NTIA Report 87-224

Millimeter-Wave Properties of the

Atmosphere: Laboratory Studies

and Propagation Modeling

Hans J. Liebe

Donald H. Layton

u.s. DEPARTMENT OF COMMERCE

Clarence J. Brown, Acting Secretary

Alfred C. Sikes, Assistant Secretary

for Communications and Information

October ,1987

CONTENTS

Page

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . • . . 1

1. INTRODU·CTION ........•.•........•••...•... .-0.... 1

2. LABORATORY STUDIES OF MOIST AIR ABSORPTION AT 138 GHz............ 3

2.1 Experimenta 1 Arrangement.................................... 4

2.2 Moist Air Attenuation Measurements 9

2.3 water Vapor and Moist Air Attenuation Results.............. 13

3. ATMOSPHERIC PROPAGATION MODEL MPM 16

3.1 Features of the Program 16

3.2 MPM Calibration 19

3.3 Interpretat ion of H20 Cont inuum Absorpt ion.......... 19

3.4 MPM Predictions 21

4. EXPERIMENTAL-VERSUS-MODEL (MPM) DATA 28

4.1 Laboratory Measurements , '."... 32

4.2 Field Measurements 32

5. CONCLUSIONS...................................................... 39

6. ACKNOWLEDGMENTS ......•.•.....•...•••.•..•...•.•••-. . • • . • . • . • • . . . . . 42

7. REFERENCES........................................................ 43

APPENDIX A: THE REFRACTIVE INDEX OF THE NEUTRAL ATMOSPHERE

FOR FREQUENCIES UP TO 1000 GHz...................... 45

APPENDIX B: PRINTOUT OF MPM-N PROGRAM FOR VERSION A

(FREQUENCY PROFILES) ..............•................. 61

iii
----~~~

LIST OF FIGURES

Page

Figure 1. Millimeter wave spectrometer for controlled moist air

studies (a) schematic and (b) cell design.................. 6

Figure 2. Photograph of millimeter-wave spectrometer................. 7

Figure 3. Mm-wave spectrometer operational data (five temperatures T;)

peak values of reference and reflected signals aK' and a;

and relative attenuation a ) for a I-hour measurement

period with an evacuated c~ll (fR = 137.8 GHz):

(a) automatic calibration to a = 0 dB for changes, ~aK = 0-1 dB; (b) detection sfability and sensitivity (amin = 0.006/0.13 0.05 dB/km) ..............•.......... 10

Figure 4. Temperature responses inside the spectrometer cell:

(a) time-response test of gas temperature (Ta) sensors,

(b) temperature-vs.-pressure behavior for a typical - dry air case.......................................... 12

Figure 5. Mixing effects of H20 + Air from time series of 138 GHz

attenuation: (a)plston effect and diffusion mixing;

(b) decompression condensation during pump-down

over open vapor source 12

Figure 6. Typical raw data plots of relative attenuation a(P)

for pressure scans at 137.8 GHz introducing (a) water

vapor, P = e, and (b) P =-el + p 17

Figure 7. MPM-predicted specific values of attenuation a and

dispersive delay a at sea level height h = 0 km

(P=101.3 kPa, T=25°, RH=O to 100%) over the frequency

range, f = 1 to 350 GHz. Window ranges are marked

WI to W5 •.•.•..•••...••.••..•.......••..••..•.....••...••.• 22

Figure 8. Water vapor absorption in window ranges for constant

relative humidity increments (~RH = 12.5%) at sea

level 24

Figure 9. Pressure broadening (Air) example of the 183 GHz

H20 1ine........................ 24

Figure 10. Attenuation a and delay rate a for three rain events

(R=10, 50, and 100 mm/h) added to moist air (RH=95%),

sea level condition. Also shown are dry air (0% RH)

and moist air (50% RH) characteristics 25

iv
Figure 11.

Figure 12.

Figure 13.

Attenuation a and delay a r~tes for three fog events

(w=0.10, 0.125, and 0.5 g/m ) added to saturated

air (RH=100%) sea level condition. Also shown are

dry air (0% RH) and moist air (50% RH) characteristics:

(a) f = 1-1000 GHz •••••••••••••••••••••••••••••••••••••••

(b) f = 1-350 GHz .••••.....••••..•........••..•••••.•.•.•

Absolute (v) and relative (RH) humidity dependence of

attenuation a and delay a at f = 94 GHz for various

sea level conditions (P = 101.3 kPa and T = -20 to 40°C) •.•

Two haze cases (A: 1 mg/m3 and C: 1 mg/m3 ) for prefog

(RH=99-99.9%) and fog (w=O.l and 0.2 g/m3 ) conditions

at three temperatures (0, 10, 20°C) displaying the

associated attenuation a and delay a rates at

f = 220 GHz •.•••••.•.•...•••.•••.••••••.•••••••••••••.••••

Page

26

27

29

30

Figure 14. Pressure profiles at f = 138 GHz simulating the

laboratory attenuation measurements presented in

Sect ion 2. 3 II ••••• D ••••••••••••••••••' • 31

Figure 15. Moist air attenuation a across the atmospheric window

ranges W5 and W6 (320 to 430 GHz) at temperatures 8.5,

25.5 and 32.9 °C: data points [21], [22]; solid lines

MPM 35

Figure 16. Moist air attenuation a(v) measured at 96.1 GHz over a

21.4 km line-of-sight path located in Huntsville, AL

(h 0.3 km) for six temperature groups between 2.5

and 37~5°C [19]:data points are 5-min averages for

4.5 days (5/4-6, 8/15-16/1986); sol id 1ines, MPM ••••••.••• 36

Figure 17. Water vapor attenuation rates a(v) across the atmospheric

window range W4 at four temperatures, 5, -7, -10, -18°C:

data points [20]; solid lines, MPM .......•••••..•.•.....•. 37

Figure 18. Terrestrial path attenuation at 94 GHz and 0.65 ~m

(visible light) under nonprecipitating conditions as

a function of absolute (v) and relative (RH) humidity [3]:

(a) data points, 5-min averages taken every 30 min during

a period of 4 months [23]; (b) MPM simulation of (a)

for absolute humidity; (c) MPM simulation of (a) over

the range, RH=95 to 100%, including'haze model C •.•.•...•. 38

Figure 19. Correlated vertical atmospheric noise temperatures TA at

the frequency pairs 10/33, 10/90, and 33/90 GHz. Pathintegrated water vapor is V = fVdh, mm. The measurements

were conducted from two sites located at height levels

ho=0.25 and 3.30 km: data points [24]; solid lines,

MPM with a mean July height profile (0-30 km) of P,

T, and RH for San Francisco, CA [3] .••.•...•...•.•••••..•.• 40

v
Page

Figure A-I. Moist air refractivity N = N' - jN" for sea level

condition (P,T) and various relative humidities (RH)

over the frequency range from a to 1000 GHz .•.••••••••••.• 58

Figure A-2. Moist air attenuation (a) and delay (B) rates for a

sea level condition (P,T) and various relative humidities

(RH) over the frequency range from 1 to 1000 GHz •••••••.•• 60

vi
LIST OF TABLES

Page

Table 1.

Table 2.

Table 3.

Table 4.

Comparison between Measured (X) and Model-Predicted (M=MPM,

see Section 3) Coefficients ks f of (5). Experimental

conditions: f = 137.8 GHz, T 282~316'K, P = e1 + p,

p = 0-110 kPa .

Attenuation Measurements of Water-Vapor/Air-Constituent

Mixtures (f=137.8 GHz, T=303 K, e1=3.80 and p=0-100 kPa)

Expressed with k~-Coefficients of (5), and Corresponding

Broadening Efficlencies mx (6). Included are Line-Core

MeasurementsmL and their Predictions m1 and k1 Transposed to 138 GHz ................•.......................

Summary Data of H20 line. Spectrum and H20 Excess

Attenuation at 137.8 GHz, T = 300 K •••••••••••••••••..••••••

Reported Data on (H202) Dimer Concentration eD/e

over the Temperature Range for 300 to 386 K ••••..•.•...•..••

14

15

20

20

Table 5. Measured (EXP) and Predicted (MPM) Dispersion in Dry Air

at 300 K (Interference Coefficients from Rosenkranz [10J) •••• 33

Table 6. Comparison between MPM-Predicted and Experimental

Attenuation for Water Vapor (e) and Moist Air

(P = e1 + p) in the Wing Region of the H20 Line

Centered at V

o = 183.310 GHz 34

Table AI. Frequency Profiles of Atmospheric Complex Refractivity ••... 57

Table A2. Frequency Profiles of Attenuation and Delay Rates •••••••••• 59

vii

MILLIMETER-WAVE PROPERTIES OF THE ATMOSPHERE

LABORATORY STUDIES AND PROPAGATION MODELING

Hans J. Liebe and Donald H. Layton*

Laboratory measurements have been performed at 138 GHz of

water vapor attenuation ~x for pure vapor (H20) and its mixtures

with air, nitrogen (N2) , oxygen (°2), and Argon (Ar) . Temperatures ranged from 8 to 43°C, relatlve humidities from

°to

95% and tota 1 pressures reached 1. 5 atm. A computer-contro lled

resonance spectrometer was employed. The results are interpreted

in terms of under ly ing absorpt ion mechan isms. Broaden ing efficiencies m of mixtures H20 + N2, 02' Ar agree among themselves

with those measured witnin cores of the 22 and 183 GHz H20

absorpt ion 1ines. The m-factors are app 1ied to pred ict what

share at of the total ax results from the complete pressurebroadened H20 spectrum. A substantial amount of the selfbroadening term proportional to the square of vapor pressure is

left unaccounted. The negative temperature coefficient of the

excess absorpt ion is cons istent with a dimer (H20) 2 mode 1. An

empirical formulation of the experimental findings is incorporated

into the parametric propagation model MPM that utilizes a local

(30x H20, 48x 02) line base to address frequencies up to

1000 GHz. Detalls of MPM are given in two Appendixes.

Predictions of moist air attenuation and delay by means of the

rev ised MPM program generally compare favorab ly with reported

(10 - 430 GHz) data from both field and laboratory experiments.

Key Words: atmospheric attenuation and delay; laboratory studies of moist air

attenuation; millimeter/submillimeter-wave spectral range;

propagation program MPM; radio path data

1. INTRODUCTION

Extending the radio spectrum into the near-millimeter region (NMMW: 0.1-

1 THz) is an active area for research. Possible applications lie in shortrange communications, radar, radiometry, and radio astronomy. Atmospheric

effects of transmission and emission are d-escribed by the complex refractivity

that provides a measure of the interactions between radiation and the

atmospheric propagation medium. A reliable N-rnodel allows calculation of

frequency-dependent rates for delay (real part) and attenuation (imaginary

part) based on measurable meteorological variables. Dry air and atmospheric

water vapor are major millimeter-wave absorbers; so are suspended droplets

(haze, fog, cloud) and precipitating water drops that emanate from the vapor

*The authors are with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U. S. Department of

Commerce, Boulder, CO 80303-3328.
--"-"""----"--"...._------

phase. Laboratory research and analytical studies have been conducted with

the primary purpose of understanding power attenuation a (dB/km) and group

delay S (ps/km). Emphasis was placed on the fundamental concepts that support

an Nformulation.

Refractivity N for moist air can be obtained, in principle, by a line-byline summation over all molecular absorption lines. In practice, various

approximations are employed to reduce labor and computer time, since the

number of contributing spectral lines by the dominant absorbers (water vapor

and oxygen) and by various trace gases (e.g., 03) exceeds 10,000. A practical

propagation model, indexed MPM (and described in Appendix A and B), consists

of local H20 (30x) and O2 (48x) lines below 1 THz and an approximation to the

contributions by H20 lines above 1 THz [IJ - [3J.

The experiments have been performed at 138 GHz to measure absolute attenuation rates by dry air, moist air, water vapor, and water-vapor mixtures with

nitrogen (N2), oxygen (02), and argon (Ar) at temperatures between 8 and 43°C,

total pressures up to 1.5 atm, and relative humidities between 0 and 95 percent. The experimentally observed absorption is not described by standard

line shape models. Such failure reveals difficulties in modeling frequency,

temperature, and pressure dependences for moist air attenuation. An unexplained excess is identified for which the name "wa ter-vapor continuum" was

coined since it appears to increase smoothly with frequency within the NMMW

range.

Experimental studies are compared with model calculations. The MPM

program is a user-friendly, PC-operated code that generates numerical values

of a(f) and S(f) for frequencies f up to 1000 GHz. Input parameters are five

measurable atmospheric quantities: barometric pressure P, ambient temperature

T, relative humidity RH (absolute humidity v), suspended droplet water content

w, and rainfall rate R. Controlled laboratory measurements were limited to

moist air studies (P, T, RH), and the data obtained at 138 GHz are reasonably

complete and accurate to assess water vapor pressure and temperature dependences for the water-vapor continuum. Both variabilities point to the distinct possibility of an absorption mechanism related to water vapor that is

not accounted for by molecular theory of H20.

This report is organized in three parts. The first part (Section 2)

gives details of the experimental setup, its achieved performance, and a

summary of reduced data. After many improvements, a detection sensitivity of

2
amin~ 0.05 dB/km or 1.2 x 10-7cm-1 was realized. In the second part (Section 3), results from the laboratory experiments are applied (a) to calibrate

the MPM program with an empirical continuum term, (b) to demonstrate the parametric flexibility of the code (i.e., f, v(RH), and P can be selected as variables), and (c) to conjecture on the physical basis for a water vapor

continuum that is defined by the limited H20 line base of MPM. Finally

Section 4 contains examples of recently reported data from laboratory and

field experiments on water vapor absorption (10-430 GHz) and their comparison

with MPM predictions.

2. LABORATORY STUDIES OF MOIST AIR ABSORPTION AT 138 GHZ

Controlled experiments that simulate atmospheric conditions provide test

cases for studying specific contributions to]i. Assessments of basic physical

principles underlying the attenuation rate a are difficult to make from

measurements in the actual atmosphere. The objective of this study was to

measure water vapor (continuum) absorption. A test frequency of 138 GHz was

selected because of its remoteness from local H20 lines. The expected window

attenuation falls in the range 0.1 to 5 dB/km and the required detection

sensitivity calls for a long (>0.1 km) effective path length, which can be

attained with a resonant absorption cell.

The response curve A(f) of an isolated, high Q-value resonance is detected with a power (square-law) detector. Both, the peak value ao at center

frequency fRand the bandwidth bo spread over a range fR ± bo/2 at the level

ao/2 might be used to detect the relative attenuation,

a

r = 8.686(/ao

/a -1) = 8.686(b/bo -1) dB, (1)

of an absorbing gas that changes the corresponding quantities to a and b when

introduced into the resonator. Around 138 GHz it is possible to design a

compact (20 cm mirror spacing) Fabry-Perot resonator with a loaded Q-value on

the order of 4 x 105, which defines (Q = fR/b o) a resonance bandwidth,

bo = 350 kHz.

A crucial question to be resolved is whether amplitude (ao/a) or

frequency (b/bo) detection schemes provide the optimum sensitivity for the

spectrometer. After extensive testing it was found that digital averaging of

A(f), displayed over a frequency span AfM= fR ± 6bo' was capable of resolving

3
--------------.

ao/a = 1.002 (512 pts)--but only b/bo = 1.015 even with 1024 pts. Amplitude

peak-value detection provided optimum sensitivity for absorption studies. The

frequency span AfMis needed to establish the baseline A(f) = 0 of the resonance response. In addition, a detection at fR avoids corrections for dispersive distortions of A(f) [4].

Absolute calibration of absorption is accomplished by defining an equivalent path length (bo in kHz),

LE = 47.71/bo km, (2)

for the resonance spectrometer operating at fRo From (1) and (2) follows that

the absolute power attenuation rate of an absorbing gas is given by

(l = 0.1820 b (1a7a - 1) dB/km.

o 0 (3)

If the estimations (ao/a = 1.002, bo = 350 kHz) can be achieved, then the projected detection sensitivity, (lmin = 0.064 dB/km, is adequate for the planned

water vapor studies.

2.1 Experimental Arrangement

The measuring system consists of the millimeter-wave resonance spectrometer and a humidity simulator. An insulated box contains a high-vacuum

stainless steel vessel that houses a temperature-controlled mini-lake (10 cm

across) and the resonator. Temperatures are controlled to better than 1/100

of a degree Celsius, pressure ranges over seven orders of magnitude (103 to

10-4 torr), and relative humidity is varied between 0 and 99.5 percent.

Schematical diagrams of physical and electronic (Figure 1) arrangements

and a photograph of the equipment (Figure 2) convey an overview of the experiment. Atemperature-controlled water reservoir serves as the vapor source.

Electropolished stainless steel was used exclusively as construction

material. Various hydrophobic coatings were studied as possible means for

neutralizing the absorption/desorption cycle of surfaces exposed to water

vapor [5], but were abandoned in favor of slightly heating the mirrors of the

resonator. Four fast-responding (T < Is) temperature sensors inside the cell

signaled any disturbance of isothermal conditions. Data acquisition was

computer controlled.

4
The resonator inside a vacuum chamber (Figure 1b) is the heart of the

absorpt ion spectrometer. A key-word summary of its specific at ions read s as

follows: Fabry-P{rot reflection-type, semiconfocal arrangement, 10 cm mirror

diameter, 40 cm curvature radius, mirror heating: 1°C/0.3 W, Fresnel number:

6; pinhole coupling: circular, 0.65 mm diameter, 0.075 mm double Mylar

vacuum/pressure seal, coupling factor k = 0.0550; resonance frequency,

selected for optimum performance of the available klystron, fR = 137.80 GHz,

temperature compensated (~f/fR= 0.9 x 10-6/ oC) and insensitive to pressure

loads from 0 to 2 atm; resonance bandwidth: bo = 334 kHz yielding an effective

path length, LE = 0.141 km (Eq. 2), mirror spacing: xR = 182 A/2 = 198.0 mm;

micrometer tuning: 0.3175 mm/rev =2500 SU/rev (SU = scale unit on micrometer)

with a resolution, ~xR = 0.127 ~m/SU, which converts into a frequency change,

(4)

Over a 2.5 cm tuning range of the micrometer, the resonance at xR was the

"best II out of 52 choices with respect to other-mode interferences and

Q-values.

The detector of the resonance pulse A(t) was an InSb bolometer, cooled to

4.2 K-LHe, and connected by a WR-12 waveguide mount. The maximum voltage

output of the preamplifier was 10 V. A power-linear response of 4.2 V/mW was

measured up to 1.0 V. With a 50-kHz detection bandwidth, the noise power was

about 5 nW. The bolometer bias (92 mY) served as cryogenic thermometer (TO).

The power source was a 138 GHz klystron (20 mW) that was frequencymodulated by a sawtooth voltage generator to provide frequency-to-time domain

conversion. The modulation frequency was exactly 500 Hz derived from a 10 MHz

frequency standard. The linear sawtooth ramp was gated at exactly 1925 ~s,

the fly-back time took only 2 ~s, which eliminated A(t) from the retrace. The

modulation sensitivity of the klystron was determined to be 12.56(13) MHz/V by

using the resonance peak ao as frequency marker, tuned with the resonator

micrometer to the end points of the ramp and checked for linearity over a

modulation voltage range from 0.500 to 3.000 V. A tuning uncertainty of 1 SU

introduced about 1 percent error in determining the frequency-to-voltage

conversion factor.

5
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Figure 1. Millimeter-wave spectrometer for controlled moist air studies:

(a) schematic and (b) cell design.

6
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The reference power ao = k~aK for (1) was measured by periodically (30s)

switching on computer command to a 36 Vmodulation voltage, which displayed

the power mode AK(t) with a peak value, aK = 909 mV and a bandwidth,

bK = 186 MHz. This feature provided an automatic calibration of a

r (1) when

the power level changed during a data run (e.g., refractive-tuning reduces fR

and the peak value aK can change when the klystron is readjusted).

An electronic lock-on circuit centered the resonance fR within one time

frame; that is, the klystron center frequency fK(aK) was prevented from drifting with reference to fRo A flat baseline A(t) = 0 was established by adjusting fK in such a way that two adjacent A(t) frames were displayed on a control

scope and kept level. The reflected resonance signal A(t) could be eliminated

by injecting a steel rod into the resonance volume. This measure provided

baseline reference data in the "low" (0.36 V) and more accurate peak readings

aK in the "high" (36 V) mode of the modulator.

The wa~eform processor for A(t) was a digital storage oscilloscope,

synchronized with the sawtooth modulator and capable of resolving 512/1024 pts

per 2000 ~s. Operational resolution was typically 3.91 ~s/pt. The modulator

voltage for A(t)-detection was 0.360 V resulting in a frequency resolution of

9.2 kHz/pt, which is an improvement over (4). Extensive averaging of the

repetitive waveforms A(t) 100 times, and AK(t) 50-times, was performed in real

time to improve the signal-to-noise ratio of the a and b results.

For a measurement of the resonance bandwidth bo' the digitizing increments were doubled (1024 pts) and the modulation voltage was varied in the

0.150 to 0.400 V range, allowing the resolution uncertainty to be reduced to

±5 kHz. The resultant error in an absolute calibration of a (3) was less than

3 percent.

The computer of the spectrometer had a control-program that was designed

to be flexible in order to allow changes in data collection procedures. It is

written in BASIC with about 500 lines of code to control the readings of eight

temperatures, two pressures, and a/b values from the waveform processor and to

store the data on a magnetic medium for future processing. The program is

time controlled. The fastest acquisition time for a complete measurement

cycle was 30 seconds.

Measurements begin by starting the internal program of the waveformprocessor, which does 100 averages on the output A(t) from the InSb

detector. Since averaging takes about 14 seconds, the computer program con8
tinues data recovery from the temperature sensors which measure chamber (Tc)'

water bath (Tw)' room (Tr), gas (T1,2,3)' mirror (Tm) temperatures, and data

from the total pressure meter (P). By this time the oscilloscope is nearly

ready with its data so the computer program returns to wait for the final

steps in the scope program. After the scope completes 100 averages on A(t) it

normalizes (by setting cursors at 0.1 and 0.9 of the time base) the trace to

remove any baseline slope, then stores the waveform. Next, an auxiliary

output from the scope switches the sweep generator voltage from low (0.36 V)

to high (36 V). The scope input cWanges to the power envelope of the klystron

with the lock-on disabled. The scope program performs 50 averages on the

power curve and stores the waveform AK• The next computer step is to call for

the alb and aklbk values of the stored waveforms.

All of the measured data were temporarily stored in computer memory and

transferred along with time-of-day to magnetic tape or disk storage for safe

keeping and later recovery and processing.

Real-time data were plotted on the CRT of the computer to follow the

progress of an experiment. The selection of what was displayed is part of the

program configuration. Two typical examples of I-hour operating periods are

shown in Figure 3. Figure 3a demonstrates the automatic calibration

to ar = 0 dB for input power variations of 1 dB. The reference power trace aK

was reduced by a factor 0.05 for display, but the correct coupling factor

k = 0.0550 was applied for the relative attenuation trace (1)

a = 8~686 (/k.aK/a - 1) = 0 dB. Each I-hour frame represents averages r .

of about 107 actually acquired data points. Detection sensitivity and longterm stability are displayed in Figure 3b.

Program configuration is stored in a separate file on disk. An autostart function is available for studies that are conducted unattended. In the

event of a power failure the program will automatically restart.

Post processing of data repeats calibrated signal corrections as done in

the real-time mode. Scatter plots of ar

are made versus pressure in a pointmode (e.g., Figure 6).

2.2 Moist Air Attenuation Measurements

The objective of the experiments was to perform pressure scans of the

attenuation rate a due to water vapor absorption in moist air. An extensive

series of controlled measurements was performed at 137.8 GHz to determine

9
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42

Temperature Readings

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Figure 3. Mm-wave spectrometer operational data (five temperatures T;) peak

values of reference and reflected signals aK' and a; and relative

attenuation (ex ) for a I-hour measurement period with an evacuated

cell (fR = 137~8 GHz):

(a) automatic calibration to ex = 0 dB for changes, Aa = 0-1 dB"

(b) detection stability and se~sitivity K'

(exmin = 0.006/0.13 0.05 dB/km).

10
a(P = e+p). Data a(T, e, p) were taken covering the following range of parameters:

T = 316 to 282 K;

e = 0 to el (RH < 95%); and

P = el + p, where p = 0 to 1200 torr (capacitance

manometer), p = (I to 3 atm (aneriod

manometer)*.

was determined by the temperature TWof the water

temperature

vapor pressure

total pressure

Maximum vapor pressure el

reservoir.

With the spectrometer performance optimized at P = 0 (see Figure 3b), an

additional set of problems appeared when the gas pressure was varied. Introducing and removing gas from an enclosure changes the temperature Tg of a

sample (Figure 4). Only pressure scan rates below ± 100 torr/min ensured

quasi-static gas conditions, Tg = TC• Typically, the pressure was varied in

steps. While the gas settled, the klystron frequency fK was retuned to

balance the baseline of A(t).

Working with water vapor often brought disappointing results with respect

to reproductibility. Condensation effects on both mirrors and pinhole

coupling were avoided (see p. 5). One source was the "piston" effect where

local compression condenses part of the vapor; another error source was the

slow diffusion-mixing of water vapor with stagnant air. We calculated the

diffusion time constant for vapor molecules to travel 30 cm inside the cell

against 1 atm of dry air to be

T (K) 315 300 285

LD (min) 5.4 6.0 6.7

It takes a period longer than 5·LD for a homogeneous moist air mixture

P = el + p to develop. Ameasurement of a(P) shown in Figure 5a indicates

even longer time periods. Water pressure el (TW) settled with no delay when

the H20-valve was opened. Dry air injection first reduced el (piston effect)

and then it took up to 1 hour to obtain a stable value a(el+p). Mixing was

accelerated to less than 5 minutes by installing a fan, driven by a magnetically coupled rotary vacuum feed-through.

*Experimental pressure scale is measured in torr; the prediction model MPM

uses the pressure unit 1 kPa = 10 mb = 7.5006 torr.

11
(a) (b)

Real Time, cR.[pt '~'f1p," 25, 1986 - REe # 195

RUN 4 7 DISK # 4

40 IN Te = 26·C

(o + 620 torr)

;-' i'O;---T (middle) o "- a> o : 'Q . T (top) L- Ara -,... T (bottom), '"

...

Lc 30 a>

Cl +1.1 x 10-3

ffi

I0)

C

'"

20 .

OUT

(620 + °torr)

-0 48 96

TIme (s)

o o .........O"""'-'::LLU..J-L.i..LLW'-LLL~~-LLLLLLl..LLLJJ",L"j...;;.O """""",,0IaJ

FROM time TO

10: 09:27 113 Ree/div .SMin/Ree 10:33:27

Figure 4. Temperature responses inside the spectrometer cell:

(a) time-response test of gas temperature (T ) sensors,

(b) temperature-vs.-pressure behavior for a ~ypical dry air case.

(a) (b)

I

! ' , !

P = Oj~P = e ~' p = e+p ---.;.i p = O!

'. e,= 32.3 p =769 torr' t 1"iI\;--=;/J.'-...:--------~.'~.._,------..-. -" -V<.::;

f------ H20-v.lve open -----~

I

!

I

" , , f

-'--+·-ir-~·""--·•. -,f~-+"""r

I

o

c • -.J

. 6 ~rrr'rTT,--,-,-..".,......,,.,..,~rrrT'TT-,-,-,--,-,-r"'T'T'>-,r-.-.-rrrrrT1

F

..J

El! .1

.4 z

o

H

I-

.3

t5I-:I .2

I

I

I

I

I

[

i

I

I

i '0 '" 40 mV

MOIST AIR

T

e =305.8 K

PRESSURE Pxl00, torr

o 60 time ("N\in)

[J 2 3 456 7 8 '3

Figure 5. Mixing effects of H20 + AIR from time series of 138 GHz

attenuat ion:

(a) piston effect and diffusion mixing; (b) decompression condensation during pump-down over open vapor

source.

12
One other effect was observed when dealing with moist air inside a

vessel: reducing the total pressure P caused the water vapor to condense by

decompression cooling. Even with the water vapor supply fully exposed to the

air mixture, it took a long time (20 min) to reestablish the initial vapor

pressure e1 as indicated byar(P) in Figure 5b (mixing fan was off).

2.3 Water Vapor and Moist Air Attenuat ion Resu lts

Moist air attenuation a at a frequency f that falls within the millimeter-wave window range centered at 140 GHz, can be expressed by [6J, [7J

dB/km, (5)

where e and p in kPa are partial pressures of water vapor and dry air, respectively. Pressure-broadening theory of the H20 rotational spectrum predicts

(e > 0.01 kPa) a fixed ratio mbetween air-(ep) and self-(e2) broadening;

i . e. ,

(6)

An extensive series of controlled laboratory measurements was performed at

137.8 GHz to determine the k-coefficients of (5) and (6). Table 1 is a summary of over 2500 individual data points a(T, e, p).

At T = 303 K, the foreign-gas broadener AIR (p) was replaced by its

principal constituents N2, O2, and Ar. These results are listed in Table 2.

The broadening efficiency m is useful to explain H20 absorption processes that

support (5) since a = kse (e+mp). Pure oxygen (02) measurements for pressures

up to 2.4 atm against Ar as the "loss-free" reference provided an estimate of

kd when multiplying the result by 0.21.

Data of Table 1 were further reduced to a reference temperature

To = 300 K. Temperature dependence of the ks,f,d coefficients was fitted to a

power law,

k(T) = kSx dB/km-kPa 2

, (7)

where S = 300/T is an inverse T-parameter.

The results for moist air attenuation at 137.8 GHz, when expressed by (5)

to (7), led to

13
Table 1. Comparison between Measured (X) and Model-Predicted (M-MPM, see

Section 3) Coefficients ks f of (5). Experimental conditions:

f = 137.8 GHz, T = 282-31b'K, P = ei + p, P = 0-110 kPa

Moist Air Dry Air

T e 1 (RH) ks kf m kd

K kPa dB/km-kPa 2 dB/km-kPa 2

x10- 2 xlO- 2 xlO- 6

X 315.5 7.49 (90%RH) 8.01 0.485 6.06 - M 7.85 0.481 6.13 1. 93

X 305.9 4.45 (90%RH) 10.9 0.540 4.95 -

M 10.81 0.530 4.90 2.10

X 303.2 3.80 (90%RH) 12.0 0.558 4.65 2.2

M 11.84 0.545 4.60 2.11

X 296.1 2.51 (90%RH) 15.0 0.59 3.9 - M 15.08 0.589 3.91 2.29

X 286.7 1.39 (90%RH) 21.0 0.65 3.1 -

M 21 .22 0.649 3.06 2.46

X 281.8 1.05 (94%RH) 25.7 0.68 2.65 - M 25.49 0.687 2.70 2.64

14
Table 2. Attenuation Measurements of Water-Vapor/Air-Constituent Mixtures

(f=137.8 GHz,T=303 K, E1=3.80 kPa) Expressed with kx-Coefficients

of (5); and Corresponding Broadening Efficiencies mx (6). Included

are Line-core Measurements mL and their Predictions ml and k1 Transposed to 138 GHz

FAR WING (303K) LINE CORE (300K)

ky k, my m, my

f(GHz) 137.8 137.8 22.2 183.3

dB/km-kPa 2 [16J [16J J[l1J

Species x10- 2 x10- 2 x10- 2

H2O 12.0 2.55 100 100 100 100 100

AIR 0.558 4.65 21.9il 20.8 22.7 22.1 ( e- o. 6) -- N2 0.627 5.23 24.6 22.8 24.9

O2 0.322 2.68 12.6 14.0 14.3

Ar 0.222 1.85 8.7 11.4 10.3

Linewidth (MHz/kPa) 135.0 143.0 151.9(e 1 • 1 )

*Reference value (line-core average)

15
~---------- ---- -~~

and

ks(T) 0.133(4)810 •

3(3),

kf(T) 5.68(5)10-383•

0(4),

kd(T) = 2.2(5)10-682•

8,

m = 0.0427/87•

3•

(8 )

Digits in parentheses give the standard deviation from the mean in terms of

the final listed digits~ Typical examples of data plots ar(e) and

ar (e1 + p) are exhibited in Figure 6. All experimental results supported the

formulation in (5). Model predictions of the experimental data are given in

Figure 14 (Section 3.4).

3. ATMOSPHERIC PROPAGATION MODEL MPM

(see Appendix Aand B for Details)

Dry air and atmospheric water vapor are major millimeter-wave absorbers;

so are suspended droplets (haze, fog, cloud) and precipitating water drops

that emanate from the vapor phase. A practical model (designated program

code: MPM) was formulated that simulates the refractive index.!!. = nI - jn II of

the atmospheric propagation medium for frequencies up to 1000 GHz [1] - [3].

Since the interaction with a neutral atmosphere is relatively weak, the

refractive index is converted into a refractivity in units of parts per million,

= (.!!. - 1) 106 ppm.

3.1 Features of the Program

A user-friendly parametric program was developed that calculates the

values of the complex refractivity for atmospheric conditions as a function

of the variables f, P, T, RH, wA (A/B/C/D), w, and R, as listed in Appendix A

(Section A.I.l).

The output of MPM are three radio path-specific quantities:

• attenuat ion

• refractive delay

• dispersive delay

a(f)

80

8{f)

16

dB/km

ns/km

ps/km
(a)

137.8 GHz

.-, I'-='

L

W

ffcc

.2

• 1

....J

W

il

I

I

,

It

./-(

e1=28.5 torr

j I I I 1 I I "I i ! ! ! I ! ! JI ! ! ! I I ! I I I

2 4

PRESSURE ex10, torr

'3

+-- -- O.225dBL

j

j

i

a(e1)

I

I

i

I

~,/

J

I

I

I

a(e1)

I

m = 4.66x1o-2

137.8 GHz

300 e

RH '" 90%

e1 '" 28.5 torr

....- V - - - -

1=. -'

(b)

c

'-'

fI1

-0

4

-,.

I-)

-

H

l- .-,

-,

- II=1..:::...-

W

f- .-,

c. fII

....J i

w

il

[1 i

F'RE~=i':LJRE (P = e,+ p)xlOO, torr

Figure 6. Typical raw data plots of relative attenuation a(P) for pressure

scans at 137.8 GHz introducing

(a) water vapor, P = e, and (b) H20 + Air, P = e1 + p.

17
The height range 30 to 100 km is treated approximately excluding the

detailed 02-Zeeman effect and trace gas spectra (e.g., 03, CO, N20, etc.). . . .

Program MPM is written with extensive comments to run on IBM-XT/AT + 8087

coprocessor, or equivalent, microcomputers.

Extensive revisions of the MPM code have been made recently. The latest

version is described in Appendix A. Details include (a) a revised set of

overlap coefficients a5 [(A-12)J in the dry air line table (see page 66) for

the 60 GHz oxygen band based on a molecular fitting scheme reported by Rosenkranz [10J; (b) a relative humidity-driven growth model for hygroscopic aerso1

addressing haze conditions for RH = 90 to 99.9% [(A-3)J; (c) a new doub1eDebye model describing the complex permittivity ~(f,T) of water for f = 0 -

1000 GHz, T = -10 to 30°C [(A-17)J; and (d) an improved fog/cloud model that

includes a dispersive delay term [(A-16)J.

A nonlinear least-squares fitting scheme was applied to dielectric data

sets ~(f,T) reported below 1 THz. Various spectral functions (relaxation and

resonance) were considered, and the doub1e-Debye model provided the best fit

[15J. The Rayleigh approximation of the fog/cloud model was tested with

experimental results on fog attenuation at 50, 82, 141, and 246 GHz and on

differential fog delay between 246/82 GHz. All measured data were found

consistent with model predictions. Moist air effects and fog effects of

and S were assumed to be additive [14J.

18
3.2 MPM Calibration

Experimental results at 1386Hz, as described by (5) and (8), contain

foremost contributions from water vapor continuum absorption. Equation (5)

was used to "ca librate" the program MPM by enforcing the agreement between

experimental and predicted data. The continuum, assuming an f2 dependence, is

defined by (see (14a) of [IJ)

5 0.1820 f N"(f), c e

where the imaginary part of refractivity is given by (Table 3)

(9)

(10 )

and f is in 6Hz. A comparison in Table 1 shows that at 1386Hz, within experimental uncertainties, a good fit was obtained.

In addition to (10), new width data [IIJ for the 1836Hz H20 line (b3

listed in Table 1 of [IJ was increased by 11.6%) were used to update the MPM

program; also, b3 parameters of the 325 and 3806Hz H20 lines were increased

by 10 percent. Other MPM modifications were a change in the nonresonant line

width y of dry air from 5.6 x 10-3 to 4.8 x 10-3 [10J, the elimination of the

roll-of~ term 1/[1 + (f/60)2J (part of equation 13a in [IJ), and the imposing

of a high frequency cut-off F"(f) = 0 [see Eq. (A-9)J for f (vo+40y) [12J.

3.3 Interpretation of H20 Continuum Absorption

Since MPM employs a limited (~'1 THz) H20 line base, it is of interest to

find out which share of ks and kf (8) can be attributed to far-wing behavior

of the rotational H20 spectrum extending beyond 1 THz [6J. Results in Table 2

indicate broadening efficiency ratios at 1386Hz; e.g.,

(11)

which are similar to those observed at cores of the 22 and 183 GHz lines.

Consequently, kf can be interpreted as a foreign-gas broadening effect whereby

MPM lines account for about 30 percent of the rotational H20 spectrum.

Table 3 lists the assessment at 300 K (8 = 1). When the line core argument

(mL = 0.208/80.

5) is extended to ks' then a substantial share,

19
Table 3. Summary Data of H20 line Spectrum and H20 Excess Attenuation at

137.8 GHz, T = 300 K

a) Experiment-versus-MPM Predictions

MOIST AIR ORY AIR

ks Xs kf xf m xm kd xd

x10- 2 x10- 2 x10- 2 x10- 6

X 13.2 10.5 0.570 3.0 4.32 -7.5 2.2 - M 13.15 10.51 0.5666 3.09 4.309 -7.42 2.10 2.35

b) Local H2 0 Lines in MPM (31% of c):

M

I 0.802 3.5 I

0.175 3.8 121 .8 0.3

c) Complete H2 0 Line Spectrum (m = 0.22 assumed ..., see Table 2 )

I 2.59 3.5 I 0.57 3.0 22 -0.5 I

d) Excess H2 0 Absorption:

10.3 12.5 I (12 )

Table 4. Reported Data on (H20)2 Dimer Concentration eD/e over the

Temperature Range for-300 to 386 K

T , kPa 300 358.4 367.1 375.9 386.4

e , kPa 2.80 58.27 81.47 111. 9 159.3

eo kPa 0.0024 0.44 0.76 1.28 2.27

eo/e , x10- 3 0.9 7.6 9.4 11.4 14.2

eo/e 2 , x10- 1t 3.1 1.30 1.15 1.02 0.895

*Reference [8] [9J

20
(12)

is not supported by the H2 where a 0 monomer line spectrum i =(ax - all

(8 12 .

5 = -4.3%/K).

At this point one might speculate about

estimate of the partial dimer vapor pressure

(H20)2 dimer absorption. An

(13 )

was obtained by fitting data on physical dimer properties given in Table 4. A

strong 138 GHz attenuation rate,

330 e 87.

5

D dB/km, (14)

7 5 results when (12) and (13) are combined (8· = -2.5%/K).

3.4 MPM Predictions

Features of the user-friendly atmospheric propagation model MPM were

discussed in Section 3.1. The microcomputer version is written in IBM Professional FORTRAN with extensive comments that guide the user to appropriate

references for specific formulations. Three parametric presentations have

been found useful in practical applications, which are addressed in separate

subprograms:

Profiles Variable Parameters

A. Frequency f P, T, RH(v) , wA' w, R.

B. Humid ity RH,v f, P, T, wA' w.

c. Pressure P f, T, RH (e) •

A copy of the line code for program MPM-N/A (frequency profiles) is shown in

Appendix B. The detailed structure of MPM comes best to light in graphical

examples. Typical sea level behavior of MPM-predicted rates, a and 8, is

illustrated in Figures 7 to 13. Across the millimeter-wave spectrum

(Figures 7 and 8) one recognizes more or less transparent window ranges (WI to

W5) separated by molecular resonance peaks. Calculations of total radio path

21
------- --------------------

v(1 00"RH)=23. 0 91m 3

Curve 1D RH,%

1 0

2 1

3 3

4 10

5 25

6 50

7 75

8 100

100

h - 0 km 'Nl.\

E P=101.3 kPa, T=25°C

10 "-

m 'A'

"0 ~~

.

Z ~\,

0 1

:J

Z

W .1

«

50 100 150 200 250

FREQUENCY, GHz

300 350

Figure 7. MPM-predicted specific values of attenuation a and dispersive

delay 8 at sea level height h=O km (P=101.3 kPa, T=25°C, RH=O to

100%) over the frequency range, f=1 to 350 GHz. Window ranges are

marked WI to W5.

22
attenuation A [dBJ, delay B [psJ, and atmospheric noise temperature TA [KJ

require distributions of P(x), T(x), RH(x) along the propagation direction x

to be known [2J.

Spectroscopic properties of the air-broadened water vapor line centered

at 183 GHz are demonstrated in Figure 9. Accuracy of supporting line parameters (stength, width, shift) determines the reliability of predictions

needed for remote sensing applications with respect to atmospheric humidity.

With respect to line shape studies one observes that wing data from the delay

spectrum a(f) are unaffected by dry air pressure p. Outside a line-center

frequency range V

o

± 5y, dispersion N'(f) is independent of a particular shape

function F'(f) such as (A-9b).

Amajor concern for most M~W systems is their performance in rain. A

simplified classification of rain events is given in Appendix A (A.I.I). When

neglecting any statistical nature of rain within a radio path, the calculation

scheme (A-I8) provides an estimate on a(f) and a(f). Predictions (Figure 10)

are based on adding to the known state of moist air (P-T-RH) only one

additional parameter, namely the point rainfall rate R.

Of some importance is the fog/cloud prediction program in MPM. Systems

operating in the MMW range offer an attractive alternative to electro-optical

systems when operation has to be assured during periods of adverse weather

(rain, cloud, fog, haze, high humidity). Current interest is focused on the

frequency range 90 to 350 GHz where an optimum trade-off between atmospheric

obscurations and angular resolution can be achieved. All atmospheric loss and

delay effects have to be known accurately in order to analyze the potential

for all-weather performance. The suspended water droplet (SWD) formulation

(A~I6) and (A-Il) of MPM is an addition to the state of saturated air (P-TRH~IOO%) as illustrated in Figure 11. Key parameters are SWD content w in

g/m3 and temperature T in °C.

Another atmospheric ingredient is the mass concentration wA of hygroscopic aerosol (HAE). Solution droplets appear for RH > 80%, and haze conditions develop as RH approaches 100 percent. These conditions can be modeled

by assuming that at the reference humidity, RH = 80%, the HAE concentration

wA(RH = 80%) is known. The RH dependent swelling/shrinking w(RH) is described

approximately up to RH = 99.9% by a growth model (A-3).

Relative humidity RH is the variable that governs physical processes

taking place in the atmosphere with respect to water vapor. Practical models

23
-----------_..~---_. ------------

W5

20

15

Z 10

o

I-

«

::::5

Z

LtJ

I- 5

I-

«

o

MOIST AIR

P 101 kPa

T 20°C

v = 17.2 91m3

vn

<x( f)

o 50 100 150 200 250 300 350

FREQUENCY, GHz

Figure 8. Water vapor absorption in window ranges for constant relative

humidity increments (ARH 12.5%) at a sea level condition.

f

f

25 r a(f)

15 I -i

........ (/l

Q.

5 .....i , w

..J

a L- 0

r w

(/1

;;:: -5 r a::

w

-15 (/1

Cl. T • 20·C

is ! RH • 100~

1000

Curve 10 I P • e + p

<x( f) 1 I ,Pa l 2.34 (p. e)

10 1

\20

i 40 1 E 100 60 E 80 -'<

........ 1100 ;

!IJ j "0 ,

z

l 7'6'

0

i=

:§ 10

Z

~. w

>-

>- 183.310 « GHz

I

I ,

I I I ,

, I 170 175 180 185 190 195

FREQUENCY. GHz

Figure 9. Pressure-broadening (AIR) example of the 183 GHz H20 line.

24
P ... 101.3 kPc T=20'e

MOIST AIR + RAIN

GHz

Attenuation a and delay S rates for three rain events (R=10, 50,

and 100 mm/h) added to a moist air (RH=95%) sea level condition.

Also shown are dry air (0% RH) and moist air (50% RH)

characteristics.

100

.

Z

o

f- 1.0

<t

::J

Z

W

f0.10

E

.::!.

"'" 10 m

1]

25

E 20

.::!.

"'"Ul ·'5

a.

- 10

>-

<t 5

.-J

W

o 0

W -5

(f)

a:: -10

W

Cl.

(f) -15

0

-20

0

Figure 10.

25
(a)

E10,000

:{,

1000

i.J

.

Z 100

Q

L...

I

4: 10 ::J

Z

W

l- to f-

<

0.10

200

E

:{,

'"

(f)

Q. 100

.

>- 4:

-.J

W

o 0

w

(f)

cr

-100

(f)

o

MOIST AIR + FOG

P=101.3 kPa T=15 lie

- 200 L.----'--~_~~=--'""_ _"___'__l._ _'__~__'_.ll..L._.L_____'_______'_....JL___.l...__'_ _'____'_____l

o 200 400 600 800 1000

FREQUENCY, GHz

Figure 11. Attenuation a and delay rates for three fog events (w = 0.10,

0.25, and 0.5 g/m3) added to a saturated air (RH=100%) sea level

condition. 'Also shown are dry air (0% RH) and moist air (50% RH)

characteristics: (a) f = 1-1000 GHz,

26
(b)

MOIST AIR + FOG

P=101.3 kPa T=15°C

-Z

0'

k- 1.0 I

«

:J

LW

fl-- 0.10

«

100

E

' .... 10

m

1J

20

0.20

E E

::f. ""

"

'" 16 "

a. 0.10

(f)

Q. ..J

W

a 0

- 12 >-

«

-I

W \

100+0,5 91m3 0 8.0

-0,20

W 0 10 20 40

> A FREQUENCY. GHz

I

(f) 4.0 I t:r

W

(L 10 (f) 0

0 RH=O"

-4.0

0 50 100 150 200 250 300 350

FREQUENCY, GHz

Figure 11. continued: (b) f 1-350 GHz and f 0-40 GHz (insert).

27
for RH parameterization exceeding saturation are not available. Both absolute

humidity (v) and suspended haze droplet concentration (wA) can be expressed in

terms of RH variability. Absolute (v) and relative (RH) humidity are interrelated through the ambient temperature T.

Sulfates are the major RH-active ingredient of both urban and rural

aerosols; so is sodium chloride for maritime species. The atmosphere is never

free from HAE, with greatest concentrations near the surface and scale heights

on the order of 1 km. Above RH = 90%, suspended water droplets have developed

carrying the HAE essence in solutions. Average values of wA lie between 0.01

and 1 mg/m3• The humidity parameterization in MPM is demonstrated by the

examples given in Figures 12 and 13.

Pressure variability comes into play when modeling height dependencies.

Cumulative calculations of ~/~ for a slanted radio path through the neutral

atmosphere (e.g., ground-to-satellite) encounter pressures, P = 100 to 0 kPa,

which narrows the molecular absorption lines until they vanish altogether.

Pressure-, Zeeman-, and Doppler-broadening [(A-II)] have to be considered over

the height range 0 to 90 km. Another need for a formulation of pressure

profiles arises from spectroscopic studies applying pressure-scanning techniques. A simulation of laboratory measurements discussed in Section 2.3 is

exhibited in Figure 14.

4. EXPERIMENTAL-VERSUS-MODEL (MPM) DATA

Corroborative experimental data of sufficient quality to scrutinize MPM

predictions are scarce. Reliability, precision, and limited scope of supporting meteorological data often compromise the accuracy of results deduced from

field observations. Generally, laboratory experiments are more accurate by

simulating controlled electromagnetic and atmospheric conditions crucial to

validate a specific model aspect. In this manner, contributions from water

vapor lines (22 and 183 GHz) and from oxygen lines (48 to 70, 119 GHz) have

been evaluated [1], [4], [10], [11], [16]. Theoretical refinements are motivated to improve the interpretation of empirical laboratory data by establishing a connection to the physics of the problem. For example, a set of our

unpublished dispersion (N ' ) results on dry air, taken during 1976 between 53.6

and 63.6 GHz, provided reference data for an elaborate reformulation of interference coefficients that describe the 60 GHz O2 bandshape [10]. The new

28
Figure 12. Absolute (v) and relative (RH) humidity dependence of

attenuation a and delay at f = 94 GHz for various sea level

conditions (P = 101.3 kPa and T = -20 to 40°C).

29
20°C

10°C

~"" I '~~;' ~~~"" I' '" I' '~I~~lml"" I" "J

P 1

n1 3 kP C\ _---1w

:

0

.

2

: t!. a HAZE MODEL :,.-' -J g/M3

wA:0.001 g/M3 A-----·~w:0.1

~'Aji I

I--

10

E.::i. 8.0

""'-

m

\J

Z· 6.0

o

I4:

:J 4.0

Z

W

lI4: 2.0

-

-

-

r 1

I

I

I

I lw:O

HAZE MODEL \'A"r- '_:';~~:~:i C

I

J J

I I

I

I

I

I

I

20"C

I

I

I

I

-

I--

o

E

.::i.

""'- 6.0

(IJ

Q.

>-' 5.0

4:

-.J

W

o 4.0

W

(f) 3.0

(t

W

0...

(f)

o 2.0

1.0 I I I I I I I I --~-- ggl'--'-J'--'-'---'-'-<-J.-l--I.--'--'---l..-...-L-J-..........L--'---'---'-'-;~:-'-'-----L.J-J--'---'--L...'--'-...L'-'-'......-J-'-'-~ 99.5 99.9 100

RELATIVE HUMIDITY, ,,;

Figure 13. Two haze cases (A:1 mg/m3 and C:1 mg/m3) f~r prefog (RH = 99-99.9%) and fog (w=O.l and 0.2 g/m ) conditions at three

temperatures (0, 10, 20°C) displaying the associated

attenuation a and delay S rates at f = 220 GHz.

30
Figure 14. Pressure profiles at f = 138 GHz simulating the laboratory

attenuation measurements presented in Section 2.3.

31
-~- ---- ~--- --~- --~-------

coefficients a5 (see page 66) were adapted for MPM, and Table 5 demonstrates

the degree of agreement.

4.1 Laboratory Measurements

The results on moist air attenuation at 138 GHz [i.e., (5), (8)J provided

clues to a formulation of an empirical MPM water vapor continuum. Data from

other researchers were evaluated to check if the assumptions of (10) held up

at different frequencies. Water vapor attenuation at frequencies between 330

and 430 GHz is compared with MPM predictions in Figure 15. The data were

available in graphic form and had to be digitized by us. Considering the many

difficulties that plague absolute calibrations, a comparison of model vs.

experiment is encouraging. No anomalous absorption features have been

uncovered.

Two laboratory studies of the 183-GHz water vapor line have been reported

by a French group [llJ, [17J. We adapted the width results [llJ for the line

table of MPM. A detailed analysis of temperature-dependent wing data [17J is

given in Table 6. Equation (5) was applied to reduce both experimental and

MPM data for an intercomparison. At +1 GHz from the line center, the attenuation rate for pure water-vapor shows a discrepancy of 21 percent. The

origin of such disagreement has to be attributed to the 183-GHz line broadening formulation but not to the rather small contribution from the continuum.

4.2 Field Measurements

Ultimately, it is up to field experiments to garner realistic evidence in

support of model predictions. When conducted with care at different locations

under a variety of natural conditions, such experiments prove to be quite

costly.

Data from ITS field studies on the propagation of millimeter waves were

evaluated for water~vapor attenuation rates at 96.1 GHz [18J, [19J. Clear air

data and MPM predictions are in close agreement, allowing for the temperature

dependence, as demonstrated in Figure 16. The miss ion of these experiments

was to establish a data base for 11.4 to 96.1 GHz propagation in a humid

climate (Huntsville, AL, April-August 1986). A similar comparison was not so

favorable for a set of data displayed in Figure 17. The results were obtained

over a 1.5 km line-of-sight path in the Soviet Union at subfreezing

32
Table 5. Measured (EXP) and Predicted (MPM) Dispersion in Dry Air at 300 K

(Interference Coefficients from Rosenkranz [10])

Dispersion N' (f) Dispersion N' (f)

Nearby EXP I MPM EXP I MPM

Line Frequency p = 53.3 kPa Frequency p = 80.0 kPa

GHz ppm GHz ppm

25- 53.588 0.30 0.300 53.585 0.43 0.439

23- 54.123 0.35 0.338 54.119 0.50 0.490

19- 55.214 0.40 0.407 55.210 0.58 0.576

17- 55.776 0.42 0.421 55.772 0.60 0.589

15- 56.356 0.41 0.398 56.352 0.59 0.565

13- 56.960 0.38 0.350 56.956 0.45 0.502

3+ 58.439 0.19 0.174 58.435 0.26 0.253

7- 59.156 0.08 0.076 59.152 0.12 0.110

5+ 59.583 0.03 0.027 59.579 0.03 0.032

5- 60.296 -0.075 -0.084 60.292 -0.11 -0.134

7+ 60.425 -0.135 -0.122 60.421 -0.17 -0.170

9+ 61.141 -0.275 -0.252 61.136 -0.383 -0.361

11 + 61.790 -0.335 -0.342 61.785 -0.510 -0.522

13+ 62.400 -0.480 -0.475 62.396 -0.685 -0.679

3- 62.475 -0.510 -0.495 62.471 -0.720 -0.705

15+ 62.987 -0.590 -0.578 62.983 -0.80 -0.800

17+ 63.558 -0.610 -0.589 63.554 -0.841 -0.831

33
w

.j::>o

Table 6. Comparison between MPM-Predicted and Experimental Attenuation for

Water Vapor (e) and Moist Air (P = e1 + p) in the Wing Region of the

H20 Line Centered at Vo = 183.310 GHz

f. GHz l -vo-:~O- ~- - -~--r Vo + 1.0 I Vo + 0.4 -- ~--

MPM - PREDICTIONS

e 1.766kPa (13.25 torr) 1.059kPa (7.94 torr) 0.529kPa (3.97 torr)

T Lines Cont. Total Lines Cont. Total Lines Cont. Total

K

a, 310 3.66 0.53 4.19 11 .35 0.19 11 .54 17 .37 0.05 17.41

dB/km 300 4.17 0.70 4.87 12.90 0.25 13 .15 19.73 0.06 19.79

290 4.76 0.95 5.71 14.17 0.33 15.05 22.49 0.08 22.58

P 100kPa (750 torr) 100kPa (750 torr) 100kPa (750 torr)

a, 310 21.52 1.83 23.52 21 .39 0.95 22.52 11 .66 0.43 12.27

dB/km 300 23.59 2.07 25.86 23.10 1.06 24.35 12.57 0.47 13.24

290 25.92 2.40 28.53 25.00 1.19 26.41 13.58 0.51 14.31

DATA REDUCTION: MPM-vs-EXPERIMENT

MPM EXP* X/M MPM EXP* X/M MPM EXP* X/M - -%- - -- -%- - -- -%-

ks 300 1.56 1.67 7.1 11.72 14.2 21.2 70.56 75.3 6.7

Xc> - 4.56 4.1 -10.1 3.99 3.9 -2.3 3.88 3.5 -9.8

kf 300 0.121 0.136t 12.4 0.107 - N.A.

Xf' - 2.48 2.7 8.9 1.96 - N.A. -.-_.

m 300 0.0776 0.0814 4.9 0.0913 - N.A.

*Reference [1 7J, tNz-result reduced by 0.907.
10

320 340 360 380 400 420

FREQUEt'~CY, GHz

80

70 MOIST AIR ["2J -LAB- L.

E P = 98.0 kPa 409 GHz

60 T = 33 °c

"'-

m +

'"0 50 + +

Z

0 40

I-« 30 =>

Z

W

I- 20

I-«

10

0

0 10 20 30

ABSOLUTE HUMIDITY, 91m3

1000

MJISTAIR

E Curve ID P T RH v

kPa DC % 91m3

"" 1 x 96.9 8.5 99.0 8.4

2 () 97.3 25.5 80.3 19

m 3 + 98.0 32.9 65.2 23

-0

Z

0 100 - W6

<{ W5 =:J

Z

W

<{

Figure 15. Moist air attenuation a(f) across the atmospheric window ranges W5

and W6 (320 to 430 GHz) at temperatures 8.5, 25.5, and 32.9°C:

data points [21], [22]; solid lines, MPM.·

35
5 . 10 15

ABSG..UTE HUMIDITY, g/m3

25

P = 98 kPa

o : EXPERIMENTAL RESllTS

10.0 0C - l5.o°C

o : EXPERIMENTAL RESllTS

20.0°C - 25.0°C

o : EXPERIMENTAL RESLlTS

30.0°C - 35.0°C

5 10 15 20

ABSG..UTE HUMIDITY, g/m3

............. l2.5°C

-------- l7.5°C

---- 22.5°C

••••••••••••• 12.5°C

---- 22.5°C

-.-.-. 27.5°C

-------- l7.5°C

---- 22.5°C

o

o : EXPERIMENTAL RESllTS

5.0°C - 10.00C

o : EXPERIMENTAL RESllTS

25.00C - 30.0°C

---- 22.5°C

-.-.-. 27.5°C

7.5°C

............. l2.5°C

•••••••• l7.5°C

7.5°C

............. l2.5°C

-------- l7.5°C

-------- l7.5°C

---- 22.5°C

.-.-.- 27.5°C

- ..- ..-. 32.5°C

o

1.5

o

z

Q

J

Z 0.5

W

lIo

E

:i.

\

ffi

" 1.0

E

:i.

\

ffi

" 1.0

E

:i.

\

ffi

" 1.0

Z

Q

J

Z 0.5

W

lIZ

Q

J

Z 0.5

W

lIFigure 16. Moist air attenuation a(v) measured at 96.1 GHz over a 21.4 km

line-of-sight path located in Huntsville,AL (h :: 0.3 km) 'for six

temperature groups between 2.5 and 37.5°C [19J data points are 5-

min averages for 4.5 days (5/4-6, 8/15-16/1986); solid lines, MPM.

36
2.0 2.0 I' 'I' I 't ' I ~T I _I

1.5 T = -7"C

.. ..

• I RH = 3411 (91ll ElIp.)

lv=Z.6)

E 1.5

.::t.

"-

z 1.0

o

z

w

l= 0.50

«

T .. 5'C

M.. "',.· ...... ,:-,.·I11····

y = to 91m3

P = 100.3 kPo

.. III.. ..

RH=15K

E

.::t.

"-

m"U

Z 1.0

o

z

w

l= 0.50

«

o I". I ,., I , . , , I .. . I . , .. I . , , ,I 0

2.0 I i 'i iii' " I i j I i I' iii, 2.0

E 1.5 T = -lO'C E 1.5 \ RH-7911 (!I9ll ElIp.) T .. -18°C

W .::t. .::t. • (v"/·3)

-....I "-

m

"-

m "0 "U I \ . . . . Z 1.0 Z 1.0

0' 0

i= i=

:3 « . :J

Z . Z

w . . w l= 0.50 . . . . . l= 0.50 . « . . ... «

0 0

180 270 180 195 21) 225 240 255 270

Figure 17. Water vapor attenuation rates a(v) across the atmospheric window

range W4 at four temperatures, 5, -7, -10, and -18°e:

data points [20]; solid lines, MPM,
-----------

e

!l

(0) 1.0 ;---------,

94 GHz

Ypenburg

h = 0 km

L = 0.935 km

P = 101.3 kPa

T = 8 ± 8 °C

11177 to 03/78

E l.5r------- 0~4·'-0--+---+---+---+---+-~

-"'"

......

co

-0 1.0

z

o 0.5

ex:

:::>

z

w

I- 0.0!'---..........'I'-'-+--..........,f-----4_ 0 4 12 40

ABSOLUTE HUMIDITY v (g/m3 ) RELATIVE HUMIDITY RH(%)

(b) (c)

1.5

c

..

.!II

"

jJ;l

"d

i

S

.5

"-ll

9

Figure 18. Terrestrial path attenuation at 94 GHz and 0.65 ~m (visible light)

under nonprecipitating conditions as a function of absolute (v)

and relative (RH) humidity [3J: (a) data points, 5-min averages

taken every 30 min during a period of 4 months [23J; (b) MPM

simulation of (a) for absolute humidity; (c) MPM simulation of (a)

over the range, RH = 95 to 100%, including haze model C.

38
temperatures for frequencies between 192 and 260 GHz [20J. Experimental

uncertainties are not discussed, the extreme environmental conditions may have

played a role. On the other hand, 335 - 420 GHz field data (included in

Figure 15), that were reported by another group from the Soviet Union [21J,

[22J agree remarkably well with MPM predictions.

Attenuation data at 94 GHz have been recorded in a coastal region of the

Netherlands [23J. Data, when presented in Figure 18 versus absolute humidity

v, display significant random excess attenuation over MPM predictions. The

same data plotted versus RH places all excess attenuation at RH > 98%. Haze

and fog conditions probably were present as evident from optical transmission

data. The highest excess of 0.8 dB/km requires w 0.16 g/m3, a value typical

for heavy fog.

Figure 19 presents atmospheric noise temperatures measured against zenith

at two different sites simultaneously at 10, 33, and 90 GHz [24J. Predictions

with the MPM radio path program reproduce the frequency correlations quite

correctly, which tends to confirm the f2 assumption made for H20 continuum

absorption (10). In addition, model data set a limit for total precipitable . .

water vapor V[mmJ carried by the air mass. Noise exceeding this limit probably originates from suspended droplets. Data trends stemming from differences in the f-dependence of moist air and SWD absorption support such assumption.

5. CONCLUSIONS

Radio properties of the atmosphere are both a barrier and a boon to

applications in the 10-1000 GHz spectral range. The first part of this report . .

gave a somewhat detailed description of a laboratory experiment that had to

apply latest advances in digital electronics and cryogenic detection to derive

at 138 GHz two attenuation coefficients, ks and kf (8). At first sight, these

two quantities describe the attenuation rate of moist air over a rather inconspicuous range from 0.1 to 10 dB/km; however, a more detailed analysis

revealed the k-formulation provides conclusive evidence on temperature and

pressure dependence of the water vapor continuum. Attaching an f2 dependence

to the 138-GHz results turned a frequency limited « 1 THz) propagation model

into a useful tool capable of operating in frequency, humidity, and pressure

domains of the atmosphere.

39
1.80 j I I

at 10 CHz

at 33 CHz

~\O~?>

/

/

\

\

/

--h- at 10 CHz

1.55

uo

1.05

0.80 LI__-'-__"-_-'-__-'-__"'-_~___'_____'

"".0 6.0 8.0 10

\

\

\

S'O~

at 33 CHz

7

\l'lr \

\

.

'I'" Q

"t"

.. at 90 CHz

'2

~\O~?>

" "

\

\

\3¢1'

\

,

~~Cl

at 10 CHz

..0

"2

2.0 1""1-------h

o

= 3.80 km

White Mountain, CA I I

"

0.8

8.0 16 26

11.5 I i I

-'"

1j

'-

G."

.Eo

.i

120

I

~ro~~ ,,/

/ / I

/ /

/

/

I I I

100

28 32.

"

" 20 12 '0

, t'l \1\

"

'I '", Q at 90 CHz /

1 / /

1 t ,-/

at 10 CHz

20 36 52 68 " r'l---------------~-------

><:

1j

.!'!

1:

......E

'0

<£

.j:>o

o

at 90 CHz

o~~ ,,"\

'\"J~+"r' ,,/"

at 33 CHz

TA,atm (Vertical) l K J

7.5

'.5

5.5

~~

,.• 1, \;;)0 I 8.0 16 2~ .52 "0 1fS"

at 90 CHz

85 '5 lOS

-+/r

ho = O.25km

(Berkeley, CA)

Clear Weather

TA,alm (Vedical) l K ]

25 '5

at 33 CHz

'0

20

12

Figure 19. Correlated vertical atmospheric noise temperatures T

A at the

frequency pairs 10/33, 10/90, and 33/90 GHz. Path-integrated

water vapor is V=Jvdh mm. The measurements were conducted from

two sites located at height'levels ho = 0.25 and 3.30 km: data

points [24J; solid lines, MPM with a mean July height profile

(0-30 km) of P, T, RH for San Francisco, CA [3J.
The report discussed details of contributions to modeling atmospheric MMW

properties, foremost the attenuation calibration of MPM employing new laboratory results on moist air. Water vapor continuum absorption and, above RH =

90%, droplet attenuation are both affected by relative humidity RH. For haze

formation, the range up to RH = 99.9% was modeled. So far, in fog and cloud

situations, when RHexceeds 100 percent, values for w cannot be modelgenerated from the atmospheric water vapor content.

The code MPM was readily accepted by radio scientists and engineers.

About 90 requests for copies of MPM have been honored since January 1986.

Quotes from received comments were encouraging: "MPM proved of cons iderab1e

value,·' -- "documentation is about the best I have ever seen," -- "technical

flow, model development and general visibility for application efforts is

superior," etc. The Microwave Group of the Internat iona 1 Rad iat ion Commiss ion

largely adopted MPM as atmospheric transmission code [25J.

Although MPM was found capable of predicting atmospheric NMMW propagation

limitations, several shortcomings still exist. They are, for example, the

missing confirmation for a physical basis of water vapor continuum absorption

(e.g., [7J, [13]) dominating transmission in atmospheric window ranges centered at 90, 140, 220, 340 GHz and higher; needed measurements of spectroscopic parameters (i.e., shape, strength, width and shift) for spectral lines

of the main absorbers (02 and H20) over the full atmospheric temperature range

(300-200 K); and a lack for reliable subfreezing transmission data to clarify

the problems that are indicated by Figure 17. Further parametric (frequency,

pressure, humidity, temperature, gas composition such as H20 + AIR) studies

are proposed to realize the benefits obtainable from the high-humidity performance of the spectrometer that has been perfected to overcome a great deal of

difficulties. Pressure-broadening of the 183-GHz line uniquely identifies

monomer behavior (see Table 6). A comparative study of wing (fo ±6 GHz) and

far-wing (220 GHz) responses to T and v(RH) variations would allow an apportioning of local line (known) and continuum (unknown) contributions.

6. ACKNOWLEDGMENTS

The authors wish to thank J. P. Stricklen for his skillful programing

efforts, and Dr. T. Manabe for a most beneficial cooperation. The work was supported in part by the Naval Ocean Systems Center

(Ref: RA35 G80), and the experimental portion (Section 2) by the U. S. Army

Research Office under Contract ARO 107-86.

41
7. REFERENCES

[lJ Liebe, H. J. (1985), An updated model for millimeter wave propagation in

moist air, Radio Science 20, no. 5, 1069-1089.

[2J Hopponen, J. and H. Liebe (1986), A computational model for the

simulation of millimeter-wave propagation through the clear atmosphere, NTIA Report 86-204, October, 32 pp. (NTIS Order No. PB 87-131173/AS).

[3J Liebe, H. J.(1987), A contribution to modeling atmospheric millimeterwave properties, FREQUENZ (Telecom. J.) 11, no. 1/2, pp. 31-36.

[4J Read, W., K. Hillig II, E. Cohen, and H. Pickett (1987), The measurement

of absolute absorption of millimeter radiation in gases: The absorption of CO and O2, IEEE Transact. Ant. &Propagation, submitted.

[5J Liebe, H., V. Wolfe, and D. Howe (1984), Test of wall coatings for

controlled moist air experiments, Rev. Sci. Instr. 55, no. 10, pp. 1702-

1705. -

[6J Liebe, H. J. (1984), The atmospheric water vapor continuum below

300 GHZ, Int. J. Infrared & Millimeter Waves ~, pp. 207-227.

[7] Hinderling, J., M. Sigrist, and F. Kneubuehl (1987), Laser-photoacoustic

spectroscopy of water-vapor continuum and line absorption in the 8 to

14 ~m atmospheric window, Infrared Phys. 27, no. 2, pp. 63-120.

[8J Suck, S. H., A. E. Wetmore, T. S. Chen, and J. L. Kassner, Jr. (1982),

Role of various water clusters in IR absorption in the 8-14-~m window

region, Appl. Opt. Q, no. 9,.pp. 1610-1614.

[9J Curtiss, L. A., D. J. Frurip, and M. Blander (1979), Studies of

molecular association in H20 and O2°vapors by measurements of thermal

conductivity, J. Chern. Phys. 2!, no. 6, pp. 2703-2711.

[10J Rosenkranz, P. W. (1987), Interference coefficients for overlapping

oxygen lines in air, J. Quant. Spectr. Radiat. Transfer, in press.

[llJ Bauer, A., M. Godon, and B. Duterage (1985), Self- and air-broadened

linewidth of the 183 GHZ absorption in water vapor, J. Quant. Spectr. Radiat. Transfer 33, no. 2, pp. 167-175.

[12J Hill, R. J. (1987), Absorption by the tails of the oxygen microwave

resonances at atmospheric pressures, IEEE Transact. Ant. &Propagation

AP-35, no. 2, pp. 198-204.

[13J Rosenkranz, P. W. {1985, 1987), Pressure broadening of rotational bands.

I. A statistical theory, J. Che~l Phys. 83, no. 12, pp. 6139-48; II.

Water vapor from 300 to 1100 cm ., J. Chern. Phys. 87, no. 1, pp. 163-

170. -

[14J Liebe, H. J., T. Manabe, and J. P. Stricklen (1987), Millimeter-wave

attenuation and delay for a fog event, IEEE Digest: 12th Int. Conf.

Infrared &Millimeter Waves, Orlando, FL, December.

42
[15J Manabe, T., H. J. Liebe, and G. A. Hufford (1987), Complex permittivity of water between·O and 30 THz,· IEEE Digest: ·12th Int. Conf. Infrared &

Millimeter Waves, Orlando, FL, December.

[16J Liebe, H. J., and T. A. Dillon (1969), Accurate foreign-gas-broadening

parameters of the 22-GHz H20 line from refraction spectroscopy, J. Chern.

Phys. 50, no. 1, pp. 727-732.

[17J Bauer, A., B. Duterage, and M. Godon (1986), Temperature dependence of

water-vapor absorption in the wing of the 183 GHz line, J. Quant.

Spectr. Radiat. Transfer 36, no. 4, pp. 307-318.

[18J Liebe, H. J., K. Allen, G. Hand, R. Espeland, and E. Violette (1985),

Millimeter-Wave Propagation in Moist Air: Model Versus Path Data, NTIA

Report 85-171, March, 62 pp. (NTIS Order No. PB 85-208700).

[19J Manabe, T., R. O. DeBolt, and H. J. Liebe (1987), Moist air attenuation

at 96 GHz over a 21 km line-of-sight path, IEEE Digest: 12th Int.

Conf. Infrared &Millimeter Waves, Orlando, FL, December.

[20J Fedoseev, L. I., and L. M. Koukin (1984), Comparison of the results of

summer and winter measurements of atmospheric water vapor absorption at

wavelengths 1.5 to 1.55 mm, Int. J. Infrared and Millimeter Waves 5,

no. 7, pp. 952-964. -

[21J Furashov, N. I., V. Y. Katkov, and V. Y. Ryadov (1984), On the anomalies

of submillimeter absorption spectrum of atmospheric water vapor, Int. J.

Infrared and Millimeter Waves i, no. 7, pp. 971-981.

[22J Furashov, N. I., and V. Y. Katkov (1985), Humidity dependence of the

atmospheric absorption coefficient in the transparency windows centered

and 0.88 and 0.73 mm, Int. J. Infrared and Millimeter Waves 6, no. 8,

pp. 751-764. -

[23J Bu~s, J. H., and L. H. Janssen (1981), Comparison of simultaneous

atmospheric attenuation measurements at visible light, midinfrared (3-5~m) and millimeter waves (94 GHz), lEE Proc. 128, Pt. H.,

no. 3, pp. 131-136. ---

[24J Costales, J. B., G. F. Smoot, C. Witebsky, G. DeAmici, and S. D.

Friedman (1986), Simultaneous measurements of atmospheric emissions at

10, 33, and 90 GHz, Radio Science ~, no. 1, pp. 47-55.

[25J Kuenzi, K. F., ed. (S. Clough, N. Grody, K. Kuenzi, H. Liebe, A.

Neuendorffer, B. Read; P. Rosenkranz, and C. Warner; Contributors)

(1987), Report of Microwave Group on ITRA-Intercomparison Campaign

Workshop, University of Maryland, 86 pp., March.

43

APPENDIX A

THE REFRACTIVE INDEX OF THE NEUTRAL ATMOSPHERE

FOR FREQUENCIES UP TO 1000 GHz

A.I. INTRODUCTION

Dry air and atmospheric water vapor are major millimeter-wave absorbers;

so are suspended droplets (haze, fog, cloud) and precipitating water drops

that emanate from the vapor phase. A practical model (designated program

code: MPM) was formulated that simulates the refractive index.!!. = nI - jn" of

the atmospheric propagation medium for frequencies up to 1000 GHz [lJ, [3J*.

The main purpose of the program is to express the electromagnetic properties

of the neutral atmosphere in terms of available and/or measurable

quantities.

The free propagation of a plane electromagnetic wave at frequency f and

an initial field strength Eo in an isotropic gas medium over distance L is

described by the complex transmission factor

! E E(L)/Eo = exp[-(2nf/c) (nil + jn')LJ

where nI (f) and nil (f) are frequency-dependent measures of delay and loss, and

c is the speed of light in vacuum. Since the interaction with a neutral

atmosphere is relatively weak, the refractive index is converted into a

refractivity

N = (.!!. - 1)106 ppm,

in units of parts per million.

Refractivity N for moist air can be obtained, in principle, by a summation over all absorption features in a given volume element. In practice,

various degrees of approximations are employed to reduce labor and computer

time required, since the number of contributing spectral lines by the dominant

absorbers (water vapor and oxygen) and by various trace gases (e.g., 03)

exceeds 10,000. The model MPM consists of local H20 (30x) and 02 (48x) lines

* [ J See 7. REFERENCES in main text.

45
----------

below 1 THz and an empirical approximation to the contributions by H20 lines

above 1 THz. To complete the model, continuum spectra for dry air, suspended

water droplets (haze, fog, cloud), and rain are added. The supporting

spectroscopic data base contains more than 450 coefficients.

A.1.1 Features of Program MPM

A parametric program was developed (see Section A.2) that calculates the

values of the complex refractivity

! = No + N'(f) - jN"(f) ppm

or corresponding path-specific quantities of particular interest to radio

engineering; i.e.,

refractive delay dispersive delay

attenuation

ns/km,

ps/km, and

dB/km;

for atmospheric conditions as a function of the variables f, P, T, RH,

wA (A/B/C/O), w, and R, as listed in the scheme below:

Variable

frequency

barometric pressure

temperature

relative humidity

Symbol

f

P

T

RH

Va 1idity Range

1000 GHz

120-0 kPa - 50- + 50°C

0-100%

Medium

Moist

Air

haze model: RH=80-99.9%

code A, B, C, 0

(or combinations thereof) Haze

plus hygroscopic aerosol

reference concentration wA(80%RH) 0-1 mg/m3

-----------------

suspended water droplet w(100%RH) 0-10 g/m3 Fog,

concentration Cloud

ra infa11 rate R 0-200 mm/h Rain

The height range 30 to 100 km is treated approximately excluding the

detailed 02-Zeeman effect and trace gas spectra (e.g., 03, CO, N20, etc.).

46
A.l.2 Physical Variables

The purpose of this section is to relate measurable variables to Nmodelspecific variables, whereby the state of dry air is described by a partial air

pressure p in kPa, a relative inverse temperature variable is 8 = 3001(273.15 + T)

with T in °C, and relative humidity is given by

RH = (e/e s)100 = (vlv s)100 = 4.151 x 10-9(e/8 5)exp(22.648) 100%. (A-I)

Equation (A-I) governs physical processes taking place in the atmosphere with

respect to water vapor. Absolute (v) and relative (RH) humidity are interrelated through

v = 1.739 x 109

RH·8 5

exp(-22.648) - 7.223 e 8 g/m3 (A-2)

where e is the partial water vapor pressure in kPa as part of the total (barometric) pressure P = P + e.

Water vapor variability at sea level (e.g., P = 101 kPa, 8 = 1.016 or

22°C) is typically

v

RH

Dry

1

5

Normal

10

50

Humid

17

85

Saturated

20g/m3

100 %

Suspended hydrometeors are described by the liquid water concentration w,

which relates approximately to optical (0.55 ]Jm) visibility U(km). A

schematic categorization can be made by

Stratus Convective

Haze Fog Cloud Cloud

w 10-2 10-1 1 5 g/m3

U 1.1 0.27 0.07 0.03 km

47
---~------

Another atmospheric ingredient is hygroscopic aerosol with a mass concentration wA in mg/m3• Solution droplets appear for RH > 80%, and haze conditions develop as RH approaches 100 percent. The growing haze droplets can

reach values (w < 0.1 g/m3) sufficient to contribute to medium losses. Haze

conditions are modeled by assuming that at the reference humidity, RH = 80%,

the concentration wA(RH=80%) is known. Any RH-dependent swelling/shrinking of

w(RH) up to RH=99.9% is modeled by

w = wA(C1-RH)/C2(100-RH) = wA g(RH), (A-3)

where g(RH) is a growth funct ion. The following values have been reported for

C1, C2:

Case Aerosol Species C1 C2 g(RH=99.9%)

._-

A Rural 117 1.87 91

B Urban 128 2.41 117

C Maritime 183 5.31 162

D C + Strong Wind 197 5.83 167

(>10 km/h)

Average values of wA for given stabilized climatic situations can be

found in the literature. Typical values for wA lie between 0.01 and 0.5 mg/m3

and the increase to w can be substantial as indicated by the maximum prefog

values g(99.9%).

Precipitation originates as a statistical event within clouds suspended

in saturated air. Its vertical distribution is separated into two regions by

the height of the aoc isotherm, which can vary between 6 km and ground level

depending on season and latitude. The lower part is mostly liquid drops, and

the upper region consists of frozen particles with occasional supercooled

droplet loadings by strong updrafts.

Point rain rates R have proven useful in modeling rain-induced

effects. Rain rate can be related to percent time, t R, a given value occurs

over the period of an "average" year; to the effective rain cell extent LR/L;

and to the instaneous suspended liquid water concentration,

3 wR = m R g/m .

In terms of these variables, an hypothetical local rain may be classified as

follows (horizontal path, L = 10 km):

48
-- -- --- ------------------------------- ----------- ------- - ---~-~------

Drizzle Steady Heavy Downpour Cloudburst

R 1 5 20 100 250 mm/h

t R 2 0.5 0.07 0.001 0.0001 % per yr

LR/L 1 1 0.7 0.35 0.2

m 0.1 0.07 0.05 0.04 0.04

These numbers may differ substantially for given locations.

The simple coefficient scheme reveals some fundamentals of rain. Changes

in the factor m indicate rain rate-dependent characteristics of drop-size

distributions. Widespread steady rain occurs more uniformly and favors small

drop sizes (~1 mm diameter) that stay in the air longer. Heavy showers are

more localized, favor larger drops, and occur less frequently.

A.2. MODEL FOR COMPLEX I~E FRACTIVITY

The complex refractivity in Nunits (i.e., ppm =10-6)

!!(f ;P/ T/ RH ,wA/w , R) = No + NI (f) - j Nil (f) ppm (A-4)

is a macroscopic measure of interactions between radiation and absorbers. The

refractivity consists of a frequency-independent term No plus various spectra

of refractive dispersion N'(f) and absorption N"(f).

In radio engineering it is customary to express the imaginary part of (A4) as power attenuation a and the real part as group delay a (with reference

to vacuum) as follows:

and

a = 0.1820 f N"(f)

a = 3.336[No + N'{f)J

dB/km

ps/km,

(A-5a)

(A-5b)

where frequency f is in gigahertz (GHz) throughout.

Radio refractivity is defined to be !! = No at f = 0 and consists of four

terms; i. e. ,

49
------ ----------

The individual contributions are described for dry air by

NO 2.588 P 8, (A-6) P

for water vapor by

NO = 2.39 e 8 + 41.6 e 82, (A-7) e

for the SWD term N~ by (A-16c), and for the rain term N~ by (A-18c). The

results (A-6) and (A-7) have been determined experimentally at microwave

frequencies where dispersive contributions N(f) are negligible.

A calculation of the spectrum ~(f) for frequencies up to 1000 GHz

consists of several additive parts:

resonance information of na=48 oxygen lines and nb=30 water vapor

1ines

nonresonant O2 and pressure-induced N2 absorption (~p)

continuum absorption from far-wing contributions of strong H20 lines

falling in the frequency range 1-30 THz (~)

suspended water droplet SWD term (~)

rain-effect approximation(~R)

Absorption and dispersion spectra are obtained from line-by-line calculations plus various continuum spectra ~,e,w,R according to

n

a

n

b

Nil (f) L (SF"). + Nil + L (SF"). + Nil + Nil + Nil (A-8a) i =1 1 P i=l 1 e w R

Dry Air 'Water Vapor 'SWD -Rain

n

a nb

N' (f) L (SF ' ). + N' + L (SF'). + N' + N' + N' (A-8b)

i=l 1 P i=l 1 e w R

where S is the line strength in kilohertz, and F' and F" are real and

imaginary parts of a line shape function in GHz-1•

A.2.1 Local Line Ab?orption and Dispersion

The Van Vleck-Weisskopf function is modified to describe to first-order

line overlap effects, which leads to local absorption and dispersion line

profiles in the form

50
and

F"(f)- [l+l_2.(VO -f +VO+f)JA - X Y Y X Y (A-9a)

(A-9b)

with the abbreviations

2 2 X = (vo - f) + Y ,

A = yf/vo'

Standard 1ine shapes F" (f), including the modified Van Vleck-Weisskopf

function (A-9), predict in frequency regions of local line dominance about the

same results for N"(f) as long as F"(f) exceeds by 0.1% the peak value at

f = vo' Far-wing contributions of smaller magnitude depend very much upon the

chosen shape function. For f + 00, the wing response of (A-9a) becomes nonphysical and is cut off; i.e., F" = °

when f (vo + 40y). So far, no line

shape has been confirmed that predicts absorption intensities over ranges 10-3

to < 10-6 of F"(vo)' Far-wing contributions from strong infrared water vapor

lines, where ~(vo) can exceed 106 dB/km, are accounted for summarily by empirical correction [see (A-15a)].

The line parameters are calculated by the expressions below:

Symbol 02 Lines in Air H20 Lines in Air Eq.

S, kHz alP s3exp[a 2(1-S)] b

1

e S3.5exP[b2

(1-S)] (A-1O)

y, GHz a3(Ps(0~8-a4) + 1.leS) b

3

(paO. 6 + 4.80ea1~1) (A-ll )

a

6 a

5

P a 6

° (A-12)

Line center frequencies v and the spectroscopic coefficients a1(~10-7 Hz/Pa)

to a6 and b1(~10-3 Hz/Pal to b3 for strength S, width y, and overlap correction 6 are listed in the Line Data File of MPM (see Appendix B).

For the 02 lines in air, (A-9) to (A-12) are valid for altitudes

h 35km (p> 0.7 kPa), where lines are pressure-broadened. Higher up, Zeemansplitting and Doppler-broadening of the Zeeman components must be taken into

account (Liebe and Gimmestad, 1978). An estimate for h > 35 km is made by

51
GHz (A-l1a)

~eometrically adding to the pressure proportional width Ya in (A-II) a second

term

where H is the scalar Earth magnetic field strength in Tesla, ranging from

0.2 to 0.9 x 10-4• The 02 spectrum vanishes around H 90 km.

For the H20 lines in air, Doppler-broadening has to be considered at

altitudes above 60 km (p < 0.07 kPa). An approximation is made by replacing

the width Yb in (A-II) with

GHz (A-lIb)

where Y~ = 2.14V~x 10-12 /8 is the squared Doppler width. In applications requiring the detailed mesospheric line shape it is necessary to apply

the more correct Voigt line shape.

A.2.2 Continuum Spectra for Air

Continuum spectra in (A-8) identify dry air and water vapor terms +

and must be added to t~e selected group of local (MPM) 02 and H20 resonance

lines described by (A-9). Contin~um absorption increases monotonically with

frequency.

The dry air continuum

N"(f) = f (2a {y [1 + (fly )2J}-1 + a p 81•

5) P8 2

p 000 p (A-12a)

and

(A-12b)

make a small contribution at ground level pressures due to the nonresonant 02

spectrum below 10 GHz and a pressure-induced N2 spectrum that is effective

above 100 GHz. A width parameter for the Debye spectrum of 02 is formulated

in accordance with (A-II) to be Yo = 4.8 x 10-3(p + 1.le)80.8(GHz) [10J. The

continuum coefficients are ao = 3.07x10-4 and ap = 1.40(1-1.2£1.510-5)10-1°.

52
Water vapor continuum absorption has been a major source of uncertainty

in predicting millimeter-wave attenuation, especially in the window ranges.

Moist-air attenuation a at a frequency that falls within a window can be

expressed by

(A-13)

A series of controlled laboratory measurements was performed at 137.8 GHz to

determine the k-coefficients. Data a(T,e,p) were taken covering the following

range of parameters:

temperature T = 8 to 43°C

vapor pressure e = a to el(RH S 95%) and

total pressure P = e1 + p, where p = a to 150 kPa.

Experimental data were reduced to a reference temperature To = 26.85 °C

(a = 1). The temperature dependence of each k'-coefficient (ks f d) was fitted , , to a power law k(T) = ka x• Moist-air attenuation at f x= 137.8 GHz behaved as

follows:

Values in parentheses give the standard deviation from the mean in terms of

final listed digits. The experimental results (A-14) contain foremost

contributions from water vapor continuum absorption and were used to

"calibrate" MPM by enforcing agreement between experimental and predicted

data; further, an f2 dependence was assumed.

The water vapor continuum is derived from fitting experimental data (A14) in the case of

(A-15a)

and based on theoretical data in the case of

(A-15b)

where

-6 b

f = 1.13 x 10 ,

b = 3 57 x 10-5a7•

5

e· and . , . -6 b

o = 6.47 x 10 .

53
--------------- ---- ---------- -----

In summary, (A-15) is needed to supplement local line (MPM) contributions, the

coefficient bf is valid only for the selected local line base treated with

line shape (A-9), and the strong self-broadening component bee2 is nearly unaffected by (A-9). The coefficient bo and both exponents in (A-15b) were

obtained by fitting dispersion results of 1ine-by-1ine calculations for the

rotational H20 spectrum above 1 THz.

A.2.3 Suspended Water Droplet Continuum (Haze, Fog, Cloud)

Suspended water droplets (SWO) in haze, fog, or clouds are millimeter

wave absorbers. Their size range of radii is below 50 ~m, which allows the

Rayleigh approximation of Mie scattering theory to be used for calculating

refractivity contributions .& to (A-8) in the form [14J (see p. 73)

~(f) (9/2)wlE" (1 + n

2), (A-16a)

N~(f) (9/2)w [l/(EO + 2) - n/E"(1 + n

2)J, (A-16b)

and

NO = (3/2)w [1 - 3/(EO + 2)J, (A-16c) w

where n = (2 + EI)/E"; E1 , E" are real and imaginary, and EO static parts of

the permittivity for water. The contribution of (A-16c) is added to equation

(A-6).

Values for the dielectric spectra f(f) of water are calculated with a new

doub1e-Oebye model [15J:

E'(f) = E2 + (EO - E1)/[1 + (f/fO)2 J + (E 1 - E2)/[1 + (f/fS)2J, (A-17a)

2 2 E"(f) = f (EO - E1)/fo[1 + (f/fO) J + (E 1 - E2)/fS[1 + (f/fS) J, (A-17b)

EO = 77.66 + 103.3(8 - 1), (A-17c)

where E1 = 5.48, E2 = 3.51,

fO = 20.09 - 142(8 - 1) + 294(8 - 1)2

f S = 590 - 1500(8 - 1)

54

GHz, and

GHz.
Equation (A-17) is valid for frequencies up to 1000 GHz over a temperature

range from -10 to +30 ae.

A.2.4 Rain Effects

The refractivity of rain is identified in (A-8) by ~R = NR + jNR• Drop

diameters (0.1 - 6 mm) and millimeter wavelengths are comparable, thus causing

appreciable interactions due to Mie absorption and scattering. Bypassing

elaborate, lengthy Mie calculations which require drop shape and size distributions as well as the complex dielectric properties of water (A-17), rain

refractivity spectra are approximated via (see p. 73)

NR(f) = aRb

NR(f) = - N~ [x2•

5 1(1 + x2•

5)]

N~ = R(3.68 -0.012R)/fR

(A-18a)

(A-18b)

(A-18c)

where fR = 53 - R(370 - 1.5R)10-3 GHz and x = f/fR~

Frequency-dependent coefficient a and exponent b were calculated using

drop size spectra of Laws and Parsons and a temperature of T = 0 ae. A

regression fit to individual (a,b)-pairs over the frequency range from 1 to

1000 GHz resulted in the following calculation scheme:

f xl x2 f x3 x4

GHz GHz

1 to 2.9 3.51 x 10-4 1.03 1 to 8.5 0.851 0.158

2.9 to 54 2.31 x 10-4 1. 42 8.5 to 25 1.41 -0.0779

54 to 180 0.225 -0.301 25 to 164 2.63 -0.272

180 to 1000 18.6 -1.151 164 to 1000 0.616 0.0126

55
A.3. CONCLUSIONS

The parametric model MPM for atmospheric refractivity

~(f,P/T/RH, wA/w,R)

was developed for applications in areas such as telecommunications, remote

sensing, and radio astronomy. Deta i ls of its structure and operat ion are

explained in the extensive COMMENTS part of the code. The memory capacity

required for MPM is 355 kbytes.

The format of the numerical print-out is demonstrated by the identical

example given in Table A-I for the version and in Table A-2 for

the a/6 version. A plotting system at the user's choice (e.g., HALO) can be

added to include features such as auto or manual scaling, multiple cases

(e.g., nine curves with up to 500 points each), special labels, etc. An

example of a graphical presentation for a sea level condition of moist air

(wA = w = R = 0) exhibits spectra at various relative humidities (RH = 0-100%)

for the N version in Figure A-I and for the identical case as a/6 version in

Figure A-2.

A.4. ADDITIONAL REFERENCE

Liebe, H. J. and G. G. Gimmestad (1978), Calculation of clear air

refractivity, Radio Science 20, no. 2, pp. 245 - 251.

56
Table A-I.

FREQUENCY PROFILES OF ATMOSPHERIC COMPLEX REFRACTIVITY

INPUT Valid Parameter ranges indicated by [ ]):

CASE PRES.,P TEMP~,T

(kPa) (C)

[1-9] [0 -110] [+/-50]

REL.

HUM. ,RH

00

[0-100]

HAZE

MODEL

(mg/m3)

[0-1]

SUSP.

DROP. ,W

(9/m3 )

[0-10]

RAIN

RATE,R

(mm/hr)

[0-200]

1 101 .3 15.0 100.0 : 0.00 1 .000 10.0

Minimum Frequency F1 0.000 (GHz)

Maximum Frequency F2 [1000.]1000.000 (GHz)

Frequency Step [max 500] dF 100.000 (GHz)

OUTPUT:

Case Number: 1 (No = 351.18 ppm)

MOIST AIR (v= 12.81 9/m3)

DRY WATER HAZE, FOG

AIR + VAPOR + CLOUD + RAIN = TOTAL

FREQUENCY N~IMAGINARY PART (ppm) N'- REAL PART (ppm)

(GHz)

0.000 +++++++++ +++++++++ +++++++++ +++++++++ +++++++++

0.220E-09 -.317E-07 0.278E-08 0.431E-08 -.244E-07

100.000 0.168E-02 0.454E-01 0.242E+00 0.317E+00 0.607E+00

-.219E+00 0.321E+00 -.139E+00 -.226E+00 -.264E+00

200.000 0.476E-03 0.149E+00 0.288E+00 0.190E+00 0.629E+00

-.170E+00 0.107E+01 -.299E+00 -.266E+00 0.334E+00

300.000 0.561E-03 0.174E+00 0.284E+00 0.120E+00 0.579E+00

-.162E+00 0.352E+01 -.391E+00 -.275E+00 0.269E+01

400.000 0.807E-03 0.481E+00 0.276E+00 0.869E-01 0.845E+00

-.157E+00 0.619E+01 -.450E+00 -.278E+00 0.530E+01

500.000 0.104E-02 0.118E+01 0.268E+00 0.675E-01 0.152E+01

-.162E+00 0.192E+02 -.495E+00 -.279E+00 0.183E+02

600.000 0.846E-03 0.225E+01 0.260E+00 0.549E-01 0.257E+01

-.159E+00 -.172E+02 -.532E+00 -.280E+00 -.182E+02

700.000 0.977E-03 0.101E+01 0.252E+00 0.461E-01 0.131E+01

-.157E+00 0.687E+01 -.563E+00 -.281E+00 0.587E+01

800.000 0.117E-02 0.112E+01 0.242E+00 0.396E-01 0.140E+01

-.161E+00 -.635E+01 -.589E+00 -.281E+00 -.738E+01

900.000 0.101E-02 0.795E+00 0.232E+00 0.347E-01 0.106E+01

-.159E+00 0.716E+01 -.611E+00 -.281E+00 0.611E+01

1000.000 0.103E-02 0.603E+01 0.223E+00 0.308E-01 0.628E+01

-.159E+00 -.134E+02 -.629E+00 -.282E+00 -.145E+02

57
----------

'"' 1000

E

a. 100 a.

""'-J

Z 10

\tO

r- 1.0

0:::

a. 0.10

0.010

G

0.001,

r~o 1ST AI R

P = 101.3 kPa

T = 25°C

3

VS= 23.0 g/m (100% RH)

Nil

'"' 100

E

a.

a.

""'-J

N'

Z 50

\tO

f0

a.

..J

0::: -50

1000

-100 &...-__~_'__....I____L___&___£___a___&.~---'---'~&----..L--4---'--....I---L-......L.--£---a---a.---4-.l

o 200 400 600 800

FREQUENCY. GHz

Figure A-I. Moist air refractivity N = N' - jN" for sea level condition (P,T)

and various relative humidities (RH) over the frequency range from

a to 1000 GHz.

58
Table A-2.

FREQUENCY PROFILES OF ATTENUATION AND DELAY RATES

INPUT Valid Parameter ranges indicated by [ ]):

CASE PRES. ,P TEMP. ,T

(kPa) (C)

[1-9] [0 -110] [+/-50]

REL.

HUM. ,RH

(%)

[0-100]

HAZE

MODEL

(mg/m3)

[0-1]

SUSP.

DROP. ,w

(g/m3)

[0-10]

RAIN

RATE,R

(mm/hr)

[0-200]

1 101 .3 15.0 100.0 : 0.00 1 .000 10.0

Minimum Frequency F1 0.000 (GHz)

Maximum Frequency F2 [1000.]1000.000 (GHz)

Frequency Step [max 500] dF 100.000 (GHz)

OUTPUT:

Case Number: 1 (Refractive delay = 1171.5 ps/km)

MOIST AIR (v= 12.81 g/m3)

DRY WATER HAZE, FOG

AIR + VAPOR + CLOUD + RAIN = TOTAL --------------------------------------------------- FREQUENCY Q(.. - ATTENUATION (dB/km)

f3 -DISPERSIVE DELAY (ps/km)

(GHz)

0.000 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

100.000 0.03 0.83 4.41 5.78 11 .05

-0.73 1.07 -0.46 -0.75 -0.88

200.000 0.02 5.44 10.50 6.93 22.88

-0.57 3.56 -1 .00 -0.89 1. 11

300.000 0.03 9.50 15.52 6.57 31 .62

-0.54 11 . 75 -1 .30 -0.92 8.99

400.000 0.06 35.02 20.11 6.32 61 .51

-0.52 20.64 -1 .50 -0.93 17.68

500.000 0.09 107.25 24.43 6.14 137.92

-0.54 64.18 -1.65 -0.93 61 .06

600.000 0.09 246.00 28.44 6.00 280.53

-0.53 -57.35 -1 .77 -0.94 -60.59

700.000 0.12 128.84 32.07 5.87 166.91

-0.52 22.92 -1.88 -0.94 19.58

800.000 0.17 162.65 35.28 5.77 203.87

-0.54 -21.20 -1 .96 -0.94 -24.63

900.000 0.17 130.27 38.08 5.68 174.20

-0.53 23.88 -2.04 -0.94 20.37

1000.000 0.19 1097.36 40.50 5.61 1143.65

-0.53 -44.84 -2.10 -0.94 -48.40

59
- -.----_.. ---

100,000

MOIST AIR

1QOOO P=101.3 kPa

T=25 C

1000

E.:f.

?olOO ""0

Z

Q 10

z

w

~1«

.1

.01

200

150

100

E

.:f.

";;;-50

a.

~ow

Cl

w -50 :2:

Ul

a::

w

a.. -100 Ul

i5

-150

'I ,~

-200 '----''-----'---'-----'---'----'---L...-'-----'--'----'----'---'---,-,-"-''--,----"'-----'--'''-L---'----'---L...-'----'

o

FREQUENCY. GHz

Figure A-2. Moist air attenuation (a) and delay (S) rates for sea level

condition (P,T) and various relative humidities (RH) over the

frequency range from 1 to 1000 GHz.

60
APPENDIX B

PRINTOUT OF MPM-N PROGRAM FOR VERSION A

(Frequency Profiles)

The computer program MPM-N is written in FORTRAN 77 with extensive

comments to run on IBM-XT/AT + 8087/80287 coprocessor, or equivalent,

microcomputers.

Program MPM-N is available on 5 1/41 diskettes, either in double

(360 kbyte) or quadruple (1.2 Mbyte) density. Requests may be addressed to

NTIA/ITS.S3, 325 Broadway, Boulder, CO 80303-3328 (ATTN: Dr. H. Liebe).

Please provide the necessary disks.

10 for FORTRAN 77 (IBM Professional 8-bit compiler) version (disk No.1):

MPM1 FOR

MPM2 FOR

MPM3 FOR

OXYGEN OAT

WATER OAT

5 File(s)

45675 7-16-87

29762 7-08-87

24564 6-11-87

3267 7-13-87

1166 10-l3-86

254976 bytes free

-N/A Frequency Profiles

-N/B Humid ity Profi 1es

-N/C Pressure Profiles

Line Data

Tables

10 for EXECUTABLE version (disk No.2):

MPM1 EXE

OXYGEN OAT

WATER OAT

3 File(s)

354565 7-08-87

3267 7-13-87

1166 10-23-86

1024 bytes free

-N/A Frequency Profiles

Line Data

Tables

The executable code length for MPM2 and 3 is 402 and 356 kbyte,

respectively.

61
----------
Adapted for IBM-PC Professional FORTRAN by:

John Stricklen (1-303-497-3195, FTS 320-3195)

[9] W. Boegel, "Neue Naeherungsgleichungen fuer den

Saettigungsdruck des Wasserdampfes, DFVLR Bericht

DLR-FB 77-52, 1977.

[2] H.J. Liebe, "A contribution to modeling atmospheric mm-wave properties", FREQUENZ (J. Telecom.), vol.

41, no. 1/2, pp. 31-36,1987.

[6] A. Bauer, M. Godon, and B. Duterage, "Self- and

air-broadened linewidth of the 183 GHz absorption

in water vapor", J. Quant. Spectrosc. Radiat.

Transf., vol. 32, no. 2, pp. 167-175, 1985.

[3] H.J. Liebe, T. Manabe, and J.P. Stricklen,

"Millimeter-wave attenuation and delay for a fog event",

IEEE Digest: 12th Int. Conf. Infrared and Millimeter

Waves, Orlando, FL, December, 1987.

[5] C.H. Zuffery, "A study of rain effects on EM waves in the 1-600 GHz range", MS-THesis, Dept.

Electrical Eng., University of Colorado, Boulder,

CO 80309, Feb., 1972.

[7] R. J. Hill, "Absorption by the tails of the oxygen

microwave resonances at atmospheric pressures", IEEE

Trans. AP-35, no.2, pp. 198-204, 1987.

[8] P. W. Rosenkranz, "Interference coefficients for

overlapping oxygen lines in air", J. Quant. Spectr.

Rad. Transf., in review, 1987.

[4] R. L. Olsen, D. V. Rogers, and D. B. Hodge,

"The aRb relation in the calculation of rain

attenuation", IEEE Trans. Ant. Prop., vol. AP-26, no. 2, pp. 318-329, 1978.

MOLECULAR effects due to oxygen, nitrogen, and water vapor are considered as detailed in [1].

The computation of attenuation A and delay B is described in

References [1] to [3].

This MPM version has been corrected for typesetting errors in [1]

and revised to include:

(a) an improved water vapor continuum spectrum and a haze model

reported in [2];

(b) an improved model for liquid water dielectric properties and

RAYLEIGH absorption and phase delay by suspended water droplets

(radii < 50 microns) such as haze, fog, and clouds [3];

(c) a rain attenuation model by Olsen, et.al. [4], as well as dispersive delay due to rain approximated from results reported by

Zuffery[5]; (d) new line data for the 183 GHz water vapor line [6];

(e) a VW shape cutoff, setting F"=O for f > (vo +40 x widths) [7];

(f) a new set of overlap correction coefficients A5 [8];

(g) an improved water vapor saturation pressure equation based on degrees Celsius [9] (see comments in program);

(h) an approximation for Zeeman (02) and Doppler (H20) line broadening [10].

REFERENCES: [1] H.J. Liebe,"An updated model for millimeter wave propagation in moist air", Radio Science, vol. 20 no. 5, pp. 1069-1089, 1985.

ppm

ppm

ppm

dB/km

ps/km

ps/km

o to 10

o to 200

o to

in

in

in

in

in

in

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

and D(C +strong wind) C

C

C

C

C

C

C

C

C

C

C

Valid Range:

1 to 1000 >= 1.E-05

(max. 500 freqs.)

0.0 to 120

-50 to 50

o to 100

v( RH, T) in g/m3

e(RH,T) in kPa.]

(specified by five

w, RR), and haze model

information to be

A(f)

B(f)

Bo

N' (f)

N' '( f)

No

in g/m3

in mm/hr

in GHz

in GHz

P in kPa T in C

RH in';

is calculated as

or

f1, f2

df

Haze model (RH = 80 to 99.9';):

code A(rural), B(urban), C(maritime),

plus hygroscopic aerosol reference

concentration wA(80,;RH) in mg/m3

Suspended water droplet

concentrat·ion w Rain Rate RR

INPUT:

Frequency range

and step size

Barometric pressure

Temperature

Relative humidity

[absolute humidity

Attenuation

Dispersive Delay

Refractive Delay

OUTPUT:

Real part of refractivity

Imaginary part of refractivity

Nondispersive Refractivity

*

*

*

*

*

*

*

*

*

*

*

*

*

Frequency range, moist air, rain conditions

meterological variables P=p+e, T, RH, wA or code (A, B, C, or D) are the required input

entered from the keyboard.

C PROGRAM MPM-N

C AUGUST 1987 C---------------------------------------------------------------------

C COMPLEX RADIO REFRACTIVITY OF ATMOSPHERIC AIR (1 TO 1000 GHz).

C Hans J. Liebe

C Institute for Telecommunication Sciences

C NTIA/ITS.S3

C 325 BROADWAY

C Boulder, CO 80303

C

C

C

C

C ~n~n~~

C A. FREQUENCY PROFILES

C B. HUMIDITY PROFILES

C C. PRESSURES PROFILES OF MOIST AIR C---------------------------------------------------------------------

C A. FREQUENCY PROFILES C---------------------------------------------------------------------

C Program MPM-N/A calculates frequency profiles of the complex radio

C refractivity N of ATMOSPHERIC AIR over a frequency range f=1 to

C 1000 GHz. The output is expressed in Real part of Nand

C ImaginarY part of N and specific rates of power attenuation A

C (Im. of N) and propagation delay B (Re. of N).

C

C

C

C

C

C or C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C COMMENTS:

0"1

W
C

C*********************************************************************

C

C

C [10) H. J. Liebe and G. B. Gimmestad, "Calculation of

C clear air EHF refractivity", Radio Sci., vol. 13,

C no. 2, pp. 245-251, 1978.

C---------------------------------------------------------------------

C

C******* LIST OF VARIABLES ********* C

C FMIN Minimum Frequency

C FMAX Maximum frequency

C STEP Step Size between frequencies.

C NF No. of frequencies.

C NCASE No. of cases.

C PBT(10) Pressures

C TCT(10) Temperatures.

C RHT(10) Rel. Humidities

C WT(10) Droplet concentrations.

C RR(IO) Rain Rate

C HZ(10) Haze growth models.

c*********************************************************************

C MAIN PROGRAM

c*********************************************************************

C

COMMON /AIR/ NCASE,PBT(10),TCT(10),RHT(10),WT(10),R(10)

COMMON /FREQS/ FMIN,FMAX,STEP,NF

COMMON /RAIN/ RR(10),WA(10)

COMMON /ANSI/ D(12,SOI,10),ATT(SOI,10),DISP(501,10)

COMMON /ANS/ FREQA(SOI),No(10),Bo(10),EV(10)

COMMON /021ine/ F002(48),A(6,48)

COMMON /H20/ FOwater(30),B(3,30)

COMMON /HAZE/ HZ(10)

CHARACTER*1 HZ

The computer will ask you which parameter you'

The value that appears in parentheses (l is the'

default value and will be used if you simply ,

press the RETURN key. To enter a new value'

type the value and press the RETURN key.'

You have found the instruction set.'

The input data includes the frequency range and'

step, the parameter that you wish to vary, the'

number of cases and the values of pressure,'

temperature, relative humidity, and rain rate.'

For RH = 80 to 99.9~, a haze model predicts for'

four cases (A=rural, B=urban, C=maritime, and'

D=C+strong wind) the shrinking and swelling by'

hygroscopic aersol concentrations specified at'

80~ RH. At 100~ RH a suspended water droplet'

concentration can be added to simulate fog or'

cloud conditions.'

menu options are:'

Instructions'

Edit Data'

Summary of current data'

Process Data'

Print Results'

Save results to Disk'

Quit'

HZ(I)=' ,

CONTINUE

20

CALL MENU(IMENU)

IF (IMENU.EQ.l) THEN

CALL INSTR

ELSE IF (IMENU.EQ.2) THEN

CALL EDITSUMM( 1 )

ELSE IF (IMENU.EQ.3) THEN

CALL SAVETABL(2)

ELSE IF (IMENU.EQ.4) THEN

CALL COMPUTE(NCASE)

ELSE IF (IMENU.EQ.S) THEN

CALL SAVETABL(O)

ELSE IF (IMENU.EQ.6) THEN

CALL SAVETABL(I)

ELSE IF (IMENU.EQ.7) THEN

WRITE(*,*)'Quitting Program ... Normal termination.'

GOTO 20

ELSE

WRITE(*,*)'NOT a valid menu option.'

ENDIF

GOTO 10

STOP

END C-----------------------------------------------------------------------

SUBROUTINE INSTR

WRITE(*,1 )

FORMAT(///)

WRITE(*,*)'The

WRITE(*,*)'1)

WRITE(*,*)'2)

WRITE(*,*)'3)

WRITE( *, *)' 4)

WRITE(*,*)'Sl

WRITE(*,*)'6)

WRITE(*,*l'71

WRITE(*,*)

WRITE(*,*)'1)

WRITE(*,*l

WRITE(*,*l'2l

WRITE(*,*) ,

WRITE(*,*l'

WRITE( *, *)'

WRITE(*,*)'

WRITE(*,*l'

WRITE(*,*l'

WRITE(*,*l'

WRITE(*,*)'

WRITE(*,*l'

WRITE(*,*)'

WRITE(*,*l

WRITE(*,*l'

WRITE(*,*l'

WRITE(*,*)'

WRITE(*,*) ,

WRITE(*,*)

WRITE(*,*) ,

3

C

C******************************************************

C

10

ATTENUATION and '

LINE DATA

CONDITIONS FOR PRESSURE, TEMP., AND HUMIDITY

DATA

INITIALIZE ALL DATA VALUES ***************

WRITE(*, 1101)

FORMAT(//////////)

WRITE(*,2)

FORMAT(80( lH*) ,/ ,SX,' Executing PA.RAMETRIC

+ 'DISPERSIVE DELAY Program',/,80(IH*»

WRITE(*,4)

FORMAT(///)

OXYGEN LINE

CALL OXYDAI

WATER VAPOR

CALL VAPDAI

NCASE=1

FMIN=10.

FMAX=100.

STEP=10.

STANDARD SEA LEVEL

DO 31=1,10

PBT ( I ) =101 .3

TCT(I)=15.0

RHT(I)=50.

C

C

2

1101

4

C

C ****** C

C

0"1

.p.
This saves the results to a file you specify.'

C

C-----------------------------------------------------------------------

SUBROUTINE MENU(IMENU)

This gives a summary of all the current input'

data. It is a good idea to request a summary'

after you edit the data to make sure that all'

of the decimals are in the right place etc. '

4 - Process Data',

5 - Print Results " 6 - Save output to Disk file',

7 - Quit' ,II)

I, '

I, ' I, ' I, '

+

+

+

+ C

100 WRITE(*,2)

2 FORMAT(' OPTION? ')

READ(*,3) IVAL

3 FORMAT(Al)

IF«IVAL.EQ. '1' ).OR.(IVAL.EQ. '2').OR.(IVAL.EQ. '3').OR. + (IVAL.EQ. '4').OR.(IVAL.EQ. '5').OR.(IVAL.EQ. '6').OR.(IVAL.EQ. '7'» + THEN

READ(IVAL,4,ERR=100) IMENU

4 FORMAT(Il)

ELSE

WRITE(*,*)'Invalid option.' GOTO 100

ENDIF

RETURN

C----------------------- END _ SUBROUTINE EDITSUMM(IFLAG)

C THIS ROUTINE PRINTS SUMMARY AND/OR EDITS THE DATA.

C

C IFLAG=l IS FOR EDIT MODE--ANYTHING ELSE IS A SUMMARY.

C NFLAG IS INDEX FOR PARAMETER VARIATION

C

COMMON IAIRI NCASE,PBT(10),TCT(10),RHT(10),WT(10),R(10)

COMMON IFREQSI FMIN,FMAX,STEP,NF

COMMON IRAINI RR(10),WA(10)

COMMON IHAZEI HZ(10)

CHARACTER*l HZ

CHARACTER*8 IVAL

C**************************************************

C

10 FORMAT(A8)

C

C ZERO OUT THE DROPLET CONCENTRATIONS

IF(IFLAG.EQ.l) THEN

DO 100 I=1,10

WT(I)=O.O

HZ(I)=' , 100 CONTINUE

ENDIF

200 CONTINUE

C ****** FREQUENCY DATA ********************** 300 WRITE(*,4) FMIN

4 FORMAT(' Minimum Frequency, GHz (',F7.2, ') ')

IF(IFLAG.EQ.l)THEN

READ(*,10) IVAL

IF(IVAL.EQ.' , )THEN

GOTO 400

ELSE

READ(IVAL,8,ERR=300) FMIN

8 FORMAT(F8.0)

ENDIF

C CHECK FOR VALID RANGE ON FMIN

IF«FMIN.GT.0.).AND.(FMIN.LE.1000.» GOTO 400

WRITE(*,*)'Minimum Freq. must satisfy 0< FMIN <= 1000.'

GOTO 300

This option causes the data to be used to ' generate a table of attenuation and dispersion.'

This must be done every time you change the ' data to update the table.'

The table of attenuation and dispersion will be'

printed to the console. To make a hard copy yoU'

may use the CTRL-PRTSC key or to make a disk'

file you can use the menu option given next'

and print the file. The output is in tabular'

form with the components of the total'

attenuation and dispersion shown in two lines'

with the attenuation above the dispersion.'

The units on the parameters are:'

Pressure in kPa. ' Relative Humidity in %'

Temperature in degrees C'

Water Droplet concentration in grams/meter' cubed'

Rain rate in millimeters per hour'

These are given in the prompt'

wish to vary and you should type P, R, or T'

for Pressure, Relative humidity, or Temperature'

respectively. The other two parameters will'

be fixed at the same value for every case'

and you will be prompted for these values.'

You will then be prompted for a value of your'

selected parameter for each separate case.'

For every case in which the relative humidity'

is 100% you will be prompted to enter a value'

for the suspended droplet concentration, and ' for cases in which the humidity is above 80%'

you will be asked for a hygroscopic aerosol'

content at 80%. This is used to calculate the'

water droplet content using the haze growth'

model of [2].'

CHARACTER*l IVAL

WRITE(*,l)

FORMAT(' Enter the number of the option you wish to choose., 'I, + I, ' 1 - Instructions', + I,' 2 - Edit Data', + I,' 3 - Summary of current data',

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*) , WRITE(*,*)'

WRITE(*,*)

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*)

WRITE(*,*)' 3)

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*)'

WRITE( *, *)

WRITE(*,*) '4)

WRITE(*,*)'

WRITE(*,*) , WRITE(*,*)'

WRITE(*,*)

WRITE(*,*)'5)

WRITE(*,*)'

WRITE(*,*l'

WRITE(*,*) , WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)'

WRITE(*,*)

WRITE(*,*)'6)

WRITE(*,*)

WRITE(*,*)'7) This stops program execution.'

WRITE(*,l)

RETURN

END C----------------------------------------------------------------------

0"\

CJ1
C LINE DATA FILES (Table I in [1])

C (read as separate data files by MPM)

C

C C

CCoefficients A5 after Rosenkranz [8], for 118.75 GHz line after Hill [7] C Width B3 of 183, 325, and 380 GHz lines increased by 10% [6] C FCl Al A2 A3 A4 A5 A6 C FO Bl B2 B3

C 49.452379 0.12 11.830 8.40 0 6.600 1.7 C 22.235080 0.1090 2.143 27.84

C 49.962257 0.34 10.720 8.50 0 6.600 1.7 C 67.813960 0.0011 8.730 27.60

C 50.474238 0.94 9.690 8.60 0 6.600 1.7 C 119.995940 0.0007 8.347 27.00

C 50.987748 2.46 8.690 8.70 0 6.600 1.7 C 183.310117 2.3000 0.653 31.64

C 51.503350 6.08 7.740 8.90 0 6.627 1.8 C 321.225644 0.0464 6.156 21.40

C 52.021409 14.14 6.840 9.20 0 6.347 1.8 C 325.152919 1.5400 1.515 29.70

C 52.542393 31.02 6.000 9.40 0 6.046 1.8 C 336.187000 0.0010 9.802 26.50

C 53.066906 64.10 5.220 9.70 0 5.719 1.9 C 380.197372 11.9000 1.018 30.36

C 53.595748 124.70 4.480 10.00 0 5.400 1.8 C 390.134508 0.0044 7. 318 19.00

C 54.129999 228.00 3.810 10.20 0 5.157 2.0 C 437.346667 0.0637 5.015 13.70

C 54.671157 391.80 3.190 10.50 0 4.783 1.9 C 439.150812 0.9210 3.561 16.40

C 55.221365 631.60 2.620 10.79 0 4.339 2.1 C 443.018295 0.1940 5.015 14.40

C 55.783800 953.50 2.115 11.10 0 4.011 2.1 C 448.001075 10.6000 1.370 23.80

C 56.264777 548.90 0.010 16.46 0 2.772 0.9 C 470.888947 0.3300 3.561 18.20

C 56.363387 1344.00 1.655 11.44 0 3.922 2.3 C 474.689127 1.2800 2.342 19.80

C 56.968180 1763.00 1.255 11.81 0 3.398 2.5 C 488.491133 0.2530 2.814 24.90

C 57.612481 2141.00 0.910 12.21 0 1.145 3.2 C 503.568532 0.0374 6.693 11.50

C 58.323874 2386.00 0.621 12.66 0 0.317 -2.5 C 504.482692 0.0125 6.693 11.90

C 58.446589 1457.00 0.079 14.49 0 6.270 0.8 C 556.936002 510.0000 0.114 30.00

C 59.164204 2404.00 0.386 13.19 0 -4.119 0.1 C 620.700807 5.0900 2.150 22.30

C 59.590982 2112.00 0.207 13.60 0 6.766 0.5 C 658.006500 0.2740 .7.767 30.00

C 60.306057 2124.00 0.207 13.82 0 -6.183 0.7 C 752.033227 250.0000 0:336 28.60

O'l C 60.434775 2461.00 0.386 12.97 0 3.290 -0.4 C 841.073593 0.0130 8.113 14.10

O'l C 61.150558 2504.00 0.621 12.48 0 -1.591 3.5 C 859.865000 0.1330 7.989 28.60

C 61.800152 2298.00 0.910 12.07 0 -2.068 2.9 C 899.407000 0.0550 7.845 28.60

C 62.411212 Hl33.00 1.255 11.71 0 -4.158 2.3 C 902.555000 0.0380 8.360 26.40

C 62.486253 1517.00 0.078 14.68 0 -4.068 0.9 C 906.205524 0.1830 5.039 23.40

C 62.997974 1503.00 1.660 11.39 0 -4.482 2.2 C 916.171582 8.5600 1.369 25.30

C 63.568515 1087.00 2.110 11.08 0 -4.442 2.0 C 970.315022 9.1600 1.842 24.00

C 64.127764 733.50 2.620 10.78 0 -4.687 2.0 C 987.926764 138.0000 0.178 28.60

C 64.678900 463.50 3.190 10.50 0 -5.074 1.8 C

C 65.224067 274.80 3.810 10.20 0 -5.403 1.9 C

C 65.764769 153.00 4.480 10.00 0 -5.610 1.8 C

C 66.302088 80.09 5.220 9.70 0 -5.896 1.8

C 66.836827 39.46 6.000 9.40 0 -6.194 1.7

C 67.369595 18.32 6.840 9.20 0 -6.. 468 1.8

C 67.900862 8.01 7.746 8.90 0 -6.718 1 .7

C 68.431001 3.30 8.690 8.70 0 -6.70 1.7

C 68.960306 1.28 9.690 8.60 0 -6.60 1 .7

C 69.489021 0.47 10.720 8.50 0 -6.60 1.7

C 70.017342 0.16 11.830 8.40 0 -6.60 1 .7

C 118.750341 945.00 0.000 16.30 0 -0.134 0.8

C 368.498350 67.90 0.020 19.20 0.6 0 1

C 424.763120 638.00 0.011 19.16 0.6 0 1

C 487.249370 235.00 0.011 19.20 0.6 0 1

C 715.393150 99.60 0.089 18.10 0.6 0 1

C 773.838730 671.00 0.079 18.10 0.6 0 1

C 834.145330 180.00 0.079 18.10 0.6 0 1 C
RAIN = TOTAL

0.00 0.00

0.00 0.00

5.77 11. 04

0.00 -0.12

6.92 22.87

0.00 2.00

6.56 31.61

0.00 9.90

6.31 61.50

0.00 18.61

6.13 137.91

0.00 61.99

5.99 280.52

0.00 -59.66

5.87 166.90

0.00 20.52

5.76 203.86

0.00 -23.70

5.67 174.19

0.00 21.31

5.60 1143.64

0.00 -47.46

0.00

0.00

4.41

-0.46

10.50

-1.00

15.52

-1.30

20.11

-1.50

24.43

-1.65

28.44

-1.77

32.07

-1.88

35.28

-1. 96

38.08

-2.04

40.50

-2.10

ATTENUATION (dB/km)

DISPERSIVE DELAY (ps/km)

0.00

0.00

0.83

1. 07

5.44

3.56

9.50

11.75

35.02

20.64

107.25

64.18

246.00

-57.35

128.84

22.92

162.65

-21.20

130.27

23.88

1097. 36

-44.84

2 (Refractive delay: 1169.10 ps/km)

0.00

0.00

0.03

-0.73

0.02

-0.57

0.03

-0.54

0.06

-0.52

0.09

-0.54

0.09

-0.53

0.12

-0.52

0.17

-0.54

0.17

-0.53

0.19

-0.53

MOIST AIR (v: 12.81 g/m3)

DRY WATER HAZE, FOG

AIR + VAPOR + CLOUD +

(GHz)

0.000

C Case Number:

C

C

C

C

C

C FREQUENCY

C

C

C

C

C 100.000

C

C 200.000

C

C 300.000

C

C 400.000 C

C 500.000

C

C 600.000

C

C 700.000

C

C 800.000

C

C 900.000

C

C 1000.000

C

C

C

C*********************************************************************** C .

MOIST AIR

+

HAZE

FOG, RAIN

0.0

10.0

RAIN

RATE,R

(mm/hr)

[0-200]

0.033

1.000

SUSP.

DROP. ,W

(91m3)

[0-10]

0.00 0.00

0.00 0.00

0.00 0.99

0.00 0.32

0.00 5.76

0.00 2.95

0.00 9.98

0.00 11.11

0.00 35.53

0.00 19.96

0.00 107.54

0.00 63.27

0.00 245.67

0.00 -57.65

0.00 129.27

0.00 22.22

0.00 163.03

0.00 -21.69

0.00 130.89

0.00 23.16

0.00 1092.96

0.00 -45.21 - "

C: 1. 00 : 0.00

HAZE

MODEL

(mg/m3)

[0-1]

0.00

0.00

0.14

-0.02

0.34

-0.03

0.51

-0.04

0.65

-0.05

0.80

-0.05

0.93

-0.06

1.04

-0.06

1. 15

-0.06

1.24

-0.07

1. 32

-0.07

99.5

100.0

REL.

HUM. ,RH (~)

[0-100]

0.00

0.00

0.82

1.06

5.40

3.55

9.44

11.69

34.82

20.53

106.65

63.86

244.65

-57.07

128.10

22.80

161.71

-21.09

129.49

23.76

1091.46

-44.61

15.0

15.0

0.00

0.00

0.03

-0.73

0.02

-0.57

0.03

-0.54

0.06

-0.52

0.09

-0.54

0.09

-0.53

0.12

-0.52

0.17

-0.54

0.17

-0.53

0.19

-0.53

101.3

101.3

Valid Parameter ranges indicated by [ ]):

FREQUENCY PROFILES OF ATTENUATION AND DELAY RATES

PRES.,P TEMP.,T

(kPa) (C)

[1-9] [0.0-110] [+/-50]

Minimum Frequency F1 0.000 (GHz)

Maximum Frequency F2 [1000.]1000.000 (GHz)

Frequency Step [max 500] dF 100.000 (GHz)

c

c**********************************************************************

C EXAMPLE FOR A.

c**********************************************************************

C

C

C

C INPUT

C

C

C CASE

C

C

C

C 1

C 2

C

C

C

C

C

C

C--------------------------------------------------------------

C OUTPUT:

C Case Number: 1 (Refractive delay: 1164.49 ps/km)

C --------------------------------------------------- C MOIST AIR (v: 12.74 g/m3)

C DRY WATER HAZE, FOG

C AIR + VAPOR + CLOUD + RAIN : TOTAL

C --------------------------------------------------- C FREQUENCY ATTENUATION (dB/km)

DISPERSIVE DELAY (ps/km)

C (GHz)

C 0.000

C

C 100.000

C

C 200.000

C

C 300.000

C

C 400.000

C

C 500.000

C

C 600.000

C

C 700.000

C

C 800.000

C

C 900.000

C

C 1000.000

C

C

en

-....I
m

00

ENDIF

400 WRITE(*,5) FMAX

5 FORMAT(' Maximum Frequency, GHz (',F7.2,') ')

IF(IFLAG.EQ.1)THEN

READ(*,10) IVAL

IF(IVAL.EQ.' ')THEN

GOTO 500

ELSE

READ(IVAL,8,ERR=400) FMAX

ENDIF

C CHECK FOR VALID RANGE ON FMAX

IF«FMAX.GE.FMIN).AND.(FMAX.LE.1000.» GOTO 500

WRITE(*,*)'Maximum Freq. must satisfy FMIN <= FMAX <= 1000.'

GOTO 400

ENDIF

500 WRITE(*,6) STEP

6 FORMAT(' Frequency Step, GHz (',F7.2,') ')

IF(IFLAG.EQ.1)THEN

READ(*,10) IVAL

IF( IVAL. EQ.' ')THEN

GOTO 600

ELSE

READ(IVAL,8,ERR=500) STEP

IF(STEP.EQ.O.) THEN

IF(FMAX-FMIN.EQ.O) THEN

STEP=1.

GOTO 511

ENDIF

WRITE(*,*)' STEP must be greater than 0'

GOTO 500

ENDIF

ENDIF

C CHECK FOR VALID I OF FREQS. (MAX=501)

511 FF=(FMAX-FMIN)!STEP+1

IF(FF.GT.501) THEN

WRITE(*,7) (FMAX-FMIN)!502

7 FORMAT(' Minimum STEP for given freq. range is ',F7.2)

GOTO 500

ENDIF

NF=INT(FF)

ENDIF

C ******** PARAMETER VARIATION *********** 600 CONTINUE

IF(IFLAG.NE.1) GOTO 700

WRITE(*,*)'Which paramo would you like to vary (P, R, T) ? '

READ(*,10)IVAL

IF(IVAL.EQ.'P'.OR.IVAL.EQ.'p') THEN

NFLAG=1

GOTO 700

ELSEIF(IVAL.EQ.'R'.OR.IVAL.EQ.'r' )THEN

NFLAG=2

GOTO 700

ELSEIF(IVAL.EQ.'T'.OR.IVAL.EQ. 't' )THEN

NFLAG=3

GOTO 700

ELSE

GOTO 600

ENDIF

C ******* NUMBER OF CASES **************** 700 CONTINUE

P=PBT( 1 )

RH=RHT(1)

T=TCT(1)

WRITE(*,11) NCASE

11 FORMAT(' No. of Cases (',I2,') ')

IF(IFLAG.NE.1)GOTO 800

READ( *,10) IVAL

IF(IVAL.EQ.' ')THEN

GOTO 800

ELSE

READ(IVAL,12,ERR=700) NCASE

12 FORMAT(I1)

IF(NCASE.GE.10) THEN

WRITE(*,*)'NO. of Cases must be less than 10.'

GOTO 700

ENDIF

ENDIF

C ***** PRESSURE, TEMPS, RH, DROP CONC. ********* 800 CONTINUE

IF(IFLAG.EQ.1) THEN

IF(NFLAG.NE.1) THEN

WRITE(*,9) P

9 FORMAT(' Pressure for all cases (kPa) (' ,F7.2,') ')

READ(*,10) IVAL

IF(IVAL.EQ.' ') GOTO 830

READ(IVAL,8,ERR=800) P

DO 831 I=1, 10

831 PBT(I)=P

GOTO 830

ENDIF

830 IF(NFLAG.NE.2)THEN

WRITE(*,19) RH

19 FORMAT(' ReI. Humidity for all cases (%) (' ,F7.2, ') ')

READ(*,10) IVAL

IF(IVAL.EQ.' ') GOTO 840

READ(IVAL,8,ERR=800) RH

DO 832 I=1,10

832 RHT(I)=RH

GOTO 840

ENDIF

840 IF(NFLAG.NE.3)THEN

WRITE(*,20) T

20 FORMAT(' Temperature for all cases (C) (' ,F7.2,') ')

READ(*,10) IVAL

IF(IVAL.EQ.' ') GOTO 850

READ(IVAL,8,ERR=800) T

DO 833 I=1,10

833 TCT(I)=T

GOTO 850

ENDIF

850 CONTINUE

C****** PRESSURE *************** IF(NFLAG.EQ.1)THEN

DO 801 I=1,NCASE

821 WRITE(*,13)I,PBT(I)

13 FORMAT(' Pressure for case I ',I1,' (kPa) (',F7.2,') ')

READ(*,10) IVAL

IF( IVAL. EQ.' ') GOTO 801

READ(IVAL,8,ERR=821) PBT(I)

801 CONTINUE
DFLAG=O

HFLAG=O

IF(IFLAG.EQ.2)THEN

OPEN(l,FILE='CON' )

GOTO 110

ENDIF

C

C

C IFLAG = 0 MEANS PRINT TO CONSOLE

C IFLAG = 1 FILE

C IFLAG = 2 PRINT SUMMARY TO CONSOLE

C

Cl=128.

C2=2.41

ELSEIF(HZ(I).EQ.'C' )THEN

Cl=183.

C2=5.13

ELSEIF(HZ( I). EQ. '0' )THEN

C1=197.

C2=5.83

ELSE

GOTO 824

ENDIF

WT(I)=WA(I)*«Cl-RHT(I))!(C2*(100.-RHT(I))))*(1.E-3)

804 CONTINUE

ELSE

WRITE( *,17)

17 FORMAT(' CASE' ,3X,' PRES. ',3X,' TEMP. ',3X,' HUM. ',5X,

+ 'DROP.' " RAIN' )

DO 805 I=1,NCASE

WRITE(*,18) I, PBT(I),TCT(I),RHT(I),WT(I),RR(I)

18 FORMAT(3X,I2,2X,5(3X,F7.2))

805 CONTINUE

ENDIF

900 CONTINUE

C******** RAIN RATE ************************ IF(IFLAG.EQ.1)THEN

DO 902 I=1,NCASE

922 WRITE(*,21)I,RR(I)

21 FORMATl' Rain Rate for case # ',11,' (mm!hr) (',F7.2,') ')

READ(*,10)IVAL

IF(IVAL.EQ.' ') GOTO 902

READ(IVAL,8,ERR=922) RR(I)

902 CONTINUE

ENDIF

1000 CONTINUE

RETURN

END C----------------------------------------------------------------------

SUBROUTINE SAVETABL(IFLAG)

COMMON !ANS1! D(12,501,10),ATT(501,10),DISP(501,10)

REAL NO,Bo

COMMON !ANS! FREQA(501),No(10),Bo(10),EV(10)

COMMON !AIR! NCASE,PBT(10),TCt(10),RHt(10i,Wt(10),R(10)

COMMON !RAIN! RR(10),WA(10)

COMMON !HAZE! HZ(10)

COMMON !FREQS! FMIN,FMAX,STEP,NF

CHARACTER*l HZ,IVAL

CHARACTER*20 SAVE

INTEGER*2 DFLAG,HFLAG

+

+

16

C

824

C

C*********** HAZE MODEL [2] ************** IF(RHT(I).LT.80.) GOTO 804

844 WRITE(*,23)I,WA(I)

23 FORMAT(' Aerosol cone. at 80% RH for case # '

+ 11,' (mg!m3) (',f6.2,') ')

READ( *,10 JIVAL

IF(IVAL.EQ.' ')GOTO 824

READ(IVAL,8,ERR=844) WA(I)

IF(WA(I).EQ.O.) GOTO 804

WRITE(*,16)I,HZ(I)

FORMAT(' Haze Model for case # ',Il,!, , (A-RURAL,B-Urban,C-Maritime,D-C+strong Wind) (' ,Al, ') ')

READ(*,10)IVAL

IF(IVAL.EQ.' ') THEN

HZ( I)=HZ( I)

ELSEIF«IVAL.EQ.'A').OR.(IVAL.EQ. 'B' ).OR.(IVAL.EQ. 'C').OR.

(IVAL.EQ.'D')) THEN

HZ(I)=IVAL

ELSE

GOTO 824

ENDIF

IF(HZ(I).EQ.'A') THEN

Cl =117.

C2=1.87

ELSEIF(HZ(I).EQ. 'B' )THEN

834

22

803

823

15

802

ENDIF

C******* TEMPERATURE *************** IF(NFLAG.EQ.3) THEN

DO 802 I=l,NCASE

WRITE(*,14)I,TCT(I)

FORMAT(' Temperature for case # ',11,' (C) (',F7.2,') ')

READ(*,10) IVAL

IF( IVAL. EQ.' ') GOTO 802

READ(IVAL,8,ERR=822) TCT(I)

CONTINUE

ENDIF

c********** HUMIDITY ***************** IF(NFLAG.EQ.2)THEN

DO 803 I=1,NCASE

WRITE(*,15)I,RHT(I)

FORMAT(' Rel. Hum. for case # ',11,' (%) (',F6.2, ') ')

READ(*,10) IVAL

IF(IVAL.EQ.' ') GOTO 803

READ(IVAL,8,ERR=823) RHT(I)

CONTINUE

ENDIF

ENDIF

c********** DROP. CONC. ****************** IF(IFLAG.EQ.l)THEN

DO 804 I=l,NCASE

IF(RHT(I).GE.99.9)THEN

WRITE(*,22)I,WT(I)

FORMAT(' Drop. Cone. for case # ',11,' (g!m3) (',F6.2,') ')

READ(*,10JIVAL

IF(IVAL.EQ.' ')GOTO 804

READ(IVAL,8,ERR=834) WT(I)

GOTO 804

ENDIF

822

14

O'l

\.0
WRITE( 1 ,45)

FORMAT(62(lH-)

WRITE(l,*)'OUTPUT:'

DO 200 LP=l,NCASE

WRITE(1,9) LP,No(LP)*3.336

FORMAT(' Case Number: ',12,' (Refractive delay + ,F7.2,' ps/km)')

WRITE(l,*)

DO 10 LP=l,NCASE

WRITE(1,8)LP,PBT(LP),TCT(LP),RHT(LP),HZ(LP),WA(LP), + WT(LP),RR(LP)

FORMAT(I3,3(3X,F7.1),7X,Al,': ',F4.2,lX,F7.3,1X,F7.1)

CONTINUE

WRITE(l,*)

WRITE( 1,2) FMIN

FORMAT(' Minimum Frequency F1 ',F8.3,' (GHz)')

WRITE( 1,3) FMAX

FORMAT(' Maximum Frequency F2 [1000.]',F8.3,' (GHz)')

WRITE(1,4) STEP

FORMAT(' Frequency Step [max 500] dF ',F8.3,' (GHz)')

WRITE(l,*)

WRITE(l,*)

IF(IFLAG.EQ.2)RETURN

IF(HFLAG.EQ.l)RETURN

WRITE(1,16)

FORMAT(11X,51(lH-)

WRITE( 1,17 )R( LP)

FORMAT(15X,'MOIST AIR (v=' ,F5.2,' g/m3)') WRITE( 1,18)

FORMAT(13X,'DRY WATER HAZE, FOG')

WRITE(1,19)

FORMAT(13X,'AIR + VAPOR + CLOUD + RAIN + '= TOTAL ')

WRITE(1,16)

WRITE(l,14)

FORMAT(' FREQUENCY ',17X, 'ATTENUATION (dB/km)')

IF(DFLAG.EQ.O)THEN

WRITE(1,15)

FORMAT(' ',24X, 'DISPERSIVE DELAY (ps/km)')

ENDIF

WRITE(l,*)' (GHz)'

DO 100 IF=l,NF

SM1=D(1,IF,LP)+D(2,IF,LP)

SM2=D(3,IF,LP)+D(4,IF,LP)

WRITE( 1 ,11 ) FREQA( IF) ,SMl ,SM2, D( 5, IF, LP) ,D( 11 , IF, LP) ,

[0-100] [0-1]' ,

+ ',R')

WRITE( 1,75)

FORMAT

+(' (kPa) (C) on',

+' (mg/m3) (g/m3) (mm/hr)')

WRITE( 1, 76)

FORMAT

+(' [1-9] [0.0-110] [+/-50]

+' [0-10] [0-200]')

2

19

15

17

16

4

9

3

18

14

C

8

10

75

C

C

76

C

C

45

IF (FFLAG.EQ.l )THEN

CALL SAVREF(IFLAG,DFLAG,HFLAG)

RETURN

ENDIF

WRITE(*,*)'Press C for Complex Refractivity output' WRITE(*,*)'or ENTER for normal output'

READ(*, 101 )IVAL

IF«IVAL.EQ. 'c' ).OR.(IVAL.EQ. 'c' »THEN

FFLAG=l

ELSE

FFLAG=O

ENDIF

WRITE(1,175)

175 FORMAT(8X,'FREQUENCY PROFILES OF ATTENUATION AND DELAY RATES')

WRITE(l,*)

WRITE(l,*)'INPUT " + 'Valid Parameter ranges indicated by [ ]):'

WRITE(l,*)

WRITE(*,*)'Press D to supress dispersion data'

WRITE(*,*)'Press H to print only the input information'

WRITE(*,*)'Press ENTER for a normal printout' WRITE(*,*)

READ(*, 101 )IVAL

101 FORMAT(Al)

IF«IVAL.EQ. 'D' ).OR.(IVAL.EQ. 'd'»THEN

DFLAG=l

ELSEIF«IVAL.EQ. 'H' ).OR.(IVAL.EQ. 'h' )THEN

HFLAG=l

ELSE

DFLAG=O

HFLAG=O

ENDIF

IF (IFLAG.EQ.l )THEN WRITE(~,*)'Enter a DOS filename (PRN for a printout), ' READ(*,12) SAVE

12 FORMAT(A20)

IF(SAVE.EQ. 'PRN')THEN

OPEN(1,FILE=SAVE,ERR=900)

ELSE

OPEN(l ,FILE=SAVE,STATUS='NEW' ,ERR=900)

ENDIF

ELSEIF(IFLAG.EQ.O)THEN

OPEN(l,FILE='CON')

ELSE

ENDIF

C

WRITE(1,6)

6 FORMAT

+( , REL. HAZE SUSP. RAIN' )

WRITE(1,7)

7 FORMAT

+(' CASE PRES. ,P TEMP., T HUM. ,RH MODEL DROP. ,W RATE' ,

C

C

C

110 CONTINUE

C

C

1 FORMAT(//)

C

-./

o
WRITE(1,*)

DO 10 LP=1,NCASE

WRITE(1,8)LP,PBT(LP),TCT(LP),RHT(LP),HZ(LP),WA(LP), + WT(LP),RR(LP)

FORMAT(I3,3(3X,F7.1),7X,A1, ': ',F4.2,1X,F7.3,1X,F7.1)

CONTINUE

WRITE(1,*)

WRITE(1,2) FMIN

FORMAT(' Minimum Frequency F1 ',F8.3,' (GHz)')

WRITE( 1 ,3) FMAX

FORMAT(' Maximum Frequency F2 [1000.]',F8.3,' (GHz)')

WRITE(1,4) STEP

FORMAT(' Frequency Step [max 500] dF ',F8.3,' (GHz)')

WRITE(1,*)

WRITE(1,*)

WRITE(1,16)

FORMAT(11X,66(1H-»

WRITE(1,17)R(LP)

FORMAT(15X,' MOIST AIR (v= ',F5.2,' g/m3)')

WRITE( 1,18)

FORMAT(13X,' DRY WATER HAZE, FOG')

WRITE(1,19)

FORMAT(13X,' AIR + VAPOR + CLOUD + RAIN + '= TOTAL ')

WRITE( 1,16)

WRITE( 1,14)

FORMAT(' FREQUENCY ',22X,'IMAGINARY PART (ppm)')

IF(DFLAG.EQ.O)THEN

WRITE(1,15)

FORMAT(' ',31X,'REAL PART (ppm)')

ENDIF

WRITE(1,*)' (GHz)'

DO 100 IF=1,NF

SM1=(D(1,IF,LP)+D(2,IF,LP»/(.182*FREQA(IF»)

SM2=(D(3,IF,LP)+D(4,IF,LP»/(.182*FREQA(IF»

SM3=D(5,IF,LP)/(.182*FREQA(IF»

SM4=D(11,IF,LP)/(.182*FREQA(IF»

WRITE(1,11)FREQA(IF),SM1,SM2,SM3,SM4,

DO 200 LP=1,NCASE

WRITE(1,9) LP,No(LP)

FORMAT(' Case Number: ',12,' (No

(C) (~)',

(g/m3) (mm/hr)')

[0-1] , ,

',F7.2,' ppm)')

[0-100]

IF(IFLAG.EQ.2)RETURN

IF(HFLAG.EQ.1)RETURN

WRITE( 1,45)

FORMAT(62(1H-»

WRITE(1,*)'OUTPUT:'

WRITE( 1,76)

FORMAT

+(' [1-9] [0.0-110] [+/-50]

+' [0-10] [0-200]')

WRITE( 1,75)

FORMAT

+(' (kPa)

+' (mg/m3)

15

4

2

19

17

18

14

16

C

3

8

10

9

C

C

76

C

75

C

45

WRITE(1,175)

175 FORMAT(8X, 'FREQUENCY PROFILES OF ATMOSPHERIC COMPLEX',

+ ' REFRACTIVITY')

WRITE(1,*)

WRITE(1,*)'INPUT " + 'Valid Parameter ranges indicated by [ ]):'

WRITE(1,*)

IF (IFLAG.EQ.1)THEN

WRITE(*,*)'Enter a DOS filename (PRN for a printout): '

READ(*,12) SAVE

12 FORMAT(A20)

IF(SAVE.EQ.'PRN')THEN

OPEN(1,FILE=SAVE,ERR=900)

ELSE

OPEN{1,FILE~SAVE,STATUS~'NEW',ERR=900)

ENDIF

ELSEIF(IFLAG.EQ.O)THEN

OPEN(1,FILE='CON')

ELSE

ENDIF

C

WRITE(1,6)

6 FORMAT

+( , REL. HAZE SUSP. RAIN' )

WRITE(1,7)

7 FORMAT

+(' CASE PRES. ,P TEMP., T HUM. ,RH MODEL DROP. ,w RATE' , + ',R')

C

C

1 FORMAT(//)

C

+ ATT(IF,LP)

11 FORMAT(F9.3,2X,F8.2,3(1X,F8.2),2X,F8.2)

IF(DFLAG.EQ.O)THEN

WRITE(1,30)D(6,IF,LP)+D(7,IF,LP),D(8,IF,LP)+D(9,IF,LP),

+ D(10,IF,LP),D(12,IF,LP),DISP(IF,LP)

30 FORMAT(12X,F8.2,4(2X,F8.2»

ENDIF

100 CONTINUE

WRITE(1,*)

200 CONTINUE

CLOSE(1)

RETURN

900 WRITE(*,13) SAVE

13 FORMAT(' ERROR Opening file: ',A20)

RETURN

END C---------------------------------------------------------------------- SUBROUTINE SAVREF(IFLAG,DFLAG,HFLAG)

COMMON /ANS1/ D(12,501,10),ATT(501,10),DISP(501,10)

REAL NO,Bo

COMMON /ANS/ FREQA(501),No(10),Bo(10),EV(10)

COMMON /AIR/ NCASE,PBT(10),TCt(10),RHt(10),Wt(10),R(10)

COMMON /RAIN/ RR(10),WA(10)

COMMON /HAZE/ HZ(10)

COMMON /FREQS/ FMIN,FMAX,STEP,NF

CHARACTER*1 HZ,IVAL

CHARACTER*20 SAVE

INTEGER*2 DFLAG,HFLAG

'-I

.....
510

800

100 CONTINUE

C

R(LP)=7.223*E*V

C NONDISPERSIVE REFRACTIVITY No in ppm and DELAY Bo in ps/km [1].

No(LP)=(2.588*P+(41.6*V+2.39)*E)*V+Nwv

Bo(LP)=3.336*NO(LP)

C COMPUTE NO,Bo

DO 510 IF=l,NF

C ADD TOTAL ATTENUATION AND DISPERSION

ATT(IF,LP)=D(1,IF,LP)+D(2,IF,LP)+D(3,IF,LP)+D(4,IF,LP)+

+ D(5,IF,LP)+D(11,IF,LP)

DISP(IF,LP)=D(6,IF,LP)+D(7,IF,LP)+D(8,IF,LP)+

+ D(9,IF,LP)+D(10,IF,LP)+D(12,IF,LP)

IF(Mt.GT.l) GO TO 40

ONLY CALC THESE FOR 1st FREQUENCY

V=300./(Tc+273.15)

RELATIVE INVERSE TEMPERATURE

COMPUTE WATER VAPOR PARTIAL PRESSURE E in kPa

Eqn. (1) [1] -- CORRECTED!

Es=2.409*V**5*10**(10.-9.834*V)

Es=0.61078*(EXP«(18.61-Tc/240.7)*TC)/(256.1+TC»)

New Es [9] -- either version may be used.

E=Es*Rh/l00.

P=Pb-E

IF(P.LT.OlTHEN

P=O.

Pb=E

ENDIF

COMPUTE LINE FACTORS S,Gamma,Delta

DO 10 1=1,48

For OXYGEN

S(I)=A(1,I)*P*V**3*EXP(A(2,I)*(1.-V»*1.E-6

GAMMA(I)=A(3,I)*(P*V**(.8-A(4,I» + 1.1*E*V)*1.E-3

IF(Pb.LT.0.7)THEN

GAMMA(I)=(GAMMA(I)**2+(25*0.6E-4)**2)**0.5

Zeeman approximation for .6 Gauss, [10]

ENDIF

DELTA(!)=A(5,I)*P*V**A(6,I)*1.E-3

DO 20 1=1,30

For WATER VAPOR

C

C

CONTINUE

CONTINUE

RETURN

C----------------------- END _

SUBROUTINE Gasl(F,Mt,Ad,Pb,Rh,Tc,W,RR,V,Es,E,P,Tau,Nwv,EPS,fr)

C******************************************************************

C COMPUTES SPECIFIC ATTENUATION & DISPERSIVE DELAY RATES

C USING LINE DATA

C******************************************************************

COMMON /02line/ F002(48),A(6,48)

OXYGEN LINES

COMMON /H20/ FOwater(30),B(3,30)

WATER VAPOR LINES

DIMENSION AD(12),GAMD2(30)

DIMENSION S(48),GAMMA(48),DELTA(48),SH(30),GAMH(30),DELH(30)

REAL NIPP,NDPP,NOXPP,NVPP,NWPP,NOXP,Ndp,NiP,Nrp,NS,NU C

C

C

C

C

C

C

C

C

10

C

C

C

C

C

NF=(FMAX-FMIN)/STEP +1.5

C NUMBER OF FREQUENCIES

DO 800 LP=l,LOOP

C********************************

Pbi=PBt(LP)

Tci=TCt(LP)

Rhi=RHt(LP)

Wi=Wt(LP)

RRi=RR(LP)

C******************************** C .

DO 55 IF=l,NF

DO 55 1=1,8

55 D(I,IF,LP)=O.

WRITE(*,56) LP,LooP

56 FORMAT(' Computing for ***** Case' ,13,' of' ,13,' *****')

C

60 DO 100 IF=l,NF

C FREQUENCY LOOP

F=FMIN + (IF-l)*STEP

FREQA(IF)=F

IF(F.EQ.O. )F=1.E-6

C SAVE FREQUENCY

CALL Gasl(F,IF,Ad,Pbi,Rhi,Tci,Wi,RRi,V,Es,E,P,Tau,Nwv,EpS,fr)

EV(LP)=E

85 DO 95 1=1,12

D(I,IF,LP)=Ad(I)

95 CONTINUE

o WRITE(*,*)'D(12)= ',D(12,IF,LP)

+ ATT(IF,LP)/(.182*FREQA(IF»

11 FORMAT(F9.3,5(3X,E9.3»

IF(DFLAG.EQ.O)THEN

SM1=(D(6,IF,LP)+D(7,IF,LP»)/3.336

SM2=(D(8,IF,LP)+D(9,IF,LP»/3.336

WRITE(1,30)SMl ,SM2,D(10,IF,LP)/3.336,D(12,IF,LP)/3.336,

+ DISP(IF,LP)/3.336

30 FORMAT(12X,5(3X,E9.3»

ENDIF

100 CONTINUE

WRITE(l,*)

200 CONTINUE

CLOSE(l)

RETURN

900 WRITE(*,13) SAVE

13 FORMAT(' ERROR Opening file: ',A20)

RETURN

END

C------------------~---------------------------------------------------

SUBROUTINE COMPUTE(LOOP)

C********************************************************************

C THIS SUBROUTINE COMPUTES THE ATTENUATION & DISPERSIVE DELAY RATES

C********************************************************************

COMMON /ANS1/ D(12,501,10),ATT(501,10),DISP(501,10)

COMMON /ANS/ FREQA(501),No(10),Bo(10),EV(10)

COMMON /AIR/ NCASE,PBt(10),TCt(10),RHt(10),Wt(10)~R(10)

COMMON /RAIN/ RR(10),WA(10)

COMMON /FREQS/ FMIN,FMAX,STEP,NF

REAL NO,Bo

DIMENSION AD(12)

N
""W

SHe I )=B( 1, I )*E*V**3. S*EXP(B(2, I )*( 1 .-V»

c Slightly different temperature dependence for width, following [6).

GAMH(I)=B(3,I)*(P*V**.6 + 4.8*E*V**1.1 )*1.E-3

IF(Pb.LT.0.7)THEN

GAMD2(I)=(2.14*FOwater(I)**2)*lE-12/V

GAMH(I)=(GAMH(I)**2+GAMD2(I»**0.S

C Doppler approximation [10)

ENDIF

20 DELH(I)=O.

C

C WATER VAPOR CONTINUUM

C Eqn. (14) [1); was revised in (2), Eqn. (10)

40 Bf= 1 . 13E-6

Bs=3.S7E-S

Nipp=(Bf*E*P*V**3.0 + Bs*E**2*V**10.8)*F

Bo=6.47E-6

Nip=E*Bo*F**2.0S*V**2.4 C

C DRY AIR CONTINUUM

C Eqn. (13) [ 1] -- CORRECTED!

Ao=6.14E-4

An=1.40E-10 *(1.-1.2E-S*F**1.S)

GAMMAo=4.8E-3*(P+l.l*E)*V**.8

C FAC=1./(1.+F**2/3600.)

C Nonresonant rolloff FAC taken out.

FAC=l.

Ndpp=(Ao*P*V**2*GAMMAo*FAC/(F*F + GAMMAo**2) + An*P*P*V**3.S)*F

Ndp =P*Ao/2.*V**2*(1./(1.+(F/GAMMAO)**2)-1.)

C

C MOLECULAR OXYGEN LINES

Sl=O

S2=0

DO 60 I=1,48

CALL FPPFP(F,F002(I),GAMMA(I),DELTA(I),FPP,FP,O)

Sl=S1+S(I )*Fpp

60 S2=S2+S(I)*Fp

Noxpp=S1

C N" FROM OXYGEN

Dox=S2 + Ndp

Ad(6)=3.336*S2

Ad(7)=3.336*Ndp

C D FROM OXYGEN

C

C WATER VAPOR LINES

Sl=O

S2=0

DO 70 I=1,30

CALL FPPFP(F,FOWATER(I"),GAMH(I),DELH(I),FPP,FP,l)

Sl =Sl+SH(I )*Fpp

70 S2=S2+SH(I)*FP

Nvpp=Sl

C N" FROM WATER VAPOR

Dv=S2 + Nip

Ad(8)=3.336*S2

Ad(9)=3.336*Nip

C D FROM WATER VAPOR

C

C LIQUID WATER DIELECTRIC CONSTANT AND

C FOG/CLOUD RAYLEIGH TERMS [3]

fD=20.09-142*(V-l)+294*(V-l)**2

NU=(F/fD)

fS=S90.-1S00*(V-l)

NS=F/fS

Epinf=S.48

Eopt=3.S1

C EPSILON SUB INFINITY

Eps=103.3*(V-1)+77.66

C EPSILON SUB S

Epp=Eopt+(Eps-Epinf)/(1+NU**2)+(Epinf-Eopt)/(1+NS**2)

C EPSILON'

Eppp=«Eps-Epinf)*NU)/(1+NU**2)+«Epinf-Eopt)*NS)/(1+NS**2)

C EPSILON"

Ep=(2.+Epp)/Eppp

C SUSPENDED WATER DROPLET EXTINCTION

Nwpp=(4.S0*W/(Eppp*(1.+Ep**2»)

C N" FROM WATER DROPLETS

Dw=-4.S*W*(Ep/(Eppp*(1+Ep*Ep»)+4.S*W/(Eps+2.)

Nwv=1.S*W*(1.-(3./(Eps+2.»)

C

C ATTENUATION DUE TO RAIN [4]

C

ARAIN=O.

BRAIN=O.

ATRAN=O.

Nrp=O.

IF (RR.EQ.O.) GOTO SOl

C ALPHA CALCULATION

IF(F.GE.2.9) GOTO 300

GA=6.39E-S

EA=2.03

GOTO 330

300 CONTINUE

IF(F.GE.S4.) GOTO 310

GA=4.21E-S

EA=2.42

GOTO 330

310 IF(F.GE.180.) GOTO 320

GA=4.09E-2

EA=0.699

GOTO 330

320 GA=3.38

EA=-0.lS1

330 ARAIN=GA*(F**(EA» C

C BETA CALCULATION

IF(F.GE.8.5) GOTO 340

GB=0.851

EB=0.158

GOTO 370

340 IF(F.GE.2S.) GOTO 350

GB=1.41

EB= -0.0779

GOTO 370

3S0 IF(F.GE.164.)GOTO 360

GB=2.63

EB= -0.272

GOTO 370

360 GB=0.616

EB=0.0126

370 BRAIN=GB*(F**(EB»
ATRAN=ARAIN*RR**(BRAIN) END

C---------------------------------------------------------------------

SUBROUTINE Oxyda1

COMMON /021ine/ F002(48),A(6,48)

C PUT MOLECULAR OXYGEN LINE DATA OF [1] IN A(1:6,1:48)

OPEN (2,FILE='OXYGEN.DAT',ERR=900)

C DUMMY READ TO ALLOW FOR COMMEMTS.

READ(2,*)

READ(2,*)

READ (2,*,ERR=910) (F002(I),(A(J,I),J=1,6),I=1,48)

CLOSE (2)

RETURN

900 WRITE(*,901) lOS

901 FORMAT('Could not OPEN OXYGEN.DAT file, error=',I6)

WRITE(*,*)'Check that OXYGEN.DAT is in the current directory.'

STOP 'Could not OPEN OXYGEN file.'

910 STOP 'ERROR READing OXYGEN file.'

END

C---------------------------------------------------------------------

SUBROUTINE Vapda1

COMMON /H20/ FOwater(30),B(3,30)

C PUTS WATER VAPOR LINE DATA OF [1] IN B(1:3,1:30)

OPEN (2,FILE='WATER.DAT',ERR=900)

C DUMMY READ TO ALLOW FOR COMMENTS.

READ(2,*)

READ(2,*)

READ (2,*,ERR=910) (FOwater(I),(B(J,I),J=1,3),I=1,30)

CLOSE (2)

RETURN

900 WRITE(1,901) lOS

901 FORMAT('Could not OPEN WATER file, error=',I6)

WRITE(*,*)'Check that WATER.DAT is in the current directory.'

STOP 'Could not OPEN WATER file.'

910 STOP 'ERROR READing WATER file.'

END

[5] who

and 20 deg. C

RAIN DELAY approximated after 2UFFEREY

used MARSHALL-PALMER drop siz~ spectra

fr=53.-0.37*RR+1.5E-3*RR**2

Nro=(RR*(3.68-0.012*RR))/fr

X=F/fr

Nrp=-Nro*(X**2.5/(1+X**2.5))

CONTINUE

C

C

C

C

C

C

C

501

C

C CALC ABSORPTION

Ad(1 )=.182*F*Noxpp

C OXYGEN LINE ABSORPTION

IF(Ad(1).LT.0.) Ad(1)=0.

Cannot be less than O.

Ad(2)=.182*F*Ndpp

C NONRESONAT DRY AIR ABSORPTION

Ad(3)=.182*F*Nvpp

C WATER VAPOR LINE ABSORPTION

Ad(4)=.182*F*Nipp

C WATER VAPOR CONTINUUM ABSORPTION

Ad(5)=.182*F*Nwpp

C SUSPENDED WATER DROPLET EXTINCTION

C Ad(6)=3.336*S2

C OXYGEN LINE DISPERSIVE DELAY (SEE ABOVE)

C Ad(7)=3.336*Ndp

C OXYGEN NON-RESONANT DISP. DELAY (SEE ABOVE)

C Ad(8)=3.336*S2

C WATER VAPOR CONTIUUM DISPERSIVE DELAY (SEE ABOVE)

C Ad(9)=3.336*Nip

C WATER VAPOR LINE DISPERSIVE DELAY (SEE ABOVE)

Ad(10)=3.336*Dw

C WATER DROPLET DISPERSIVE DELAY

Ad(11)=ATRAN

C ATTENUATION DUE TO RAIN

Ad(12)=3.336*Nrp o WRITE(*,*)'Ad(12)= ',Ad(12)

C RAIN DELAY

RETURN

END C-----------------------------------------------------------------

SUBROUTINE FPPFP(F,Vo,GAMMA,DELTA,Fpp,Fp,FLAG)

C******************************************************************

C CALC Fpp & Fp -- VW line shape functions

C******************************************************************

G2=GAMMA*GAMMA

VMF=Vo-F

VPF=Vo+F

CUTOFF=40.

Fpp=F/Vo*«GAMMA-VMF*DELTA)/(VMF**2+G2) +

+ (GAMMA-VPF*DELTA)/(VPF**2+G2))

IF(FLAG.EQ.1)THEN

IF(F.GT.(Vo+CUTOFF*GAMMA)) Fpp=O.

SET ABSORPTION TO ZERO IF F IS > NU+40*GAMMA

High-frequency wing problem of VW shape function for H20 lines [7]!

Intensities «approx. 7.5 E-4 Fpp) are neglected.

ENDIF

Fp=(VMF + GAMMA*(GAMMA+F*DELTA)/VO)/(VMF**2+G2) +

+ (VPF + GAMMA*(GAMMA-F*DELTA)/Vo)/(VPF**2+G2) - 2./Vo

RETURN

-...J
FOHt~ NTIA-29

(4-80j

BIBLIOGRAPHIC DATA SHEET

I----------r-::-;::;;~~=:;:_;_;:~------'-__,;:;___;::;____::__:_-----,____;~____,~_;:;_-__:c__:_-----,_;_:_------J 1. PUBLICATION NO. 2. Gov't Acce5sion fJo. 3. ReCip,,,nts Accession No.

NTIA Report 87- 224

4. TITLE AND SUBTITLE

Mi 11 imeter-Wave Properties of the Atmosphere:

Lahoratory Studies and Propagation Modeling

5. Publication Date

October 1987

6. Performing Organization Code

NTIA/ITS.S3

7. AUTHOR(S) 9. Project/Task/Work Unit No.

l--_""""-~-=-=-=-:-:-:-::::-:-=-:::7:'"":":'-:-:-=-:-:-:::--=::=:::-- ---!91 a 7108/910 5398 I 8. PERFORMING ORGANIZATION NAME AND ADDRESS

U.S. Dept. of Commerce/Nat' 1 Telecomm. and

Informa ti on Administra ti'on 10 Contract/Grant No.

Institute for Telecommunication Sciences

325 Broadwav. Boulder. CO 80303 3328

11. Sponsoring Organization Name and Address 12. Type of Report and Period Covered

U.S.Dept. of Commerce

National TelecommunicaUons and Information Administratlcn-P-:-:::-------------j Herbert C. Hoover Butldtng 14th & Constitution Ave. NW 13

Washinqton. D.C. 20230

14. SUPPLEMENTARY NOlES

15. ABSTRACT (A 200-word or less factual summary of most significant information. "document includes a significant bibliography or literature

survey. mention ithere.). .' •

LaBoratory measurements have been performed at D8 GHz of water vapor attenuatTon

a. for pure vapor (H 0) and its 'mixtures with air, nitrogen eN ), oxygen (0 J, and A~gon(Ar). A comput~r..controlledresonancespectrometer was e~ployed.. The2results

are interpreted i'n terms of l1nderlyingabsorption mechanisms. Asubstantial amount

of the self-broadening term'proporti'onal to the square of vapor pressure is 1eft

unaccounted. The negative temperature coefficient of the excess absorption is consistent with a dimer (HO) model .An empirical formulation of the experimental

findings is incorporate6 fnto the parametric propagation model MPM that utilizes a

local (30x H?O, 48x O?)linebase to address frequenc;:es up to 1000 GHz. Details

of MPM are gtven in two Appendices. Predi'ctions of moi'st air attenuation and

delay by means of therevi'sedMPM·program generally compare favorably with reported

(lo - 430GHz) data from both fi eldandlaboratory measurements.

16. Key Words (Alphabetical order. separated by semicolons)

atmospheric attenuation and delay; 1'aboratory studies of moist air attenuation;

mi 11 imeterlsubmi 11 imeter-wave spectral range; prop'agati on program MPM; terrestri a1

radi 0 pa th da ta

17. AVAILABILITY STATEMENT

UNLIMITED.

o FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

unclassified

19. Security Class. (This page)

unclassified

20. Number of pages

80

21. Price.

* U.S. GPO: 1987 573-002/8()'iW
-------------------