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Keywords:

  • data assimilation;
  • humidity analysis;
  • limited-area modelling;
  • numerical weather prediction

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

Ground-based receiver networks of the Global Positioning System (GPS) provide observations of atmospheric water vapour with a high temporal and horizontal resolution. Variational data assimilation allows researchers to make use of zenith total delay (ZTD) observations, which comprise the atmospheric effects on microwave signal propagation. An observing-system experiment (OSE) is performed to demonstrate the impact of GPS ZTD observations on the output of the High Resolution Limited Area Model (HIRLAM). The GPS ZTD observations for the OSE are provided by the EUMETNET GPS Water Vapour Programme, and they are assimilated using three-dimensional variational data assimilation (3D-Var).

The OSE covers a five-week period during the late summer of 2008. In parallel with GPS ZTD data assimilation in the regular mode, the impact of a static bias-correction algorithm for the GPS ZTD data is also assessed.

Assimilation of GPS ZTD data, without bias correction of any kind, results in a systematic increase in the forecast water-vapour content, temperature and tropospheric relative topography. A slightly positive impact is shown in terms of decreased forecast-error standard deviation of lower and middle tropospheric humidity and lower tropospheric geopotential height. Moreover, verification of categorical forecasts of 12 h accumulated precipitation shows a positive impact. The application of the static bias-correction scheme is positively verified in the case of the mean forecast error of lower tropospheric humidity and when relatively high precipitation accumulations are considered. Copyright © 2010 Royal Meteorological Society


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

Ground-based receiver networks of the Global Positioning System (GPS) provide a continuous data flow for geodetic and geophysical research and applications. One such application, called ground-based GPS meteorology, provides information on atmospheric water vapour. This information is a by-product of geodetic data processing and it is obtained in the form of vertically integrated atmospheric refractivity (zenith total delay, hereafter ZTD: (Bevis, et al.1992; Elgered, et al.2005)). It is possible to estimate ZTD at each receiver station with a temporal resolution of the order of a few minutes. These observations are nowadays assimilated in operational numerical weather prediction (NWP) systems at several meteorological institutes (Poli, et al.2007; Yan, et al.2009). The new observation type is considered welcome by the meteorological community, because of the limitations of traditional observing systems for atmospheric water vapour. In particular, as operational NWP approaches meso and convective scales, the need for high-resolution observations is increasingly evident.

A number of studies concentrating on meteorological GPS data assimilation have been reported in the scientific literature. Some of the data-assimilation experiments have been carried out with GPS-derived estimates of precipitable water (PW) (Kuo, et al.1996; Guo, et al.2000; Pacione, et al.2001; Falvey and Beavan 2002). The GPS-derived PW has a direct meteorological interpretation and it can be easily intercompared with other observation types. Moreover, PW observations have the potential for production of PW maps for operational applications and nowcasting. From a data assimilation point of view, the usability of GPS-derived PW is, however, decreased by the assumptions that one needs to make about the vertical profiles of temperature and water vapour. Due to these assumptions, the observation-error characteristics become complicated and the data-assimilation scheme may not reach statistical optimality.

The possibility of a more straightforward method for making use of the GPS data in NWP is provided by ZTD observations. Retrieval of ZTD from geodetic GPS data processing makes use of fewer assumptions than the retrieval of PW; in fact, the retrieval of PW from GPS measurements requires the estimation of ZTD as an intermediate step. Therefore, significant attention has been placed on the data assimilation of ZTD observations, instead of PW, during the past decade (De Pondeca; Gustafsson 2002; Vedel and Huang 2004; Poli, et al.2007; Macpherson, et al.2008; Yan, et al.2009). These studies differ from each other in terms of NWP system implementation, grid spacing, domain size and experiment time period. In general, indications of a slightly positive impact on numerical forecasts are reported, in particular for forecasts of heavy precipitation in case studies. The impact on standard long-term verification scores is usually less pronounced.

The ZTD estimates are nowadays produced in an additional pre-processing step prior to meteorological data assimilation. In Europe, the production of ZTD in near-real-time (NRT) is coordinated by the EUMETNET GPS Water Vapour Programme (E-GVAP: see http://egvap.dmi.dk for details of the E-GVAP programme). There are several geodetic analysis centres that take care of the pre-processing of the raw GPS data in an operational sense, and each analysis centre is responsible for providing ZTD for a subset of all available receiver stations. The estimated ZTD for a number of receiver stations is obtained as a solution to a single geodetic network problem at each analysis centre. Owing to the characteristics of the GPS ZTD observing system, the ZTD observations cannot be considered independent from each other and spatial observation-error correlations may exist (Jarlemark, et al.2001; Stoew, et al.2001; Eresmaa and Järvinen 2005). To our knowledge, no observing-system experiment (OSE) has been conducted with the ZTD data with an attempt to account explicitly for the spatial observation-error correlation. Instead, the OSEs have been based on the assumption of negligible observation-error correlations. In order to justify this assumption, horizontal thinning of the ZTD data is applied in some studies (Macpherson, et al.2008; Yan, et al.2009).

Receiver-station-dependent observation biases have been reported to characterize the GPS ZTD observing system (Gustafsson 2002; Poli, et al.2007). The source of the biases is unknown, and the role of geodetic pre-processing cannot be excluded. In most impact studies, the ZTD observation biases are corrected by relatively simple algorithms, such as using a three- or ten-day running mean of ZTD observation minus background as an estimate of the bias at each receiver station (Gustafsson 2002; Macpherson, et al.2008), or applying a static bias correction at each receiver station (Poli, et al.2007; Yan, et al.2009). Air-mass-dependent bias-correction algorithms have also been tested (R. Randriamampianina, personal communication).

This article reports an OSE that has been conducted with the GPS ZTD data in the framework of the High Resolution Limited Area Model (HIRLAM: (Undén, et al.2002)) using the three-dimensional variational data-assimilation scheme (3D-Var: (Gustafsson, et al.2001; Lindskog, et al.2001)). The implementation of GPS ZTD data assimilation in HIRLAM 3D-Var has recently been improved by several technical corrections, which result in improved diagnostic measures of data-assimilation performance. Two different set-ups of the GPS ZTD data assimilation are investigated; these aim to assess the forecast impact of ZTD data assimilation with and without attempting to correct for observation biases.

The article is structured as follows. The HIRLAM NWP system framework is described in section 2, followed by a discussion on the characteristics of the GPS ZTD observing system in section 3. The OSE set-up is outlined in section 4. The results of the OSE are presented in section 5. Finally, our conclusions are summarized in section 6.

2. The HIRLAM framework

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

The HIRLAM NWP system is maintained and developed as a cooperative effort of the national meteorological institutes of nine European countries, and it provides guidance for short-range operational weather forecasting. The operational set-up of the HIRLAM system differs from one country to another. In most countries there are at least two operational implementations which aim to describe both synoptic-scale and mesoscale atmospheric motions.

Meteorological observations are assimilated into the HIRLAM system using either three- or four-dimensional variational data assimilation 3D- and 4D-Var: Gustafsson, et al. (2001), Lindskog, et al. (2001). Assimilation of a wide range of observational data is under development. In addition to the conventional observation types (surface pressure at synoptic stations, ships and drifting buoys, radiosonde observations of wind, temperature and humidity, aircraft observations of temperature and wind and pilot-balloon wind reports), the most advanced operational HIRLAM 4D-Var systems make use of microwave radiance data (the Advanced Microwave Sounding Unit A, hereafter AMSU-A) from polar-orbiting satellites as well as atmospheric motion vectors derived from the Meteosat geostationary satellite data. The assimilation of remote-sensing data is expected to be enhanced in the near future by the inclusion of ground-based radar radial wind data and GPS ZTD observations, as well as by widening the use of satellite radiance data in both microwave and infrared regimes and by inclusion of scatterometers.

3. GPS ZTD observing system

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

ZTD is a vertically integrated measure of atmospheric humidity. As outlined by et al. (1992) and et al. (2005), ZTD consists of the zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD), which are linked with surface pressure and integrated water vapour (IWV), respectively, through

  • equation image(1)

and

  • equation image(2)

where Rd and Rw are the gas constants for dry air and water vapour, respectively, pr is the atmospheric pressure at the GPS antenna height, g* is the gravity acceleration at the centre of mass of the atmospheric column, k1, k2 and k3 are empirical refractivity coefficients and Tm is the water-vapour-weighted mean temperature of the atmospheric column. Determination of the empirical coefficients is reviewed by et al. (1994) and et al. (2005). Despite the fact that ZHD dominates over ZWD in the computation of ZTD, it is the effect of IWV on ZWD that makes the ZTD observations potentially valuable for NWP applications. This is mainly because the weather observing systems provide a very accurate description of the surface pressure.

Equations (1) and (2) constitute the basis for the GPS ZTD observation operator that is applied in the HIRLAM 3D-Var system (Gustafsson 2002; Vedel and Huang 2004).

ZTD is measured in units of length, thus expressing the excess path length that is introduced by the neutral atmospheric medium to the microwave signal propagation. In addition to this effect, the atmospheric effect consists of the ionospheric refraction, which is dispersive and can be almost completely eliminated in data processing as long as dual-frequency measurements are available. A typical value of ZTD is around 2.5 m at mean sea level, and the contribution of ZWD is usually between 10 and 50 cm. As indicated by Eq. (2), the conversion factor from IWV to ZWD is a function of Tm and therefore differs from case to case, but is usually of the order of 0.006 m3 kg−1. Note that IWV is given in units of kg m−2.

The total number of receiver stations in NRT processing in Europe has been increasing rather uniformly during the past decade. Figure 1 illustrates the status of the ground-based GPS observing network, consisting of 976 receiver stations, in August 2008. The overall distribution of the receiver stations is fairly inhomogeneous, and there are large variations between the receiver-station numbers in different countries. Moreover, since the details of geodetic pre-processing differ from one analysis centre to another in terms of e.g. network sizes and densities, data-processing software and processing methods, the ZTD estimates that are processed at different analysis centres are not necessarily consistent with each other. This aspect sets an additional complication for the assimilation of GPS ZTD data in Europe.

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Figure 1. Positions of the ground-based GPS receiver stations providing data for near-real-time processing in Europe in August 2008. Dots indicate those receiver stations that are included in the observing-system experiment (OSE). Circles indicate those receiver stations that are not included in the OSE. A rectangle indicates the OSE domain.

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4. Experimental set-up

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

4.1. Experiment period and NWP system domain

The OSE described in this article covers the five-week period 28 July– 31 August 2008. The period is characterized by continuous convective activity in western and northern Europe. The applied domain of the HIRLAM NWP system is shown in Figure 1 together with the GPS receiver stations from which the ZTD data are assimilated in the OSE (dots). Data from the receiver stations shown by circles in Figure 1 are not assimilated in this study. Over this domain a horizontal grid spacing of 11 km at 60 levels spanning the troposphere and stratosphere up to a pressure level of 10 hPa is applied.

4.2. Observation selection

As discussed in section 3, there is an additional complication in the data assimilation of GPS ZTD data in Europe, which is due to the distributed pre-processing of raw GPS measurement data and differing pre-processing practices at different geodetic analysis centres. One possible solution to mitigate this problem of inconsistency is to limit the data usage to ZTD data that are pre-processed at one geodetic analysis centre only. The drawback of this solution is that the number of ZTD data entering into the data assimilation is considerably reduced, and the geographical distribution of the assimilated data becomes more inhomogeneous. Therefore, ZTD data from more than one geodetic analysis centre are made use of in this study.

In order to minimize the effects of inconsistency and, at the same time, to maximize the number of receiver stations entering the data assimilation, the analysis centres to be used here are chosen on the basis of their productivity during the OSE time period, as evaluated in terms of the number of receiver stations involved in NRT processing. Large variations are found between the productivities of different analysis centres. The most productive ones include the UK Met Office (METO; 276 receiver stations), the Nordic GNSS data analysis centre (NGAA; 262 stations), the German Research Centre for Geosciences (GFZ; 185 stations), the French Institute of Geography (SGN; 181 stations) and the Royal Observatory of Belgium (ROB; 174 stations). The remaining six analysis centres each process data from fewer than 100 receiver stations (the National Geographical Institute of Spain (IGE) processes data for 155 receiver stations, but only a few of these receiver stations are located within the OSE domain). On the basis of these numbers, the five most productive analysis centres are chosen for the OSE described here. This choice is believed to provide a reasonable compromise between observation usage and the internal consistency of the observing system. The applied strategy results in a total of 651 unique receiver stations in the OSE.

4.3. Observation quality assessment

A three-week monitoring period (7– 27 July 2008) prior to the OSE period is applied for monitoring of the ZTD data quality. The ZTD observations are monitored with respect to operational six-hour HIRLAM forecasts. The results of the monitoring period are used for tuning of the background quality control (BgQC) and for specification of the ZTD observation-error standard deviations and bias corrections.

The monitoring makes use of forecast ZTD, which is computed by applying the ZTD observation operator to model profiles that are interpolated to the observation location. Figure 2 shows an example of the observation minus forecast (OmF) ZTD statistics in terms of a frequency distribution (solid line) for the geodetic analysis centre NGAA. The dashed line shows a Gaussian fit to the data. The OmF departure follows the Gaussian fit roughly within the interval (−0.035 m, 0.055 m). This interval corresponds to three standard deviations on both sides of the mean, and is used as the basis for BgQC. Outside this interval, the number of OmF data is larger than expected on the basis of the Gaussian fit, and these data are rejected by the BgQC due to likely contamination from gross errors.

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Figure 2. Frequency distribution (solid line) of ZTD observations minus ZTD computed from operational six-hour forecasts for the Nordic GNSS data analysis centre. The dashed line shows the Gaussian fit to the data.

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The maximum of the frequency distribution in Figure 2 is roughly at 0.01 m, indicating that on average the observed ZTD is higher than the forecast ZTD. This is a relatively large value for the bias. Figure 3 gives a closer look at the mean OmF -departures at each receiver station. The biases are most prominent in the data processed by NGAA and ROB, but appear also to be non-negligible in the data processed by GFZ. Moreover, the biases are highly receiver-station-dependent. Overall, the structure of the bias depends strongly on the data provider. This suggests that the mean OmF departure is primarily affected by biased observations, and only to a lesser extent by biased NWP forecasts. Application of a bias-correction algorithm is therefore probably necessary in the assimilation of GPS ZTD data. Nevertheless, one of the components of the OSE described here is constituted by a reference run where ZTD is assimilated without attempting to correct for observation biases.

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Figure 3. Mean observation minus forecast ZTD at different GPS receiver stations for processing centres (a) GFZ, (b) METO, (c) NGAA, (d) ROB and (e) SGN during the monitoring period (7– 27 July 2008).

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4.4. Performed NWP model runs

The OSE consists of three runs with the HIRLAM NWP system, the first run being the control run (hereafter CNTL) in which no GPS data are assimilated. Data assimilation is carried out every sixth hour, and a deterministic 48 h forecast is produced at each forecast cycle. The time step in the semi-Lagrangian integration is 225 s. A warming-up period of ten days (18– 27 July 2008) is allowed for the analysis– forecast system prior to the actual experiment time period. The warming-up period consists of data assimilation and a deterministic nine-hour forecast with six-hour cycling. CNTL makes use of release 7.1.4 of the HIRLAM system. This implies the following set-up for CNTL.

  • (1)
    3D-Var data assimilation is applied in the analysis. The option of First Guess at Appropriate Time (FGAT) is used. The background-error covariances that are originally derived for the operational HIRLAM NWP system are applied. These covariances are derived using the NMC method with 24 and 48 h operational forecasts.
  • (2)
    Only conventional observation types, as listed in section 2, are assimilated.
  • (3)
    Adigital filter method is used for initialization.
  • (4)
    Physical parametrizations make use of the STRACO scheme for condensation (Sundqvist, et al.1989), the ISBA scheme for surface– atmosphere interaction (Noilhan and Mahfouf 1996) and the Savijärvi scheme for radiation (Savijärvi 1990). A prognostic scheme for atmospheric turbulence is applied (Cuxart, et al.2000).
  • (5)
    The operational strategy is followed for the lateral boundary condition. This implies retrieval of the boundary fields from the global operational forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF).

It is acknowledged that assimilating only conventional observation types means that the OSE is performed using a potentially degraded forecast system. In principle, the HIRLAM context allows assimilation of a wide range of satellite-based observations. However, only a few satellite-based observation types have so far reached operational status in HIRLAM: such observation types include AMSU-A radiance data over open sea and atmospheric motion vectors from geostationary satellites, but the observation counts within the NWP system domain are typically small. Therefore, there is no clear evidence of a significantly positive impact from the assimilation of satellite data in HIRLAM (Amstrup 2003). Moreover, given the lack of practical experience of satellite data assimilation at the Finnish Meteorological Institute (FMI), it is here considered appropriate to refrain from using satellite data in this OSE.

In addition to CNTL, two runs assimilating the GPS ZTD data are performed as follows.

  • (1)
    Firstly, a regular GPS run (hereafter RGPS) is performed for reference by assimilating the GPS ZTD observations without applying observation bias correction. At this point, the ZTD observation errors are assumed to be Gaussian with a zero mean (despite the fact that this assumption is probably wrong, as suggested by Figures 2 and 3). Processing-centre-dependent standard deviations of 10 mm (GFZ and METO), 11 mm (SGN) and 15 mm (NGAA and ROB) are used for the ZTD observation error. The ZTD background-error standard deviation is assumed to be 9 mm in BgQC (Eresmaa and Järvinen 2005). On average, ca. 530 (out of ca. 560 available) ZTD observations pass BgQC and are assimilated in each cycle.
  • (2)
    Secondly, a bias-corrected GPS run (hereafter BGPS) is performed. The GPS ZTD observations are assimilated after applying a static bias-correction algorithm for the data. The observation biases are estimated as mean OmF, separately for each receiver station. Data from the three-week monitoring period are used for the determination of the biases, and these are not updated during the experiment. The estimated biases at each GPS receiver station are shown in Figure 3. The biases vary roughly between − 15 and 35 mm at different processing centres. On average, ca. 510 (out of ca. 560 available) ZTD observations are assimilated in each cycle.

It should be noted that the mean number of observations screened out by the BgQC is larger in BGPS than in RGPS. We believe this is related to the application of a static bias-correction scheme. It is thus possible that the applied bias correction is sometimes a poorer estimate of the real bias compared with the zero-bias assumption that is applied in RGPS.

5. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

In this OSE study, the model runs are verified against observations only. The verification is carried out using GPS ZTD data, radiosonde data at standard pressure levels and surface-precipitation data.

5.1. Impact on GPS ZTD forward modelling

Figure 4 shows the mean and standard deviation of observed minus forecast GPS ZTD for CNTL and RGPS for forecast lead times of 0, 3, 6 and 9 h. The verification applies the same GPS ZTD data set that is assimilated in RGPS and BGPS. At 0 h lead time (analysis), both bias and standard deviation are smaller for RGPS than for CNTL, i.e. RGPS is much closer to the ZTD observations than CNTL. This indicates that the GPS ZTD data influence the data assimilation and make the analysis fit closer to the observations. As the forecast lead time increases, the difference between the statistics of the two model runs decreases, but remains clear during the first nine forecast hours. We conclude that the data assimilation of GPS ZTD observations improves ZTD forward modelling.

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Figure 4. Mean (lower curves) and standard deviation (upper curves) of observed minus forecast ZTD as a function of forecast lead time for CNTL (solid lines) and RGPS (dashed lines).

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5.2. Impact on atmospheric analysis and forecasts

5.2.1. Impact on mean analysis and forecast error

Vertical profiles of the mean forecast error of atmospheric parameters are shown in Figure 5 for CNTL, RGPS and BGPS. Forecast error is here defined as the difference between forecast and radiosonde observation. Each panel consists of two parts, such that the left-hand side shows the scores for analyses while the right-hand side shows the scores for 12 h forecasts. Scores for RGPS (dashed line) and BGPS (dash– dotted line) are given relative to CNTL (thick solid line) to highlight differences between the runs. As RGPS includes no attempt to correct for ZTD observation biases, major differences can be pointed out between RGPS and CNTL. The differences between BGPS and CNTL are mainly smaller. In RGPS, the impact of GPS data is to increase both specific and relative humidity (Figure 5(a) and (b), respectively) in the whole of troposphere. The systematic impact is largest in the lower troposphere, which follows from the specification of the humidity background-error standard deviation. There is no similar systematic difference between BGPS and CNTL. In the lower troposphere, the positive humidity bias of CNTL coincides with a negative forecast-error difference of BGPS, implying a positive forecast impact for BGPS. On the other hand, the impact of BGPS appears negative in the middle troposphere.

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Figure 5. Vertical profiles of mean forecast error (i.e. forecast minus radiosonde observation) for (a) specific humidity, (b) relative humidity, (c) temperature and (d) geopotential height for analyses (on the left-hand side of each panel) and 12 h forecasts (on the right-hand side). Solid, dashed and dash– dotted lines refer to CNTL, RGPS and BGPS, respectively, and scores for RGPS and BGPS are given relative to CNTL. The relative forecast errors apply scales on top of each panel.

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In RGPS, there is a systematic impact from GPS data assimilation on temperature and geopotential (Figure 5(c) and (d), respectively) as well. In analyses this impact is marginal, but it becomes evident as the forecast lead time is increased. The vertical structure of the impact is such that the temperature is increased in the whole of the troposphere, in particular at 700 hPa, and geopotential height is increased (decreased) in the upper (lower) troposphere. A potential explanation for this structure is as follows. The contribution of temperature and geopotential increments to the linearized ZTD observation operator is very small. Therefore, the assimilation of ZTD data contributes only a little to the analysis of temperature and geopotential. However, the GPS data assimilation leads to a systematic increase of atmospheric water-vapour content. The response of the NWP system to the increased water-vapour content is to increase both relative humidity and temperature. This ensures that no unphysically high values of relative humidity are reached, and temperature and humidity remain in an approximate balance with each other. Increased temperature implies increased relative topography within the depth of the troposphere, and this is achieved by increasing geopotential near the tropopause while decreasing it near the surface. Overall, assimilating GPS data without bias correction results in a mainly positive impact on mean forecast errors in the upper troposphere, but the impact is negative in the lower troposphere.

5.2.2. Impact on forecast-error standard deviation

Figure 6 shows the impact of RGPS, with respect to CNTL, in terms of scaled forecast-error standard-deviation difference. The difference between the forecast-error standard deviations of RGPS and CNTL is scaled by dividing by the standard deviation of CNTL. The purpose of the scaling is to account for the natural increase of forecast-error standard deviation as a function of increased forecast lead time. Negative values are associated with a positive impact from GPS data assimilation (decreased forecast-error standard deviation). The curves are plotted for forecast lead times of 12 (solid line), 24 (dashed line), 36 (dash– dotted line) and 48 (dotted line) h. Figure 7 shows the same statistics for BGPS.

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Figure 6. Vertical profiles of scaled forecast-error standard deviation difference for (a) specific humidity, (b) relative humidity, (c) temperature and (d) geopotential height forecasts for RGPS. Solid, dashed, dash– dotted and dotted lines refer to 12, 24, 36 and 48 h forecasts, respectively.

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Figure 7. As Figure 6, but for BGPS.

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Overall, the impact of GPS data assimilation appears to be of the level of 1– 3% of the forecast-error standard deviation. Apart from the boundary layer (925 hPa), the impact on humidity-related variables (panels (a) and (b)) is usually positive in the lower troposphere. Moreover, the impact appears to increase as a function of increasing forecast lead time (despite the fact that scaled differences of forecast-error standard deviation are shown). In the case of temperature (panel (c)), the impact is more mixed. The same conclusion holds for geopotential (panel (d)), except for the 48 h forecast in the lower troposphere, where a clear positive impact is found. Comparison between Figures 6 and 7 suggests that the verification scores are slightly better for RGPS than for BGPS. In other words, the impact of GPS data assimilation on forecast-error standard deviation is more positive when observation-bias correction is not applied.

It appears that despite the significant biases, as revealed by the OmF statistics, the impact of GPS data assimilation on atmospheric forecasts is more positive when bias correction is switched off. This suggests that more advanced methods for bias correction are needed. This OSE study applies static site-specific bias corrections, which are not updated during the experiment runs. A more sophisticated approach would either allow updating of the biases using the most recent OmF departure data or rely on air-mass-dependent predictors for the bias correction. The approach based on updating the bias corrections has earlier been applied by Gustafsson (2002) and Macpherson, et al. (2008).

5.3. Impact on surface parameters

Next, the verification scores of categorical forecasts of accumulated precipitation are studied. The precipitation accumulations are measured every 12 h at the synoptic observing stations. The subset of the synoptic observing network that is constituted by the station list of the European Working Group on Limited Area Modelling (EWGLAM) is used. The categorical forecasts are binary forecasts that provide answers to questions such as: ‘Will the 12 h accumulated precipitation exceed a given threshold?’. Any categorical forecast falls into one of four classes depending on whether a particular event was both observed and forecast (hit, H), forecast but not observed (false alarm, FA), observed but not forecast (missed forecast, MF) or neither forecast nor observed (correct no-forecast, CN). As illustrated in Figure 8, for a population of N forecasts, the number of forecasts falling into each class can be given in a 2 × 2 contingency table, which allows further determination of various categorical verification scores. In this OSE study, we make use of four specific scores, which are defined as follows.

  • (1)
    Probability of detection (varies in the range [0,1]),
    • equation image(3)
  • (2)
    False-alarm rate (varies in the range [0,1]),
    • equation image(4)
  • (3)
    True-skill score (varies in the range [−1,1]),
    • equation image(5)
  • (4)
    Equitable-threat score (varies in the range [−3−1,1]),
    • equation image(6)
    where
    • equation image
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Figure 8. Definition of a contingency table.

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Apart from FAR, these verification scores increase with increasing forecast skill.

It would perhaps be better to use precipitation data from shorter accumulation times than 12 h. Unfortunately, most of the SYNOP stations do not provide precipitation accumulations over shorter time intervals. One possibility to investigate shorter accumulation times would rely on the use of ground-based radar measurements, but additional uncertainties and difficulties present in the radar measurement would further complicate the analysis.

Table I shows the constituents of contingency tables, as well as POD, FAR, TSS and ETS, for 12 h forecasts from CNTL, RGPS and BGPS; the scores of the two latter runs are given relative to those of CNTL. The thresholds of precipitation are chosen such that increasing forecast lead time is always associated with decreasing forecast skill. This criterion results in thresholds of 1, 3 and 10 mm being the most relevant ones.

Table I. Constituents of contingency tables and categorical forecast-verification scores for 12 h forecasts of accumulated precipitation.
RunThresholdHFAMFCNPODFARTSSETS
  1. Notes: H, FA, MF, and CN refer to hits, false alarms, missed forecasts and correct no-forecasts, respectively.

  2. Values for RGPS and BGPS are given relative to CNTL, and positive (negative) forecast impacts are highlighted by bold face (italics).

CNTL1 mm1652169842910297.794.507.287.352
RGPS + 16+ 29− 16− 29+.008+.002+.006.000
BGPS − 17− 54+ 17+ 54−.008−.005−.003+.003
CNTL3 mm85693746411819.648.523.126.329
RGPS + 27+ 16− 27− 16+.020−.004+.024+.009
BGPS − 16− 56+ 16+ 56−.012−.011−.001+.003
CNTL10 mm18735724513287.433.656−.223.221
RGPS + 2− 1− 2+ 1+.005−.003+.008+.003
BGPS − 8− 26+ 8+ 26−.019−.007−.011−.002

The contingency table values for 12 h forecasts indicate that the number of hits is approximately the same as the number of false alarms, and the number of missed forecasts is much smaller when the two lowest thresholds are considered. This means that precipitation events are forecast more often than observed, i.e. the forecast system is biased towards producing too much precipitation. This tendency is slightly enhanced when the ZTD data are assimilated in the regular mode (without bias correction), and more effectively reduced when the ZTD observation biases are accounted for. When higher precipitation amounts are considered, the numbers of both false alarms and missed forecasts exceed the numbers of hits. The interpretation of this is that the forecast skill becomes increasingly limited when high precipitation amounts are forecast.

In terms of the verification scores, both RGPS and BGPS fail to provide a clear impact over CNTL at the smallest threshold. The differences between the runs are very small. At a threshold of 3 mm, RGPS provides a small positive impact, as revealed by the increased POD, TSS and ETS, and decreased FAR compared with CNTL. At a threshold of 10 mm, the scores of RGPS are only marginally better than those of CNTL. The verification scores of BGPS are mainly similar to or slightly worse than those of CNTL. It should be noted that while the absolute values of FAR are relatively large (higher than 0.5), there is a potentially important positive impact in BGPS revealed by the decreased FAR.

The verification scores for categorical 18 h forecasts are given in Table II. The impact of GPS data assimilation appears to be less positive for 18 h forecasts than for 12 h forecasts. At a threshold of 10 mm, the verification scores are systematically degraded when GPS data are assimilated. At thresholds of 1 and 3 mm, there is a marginal improvement in TSS and POD in RGPS, but at the same time FAR is degraded. At these smaller thresholds, BGPS shows a mainly neutral impact compared with CNTL.

Table II. As Table I, but for 18 h forecasts.
RunThresholdHFAMFCNPODFARTSSETS
CNTL1 mm1618171849510508.766.515.251.337
RGPS + 25+ 72− 25− 72+.012+.006+.005−.003
BGPS − 6+ 1+ 6− 1−.003+.001−.004−.002
CNTL3 mm83296551012032.620.537.083.310
RGPS + 17+ 58− 17− 58+.013+.009+.003−.003
BGPS − 6− 12+ 6+ 12−.004−.001−.003−.001
CNTL10 mm17035127313545.384.674−.290.198
RGPS − 7− 1+ 7+ 1−.016+.009−.024−.008
BGPS − 3+ 6+ 3− 6−.007+.008−.014−.005

In contrast to the 18 h forecasts, the verification scores of 24 h forecasts (Table III) show a mainly positive impact from GPS data assimilation. In the case of RGPS, there is a clear positive impact at all thresholds. At a threshold of 10 mm, the positive impact is further enhanced when the observation biases are corrected for.

Table III. As Table I, but for 24 h forecasts.
RunThresholdHFAMFCNPODFARTSSETS
CNTL1 mm1589174749910283.761.524.237.328
RGPS + 26− 22− 26+ 22+.012−.007+.020+.010
BGPS − 4− 60+ 4+ 60−.002−.008+.006+.007
CNTL3 mm80399952311793.606.554.051.294
RGPS + 16+ 14− 16− 14+.012−.001+.014+.005
BGPS − 10− 9+ 10+ 9−.008+.001−.008−.003
CNTL10 mm15136328213322.349.706−.357.173
RGPS + 7+ 14− 7− 14+.016−.002+.018+.005
BGPS + 9− 1− 9+ 1+.021−.013+.034+.012

At longer forecast lead times the impact of GPS data is more mixed (not shown). It is noteworthy that the impact of GPS data on forecasts of accumulated precipitation is positive both in 12 and 24 h forecasts, but neutral or negative in 18 h forecasts. This is possibly related to observing practices at the synoptic stations. The accumulated precipitation is observed at 0600 and 1800 UTC each day. This means that those forecasts that are verifiable by observations of accumulated precipitation are either 12 and 24 h forecasts from analyses valid at 0600 and 1800 UTC or 18 h forecasts from analyses valid at 0000 and 1200 UTC. As there are usually much more radiosonde data available for analysis at 0000 and 1200 UTC than at 0600 and 1800 UTC, the GPS data are likely to influence the humidity analysis more at 0600 and 1800 UTC than at 0000 and 1200 UTC. The analyses at 0000 and 1200 UTC are more likely to be dictated by the radiosonde data.

However, the results of the verification against radiosonde data do not really support this hypothesis. All of the radiosonde observations that are used for verification in the previous subsection are made at either 0000 or 1200 UTC. Therefore, given that there is a hypothetical semi-diurnal cycle in the amount by which the GPS ZTD data influence the analysis, RGPS and BGPS should verify relatively better in 06, 18, 30 and 42 h forecasts than in 12, 24, 36 and 48 h forecasts. Such a 12 h cycle is not detected in the standard scores from the radiosonde verification.

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

An OSE with ground-based GPS ZTD observations has been conducted in the HIRLAM 3D-Var framework. The OSE makes use of the GPS ZTD observations as provided by the EUMETNET E-GVAP programme for 651 permanent GPS receiver stations in Europe, in addition to the conventional observation types. No satellite data are included in the OSE. The OSE covers a single five-week period in the late summer of 2008. No other seasons are studied. The experiment period is characterized by continuous convective activity. Three parallel runs are performed to allow evaluation of the impact of GPS ZTD data assimilation under the zero-bias assumption on the one hand and under the influence of static site-specific bias corrections on the other. The verification of the OSE runs is based on GPS ZTD, radiosonde and surface-precipitation observations. The conclusions that are drawn are as follows.

  • (1)
    Assimilation of GPS ZTD data makes the NWP analyses and forecasts approach the GPS ZTD observations and therefore improves the forward modelling of these observations.
  • (2)
    Regular assimilation (i.e. without applying bias correction) of GPS ZTD data systematically increases not only the atmospheric water-vapour content (specific humidity) but also the temperature in the lower and middle troposphere. Furthermore, the impact of GPS ZTD data is to increase (decrease) the upper (lower) tropospheric geopotential heights.
  • (3)
    The impact of GPS ZTD data on forecast-error standard deviations is small. At forecast lead times of 24, 36 and 48 h, a positive impact can be pointed out in the lower and middle tropospheric specific and relative humidity, as well as in the lower tropospheric geopotential height.
  • (4)
    Application of a static scheme for observation-bias correction results in a slightly positive (negative) impact on mean forecast error of lower (middle) tropospheric humidity, when verification is carried out against radiosonde data. The impact on temperature and geopotential height is neutral.
  • (5)
    Verification of categorical forecasts of accumulated precipitation shows a mixed impact from GPS ZTD data assimilation. At 12 and 24 h forecast lead times the impact is slightly positive, but at 18 h forecast lead time it is slightly negative.
  • (6)
    Observation-bias correction with a static algorithm shows a positive impact on top of the regular GPS data assimilation when categorical forecasts of high precipitation amounts (in excess of 10 mm per 12 h) are considered. Decreased FAR suggests a slightly positive impact at smaller precipitation amounts as well.

In summary of the conclusions above, it is found that the impact of GPS ZTD data assimilation in the HIRLAM 3D-Var system is modest. Ongoing activities in the context of the HIRLAM Comprehensive Impact Study (CIS) are aimed at demonstrating the impact from GPS ZTD data in a 4D-Var environment, when some satellite-based observation types are included in the data assimilation. Applying 4D-Var allows the use of approximately six times larger observation counts, as well as improved dynamical response from the GPS ZTD data.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References

Dafe Offiler (UK Met Office) and Henrik Vedel (Danish Meteorological Institute) are acknowledged for assistance in retrieving the GPS ZTD data from the EUMETNET E-GVAP data archive.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The HIRLAM framework
  5. 3. GPS ZTD observing system
  6. 4. Experimental set-up
  7. 5. Results
  8. 6. Conclusions
  9. Acknowledgments
  10. References
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