Applied Optics Letters to the Editor
Letters to the Editor should be addressed to the Editor, APPLIED OPTICS, 1155 16th St., N.W., Washington 6, B.C.
Mean Atmospheric Moisture Profiles to 31 km for Middle Latitudes
Murray Gutnick Meteorological Development Laboratory, Air Force Cambridge Research Laboratories, Bedford, Massachusetts. Received 1 June 1962.
Average yearly vertical profiles up to 31 km in middle latitudes of mixing ratio and dewpoint-frostpoint, derived independently, are presented in a table and a figure. Also, since the relation between mixing ratio and frostpoint is nonlinear, other moisture expressions were derived from each of the basic profiles, using Standard Atmosphere conditions. Up to 7 km the basic profiles were developed from conventional radiosonde humidity measurements; above tha t level they are based upon experimental humidity ascents, subjectively selected and weighted.
The annual mid-latitude mixing ratio profile decreases from 6150 ppm (mg/kg) at the surface to 9 ppm at 16 km, then increases slightly with height; the surface dewpoint is taken at 4°C, decreasing to 78°C at 18 km, then increasing 0.5 deg/km.
This letter is a brief summary of a comprehensive study1 presenting preliminary models of the variation of atmospheric moisture with height. The concept is similar to tha t of other standard atmospheres. The paucity and ambiguity of upper-air moisture data make the models offered here quite crude. As observations increase, the models can be revised, refined, and extended evolving in the same way as other representations of atmospheric structure.
The tropospheric portion of the mixing ratio profile was derived by estimating, from recent maps, the mean annual pre-cipitable water above each of four widely separated surfaces at 45°N. The corresponding mean mixing ratios were assumed to be those of two stations having the same precipitable water as the derived mean annual values. The stratospheric portion of the mixing ratio profile is a weighted average of the best soundings from each of half-a-dozen sets of experimental moisture ascents, and the means of all valid ascents of the two sets of routine
stratospheric moisture measurements. In the figure, symbols represent:
BRL—Mean of 2 hygrometric ascents by Ballistic Research Laboratories;
NRL—Mean of 3 hygrometric ascents by U.S. Naval Research Laboratories;
U of D—One hygrometric and one spectroscopic ascent by University of Denver;
JMA—Means of the Japanese Meteorological Agency hygrometric ascents; 100 of which reached or exceeded 300 mb and two of which reached 10 mb;
MRF—Means of the British Meteorological Research Flight hygrometric ascents, 400 of which reached or exceeded 300 mb;
Vapor Trap—Mean of seven ascents of the United Kingdom Atomic Energy Authority's water vapor absorption device;
Molecular Sieve—A single ascent of the General Mills, Inc., water vapor absorption device.
The dewpoint profile was constructed by the same procedure. Stratospheric frostpoints were approximated when unavailable from the soundings.
Resulting mean annual vertical profiles to 31 km in middle latitudes (35 to 55°N) of mixing ratio and dewpoint-frostpoint, obtained as independent means from the same basic measurements of stratospheric moisture and routine tropospheric radiosonde observations, are presented in the accompanying table. Neither profile can be obtained from the other, since the nonlinear relation between mixing ratio and condensation temperature (dewpoint-frostpoint) insures that the means, separately obtained, will differ.
From each of the basic profiles, other expressions for the moisture content of the atmosphere have been derived, using Standard Atmosphere conditions where required. The two sets of values for absolute humidity (vapor density), vapor pressure, precipitable water, and relative humidity differ, of course. Preferred values are indicated by asterisk. Relative humidity up to 7 km was computed directly from radiosonde data.
The most reliable single element is the mixing ratio, because all the selected data were given in terms of mixing ratio and required no approximations, such as those used for the dewpoint-frost-
670 APPLIED OPTICS / Vol. 1, No. 5 / September 1962
a Bas
ed o
n av
aila
ble
rout
ine
and
expe
rim
enta
l dat
a co
nsid
ered
relia
ble,
with
rel
ated
qua
ntit
ies
com
pute
d (w
here
req
uire
d) fo
r con
ditio
ns o
f R
evis
ed U
.S.
Stan
dard
Atm
osph
ere,
196
2.
Stan
dard
atm
osph
ere:
fr
om U
.S.
Stan
dard
Atm
osph
ere,
196
2 ("
USS
A")
-T,
P, ρ
: te
mpe
ratu
re (
°C),
pre
ssur
e (m
b),
dens
ity o
f ai
r (g
/m3)
(ass
umed
dry
).
Pres
sure
of w
ater
vap
or,
in m
icro
bars
: 1 μ
b =
0.00
1 m
b =
1 dy
n/cm
2. e s
: if
sat
urat
ed a
t am
bien
t U
SSA
tem
pera
ture
; fr
om S
MT
94
and
96.
e v:
havi
ng m
ixin
g ra
tio w
at
ambi
ent
USS
A p
ress
ure;
e v
= w
P/0
.622
. e v
' *:
ha
ving
dew
poin
t T d
or
fros
tpoi
nt T
f; fr
om S
MT
94
and
96.
Abso
lute
hum
idity
or
vapo
r de
nsity
or
vapo
r co
ncen
trat
ion
in m
g/m
3 (1
mg/
m3 =
0.0
01 g
/m3).
p s
: If
sat
urat
ed a
t am
bien
t U
SSA
tem
pera
ture
and
den
sity
, fr
om S
MT
108
and
109
. p v
: ha
ving
mix
ing
ratio
w a
t am
bien
t U
SSA
pre
ssur
e an
d de
nsity
; ρv
= ρ
w.
p v'
*:
havi
ng d
ewpo
int
T d o
r fr
ostp
oint
Tf ;
from
SM
T 1
08 a
nd 1
09.
Mix
ing
ratio
, rat
io o
f mas
s of
wat
er v
apor
to t
hat o
f dry
air
in m
ixtu
re, i
n m
g/kg
, or p
arts
per
mill
ion.
w
s: if
sat
urat
ed a
t am
bien
t U
SSA
tem
pera
ture
and
den
sity
; w
s =
ρ s
/ρ.
w *
: es
timat
ed m
ean
mid
-lat
itude
val
ue,
from
ava
ilabl
e m
ixin
g ra
tio d
ata
cons
ider
ed r
elia
ble.
w
': ha
ving
dew
poin
t T d
or
fros
tpoi
nt T
f at
USS
A d
ensi
ty;
w'
= ρ v
'/ρ.
Pr
ecip
itabl
e w
ater
, w
ater
vap
or c
onte
nt o
f ai
r in
2-k
m la
yer
abov
e in
dica
ted
leve
l, if
con
dens
ed to
liqu
id,
in m
icro
ns (
1 μ =
0.00
0 1
cm =
0.0
00 1
g/c
m2).
W
*:
= (p
2 —
p1)w
/g;
w is
mea
n m
ixin
g ra
tio b
etw
een
pres
sure
s p\
and
p2
2 km
apa
rt (
USS
A);
g =
980
cm
/sec
2. W
': ρv'h
, whe
re h
is la
yer
thic
knes
s in
met
ers,
= ρ
v'(
Z1) +
ρv'(
Z1 +
2 k
m).
Re
lativ
e hu
mid
ity,
in p
erce
nt.
U:
rati
o of
pre
ssur
es o
f w
ater
vap
or a
t mix
ing
ratio
w a
nd if
sat
urat
ed a
t USS
A t
empe
ratu
re;
U =
e v
'/es.
U' *
: up
to 6
km
, wei
ghte
d av
erag
e of
obs
erve
d re
lativ
e hu
mid
ities
; ab
ove
6 km
, U
' =
e v'/e
s, fo
r ai
r hav
ing
fros
tpoi
nt T
f and
USS
A t
empe
ratu
re.
Dew
poin
t and
fros
tpoi
nt t
empe
ratu
re,
in d
egre
es C
elsi
us.
T d,
T ƒ:
from
SM
T 9
4 an
d 96
, us
ing
e w a
s de
rive
d fr
om w
. T d
*, T
f : es
timat
ed m
ean
mid
-lat
itude
val
ues,
fro
m a
vaila
ble
data
exp
ress
ed a
s de
wpo
ints
and
fro
stpo
ints
. N
otes
: *
Indi
cate
s va
lues
rec
omm
ende
d fo
r ge
nera
l use
; ot
her
valu
es d
eriv
ed f
or c
ompa
riso
n on
ly.
SMT
= S
mith
soni
an M
eteo
rolo
gica
l Ta
bles
, si
xth
revi
sed
editi
on,
prep
ared
by
R. J
. Lis
t, W
ashi
ngto
n 19
51.
Satu
ratio
n as
sum
ed w
ith r
espe
ct to
pla
ne s
urfa
ces
of li
quid
wat
er a
bove
— 4
0°C
, of
ice
belo
w —
40°C
.
September 1962 / Vol. 1, No. 5 / APPLIED OPTICS 671
Fig. 1. Mean annual mid-latitude mixing ratio.
points. However, the values derived from the dewpoint-frost-point are more reliable than those based on the mixing ratio, because fewer Standard Atmosphere assumptions are used.
The tentative moisture profiles presented herein undoubtedly will be revised and extended as the state-of-the-art advances. The large amount of subjectivity used in deriving the stratospheric portion of the moisture profiles makes revision especially desirable. Despite their deficiencies, these models are suggested for general use as mid-latitude standards.
Reference 1. M. Gutnick, Air Force Survey in Geophysics 147, AFCRL,
Bedford, Mass. (July 1962).