JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D03302, doi:10.1029/2006JD007850, 2007
Observed relationship between surface specific humidity, integrated
water vapor, and longwave downward radiation at different altitudes
Christian Ruckstuhl,1 Rolf Philipona,2 June Morland,3 and Atsumu Ohmura1
Received 28 July 2006; accepted 27 September 2006; published 2 February 2007.
[1] Atmospheric water vapor and surface humidity strongly influence the radiation budget
at the Earth’s surface. Water vapor not only absorbs solar radiation in the atmosphere,
but as the most important greenhouse gas it also largely absorbs terrestrial longwave
radiation and emits part of it back to the surface. Using surface observations, like
longwave downward radiation (LDR), surface specific humidity (q) and GPS derived
integrated water vapor (IWV), we investigated the relation between q and IWV and show
how water vapor influences LDR. Radiation data from the Alpine Surface Radiation
Budget (ASRB) network, surface humidity from MeteoSwiss and GPS IWV from the
STARTWAVE database are used in this analysis. Measurements were taken at four
different sites in Switzerland at elevations between 388 and 3584 m above sea level
and for the period 2001 to 2005. On monthly means the analysis shows a strong linear
relation between IWV and q for all-sky as well as for cloud-free situations. The slope
of the IWV-q linear regression line decreases with increasing altitude of the station.
This is explained by the faster decrease of IWV than of q with height. Both q and
IWV are strongly related with LDR measured at the Earth’s surface. LDR can be
parameterized with a power function, depending only on humidity. The estimation of
LDR with IWV has an uncertainty of less than 5% on monthly means. At lower
altitudes with higher humidity, the sensitivity of LDR to changes in q and IWV is smaller
because of saturation of longwave absorption in the atmospheric window.
Citation: Ruckstuhl, C., R. Philipona, J. Morland, and A. Ohmura (2007), Observed relationship between surface specific humidity,
integrated water vapor, and longwave downward radiation at different altitudes, J. Geophys. Res., 112, D03302,
doi:10.1029/2006JD007850.
1. Introduction
[2] Atmospheric water vapor being the most important
greenhouse gas strongly influences the surface radiation
budget and hence temperature and the water cycle. Climate
models predict increased atmospheric content of water
vapor with small changes in relative humidity as the global
mean temperature rises in response to increased CO2 and
other greenhouse gases [Dai et al., 2001]. This water vapor
feedback is expected to almost double the warming from
what it would be for fixed water vapor by doubling the CO2
content in the atmosphere [Houghton et al., 2001]. Accurate
measurements of the surface radiation budget and investigations with respect to temperature and water vapor
increase show that 70% of the recent rapid temperature rise
in central Europe is related to strong water vapor feedback
greenhouse warming [Philipona et al., 2005]. However, the
peculiarity of water vapor feedback compared to other
1
Institute for Atmospheric and Climate Science, Eidgenössische
Technische Hochschule Zurich, Zurich, Switzerland.
2
Physikalisch-Meteorologisches Observatorium Davos, Davos,
Switzerland.
3
Institute of Applied Physics, University of Bern, Bern, Switzerland.
Copyright 2007 by the American Geophysical Union.
0148-0227/07/2006JD007850
greenhouse gases is its strong diurnal, annual and spatial
variability [e.g., Held and Soden, 2000; Dai et al., 2002;
Trenberth et al., 2003].
[3] Different terms are used to express the amount of
surface humidity and the total water vapor content in an air
column aloft. In our study we use the term specific humidity
(q), which is approximately equal to the mixing ratio (r), to
describe the moist air at the surface. Specific humidity is the
ratio of the masse of water vapor to the masse of water
vapor and dry air, whereas the mixing ratio is the quotient of
the masses of water vapor and dry air. Integrated water
vapor (IWV) or precipitable water is the total atmospheric
water vapor contained in a vertical column from the Earth’s
surface to the top of atmosphere. IWV is expressed as the
depth of the water column in millimeters if all the water
vapor from the air column is condensed in a vessel of the
same cross section.
[4] The relation between surface humidity and IWV has
been investigated in the past by comparing surface moisture
to radiosonde (RS) measurements [e.g., Reitan, 1963;
Lowry and Glahn, 1969; Liu, 1986]. Reitan [1963] found
a linear relationship between surface dew point and the
natural logarithm of precipitable water with high correlation
(r = 0.96 – 0.99) at 15 stations over continental United
States using monthly data. Lowry and Glahn [1969] expanded the relation with the variables sky cover and
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weather. Studies from Liu [1986] and Liu et al. [1991] show
the relation between surface specific humidity, mixing ratio
and IWV over oceans. Using monthly mean data from
weather ships and small islands Liu [1986] found a global
fifth-order polynomial regression. This relation was verified
by Hsu and Blanchard [1989] and also by Gautam et al.
[1992] who applied it on instantaneous data from the Indian
Ocean, but this resulted in root mean square errors (rmse)
that were much larger than Liu obtained using global mean
monthly data.
[5] New Global Positioning System (GPS) methods are
now available to determine IWV from GPS signal delays
[Bevis et al., 1992]. The high spatial and temporal resolution of GPS IWV measurements allows investigating surface
moisture versus IWV in more detail at specific locations and
different elevations and also for different sky conditions.
[6] The aim of this paper is to show the relation between
surface specific humidity and GPS determined IWV at
different altitudes, and in addition to investigate their
relation to thermal longwave downward radiation (LDR).
Ångström [1916] first used empirical relations to estimate
LDR from vapor pressure and temperature near the surface.
Many others [e.g., Brunt, 1932; Swinbank, 1963; Idso,
1981] followed Ångström’s ideas and parameterized LDR
depending on temperature and/or humidity. As LDR is
emitted not only from the nearest surface layer but also
from higher levels, the total amount of water vapor is
regarded as a more adequate measure to estimate LDR than
surface humidity only. We propose using the LDR-IWV
relation as a possible way to approximate LDR. This method
will help to estimate LDR in former time periods when
longwave radiation has not been measured, but humidity
measurements are available, and will finally allow to
analyze the radiation balance on longer timescales. Furthermore, this parameterization is not explicitly temperaturedependent and this will allow investigating the influence of
the radiation budget on temperature changes. The motivation to investigate LDR-humidity relations stems from
observations of increasing water vapor and rapid greenhouse warming, which is manifested by a strong increase of
longwave downward radiation during the recent temperature rise in Europe [Philipona et al., 2005]. Vibrational and
rotational water vapor bands on both sides of the atmospheric window strongly absorb thermal radiation such that
more than 90% of LDR is emitted from the first 1000 m
above the surface during cloud-free situations [Philipona et
al., 2004]. Only a few percents are from higher altitudes
from emissions primarily from within the atmospheric
window.
[7] The investigations are based on data from four radiation and GPS stations in the Swiss Alps, where all
measurements are available. The sites cover an altitude
range between 388 and 3584 m above sea level (masl),
with two lowland stations Locarno-Monti (LOM) at 388 m
and Payerne (PAY) at 498 m, as well as two mountain
stations Davos (DAV) at 1598 m and Jungfraujoch (JFJ) at
3584 masl. Data from 2001 to 2005 are analyzed. In the
following chapter, an overview of the observational data
and a description of the cloud-free detection method are
given. The quality of the GPS IWV data is evaluated in a
comparison with radiosonde data in section 3. In section 4
we use this evaluated data to investigate the relation
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between IWV and specific humidity. The influence of
moisture on LDR and its parameterization is shown in
section 5.
2. Observational Data
[8] For the analysis we used observational data from the
Automatic GPS Network Switzerland (AGNES), the
MeteoSwiss aerological station at Payerne, the Automatic
Network (ANETZ) of MeteoSwiss and the Alpine Surface
Radiation Budget (ASRB) network. A summary of the
networks is given bellow.
[9] IWV is derived from AGNES and radiosoundings at
Payerne. AGNES covers Switzerland with 30 stations
located between 366 and 3584 masl. Bevis et al. [1992]
describe a method to calculate the IWV content from GPS
Zenith Total Delay (ZTD), surface temperature and surface
pressure. This method has been applied for 30 AGNES
stations since 2001 on an hourly basis [Morland et al.,
2005]. The Jungfraujoch data (3584 masl) suffer from a bias
due to an incorrect modeling of the antenna and are
therefore corrected [Morland et al., 2006]. The correction
is based on comparisons with Precision Filter Radiometer
(PFR). Because of very low IWV content at this high
altitude, Jungfraujoch data have still a large relative uncertainty. The second source of IWV measurements is the
MeteoSwiss aerological station at Payerne, where a Swiss
radiosonde SRS400 is launched twice a day. IWV is
obtained from the integration of vapor density (r) over
height (h):
Zhlim
IWV ¼
r dh ;
ð1Þ
h0
where h0 is the height at ground level and hlim the upper
height limit, i.e., the 200 mbar level at approximately 12 km
[Morland et al., 2005]. Radiosonde measurements with
humidity sensors (on SRS400 a resistive carbon hygristor)
are the only way of direct in situ measurements of
atmospheric water vapor. Even so, IWV derived from
radiosondes contain uncertainties: radiative heating of the
temperature sensor is corrected according to Ruffieux and
Joss [2003], but humidity tends to be underestimated near
humidity saturation [Jeannet, 2004], whereas by passing
clouds or fog the sensor becomes wet and relative humidity
is overestimated when the sensor reaches drier areas again
[Haase et al., 2003].
[10] The ASRB network offers accurate radiation flux
measurements at altitudes between 388 and 3584 masl in
the Swiss Alps since 1995 [Philipona et al., 1996]. LDR is
measured with Eppley Precision Infrared Radiometer (PIR).
The sensors are modified with dome thermistors to improve
uncertainty [Philipona et al., 1995] and they are slightly
heated to prevent accumulation of dew, rime and snow on
the domes. The ASRB stations chosen for this study are
collocated with the ANETZ of MeteoSwiss, where air
temperature and relative humidity is measured with a
ventilated thermo hygrometer VTP6, called THYGAN.
[11] To separate cloud-free from all-sky situations we use
the Automatic Partial Cloud Amount Detection Algorithm
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RUCKSTUHL ET AL.: RELATION BETWEEN q, IWV, AND LDR
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Figure 1. (a) Scatter diagram between radiosonde (RS) measured IWV and IWV retrieved from GPS
measurements. Measurements are taken daily at 1200 UTC from 2001 to 2004 at Payerne, Switzerland.
GPS data points are 2 hour means. All units are in mm. The dashed line indicates the one-to-one line, and
the solid line is the fitted linear regression curve. (b) Same as Figure 1a but at 0000 UTC.
(APCADA) from Dürr and Philipona [2004]. APCADA
allows determining cloud cover in octas on a 10-min time
resolution. The algorithm calculates cloud cover as a
function of LDR, standard deviation of LDR during the last
hour, temperature and humidity measurements at screen
level height and a set of empirical rules. In the following,
we define as cloud-free if the hourly average of cloud cover
is smaller than 0.8 octas. The cloud-free limitation of
0.8 octas assures that in the worst case cloud cover can
reach a maximum of four octas during one 10-min period.
APCADA has the advantage to other cloud detections
algorithms [e.g., Long and Ackerman, 2000] that it is
independent of shortwave radiation measurements and
therefore also works at nighttime.
3. Comparisons of IWV Derived From GPS
and Radiosoundings at Payerne
[12] To asses the quality of IWV data derived from GPS
measurements, different comparisons have been carried out
[e.g., Ohtani and Naito, 2000; Haase et al., 2003; Li et al.,
2003; Deblonde et al., 2005; Guerova et al., 2005]. These
studies report mainly that IWV data obtained from GPS
receivers are slightly higher than IWV values obtained from
radiosondes (RS). Haase et al. [2003] assume that part of
the bias they found is rather due to day/night RS biases and
not due to GPS data processing. They argue that these
biases are largest during high humidity summer months, but
only at daytime. Guerova et al. [2005] found at Payerne for
the period January 2001 to June 2003 a positive GPS – RS
bias (0.9 kg m2) at 1200 UTC and a negative bias (0.4 kg
m2) at 0000 UTC.
[13] We perform a GPS IWV – RS IWV comparison for a
full four year period from 2001 to 2004, hence there is no
distortion due to seasonal effects. Also the very close
location of GPS receiver and RS launches at Payerne,
Switzerland helps to get adequate data for a comparison
as no additional uncertainty is added because of spatial
displacement. Because daytime RS are influenced by solar
radiation, we analyze daytime and nighttime soundings
separately. Over the four year period 1356 daytime and
1334 nighttime soundings were compared with GPS IWV
measurements. GPS values are 2 hour means symmetric to
the RS ascent, 1 hour before and 1 hour after the launch.
[14] Figure 1a shows a scatter diagram of RS IWV
measurements versus GPS IWV measurements at 1200 UTC.
The bias (GPS IWV minus RS IWV) is 1.18 mm, whereas
the rmse is 2.19 mm. Especially at high humidity the GPS
IWV is larger then RS IWV, this effect has also been stated
by Morland and Mätzler [2007]. Figure 1b shows the same
as Figure 1a but at nighttime (0000 UTC). At nighttime the
bias is 0.01 mm and the rmse reduces to 1.58 mm. Also
the high humidity bias becomes smaller. The day/night bias
we found is slightly different from those from Guerova et
al. [2005] because of another time period analyzed and
because we take 2 hour GPS IWV data instead of 1 hour as
they did. The day/night differences in bias and rmse at high
humidity we found in PAY confirm the measurements of
Haase et al. [2003] and their conclusion that the difference
between GPS and RS can rather be contributed to RS errors
than to GPS data processing. Therefore we use GPS IWV
data without any corrections in the following analysis.
Nevertheless the bias cannot be completely attributed to
the RS.
[15] As our following study is mainly based on monthly
means, we also perform an error estimation based on
monthly values. On monthly means (here we use 24 hour
values per day for GPS IWV and two RS measurements per
day) the rmse reduces to 1.09 mm, which is 6.8% of the
mean IWV content and the bias is 0.49 mm for the same
observation period (Figure 2). Especially during the summer
months, when the IWV content is relatively high, GPS IWV
is significant larger than IWV derived from RS. This is in
consistency with the RS IWV underestimation at high
humidity content due to measurements effects of the RS
hygristor, mentioned by Morland et al. [2005].
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RUCKSTUHL ET AL.: RELATION BETWEEN q, IWV, AND LDR
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more than two times higher than at its minimum in February
(see also Figure 2).
[18] IWV and q are closely related, because most of the
humidity is concentrated close to the surface layer. In
Figure 3 we depict the relation between IWV and q at the
lowland station PAY and at the mountainous station DAV.
Monthly means show a strong linear correlation for all-sky
(circles) and cloud-free (asterisks) situations. All stations,
except JFJ, have at least a regression coefficient r2 of 0.97.
IWV can be expressed with the linear equation
IWV ¼ m q þ p ;
Figure 2. Four year (2001 – 2004) monthly mean of GPS
IWV (solid line) and RS IWV (dashed line). During the
summer months, GPS IWV is larger than RS IWV.
4. Altitude-Dependent Relation Between
Surface Specific Humidity and IWV
[16] Here we present results of the IWV-q relation based
on observational data. Using hourly GPS IWV data and
APCADA for clear-sky detection opens the possibility to
analyze the relation between surface specific humidity and
IWV for clear-sky situations separately and we can also take
a look at the altitude effect of the IWV-q relation.
[17] Atmospheric water vapor decreases rapidly with
altitude. The annual average surface specific humidity (q)
decreases from 6.4 g kg1 at LOM to 2.7 g kg1 at JFJ,
whereas IWV decreases from 17.8 mm to 3.2 mm at the
respective locations. Beside this altitude dependence of
water vapor, humidity also shows a strong annular cycle.
This seasonality is most pronounced at the lowland stations
(LOM and PAY), where IWV at its maximum in August is
ð2Þ
where m is the slope and p the intercept. The coefficients
(m, p), correlation coefficient r2 and rmse for cloud-free and
all-sky situations for all stations are shown in Table 1. The
slope (m) of the IWV-q relation decreases with increasing
altitude. This decrease can be explained with the faster
decrease of IWV than of q with height. At lower elevations a
change of q leads to the larger changes in IWV than the
same change of q at higher elevations and hence to a steeper
regression line.
[19] Even hourly values show a good linear correlation
between IWV and q, although scattering is larger (Figure 4).
r2 ranges from 0.83 to 0.91 for the three stations LOM, PAY
and DAV.
5. Relation Between Humidity and LDR
[20] Besides the climatological water vapor feedback
mechanisms, the relation between humidity and longwave
radiation has long been recognized as a method to estimate
LDR. Here we present the relation between humidity and
LDR and an empirical method to estimate thermal radiation.
[21] Figure 5 shows the LDR-q and LDR-IWV relation at
elevations from LOM at 388 masl up to JFJ at 3584 masl.
Lower amount of LDR is found at higher elevations, this has
also been observed by Marty et al. [2002] and they show
that LDR decreases linearly with increasing altitude. De-
Figure 3. Scatterplot of monthly means (2001– 2005) of IWV and surface specific humidity (q) for allsky (circles) and cloud-free (asterisks) situations at (a) Payerne and (b) Davos.
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Table 1. Slope (m) and Intercept (p) of Regression Line From the Monthly IWV – q Relation for All-Sky (as) and for Cloud-Free (cf)
Situations and Their Linear Correlation Coefficients r2 and Root Mean Square Errors (rmse)
Locarno-Monti
Slope m, mm/g kg1
Intercept p, mm
r2
rmse, mm
Payerne
Davos
Jungfraujoch
as
cf
as
cf
as
cf
as
cf
2.67
0.68
0.99
0.77
2.58
0.28
0.98
0.92
2.54
0.31
0.98
0.85
2.40
1.60
0.97
1.08
2.23
0.01
0.99
0.44
2.15
0.82
0.97
0.74
1.11
0.21
0.88
0.49
1.10
0.26
0.84
0.49
creasing moisture, the most important greenhouse gas, and
lower temperatures at higher elevations are the main contributors of this altitude-dependency of LDR. The period
2001 to 2004 (circles in Figure 5) is used to parameterize
LDR as a function of q and as a function of IWV. Best fitting
of the measurements is achieved by using a power law:
LDR ¼ a qb
ð3Þ
LDR ¼ c IWV d ;
ð4Þ
where the coefficients (a, b) from equation (3) and the
coefficients (c, d) from equation (4) slightly differ for cloudfree and for all-sky situations. Coefficients, r2 values and
rmse are given in Table 2. The LDR-IWV relation allows
estimating LDR depending only on IWV. Data from 2005
(asterisks in Figure 5) are used to check the quality of the
approximation of LDR with IWV (equation (4)). By
estimating LDR in 2005 a rmse of less than 11 W m2 on
monthly means is expected for all-sky as well as for cloudfree situations. This is 3.7% of the average LDR of the
four stations for all-sky situations and 3.8% for clear-sky
situations, respectively. When the previous four years of
data are considered, the rmse are 3.2% and 4.9% for the
respective conditions.
[22] With increasing q and IWV the fitted power LDR
function flattens. This effect is connected with the atmospheric window. The atmospheric window is a range of
wavelengths (8– 13 mm) where strong dominant absorption
bands are missing. Water vapor is absorbing but weakly in
this range, and this absorption is called the water vapor
continuum. Water vapor is most effective in the continuum
if little water is available and its effectiveness decreases
with increasing water amount. Therefore at high humidity
further increasing water vapor cannot increase LDR in the
same efficient way as it does at a low moister content. This
can be shown with the first derivative of the fitted power
LDR function (equations (3) and (4)) with respect to
humidity (@LDR/@q = a b qb1 and @LDR/@IWV = c d IWVd1). The first derivative of the LDR-humidity
functions gives also an estimation of the sensitivity of
LDR to changes in humidity. In other words, a change in
LDR in W m2 with respect to a change in IWV in mm
decreases with increasing amount of humidity.
6. Summary
[23] GPS IWV data, whose quality has been verified in
detail with radiosoundings, have been used to investigate
the IWV-q relation at different altitudes in midlatitudes. The
IWV-q relation is from high linearity and correlation (r2 >=
0.97 for LOM, PAY and DAV) for monthly means and still
between 0.83 and 0.91 for hourly data. IWV values from JFJ
are uncertain because of measurement difficulties [Morland
et al., 2006] and very low absolute values. The slope of the
linear IWV-q regression line is altitude-dependent. It is
decreasing with increasing altitude. Although the IWV-q
relation is highly linear, we do not propose to use this
Figure 4. Relation between IWV and surface specific humidity (q) for hourly data for (a) all-sky and
(b) cloud-free situations at Payerne.
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RUCKSTUHL ET AL.: RELATION BETWEEN q, IWV, AND LDR
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Figure 5. Monthly means of longwave downward radiation (LDR) (a and b) as a function of specific
humidity (q) and (c and d) as a function of IWV. Figures 5a and 5c are from cloud-free data, whereas
Figures 5b and 5d are all-sky situations. Data are from the lowland stations Locarno-Monti (red) and
Payerne (blue) and the mountainous stations Davos (green) and Jungfraujoch (magenta). Data points
indicated as circles are the years 2001 to 2004; they are used for the curve fitting, whereas data points
indicated as asterisks are from the year 2005 and are used for quality checking of the fitted relation.
relation for instantaneous IWV estimations, as for hourly
data the scattering is quite large. However, we show that
surface humidity measurements on a monthly scale can be
used as a good approach to determine the tropospheric IWV
content.
[24] With surface humidity measurements, IWV data from
GPS receivers and ASRB radiation measurements we investigated the LDR-q and LDR-IWV relationship. LDR
depends with a power function to q and IWV, and shows
high correlation on monthly means. This allows estimating
LDR from humidity measurements, with a rmse of less than
5% on monthly means by using the LDR-IWV relation
(equation (4)). Furthermore, the LDR-humidity relation
shows that the sensitivity of LDR to changes in q and also
in IWV decreases with increasing humidity. This is
explained with the increasing saturation within the atmospheric window with increasing humidity. This results
are consistent with those found by Allan et al. [1999] for
clear-sky outgoing longwave radiation (OLR), where they
state that the sensitivity of clear-sky OLR to changes
in relative humidity diminishes with increasing relative
humidity.
Table 2. Coefficients of LDR-q and LDR-IWV Relation for AllSky (as) and for Cloud-Free (cf) Situations and Their Correlation
Coefficients r2 and Root Mean Square Errors (rmse)a
LDR = a qb
a and c
b and d
r2
rmse, W m2
LDR = c IWVd
as
cf
as
cf
181.4
0.29
0.93
12.5
150.2
0.35
0.94
13.5
173.1
0.22
0.96
9.2
147.8
0.26
0.95
12.0
a
Coefficients are retrieved from monthly mean data from 2001 to 2004.
In column 1, coefficients a and b are used in columns 2 and 3, and
coefficients c and d are used in columns 4 and 5.
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[25] Acknowledgments. This work was supported by the framework
of the National Center of Competence in Research on Climate (NCCR
Climate), an initiative funded by the Swiss National Science Foundation
(NSF). We thank the Swiss Federal Office for Meteorology and Climatology (MeteoSwiss) for providing temperature, humidity, and pressure data
and valuable help at the ASRB stations.
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