Assessment of small-scale integrated water Assessment of small-scale integrated water vapour variability during HOPE

The spatio-temporal variability of integrated water vapour (IWV) on small-scales of less than 10 km and hours is assessed with data from the two months of the High Deﬁnition Clouds and Precipitation for advancing Climate Prediction (HD(CP) 2 ) Observational Prototype Experiment (HOPE). The statistical intercomparison of the unique set of ob- 5 servations during HOPE (microwave radiometer (MWR), Global Positioning System (GPS), sunphotometer, radiosondes, Raman Lidar, infrared and near infrared Moderate Resolution Imaging Spectroradiometer (MODIS) on the satellites Aqua and Terra) measuring close together reveals a good agreement in terms of standard deviation ( ≤ 1 kg m − 2 ) and correlation coe ﬃ cient ( ≥ 0.98). The exception is MODIS, which ap- 10 pears to su ﬀ er from insu ﬃ cient cloud ﬁltering. For a case study during HOPE featuring a typical boundary layer development, the IWV variability in time and space on scales of less than 10 km and less than 1 h is investigated in detail. For this purpose, the measurements are complemented by simulations with the novel ICOsahedral Non-hydrostatic modelling framework (ICON) which 15 for this study has a horizontal resolution of 156 m. These runs show that di ﬀ erences in space of 3–4 km or time of 10–15 min induce IWV variabilities in the order of 4 kg m − 2 . This model ﬁnding is conﬁrmed by observed time series from two MWRs approximately 3 km apart with

servations during HOPE (microwave radiometer (MWR), Global Positioning System (GPS), sunphotometer, radiosondes, Raman Lidar, infrared and near infrared Moderate Resolution Imaging Spectroradiometer (MODIS) on the satellites Aqua and Terra) measuring close together reveals a good agreement in terms of standard deviation (≤ 1 kg m −2 ) and correlation coefficient (≥ 0.98). The exception is MODIS, which ap- 10 pears to suffer from insufficient cloud filtering. For a case study during HOPE featuring a typical boundary layer development, the IWV variability in time and space on scales of less than 10 km and less than 1 h is investigated in detail. For this purpose, the measurements are complemented by simulations with the novel ICOsahedral Non-hydrostatic modelling framework (ICON) which

Introduction
Water vapour is not only the most effective greenhouse gas (Kiehl and Trenberth, 1997) but also an important part of the hydrological cycle, so that the exact knowledge on atmospheric moisture is absolutely essential for both numerical weather prediction (NWP; e. g., Weckwerth et al., 1999) and climate modelling (e. g. Bony et al., 2006). 5 However, the interaction between atmospheric humidity and convection is still poorly understood (Sherwood et al., 2010).
The amount of atmospheric water vapour is influenced by processes on various scales, which results in a high variability in both space and time. A prominent example is the convective atmospheric boundary layer where evaporation from the heterogeneous land surface and turbulate mixing create strong water vapour variability (Shao et al., 2013, cf. Fig. 10). Knowledge on water vapour variability is valuable for improving subgrid-scale model parametrizations, for model evaluation, and for instrument intercomparisons. Kahn et al. (2011) compare the IWV variability in NWP and climate models with those directly observed by Atmospheric InfraRed Sounder (AIRS) obserthe same altitude range needs to be considered and therefore corrections are necessary (cf. Böhme et al., 2011;Buehler et al., 2012). Many studies compare various IWV measurements in different geographical regions and for different time periods using different criteria for temporal and spatial matching and elevation corrections (cf. Bennouna et al., 2013;Martin et al., 2006;Morland et al., 2009;Palm et al., 2010;Schneider et al., 20 2010; Torres et al., 2010). Frequently, these comparisons involve data sets with more than 1 h temporal and more than 20 km spatial difference as well as with different horizontal resolutions. Buehler et al. (2012) investigate the representativeness error resulting from insufficient collocation and resolution mismatch for a high latitude region using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Satoh et al., 2008) with 25 3.5 km horizontal resolution. GPS data are used as reference and the representativeness error is calculated for ground-based slant column and satellite measurements as well as for the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis ERA-Interim. They derive values of approximately 0.6-1.4 kg m −2 for spatial scales of several 10 km. It has to be noted that GPS does not provide true column measurements as one observation over a 15 min interval includes the atmospheric delay measured along several links between the GPS ground station and multiple satellites. The goal of the present study is three-fold: firstly, we aim to characterize the variability of IWV for spatial scales smaller than 10 km and temporal scales smaller than 5 1 h and to estimate the ability of different measurements to represent this variability. In doing so, we extend previous studies to even smaller scales, by using zenith-pointing MWR measurements which are available at a temporal resolution of approximately 2 s. To this end, a case study at the continental mid-latitude site JOYCE is presented and the unique set of instruments from HOPE is complemented by very high-resolution 10 (156 m) simulations from the novel atmospheric model ICON. Secondly, with the goal of providing a realistic error estimate for the individual instruments observing IWV, we perform a statistical, multi-instrument comparison covering the HOPE period. This includes the investigation of the variability of IWV on a wide range of temporal scales from a few minutes, over a couple of hours to its mean diurnal cycle. Thirdly, the ability 15 of the novel ICON model to capture the daily IWV cycle of a realistic case is assessed.
The study is structured as follows: an overview of all instruments and the respective retrievals used in this study is given in Sect. 2.1. A first version of the ICON model is introduced together with the operational regional NWP model of Deutscher Wetterdienst (DWD) at 2.8 km horizontal resolution in Sect. 2.2. Details on how to match the vari-20 ous data sets are given in Sect. 2.3. Observations and model runs are analysed within a case study for a day with typical boundary layer development in order to estimate scale dependent IWV variability (Sect. 3). The analysis is extended over the full duration of HOPE, providing statistics on the agreement between the different instruments, the relative merits of the different instruments to capture the temporal IWV variability, Introduction

Observations
In the following, the instruments used in the present study, their measurement principle, and their retrieval methods are introduced. Table 1 gives an overview of the accuracy, spatial and temporal resolution, and limitations in terms of weather conditions of the 5 individual instruments.

Microwave radiometer
Two microwave radiometers (MWR), one located at JOYCE and one 3.3 km south of JOYCE (cf. Fig. 1) are used in the present study. Both MWR are Humidity and Temperature PROfilers (HATPRO; Rose et al., 2005). Here only zenith pointing HATPRO 10 measurements with a temporal resolution of up to 2 s are used. The antenna has a half power beam width of 3.5 • for the water vapour sensitive channels. Thus, the MWR measures a comparatively narrow part of the atmosphere. From this volume, it receives brightness temperatures at seven frequencies along the water vapour absorption line (22.24,23.04,23.84,25.44,26.24,27.84 GHz) and one frequency in an atmospheric 15 window (31.40 GHz). With a low noise level of approximately 0.05 K in the measured brightness temperatures HATPRO is able to detect small variations in atmospheric water vapour but also cloud water whose emission increases with frequency in the microwave spectral range. The absolute accuracy of the observed brightness temperatures determined by the calibration procedure (Maschwitz et al., 2013) is 0.5 K.

20
IWV is derived following a statistical approach based on a least squares linear regression model (Löhnert and Crewell, 2003) from the multi-frequency brightness temperatures assuming the error characteristics mentioned above. To derive the coefficient vectors, a training data sets of more than 13 000 non-precipitating radiosoundings at De Bilt, Netherlands, is used. With this algorithm, IWV can be derived with a random Introduction is assumed to be 0.5 kg m −2 and the noise level is 0.05 kg m −2 . Note that the MWR is able to measure automatically under all weather conditions with the exception of when the radome is wet. In these cases, no IWV values are provided.

GPS ground station
Although the main aim of GPS, is precise positioning for navigation, remarkable 5 progress in using GPS for retrieval of IWV has been achieved during the last decades (Bevis et al., 1992;Rocken et al., 1997;Fang et al., 1998). The basic quantity estimated by any GPS receiver is the signal travel time from the GPS satellite to the receiver. From the travel times of up to 12 GPS satellites with an elevation angle larger than 7 • and the satellite positions, the receiver position is esti-10 mated. The GPS signal consists of electromagnetic waves propagating through the atmosphere with frequencies of 1575.42 and 1227.60 MHz. The travel time also provides information on the atmosphere along the signal path. The signal is slightly delayed by the atmosphere and this delay, as compared to an undisturbed signal propagation in vacuum, depends on the atmospheric state. There are two major contributions to the 15 signal delay: the ionosphere and the neutral atmosphere. The ionospheric delay can be estimated by comparing two GPS signals at different frequencies (dispersion). The remaining part of the delay is due to the neutral, moist atmosphere. The neutral atmosphere is non-dispersive and GPS cannot provide any information to separate the impact of water vapour from the impact of the dry atmosphere. There-20 fore additional meteorological observations are required. Usually, the pressure and temperature at the GPS receiver are observed. The signal delay due to the dry gases, that is all atmospheric gases without water vapour, can be estimated reliably using the pressure observation and certain empirical models. The remaining wet delay can be converted to the slant integrated water vapour by using the temperature observation. Introduction The GeoForschungsZentrum Potsdam (GFZ) processes the data of approximately 300 German GPS stations operationally in near-real time and provides IWV estimates with a temporal resolution of 15 min and an accuracy of 1-2 kg m −2 (Dick et al., 2001;Gendt et al., 2004).

5
The sunphotometer (CE 318 N-EBS9, Cimel Eletronique) measures the extinction of direct solar irradiance and sky radiance at 9 wavelengths (340,380,440,500,675,870,937,1020, and 1640 nm) fully automatically. Allowing for the extinction due to aerosols, the extinction due to the amount of water vapour in the line of sight to the sun T w can be derived from the extinction at 937 nm. The extinction can be described with 10 the following equation where a, and b are constants, and m is the relative optical air mass (Schmid et al., 2001). From this relationship, IWV can be derived with an accuracy of 10 % (Alexandrov 15 et al., 2009) The sunphotometer at JOYCE is part of AERONET, meaning that data processing is performed by the National Aeronautics and Space Administration (NASA) (Dubovik et al., 2006). The data used within the present study is of quality level 1.5 (cloudscreened) and has a temporal resolution of 10 min.

20
Since the sunphotometer measures the direct sunlight, its IWV retrieval is limited to daytime and clear-sky conditions. Additionally, since the instrument tracks the sun, the retrieved IWV is not zenith viewing, but along a slant path through the atmosphere. This implies that it samples a different atmospheric volume than the zenith-pointing instruments. Introduction launched 3.9 km to the south-east (cf. Fig. 1). The comparison between the lidar power ratio and the radiosonde mixing ratio profiles for the purposes of the calibration is typically carried out in the vertical region 2.5-3.5 km. Considering this altitude region above the boundary layer minimize the air mass differences related to the distance between the lidar and the radiosonde station and allows to minimize effects associated with the 15 lidar overlap function. Due to missing overlap near the instrument, the lowest usable signal from BASIL is from a height of 150-180 m above ground. Above this height, water vapour profiles with a vertical resolution of 30 m are provided every 5 min up to a height of approximately 3-8 km depending on day or night operation (max. time resolution 10 s). Additionally, 20 the Raman Lidar is not able to measure in and above clouds because its signal is rapidly extinguished. Due to incomplete profile information, IWV cannot be derived by BASIL measurements without the use of complementing measurements from other instruments.

25
During HOPE, 226 radiosoundings were performed with Graw DFM-09 sondes. These feature a thin film capacitance sensor in order to measure relative humidity. with the temperature measurements and the pressure profile derived from GPS measurements, the absolute humidity is computed. Afterwards, the absolute humidity is integrated to derive IWV from the radiosoundings. Many studies asses the error of radiosonde measurements. They show that the error strongly depends on the type of radiosonde (Nash et al., 2010). Furthermore, the systematic and random error of the relative humidity sensor depend on temperature and differ between day-and nighttime. A comparison to IWV derived from GPS showed that the difference Graw DFM-09 -GPS is 2 kg m −2 higher during daytime than during nighttime. Other radiosonde types showed the opposite behaviour. The reason for this could be that the correction algorithm applied by the Graw software probably overcorrects the original dry bias. In general, IWV comparisons of radiosondes with capacitance sensors to GPS measurements show a dry bias for the radiosondes of approximately 1.2 kg m −2 during daytime due to sensor exposition to solar radiation (Wang and Zhang, 2008). Note that the drift of radiosondes during ascent is not negligible: at 850 hPa the 15 HOPE radiosondes drift on average 5 km and 8 km at their maximums, and at 200 hPa the distance is on average 39 km and 106 km at their maximums. Therefore, it has to be kept in mind that a radiosonde may well be in a different air mass than the zenith pointing ground-based instruments are sampling. However, IWV variability is low above the boundary layer because the flow is determined by large-scale advection and therefore 20 homogeneity is high (Shao et al., 2013). Therefore, IWV from radiosondes is nevertheless included in our multi-instrument comparison.

MODIS
The Moderate Resolution Imaging Spectroradiometer (MODIS) is a space-borne, passive, whisk-broom scanning radiometer which measures the radiation backscattered 25 and emitted from Earth, clouds, and atmosphere at 36 spectral bands between 0. Terra and Aqua platforms (http://modis.gsfc.nasa.gov/). This enables a full global coverage every one to two days. With an orbit height of approximately 705 km and a scanning pattern of ±55 • , the swath dimension of MODIS amounts to 2330 km across-track and 10 km along-track (at nadir). Two standard IWV retrievals exist for MODIS: the infrared retrieval (MODIS-IR) and 5 the near-infrared retrieval (MODIS-NIR). Within the present study, MODIS Level 2 MODIS-IR and MODIS-NIR products from Collection 5.1 are used, which have a grid resolution of 3 and 1 km, respectively (http://modis.gsfc.nasa.gov/data/). MODIS-NIR utilizes three channels located within the water vapour absorption wavelengths, namely 0.905, 0.936 and 0.94 µm, and two non-absorbing channels, namely 0.865 and 1.24 µm. The ratios in reflected NIR radiation from water vapour absorption channels to window channels give the atmospheric water vapour transmittances. From these, IWV is obtained from look-up tables based on line-by-line calculations. Note that single and multiple scattering effects are assumed to be negligible. The estimated errors in retrieved IWV are typically 5-10 % and are mostly assigned to uncertainties in 15 the spectral reflectance of the surface targets and in uncertainties in the amount of haze over dark surfaces. For details on the MODIS-NIR retrieval see Gao and Kaufmann (2003).
MODIS-IR utilizes two water vapour absorption bands which deliver information on the moisture distribution and three window bands which also have weak water vapour ACPD 14,2014 Assessment of small-scale integrated water vapour variability S. Steinke et al. MODIS-NIR, which is additionally restricted to daytime and highly reflective surfaces that means land and no ocean. Both MODIS retrievals, if applied to overcast scenes, miss information from within and below clouds.

5
The ICOsahedral Non-hydrostatic (ICON, Zängl et al., 2014) modelling framework is currently being developed jointly by DWD and the Max Planck Institute for Meteorology (MPI-M) as the next generation NWP and climate model. The dynamical core is formulated on an icosahedral-triangular Arakawa-C grid (Arakawa and Lamb, 1977). Within the HD(CP) 2 project, ICON is extended to perform high-resolution regional simulations.
For the presented case study in Sect. 3, ICON is run in limited area mode with a horizontal resolution of 156 m on a circular domain with a diameter of 265 km centred in Cologne (50 • 56 33 N, 6 • 57 32 E). 50 generalized height-based levels are used in the vertical with a model top at 21 km and reduced level spacings in the lower troposphere. Distances between layer midpoints range from 30 m between the lowest levels 15 to 1170 m between the top levels. The simulation is initialized and nudged hourly on the lateral boundaries with COSMO-DE analysis. In contrast to COSMO-DE, a higher resolution topography dataset is used when generating the lower boundary conditions. High frequency output is stored at 40 grid points arranged radially around JOYCE with 1 km spacing (cf. Fig. 1) every 135 s. 20

COSMO-DE
COSMO-DE (Baldauf et al., 2011), an application of the Consortium for Small-scale Modelling (COSMO) covering Germany and its neighbouring countries, is the operational regional NWP model of Germany's National Meteorological Service, the DWD. It is a non-hydrostatic, fully compressible model of the atmosphere. The thermo- hydrodynamical equations describing compressible flow in a moist atmosphere are solved using a finite-difference method on an Arakawa-C grid (Arakawa and Lamb, 1977). As for the coordinates, the model uses rotated latitude/longitude coordinates in the horizontal and time-independent terrain-following coordinates in the vertical. The horizontal resolution is 2.8 km and the vertical spacing of the 50 hybrid levels ranges 5 from approximately 20 m at the Earth's surface to 1000 m in 22 km height. Operationally, 21 h forecasts with COSMO-DE are initialized every 3 h from new analysis and are nudged hourly on the domain boundaries with 3 h old COSMO-EU forecasts, which is a coarser resolved application of the same model covering Europe. Latent heat nudging towards radar data is applied during the first 30 min of each forecast. COSMO-DE output is available every 15 min.

Matching the data
In the following, the spatial matching of all data sets is addressed first, before the temporal matching is addressed in the final section. All JOYCE instruments are located within a distance of 110 m to each other. GPS receiver and sunphotometer are situated 15 on the same roof of a building at a height of 111 m above mean sea level (AMSL) 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 sunphotometer from the water vapour density measured in heights of 20 2, 10 and 20 m above ground. The amount of water vapour substracted 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 is 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. 3 is at a dis-25 tance of 3.3 km south of JOYCE (cf. Fig. 1 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, again the water vapour density of the meteo-5 rological tower is used resulting in a maximum correction of 1.5 kg m −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. 1). 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 10 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. 2 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. 15 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, too, is available with a resolution of 15 min. MWR and sunphotometer 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 20 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.
3 Case study 25 The capabilities and limitations of the different techniques to measure IWV are demonstrated exemplarily for a case study with fair weather conditions on 5 May 2013, when Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a high pressure system dominated the synoptic situation over western Germany. The day was characterized by a classical development of the atmospheric boundary layer. Approximately 2 h after sunrise the convective mixing layer (ML) started to form and completely replaced the residual layer of the last day around 08:00 UTC (cf. top panel in Fig. 2) as indicated by the ML height (MLH) derived from JOYCE wind lidar mea-5 surements . After 08:00 UTC, when the ML is fully developed, the vertically resolved BASIL measurements reveal the strong water vapour gradient between the moist ML and the dry free troposphere above. Even though the ML does not extend higher than approximately 1.5 km on this day, it contains roughly 50 % of the total IWV (estimated from radiosondes). Furthermore, the ML is characterized by 10 a strong temporal water vapour variability as clearly seen from BASIL measurements. Clear-sky conditions prevailed until 09:00 UTC. Later, occasional cumulus evolved which did not significantly limit the BASIL lidar observations (cf. top panel in Fig. 2). The MODIS overflight at 10:25 UTC (cf. middle panel in Fig. 3) shows the high spatial IWV variability with values between 13 and 16 kg m −2 around JOYCE. In general, the north- 15 and southwest of the domain is drier by up to 3 kg m −2 than the rest of the domain. Note that this MODIS map, in contrast to the MODIS data included in the statistics and the time series, is not height-corrected. For this reason, the open pit lignite mining site, which is up to 400 m lower than JOYCE (cf. Fig. 1) is recognizable on the MODIS map by the larger IWV values next to the radiosonde station (approximately 2 kg m −2 20 higher than the rest of the domain). Note also that those areas identified as cloudy by the MODIS cloud mask are displayed in white, since the IWV would only include water vapour up to cloud top. Still, some pixels stand out for their low IWV values in comparison to the surrounding IWV values, which might indicate that some clouds may not have been detected by the MODIS cloud mask. 25 The time series of IWV from all instruments and the two models (cf. top panel in Fig. 2) shows that during this day, IWV varies between 12.5 and 18 kg m −2 . The lowest value can be observed around 07:00 UTC when the residual layer collapses. Afterwards IWV gradually increases during the course of the day, corresponding in part to the increase in MLH as seen from BASIL (cf. top panel in Fig. 2). Clearly, the ML development is also associated with both high fluctuations in the water vapour mixing ratio visible in BASIL measurements and high IWV fluctuations visible in the temporally highly resolved MWR observations (5 s) and to a similar degree in the ICON simulations (135 s). The amplitude of these fluctuations exceeds the noise level of the MWR 5 (0.05 kg m −2 ), indicating that these fluctuations are due to true atmospheric variations. The diurnal development of the standard deviation of IWV over 1 h further confirms this feature (cf. bottom panel in Fig. 2). Due to the lower temporal and/or spatial resolution the other observations and the COSMO-DE simulation cannot reproduce these fluctuations. However, as mentioned above they are identified by BASIL to be caused by ML 10 dynamics (cf. top panel in Fig. 2).

IWV intercomparison
Several features can be identified in the comparison of the time series of the different IWV data sets (cf. middle panel in Fig. 2). They are described in this section. Only GPS and MWR provide continuous observations over the full day. Though they 15 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 kg m −2 .
These jumps are caused by the near-real time processing routine of the GPS retrieval at GFZ (Gendt et al., 2004). Secondly, an even larger difference (ca. 5 kg m −2 ) is seen 20 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 25 investigations. During daytime, when IWV is available from the sunphotometer, its 15 min IWV averages agree 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. 4.3).
The MODIS-NIR estimates availabe for the two overpasses are perfectly within the uncertainty range of MWR and sunphotometer while MODIS-IR measurements which 5 are also available during nighttime are up to 4 kg m −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, sunphotometer, 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 15 launched closest to the MODIS overpass at 11:00 UTC (cf. Fig. 3). 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 20 the observations until 06:00 UTC when the increase in IWV can not be reproduced as strong 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 25 BASIL. This gives us the confidence that the model is suitable to further investigate the spatial and the temporal variability of IWV.

Assessment of representativeness
While all measurements have sampling issues, the use of a dynamic atmospheric model allows to sample IWV nearly continuously in both time and space. Here we selected 40 ICON grid points (cf. Fig. 1) in an area of approximately 10 km around JOYCE for which IWV output was stored at high temporal resolution (2.25 min). The 5 height above mean sea level of the sampled grid points (dx = 625 m) does not vary by more than 150 m. From the time series at the 40 grid points, the average IWV correlations and standard deviations for distances smaller than 10 km and shorter than 1 h can be assessed (cf. Fig. 4). The correlation decreases distinctly with both temporal and spatial mis-10 match. 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 30-15 45 min (0.6 kg m −2 ) that is around the specified uncertainty of the different observations (cf. Table 1). 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 kg m −2 ) for 10 km and 1 h difference. In order to investigate whether the model behaviour is consistent with the obser-20 vations, 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. 4)

Statistical assessment
The two months of HOPE provide the opportunity to investigate IWV characteristics over a wide range of atmospheric conditions for a typical continental, mid-latitude site. The period was characterized by dry polar air masses at the beginning of April that transitioned into a strong synoptically forced regime in mid April with frequent passages 5 of frontal systems over JOYCE during May. There were only a few rain events in April but more in May, which accumulate to 77 mm of total precipitation over the two months (cf. bottom panel in Fig. 5).
In this period, IWV varies by 25 kg m −2 , namely between 5 and 30 kg m −2 (cf. main panel in Fig. 5). IWV can increase or decrease by 10-20 kg m −2 within one to two 10 days. The different IWV data sets reveal a broad frequency distribution with a maximum around 15 kg m −2 (cf. right panel in Fig. 5). This distribution reveals the influence of the instrument sampling: GPS, MWR, radiosondes, and COSMO-DE show rather similar characteristics. In contrast, the distribution for the sunphotometer is shifted to lower IWV values as it is restricted to daytime clear-sky measurements. 15 In the following, we first investigate the instrument performance during the whole period of HOPE before we analyse whether the small-scale temporal IWV variability (< 1 h) revealed in the case study is typical for the complete HOPE period.

Instrument intercomparison
Since none of the instruments can be considered as "the truth", every instrument is 20 compared to all other instruments (cf. Fig. 6). All measurements are considered at 15 min resolution (see Sect. 2.3). 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 agree-25 ment between the instrument pairs is good. The standard deviation is not higher than 1 kg m −2 and the correlation coefficient is never lower than 0.98. The absolute bias ACPD 14,2014 Assessment of small-scale integrated water vapour variability S. Steinke et al. varies from 0 for GPS-sunphotometer to 1 kg m −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 as both instruments also measure during cloudy conditions. The bias (0.2 kg m −2 ) is very low and the standard deviation (0.9 kg m −2 ) is within the expected 5 measurement uncertainty (cf . Table 1). However, there are some IWV values which are up to 5 kg m −2 lower than observed by the MWR (cf. Fig. 6). 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 kg m −2 and of the standard deviation to 0.8 kg m −2 . This problem is further investi-10 gated in Sect. 4.3. Furthermore, a small dependency of the error on the IWV is found. For large IWV values the difference GPS-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 However, only a small difference of 0.2 kg m −2 between day and nighttime soundings could be identified probably due to the correction within the Graw software (cf. Sect. 2.1.5).

20
The comparisons 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-sunphotometer comparisons, since there are no sunphotometer measurements at these times. The reason for this is probably that cloudy cases are not reliably detected by the MODIS cloud identifying algo- double the standard deviation of the first, which could be due to the coarser resolution but also 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 kg m −2 . To allow 5 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 seperately. The mean of these comparison then only differs by 0.4 kg m −2 (cf. Fig. 6) and the standard deviation is reduced for all instrument combinations to be lower than 1 kg m −2 . This results likely from sampling more homogeneous conditions. By including only measurements when the sunphotometer is measuring, nighttime 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 kg m −2 with the exception of MODIS. How-15 ever, it has to be kept in mind that the representative error of IWV at 4 km spatial distance is only 0.4 kg m −2 . The representativeness analysis for 5 May 2013 estimated the effect of atmospheric variation to be approximately 0.4 kg m −2 (cf. Sect. 3.2). As expected, a reduction of the compared data sets by only including coincident measurements simultaneously excluding all nighttime, rainy and cloudy cases, leads to 20 an improvement in the overall agreement. However, the mean values over the HOPE period range from around 16 kg m −2 (GPS, MWR) to lower than 14 kg m −2 (sunphotometer, 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.

Temporal variability
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 auto-correlation of the continuous data sets, namely MWR, GPS, and COSMO-DE, is computed (cf. Fig. 7). All three data sets with a temporal resolution of 15 min show a similar behaviour: their auto-correlation 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 synop-5 tic variability (cf. Fig. 5), but it gives important limitations on the influence of temporal matching in IWV comparisons and on generation 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 10 deviation during HOPE is computed over varying time intervals from 5 min to 3 h (cf. top panel in Fig. 8). 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 kg m −2 at 5 min to 0.4 kg m −2 at 1.5 h showing some saturation with 0.6 kg m −2 at 3 h intervals.

15
For time intervals of 1.5 h and longer, MWR, GPS and COSMO-DE again show a similar behaviour as seen in the auto-correlation. In fact, they lie within their 25 and 75 %percentiles. However extreme values reach standard deviation of 2.0 kg m −2 and higher at time intervals > 1 h. Interestingly, none of these points is evident during the day of the case study (cf. Sect. 3) as the highest standard deviations stem from cloudy situations 20 (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. 2 GPS measurements within 1 h are relatively smooth. However, the mean standard deviation of the 15 min MWR averages are overall only slightly smaller than the mean standard deviation of the 5 s 25 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, that for these time intervals, GPS is well-suited as a reference instrument for model evaluation For time intervals shorter than 1 h, only the 5 s MWR data can partially resolve the short-scale, turbulence-induced variability of IWV. The minimum detected average standard deviation at 5 min averaging time of 0.1 kg m −2 is twice as high as the 5 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 10 variability is probably dominated by the variability of subsequent updraught and downdraught regions. Noteworthy are also standard deviation values larger than 1 kg m −2 even at the shortest time scales, which are predominantly caused by clouds.
Focusing on clear-sky, daytime cases allows to include the sunphotometer (cf. bottom panel in Fig. 8). When only coincident data from MWR, GPS, sunphotometer 15 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. 8). 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 scences are filtered out. The IWV standard deviation observed dur-20 ing the case study seems to be representative for 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 25 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 sub-grid 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.

Diurnal cycle
The previous sections show the importance of the IWV variabilty associated with atmospheric turbulence. In this section we focus on the mean diurnal cycle of IWV over 5 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 provides a test to which degree different instruments and/or models can provide a consistent answer. Only those measurements, which are available on a near-continuous basis, that is MWR, GPS, and sunphotometer, and COSMO-DE output, are included in 10 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 rather a true mean behaviour of IWV. Figure 9 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 15 range varies from 1 to 2 kg m −2 depending on the data set. This is significantly higher than the daily IWV range reported by Morland et al. (2009) for a five year data set from Bern, Switzerland (0.6 kg m −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 20 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. 2.2 kg m −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 for the atmospheric temperature as found by Morland et al. (2009). They apply a dampened mean atmospheric temperature, to compansate for this surface 5 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 kg m −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 Dai (2002). 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 kg m −2 ) is between COSMO-DE and GPS. However, it needs to be 15 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 in Fig. 6 with 0.2 kg m −2 , the GPS mean diurnal variation is clearly 1 kg m −2 larger than from the MWR. Due to its measurement principle, the sunphotometer (cf. Sect. 2.1.3) is limited to 20 clear-sky conditions from 05:00 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 as 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 sunphotometer measurements. 25 For the difference between the sunphotometer and MWR, a dependency on the position of the sun is found (not shown). In the morning and in the afternoon, IWV from the sunphotometer is smaller than from the MWR because here the sunphotometer measures under lower elevation angles. At noon it is the other way around. This could be due to an inaccurate relative air mass (Eq. 1) used by the retrieval. 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 5 indicate that the operational COSMO-DE model underestimates the amplitude of the diurnal cycle.

Summary and conclusions
The present study uses multi-instrument observations and model simulations of IWV at the mid-latitude site JOYCE  to investigate its spatial-temporal 10 variability. The -to our knowledge -unprecedented set of instruments (MWR, GPS, sunphotometer, radiosondes, Raman Lidar, MODIS-IR, MODIS-NIR) located in close proximity during the two months of the HOPE campaign (http://hdcp2.zmaw.de/HOPE. 2306.0.html) is complemented by a well-established operational NWP model (COSMO-DE) and -in the frame of a case study -the novel high-resolution atmospheric model 15

ICON.
The different instruments have different sampling characteristics, uncertainties and limitations (cf. scale spatial structure of IWV -once corrected for elevation and filtered for cloudsover the whole globe. The multi-instrument intercomparison reveals a number of pecularities of the individual instruments. Sunphotometer measurements show a good agreement with the other measurements but can only be conducted during clear-sky at daytime and seem 5 to suffer from problems when the sun is low. IWV from MWR and GPS slightly varies (bias: 0.2 kg m −2 (1 %), standard deviation: 0.9 kg m −2 (6 %), cf. Fig. 6) taking the specified instrument uncertainties into account. However, the near-real time processed GPS data exhibit inconsistencies at the beginning of each day and each hour due to the processing procedure that might also lead to a shift in the diurnal cycle of IWV. Further 10 work on the processing might increase the performance of the GPS measurements. In contrast to MWR, a comprehensive GPS networks exist, thus making GPS better suited to evaluate models over their whole domain.
The analysis of the temporal variability of IWV reveals three distinct forcings. First synoptic influence is mainly responsible for the fact that IWV auto-correlation is lost 15 after approximately half a day. Secondly, clouds and broken cloud fields can cause standard deviations of IWV of over 1.5 kg m −2 within time intervals of a few hours. When only daytime clear-sky IWV estimates are considered, the high end tail of the distribution of IWV standard deviation disappears. Therefore, instrument intercomparisons under cloud free conditions are advantageous to assure more homogeneous 20 conditions (cf. Fig. 8). Thirdly, atmospheric turbulence determines IWV variability also in cloud free conditions on scales below 1 h, which can be assessed using MWR data available in second resolution. Standard deviations of higher than 0.5 kg m −2 can be observed even for time intervals less than 30 min. This information is interesting for the development of sub-grid parameterizations for atmospheric models but also implies 25 that instrument intercomparisons should make use of suitable measures to identify atmospheric conditions with low variability in order to isolate instrument errors. The standard deviation derived from high-resolution MWR time series is able to identify turbulent mixing within the growing ML, as demonstrated for a case study with the help of vertically resolved water vapour and wind lidar data. For the same day, simulations at 156 m grid resolution with the novel ICON model were used to assess the spatio-temporal IWV correlation and standard deviation for time differences smaller than 1 h and shorter than 10 km. It is shown that a temporal mismatch of 30-45 min or a spatial mismatch of 8-10 km can already lead to a random error of 0.6 kg m −2 .

5
A combination of temporal and spatial mismatch introduces even higher errors. The results are confirmed from observations of two MWR operated 3.3 km apart. An important aspect for climatological studies is that mean IWV over HOPE, as derived from the different sources, differs by up to 3 kg m −2 since different time periods are included in the measurements. These differences occur due to limitations of the 10 measurement principles and measurement gaps of instruments. These differences introduce deviations in the statistics of the different instruments or models. Therefore, as done in this study, only coincident data should be compared. This is particularly true for the mean diurnal cycle over the whole campaign where our study reveals an underestimation of the amplitude by the operational COSMO-DE model. In the future, longer 15 simulations with the novel ICON model, which are yet not possible due to limited computing power, will be performed to investigate whether the encouraging results from the case study presented here can be confirmed in more general terms. Introduction

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