In the following, the instruments used in the present study, their measurement principle, and their retrieval methods are introduced. Table  gives an overview of the accuracy, spatial and temporal resolution, and limitations in terms of weather conditions of the individual instruments.

In the following, the spatial matching of all data sets is addressed first, and the temporal matching is addressed in the final section. All JOYCE instruments are located within a distance of 110 m to each other. The GPS receiver and sun photometer are situated on the same roof of a building at a height of 111 m above mean sea level, while the MWR and BASIL are located on the ground. The height difference to the instruments on the roof is 21 m and therefore the MWR IWV needs to be corrected. For this, the 120 m meteorological tower nearby is used to adjust the IWV of the MWR to the level of GPS and sun photometer from the water vapour density measured in heights of 2, 10, and 20 m above ground. The amount of water vapour subtracted from the MWR measurements is 0.3 kg m-2 at its maximum. BASIL data are not height corrected since only the profiles and not IWV are used.

The location of the radiosonde launches is at exactly the same height as JOYCE at a distance of 3.9 km to the south-east. The second MWR used in Sect.  is 3.3 km south of JOYCE (cf. Fig. ). For MODIS, the horizontal and height distance to JOYCE varies with flight track. The topography of the MODIS measurements is taken from the Consultative Group on International Agricultural Research-Consortium for Spatial Information Shuttle Radar Topography Mission (CGIAR-CSI SRTM) 90 m database (http://srtm.csi.cgiar.org). The topography of the nine nearest CGIAR-CSI SRTM pixels is averaged to retrieve the height of the MODIS pixel. The nearest MODIS pixel within a distance of less than 7 km and a height difference of less than 100 m is used. To correct for the height difference the water vapour density of the meteorological tower is again used, resulting in a maximum correction of 1.5 kgm-2.

The grid point of COSMO-DE used in the present study is with a distance of 1.9 km the second nearest grid point to JOYCE (cf. Fig. ). This grid point is selected because it is only 1 m lower than the JOYCE site, whereas the nearest grid point in a distance of 1.8 km has a height difference of 10 m. Due to the small height difference, no height correction is applied to the IWV from COSMO-DE.

For ICON, no height correction is applied. The height difference between the ICON grid point used for Fig.  is only 4 m, so the bias introduced by this height difference is very small.

Apart from the spatial differences, the temporal differences need to be considered. If not stated otherwise, the resolution of compared IWV values is 15 min. GPS measurements are originally available in this resolution. The output of COSMO-DE is also available with a resolution of 15 min. MWR and sun photometer measurements are averaged over 15 min. IWV from the other measurements is available only with a coarser temporal resolution. MODIS measurements are matched to the corresponding 15 min period. The ascent of a radiosonde takes approximately 1 h. Since the largest amount of water vapour is in the lower atmosphere, the radiosoundings are matched to the 15 min interval during which they are started. This results in a maximum time difference of less than 15 min between two individual measurements of different instruments.

Several features can be identified in the comparison of the time series of the different IWV data sets (cf. middle panel in Fig. ). They are described in this section.

Only GPS and MWR provide continuous observations over the full day. Though they overlap within their uncertainty estimates, GPS measurements tend to lie below the MWR measurements. The GPS measurements exhibit two distinct features: firstly, they show a jump at the beginning of most full hours, which can be up to nearly 1 kgm-2. These jumps are caused by the near-real-time processing routine of the GPS retrieval at GFZ . Secondly, an even larger difference (ca. 5 kgm-2) is seen at the end of the day from 23:45 to 24:00 UTC.

These two issues occur in nearly all cases investigated so far and are not limited to the case selected for the present study. First attempts in reprocessing the data resulted in a smoothing of the hourly jumps and a reduction of the differences at the beginning of the day. However, the bias of the reprocessed data is increased. Therefore, the reprocessing is under further investigation.

During daytime, when IWV is available from the sun photometer, its IWV agrees very well with the MWR. However, the agreement is reduced during the early and late hours of daytime when the sun is at low elevation (cf. Sect. ).

The MODIS-NIR estimates available for the two overpasses are perfectly within the uncertainty range of MWR and sun photometer, while MODIS-IR measurements also available during night-time are up to 4 kgm-2 too dry. The larger pixels of MODIS-IR (3 km) could partly be covered by clouds which are not detected. The smaller pixels of MODIS-NIR (1 km) are less likely to be partly cloudy, which could lead to a more precise cloud detection.

The seven radiosondes which were launched during this day give IWV within the uncertainty range of the MWR, sun photometer, and/or GPS. The daytime soundings show that roughly 50 % (maximum 64 %) of the IWV is contained in the convective ML. Since the radiosonde provides point measurements along its trajectory, deviations from true-zenith measurements can occur due to sampling issues. For this case study, the horizontal drift within the ML is relatively short with approximately 4 km for the sonde launched closest to the MODIS overpass at 11:00 UTC (cf. Fig. ). However, on this day, which does not feature a larger synoptic IWV gradient in the vicinity of JOYCE, it can be expected that differences to true-zenith estimates arise when the radiosonde is moving within dry/moist eddies in the convective ML.

The IWV simulations by the dynamic models COSMO-DE and ICON agree well with the observations until the 06:00 UTC when the increase in IWV can not be reproduced as strongly as in the observations. This might be due to problems in the forcing at the model boundaries – in particular for the ICON model, which is forced by COSMO-DE. Nevertheless, it is encouraging to see that the novel high-resolution ICON depicts a similar temporal IWV variability during the development of the convective ML as MWR and BASIL. This gives us the confidence that the model is suitable to further investigate the spatial and the temporal variability of IWV.

While all measurements have sampling issues, the use of a dynamic atmospheric model allows sampling of IWV nearly continuously in both time and space. Here we selected 40 ICON grid points (cf. Fig. ) in an area of approximately 10 km around JOYCE for which IWV output was stored at high temporal resolution (2.25 min). The height above mean sea level of the sampled grid points (dx = 156 m) does not vary by more than 150 m.

From the time series at the 40 grid points, the IWV correlations and standard deviations for distances smaller than 10 km and shorter than 1 h can be assessed (cf. Fig. ). The correlation decreases distinctly with both temporal and spatial mismatch. For a fixed time a distance of 10 km reduces the correlation to 0.9. A similar decrease in correlation occurs when the location is fixed but a time mismatch of 30 min occurs. A mismatch of 10 km and 1 h leads to a correlation of 0.8.

A similar behaviour as for the correlation is evident in the standard deviation. Observations with a distance of 8–10 km can induce the same error as a time shift of 30–45 min (0.6 kgm-2) that is around the specified uncertainty of the different observations (cf. Table ). The combination of temporal and spatial mismatch, which is the case for radiosondes, can lead to even higher errors amounting to more than 0.8 kgm-2 for 10 km and 1 h difference.

In order to investigate whether the model behaviour is consistent with the observations, we use time series of 2.25 min IWV averages from two zenith-pointing MWRs located 3.3 km apart from each other. Both correlation and standard deviation decrease similarly as depicted by ICON (cf. Fig. ). Interestingly, there are slight differences in the absolute values. Nevertheless, the comparison indicates that ICON simulations can be used to assess the small-scale variability of water vapour and help to determine to which degree instrument intercomparisons may be affected by atmospheric effects. However, it is important to note that this is a case study and the results might be rather different for different synoptic situations or geographic regions.

Since none of the instruments can be considered as “the truth”, every instrument is compared to all other instruments (cf. Fig. ). All measurements are considered at 15 min resolution (see Sect. ). For the following comparison, it has to be acknowledged that the maximum distance between instruments is approximately 4 km.

For the MODIS–radiosondes comparison, too few coincident measurements are available due to the infrequent satellite overflights. Excluding MODIS, the overall agreement between the instrument pairs is good. The standard deviation is not higher than 1 kgm-2 and the correlation coefficient is never lower than 0.98. The absolute bias varies from 0 for GPS–sun photometer to 1 kgm-2 for radiosondes–MWR. In the following, the individual instrument comparisons are examined in more detail.

With more than 3800 measurements, the GPS–MWR comparison includes the most cases because both instruments also measure during cloudy conditions. The bias (0.2 kgm-2) is very low and the standard deviation (0.9 kgm-2) is within the expected measurement uncertainty (cf. Table ). However, there are some IWV values up to 5 kgm-2 lower than observed by the MWR (cf. Fig. ). These differences occur due to problems in the processing of the GPS data at the beginning of the day, as mentioned above. Excluding the first hour of the day leads to a reduction of the bias to 0.1 kgm-2 and of the standard deviation to 0.8 kgm-2. This problem is further investigated in Sect. . Furthermore, a small dependency of the error on the IWV is found. For large IWV values the difference between GPS and MWR tends to be smaller than for small IWV values. Other dependencies, such as the influence of wind direction, spatial IWV gradient, temporal IWV variability, liquid water path, and distribution of GPS slants, which are used to retrieve the IWV, are tested but no significant dependency is found (not shown).

Even if the sun photometer only measures during clear-sky, daytime situations there are nearly 900 coincident measurements with GPS and MWR. To both the sun photometer shows nearly no bias (GPS < 0.01 kg m-2, MWR: -0.35 kg m-2) and standard deviations of 0.8 kg m-2. The AERONET cloud screening and quality assurancce conducted for level 2.0 sun photometer data reduces the data set by a factor of 2, while the bias hardly changes (< 0.1 kg-2) and standard deviation is reduced by 0.1–0.2 kg m-2 (not shown).

On average, the radiosondes are 0.8 kgm-2 (1.0 kgm-2) drier than GPS (MWR). However, only a small difference of 0.2 kgm-2 between day- and night-time soundings could be identified, probably due to the correction within the Graw software (cf. Sect. ).

The comparisons of MODIS–GPS and MODIS–MWR show that IWV measurements from both MODIS-IR and MODIS-NIR are frequently too low. However, these MODIS measurements are not included in the MODIS–sun photometer comparisons, since there are no sun photometer measurements at these times. The reason for this is probably that cloudy cases are not reliably detected by the MODIS cloud-identifying algorithm. Clouds lead to a lower IWV because the amount of IWV below and inside the cloud is not detected by MODIS. A clear difference can be seen in the standard deviation in the comparisons involving MODIS-NIR and MODIS-IR; the latter has more than double the standard deviation of the first, which could be due to the coarser resolution or due to poorer physical constraints in the algorithm.

Since each instrument intercomparison is carried out during different atmospheric conditions (a consequence of the varying instrument limitations), the mean IWV of the measurements included in each comparison differs by approximately 3 kgm-2. To allow for a better comparison of the errors of different instrument combinations, 57 simultaneous measurements of all instruments with the exception of MODIS are also investigated separately. The mean of these comparison then only differs by 0.4 kgm-2 (cf. Fig. ) and the standard deviation is reduced for all instrument combinations to be lower than 1 kgm-2. This results likely from sampling more homogeneous conditions. By including only measurements when the sun photometer is measuring, night-time measurements and most importantly all rainy cases and cases with clouds in the direction of the sun are excluded.

In summary, the agreement of the IWV measurements on the 15 min basis is very good with standard deviations of around 1 kgm-2 with the exception of MODIS. However, it has to be kept in mind that the representative error of IWV at 4 km spatial distance is only 0.4 kgm-2. The representativeness analysis for 5 May 2013 estimated the effect of atmospheric variation to be approximately 0.4 kgm-2 (cf. Sect. ). As expected, a reduction of the compared data sets by only including coincident measurements simultaneously excluding all night-time, rainy, and cloudy cases, leads to an improvement in the overall agreement. However, the mean values over the HOPE period range from around 16 kgm-2 (GPS, MWR) to lower than 14 kgm-2 (sun photometer, MODIS). This difference, which is distinctly higher than the bias of most of the instrument comparisons, implies significant errors when climatologies are constructed from data sets with a poor sampling.

Having assured the good general agreement between the different instruments during HOPE, the temporal variability of IWV is investigated in more detail in the following. For this, the autocorrelation of the continuous data sets, namely MWR, GPS, and COSMO-DE, is computed (cf. Fig. ). All three data sets with a temporal resolution of 15 min show a similar behaviour: their autocorrelation function decreases monotonically with increasing lag time and they have a similar e folding time of roughly 13 h. This result is not surprising considering the large IWV changes associated with the synoptic variability (cf. Fig. ), but it gives important limitations on the influence of temporal matching in IWV comparisons and on generations of climate data records. Interestingly, the e folding time decreases to 12 h when MWR measurements with higher resolution, that is 5 s, are used, indicating the importance of small-scale processes.

For a closer look at the variations due to small-scale processes, the IWV standard deviation during HOPE is computed over varying time intervals from 5 min to 3 h (cf. top panel in Fig. ). Note that only coincident measurements and simulations are used and only the MWR can provide estimates below 1 h. Generally, the mean standard deviation increases from 0.1 kgm-2 at 5 min to 0.4 kgm-2 at 1.5 h, showing some saturation with 0.6 kgm-2 at 3 h intervals.

For time intervals of 1.5 h and longer, MWR, GPS, and COSMO-DE again show a similar behaviour, as seen in the autocorrelation. In fact, they lie within their 25 and 75 % percentiles. However, extreme values reach standard deviation of 2.0 kgm-2 and higher at time intervals > 1 h. Interestingly, none of these points are evident during the day of the case study (cf. Sect. ) because the highest standard deviations stem from cloudy situations (see discussion below).

The GPS measurements show an offset for the 1 h interval. This is caused by the processing method. As seen in the middle panel of Fig. , GPS measurements within 1 h are relatively smooth. However, the mean standard deviation of the 15 min MWR averages is overall only slightly smaller than the mean standard deviation of the 5 s averages. This indicates, firstly, that for time scales of a few hours, the coarser resolution of 15 min is sufficient enough for resolving the mean IWV variability. Secondly, for these time intervals GPS is well suited as a reference instrument for model evaluation since it captures the same variability as the MWR. Thirdly, operational NWP model COSMO-DE is capable of reproducing the observed mean variability of IWV.

For time intervals shorter than 1 h, only the 5 s MWR data can partially resolve the small-scale, turbulence-induced variability of IWV. The minimum detected average standard deviation at 5 min averaging time of 0.1 kgm-2 is twice as high as the MWR noise level and thus represents a lower boundary for the evaluation MWR measurement. As for the variability on intervals greater than 1 h, the standard deviation increases with increasing time interval; however, the slope is steeper on the shorter time scales. At the shortest time scales, the variability is dominated by a cascade of turbulence elements in the inertial subrange, whereas at increasing time scales the variability is probably dominated by the variability of subsequent updraught and downdraught regions. Noteworthy are also standard deviation values larger than 1 kgm-2 even at the shortest time scales, which are predominantly caused by clouds.

Focusing on clear-sky, daytime cases allows to include the sun photometer (cf. bottom panel in Fig. ). When only coincident data from MWR, GPS, sun photometer, and COSMO-DE are used, the mean standard deviations are lower by approximately 0.25 kg m-2 compared to the full time series (cf. bottom panel in Fig. ). This is caused by the exclusion of cloudy cases that lead to the disappearance of high standard deviations, that means hardly any standard deviations higher than 1 kg m-2 occur once (partially) cloudy scenes are filtered out. The IWV standard deviation observed during the case study seems to be representative of the whole HOPE campaign on time scales shorter than 1 h.

In summary, the change of the mean standard deviation with different time intervals, over which it is computed, shows that the variability of IWV is high even for time periods shorter than 1 h, which is mostly due to clouds, and that this variability cannot be resolved by more coarsely resolved data. High-resolution time series from MWR are therefore well suited to high-resolution atmospheric models, like ICON, aiming to derive better subgrid parametrizations for climate models. However, for more synoptic scale comparisons, a resolution of 15 min is sufficient to resolve the mean standard deviation and therewith variability of IWV.

The previous sections show the importance of the IWV variability associated with atmospheric turbulence and convection. In this section we focus on the mean diurnal cycle of IWV over the HOPE campaign as this is strongly influenced by combined effects of land-surface processes and boundary layer dynamics. It represents an aggregated quantity that tests to which degree different instruments and/or models can provide a consistent answer. Only those measurements that are available on a near-continuous basis, that is MWR, GPS, and sun photometer, and COSMO-DE output are included in this comparison with 1 h means. Note that it is ensured (by manual checking) that this daily cycle is not due to a few singular synoptic-induced events but is rather a true mean behaviour of IWV.

Figure  reveals a clear mean daily IWV cycle over the HOPE period with lowest values in the morning and maximum in the afternoon/evening hours. The daily IWV range varies from 1 to 2 kgm-2 depending on the data set. This is significantly higher than the daily IWV range reported by for a 5-year data set from Bern, Switzerland (0.6 kgm-2), and can be attributed to the comparably high surface fluxes during springtime.

As mentioned before, the mean IWV is instrument-dependent because of sampling issues, which leads to differences in the absolute values in the mean diurnal cycle and also to differences in the amplitude of the mean diurnal IWV cycle. The amplitude is smallest for the COSMO-DE forecasts (1.3 kgm-2) that are here represented by the ensemble of differently aged forecasts (cf. Sect. ). Interestingly, the spread between the different ensemble members is highest around the time of maximum IWV (∼17:00 UTC). Since there is interaction between humidity, time, and strength of convection, and resulting precipitation this might be associated with difficulties of the forecast model with convective precipitation.

The GPS is the only instrument that provides data under all weather conditions and can directly be compared to the COSMO-DE output. With 2.2 kgm-2 GPS shows a stronger diurnal cycle than COSMO-DE, with the maximum IWV occurring also 4 h later around 21:00 UTC. The later maximum of IWV in the GPS might be due to the use of surface temperatures in the GPS retrievals as these are not representative of the atmospheric temperature as found by . They apply a dampened mean atmospheric temperature to compensate for this surface effect, which leads to a better agreement of the diurnal cycle with coincident MWR measurements.

The high IWV range of GPS measurements might partly be caused by a dry offset of approximately 1 kgm-2 in the beginning of the day compared to the end of day. This is a known characteristic of the near-real-time processing of GPS data, which is also seen in the investigation of the daily cycle at stations in North America by . The exact reason for this feature is not finally clarified yet and subject of ongoing investigation.

The MWR IWV exhibits a similar shape of the diurnal cycle as GPS and COSMO-DE though the time of the maximum IWV is earliest in the MWR around 15:00 UTC and its IWV range (1.9 kgm-2) is between COSMO-DE and GPS. However, it needs to be considered that the outdoor MWR HATPRO cannot measure during rain and therefore a fair comparison can only be guaranteed if GPS data are filtered accordingly. While such a filtering gives a similar bias as the analysis shown in Fig. , the mean diurnal variation of the GPS (2.8 kg m-2) is clearly 1 kg m-2 larger than that of the MWR.

Due to its measurement principle, the sun photometer (cf. Sect. ) is limited to clear-sky conditions from 5 to 17:00 UTC, resulting in the lowest IWV values of all data sets. Nevertheless, an increase in IWV during daytime with an even stronger slope than for the other data sets can be seen. These measurements show the same trend of smaller IWV values in the morning than in the afternoon. The diurnal cycle of coincident GPS measurements shows a good agreement with the sun photometer measurements. For the difference between the sun photometer and MWR, a dependency on the position of the sun is found (not shown). In the morning and afternoon, IWV from the sun photometer is smaller than from the MWR because the sun photometer measures under lower-elevation angles. At noon it is the other way around. This could be due to an inaccurate relative air mass (Eq. ) used by the retrieval or the transmission approaching 0 at low elevation angles.

In summary, the accurate description of the mean diurnal cycle is strongly limited by instrumental and sampling effects requiring an accurate matching when different data sets are compared. Longer time series are desirable. Nevertheless, the results indicate that the operational COSMO-DE model underestimates the amplitude of the diurnal cycle.