The performance of numerical weather prediction (NWP) and climate models typically goes in line with the accuracy of the simulated tropospheric and, in particular, the planetary boundary layer (PBL) water vapor fields . All of the global circulation models that are employed for operational forecasting or retrospective analyses (reanalyses), ingest vast numbers of atmospheric water vapor observations, mostly based on satellite remote sensing. The benefits of this practice are well proven, e.g., for the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts ECMWF; or the ERA-Interim reanalysis of ECMWF . While the global operational NWPs develop towards convection-resolving resolutions, ∼ 13 km for the Global Forecast System (GFS; ) and ∼ 9 km for ECMWF's IFS, the global reanalyses stay a bit behind, with resolutions of up to ∼ 30 km for ECMWF's ERA5. A further increase in the spatial resolution can be achieved with limited area models (LAMs) that perform a downscaling for subregions of the global models. Typically, LAMs exhibit more detailed process descriptions as, for example, with a non-hydrostatic formulation of vertical motion, the consideration of air compressibility, or acoustic gravity waves. The quantitative performance of the LAMs depends on the quality of initial state and on time-varying boundary conditions.

The incorporation of additional water vapor information, even on a smaller scale, is possible through data assimilation. The positive impact of the assimilation of InSAR data and GNSS stations is shown for numerous studies and regions. Variational data assimilation schemes merge atmospheric models and observations while considering their respective error statistics by iteratively minimizing a cost function. For further information, we refer the reader to , , and .

Each of the above-discussed techniques for atmospheric water vapor estimation has specific strengths and weaknesses. The fusion of different data products and modeling approaches allows the exploitation of the complementing characteristics so that the tropospheric water vapor estimation becomes more accurate, reliable, and robust.

The core region is defined by the transnational GURN that was originally established for the investigation of tectonic activities . It encompasses the southwestern part of Germany and the eastern part of France, with the Upper Rhine Graben (URG) in the center, the Black Forest in the east, and the Vosges in the west, plus a small area of northwestern Switzerland (Fig. ).

The Upper Rhine Valley is one of the warmest regions of Germany, with lower annual rain amounts (approx. 600 mm a-1) but with high convective activity in the summer months. Up to 1500 mm a-1 of annual rain amounts are measured in the low mountain ranges of the Black Forest, the Vosges, and the Swiss Jura and about 1000 mm a-1 in the flatter western and northwestern area.

The global positioning system (GPS) observations of 66 stations of the GURN were used to estimate IWV. GURN was established by the Geodetic Institute (GIK) of Karlsruhe Institute of Technology, Germany, and the École et Observatoire des Sciences de la Terre of the University of Strasbourg and the French National Center for Scientific Research. Currently, GURN consists of ground-based GNSS stations from permanent authoritative and private GNSS networks. In Germany, this refers to SAPOS (the German satellite positioning service operated and maintained by the mapping agencies of the German federal states) and GREF (Integrated Geodetic Reference Network of Germany; this is the responsibility of the Federal Agency for Cartography and Geodesy, BKG). In France, the respective networks (providers are given in parentheses) are RENAG (national GNSS network of French research laboratories; French National Centre for Scientific Research, CNRS), RGP (National Institute for Geographic and Forestry Information, IGN), and the GNSS networks of the providers TERIA and SATINFO. In Switzerland, data from the permanent GNSS network of the federal mapping agency swisstopo are used. Several stations from International GNSS Service (IGS) and EUREF are also included. For the availability of the raw GNSS observations, readers are referred to the data providers' specific policies. Up to now, only GPS observations have been processed. Other GNSS systems like GLONASS (Russian satellite navigation system) and Galileo will be added in the future.

The GPS data were processed with the GAMIT software version 10.7; for all InSAR dates and for the four seasonal investigation periods. To model the tropospheric delays of GPS signals received by the ground-based stations, we adopted the following equation to map the slant signals into zenith: 1STD(a,e)=ZHD⋅mfH(e)+ZWD⋅mfW(e)+grad(a,e)2ZTD=ZHD+ZWD, with the corresponding mapping functions mfH and mfW. The term grad is a function to model the effects of azimuthal asymmetry in the tropospheric delays, where a and e are the azimuth and elevation angles of the GPS signals, respectively: 3grad(a,e)=GNS⋅mfG(e)⋅cos⁡a+GEW⋅mfG(e)⋅sin⁡a4mfG(e)=1/(sin⁡e⋅tan⁡e+0.003).

In this study, we used the a priori zenith hydrostatic delay from European Centre for Medium-Range Weather Forecasts (ECMWF; ), the state-of-the-art Vienna Mapping Functions 1 (VMF1; ), provided by the Vienna University of Technology, and the tropospheric gradient model proposed by . Moreover, we also conducted the GPS data processing with other advanced strategies and models. For example, we removed the first-order effect of the ionospheric delay with linear combinations of observations and modeled its second- and third-order effects with International Geomagnetic Reference Field 12 (IGRF12; ) and ionospheric data from the Center for Orbit Determination in Europe (CODE; ). We removed the observations with elevation angles lower than 10∘ and weighted the other observations according to their elevation angle and their post-fit-phase residuals. We modeled and corrected solid Earth tides, ocean tides, and pole tides according to International Earth Rotation and Reference Systems Service (IERS) Conventions 2010 . We used the IGS final orbits, IGS absolute-antenna-phase center models , and ITRF2014 reference frame .

The tropospheric products derived by the GPS data processing include ZTD, gradients in the north/south and east/west directions, and their corresponding standard deviations, respectively. The ZTD estimates were further used for the retrieval of IWV, with auxiliary information (i.e., Ps and Tm) obtained from ERA5 pressure-level products. Detailed procedures for the IWV retrieval from ground-based GPS are provided in the Appendix .

The GPS tropospheric outputs for all the stations, auxiliary variables from ERA5, and the retrieved IWV are saved day by day in ASCII files in Solution (Software/Technique) INdependent EXchange Format for TROpospheric and meteorological parameters version 2.00 (SINEX_TRO V2.00). The SINEX_TRO V2.00 format was designed to accommodate related developments. For example, it supports tropospheric variables derived by numerical weather prediction models and reanalyses in addition to space geodetic techniques. The SINEX_TRO V2.00 file is composed of groups of data termed as blocks. Each block has a specific format. Some of the blocks are mandatory (e.g., reference block), whereas the others are optional (e.g., comment line). Thus, the structure of the SINEX_TRO V2.00 format is very simple and flexible. For the details on the definition of the SINEX_TRO V2.00 format, readers are referred to .

The file names of the GPS tropospheric products are in the style of gikyrdoy0.txt, where gik is the name of the data provider, yr and doy are year in two characters and day of year in three characters, respectively. The files start with metadata blocks and end with data blocks. The metadata blocks include information on the data providers, data processing strategies and models, station names, coordinates, receiver types, antenna types and eccentricities, and so on. The data blocks list the GPS-derived ZTD, gradients, and their corresponding standard deviations, respectively. In addition, the data blocks also include the Ps, ZHD, and Tm from ERA5, as well as the final ZWD and IWV estimates.

To derive double differential slant total delays in phase values (ddSTDP) and IWV from PSI, we use Sentinel-1A/B data, acquired at an altitude of around 690 km in interferometric wide swath mode (IW), with a ground resolution of around 5 × 20 m and a swath width of 250 km. The data were recorded by both satellites (A and B) along ascending orbit 88 between March 2015 and July 2019. All available datasets are visualized over time and the along-track coverage in latitude is indicated in Fig. S4 in the Supplement. Each scene is displayed in a different color, with additional labels for the four study events. The satellite repeat cycle is 12 d, and combining data from both satellites has nominally provided an acquisition on every sixth day since the launch of Sentinel-1B in October 2016. The acquisition time, 17:26 UTC, is constant for both satellites. With the given repeat cycle of the two satellites, 213 scenes could be theoretically available. But some gaps occur in the dataset at certain time intervals, e.g., when the project area was not covered for different reasons, leading to the finally processed 169 scenes. In this study, we processed the VV (vertical transmit, vertical receive) polarized data and used the Shuttle Radar Topography Mission (SRTM) 1 as a reference digital elevation model during processing. The orbit correction was performed with the provided precise orbit files.

InSAR processing was performed using the software SNAP, starting with version 7.0, and from the coregistration step onward, version 8.0 was used . For further PS processing, we then used the program StaMPS version 4.1-beta; for the PSI processing. The master scene for the interferometric processing is from 17 March 2017. The spatial reference point was chosen at the town of Épinal at (6.45066∘ E, 48.175043∘ N), with a reference radius of 1 km. As such, we obtain an intermediate dataset of raw double differential slant total delays (ddSTDP) for each interferogram and each PS, which is provided in the dataset publication in the common StaMPS format. Afterwards, we estimated the linear displacement at each PS point with a weighted ensemble estimation and removed the displacement phase from the observations. The resulting corrected partial differential slant-phase delays (pSWDs) are used for the tomographic approach. They are then mapped to zenith direction using the sine function, as follows: 5pZWDi=pSWDi⋅sin⁡(ψ), with the looking angle ψ and the partial wet delays in the slant (pSWD) and zenith (pZWD) direction. Those corrected-phase observations in the zenith direction were then used as input to the Atmospheric Phase Screen (APS) inversion. It is based on the zero-mean assumption and is performed point-wise for each PS point independently. The zero-mean assumption does not consider the different heights of PS points. This results in a systematically different behavior of the different PS points due to the stratification of the water vapor in the atmosphere. Therefore, we refer to these values as partial zenith wet delays (pZWDs). The bias induced through the zero-mean assumption is corrected point-wise using reference values extracted from the ERA5 reanalysis to ensure a datum adjustment to the true mean wet delay. The calculation of the required ZWD and mean temperature (Tm) was performed analogously to that described in the GNSS processing section (Sect. ) and in Appendix .

PSI pZWD contains signal components with long wavelengths which can be biased for several reasons. Therefore, spatial trends over the whole imaged region were re-estimated in the next step. To include only the atmospheric signal, a quadratic function f(ϕ,λ), as in Eq. (), was estimated, which describes the difference between pZWD derived from the ERA5 dataset and the PS–InSAR mean-corrected data. This function depends on geographic longitude λ and latitude ϕ. The estimation parameters a,b,c,d, and e differ for each of the 169 scenes. 6f(ϕ,λ)=a⋅ϕ2+b⋅λ2+c⋅ϕ+d⋅λ+e. The optimal function is determined using a bootstrapping approach. This approach uses several small subsets of all available PS points to reliably calculate the optimal function . The ZWDs were then calculated using the optimal function to correct the mean-corrected ZWDs. Subsequently, the ZWDs were transformed to IWV according to Eq. ().

Finally, we derive the IWV for each PS point, which is corrected for height errors and includes long wavelength atmospheric signals. The precision of the IWV is estimated for a given PS point as standard deviation of all points located in a 200 m radius with regard to this point. The inner precision of the IWV dataset is 0.27 kg m-2, which is the average value over all PS points.

The two products provided in the data compilation, for all 169 dates and at each PS point location, are (1) the double differential slant total phase delays (ddSTDPs) and (2) the integrated water vapor (IWV). A potential application of these products is the improvement in methods for gridding and the calculation of APS to IWV. The second product can be used for assimilation purposes in weather models.

We applied the three-dimensional variational data assimilation (3D-Var) system provided by WRF to assimilate IWV, WVD, and additional synoptic station data.

Convection permitting WRF simulations with hourly output were performed for each of the four seasonal study events on the basis of hourly ERA5 driving data . The choice of model physics (see Table ) is widely adopted from another study in the same region by and outlined in more detail in .

The domain encompasses an area of approximately 650 × 670 km, with a grid spacing of 2.1 km and 72 vertical levels (created automatically by the WRF). This domain size should guarantee spatial spinup. The temporal spinup is based on several weeks of open-cycle simulations before each event to achieve satisfying soil conditions. Open-cycle simulations are WRF simulations with hourly ERA5 input but no assimilation of additional variables. In this way, reliable starting conditions for the assimilation comparisons were obtained. We performed three simulation runs for each of our chosen events. Run1 is based on the assimilation of meteorological stations, GNSS and InSAR data. For Run2, meteorological station data and tomography data were used, and Run3 is an open-cycle simulation. The 3D-Var technique, which is implemented in the WRF Data Assimilation (WRFDA), was applied for the assimilation runs. The multivariate background error statistics option cv6 was chosen . In this way, temperature is also able to show a direct impact on moisture, and vice versa. A spatial thinning of 10 km was used to minimize correlation artifacts. To tie the simulations closer to the measurements, all assimilation input data, except InSAR data, were assimilated on an hourly basis. This is particularly useful when the variations in water vapor in the lower atmosphere are more complex due to dynamic weather conditions. Temperature, pressure, and relative humidity from meteorological stations were used, along with ZTDs from GNSS, InSAR, and interpolated fields, by means of collocation. The tomography data are based on the same GNSS data as in Run1 but offer gridded input on the WRF grid. The calculation of the ZTD values from GNSS stations and tomography is explained in the respective chapters. ZWD data were provided from InSAR measurements. The dry signal part (ZHD) was calculated from the respective WRF open-cycle simulation and was added to the InSAR ZWDs in order to achieve ZTD values for assimilation.

The applied solvers, model time steps, and other simulation parameters in WRF are defined in a table called namelist.input. This file is included in the dataset together with a netCDF file called geo_em.d01.nc. It contains all static fields in 2D or 3D for the WRF model in the chosen projection, such as altitude, land use, soil information, etc. Additionally, the background error covariance matrix (be.dat) is required for the assimilation. It was calculated with the NMC method for each of our events. Based on month-long WRF simulations with the same setup as our open-cycle simulations, averaged forecast differences in the 12 and 24 h forecast (valid at the same time) were applied. Furthermore, the assimilation input for Run1 is provided (obsproc_hour). This is a pre-processed input, where observation errors were included and duplicates and inconsistence data due to certain tests were removed. For raw assimilation data, we refer to the other datasets presented in this section. The meteorological station data are available at DWD German Meteorological Service;. The forcing data from ERA5 can be obtained from the ECMWF website .

WRF output is available on the 3D model grid. The direct nesting from 31 to 2.1 km reduces possible artifacts due to intermediate domains and the respective parametrizations (e.g., convection), on the one hand. On the other hand, model physics require a larger area to evolve. That is why we discarded an area of 50 pixels at the borders to achieve reliable simulation outcomes. The results are provided after 1 h of free WRF simulations to obtain consistent model data, since the assimilation of variables modifies only certain model variables. Temperature, pressure, and water volume density are provided on a 3D grid (219 × 209 × 72). In 2D, temperature and pressure are provided in 2 m, and integrated water vapor (IWV) and rain amounts are given as column values.

The least-squares collocation approach is based on a functional and a stochastic component, where correlated parts are determined and separated from uncorrelated measurement noise as follows for instance, from: 7l=f(u,x,t)+s(Css,x,t)+ϵ, where l is the measurement, f(u,x,t) is the functional part representing realistic physical models of meteorological variables with u, x, and t, which are, respectively, the state vector to be estimated, the coordinates, and the time. The so-called signal s(Css,x,t) depends on an empirically modeled covariance Css, and the noise ϵ is assumed to be stochastically uncorrelated.

In our collocation software, the state vector to be estimated is u=(ZTD0,aZTD,bZTD,cZTD,HZTD). ZTD0 is the ZTD at reference position (x0,y0,h0,t0), aZTD, bZTD, and cZTD are gradients in the x,y coordinates and time, and HZTD is the scale height. x,y,h,t represent the coordinates and time of a measured point. MFs are mapping functions used to map zenith delays in the slant direction. Thus, according to and , the ZTDs and ddSTDs (both in millimeters) are modeled as follows: ZTD(x,y,h,t)=[ZTD0+aZTD⋅(x-x0)+bZTD⋅(y-y0)+cZTD⋅(t-t0)]8⋅e-h-h0HZTDddSTD(x,y,h,t)=[MFp1t1⋅ZTDp1t1-MFpreft1⋅ZTDpreft1]-[MFp1tref⋅ZTDp1tref9-MFpreftref⋅ZTDpreftref].

For the ddSTDs, the superscripts t1,tref represent the time of acquisition of an InSAR image and the reference image acquisition time, thus forming the time difference, while the subscripts p1,pref refer to the positions of an InSAR PS point in the image and the position of the reference PS point forming the spatial difference. The formulas describing the covariance of the signal part can be found in and .

For the collocation of GNSS and InSAR measurements, the following two steps are required:

Screening of GNSS ZTDs and InSAR ddSTDs, based on a simple least-squares estimation and gross error detection. The value of the residuals divided by the product of the a posteriori standard deviation and measurement noise is compared to a preselected threshold.

The refractivity (N, in parts per million) equals the derivative of the delay in the direction of the ray. Thus, by deriving the zenith delays with respect to height, we obtain the following: 10N(x,y,h,t)=-∂ZTD(x,y,h,t)∂hN(x,y,h,t)=1HZTD⋅[ZTD0+aZTD⋅(x-x0)+bZTD⋅(y-y0)+cZTD⋅(t-t0)]11⋅e-h-h0HZTD.

The covariance matrices relating delays with refractivity, as shown in , are obtained by deriving the covariance of the delays with respect to height.

Two kind of products are provided in this study, namely (1) 2D maps of ZTDs interpolated onto the grid of the WRF domain (Sect. ) which contain structural information of the lowest tropospheric layer and (2) 3D tomographic products in the form of refractivity fields on the horizontal grid of the WRF domain. For the vertical distribution, the refractivities are computed for 16 equally distributed layers, from the lowest WRF layer up to 8 km.

Examples of ZTDs and refractivity fields, obtained using our approach, are shown in Fig.  for the spring event of 2016. From the top plot in Fig. , it can be noticed that the ZTDs and the refractivity fields for the lowest layer follow the topography of the terrain, while, in the bottom plot, the decrease in refractivity with altitude is visible.

A further, extended, time series of tomographic products is provided based on the InSAR and GNSS collocated tropospheric products, as described in Sect.  and . The length of the time series corresponds to the number of InSAR acquisitions, since the scope is to exploit the two techniques simultaneously. Therefore, the temporal resolution is similar to that of the InSAR products, while the spatial resolution of these products is identical to the 2D maps of ZTDs or 3D fields of refractivity described above.

For the four seasonal events (Sect. ), the 2D maps of ZTDs were stored as ASCII files, where each line corresponds to one epoch and the number of columns to the number of points in the horizontal grid of the WRF model. For the 3D tomographic products, the structure is identical; however, the number of columns is 16 times larger since there are 16 layers. For each WRF point, the 16 refractivity values are written and then go on to the next point until the last one.

Potential applications of our data are the fusion in numerical weather prediction models and use of retrieved ZTDs and refractivities for validation purposes. Regarding the retrieval of IWV and WVD fields, more information is provided in the Appendix.