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.
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 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 greenhouse gases is its strong diurnal, annual and spatial variability [e.g., Held and Soden, 2000; Dai et al., 2002; Trenberth et al., 2003].
 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.
 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  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  expanded the relation with the variables sky cover and weather. Studies from Liu  and Liu et al.  show the relation between surface specific humidity, mixing ratio and IWV over oceans. Using monthly mean data from weather ships and small islands Liu  found a global fifth-order polynomial regression. This relation was verified by Hsu and Blanchard  and also by Gautam et al.  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.
 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.
 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  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 temperature-dependent 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.
 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 between IWV and specific humidity. The influence of moisture on LDR and its parameterization is shown in section 5.
2. Observational Data
 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.
IWV is derived from AGNES and radiosoundings at Payerne. AGNES covers Switzerland with 30 stations located between 366 and 3584 masl. Bevis et al.  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 (ρ) over height (h):
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 , 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].
 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.
 To separate cloud-free from all-sky situations we use the Automatic Partial Cloud Amount Detection Algorithm (APCADA) from Dürr and Philipona . 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
 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.  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.  found at Payerne for the period January 2001 to June 2003 a positive GPS – RS bias (0.9 kg m−2) at 1200 UTC and a negative bias (−0.4 kg m−2) at 0000 UTC.
 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.
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 . 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.  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.  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.
 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. .
4. Altitude-Dependent Relation Between Surface Specific Humidity and IWV
 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.
 Atmospheric water vapor decreases rapidly with altitude. The annual average surface specific humidity (q) decreases from 6.4 g kg−1 at LOM to 2.7 g kg−1 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 more than two times higher than at its minimum in February (see also Figure 2).
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
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.
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)
Slope m, mm/g kg−1
Intercept p, mm
 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
 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.
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.  and they show that LDR decreases linearly with increasing altitude. Decreasing 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:
where the coefficients (a, b) from equation (3) and the coefficients (c, d) from equation (4) slightly differ for cloud-free 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 m−2 on monthly means is expected for all-sky as well as for cloud-free 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.
Table 2. Coefficients of LDR-q and LDR-IWV Relation for All-Sky (as) and for Cloud-Free (cf) Situations and Their Correlation Coefficients r2 and Root Mean Square Errors (rmse)a
LDR = a · qb
LDR = c · IWVd
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.
a and c
b and d
rmse, W m−2
 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 μm) 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 · qb−1 and ∂LDR/∂IWV = c · d · IWVd−1). 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 m−2 with respect to a change in IWV in mm decreases with increasing amount of humidity.
 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 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.
 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.  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.
 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.