Data assimilation in numerical weather prediction (NWP) optimally blends observations with an atmospheric model in order to obtain the spatial distribution of atmospheric variables and to produce the best possible model initial state. It was realized early that the forecast quality is strongly dependent on an accurate description of the initial state . There are strong requirements on the infrastructure and computing power for today's state-of-the-art high-resolution modelling systems. As model resolutions increase it is increasingly important to utilize observations with high spatial and temporal resolution to initialize mesoscale phenomena, such as convective storms and sea breezes.

The meteorological weather services of Sweden, Norway and Finland recently joined forces around a common operational kilometre-scale forecasting system named MetCoOp . The forecast model used within MetCoOp is developed in the framework of the shared Aire Limitée Adaptation dynamique Developpement InterNational (ALADIN) High Resolution Limited Area Model (HIRLAM) NWP system. This system can be run with different configurations and in MetCoOp the HIRLAM-ALADIN Regional Meso-scale Operational NWP In the Europe Application of Research to Operations at Mesoscale (HARMONIE-AROME) is used . The main components of the ALADIN-HIRLAM NWP system are surface data assimilation, upper-air data assimilation and the forecast model for the forward time integration.

The only direct humidity measurements used in the MetCoOp upper-air analysis are provided by vertical profile measurements from radiosondes. In addition, humidity-related information is provided by radar measurements , by satellite-based information and by moisture-related observations from the Global Navigation Satellite System (GNSS) zenith total delay (ZTD). Satellite observations are coupled to the moisture through the dependence of the radiative transfer at the top of the atmosphere on the atmospheric moisture distribution. The disadvantage of all of these humidity-related observation types, except GNSS ZTD, is that they are only available at particular times of the day (radiosonde and satellite measurements) or their availability is dependent on weather conditions (radar measurements). GNSS ZTD estimates, on the other hand, are available at all times with high temporal resolution (15 min), for all weather conditions. The ZTD is in fact an estimation, but for simplicity we hereafter refer to it as an observation. Moisture-related observations in the form of GNSS ZTD are a relatively new source of mesoscale atmospheric humidity information. ZTD observations obtained from the network of ground-based GNSS receivers contain horizontally dense information on the total columnar amount of water vapour (TCWV). A number of assimilation studies have shown a positive impact of GNSS ZTD observations on NWP systems at a horizontal model grid resolution on the order of 10 km . The importance of combining the GNSS data with other types of observations has been highlighted in several studies . Some encouraging results from assimilation of these observations at a kilometre-scale horizontal resolution have been obtained , and GNSS ZTD from 28 receiver stations are assimilated operationally in MetCoOp. These 28 receiver stations have been selected from the rather few receiver stations over the MetCoOp domain. Most of these so-called supersites, processed by several centres for comparison purposes. MetCoOp operationally uses data processed by the Met Office processing centre in the United Kingdom (METO) and by the Royal Observatory processing centre of Belgium (ROBH).

The EUMETNET GPS Water Vapour Program (E-GVAP) is a collaborative effort between the European geodetic community and several European national meteorological institutes. The purpose of E-GVAP is to provide atmospheric water vapour observations for use in operational meteorology. ZTD observations obtained from the E-GVAP network of ground-based GNSS receivers contain horizontally dense information and are available with a temporal resolution of up to 5 min and therefore have the potential to provide humidity-related data for kilometre-scale short-range weather forecasting. To stimulate further enhancements in the preprocessing and use of GNSS ZTD observations in NWP and nowcasting applications, in particular when forecasting severe weather, a European COST Action (ES1206) is ongoing between 2013 and 2017. One outcome of the action was a recent review of the current state of the art and future prospects of the ground-based GNSS meteorology in Europe . The action resulted furthermore in revitalization of the Nordic GNSS Analysis Centre (NGAA), now located at Lantmäteriet in Sweden, where GNSS data are processed for a large number of receiver stations, mainly from the Nordic countries. The dense network of GNSS ZTD observations provide an attractive source of supplementary humidity information to the MetCoOp modelling system.

Like all other types of measurements, the GNSS ZTD observations are associated with errors that need to be properly characterized. It has earlier been demonstrated that adaption of variational bias correction to be used together with GNSS ZTD data was successful for handling systematic observation errors . The sources of bias in the ZTD observation data with respect to the ZTD model data may be for several reasons, such as GNSS data-processing algorithms (use of mapping functions, formulation of hydrostatic delay, errors in the conversion of ray path to zenith delay) and systematic errors in both the model fields and the ZTD observation operator. In particular, a low model top will generally result in a systematically too-low model equivalent of the GNSS ZTD observations. In Sánchez-Arriola et al. only one predictor was used in the variational bias correction. Earlier, studied the behaviour of a non-adaptive multilinear bias correction scheme inspired by the one proposed by and found a benefit in using more than one predictor. The question is whether an adoptive bias correction scheme like the one used by Sánchez-Arriola et al. would also benefit from using more predictors.

Due to the measurement and processing techniques, GNSS observations are very likely to have correlated errors. The difficulties of spatially and temporally correlated observation errors have generally been circumvented in data assimilation by applying thinning of data, or through observation processing algorithms that are assumed to remove the observation error correlations . Methods have been developed to account for serially correlated errors , but there is certainly room for improvement regarding spatially correlated errors, although some general research within this area has been carried out . Some studies have focused on GNSS ZTD observations , but the handling of the correlated observation errors is still an active area of research.

GNSS ZTD observations processed by the NGAA centre have been used within the MetCoOp forecasting system, aiming at improving short-range forecasts of, in particular, moisture, clouds and precipitation. Two different GNSS ZTD processing techniques applied at NGAA are described, compared and evaluated. The sensitivity of the results to various aspects of the GNSS ZTD observation handling and data assimilation was investigated. The evaluation includes both an individual case study and statistics based on extended parallel experiments.

The paper is organized as follows. The GNSS data processing is the topic of Sect. . In Sect.  the NWP modelling system is described. Section  deals with the design of parallel data assimilation experiments, and their corresponding results are presented in Sect. . Finally, conclusions are presented in Sect.  together with some future plans.

In June 2016 Lantmäteriet (Swedish Mapping, Cadastre and Land Registration Authority) became NGAA, one of the analysis centres in E-GVAP, and it is in charge of the data processing for the GNSS stations in Sweden, Finland, Norway, Denmark and some IGS stations in order to provide near-real-time (NRT) ZTDs. For E-GVAP data processing the NRT product means that the estimated ZTD for the previous hour needs to be ready within 45 min. NGAA includes in total approximately 700 stations and currently provides two NRT ZTD products (NGA1 and NGA2). The NGA1 product is obtained from the Bernese v5.2 network solution, while NGA2 is given by the GIPSY/OASIS II v.6.2 data processing using the precise point positioning (PPP) strategy .

In a network solution there is no need for the precise clock product for the GNSS satellites due to the differential observables. However, the computing time will be exponentially increased as the number of GNSS stations in the data processing increases while the station-related errors are correlated to each other. During PPP processing, the data from only one GNSS station is processed at a time, meaning that station-related errors are independent from others. However, high-quality satellite clock product is critical for the accuracy of PPP data processing. More details about the two types of data processing can be found in Sect.  and .

The main components of the MetCoOp ALADIN-HIRLAM NWP system are surface data assimilation, upper-air data assimilation and the forecast model.

The forecast model configuration, e.g. dynamical core and physical parameterizations, are described in detail in and . It has a spectral representation with a non-hydrostatic formulation. Stratiform and deep convective clouds are explicitly represented, while for shallow convection a sub-grid parameterization is applied using the EDMF (eddy-diffusivity mass-flux) scheme. The representation of the turbulence in the planetary boundary layer is based on a prognostic turbulent kinetic energy (TKE) equation combined with a diagnostic mixing length . The radiative transfer of the shortwave spectrum is described with six spectral bands , and the long-wave radiation is modelled in accordance with . Surface processes are modelled using SURFEX . Lateral boundary conditions were provided by 6-hourly European Centre for Medium-Range Weather Forecasts (ECMWF) operational forecasts with a 1 h time resolution. In addition, a spectral large-scale mixing of the background state, the 3 h HARMONIE forecast, fields with the lateral boundary ECMWF fields was applied. In this way we hoped to benefit from the high-quality large-scale information from the ECMWF global forecasts in the regional MetCoOp data assimilation.

In the MetCoOp setup there are 750 × 960 horizontal grid-points at each of the 65 vertical levels extending up to 10 hPa, which approximately corresponds to a height of 32 km in the atmosphere. The horizontal grid distance is 2.5 km. The model domain is illustrated by the black frames in Fig. . In the surface data assimilation SYNOP observations of temperature and relative humidity at the vertical level of 2 m were utilized. In addition sea surface temperature and sea ice concentration from an oceanographic model were used. In the MetCoOp upper-air data assimilation conventional types of in situ measurements were used and these include radiosonde, pilot-balloon wind, SYNOP, ship and aircraft measurements. In addition radiances from the AMSU-A, AMSU-B/MHS and IASI instruments onboard polar-orbiting satellites, as well as surface winds from the Advanced Scatterometer (ASCAT) instrument, were used. Furthermore, humidity observations from networks of ground-based weather radars and GNSS receiver stations were used. The radar reflectivity is not directly assimilated into the model since there is a complicated, non-linear relationship between the model variables and reflectivity. This includes parameterizations of microphysical processes and non-Gaussian error distributions. Instead a vertical moisture profile is retrieved through a one-dimensional (1-D) Bayesian retrieval based on a comparison between observed and simulated reflectivities . Observations used were obtained from the Global Telecommunications System (GTS), the EUMETSAT Advanced Retransmission Service (EARS), the advanced weather radar network for the Baltic Sea Region (BALTRAD) data hub and the E-GVAP retransmission service.

The surface data assimilation uses an optimal interpolation scheme . In the current study a 3-D variational upper-air data assimilation (3D-Var) scheme was applied within a 3 h data assimilation cycle. The climatological background error statistics used in the current study were derived from an ensemble of MetCoOp forecast differences obtained through downscaling of the forecast fields based on the ECMWF ensemble data assimilation (EDA). The ECMWF EDA-based forecast fields were horizontally and vertically interpolated to the HARMONIE AROME 2.5 configuration geometry and used as initial conditions for high-resolution non-hydrostatic model runs. The ECMWF EDA uses T399 horizontal resolution and 91 vertical levels. Then the evolved high-resolution ensemble was scaled to be consistent with the amplitude of the 3 h forecast error for HARMONIE-AROME. The values applied correspond roughly to a GNSS ZTD background error standard deviation. Recently ECMWF have increased the horizontal resolution of the EDA system to T639 and demonstrated clear improvements from this change of resolution . One could expect that re-derivation of the MetCoOp forecast differences utilizing the enhanced ECMWF EDA system would lead to improved MetCoOp background error statistics and thus an improved data assimilation system. We have therefore re-calculated the background error statistics utilizing the enhanced ECMWF EDA system and carried out sensitivity experiments with the new background error statistics. Results are presented in Sect.  as an example of how GNSS ZTD data assimilation can gain from more general data assimilation improvements. The background error statistics are specified for assimilation control variables. These are vorticity, unbalanced divergence, unbalanced temperature, unbalanced surface pressure and unbalanced specific humidity . Important upper-air data assimilation observation-handling components are the modelling of observation counterparts with an observation operator, quality control mechanism, thinning, bias correction and error specification. The observation operator projects the model state onto the GNSS ZTD observation. Since a variational framework is used, non-linear and the corresponding tangent-linear and adjoint versions of the observation operator are needed. The ZTD observation operator (H), given a station location (including altitude), calculates the model equivalent of the GNSS ZTD by integrating the model-calculated refractivity vertically from the station height to the model top, as described in . In the MetCoOp system, following the ideas of , we have extended the observation operator with the possibility of accounting for the contribution to the ZTD by the part of the atmosphere above the model top. Details of the observation handling within the data assimilation with emphasis on GNSS ZTD are given in .

The GNSS ZTD observation errors of the observations accepted for the data assimilation were assumed to have a Gaussian error distribution with an observation error standard deviation of 12 mm. This observation error standard deviation was derived from observation minus background and observation minus analysis departures, and it was empirically adjusted so that roughly the same weight was given to the observation and to the background. Objective methods such as the one proposed by could in future be tried instead to tune the observation error variance.

There is also an additional quality control mechanism within the assimilation. The purpose of this quality control mechanism is to remove observations affected by gross errors and a central part is the background check. The observation, yi, is rejected if it does not satisfy the following inequality:

[H(xb)]i-yi2/σb,i2>L×λ, where λ=1+σo,i2/σb,i2, L is the rejection limit and [H(xb)]i denotes the projection of the model state on observation i. In the background guess check, the background and observation error standard deviation were set to 10 and 12 mm, consistent with the values used in 3D-Var. The rejection limit for GNSS ZTD observations in the HARMONIE system was set to 4. This value resulted in a relatively strict background quality control mechanism of GNSS ZTD observations.

To alleviate the effects on the initial state of spatially correlated observation errors caused by, for example, orographic effects, we applied spatial thinning to GNSS ZTD observations. The default thinning distance was on the order of 80–100 km. The thinning distance was used when selection receiver stations so that receiver stations closer than 80–100 km to each other were not used. This thinning distance was also rather empirically determined. The thinning is applied in the form of a static whitelist based on studies of data availability and statistics of observation minus background equivalent statistics from a spin-up period. Thus the thinning is static so that each data assimilation cycle of observations from the same set of GNSS ZTD receiver stations is used. A study of the sensitivity of reducing the thinning distance can be found in Sect. . A next step would be to apply objective methods such as the one proposed by ; instead of tuning the thinning distance, the observation error covariance could be modelled.

Systematic errors in the GNSS ZTD data were handled by an adaptive variational bias correction (VarBC). Within VarBC the bias was represented by coefficients for the selected predictors. These predictors were estimated within the variational data assimilation process simultaneously as deriving the assimilation control vector for the model state while minimizing the cost function . The bias correction was carried out individually for each receiver station and in the default version only one predictor, in the form of an offset value, was used. However, there is also the possibility of introducing more predictors, like 1000–300 hPa thickness and TCWV. The sensitivity to introducing extra predictors is investigated in Sect. .

In order to investigate the potential benefit in the MetCoOp system of utilizing NGAA GNSS ZTD, a number of parallel data assimilation and forecast experiments have been carried out. Furthermore the parallel experiments were aimed at investigating the sensitivity of the GNSS ZTD data assimilation to various aspects of the data assimilation. A copy of the MetCoOp operational configuration was run with a 3 h data assimilation cycle for the period 1–30 June 2016 and with a 1-month spin-up period before that. This particular month was chosen because it was characterized by several heavy precipitation events. We expect that additional moisture-related observations should be particularly beneficial for prediction of such weather conditions. We ran short-range forecasts every 3 h to provide the background for the next analysis, and we launched forecasts of up to 36 h, four times per day, from 00:00, 06:00, 12:00 and 18:00 UTC. In total there were four data assimilation studies (A–D), each involving two or more parallel data assimilation experiments. These parallel experiments are explained as follows:

A 

Assessing the impact of assimilating GNSS ZTD from the NGAA processing centre.

B 

Assessing the impact of different VarBC predictor choices.

C 

Assessing the impact of modifying thinning distances for GNSS ZTD.

D 

Assessing the potential benefit of general data assimilation improvements on GNSS ZTD utilization for NWP.

The MetCoOp model domain and the GNSS ZTD observation usage in the operational set-up and in the NGAA ZTD observation usage when applying different thinning distances are illustrated in Fig. , where the left panel shows experiment A1, the middle panel A2 (and A3, B1, B2, B3, C1, D1, D2) and the right panel shows experiment C2. Note that in all experiments of studies A, C, and D only one predictor in the form of an offset value was used. In all experiments in studies B and D a 100 km thinning distance was used. All experiments in studies A, B and C used the operationally used B matrix and all experiments in studies B, C and D used the NGA1 data set, processed with the Bernese approach.

The processing of GNSS ZTD data from the newly vitalized NGAA processing centre has been described in detail. It is shown that these data have the capability to enhance the NWP forecasts, in particular for humidity, when introduced, in addition to other observations, in the HARMONIE-AROME model. The sensitivity of the forecasts to the two solutions provided for estimating ZTD and to the various settings in the GNSS ZTD data processing has been investigated. The two different methods of estimating ZTD generated very similar results and the impact on the forecasts was therefore also very small. It was also found that the results were rather insensitive to the number of predictors used in the variational bias control. In this study only two predictors were tested at the same time. It might be useful as a next step to test more than two and other parameters, e.g. surface pressure. In contrast to the small impact from the VarBC predictors, the results were rather sensitive to the choice of thinning distance applied. There are potential improvements from reducing the thinning distance of the ZTD observations to make use of more data, but there are also related issues. Reducing the thinning distance resulted in increased humidity forecast biases in the lower troposphere. This may have been due to increased influence from correlation errors; this needs to be investigated further to find the best trade-off between the number of observations and the influences of error correlations. In general the horizontal observation error correlations need to be investigated further, for example by applying techniques proposed by and by taking spatial error correlations into account.

The assimilation of GNSS ZTD in NWP can benefit from more general data assimilation improvements, such as enhanced description of statistical information or improved data assimilation algorithms. In this paper this was highlighted by providing an example in the form of an additional run carried out with what we think is an enhanced description of the background error statistics. Clearly the enhanced description resulted in better use of the GNSS ZTD observations in the NWP system. It is important, however, to keep in mind that such general data assimilation aspects influence not only the GNSS ZTD observation usage but also all other observations. In addition, further developments of the data assimilation algorithms, e.g. the impact on utilization of GNSS ZTD observation in a 4-D variational data assimilation, will be investigated.