Spatial interpolation of GPS integrated water vapour measurements made in the Swiss Alps

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1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 14: (7) Published online in Wiley InterScience ( Spatial interpolation of GPS integrated water vapour measurements made in the Swiss Alps June Morland* and Christian Mätzler Institute of Applied Physics, University of Bern, Sidlerstrasse 5, 12 Bern, Switzerland ABSTRACT: The 31 stations in the Swiss GPS network are located at altitudes between 3 and 3584 m and have provided hourly Integrated Water Vapour (IWV) measurements since November. A correction based on an exponential relationship is proposed for the decrease in IWV with altitude. The scale height depends on the ratio of IWV measured at Jungfraujoch (3584 m) to that measured at Payerne (498 m). An additional coefficient, dependent on the east-west and north-south spatial differences in the IWV, improves the fit to the data. The IWV at heights between 75 and 35 m was estimated from GPS measurements at Payerne and compared with the Payerne radiosounding. The altitude correction introduced an additional bias of.2 to.4 mm between GPS and radiosonde. The IWV was normalized to 5 m and the increases and decreases due to the passage of a series of frontal systems between 11 and 14 January 4 were mapped. A four-year climatology of IWV normalized to 5 m showed that the Alpine stations are more moist in spring, summer and autumn than the stations in the Swiss plains to the north of the Alps. This was attributed to more moist Mediterranean air being blocked by the Alps. Copyright 7 Royal Meteorological Society KEY WORDS GPS; integrated water vapour; interpolation; Alpine; mountains Received 17 January 6; Revised 1 December 6; Accepted 1 December 6 1. Introduction Water vapour is a natural greenhouse gas. Because the amount of water vapour in the atmosphere generally increases with increasing temperature, it could cause important feedback effects in a changing climate. In addition to displaying a seasonal cycle, which peaks in summer, water vapour is highly variable on timescales of a day or less, depending on the meteorological situation. Until the advent of remote sensing techniques, information on total atmospheric water vapour was available only from in situ relative humidity observations made by radiosondes. The infrared channels on weather satellites, such as the METEOSAT Second Generation (MSG) geostationary satellite, allow the upper atmospheric humidity to be determined. Water vapour information can be obtained over the ocean using microwave radiometers (MR) on polar orbiting satellites, such as the Special Sensor Microwave Imager (SSM/I), which gives column water vapour amounts, or the Atmospheric Microwave Sounding Unit (AMSU), which yields profiles. Over land, however, it is extremely difficult to obtain water vapour information for the lower atmospheric layers because land surface emissivity is high and extremely variable, although attempts are being made to include land surface effects in order to obtain humidity profiles (Karbou * Correspondence to: June Morland, Institute of Applied Physics, University of Bern, Sidlerstrasse 5, 12 Bern, Switzerland. June.Morland@mw.iap.unibe.ch et al., 5). At present, satellite measurements of column water vapour are possible from infrared spectrometers such as GOME (Global Ozone Monitoring Experiment), which has a revisit time of three days. Because of the lack of satellite observations at sufficiently high temporal resolution, it would be extremely valuable to be able to map atmospheric water vapour over land using existing ground-based sensors. Networks of fixed Global Positioning System (GPS) receivers can be used to provide regular estimates of integrated water vapour (IWV). A network of 31 fixed receivers is operated by the Federal Swiss Office of Topography and it delivers hourly estimates of IWV. An interesting feature of this network is that the receivers are located in the Alps and the Swiss plains at altitudes between 3 and 3584 m (Figure 1). These altitudes correspond to annually averaged station surface pressures of 98 to 655 hpa. Measurements of atmospheric water vapour at different altitudes are valuable from the point of view of climate monitoring. However, IWV decreases rapidly with altitude and it is necessary to first correct for station height differences in order to map the horizontal distribution of water vapour. The possibility of mapping IWV measured by a GPS network has already been explored by Basili et al. (4), who combined GPS and SSM/I data to produce IWV maps for the Mediterranean area. They considered data from GPS stations lying between 19 and 633 m altitude and used kriging with external drift to compensate for the dependence of the IWV measurement on altitude. Copyright 7 Royal Meteorological Society

2 16 J. MORLAND AND C. MÄTZLER Latitude 48 N 47 N Saint Croix 15 Geneva 4 46 N GPS stations in the AGNES network Schaffhausen 592 Kreuzlingen Muttenz Pfan St Gallen Frick Zurich Bourrignon 547 Uznach 892 Huttwil 429 Bern Ardez Neuchatel Luzern 7 Sargans Zimmerwald 1218 Falera Payerne 97 Andermatt Jungfraujoch 1296 Davos Lausanne 3584 Samedan1598 Saanen San Bernardino Hohtenn 935 Martigny Locarno Stabio E 7 E 8 E 9 E E Longitude Figure 1. The GPS stations in the Automated GPS Network of Switzerland (AGNES). Altitude in metres is given below the station name. A different approach is taken in this paper, which is that of explicitly modelling the altitude dependence and correcting for it before spatially interpolating the data. The IWV will be expressed in units of mm, which is equivalent to precipitable water content in kg m Description of GPS network Figure 1 shows the locations and altitudes of the 31 stations in the Automated GPS NEtwork of Switzerland (AGNES). Microwave signals from a constellation of orbiting satellites are received by the GPS receivers. These signals get delayed as they pass through the atmosphere. The total delay is known as the Zenith Total Delay (ZTD) and is expressed as an apparent extra distance rather than as a time delay. A part of the delay, known as the Zenith Hydrostatic Delay (ZHD), is due to dry gases such as oxygen and nitrogen. The remaining part of the delay, known as the Zenith Wet Delay (ZWD), is due to water vapour. The ZWD can be calculated from the difference between the ZTD and the ZHD, as shown in Equation (1). ZWD = ZTD ZHD (1) The AGNES network provides hourly estimates of ZTD. IWV was calculated from these data using the method described in Bevis et al. (1992) and Emardson et al. (1998). This involves calculating ZHD from the surface pressure measurements in order to obtain ZWD. ZWD is converted to IWV using a relationship based on surface temperature. Pressure and temperature were obtained from the closest stations in the Swiss meteorological network (ANETZ). Where there was a height difference between the meteorological station and the GPS station, the ANETZ station pressure was interpolated to the GPS station height using the hydrostatic relationship. GPS data from the AGNES network were compared with coincident Precision Filter Radiometer (PFR) data or with the closest radiosonde data, and it was found that they agreed to within ±1 mm(morlandet al., 6b). A bias in the GPS receiver at Jungfraujoch (3584 m) was corrected using a relationship based on coincident PFR measurements (Morland et al., 6a). At Jungfraujoch, where measurements as low as.2 mm have been recorded by the PFR, negative GPS values occur about 8% of the time owing to the fact that the measurement error (around.7 mm) is larger than the value being measured. In order to provide a complete IWV data set for the Jungfraujoch station, temperature, relative humidity and radiation measurements recorded at Jungfraujoch were used to estimate IWV when the GPS receiver delivered a negative value. This process is described in the Appendix: Estimation of Jungfraujoch IWV data. 3. Description of data homogenization The dependence of IWV on station altitude is demonstrated in Figure 2, where the mean January and July IWV for the 2 4 period is plotted against station altitude. Figure 2 shows that IWV has a strong seasonal dependence. Owing to increased atmospheric temperatures in summer, the July IWV is considerably larger than the January IWV at all altitudes. A large decrease in IWV with increasing altitude is also seen, which is more marked in July than in January. In order to view the spatial changes in IWV, it is necessary to correct for the altitude effect. In this case, the IWV measurements were normalized to a height of 5 m, or.5 km. As already noted in Basili et al.

3 GPS IWV INTERPOLATION 17 IWV, mm Monthly mean IWV at Swiss GPS stations plotted against altitude January July Altitude, m Figure 2. The monthly mean IWV values for all Swiss GPS stations plotted against station altitude for the months of January and July. The monthly mean is calculated from data obtained between 1 and 4. (4), the dependence of IWV on altitude takes an exponential form. The following relationship was used to estimate the IWV at.5 km, IWV (.5), from the IWV at a given height h, IWV(h ), where height is in km and IWV is in mm (equivalent to kg m 2 ): [ ] (h.5) IWV (.5) = a IWV (h ) exp H (2) The GPS IWV data for 4 were averaged over 6-h time intervals and the relationship between IWV at Payerne (.498 km) and IWV at all other altitudes was modelled according to Equation (2). For each 6-h data set, values of a and H were obtained. These are plotted against time in Figure 3, along with the statistics of the fit to Equation (2), namely, the square of the correlation coefficient (r 2 value) and the standard deviation of the residuals in mm. Table I gives the yearly mean, standard deviation, minimum and maximum values of the a and H coefficients calculated from the 4 GPS observations. The corresponding yearly mean values for r 2 and the standard deviation of the residuals are also given. As expected, the average value of a is very close to 1. The mean annual value of the standard deviation of the residuals is 1.5 mm. The mean annual value of r 2 is.85, and it is less than.5 just 2% of the time. The occasions when r 2 is low are associated with large, temporary differences in IWV (.5) over the geographical area. For instance, the period from 25 June to 3 July 4 is notable in Figure 3 because the r 2 value is less than.5 on seven occasions (of a possible 36 6-h time intervals). On 28 June, between 15 and UTC, for instance, the mean IWV (.5) value for Bourrignon (891 m) in the north-west was 12.1 mm, whereas the value for Martigny (593 m) in the south-west was 39.4 mm. On 1 July, a similar situation existed between 9 and 14 UTC. The mean IWV (.5) values during this period were 24. and 34.8 mm at Bourrignon and Martigny, respectively. Even higher mean IWV (.5) values of over 45 mm were calculated for the two southernmost stations, Locarno (388 m) and Stabio (366 m). In such situations, two separate altitude relationships for the north and south of the Alps, or for the east and west side of the GPS network, would be more appropriate. However, one relationship is Results of fitting IWV-altitude relation to the 4 GPS observations std res r 2 H a Jan4 5 Jan4 1.5 Jan4 5 Jan4 Apr4 Jul4 Oct4 Jan5 Apr4 Jul4 Oct4 Jan5 Apr4 Jul4 Oct4 Jan5 Apr4 Jul4 Oct4 Jan5 Figure 3. Results of fitting the exponential IWV altitude relationship defined in Equation (2) to the 4 GPS observations. The fit was made for measurements from the 31 GPS stations averaged over six-hourly intervals. H is scale height in km, r 2 is square of the correlation coefficient and std res is standard deviation of the residuals in mm.

4 18 J. MORLAND AND C. MÄTZLER Table I. The yearly statistics for the a and H altitude coefficients calculated from both GPS and radiosonde data acquired during 4. The corresponding statistics for the r 2 value (square of the correlation coefficient) and the standard deviation of residuals calculated from the six-hourly fits to the GPS data are also shown. Coefficient Mean Standard deviation Minimum Maximum a from GPS H from GPS, km r Standard deviation of residuals, mm a from radiosonde H from radiosonde, km sufficient for most situations, as evidenced by the high mean value for r 2. The ratio of the IWV at Jungfraujoch (3584 m), IWV JUJO, to that at Payerne, IWV PAYE, was found to be related to the scale height, H, in kilometres through the following relationship where the square of the correlation coefficient (r 2 ) was.83: ( ) IWV JUJO H = (3) IWV PAYE The possibility of modelling H based on the difference between measurements at Payerne and those at Andermatt (2318 m), the next highest station in the network, was investigated. The relationship was slightly weaker in this case, with an r 2 value of.64. Therefore, Jungfraujoch was chosen as the reference station for estimating H. The coefficient a was related to both, the north south IWV gradient between Payerne (46.81 N, 6.94 E, 498 m) and Stabio (45.86 N, 8.94 E, 366 m) and the east west IWV gradient between Payerne and St Gallen (47.44 N, 9.34 E, 77 m). An r 2 value of.72 was obtained when a was modelled as follows (where IWV PAYE, IWV STGA and IWV STABIO are the IWV values measured at Payerne, St Gallen and Stabio, respectively): a = IWV STABIO IWV PAYE.37 IWV STGA IWV PAYE (4) The relationship between the scale height, H, andthe Jungfraujoch to Payerne IWV ratio was confirmed by applying Equation (2) to the radiosonde data obtained at Payerne in 4. The scale height, H, calculated from the radiosonde data, was dependent on the ratio of the IWV above 3584 m, IWV (3.584), to that above the radiosonde launch height of 492 m, IWV (.492). ( ) IWV (3.584) H = (5) IWV (.492) The higher r 2 value of.93 found between IWV and H for the radiosonde data reflects the fact that the radiosounding is much more local than the GPS observations, which are spread throughout Switzerland. As might be expected, the a coefficient calculated from the radiosonde data appears to vary randomly and to be unrelated to other variables. The statistics for the a and H values calculated from the 4 radiosonde data are given in Table I. The mean value of a calculated from the radiosonde is very close to 1 and the mean value of H is some m lower than that calculated from the GPS data, which may reflect differences between the vertical distribution of water vapour at Payerne, in the plain, and over the whole Swiss GPS network, which includes the Alps. The higher value of H for the GPS network implies that the atmosphere at higher levels over the Alps is more moist than at the same levels over the plains. 4. Evaluation of altitude correction The altitude correction was cross-validated by taking groups of GPS stations located at different altitudes and using Equations (2) to (4) to estimate IWV at 5 m, IWV (.5), from the measurements made in the 2 4 period. For this test, four groups of stations lying relatively close to one another were chosen, with three stations in each group. The names and heights of the stations in each group are given in Table II. It was assumed that the stations in each group were in the same climatological regime, and that large differences in IWV (.5) would reflect errors in the altitude correction. For each group, the difference in IWV (.5) was calculated between the higher stations and the station closest to 5 m. The reference station was always the lowest in the group. The results, expressed as a percentage of the monthly mean IWV (.5) at the lowest station, are plotted in Figure 4 for each group, and the mean percentage difference for the 2 4 period is given in Table II. It can be seen, for instance, that the average differences between the three stations in the south-east of Switzerland (Falera, San Bernardino and Locarno) are of the order of 1% or less over the three-year period, although the differences between San Bernardino and Locarno are larger than % for the months of February 3 and January 4. In Group 1 and Group 3, the mountain stations have higher IWV (.5) values than the lower stations. This is not the case in Group 4, where the estimate for Jungfraujoch (3584 m) is on average 12% lower than that for Luzern (494 m). Some of the differences between the stations are undoubtedly due to climatological factors and others are due to errors in the altitude correction, and it is difficult to separate the two.

5 GPS IWV INTERPOLATION 19 Table II. Names and height in metres of the stations in the four groups used for station intercomparison. The last two columns give the mean differences (in mm and % of the mean monthly IWV) over the 2 4 period between IWV (.5) at the higher stations and that estimated for the station closest to 5 m. The standard deviation is given in brackets. Group Station name and abbreviation Station height (m) Mean difference (std) in estimated IWV (.5), (mm) Mean percent difference (std) in estimated IWV (.5) 1 Kreuzlingen (KREUZ) St Gallen (STGA) (.4) 8. (2.5) Pfan (PFAN) (1.2) 9.9 (7.8) 2 Locarno (LOCO) Falera (FALE) (.8) 1.1 (5.5) San Bernardino (SANB) (1.).1 (8.4) 3 Bern (BERN) Zimmerwald (ZIMM) 97.7 (.4) 4.4 (2.1) St Croix (STCX) 15.6 (.4) 4.5 (3.5) 4 Luzern (LUZE) Huttwil (HUTT) 7.2 (.3) 1.3 (1.7) Jungfraujoch (JUJO) (1.3) 12.4 (4.6) Group 1 Group 2 IWV difference, % KREUZ 483 m STGA 77 m PFAN 45 m Jan2 Jan3 Jan4 Jan5 IWV difference, % LOCO 388 m FALE 1296 m SANB 1653 m Jan2 Jan3 Jan4 Jan5 IWV difference, % Group 3 BERN 577 m ZIMM 97 m STCX 15 m IWV difference, % Group 4 LUZE 494 m HUTT 7 m JUJO 3584 m Jan2 Jan3 Jan4 Jan5 Jan2 Jan3 Jan4 Jan5 Figure 4. The percentage differences between IWV (.5) estimated at the two higher stations in each group listed in Table II and that estimated from the measurements made at the lowest station. Statistics are calculated on a monthly mean basis. As an independent check on the altitude correction, the GPS IWV data obtained at Payerne (498 m) between 2 and 4 were compared with measurements made by the Payerne radiosonde. Using the method described in the previous section, the IWV was calculated at a range of altitudes between 75 and 35 m. The coefficients H and a were estimated according to Equations (3) and (4), and Equation (2) was rearranged as shown in Equation (6), where IWV (.498) is the IWV measured by the GPS at Payerne, h is the height in kilometres for which IWV is being estimated and IWV(h) is the estimated IWV at height h. [ ].498 h IWV (h) = a IWV (.498) exp H (6) The total IWV above Payerne was calculated from the radiosonde data as well as the IWV at altitudes between 75 and 35 m. The radiosonde data set (measured IWV values) was then compared with the GPS data set (IWV measured at 498 m and estimated at higher altitudes). The monthly mean bias in the GPS data relative to the

6 J. MORLAND AND C. MÄTZLER radiosonde data was calculated for each month and for each altitude level. The biases for four levels (498,, and m) are shown in Figure 5. Figure 5 shows that the GPS is generally positively biased relative to the radiosonde, with the exception of the period January April 3. The Swiss RadioSonde (SRS4) is a carbon hygristor that has a decreasing response to relative humidity at low temperatures. It also tends to slightly underestimate water vapour near saturation. The overall effect on the IWV is a slight negative bias. However, when a dry troposphere occurs above low stratus in winter, the bias is positive (Jeannet, 4). The positive bias in the GPS relative to the radiosonde at the surface level is probably mainly due to the tendency for the radiosonde to underestimate IWV. For the 3-year period, an average bias of.86 mm was observed between the GPS IWV measured at 498 m and the radiosonde IWV. Table III summarizes the mean GPS bias relative to the radiosonde for the four seasons. Winter months are taken as December, January and February, spring GPS IWV Sonde IWV. mm Bias in GPS IWV relative to sonde IWV.5 Jan2 Jan3 Jan4 498 m m m m Jan5 Figure 5. The monthly mean bias in the GPS IWV measured at Payerne (498 m) with respect to the Payerne radiosounding launched at 492 m. The GPS IWV is estimated at higher altitudes using Equation (3), (4) and (6). months as March, April and May, summer months as June, July and August and autumn months as September, October and November. The GPS bias at 498 m increases from.3 mm in winter to 1.8 mm in summer. The bias expressed as a percentage of the monthly mean IWV also increases from 3% in winter to 8% in summer. Guerova et al. (5) observed that the bias in both GPS and microwave radiometer data relative to the Payerne radiosonde is negative at night and positive during the day. This was attributed to the effect of solar heating on radiosonde measurements. Since solar radiation is stronger in summer than in winter, it is no surprise that a stronger positive bias is seen in the GPS data during the summer months. The GPS estimates of the IWV at higher altitudes also show a positive bias relative to the radiosonde IWV, which follows the same pattern as the surface bias. The difference between the GPS bias at a given altitude and the bias at the surface is given in the last column of Table III. The GPS bias at higher altitudes is.2 to.4 mm higher than that at the surface. In general, the altitude correction slightly increases the IWV bias at higher levels. This is to be expected, given the difference in scale heights reported in Section 3. The water vapour scale height estimated from the GPS network (including the Alps) is generally higher than that estimated from the radiosonde. This influences the altitude correction and adds an additional wet bias to the GPS IWV estimates at higher levels in comparison to the radiosonde measurements. 5. Case study A series of frontal systems that passed over Switzerland between 11 and 14 January 4 were studied. Figure 6 shows the time series of measurements made by MR at Bern (575 m) and Payerne (498 m) as well as the GPS receivers at Bern (575 m), Saanen (1369 m), Andermatt (2318 m) and Jungfraujoch (3584 m). The microwave radiometer measurements agree fairly well with the GPS observations made at Payerne. In this figure, no altitude Table III. The mean IWV bias in the Payerne GPS measurements relative to the radiosonde is given for winter (December, January, February), spring (March, April, May), summer (June, July, August) and autumn (September, October, November). The mean difference between the GPS bias at a given height and the GPS bias at the surface (498 m) is given in the last column. The standard deviation of the bias is given in brackets. Height (m) Mean winter bias (std), mm Mean spring bias (std), mm Mean summer bias (std), mm Mean autumn bias (std), mm Mean Bias (height) -Bias (498) (std), mm (.4).4 (.5) 1.8 (.4).9 (.7) / 75.4 (.4).7 (.5) 2.3 (.5) 1. (.7).2 (.3).5 (.4).6 (.5) 2.1 (.6) 1.1 (.7).2 (.3) 15.7 (.4).7 (.5) 2. (.6) 1.2 (.6).3 (.3).8 (.4).8 (.5) 2. (.5) 1.3 (.5).3 (.4) 25.9 (.4).8 (.5) 2.1 (.5) 1.3 (.5).4 (.4).9 (.3).8 (.5) 2. (.4) 1.3 (.4).4 (.4) 35.9 (.3).8 (.4) 2. (.4) 1.3 (.4).4 (.4)

7 GPS IWV INTERPOLATION 21 IWV, mm IWV observed by GPS and microwave radiometer between 11/1/4 and 15/1/4 MR PAYE 491 m MR BERN 575 m GPS BERN 575 m 25 GPS SAAN 1369 m GPS ANDE 2318 m GPS JUJO 3584 m /1 12/1 13/1 14/1 15/1 Figure 6. IWV observed by GPS and two microwave radiometers (MR) between 11 and 15 January 4. correction has been made to the GPS data and they show a strong decrease in IWV with increasing altitude. Despite the differences in the magnitude of the IWV measurements at the different stations, all instruments show an increase in IWV around midday on 11 and 12 January, followed by a large increase on 13 January. The IWV values were normalized to 5 m at all the stations using Equations (2) to (4). The IWV (.5) values were interpolated onto a grid and then mapped in Mercator projection using the Matlab griddata and surfm functions. The results are plotted at four-hourly intervals in Figure 7. The mapped values agree very well with the time series shown in Figure 6. At UTC on 11, 12 and 13 January, the mean value of IWV (.5) was 11.9, 13.5 and 11. mm, respectively. Increased values occurred across Switzerland at UTC and 16 UTC on 11 January when the mean IWV (.5) was 17. and 18.2 mm, respectively. Between UTC on 11 January and UTC on 12 January, the mean 11 Jan UT. 11 Jan 4 UT. 11 Jan 8 UT. 11 Jan 12 UT. 11 Jan 16 UT. 11 Jan UT. 12 Jan UT. 12 Jan 4 UT. 12 Jan 8 UT. 12 Jan 12 UT. 12 Jan 16 UT. 12 Jan UT. 13 Jan UT. 13 Jan 4 UT. 13 Jan 8 UT. 13 Jan 12 UT. 13 Jan 16 UT. 13 Jan UT. 14 Jan UT. 14 Jan 4 UT. Figure 7. IWV (.5) is estimated from the GPS measurements made at all the 31 Swiss stations and spatially interpolated across the study area. The maps are shown at four-hourly intervals between UTC on 11 January 4 and 4 UTC on 14 January 4. This figure is available in colour online at

8 22 J. MORLAND AND C. MÄTZLER cumulative precipitation recorded by the 66 stations in the MeteoSwiss ANETZ meteorological network was 8.1 mm, with a maximum of 32.2 mm recorded at La Dole (167 m) in north-west Switzerland. Another increase occurred at 16 UTC on 12 January when the mean value of IWV (.5) was 17. mm. The mean cumulative precipitation recorded by the ANETZ meteorological stations between UTC on 12 January and UTC on 13 January was 19.6 mm, with a maximum of 76.7 mm recorded at Grand St Bernard (2472 m) in south-west Switzerland. The strongest increase occurred on 13 January when the mean value of IWV (.5) was 21.4, 22.9 and.3 mm at 8, and 16 UTC, respectively. At UTC on 13 January, an IWV value of over 26 mm was measured by the GPS station at Payerne (498 m), and Muttenz (3 m) in the north of Switzerland recorded a value of over 28 mm. These represent the highest IWV values measured by the AGNES GPS network during the 3 4 winter. Between UTC on 13 January and 7 UTC on 14 January, the mean cumulative precipitation measured by the ANETZ network was 36.5 mm. Only Stabio and Lugano on the south side of the Alps recorded no precipitation. The highest cumulative precipitation of 123 mm was observed at La Dole. The meteorological station at Payerne recorded 36.6 mm rain. The IWV (.5) values were considerably lower by 4 UTC on 14 January, when the average was 13.7 mm. However, values of over 28 mm were calculated for three stations in the south-east (St Bernardino, Samedan and Ardez). 6. Climatology The altitude correction (Equations (2) to (4)) was applied to data collected at all the stations between 1 and 4. The statistics for the IWV (.5) values calculated for the winter, spring, summer and autumn seasons are given in Table IV. The mean value at each station, for each season, is plotted in Figure 8. Table IV shows that the variability in the seasonal mean is highest in summer, when the IWV (.5) is higher, and lowest in winter, when the IWV (.5) is lowest. The range of seasonal mean IWV values increases from 2.6 mm in winter to 6.8 mm in summer, and this should be borne in mind when looking at the plots in Figure 8. Figure 8 shows that the Alps and the area south of the Alps have higher IWV (.5) values in spring, summer and autumn than the stations to the north. This is probably due to moist air from the Mediterranean being blocked by the Alps. In winter, Uznach, Kreuzlingen and Sargans in the northeast of Switzerland have the lowest seasonal mean IWV (.5), along with Jungfraujoch in the Alps, and Stabio, the southernmost station. Jungfraujoch (3584 m) and Uznach (429 m) stand out as having lower seasonal mean IWV (.5) values than the surrounding stations. In winter, the seasonal mean at Jungfraujoch is 8.9 mm, which is similar to that measured Table IV. Statistics for the seasonal mean IWV (.5) values calculated for the 31 Swiss GPS stations over the 1 4 period. The seasons are winter (December, January, February), spring (March, April, May), summer (June, July, August) and autumn (September, October, November). Season Mean IWV, mm Min IWV, mm Max IWV, mm Standard deviation, mm Winter Spring Summer Autumn Winter Spring Summer Autumn Figure 8. Seasonally averaged values of IWV (.5) for the Swiss GPS stations for the 1 4 period. This figure is available in colour online at

9 GPS IWV INTERPOLATION 23 at the surrounding stations: 9.1 mm at Huttwil (7 m), 9.2 mm at Locarno (388 m) and 8.7 mm at Stabio (366 m). However, in all other seasons, the IWV (.5) at Jungfraujoch is 2 to 5 mm lower than that measured at Huttwil and Locarno. It is unlikely that this is caused by measurement errors because the GPS data have been checked against both PFR and lidar data (Morland et al., 6a). It is possible that the altitude correction gives poorer results at the high altitude station, although this seems unlikely considering the good results that were obtained when comparing the GPS and radiosonde data at Payerne (Section 4). To resolve the question of whether the performance of the altitude correction is poorer in summer than in winter, the statistics of the fit of Equation (2) to the IWV observations were examined. The seasonal monthly mean of the r 2 value shown in Figure 3 is.89 in summer and.79 in winter. The mean root mean square error in the residuals is 1.13 mm in winter and 1.88 mm in summer. However, the mean IWV is 7.5 mm in winter and 21.3 mm in summer, giving a smaller relative error in summer (9%) than in winter (15%). The model fits the data better in summer, when IWV (.5) is significantly drier at Jungfraujoch, than in the winter, when IWV (.5) at Jungfraujoch is similar to that at the surrounding stations. As an additional check, the IWV (.5) data were recalculated using an expression for the scale height, which had the same form as Equation (3) but was dependent on the Andermatt to Luzern IWV ratio. As an additional check, the IWV (.5) data were recalculated using an expression for the scale height which had the same form as equation 3, but which was dependent on the Andermatt to Luzern IWV ratio. This altitude correction was independent of the Jungfraujoch data and the seasonal mean climatology was recalculated based on these results. The seasonally averaged IWV(.5) values showed similar values and the same spatial patterns as those plotted in Figure 8. We therfore concluded that the drier values of IWV (.5) observed at Jungfraujoch are independent of the way in which the altitude correction is carried out. The IWV (.5) for Uznach is.7 to 1.8 mm lower in all seasons than that calculated for the two stations to the north, Kreuzlingen (484 m) and Schaffhausen (592 m). Measurement biases are suspected in this case because this station was also an outlier in a comparison between the GPS and ECHAM4 climate model climatologies (Martin Wild, personal communication). 7. Conclusions The 31 stations in the Swiss AGNES GPS network are located at altitudes ranging between 3 and 3584 m. The stations have a mean annual pressure ranging between 98 and 655 hpa, which is interesting from the point of view of monitoring water vapour in different atmospheric layers. However, it would also be very valuable if the stations can be used to map the spatial distribution of water vapour. In order to do this, an altitude correction was developed for the Swiss GPS stations. This takes the form of an exponential relationship, where the scale height is dependent on the ratio of the IWV measured at the highest station, Jungfraujoch (3584 m), and that measured at Payerne (498 m), which is the station closest to our reference height of 5 m. A similar relationship between IWV and scale height was observed using the Payerne radiosounding data. For the GPS data, the fit between the model and the observations was improved by introducing a coefficient that was dependent on the spatial differences between Payerne and Stabio (366 m) in the south of Switzerland and Payerne and St Gallen (77 m) in the east of Switzerland. The altitude correction was validated by applying it to the GPS data from Payerne to estimate IWV at higher levels and by comparing the results with the Payerne radiosoundings. The altitude correction introduces an additional wet bias of.2 to.4 mm in the GPS data, which was not unexpected considering that the average water vapour scale height estimated from the whole GPS network, including the Alps, is about m higher than that estimated from the Payerne radiosounding. IWV at all stations was normalized to an altitude of 5 m, IWV (.5), for the period January 4 when a series of frontal systems passed over Switzerland. This example showed that it is possible to map the response of water vapour to the changing meteorological situation. The seasonal mean climatology of IWV (.5) for the four-year measurement period showed that stations in the Alps tended to be more moist than those in the plains to the north in spring, summer and autumn. Jungfraujoch (3584 m) was drier than the surrounding stations in spring, summer and autumn when IWV values were higher, but had similar values in winter. IWV (.5) was recalculated using an alternative expression for the scale height, which used data from Andermatt rather than Jungfraujoch, and similar results were obtained. The fact that Jungfraujoch has similar IWV (.5) to the surrounding stations in winter, when there is little or no convection, but not in summer, when convection is strong, possibly provides a clue regarding how water vapour is mixed into the higher layers of the atmosphere, and this should be investigated in more detail. The data from Uznach (429 m) were significantly drier than the data from surrounding stations in all four seasons, and these data should be checked, if possible, against another instrument, in order to check for the existence of a bias. Using a relatively small, but challenging, study area, it was shown that it is possible to correct for the effect of altitude on IWV measurements in order to map the spatial distribution of water vapour. Future work will involve applying the method to a larger study area and using GPS, radiosonde and meteorological measurements from Switzerland and surrounding countries to investigate whether separate relationships are required for different regions. The effect of changing weather conditions on the relationship between IWV and altitude will also be examined.

10 24 J. MORLAND AND C. MÄTZLER Appendix Estimation of Jungfraujoch IWV data The GPS IWV data have an error of around.7 mm. This means that at Jungfraujoch, where measurements as low as.2 mm have been recorded by the PFR, negative GPS values occur about 8% of the time (Morland et al., 6a). The PFR operates only during sunny conditions, and hourly PFR measurements were available 9% of the time over the four-year period between and 4. Therefore, when GPS data were negative, the PFR could not always provide an alternative data source. Ruckstuhl et al. (6) observed that IWV is dependent on specific humidity and longwave downward radiation (LDR), and that the relationship is somewhat different in cloudy and clear sky conditions. The possibility Relationship between radiation and IWV at Jungfraujoch (3584 m) GPS Clear GPS Cloudy Best fit clear Best fit cloudy GPS IWV, mm Radiation, Wm Figure A1. IWV measured by the GPS in mm plotted against longwelling downwave radiation for both clear ( to 2 oktas) and cloudy (7 to 8 oktas) conditions Relationship between water vapour density and IWV at Jungfraujoch (3584 m) GPS Clear GPS Cloudy Best fit clear Best fit cloudy GPS IWV, mm Water vapour density, gm Figure A2. IWV measured by the GPS in mm plotted against water vapour density for both clear ( to 2 oktas) and cloudy (7 to 8 oktas) conditions.

11 GPS IWV INTERPOLATION Relationship between temperature and IWV at Jungfraujoch (3584 m) GPS Clear GPS Cloudy Best fit clear Best fit cloudy IWV, mm Temperature, C 5 15 Figure A3. IWV measured by the GPS in mm plotted against temperature in degrees Centigrade for both clear ( to 2 oktas) and cloudy (7 to 8 oktas) conditions. Table A1. The coefficients and statistics of the best-fit relationship between IWV, ρ, LWR and T, as described in Equation (4). Std(res) refers to the standard deviation of the residuals. Sky conditions c b 1 b 2 b 3 b 4 r 2 Std (res) Clear E Partly overcast E Cloudy E of estimating IWV from meteorological observations for the period when the GPS does not provide valid measurements was investigated. The IWV data used to develop the relationship came from either the GPS receiver or the PFR. LDR data from the Alpine Surface Radiation Budget (ASRB) network as well as temperature and humidity data from the Jungfraujoch ANETZ station were also used. Information on the cloudiness came from the Automatic Partial Cloud Amount Detection Algorithm (APCADA)developed by Dürr and Philipona (4). The APCADA is an estimate of the cloud cover in oktas on the basis of LDR, temperature and humidity. Figures (A1), (A2) and (A3) show the relationships between GPS IWV and LDR, water vapour density and temperature measured at Jungfraujoch. The data are plotted separately for clear and cloudy sky conditions. A linear relationship was modelled between IWV and water vapour density (calculated from temperature and relative humidity measurements). The IWV is modelled as being dependent on the square of the LDR and the exponential of the temperature. The best-fit relationship between IWV and LDR, temperature and water vapour density, was calculated for both clear (APCADA 2 oktas), partly overcast (APCADA 3 6 oktas) and cloudy (APCADA 7 8 oktas) conditions. For clear conditions, IWV from the PFR was taken to be the dependent variable since the GPS cannot adequately resolve small IWV values and 11% of the clear sky GPS measurements are negative. When the analysis was repeated for clear conditions using the GPS IWV data, coefficients very similar to those calculated using the PFR were obtained. The PFR only measures data in direct sunlight and so the GPS IWV data were used to develop the relationships for partly overcast and cloudy conditions. In partly overcast and cloudy conditions, the GPS recorded negative values only 2 3% of the time. Equation (A1) gives the relationship between IWV and LDR, water vapour density and temperature. IWV est is the IWV estimated from ρ, the water vapour density in gm 3, LDR, the downward longwave radiation in Wm 3 and T is the temperature in C. IWV est = c b 1 b 2 LDR b 3 LDR 2 b 4 exp(.873 T) (A1) The constants c and b i as well as the square of the correlation coefficient and the standard deviation of the

12 26 J. MORLAND AND C. MÄTZLER residuals are given in Table AI for the three different cloud cases considered. The statistics are significantly better for clear conditions when the PFR was used to provide IWV information. This is because the measurement uncertainty in the GPS (.7 mm) is relatively high compared to the low IWV values (.2 14 mm) observed at Jungfraujoch, whereas the measurement uncertainty in the PFR is much lower (5 to %). In order to produce a complete IWV data set for Jungfraujoch, the rules summarized in Equations (A2) to (A4) were applied to estimate IWV in mm, where denotes or, IWV est is the IWV estimated from LDR, temperature and water vapour density, and IWV PFR and IWV GPS are the PFR and GPS IWV measurements. IWV GPS <.2mm IWV =IWV PFR IWV est (A2).2mm IWV GPS < 1mm IWV =.5 (IWV GPS IWV PFR ).5 (IWV GPS IWV est ) (A3) IWV GPS > 1mm IWV = IWV GPS (A4) Acknowledgements This study was funded by the Swiss National Centre for Competence in Research Climate project (NCCR-Climate). The authors are grateful to the Federal Swiss Office of Topography for providing the GPS ZTD data set and to Elmar Brockmann for advice and information on the GPS observations. MeteoSwiss provided the meteorological data from which the GPS IWV was calculated. We are grateful to Christian Rückstuhl (ETH Zürich) and Rolf Philipona (Physikalisch-Meteorologisches Observatorium Davos) for providing ASRB and APCADA data. References Basili P, Bonafoni S, Mattioli V, Ciotti P, Pierdicca N. 4. Mapping the atmospheric water vapor by integrating microwave radiometer and GPS measurements. IEEE Transactions on Geoscience and Remote Sensing 42(8): , Doi:.19/TGRS Bevis M, Businger S, Herring TA, Rocken C, Anthes RA, Ware RH GPS Meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. Journal of Geophysical Research 97(D14): , Doi:.29/92JD1517. Dürr B, Philipona R. 4. Automatic cloud amount detection by surface longwave downward radiation measurements. Journal of Geophysical Research 9: D51, Doi:.29/3JD4182. Emardson TR, Elgered G, Johansson J Three months of continuous monitoring of atmospheric water vapor with a network of Global Positioning System receivers. Journal of Geophysical Research 3(D2): , Doi:.29/97JD15. Guerova G, Brockmann E, Schubiger F, Morland J, Mätzler C. 5. An integrated assessment of measured and modeled IWV in Switzerland for the period 1 3. Journal of Applied Meteorology 44(7): 33 44, Doi:.1175/JAM2255. Jeannet P. 4. TUC Experiment: Soundings data set V1., MeteoSwiss Report (Available from MeteoSwiss, Aerological Station, Les Invuardes, Payerne 15, Switzerland). Karbou F, Aires F, Prigent C, Eymard L. 5. Potential of Advanced Microwave Sounding Unit-A (AMSU-A) and AMSU- B measurements for atmospheric temperature and humidity profiling over land. Journal of Geophysical Research 1: D79, Doi:.29/4JD5318. Morland J, Liniger M, Kunz H, Balin I, Nyeki S, Mätzler C, Kämpfer N. 6a. Comparison of GPS and ERA4 IWV in the Alpine region, including correction of GPS observations at Jungfraujoch (3584 m). Journal of Geophysical Research 111: D42, Doi:.29/5JD643. Morland J, Deuber B, Feist DG, Martin L, Nyeki S, Kämpfer N, Mätzler C, Jeannet P, Vuilleumier L. 6b. The STARTWAVE atmospheric water vapour database. Atmospheric Chemistry and Physics 6: 39 56, &SRef-ID: /acp/6-6-39, Ruckstuhl C, Philipona R, Morland J, Ohmura A. 6. Observed relationships between surface specific humidity, integrated water vapor and longwave downward radiation at different altitudes. Paper accepted by Journal of Geophysical Research-Atmospheres. Doi: 6JD785.