPEAS

80 i

78 I

76 I

74 I

72 I

70 I68

66 I

64 I

62 I

60 I

58 I

56 I

54 I

52 I

50 148

46 I

44 I

42 I40 I

38 I **

36 I **

34 I ******

32 I ******

30 I Y**x::

28 I ******

26 I *******

24 I *******

20 I *******

16 I *********

14 I**********

12 I*********

10 I***********

g I+:ra*******x

6 I*************

4 I************* ***

2 *****************

-90 -60 -30 0 +30 +60 +90


Magnitude or Vector Difference in Knots


MEAN n 18.6636086VARIANCE = 131.788982MEAN (ABSOLUTE DIF.); 18.6636086STANDARD DEVIATION = 11.479938290% CONFIDENCE LIMITS - .220889824 TO 37.548107TOTAL OCCURRENCES o 327

CARRIER: RED DIRECTION: Westbound REGION: North Atlantic

A-49

^i "^ SPEAS

A-508078767472706866646260585654525048464442403836343230282624222018161412.

108

6 ^+ 14 ^e

'Z 1t ah v !E a ii iS ii ?F'. 3e

+---------+------------------------+----+----+----+---------+-30 -20 -10 0 +10 +20 +30




MEAN = -.694444444VARIANCE = 10.2677469MEAN (ABSOLUTE DIF.)= 2.75STANDA9D DEVIATION = 3.2043325290% CONFIDENCE LIMITS -5.96557145 TO 4.57668256TOTAL OCCURRENCES = 36

CARRIER: RED DIRECTION: Eastbound REGION: Polar

c

—f' ' SPEAS

8o { A-51

78 {76 {747270686664 {62 {6058 {56 {54 {52 I5048 {4644424038 I36 I34 I32 ;30282624222018 {16141210 {

864^ ?r2 # :' ??E ?i x?f $?ij t: yr i?i4 £i? '.:'k iE

----_-----i._-__-___-----"'?'___-i---------_-____+___.----__-____+_go _6o -30 0 +30 +60 +90

NUMBER OF OCCURRENCES P,. DIFFERENCE


Operational Se gments MINUS AIDS Derived Segments

MEAN = -3.80555556VARIANCE = 1738.26775MEAN (ABSOLUTE DIF.)= 22.25STANDARD DEVIATION _ 41.E92538390% CONFIDENCE LIMITS -72.3897811 TO 64.77860599TOTAL OCCURRENCES = 36

CARRIER: RED DIRECTION: Eastbound REGION: PolarSPEAS

A-52

iI

80787674'T 270686664626058565452

4846444240383634323028262422201816141210

1

i{

'i

d

u

6 le4'Z ?F x Y u?:2r?inn r1 3i

•i•----•?•----+-------------- ---------------+-----!-----+-....-.1........j.-90 -60 -30 0 +30 +60 +90

NUMBER OF OCCURRENCES B't DIFFERENCE


Operational Segments MI14US AIDS Derived Segments

MEAN = -5.72222223VARIANCE o 308.811729MEAN (ABSOLUTE DIF.)c 12.3888889STANDARD DEVIATION = 17.573039890 00 CONFIDENCE LIMITS -34.6298728 TO 23.1854283TOTAL OCCURRENCES = 36

CARRIER: RED DIRECTION: Eastbound REGION: PolarSPEAS

78 A-53

76 !74 I72 I70 I68 I66 I64 I6260

58 I56 I54 !52 I50 I48 I4b I

4240 I38 I36 I34 I32 I30 I28 I26 I24 I22 I20 I16 I16 I14 I12 I10 I8 * I*6 * I4I

2 **^,,w*

-90 -60 -30 0 +30 +60 +90

NUIEER OF OCCURRENCES BY DIFFERENCE



MEAN = .638888889VARIANCE = 92.73071MEAN (ABSOLUTE DIF.)= 7 .58333334STANDARD DEVIATION = 9.6296786190e CONFIDENCE LIMITS -15.2019324 TO 16.4797102TOTAL OCCURRENCES = 36

CARRIER: RID DIRECTION: Eastbound REGION: Polar

SPEAS

88 A-54

7472 I ^^70 I !?68 I I

66 I64 I i6260 I

56 I54 I ''5250 I48 I4b I4442 I40 I38 I36 I34 i32 I3028 I262422 I20 I18 I16 I

14 I12 I10 I8 I6 * I4 *ar I2 * * *•s•#t^* a

-90 -60 -30 0 +30 +60 +90




MEAN _ -8.72222223VARIANCE = 400.533951MEAN (ABSOLUTE DIF.)= 15.1111111STANDARD DEVIATION = 20.013344390% CONFIDENCE LIMITS -41.6441737 TO 24.1997292TOTAL OCCURRENCES = 36

CARRIER: RED D1.BECTION: Eastbound REGION: Polar

SuIE4S

80 I A-55

78 I76 I74 I72 I70 I68 I66 I64 I62 I6o I58 I56 i54 i52 {

5048 I46 I44 I42 i4038 I36 I34 I32 I30 I28 i26 I24 I22 I20 I18 I16 I14 I12 I10 I

8 16 I#4 {#**2 I* A ,^

-90 -6o -30 0 +30 +60 +90




MEAN = 18.0833333VARIANCE = 240.465278MEAN (ABSOLUTE DIF.)= 18.0833333STANDARD DEVIATION = 15.506942990% CONFIDENCE LIMITS —7.42558775 To 43.5922544TOTAL OCCURRENCES = 36

CARRIER: REM DIRECTION: Eastbound RF,GION: Polar

SPEdS

807876747270686664626058565452

48464442403836343230282624222018161412108642

i

f

A-56

I

I*

si i'r ir,# if Y^?; 3'rx yr i4^ ii--------------------- -- -------- -------------------- _ ------ -_a.

-30 -20 -10 0 +10 +20 +30




MEAN = .391304348VARIANCE - 11.1077505NEAN ' (ABSOLUTE DIF.)= 2.65217391STANDARD DEVIATION = 3.332829290°n CONFIDENCE LIMITS -5.09119969 TO 5.87380838TOTAL OCCURRENCES = 46

CARRIER: RED DIRECTION: Westbound REGION: Polar

SFEAS

A-578078767472706866646260585654525048464442403836343230282624222018

16

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