In this study we present a simple relation between the tropospheric opacity τ near 22.235 GHz and the integrated water vapor (IWV) content of the troposphere. The opacity is measured at Bern, Switzerland, by the radiometer Middle Atmospheric Water Vapour Radiometer (MIAWARA), designed for middle atmospheric water vapor profile measurements. In contrast to typical radiometers for tropospheric monitoring, this middle atmospheric water vapor radiometer only measures in the vicinity of the 22.235 GHz water vapor line with a bandwidth of 1 GHz. With this study we show that it is even possible to derive the integrated tropospheric water vapor (IWV) content of the atmosphere using this limited frequency range if the liquid water content of the atmosphere is negligible. IWV measurements of the tropospheric monitoring instruments Tropospheric Water Vapour Radiometer (TROWARA, two-channel radiometer), All-Sky Multi Wavelength Radiometer (ASMUWARA, multichannel radiometer), and GPS, which are operated next to MIAWARA, are used to derive a linear relation between the opacity and the water vapor content of the troposphere. In a second step, the mean tropospheric temperature is taken into account and a slight improvement of the linear relation is achieved. All instruments involved in this study are contributing to the Studies in Atmospheric Radiative Transfer and Water Vapour Effects (STARTWAVE) project of the Climate program of the National Competence Center in Research. The MIAWARA measurements in the subarctic winter in northern Finland during the Lapbiat Upper Tropospheric Lower Stratospheric Water Vapor Validation Project (LAUTLOS/WAVVAP) campaign in 2004 are compared to radiosonde measurements by the Finnish Meteorological Institute using the same algorithm that was derived for Bern. The agreement of MIAWARA IWV and radiosonde IWV is of the same order as for Bern. Finally, Payerne radiosonde measurements and model simulation using the Atmospheric Radiative Transfer Simulator (ARTS) software and the continuum absorption models of Rosenkranz (1998) and Liebe (MPM87/MPM93) confirm the derived opacity-IWV relation. This study shows that the integrated water vapor content of the troposphere can be measured by a radiometer operating near the 22.235 GHz water vapor line using a bandwidth of 1 GHz, if the liquid water content of the atmosphere is negligible.
 The Middle Atmospheric Water Vapour Radiometer (MIAWARA) is designed to measure the water vapor profile between 20 and 80 km. It measures the 22.235 GHz rotational emission of water vapor. A detailed description of the instrument, its calibration and profile retrieval can be found in work by Deuber et al. [2004a] and Deuber and Kämpfer . The profile retrieval of MIAWARA was validated using balloon-borne and satellite-borne data. This validation study (presented by Deuber et al. ) showed that MIAWARA measures good quality water vapor profiles.
 In this study 1 year of tipping curve measurements are compared to measurements of integrated water vapor from three different instruments (All-Sky Multi Wavelength Radiometer (ASMUWARA (ASMUWARA), Tropospheric Water Vapour Radiometer (TROWARA), and GPS) operated at the same location at Bern, Switzerland, and the relation between the opacity τ and the integrated water vapor is derived. The derived relation between τMIAWARA and IWV is verified using 8 months of Payerne radio-sounding data and τ simulated using the Atmospheric Radiative Transfer Simulator (ARTS) software.
2. MIAWARA Instrument
 The ground-based radiometer MIAWARA measures the intensity of the pressure-broadened water vapor emission line at 22.235 GHz with an overall bandwidth of 1 GHz and a spectral resolution of 1.2 MHz for the broadband acousto-optical spectrometer and 40 MHz bandwidth with 14 kHz resolution for the narrowband chirp transform spectrometer.
 The instrument is operated with a combined calibration scheme using tipping curve and balancing calibration. The concept of the instrument and the calibration technique as well as a validation of the calibration are described in detail by Deuber et al. [2004a] and Deuber and Kämpfer .
 MIAWARA is designed to measure middle atmospheric water vapor profiles in the range of 20–80 km. As the cold sky is used as cold calibration load [Deuber et al., 2004a], a tipping curve is included in the calibration scheme. From this tipping curve the tropospheric opacity τ is known with a time resolution of 1 hour.
 An extensive validation study of the profile retrieval as well as the validation of the tipping curves is presented by Deuber et al. . Algorithms used in the tipping curve procedure are described in detail by Deuber et al. [2004a].
3. Reference Data
3.1. Reference Instruments
 The Institute of Applied Physics (IAP) operates various instruments which monitor the tropospheric water vapor as well as the liquid water content of the troposphere. The radiometers TROWARA, ASMUWARA, and the GPS receiver provide columnar water vapor with a high time resolution.
 The radiometers ASMUWARA [Martin, 2003] and TROWARA [Morland, 2002] have radiometric channels at 23.2 GHz and 31.5 GHz; therefore it is possible to obtain the integrated water vapor IWV as well as the integrated liquid water ILW content using the linear relations
 The frequency of 31.5 GHz is more sensitive to liquid water, whereas at 23 GHz the absorption of water vapor is dominant. The coefficients a0,1,2 and b0,1,2 for these instruments were calculated using radiosonde measurements made by MeteoSwiss at Payerne, which is approximately 50 km from Bern. The additional microwave channels of ASMUWARA at 51 and 151 GHz have not been used for the IWV retrieval so far. They are used for the determination of the temperature profile in the troposphere. Using a GPS receiver [Guerova et al., 2004] the integrated water vapor IWV content can be obtained by measurements of the Zenith Total Delay as described by Rocken et al. .
 MIAWARA made measurements from January to November of 2003 in Bern. During this time period the reference instruments also made measurements in Bern (ASMUWARA left for a campaign in early November). Therefore the time period from January to October 2003 was chosen as reference period. In Table 1 an overview of the time resolution of the individual instruments is given.
 STARTWAVE is a project within work package 2 on climate forecasting and predictability of the NCCR Climate program funded by the Swiss National Science Foundation (NFS). As the name suggests, STARTWAVE has among its goals the improvement of our understanding of radiative transfer through the atmosphere and in particular its modification by water vapor. The database is available to registered users; new users can apply for access on the STARTWAVE Web page (see URL above).
3.3. Data Consistency
 In Figure 1 the integrated water vapor values for the three instruments TROWARA (crosses), ASMUWARA (asterisks) and GPS (pluses) are shown as an example for September 2003. Figure 1 shows that in general the agreement between these instruments is good.
 The consistency between these instruments is demonstrated in the scatterplots in Figures 2a (TROWARA-GPS), 2b (TROWARA-ASMUWARA), and 2c (GPS-ASMUWARA) and in Table 2. The individual data points were compared if the time difference was less than 1 hour for the measurements of IWV.
Table 2. Comparison of Reference Instrument IWV Values (Time Difference Less Than 1 Hour)
Percent of Mean
Percent of σ
 The GPS and TROWARA data (Figure 2a) correspond well. The linear regression curve (solid line) is almost the same as the diagonal line of the scatterplot (dashed line). The mean difference for these two instruments is less than 0.2% with a standard deviation of 12.9% and the correlation coefficient r2 is better than 0.97.
 The ASMUWARA and TROWARA comparison (Figure 2b) shows that ASMUWARA values are slightly lower than those measured by TROWARA. The mean difference is 4% (σ 11%, r2 > 0.97) for all corresponding values. The difference in these instruments, even though the same channels have been used, could be due to the fact that ASMUWARA is an all-sky instrument scanning the sky at all azimuth angles, whereas the TROWARA instrument measures at a fixed azimuth angle.
 For the ASMUWARA and GPS data (Figure 2c) the situation is similar to the TROWARA-ASMUWARA case. ASMUWARA reports slightly lower values than the GPS measurements. The mean difference is 3.7% (σ = 10.7%, r2 > 0.98) for all corresponding values.
 As summarized in Table 2 the IWV values of the three instruments, TROWARA, GPS, and ASMUWARA, are clearly consistent on a 1σ level with good correlation. The r2 correlation coefficients are higher than 0.97. TROWARA and GPS in particular report almost the same IWV values.
 In a validation study of MIAWARA [Deuber et al., 2005], the opacities measured by ASMUWARA (in the 22.2 GHz channel of ASMUWARA) were compared to the MIAWARA opacities in the same frequency range. For the same time period as this study, the agreement in the opacity between these two instruments was better than 1%.
 This good agreement qualifies the TROWARA/ASMUWARA/GPS data to be used as reference for deriving a relation between the measured MIAWARA opacity around 22.235 GHz and the tropospheric integrated water vapor.
4. Estimating IWV From MIAWARA Opacity Measurements
 The MIAWARA calibration process [Deuber et al., 2004a] includes tipping curves which are performed on an hourly basis. The hourly frequency is selected, despite the recommendation of Cimini et al.  to perform tipping curves as often as possible, since the main goal of MIAWARA is to measure middle atmospheric water vapor profiles. The tipping curve consists of three angles with elevations between 30° and 70° [Deuber et al., 2004a] and takes approximately 2–3 min. The instrumental state is monitored by different sensors (temperature, stable frequency) and the tipping curve results undergo a quality control procedure. From these tipping curve calibrations, the tropospheric opacity τ at 22.235 GHz ± 500 MHz can be calculated. Since the opacity at 22 GHz is mostly influenced by the water vapor content of the troposphere and since MIAWARA only measures under favorable weather conditions (no rain, almost no liquid water in the atmosphere) it should be possible to find a relation between the IWV and the opacity τ using the IWV values measured by the instruments TROWARA, ASMUWARA, and GPS.
 In a first step, the MIAWARA opacities (mean value over the whole bandwidth: 21.735 GHz to 22.735 GHz with a channel bandwidth of 600 Hz) and IWV measured by the other IAP instruments are compared directly. In a second step, the influence of the mean tropospheric temperature Ttrop is investigated.
4.2. Deriving a Linear Relation Between τ and IWV
 At 22 GHz the water vapor is the dominant contributor to the absorption; therefore as initial relation between the opacities measured by MIAWARA and the IWV values reported by the ASMUWARA, TROWARA, and GPS instruments can be derived using the linear regression method. In Figure 3 the IWV values in mm are plotted against the corresponding opacities τ measured by MIAWARA. Similar to the data consistency check, data were compared if the temporal difference was less than 1 hour. As the data intercomparison in section 2 would lead us to expect, the values for TROWARA (crosses) and GPS (pluses) are almost equal and the linear regression curves for these two instruments overlap. ASMUWARA (asterisks) reports, as expected from the consistency check, slightly lower IWV values.
 In general for very high values of the tropospheric opacity (τ > 0.2), the linear relation overestimates the integrated water vapor content. This might be due to the contribution of liquid water (e.g., clouds) to the absorption during these situations which would lead to an overestimation of the integrated water vapor content, since we assumed that liquid water makes a negligible contribution to our opacity values.
 The MIAWARA IWV values (in mm)
derived from the linear regression between the MIAWARA opacities and the data set of GPS, TROWARA, and ASMUWARA IWV values are plotted in Figures 4 (all coincident data) and 5(outliers removed and opacities higher than 0.2 not considered). The coefficients a and b and the correlation coefficients r2 for both cases are given in Table 3. Even with the cutoff criteria at opacities greater than 0.2 a tendency of overestimation of the IWV by MIAWARA for high IWV values is remaining. This is most likely, as stated earlier, that in these cases the liquid water content of the troposphere contributes to the opacity and is not correctly monitored by the MIAWARA frequency range.
Table 3. Linear Regression Coefficients for the Relationship Between MIAWARA Opacity and IWV Measured by GPS, TROWARA, and ASMUWARA
All instruments/all cases
All instruments/outliers removed
 As Table 3 indicates, the linear regression is of acceptable quality with r2 better than 0.9. For the reduced data set, where high opacities and outliers (cases where the MIAWARA tipping curve measurements apparently failed and no water vapor profiles could be calculated from the measured spectra) are not considered, the correlation r2 is almost 0.95.
4.3. Influence of the Mean Tropospheric Temperature Ttrop
 In the tipping curve calibration applied here, the troposphere is treated as one layer with a mean tropospheric temperature Ttrop and an opacity τ. As described by Deuber et al. [2004a], a Taylor series approximation of the radiative transfer equation
is used. The first-order approximation of the Taylor series has the following form:
where Tb,ground is the measured brightness temperature on ground, T0 the incoming radiation on top of the troposphere, and A is the air mass factor. Since in this study the opacities are referenced to zenith direction, the air mass factor A is equal to 1. The first term of the sum in equation (5) is the attenuation of the middle atmospheric signal in the troposphere, whereas the second term is the emission contribution of the troposphere itself. Ttrop (in Kelvin) is derived according to the linear relation given by Han and Westwater  using the ground surface temperature (in degrees Celsius) θground:
At 22 GHz the coefficients c0 and c1 are 0.69 K/°C, and 266.3 K, respectively.
 From equation (5), a very simple approach for the estimation of the integrated water vapor taking the mean tropospheric temperature into account can be derived. We assume that the IWV content of the atmosphere has the same dependence on τ and Ttrop as the brightness temperature measured from the ground and again use the TROWARA/GPS/ASMUWARA data set to derive the coefficients a, b, c using multiple linear regression method:
 The coefficients derived using the TROWARA/GPS/ASMUWARA data set are given in Table 4. The MIAWARA IWV values derived with this approach are plotted in Figure 6 versus the TROWARA/GPS/ASMUWARA IWV values.
Table 4. Linear Regression Coefficients Taking Ttrop Into Account
 As Tables 3 and 4 show, the r2 correlation coefficient is improving by taking Ttrop into account. Furthermore, the standard deviation of the residuals decreased from 1.46 mm/16.73% for the τ-only regression by almost 2% to 1.38 mm/15.07% for the τTtrop regression.
 A literature search for other algorithms used for the estimation of integrated water vapor using the opacity near 22.235 GHz showed no results, where the measured opacity at 22.235 GHz is directly related to the integrated water vapor. Takamura  presented a method to calculate the IWV content from the measured mean brightness temperature between 18 and 26.5 GHz.
 A paper by Smith  shows the relation between the tropospheric water vapor content and the attenuation and therefore the opacity at centimeter and millimeter wavelength. This paper was used by the Water Vapor Millimeter Wave Spectrometer (WVMS) group of the Naval Research Laboratory (NRL, Washington, D. C.) to estimate the integrated water vapor amount using the tropospheric opacity τ at 22 GHz. The NRL operates two water vapor radiometers at 22 GHz [Thacker et al., 1995; Nedoluha et al., 1996, 1998], similar to the MIAWARA instrument. They applied an algorithm derived from Smith [1982, Figure 2] and adapted it for the measurement site on Mauna Loa, Hawaii. The relation is of the following form (G. Nedoluha, personal communication, 2004):
 The coefficient b is altitude-dependent and modeled as
where z is the altitude (in meters) of the measurement site.
 In Figure 7 this relation was applied to our opacity measurements and compared with the τ + τTtrop approach. As Figure 7 shows, the NRL algorithm does underestimate the integrated water vapor by approximately 20%, if it is applied to the data from Bern, Switzerland.
4.4. Application at Other Measurement Sites
 The absorption coefficient α of the 22.235 GHz water vapor transition is only weakly dependent on the atmospheric temperature. This effect is illustrated in Figure 8, where the absorption coefficients for the frequencies of MIAWARA and a typical two-channel radiometer are given. The change of temperature in the range of ±20 K from a typical atmospheric condition at pressure of 900 hPa results in a change of the absorption coefficient of only a few percent at 22.235 GHz, whereas at 31.5 GHz, where the oxygen absorption is also substantially contributing to α, the absorption coefficient is changing significantly.
 As the opacity τ is the integral of the absorption coefficient α over the altitude z, τ is also only marginally dependent on the atmospheric temperature. The method described here therefore has an advantage over the widely used two-channel method as the linear regression coefficients of the two-channel method have a higher dependence on the atmospheric temperature profiles. Therefore the coefficients need to be modified if the instrument is applied in regions with largely different atmospheric conditions such as polar or tropical regions. The study by Takamura  showed that the relation between the brightness temperature in the frequency range of 18 to 26.5 GHz and the IWV is marginally dependent on the measurement location in all regions from subarctic to tropical conditions.
 From the end of January to March 2004, MIAWARA took part in the Lapbiat Upper Tropospheric Lower Stratospheric Water Vapor Validation Project (LAUTLOS/WAVVAP) campaign [Deuber et al., 2004b, 2005] at the Arctic Research Centre of the Finnish Meteorological Institute (FMI) in Sodankylä. Sodankylä is located north of the Arctic Circle in Lapland. The FMI research station provides a balloon launch facility and is part of the global network of radiosonde stations. A VAISALA RS90 radiosonde is launched daily at 0000 and 1200 UTC. The VAISALA RS90 is a new generation radiosonde developed to solve the “dry bias” of the VAISALA RS 80 sensors [Westwater et al., 2003; Revercomb et al., 2003].
 MIAWARA measured next to the balloon launch site during the LAUTLOS/WAVVAP campaign; therefore we can apply our τ + τTtrop relation to the tipping curve measurements at Sodankylä and compare it with the integrated water vapor amount from the radiosonde measurements.
 In Figure 9 the comparison between the MIAWARA IWV values using the τ + τTtrop relation and the integrated radiosonde humidity measurements is shown. The troposphere in the subarctic winter was very dry and the IWV values are all less than 10 mm.
also provides an acceptable estimate of the IWV from the opacity measured in the subarctic case. The mean difference between MIAWARA and the radiosonde is less than 3% with a large standard deviation of 22.5%. The r2 correlation coefficient is 0.75. The large standard deviation can be explained by the small values of IWV. As Figure 6 shows, the variation is more or less independent from the absolute IWV value. Therefore the relative standard deviation is high if the data set consists only of small IWV values. For the situation at Bern, illustrated in Figure 6, the standard deviation would also increase to 22% if only the IWV values below 10 mm were considered.
Table 5. Mean Difference in MIAWARA IWV and IWV Integrated From Radiosondes at Sodankylä
Mean Difference, mm
Percent Mean Difference
Percent of σ
5. Simulation Using ARTS and Payerne Sondes
 To validate the relation derived in equation (10), a simulation study was carried out using the MeteoSwiss Payerne radiosonde data. At Payerne, MeteoSwiss launches a meteorological radiosonde in the troposphere twice a day (at 0000 and 1200 UTC). The measured temperature, pressure, and humidity profiles were used to (1) calculate the integrated water vapor amount over Payerne and (2) calculate the opacity in the MIAWARA frequency range using ARTS.
5.1. Integrating the Radiosonde Humidity Measurements
 The integrated water vapor in kg/m2 (which is equivalent to column water vapor in mm) can be calculated as the integral of the water vapor density ρ over the altitude z from the ground, z0, to the top of the troposphere, ztop, (for all equations in this section SI units must be used):
 The density ρ can be calculated from the measured relative humidity RH, temperature T, and pressure p under the assumption of the ideal gas law as
where pN and TN are the standard pressure and temperature respectively (pN = 101325 Pa, TN = 273.15 K). Here ew is the saturation pressure of water vapor, nV is the molecular volume of water vapor at standard pressure and temperature, and Mn is the molecular mass of H2O (nv = 44.61478 mol/m3, Mm = 0.018 kg/mol).
 Under the assumption that condensation occurs at relative humidities above 90%, RH values greater than 90% were not considered in the water vapor integration. The Payerne radiosonde does not normally reach the tropopause, but since the water vapor content in the upper troposphere is several orders of magnitude smaller than that at ground level this region contributes only marginally to the integrated value and may be neglected. Payerne is located at approximately 470 m above sea level (asl). Since MIAWARA is located at 550 m asl, the lower integration limit z0 was set to this altitude and ztop was set to the maximum altitude of the radiosonde flight. All radio soundings between January and August 2004 were chosen for this simulation.
5.2. Modeling the Opacity With ARTS
 The Atmospheric Radiative Transfer Simulator (ARTS) [Buehler et al., 2005] is a general tool for radiative transfer simulations in the 0–1000 GHz frequency range.
 The tropospheric opacity τ is the integral of the absorption coefficients α over the altitude z,
The absorption coefficient α is a function of frequency, temperature, pressure, and the atmospheric composition. At 22 GHz the water vapor absorption contributes dominantly to α. In this study we used the ARTS forward model and the continuum absorption models of Rosenkranz  and the MPM-87 [Liebe and Layton, 1987] and MPM-93 [Liebe et al., 1993] model by Liebe to calculate the tropospheric opacity using the Payerne radiosonde measurements as input for the water vapor, pressure, and temperature profile.
 The tropospheric opacity was calculated using the MIAWARA frequency band from the radiosonde profiles and the ARTS forward model. The relation (equation (7)), derived in section 4.3, was then used to calculate the IWV from the simulated opacity.
5.3. Comparison of Radiosondes With ARTS
 In Figure 10 the results of the ARTS simulation and the integration of the radiosonde profiles from January 2004 to August 2004 are shown. The three different absorption models show slightly different results.
 The Rosenkranz model, using the algorithm derived in section 4.3 (equation (7)), underestimates the integrated water vapor amount of the radiosonde profile for IWV values smaller than 10 mm. For IWV values larger than 10 mm the agreement between the ARTS IWV and the radiosonde IWV is good. The MPM-87 as well as the MPM-93 (slightly larger) model in contrast overestimate the integrated water vapor amount for larger IWV values and have better agreement for smaller values. In Table 6 the characteristics of this comparison (mean difference, σ, r2) are listed. The standard deviation is at least twice as big as the mean difference and the correlation coefficient r2 is better than 0.98. If we take into account that the standard deviation of the data consistency checks in section 3.3 was also in the range of 10–15% for instruments measuring at the same location, the results of the simulation seem to be of sufficient quality to confirm our simple model approach.
Table 6. Difference Radiosonde IWV and ARTS IWV
Mean Difference, mm
Percent Mean Difference
Percent of σ
 The IAP instruments TROWARA, ASMUWARA, and GPS make independent measurements of the integrated water vapor content IWV at Bern with good agreement. From these measurements one can derive a linear relation between the measured opacity τ of MIAWARA and the IWV content. The agreement can be slightly improved if the mean tropospheric temperature Ttrop, used in the one layer troposphere model of the MIAWARA tipping curve calibration, is taken into account.
 The measurements of the LAUTLOS/WAVVAP campaign, where MIAWARA was operated in northern Finland, show that the derived relation at Bern is also valid in subarctic winter conditions. This is expected, as the 22.235 GHz absorption has only a weak dependence on the atmospheric conditions.
 The estimation of IWV using the MIAWARA tipping curve is limited to days where the liquid water content of the troposphere is negligible. For high-opacity situations (τ > 0.2) the derived relation overestimates the water vapor content of the troposphere. A simulation using the ARTS forward model and Payerne radiosonde data confirmed the derived relation within the expected uncertainty. In general the integrated water vapor content can be estimated with an accuracy of approximately 1.4 mm (1σ) in the range of 0–30 mm of IWV.
 The authors would like to thank MeteoSwiss at Payerne and the Arctic Research Centre of the Finnish Meteorological Institute at Sodankylä for providing the radiosonde measurements. This work was supported by the Swiss National Science Foundation under grant NCCR Climate.