THE EFFECT OF VARIABILITY AND INSTRUMENTAL ERROR ON MEASUREMENTS IN THE FREE ATMOSPHERE

89 Pages·4.24 MB·English

by  RAPP, R. ROBERT

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Bapp, Robert K 1920-
m The effect of variability and instru**
•«3 mental error on measurements in the
free atmosphere.
vi,80p. tables, diagrs*
Thesis (Ph.D.) - N.Y.U., Graduate
School, 1952.
Bibliographysp.78-80.
091*4.85
1.Atmosphere* 2.Dissertations,
Academic — N.Y.U. — 1952* 1. Me asure •
ments in the fr atmosphere*
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Xerox University Microfilms, Ann Arbor, Michigan 48106
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
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UNIVEK"TY HEIGH. ■-
THE EFFECT OF VARIABILITY AND INSTRUMENTAL ERROR
ON MEASUREMENTS IN THE FREE ATMOSPHERE
R. Robert Rapp
November^" "1951'
* 'I &
>.
A dissertation in the Department of Meteorology
submitted to the faculty of the Graduate School
of Arts and Science of New York University in
partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
Table of Contents
Page
Preface ................................................ v
Abstract.............................................. vi
Chapter I. The Problem.................................... 1
1. Introduction ...................................... 1
2. Prior work on the problem.......................... 3
3. Method of procedure ................................ 5
Chapter II. Design and Analysis of the Experiment ........ 7
4. Design factor for instrumental error .............. 7
5. Design factor for the small-scale variations . . . . 10
6. The complete experiment............................ 13
7. Estimate of the variance due to the instrumental
error.............................................. 14
8. Test for the reality of the fluctuations from the
large-scale value .................................. 18
9. The estimate of the small-scale variance.......... 21
10. The reality of the constants in the equation for
the large-scale component .......................... 23
11. Summary of the design and analysis of the experiment. 26
Chapter III. The Experiment of 10 October 1950 ............ 27
12. The d a t a ...................................... 27
13. The temperature of the standard isobaric surfaces . . 31
14. The height of the standard isobaric surfaces . . . . 36
15. The horizontal wind components................ 42
Chapter IV. Further Applications of the Experimental Design. 6l
16. The April 1951 experiments.................... 6l
17. The instrumentation of the April experiments . . . . 6l
<ltiH003
i
Page
18. The instrumentale rrors for the April data......... 63
19. The reality of thes mall-scale deviations, April
data.............................................. 64
20. The magnitude of the small-scale fluctuations,
April data........................................ 69
21. An application to objective map analysis........... 70
Chapter V. Conclusions, Inferences and Speculation . . . . 74
22. Conclusions........................................ 74
23. Inferences........................................ 75
24. Speculation ...................................... 76
Bibliography .......................................... 78
List of Tables
I. The method for displaying the data derived from
an experiment.................................... 14
II. Sample computation form for wind velocity components 29
III. Estimates of the error variance of the temperature
at standard isobaric levels .............. . . . . 33
IV. The F ratios for testing the reality of deviations
from the mean for the temoerature data of 10 October
1950 ...................'.......................... 34
V. The estimate of the constants for fitting a second-
degree equation in time to the temperature data . . 35
VI. Estimates of the error variance of the heights at
standard isobaric levels .......................... 39
VII. The F ratios for testing the reality of deviations
from the mean for the height data of 10 October 1950 41
VIII. The estimate of the constants for fitting a second-
degree equation in time to the height data........ 42
IX. The wind errors deduced from engineering estimates
of the error variances of Rawin set AN/GMD-1 . . . . 45
ii
Page
X. Estimates of the error variances of the west-east
wind component.................................. 48
XI. Estimates of the error variances of the south-north
wind component .......................... 49
XII. The values of F based on the null hypothesis that
the wind does not change with time.............. 53
XIII. The values of F based on the null hypothesis that
the wind varies linearly with time.............. 55
XIV. Summary of the conclusions which may be drawn
from the analysis of the wind data on 10 October
1950 ............................................ 57
XV. The best estimates of the variance of the small-
scale deviation from the trend on 10 October 1950. 59
XVI. The F values for testing the reality of the
variance about the m e a n ........................ 66
XVII. The F values for testing the reality of the
variance about the trend ............ 67
XVIII. Summary of the conclusions which may be drawn from
the analysis of the wind data on 6, 9 and 10
April 1951...................................... 68
X3X. The best estimates of the variance of the small-
scale deviation from the trend on 6, 9 and 10
April 1951...................................... 71
List of Figures
1. Schematic representation of the effect of error and
small-scale variation on the measurement of a
meteorological parameter ........................ 2
2. Velocity-height curves for the balloon released at
0900 on 10 October 1950 .......................... 30
3. The errors in the height of the standard isobaric
surfaces as a function of height ................ 40
4. The positions of the balloons relative to the point
of observation at km intervals . .............. 46
iii
!
Page
5. The error variances and confidence limits for
the u component of the wind velocity as a function
of height, 10 October 1950...................... 51
6. The error variances and confidence limits for
the v component of the wind velocity as a function
of height, 10 October 1950...................... 51
7. The error variances and confidence limits for
the u component of the wind velocity as a function
of height, 6, 9 and 10 April 1 9 5 1 ............. 64
8. The error variances and confidence limits for
the v component of the wind velocity as a function
of height, 6, 9 and 10 April 1 9 5 1 ............. 65
iv
I
Preface
The Signal Corps of the U. S. Army was faced with the
problem of determining how much of the observed difference in
upper air observations was due to instrumental error and how
much was due to natural variations of the element being measured.
This study was made under the sponsorship of the Evans Signal
Corps Laboratories at Belmar, New Jersey, for the purpose of
providing a partial answer to this problem.
I wish to express my gratitude to the members of the
Department of Meteorology at N.Y.U. for their assistance and
cooperation and to the personnel of the Evans Laboratories for
collecting the data which made this report possible. I wish
to thank Professor J, E. Miller for his guidance and help during
the course of the work} Dr. A. K. Blackadar for his many help­
ful suggestions; Dr. Bernard Friedman for his criticism of the
statistical techniques} Mr. A. Arnold who acted as liason be­
tween the Signal Corps and the University} Messrs. A. Isnardi,
A. Engelman, K. Telegadas and J. Tuttell for performing the
computations} Mrs. Gertrude Fisher for preparing the illus­
trations} and Mrs. Sadelle Wladaver for typing the manuscript.
Above all, I wish to thank my wife, Marjorie, for her material
assistance in preparing the manuscript and her constant en­
couragement during the course of the investigation.
v
Abstract
The nature of the variation of meteorological measure­
ments is discussed and a precise, albeit arbitrary, meaning
is given to the term variability. An experiment is designed
following the precepts of the technique of analysis of variance.
The results of one such experiment are discussed in detail
for the temperature and height of standard isobaric surfaces
and for components of the wind. The application of the de­
sign to several other experiments is considered and some con­
clusions are drawn concerning the occurrence of small-scale
variations in the free atmosphere.
vi
I
1
CHAPTER I
THE PROBLEM
1. Introduction
The study of meteorology is based primarily on the
measurement of various parameters of the physical state of
the atmosphere at many times and many places. These measured
parameters are then used to construct models of the physical
state of the atmosphere, either by the subjective process of
map analysis, or by fitting a mathematical model to the data.
In order to interpret properly meteorological measurements,
it is necessary to know the accuracy with which they are made
and the nature of the variation of the parameter which is
being measured.
Prom the study of the records of autographic instruments
and the analysis of data from a dense network of reporting
stations, it appears that the variation of the physical para­
meters of the atmosphere can be expressed as the sum of the
large-scale changes in time and space (which are studied by
the customary process of map analysis) and a number of short-
period, small-scale, apparently random variations. Thus, any
measurement differs from the value which would be appropriate
to the analysis by a factor due to the small-scale fluctuations
plus a factor due to the error of the instrument. Suppose E
represents the physical parameter which is under study: the
measuring instrument provides a value EQ which differs from
the value which should be used for the analysis, say E, by