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i CCRRECTION OF LASER RANGE" TRACKING-DATA FOR ATMOSPHERIC 'i_., REFRACTION AT ELEVATIONS 'ii

ABOVE I0 DEGREES -..-UlNWSIp _ R mira

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X-591-73-351

CORRECTION OF LASER RANGE TRACKING DATA FOR ATMOSPHERIC

i. REFRACTION AT ELEVATIONS ABOVE 10 DEGREES

$.

J. W. Marini

_ C.W. Murray, Jr.

November 1973

GODDARD SPACE FLIGHT CENTER

Greenbelt, Maryland

1 .Q7ANN7NqT_T_ A nq

. • .++ , + 11

!

• CORRECTION OF LASER RANGE TRACKING DATA FOR ATMOSPHERICREFRACTION AT ELEVATIONS ABOVE 10 DEGREES

J. W. Marini

C. W. Murray, Jr.

ABSTRACT

A formula for oorrecting laser measurements of satelliterange for the effect of atmospheric refraction is given. Thecorrections apply above 10° elevation to satellites whoseheights exceed 70 kin. The meteorological measurements

required are the temperature, pressure, and relative humi-dity of the air at the laser site at the time of satellite pass.

The accuracy of the formulr was tested by comparison withcorrections obtained by ray-tz.acing radiosonde profiles°The standard deviation of the difference between the refrac-

tive retardation given by the formula and that calculated by +ray-tracing was less than about O. 04% of the retardation or

about 0.5 cm at 10° elevation, decreasing to 0.04 cm near i _+zenith, i, _,,,

_, v'-

t '++

t

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t Q'TA ¢_-7r_---; -_t-_ ^ ,._ •

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CONTENTS

pag.___c

ABSTRACT .......................... iii

' 1i INTRODUCTION ........................

! REFRACTMTY AT OPTICAL FREQUENCIES .......... 1!

GEOMETRY AND NOTATION .................. 2

EXPANSION FORMULA ..................... 2

EVALUATION OF INTEGRALS ................. 5

CORRECTION FORMULA .................... 5

TEST OF ACCURACY ..................... 6

SUMMARY ........................... 7

REFERENCES ......................... 18

Appendices Pag__..ee

1 Neglect of Satellite Range .............. AI-I ¢

2 Evaluation of Integrals A2-1• • • • • • • • tt • • • • • • •

3 Program for Calculating Refractivity .;_.Profiles from Radiosonde Data ........... A3-1 _

4 Program Listing and Example Calculation ....... A4-1

ILLUSTRATIONS

• Figure Pag.___ee J

I Geometry ..................... 3

2 Tropospheric Range Error at About 80 DegreesElevation for Laser Frequency of O. 6943 Microns . . . 8

6

v PRECEDING PAGE BLANK NOT FILM_D _.t

1974007037-TSA05

5'

ILLUSTRATIONS (Continued)

FI_ Pag_.__c

3 Tropospheric Range Error at About 80 DegreesElevation for Laser Frequency of 0. 6943 Microns ...... 9

4 Tropospheric Range Error at About 40 DegreesElevatiou for Laser Frequency of 0. 6943 Microns ...... 10

fi Tropospheric Range Error at About 40 DegreesElevation for Laser Frequency of 0.6943 Microns ...... 11

- " 6 Tropospheric Range Error at About 20 Degrees

i Elevation for Laser Frequency of 0. 6943 Microns ...... 127 Tropospheric Range Error at About 20 Degrees

Elevation for Laser Frequency of 0.6943 Microns ...... 13

•_ ' 8 Tropospheric Range Error at About 15 DegreesElevation for Laser Frequency of 0. 6943 Microns ...... 14

p

_, _ 9 Tropospheric Range Error at About 15 Degrees" _ Elevation for Laser Frequency of 0. 6943 Microns . 15

' 10 Tropospheric Range Error at About 10 Degrees_ ,: ELevation for Laser Frequency of 0. 6943 Degrees ...... 16

.: ,' II Tropospheric Range Error at About I0 Degrees•., • Elevation for Laser Frequency of 0.6943 Microns .... 17 '_

197413ri71'l 7_T_qn n_

CORRECTION OF LASER RANGE TRACKING DATA FOR ATMOSPHERICREFRACTION AT ELEVATIONS ABOVE 10 DEGREES

INTRODUCTION

The correction of tracking data for atmospheric refraction has been exhaustively• studied, and many correction formulas have been published {1-6 I. For certain

earth and ocean physics applications, however, position accuracies of better_ than a few centimeters are desirable [7}, and these accuracies are much greater

! . than required for most previous applications. Out of the work cited, only theapproach given by Marini [3}, and the expansion and integral evahmttons ofSaastamoinen [5, 61 provide the desired accuracy at lower elevation angles (10° -

20= ). In this report Saastamoinen's integral evaluations are incorporated intoMarini's continued fraction form to provide relatively simple algorithms forcorrecting laser range-data using surface meteorological measurements.

REFRACTIVITY AT OPTICAL FREQUENCIES _

There are a number of formulas [8-11} for the refractive index n of air and forthe corresponding refractivity

N-=IO 6(n- !) (I)

all of which have sufficient accuracy for use here. 2'he formula employed is [12}

(2 , 1N = 87.604+_X2 _4 ,] 1013.25 I +0.003661 t

(2)

(, /('/760 'I+ ..-0.055 013.25 0.00366t _'

where _=_..

- wavelengthof radiationin microns,P

P - atmospheric pressure in millibarse 3 partial water vapor pressure in millibarst -= temperature in degrees Celsius

Because air is dispersive at optical frequp-cies, the group refractivity Ng isalso required

s, ,, d(rN) =s- xdNd"_" (3) .

1

1.c)74nn7n_7_T_ n n-7

. v ¢

Ii

! where f is the frequency. The expression for the group refractivity can bewritten as

f P e

N8 = 80.343 f(X)_-:- |1.3 (4)¥

where

P = Total air pressure in millibars

e = Partial pressure of water vapor (rob)T = Temperature (°K)

and

0.0 ! 64 0.000228f(X) - 0.9650 + + (5)

7,2 7,4

which, at the 0.6943 micron wavelength of the ruby laser becomes

f(0.6943) = i.0000 (6)• it"

" GEOMETRY AND NOTATION

The geometry of the satellite-tracking station configuration is shown in Figure 1._"?; Spherical symmetry is assumed, I.e. the refractivity is taken to be a function of.- height only. The height h is measured from the tracking station upward. The"_i subscript "0" designates quantities evaluated at the tracking station, the subscript.....'" I ttltt, quantities evaluated at the satellite. The rat or phase path between tracking .

,' ] station and satellite is shown as a curved line. _.. ,'rue range R is the distance_ along the straight line connecting the tracking station and the satellite, and thep'_,_| tr,._ elevation angle E is the angle between this line and the horizontal at the,_"!i_,_t_.__,_: station. The nominal earth radids used is re = 63"/8 kin, and H is the height_]_t_i of the tracking station above sea level. The latitude of the tracking st_Ltion is

_i!l_ degrees above the equator. _"

L_2',,:,._'f EXPANSION FORMULA

_ The apparent range Re between the ground station and the satellite as measuredby a pulsed system is given by the integral of the group index of refraction alongthe phase path [13,14]

b' '

,.11_

q

...........i i ................. ......1974r}NTnaT_-T-_

_'t- ' t-• o

i

_, SATELLITE

/

Figure 1. Geometry

|

1974007037-TSA09

o'o •

frorli Rc = sin0 dr (7)

where the angle 0 is given by Shell's law for a spherically stratified medium

nr¢osO = no ro ¢osOo (8) .

The correction sought is the difference between the measured and the true value

of the range

AR = |Ie -R (O)

The expansion of AR in inverse powers of sin0 o, following Marinl [3] gives

AR o_ 10.6fNgdhsin0 o

f; L'_'-o hNgdh -I0 "!2 No Ngdh! (10)

I ]+ 10.12. (NNg-_N 2) dh .sin300

+ooo

where the range of integration is from the tracking station (h = 0) upward toabove the atmosphere (h = 0"). The terms containing the satellite range R thatappear in reference [3] can be neglected, as shown in Appendix 1, because (10)

is to be applied only where E > 10° and h i > 70 kin.

tThe expansion (10) is not the most useful one for many orbit determination pro- t

grams because the correction is _xpressed as a function of arrival angle 00, _ iwhich may not even be measured, rather than as a function of elevation angle E, Iwhich is computed, To convert (10) to the desired for:. the first term of theexpansion of the angular correction is used

o

0o-E = 10.6 NOcotE (ll)

substituting (11) into (10), and making suitable approximations

I

4 ",

"lQTAAN7_'_7 TO ^ _

[ f ]'AR = 10.6 Ng dh •

.r,¢° ,_x_ ,,:,l ro ,,lin_l!+ooo

i' Equ',tion (19-) above is the expansion that provides the basis for the correctionl formula that is the subject of this report.

I

: EVALUATION OF INTEGRALS

t The evaluation of the integrals, appearing in 112), as functions of the pressure,temperature, and relative humidity of the surface air at the tracking station, "

i has been treated by Saastamoinen 161. For completeness, and because they ,idiffer in detail, our evaluations are given in Appendix 2. The results are

10.6 Ng dh - f('_,H) [0'002357Po + 0.000141%] (13)

10"el hNgdh = f(lt) (!.084 x 10"8) P0 TO K (14)

, llyiT" (NNlt" N2)dh = f(lt)(4.734xilY s) • _ (15) r

i

where

''"' f(q,H)= I-0.0026cos2_-0.00031H (16)_,'

_,_- and

'." K " 1.163 - 0.00968 cos2_

,, 117)

_" ' - 0.00104 TO+ 0.00001435P o i

ICORRECTION FORMULA

The formula for calculating the rule error AR from the satellite elevation Eis obtained by approximating (11)by a emtimmd faction form

1974007037-TSA11

fiX) A + IIAR = ...... .

f{_,ll) _inl!+ II/{A+B) (lt"ilshlF,+ 0,01

where

A = 0.0023571' o 40.000141% (1'))

B = (I.084 x I0 "n) Po To K +(4.734x I0"_) P°2 210 (3- I/K) (20)

K = 1.163-O.O0968cos2¢-0.00104To+0.00001435Po (21)

Here

A R -" Range correction (meters)E = True elevation of satellite

P0 = Atmospheric pressure at the laser site (millibars)TO = Atmospheric temperature at the laser site (degrees Kelvin)

, e 0 = Water vapor prensure at the laser site (millibars)f(_) = 1 for a ruby laser, and is given by (5) otherwise

f(¢, H) = 1 for a laser site at 45 ° latitude and at sea level, and is given by (16). _,, for sites at different latitudes ¢ and elevations H (in km) '

J

The water vapor pressure e 0 may be calculated from a relative humidity mea-surement Rh (%)

• 7.5(TO -273.15)

Rh 1023"/"3 + (To " 273.15)- --x 6.11 x (22)ell i O0

In (18) the quantity, 0.01 ts an empirical constant that serves to compensate forthe neglect of higher order terms, The divisor f(,:, H) can be factored out of

.q.,..

•_'' the s_rles (12) and consequently the fraction (18) because the error thereby tn-_'. _* surreal in the second term of (12) is negllgable. The use of the sum A + Bil!_,.,_' where it appears in (18) instead of using A alone is an optional adjustment usedi'.-.;' to reduce at elevations near 90° a small bias that occurs in the expansion (12)"_" because of approximations made in its derivation.

TEST OF ACCURAC'/

, To test the accuracy of formula 118), which ts based on surface measurements,

{ range corrections obtained using the formula6 were compared with corrections /

' ...... ....I 11_- I............

obtained hy ray-tracing radiosonde refractivity profiles. The ray-t_acc cor-

i rcctions arc considered to have statc-of-the-_rt accuracy, so that the differences

between these corrections and those calculated from the simpler formulas re-present the penalty pahl for simplicity in calculation and ._oasurcme_t.

The data used In Figures 2-11 was obtained from the National Climatic Center atAshcvillc, North Carolina. It consists of radiosonde observations taken nearDullcs Airport, Virginia, during the year 1967.

Using the procedure described in Appendices 3 and ,t, 634 refractivity profileswere calculated up to a height of 1000 kilometers from the radiosonde observa-w

tions. The calculatc._i profiles were ray-traced 116] at arrival angles of 10° ,15° , 20 ° , 40° , and 80° , and the tropospheric errors in range and elevation angle

' were obtained. The histograms of these errors are eaown in F_gures 2,4,6,8,

and 10. The correction formula (18) was applied using only surface data and theknown elevation angle to obtain approximate tropospheric corrections. The dif-ferences between these algorithm corrections and the ray-trace corrections werecalculated. The histograms of these differences is rhown in Figures 3,5, 7,9,and 11. The maximum bias of the error remaining after correction was -0.1 cm,and the maximum stondard deviation was 0.49 em at 10° , decreasing to 0.04 cm

'_ at 80° .

In addition formula (18) was compared with range cor:reetions obtained by ray

' tracing (at arrived angles of 10°, 15% 20", 40 °, and 80 _) ,radiosonde refrac- ," tivity profiles calculated at Jananarive (85 profiles), F_tirbanks, Alaska (200

profiles), Athens, Georgia (200 profiles), Greensboro, North Carolina (200profiles), and Nashville, Tennessee (135 proflleas). Th,_ maximum standard ideviation of the error in the algorithm at 10° was 1 centimeter and the maximmnat 80° waI_ 0.06 centimeters. The maximum mean error of the algorithm at 10O _"was 0.16 cm and the maximum at 80° was 0.07era.

1

r._,,:, CONC LUSIONS

.,, An equation that corrects laser range data for atmospheric refraction using sur-".' face meteorological measurements has been de_,iwxi, end a comparison made

r' * '_" •

_. ,. between the ccrreetiolm calculated using this squat;ion (equation 18) and the cor-" reotlon_ calculated by ray-tracing through a radiosonde profile. The compari-

_", son (Ftgurea 2-11) lnd_!cates that the dtfferenc_Js bet_reen the corrections calcu-lated be the two methods are negligible for practt,_al applications. Henceaccurate refraction correction of laser range dat_ c_m be made without the re-

quirement for radiosonde measurements or lengthy ray-tracing algorithms. _.

L

1974007037-TSA13

.8

1974007037-TSA14

o

• e p

• o

4"

1974007037-TSB02

' ' r p _,

• o_ °"

i._ •

: II

1974007037-TSB06

1974007037-TSB07

1974007037-TSB08

1974007(3.37-T.qRnQ

It should be pointed out that only the relative accuracy of the two procedures hasbeen tested, and that errort, caused by factors common to both methods arc notin evidence. For example, equation (4) for the group refractive index is usedboth in 118) and in the ray-trace equations, and any error in its magnitude wouldreflect equally in the corrections. Similarly, the hydrostatic equation used inequation (2-1) and hence (18) is also implicit in the ray-tracing method becausethe heights that appear in radiosonde profiles are not measured quantities butrather are calculated from the measured pressures, temperatures, and relativehumidities using the hydrostatic equation. Also, both methods assume horizontalhomogeneity. Saastamoinon 16l has estimated the standard error from suchsources to be less than 1 or 2 centimeters at 10° elevation.

REFERENCES

i [1] Freeman, J. (1962), Range error compensation for a troposphere withP

i exponentially varyin__g refractivity, J. Res. Nat. Bur. Stand. Sect. D., 66t (6), 695-697.

[2] Hopfield, H. (1969), Two-quartic tropospheric refractivity profile for cor-recting satellite data, J. Geophys. Res., 74 118), 4487-4499.

:, [3] Marini, J. 11972), Correction of satellite tracking data for an arbitrary tro-

" por_pheric profile, Radio Sci., 7(2), 223-231.

[4l Rowlandson, L. and Moldt (1969), Derivation of closed functions to compen-: sate range and angle errors in an exponential atmosphere, Radio Sci. 4(10),

927-933.

, (5] Saastamoinen, J. (1972), Atmospheric correction for the troposphere,_,**, and stratosphere in radio ranging of satellfles, Cecphysical Monograph 15,_:'_ "The Use of Artlflcal Satellites for Goedesy," Amcz'lcan Geophysical Union,_' Washington D.C.

;' 161 Saastamoinen, J. 119721,Contributions to the theory of Atmospheric Re-

:_:, fraction, Bulletin Geodesique 105-107, pp. 279-298, 383-397, 13-34.

(7] (1970) The Terrestial Environment: Solid-Earth and Ocean Physics, NASA, Contractor Report 1579, Prepared under contract NA_' 12-2180 by the Massa-

, chusetts Institute of Technology.

,. [8) Peck, E. and ReederD K. (1972), Dispersion of air, J. Opt. _ec. Am. 62 '(8), 958-962.

i 18i "qI

1974NNTNRT_T n

[9] Barrell, H. and Sears, J. The refraction and dispersion of air for the visi-ble spectrum, (1939) Trans. Roy. Soc. London A238 (1), 1-64.

[10] Edlenp B. (1953), The dispersion of standard alr, J. Opt. Soc. Am. 43 (5)339-344.

[II] Edlen, B. (1966), The refractive index of air, Mctrologia 2(2), 71.

[12] International Association of Geodesy, Resolution No. I of the 13th Geh_eralAssembly, Bulletin Geodesique, 70 p. 360, 1963.

[13] Bennett, J. (1967), J. Arm. Terrestial Phys. 29, 893-896.

i [14] T/ther/dge, J. (1965), J. Arm. Terrestial Phys. 27, 1115-1116. i

i [15] List, R., Smithsonian Meteorological Tables, _,mithsonian Institution,Washington D. C., 1963.

[16] Thayer, G. D., "A Rapid and Accurate Ray Tracing Algorithm for a Hori-•_ zonl_tlly Stratified Atmosphere," Radio Science, Vol. 1, N_. 2, pp. 249-

252_ Feb. 1967.

iiI

19

I .cI741"IN7NCIT_Tq _ I

• '._r_ t%_'_-' '

0

IAPPENDIX 1

NEGLECT OF SATELLITE RANGE

............................................................................................................................................. -- _ - ,i _= ......_ "

1974007037-TSB12

I

I APPENDIX 1

NEGLECT OF SATELIJTE RANGE

The correction

frl I ngAR = sin'--'0dr- R ( I- I)

• can be written as

jro sin0 + _dr- (I-2)0

t The expansion of the first term tn 11-2), using suitable approximations [31, gives

f/rt N8 dr !0:6.ro

n

, '"_ ! 10.6 f-' -_ lh Ng dh

-. sin30o r0 d (I-3)

'_ -I0"I2 Ng (NO N) dl" iI -

+ooo it I

" ... The expansion of the bracketed second term in (1-2), which represents the dif- 1

";_" ference ARg between the geometrical lengths of the phase and th_ straight-line II?. paths between the satellite ,and the tracking station, can be obtained by expanding t:_,9,'_' i

_'_,, equation(AS)of reference [31in inversepowers of sineo giving 1

•.". I i 10. I2f dh l,,: : _, • AR, - • -- N2

._.', , sin30 o 2 J t" (1-4)

I!: i!; I (f N dh)2 COS20o i.-- 10-i 2 .---- _

2 R sin0o4i.

i

II I II I ,J_ _. . __ -; _ - "AI

1974007037-TSB13

st ' .

The relative error incurred in neglecting the last term tn (1-4) is estimated bydividing it by the (dominant) first term in (1-3), ignoring the small differencebetween the mnl_mitudes of N and N g

I 10"6.fN dh ¢os20t_ il-5)l'(2hdJv¢error = -- -

R sin300, m

_, q_ne satellite height h I is roughly approximated by approximated by R sin0 o,and the zenith integral is about 2 meters:

! (1.(,)rclativa error _. _ tdn200

where hi is the satellite hetgi_t in meters. Taking hi >-70kin an._ 0o ;_ 10 ° , theerror calculated from (1-6) is less than 0.05% which can be neglected.

Ib_

1

A1-2

,e I I • _"_ ; ..... ; -- -

1974007037-TSB14

APPENDIX 2

EVALUATION OF INTEGRALS

From the perfect-gas law, the law of partial pressures, and the hydrostaticequation

dP _ Mg (P-e)+ Mwg...__edh RT RT

(2-1)MgP 0.378 MgeRT RT

where LlS]

M ffi 28.966 = Molecular weight of dry airMw = 18.016 = Molecular weight of water vapor

R = 83,1.4.36 Joules (°K)'t (Kg- Mole) d= Universal gas constant

" g = acceleration of gravity (m/s)h = height (m)

Combining (2-1) and (4)

fNg dh=-80.343 fO,) -f- dV(2-2)

+ [30.5f(_)-11.31/Tdh

_,, The first integral on the right side of (2-2) above can be evaluated using the ap-_ .... proximation {15].

- :. g = 9,806 [ 1 - 0.0026 cos2_- 0.00031 (H + h)] (2-3)

.. 1 ° 1

9.806 [ i + 0.0026 ¢os29 + 0.00031 (H + h)] (2-4)

A2-1

1 .qT_.NN7N_.7_T_Pr_ 4

• 4 #

6

qp"

from which, integrating the last term by parts,

I _ [) + 0.0026cos2_o+ 0.00031(II+--LlfPdh)l- _dP = Pc 9.806 Pc(2-5)

= Po/g

where _ is the value of g at the height

ffiDI._-...I'pdh (2-6)"oJ

: above the tracking station or H + h above sea level. Saastamoinen use_ a gravi-_,ational constant evaluated at*

"_H + h = 7._ + 0.9 ti km (2-7)

From (2-7) and (2-3)

" _ = 9.784 (1 - 0.0026 cos 29 - 0:)0028 H)_,, (2-8)

ffi9.784f(9,H)

"" - _ where _ is the station elevation in kilomaters. Saastamoinen has also evaluated ,

• _ .. the integra)

• . dh = 4-_e0 (2-9)r

.,.; imatton. The expression for the zenith integral becomes

mt=,.,,..r,:,, , /Ndhffi80.343 f(7,)_P o

2,1:,'.b m _

f(1,) - 11.31 -_%(2-10)

ti _ *Anequivalentresultcanbe obtainedby numericallyestimatingh using(2-17) with TOset equalto

• Tc + _t! wheie Te is the sea level temperature.

IIill A2-2 ' .,..

,, Tr i , _,

"1974007037-TSCOR

Neglecting small errors in the second term of 12-11), equation 113) results.

ii SECOND INTEGRAL

In equation (12), the magnitude of the coefficient of 1/sin E is about 2.4 meters,while the coefficient of 1/sin 3 E, is only about _ centimeters. At E = 10° , themagnitude of the first term is about 12 meters, while the second is about half ameter. Consequently the second term need not be as accurately evaluated as thefirst, and it is sufficient to use the approximation

i

Ir'_/hN'dh "T"°10+f 80"S4Sf(X)Phdhw (2-12)

• 1where r e ts a nominal earth radius 16378km1 and the air is assumed to be dry.It is also sufficient to treat g as a constant throughout.

From (2-1), and integrating by parts

hdh = _gg Pdh (2-13).j1

• f

The pressure P in (2-131 is obtained by integrating 12-1) _ _:

pffi po exp [_M._f.._ dh] (2-|4) ,_i

• The temperature T is assumed to have a linear slope

T = TO+_h (2-15)

and the integration in 12-14) is carried out g/vtng

/ •P + Po k_O0 / (2"16)

A2-3

q

1974007037-TSC03

IL_ _ •

1!

I

[ ,r1

The integration in (2--13) may now be performed

i R TO i

i f Pdh = Po" M'-'g'' _ (2-17). Mg

From (2-12), (2-13), and (9.-17)

10"6 _ oh Ng dh = f(X) 10"6 (80"343)R2 Po To Kro .J re M2 82 (2-18)

= f(_,)(1.084 x 10"8)Po TOK

where g has been set equal to 9.784 and the factor

K -_ 1 (2-19)

M8

is equal to unity in an isothermal atmosphere (_ = 0) and is equal to about 0.8'" ' in an atmosphere in which the temperature lapse rate is a constant 6° Ikm (ii =

-6°/km).

_ Rather than use the theoretical value for K given by (2-19), which is based on a"_I:." constant lapse rate, the valueof K used in the corrections equations is taken to

- be an empirical constant which was determined by solving (Z-18) for k and cal-•",,, ", culating its value by numerically integrating through the atmospheres of the U.S.",'- Standard Atmosphere Supplements, 1966. Using linear regression on the values

_"+ so obtained, the formula

' '" K = I.163 - 0.00968 cos2_o-0.00104 TO+ 0.00001435 Po (2-20)

"; ,.t resulted. Here I is the latitude of the tracking station.

;"_' THIRD INTEGRAL:L ',"

_ '_"_;" The contribution from the third integral in (12) is only marginally significant,•.,.. and the term can be approximated by

I,_lO-12fNlNdh--- I.Llo'12(80.343)2f(lt)f_2dh (2-21)¢,

i'

A2-4 • ,°,

t

ii i

1974[";(371337_TRrt.n,a_

L_

Assuming a constant temperature gradient, and using (2-16)

f ( 1 )0 1042 ----R P02 I.10-12 N Ng-._-N 2 dh = _(80.343) 2 f(_) Mg To ! + R.P.P (2-22)2mg

The last fa,3tor _,. (2-22) can be expressed in terms of K using (2-19), giving (15).

1974007037-TSC05

b

APPENDIX 3

PROGRAM FOR CALCULATING REFRACTIVITY "

PROFILES FROM RADIOSONDE DATA

Q

,,. ' - =- -_:-I

1974007037-TSC06

IV%

i APPENDIX 3

PROGRAM FOR CALCULATING REFRACTIVITY PROFILESFROM RADIOSONDE DATA*

RADIOSONDE DATA

Radiosonde observations are measurer_ents of pressure, temperature, andhumidity taken from the surface up to the point where the balloon that carriesthe sensors bursts [ 1]. The values of temperature, pressure and relativehumidity measured at certain standard and significant levels during each balloon

i ascent from numerous weather stations is available from the National ClimaticCenter. This data can be used to construct continuous refractivity profiles fromthe surface up to the point of highest measurement. Above the latter point, therefractivity profile can be extended by assuming a suitab]e temperature profile.

GEOPOTENTIAL ALTITUDE

The equations used to calculate the refractivity profiles employ the geo-potential altitude H [ 2, p. 217], which is given by

_'- lSo'_.,"" H - _ gdZ (1)

,%7• ,t

",_ :." where Z is the geometric altitude, and the lower limit of integration is from sea!.: _ level (Z = 0). H is in geopotential meters when G equals 9. 8 m/sec 2. The local............. acceleration cf gravity is calculated from the latitude ¢ by [2, p. 488]'" _ .

, go = 9.780356 (1 + 0.0052885 sin 2 _ - 5.9 ,_10-e sin 2 '_) (2)

_:_, and [2, p. 217]

_:_:" " go r

" . g - (m/sec 2) (3),,,_. (% + Z)2

_,_,. Here ro is an effective earth radius given by [2, p. 218] 1

,,- ' 2 go"';_." r0 = (m) (4)

' " _ 3.085462 x 10-_ + 2.27 x 10-9 cos 2q> - 2 x 10-t2 cos 4_

*Thitappendixis lelf-eontained. It hasseparatereferences,and the notationuseddiffersfromthatin the'Y t

_:.,,:_ rest of the report, tI

_ A3-1 ] 'i"i! ._.

1974007037-T£_N7

• • m _.

_' • /- v

From (1) and (3) the conversion between geopotentlal and gecmetrlc altitude is /

given by [ 2, p. 218]

H = g \r ° + Z/ ,1(5)

and

r0 HZ = (6)

go roH

i- G

VIRTUAL TEMPERATURE

i '' The calculations also make use of the virtual temperature T, [31 which is

related to the ordinary temperature T (°K) by

Tv -- e (7)o, ,: . I - 0.379

where e is the partial pressure of the water vapor in the air, and is given by i

[4, p. 343]

• ,,_ , 1_ 7.s(T- 273.1s),.i023'7.a * -',;_': -- (6.11) (T 273.1S)(mbar) (8)

.' ,,_:, Rh being the relative humidity in percent.*t'L_ :"

_J";,. CALCULATION OF GEOPOTENTIAL ALTITUDES

? _ The first step in the calculation of refractivity profiles from the redlosonde" measurements of pressure, temperature, and relative humidity is to establish a

i_

_ *If the dewpoint temperature Td (°K) isgieen instead of the relative humidity, • can be calculated_i_ :. from(8) by .setting Rh - Ifa and T : Td.

i

A3-2

IIII II

19740071337_T.q_nR

table of pressure, temperature, and virtual temperature versus geopotential alti-

tude. The virtPal temperatures at the given points are calculated from the: measured values of P, T, and R h using (8) and (7).

i To c,tlculate the geopotential altitudes, it is necessary to assume hydrostatict

[' ' equilibrium [3]

dP - -pgdZ (9)

The density p is given with sufficient accuracy by [ 3]

• _ MP

P - RT-'-: (10) .

The apparent molecular weight of dry air is taken to be L2, p. 289]

M- _.966 (II)

• ,_ and the universal gas.constant [ 2, p. 289]

,. _ R = 8314.36 Joutes (°K)'! (Kg-mole) -x (12)

.. Using the assumption that the virtual temperature is a linear function of geo-

,,. potential height between any two adjacent measured points H l and H 2, (9) may be• . integrated with the use of (I) and (I0) to give

_, ' ". GM (H a " S_l)

,.'"_'"'_, P2 : IT,,_ (T,2"T,,)

_::" ' which may be written as

,,..,,, X tn (P2/PI )

Ha Hi + \ GM / in(t + X)

r_

" _

p:

] 974007037-TSC09

X _ (Tv2 - Tvl),/l'v_ (15)

Equation (14) can be used stepwise starting at the known geopotentlal elevation ofthe radiosonde station to compute the geopotential altitudes.* In this way therequired table of pressure, temperature, and virtual temperature versus heightis established.

-- CALCULATION OF REFRACTIVITY PROFILES

-_., The radio refractivity N is given by the formula t [5, p. 71

P (16)_ N = 77.6"_"+ 3.73x10 s eT2._

•_ with P and _ expressed in millibars and T in degrees Kelvin.

To calculate N at a given height, i.e., to obtain a point of a refractivityprofile, it is necessary to know the values of P, T and e at that height. Theseare obtained as follows:

The height is converted to a geopotentlal altitude by adding It to the geometricstation elevation to obtain the geometric altitude Z, and applying (5). Using thegeopotentlal altitude so calculated, the temperature and the virtual temperatureat the given height are obtained from the table of P, T, and Tv vs. H by linearh_terpolation. The pressure at the given height is calculated using (13) with P_,Tv 2 and H2 replaced by the values associated with the given height. Finally thevapor pressure e is calculated from (7). Substitution into (16) then gives therequired refractivity.

*The8eopotenttalaltitudesarecomputedat the radio.sondestationsandare includedin the data stored atthe NationalClimaticCenter. Thealtitudesarezecomputedbothasa check of the self.condstencyof thedataandalsoto senarate 8eopotentlalaltitudesconsktentwith the valuesof the fundamentalconstants

_' ". (R and M, forexample)adopted.

tAt optical frequencies(2) and (4) of the main text areused.

N _ 77.6"_ 1+ _2 J

whet©the wavelen$th S is in microns.

t

A3-4 _i_t

ii

A listing of the FORTRANH program with a sample profile calculated frommetc:_rological data taken at IXIlles airport on 1 January 1967 is shown inAppendix 4,

Also shown are the surface measurements of temperature, pressure andrelative humidity, the tropospheric range error obtained from ray-trace (RANGEERROR), the tropospheric elevation angle error, the tropospheric range error

i approximation (RANGE ERROR APPROX) obtained from using equation (18) of: the main text, and the dtffercr.._e between the ray-trace and the approximation

(RANGE DIFF) for arrival angles of 10°, 15 °, 20 °, 40 ° and 80%

REFERENCES FOR APPENDIX 3P

1. Federal Meteorological Handbook No. 3, "Radiosonde Observations," U.S.Department of Commerce, U.S. Department of Defense, Washington, D.C.,

i January 1,1969.2. List,R. J.,"SmithsonianMeteorologicalTables,"SixthRevised Edition

(Second Reprint), Publication 4014, 1963.

3. U.S. Standard Atmosphere Supplements, 1966, Environmental Science ServicesAdministration, National Aeronautics and Space Administration, United StatesAir Force.

4. Berry, F., Bollay, E., and Beers, N., "Handbook of Meteorology," McGraw-Hill, N.Y., 1945.

5. Bean, B. and Dutton, E., "Radio Meteorology," NBS Monograph 92, March 1,1966.

1974007037-TSCll

i II II

6

,iJt ' APPENDIX 4

, PROGRAM LISTING AND EXAMPLE CALCULATION

}_'

r_ "

/,

t

I

1974007037-TSC12

Jl

*_

I*

#,

_f

1974 0(3713.o,7-T.qP..1q

I

1.q7_.NN7rY_.7_T_P _ ,4

'|

+I@N 0167 .......... MFFI e ._'f .I.........................................................|e_N Gt58 IF iMTF*t ,GE, h) GG TG ?2_,

|_N ¢1/_! T_(|) = TPMP*(V(_)18N <.16,2 ..... _:13. T_J_@|I =-4"I((.1,_ ............................................

C C(2I*PUT_ TH[ HRF.SSUf',_ PR(I) AT TH -+ _A_IOUS *FIXED* L([V[LS*),_N Olf=3_ .- ?aO MTM_,..s-MT _. L ............................

I_N C|64 PR(I) = PRFS$(I)iSN OIlS ..... I_J 789 I_ = ._, HM]b ............|SN 0166 0_ 789 | = |,/4T_I

[SN 0|67 .......... IF((;RMRk:F'([-+I ) .GG..I_G4taR(K.) ....4N_. ,_Hk'F'F(4.el.,I-+.I_Ir_.--HQ_R¢I_&I) ...../_GO TO ?P8

ISN G|69 ........ GO.TO 789 .............ISN 0170 7a_ t_s3 = DAI_S(SI.PKV(K))ISN D_7_ ...... |_:(di_.LE.t.I_C) SI..HK_(I() = t*0._-|_) .....ISN 0173 r_pT = (G_FP4D)/(f_S'rAk_$t.PKV(K))

|&N 0|74_ .... TQP 41 T[ [_RK¥(K| ......ISN 0|7_ 80T = TPMPKV(K) t. St.p_V(K)_(GFMP-_F|IeI| -- HGPR(K))Z _ N 0176 ......... _R (t+[,s). a PPtESSLK) ;; l 0. ODOr _( +I_IILT_O_ n (TOP/_t03) |

ISN 0|77 7_9 COhT|NU_

ISN 01179 St.P_[ • 1,_i+,10ISN OIGG ........ OQ-?_0 i = NT..tNMI ...........

ISN O|@t EXPT = (G_F,'_O)/(PSTAR_$1.OP r'). |SN+ 031,_P..+.......... 'rr)+O..r.. TEMIOKV|.H; ........................................

ISN 0183 B_T _ TE'M_KVAM)+SI-CP_(._PMRFFAI+A)-H,_PR(N)|

_ C COMPUTE THE PARTIAL PRESSURE PJF T,_ _ATI[R VAHCR E(1) AT THE *PIXI[D _

ISN 018_ DO 716 I • 3,N,!SN O| 86 ................ .,_;-.-=. -|.*_J_O .'_ -'( _'_*(-| )/Tl£t_( ;. _.._ ...........

,, [SN ¢1_7 F_ = I,C0010,37_00"'+' ._SN 018,8 ........ 7]._+._(.|J._.a .F2_PR(.|I_FI ............ _ ............

%,C CAt.CUt..ATE_ T_MI=_.I;ATUHF. IN O_GR£_$ C_k.,;IU$ TC(I) FRCM TEMPERATURE |N

; ................. _,, ...... gLE.G&_..¥,_t..V ZN..- TK.( I-)-. FGR .- -N---J.F-._&..T,_* -I,,-_VrtJ,_, ............|SN 01_9 PO 717 | • 1. N

4:; CCI_PUTE 0_Y REFR_CTtVITYe WET RE_RAGF|V[TY, AND TCTA_ REFRACTIVITY

.,. |Sbl Ot$; ..... FGS-TI .= ;R4?.GAtb|)O ........................

ISN 0193 .............. FG &1_3 = 01013_ IIW_MI G RI8 $ ...........

ISN _1¢14 FST£ • FCST I + FCST2 4. PEST3I._N 0_95 .... FSTDG = F¢SZL _" 2,Ur;_I_F¢ST2._-.5=J;)J_eGST3 .......

ISN 0196 FPIf_F = (0,r)SSOC_,70_lo0D0_;-)7361_O0)/_,_ 4,_5D0|SN 0197 ............ .IR_J,.a 27_,2_.,_0/.tC13,2EI)0 ..............

ISN C1_0 UU 710 I • te N"', ISN Clgg ........ H_.,.FD.RY(I) = [??.,£2400_'PRi.Z)I/T_|.]) -- -- -- --

I_t.FwET(I) • (3?3q_Oe')DOIE(|))I(T<(I)e_2)-I2*q_DOe(F(I)/TK(I));SN 0200

,, I_N 0,_0_ HG_R_P(!) = HG*4Rr.F(t 1_1,00-3=-:--.< . 15h. G_"_:I ........ .R_P_AT(L.|a(LFSTI_PRAI)IIF_TD)_IrJttI|I-ttFe_,RP_(II.|/T&LLL)

... ISN 0_04 RI-_FPAG(I) • ((FSTI_'PR(I)_F_'rfl'3)tT_(I))-((FPARP_F.(I))ITK(|))1 SN 02_ IF (F (_P'r I_Q,

' IS*4 _,2+)? 910m. . lF(P0gT*t(_* _*011¢_ f'LFRAG(I) • R_FRAT(I)

');., ' tSN f,,_.09 _Vkl _" _,FFR/_.T(t) .....C ¢Ol4111_Y_ l,_,t,.a'riVt ,'IUllOliY lHili *1" =4_.H OF I_* *FIXEO''UEVI[I,.S+" "+

..... C FJ_£'_ TH! PARTIAL PH_SSt,,R_ OF T_ IIA']r-'H V4P_ [111 AND THE TEMP-G FIIATU'_I IN ;)I'GI:LI'5 CI'L.C|US ?C(1),

I

I,¢,N ('al_ _H(I) : ((t_',(_*Ol'('t:(I))t_l|I_'_)tL')*)Jl'':X

'_tl CRib it I-_lf':4AT(1HI, I"/X)

t iN a_0 N_T_ _= N

i ,,,, SN 022t _'_I *30 _¢ = t _N ....._N ('2_ "_ X(K) := HG',_I_f':'(K)

ISN 0224 CALL ('._P|NT(3U,I)._ tSN (_22.S ........... .='J_'P = ¢-_._ ..........................................................

i ISN 0226 IF (laRlhl) 1_1_ _t E14,1 =.12• }_N-@2t_7 .......... t(_It _N,-tlre-(_,t0*} .......................ISN 0228 _RITE (_t1_¢,)

t.SN. _-22_ ........... w_ _-TP..- .(-6,rt _-t- ...........................................

ISN 0230 _PlT_ (_I_I3)E_N--_-2._I ............ .-l-P.l--3- Ft_-N.AT(- | (_H .... --H_.T _-M_a.st @_-- _-S_ ( _ )-_-J-_t'_--T_# _-.._--,r_l QH-..---_._H- ;(_-T _- .....

IIOH CALHGT)

I._N 0233 |C_ FOI,,XAT(IH0,1?X).- -_ 4 -11_-_--* .l-_-._- ....................................................................................

ISN 0235 11_ _qI'rF (0,1|1) PRGP(II_,F*_S'I(IltT._4_).,;( I),_I'X. HUM(I},¢ALCI'_(I)

I-_N ¢'2_? _RITE ((_,:'*1)-FSN---e.L-_3e-- ..... "- .|.S- .I_I.-FT [.-,-(- b r_t ?4 ..............................................................................

ISN 023q I=17 Fk,IRMAT(C_H H(KMI,,';H TEMP(KItQd _F((ttdlt¢IH ktV(MU)DOH RH(PCT)

• , ISN 0240 wRITF. (6,I0_1

':' , |_L.FkAT( | ). _,_F_AG( _ )

"' 1 _N_(_4k4 .......... -_14.| tE-.4@ * 104 ) ......................I._N 0245 wRITF (_,1_.4}

I_N 0_._.? |eSq, DO 13 K : I. NTH' | SN- 4;_ ........... T4_.__:AO- .m t h_. T A(.K-), = ..........................................

I_N 0249 CAt.t, RAYT tR(NtHGMNFFtREFRATDTH_T_)D-"-_tHNGI RRtF_A_IGI_tRVFRAG)

_'_...., |SN 0251 wNITI_ (4t_) [_TATtlYFARt|Mr'NTHtI.3AY,IHI)U_

" ;,"; - ISN 0253 WRITE (4tI(_} THETAQ

,.,_. |_N-(N)(r_ - • - N FUf_MAT(IXt|LN,#F#.¢_VAT=_IN ANGL_. .= t J| $,!ItIXt'/'Hf.At |ANSI_m'" _' 15N @255 wRITF(b*|I) R&NGF

,_=_o |_N.O._6 .. WH|.I'E(4tI,|) RANGE •|SN 025? |I FOPMAT(|Xt@HRAN(_ == t_'ISe_*IX_I(•4KIL. J.4F'T|f_)..¢ .

ISN 0259 |¢_ FII;MAY(IX,_.HSU_ (3F NCFrtACIIvI _' = ,.)I23._), . ..._, .'_ |SN O_lNkO ....... wl;IIT,I_ (6.1_l) GMRi'F_.(I|

:):,'. • |SN OEbl WRITE (4,!_.) GM¢FFP(I)r '" : i&N IIIiI4D_..... I,_ f'_IRMAT(|AeqHH_|GPLT =t .O|_.EetX,IJHKI_.JMET_I;$)

' "' I_ gA& WHIT_ (4*It| l;kl(l} .....................

; IRN 0;!65 I_P F(3!;MMT(|XtIIHF_f,;¢_,3UQF" = ,()lfi.lttI,?,t41LLt_Af;._)

Iq7413137r1_7_T_ nn_

• • Tt' ',110 ,:

• +l , It . 6, IiI

ql+

......... _'OMIIt LLR"*GFT I _,+-;'- - ;.m_-n_." +.. ,,_, ++_-,........ "+,.... ,_, ;.+---,;,.,+.-;+v , :+ ; ;_8 _ ................*JOURCF oF E_Ct; I G oNOI. I S T oN30 _.(_K oo O AO o_A F . NOFL+I T t IO oNOXREF

+ IS+I 0_01_ .......... 5 Ue I+¢O+ I NI-3--_I NT ,".+_+.".._'+', _' lSN 0(03 IMPl. lrlT RR.61. ilJIA-PIo_h"Z)

+ 15N O004k .... Cr¢-_MCN JI(|S00),Ui+,__t_4NI_F_N#Y_; -- .........,' +':'- |$N 00+5 M z hPT$., |r |5N _H)+b lug' • O-e,)O(4,+ ................. +

ISN 00C_7 DU I | • Its4JSN OOO_ ......... It e. teQf._)1*l_k*O_4HillJ4-1.|;'_;_:-_

1_ :SN COOV I SUm - +Um + ZItXIItl)-XIII)*I_,II*II-JII)I

ISN o010 -- mu TUt, N ..................................ISN CO! I F,NO

A4 -8

1.Cl7,4tin 71"Y'.l7_T _ r_r_A

,_ C ([,{MFh. r ICNI ' ¢.%) V({,5_:', ,eL l_,ltT ;._:;,r( {{ {N I_|}L_MI'T,Z_5%t TtiI'_A_ IN

_ ........ ¢ _kG_ #,r_r_,_r¢ T &Ok. _,'40..,':_.K &N K[_.L;,_.. r,l_,_o ........................

,_, 13N 0(;06 DiMrhS|P.N _[iFr<_(l), ,_EF|N¢,t I_)C1)';,. 4LC,N 0(_.0'_ ......... 'T_( TA( I ) = THFTAO_" ISN 0¢08 47b O0 5 I = I,N

44_4.4)4)_0 ............. RrGINO4-I)--= t.O{',O 4. (l,30-,o)_R_,t:-lATttl; .........

ISN 00t0 5 R|I) = HGTIt) �_3?_,,00D)

; ir=_ 0¢-1l - Oo ¢, ! : _,_ ....

' I,_N 0012 0F.I. N2 = ( |.Cn-6)_(I_t_F_AT(t)-_EF¢_T(I-1) )

I_N, 0_{.l$-- _EL'RE *._(t) - R(I-I)ISN 0©|4 P "- _! LNP!I;f_f t;_(l-t)

,I';, .I_N*-WMI'4.e,,-......... O _ GFI_PJ_(|-W} ........:s {';N C016 TIlP = to0('0 - (P/2.060} + (Pm$2/J,,IJ,_I

_' [,_N 00{lq O A(I) -- (PeT(_I.))/(G_t)_)T)" [SN 0Ole .. or'. ? [ = g,N

i I._N 0020 AA -" R( I )/(P,*ODttR([))Z _ _ I l ............ a U :...a..OUG_ { [)S{ h ( T_'¢, TA ( I ) 4(_, _.D: ) _sZ. )

( 15N 00_ CC --- (I;(I) - P(I))/¢_(t)

_ OG _ J ...... _ : t,I;FFAAT(;) - Rf.J:RATK|&)/G_.I-i;_J(;{ISN G024 EE. = (t.CD-6)*GCOS(rHCTA(t))/ --

K-' ,=. =o=,, = ,,.,,, + . cD,=,) .ISN 0028 SIhA = [SQRT(_INSrJ) ..............................

I ,J,&N--GO_._ ...................ARGI' ,= P.ARS;N(S._N,t4 .................................ISN 0028 7 TPETA(I) : ?.O00*.4RGT

' 1 i-$N O0,,_q T4t* :-0.000%

, [SN 0¢_.,10 r)0 el I = _:*N

^ .i.r_l_-0G$1- qA :-.Tt4FT_([) - Tt_ET&([-I|

,_ . ISN 0032 BB = -A(I)/(|,01_9 t A(I))I.#¢N GGI4L- ....... ¢.¢ z. A,t*._B ...................

' ISN (_034 9 TAt,. = T#t., t. CC

"_ I_,4_ ¢14_31_ PHI = 0.0O0

" , ISN 0038 OO It [ = _tN"_- ¢,_N O@3T AA : I'hlrTA(|)- TH_°TA([-|)

: [_N 003_ Od = 1,0r0/(A([) + _,t103)

' i&N. OO.1RI .... C.,¢ _ .AA,_R_

.. I_N 004(_ I| PHI = PHI • CCi_ #041 R_ =, 0,0D0

;+,, [SN 0C4_ I_0 114 { = {, N

"' ' I SN 0044 Dr) 13 I = _,N

'_,. _', I_N 004_ Bit : ")TAN(THE'TA(|)) - 01"AN(TH_TA([-I))m ,,,_ ISN 00_? CC = 1.GO0 + AtII

15,N 0049 1_ HI;" = RP + ¢'nISN 00_0 RAkGSQ : (R(N) -- H(t)J$$_tfA*0_t+) * _(1 )_ 4(N)'$l _|N(').hl]_tf'ttl |t$2

' '' 15N 00B1 R_f_GE = _SOf_T(RANGL;U)

_i,,, " ISN ("0_2 RNCI fir : R ¢' - qAhGr

I'tN 00q3 ..... 1'n_', : PCOS(TAUl - r'SI.I(I'_UI,*C:TANI l'r_.'T^(h))ISN C0._4 Trif = rr)P- (RCFINC'{N)/R{FINC(II)

• 4_N (H3q._- EOT , (#f;INO|N)#Rt-.FIN(;(|))$_TANt PHt;TA( {)t

I':N 0(.56 d,_t : _1_'t - f, SI_('rAU)

I-_N _O-_q? Ht)T : _PT - PCUS(TA@)'_eYAN(TftFTA(N#)

15N O05.q h_P : PA/_N(rOF:tI1Cr)

IqN (_4_MHt @_ 'l'l _N

l_l of_o ENf)

,-,_:,+_?'+.'P..++_,:_+:_+" I+":+' .,J

1 .CIT_AA7A'_TmT_ I_n=

_g74007037-TSD06

1974007037-TSD08

_I_l II II" -_T -_- " ' "llllqllIII_-

• t" _'

• _,' I'.

I

1974007037-TSD09

%'

Q*

4

A4-1|

"1974007037--I-$D'I0

' _I_ ++""

v• ,

1."+,y+-_+ : j+j_+". ° d

I.

d

o,, o._oo0o, o ,o,o o, o, ooo, :_:_

o o+oo -+ o,o ,_, ,'_'_ ,o ,..,, o o, ,_,ooo, o _,+" ."',_m" "' "+ + m+ "," '+'O OC +, Oq O, ON: _qOil_ _ ,I O+: ,Ol+_q1',,IO O, O_m4m+m,O0 _' _O, Oq

, ++,+,,, o,+,_+o.o,_,+,+..++++o+_,:,+o ,,,,,+ o_+m.+ ,_.+,,+_t +tt. I') .,+, ,,Oi+*O, w _ m If) _*('P, m @+ l".i k'lW,-,o' _'I,

- - i i +• . • . , . qll ¢_ ¢_ ,+4 ¢_ "++ +' , 0+, ,_

++1_I l_l (%1(_ A'_l(_I 1_ +{i i ,qN GI_ 1%Iq O1_I a._, i m 4 1.0 _ m011040 O< 00 ¢_ ,4_)1 O 4_1_O+ tGIQl(_ic_i4NI,OIPIO_)O,1_ Ptt _ I_il _1o +O _i ,O O' O O ID <, O

, _ .__+. =_ _=, ,_,,_ _p_i+'_ . _, ,,;._p..: :_+, +..,,-, o, _! ,,,, ; P. _: ++"_' _m +_i+.+.-m_+ m®' """" "" + "+k+','_-++._ : _ <,, ® ,®, ,,.,,+o o

|_-+Ii ,++ '° +o,¢+,o+ +'_+'+' +' t_+m. I mP,._ ,+*, _ _: _+ m,*,.,_ ++,+ ++.,++ .++p, m -. o_t_l _4,., O++ +b.t'+'''b" +,q + + : + + + I_ +I_, +:,F)+ + OlqlltD' ..+ ,_, q , , + I+1 + : , + + +1++. C ,m++, :+0

• • + • + • + • L_ • + •+'.,o o, o ,.",,o +_",o '_ .':,,_.:+, ++ o,o.o: ,,=' ,_¢tt

t t +i ' I :; I '

_o.+..o.++._tl:,o,,o.... o,.o,o+o+o_+_'°"+°13'"+°'°I' _ '°'+'+''="+"+"3't:'°_'oo o ooo ,,',.,,'+ <_+ ,o+o+o" ' ,o'*'+,.":,_ ,ooo,',+, + ,_I.+

_+..3,+oo0,,,_,o ,o o.,,,,,.++........,0.-o++,+++,o ,o,_+.o........o ,,-,0o,o, o..0.+,+.,+.',,: +

i I ii ! : t _ t

_ ° _"-'"'++ _ _ _ '_ +,i +, _}_'+"i,:'" _ _ ''+ ',' _ ,-

. ......... ,_ ....... ,... , _+. _o

i !!++:_+_++"1I_ t_+_._.l_,G, I._, ._0+ ,,1) 1_1 +-"I'+- _ m ,q,_4

• . ...,. .... _,_. _+,. ,.. _.. ,_ +

+, ii_,+• • • I It i) _o _ I • ) • + • + •

"+ 41N

+ i , t

: _ l t ++++++.++.""" """" "+....+'+" +s FI /) 41 _ ,I _ q +m_

_ ,oo+.. **m.o _ _r,.+ © m ,o r+'_ ,_ , P,,+........... _ +_+:. ,+,<+,pt t.+ !.i1_

_+iA4-15

.++

1974007037-TSD13

g_

A4-XO

e+

1

_A__ _--.

+1%+" ,+

1974NNTN':t-/_T(_ =r_ _

A4-18

1974007037-TSE02

ST_ITION s 9373++ YEAR • b? M_NTtt : I LPY a I H()UF • 1 ")

I. Oi+-,4,1+i_._+--.O_ ?463 8; _I_- O0 -RAG lAbS ...................

m+l_+_ -- o,-_7"P0a01eo 04 K|LI_Mr_t+'I_+

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T_PI+RATURS • -O.420_O000D 01 P.LGR_[S C_,I.CIU. c

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r STATION • 93734 YEAR = b? _¢NTH • | BAY • ] HOUiq • 12t

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TEI*P,:RATURE - -0.42¢00¢,0CC' 01 OF.OR_.ES Ct_l._.IUS

' ANGI.R O. 11CSOP;63P.-PP. t_.AO | ANSI[.kEVAT ICl_ ERRCR II

RANGE CliFF • 0.11_+t+lS|+el'+ _0 ¢MSTATION • (;3734 YEAR = b? MCNTH a l ray z I HOUR _ 1_

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i _ STATION • 93134 YEAR - OT MONTH " I COY _ 11 HOUR • |_,

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A440

'1974007037-TSE04