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  • View in gallery
    Fig. 1.

    Domain extent of COSMO-DE with conventional observations. The circles indicate positions of the surface-based stations. The areas of the circles correspond to the average daily number of single observations of the wind variable per station. The average number of observations per day are 11 851 PROF, 5813 SYNOP, and 1571 TEMP.

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    Fig. 2.

    (a),(b) The horizontal density of assimilated aircraft observations of AMDAR and the full Mode-S EHS set per average day. The color scale in (b) is enhanced by a factor of 10 with respect to (a). (c),(d) The vertical density against longitude. Differences in the low-level distributions are due to highly frequented airports and are overly exaggerated by their color scales. (e),(f) The overall vertical density.

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    Fig. 3.

    Mean RMS () of the ensemble members for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv.

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    Fig. 4.

    Mean () of the ensemble members for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv.

  • View in gallery
    Fig. 5.

    STD of the ensemble and RMS of the ensemble mean for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv. Where data are actively assimilated, the consistency ratio CR is computed using the estimated values of Fig. 9, and is scaled by the respective RMS to fit into the x axes of the plots.

  • View in gallery
    Fig. 6.

    As in Fig. 3, but for experiments NoDA, MAconvTh10, MAconvTh50, and MAconv. A two-colored diamond on a level means that the RMSs of the left experiment are significantly smaller than that of the right experiment.

  • View in gallery
    Fig. 7.

    As in Fig. 5, but for experiments NoDA, MAconvTh10, MAconvTh50, and MAconv.

  • View in gallery
    Fig. 8.

    Forecast RMS of the Mode-S EHS thinning experiments and Aconv, evaluated for the last hour of the 3-h forecast windows from 0900 to 1200 UTC and 2100 to 0000 UTC. A two-colored diamond on a level means that the RMSs of the left experiment are significantly smaller than that of the right experiment. At levels where the RMS of an experiment is smaller than the RMS of NoDA, the difference is always significant and the diamonds are not plotted.

  • View in gallery
    Fig. 9.

    Estimated observation error STD for AMDAR and Mode-S EHS observation spaces; is the initial error standard deviation value used as input for the LETKF for both AMDAR and Mode-S EHS for all experiments.

  • View in gallery
    Fig. 10.

    (a) Adaptive covariance inflation factor, averaged over the experimental period on the pressure levels of the analysis grid. (b) Adaptive localization length scale. (c) Snapshot of the localization length scale at the surface level at 1200 UTC 8 May 2014. The plotted circles are centered on every eighth point of the coarse analysis grid, so the overlap of the local LETKF solutions is denser than in this illustration.

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    Fig. 11.

    Kinetic energy of the difference wind fields from NoDA (along latitudes between 10 and 12 km MSL), scaled by absolute kinetic energy of the NoDA wind field. The upper-air spectra are shown for the experiments (a) Aconv, (b) MAconvTh10, (c) MAconvTh50, and (d) MAconv.

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Assimilation of Mode-S EHS Aircraft Observations in COSMO-KENDA

Heiner LangeHans Ertel Centre for Weather Research, Data Assimilation Branch, Ludwig-Maximilians-Universität München, Munich, Germany

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Tijana JanjićHans Ertel Centre for Weather Research, Data Assimilation Branch, DWD Offenbach, Germany

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Abstract

Aircraft observations of wind and temperature collected by airport surveillance radars [Mode-S Enhanced Surveillance (Mode-S EHS)] were assimilated in the Consortium for Small-Scale Modeling Kilometre-scale Ensemble Data Assimilation (COSMO-KENDA), which couples an ensemble Kalman filter to a 40-member ensemble of the convection permitting COSMO-DE model. The number of observing aircrafts in Mode-S EHS was about 15 times larger than in the AMDAR system. In the comparison of both aircraft observation systems, a similar observation error standard deviation was diagnosed for wind. For temperature, a larger error was diagnosed for Mode-S EHS. With the high density of Mode-S EHS observations, a reduction of temperature and wind error in forecasts of 1 and 3 hours was found mainly in the flight level and less near the surface. The amount of Mode-S EHS data was reduced by random thinning to test the effect of a varying observation density. With the current data assimilation setup, a saturation of the forecast error reduction was apparent when more than 50% of the Mode-S EHS data were assimilated. Forecast kinetic energy spectra indicated that the reduction in error is related to analysis updates on all scales resolved by COSMO-DE.

Denotes Open Access content.

Corresponding author address: Heiner Lange, Meteorological Institute Munich, Theresienstrasse 37, 80333 Munich, Germany. E-mail: heiner.lange@lmu.de

Abstract

Aircraft observations of wind and temperature collected by airport surveillance radars [Mode-S Enhanced Surveillance (Mode-S EHS)] were assimilated in the Consortium for Small-Scale Modeling Kilometre-scale Ensemble Data Assimilation (COSMO-KENDA), which couples an ensemble Kalman filter to a 40-member ensemble of the convection permitting COSMO-DE model. The number of observing aircrafts in Mode-S EHS was about 15 times larger than in the AMDAR system. In the comparison of both aircraft observation systems, a similar observation error standard deviation was diagnosed for wind. For temperature, a larger error was diagnosed for Mode-S EHS. With the high density of Mode-S EHS observations, a reduction of temperature and wind error in forecasts of 1 and 3 hours was found mainly in the flight level and less near the surface. The amount of Mode-S EHS data was reduced by random thinning to test the effect of a varying observation density. With the current data assimilation setup, a saturation of the forecast error reduction was apparent when more than 50% of the Mode-S EHS data were assimilated. Forecast kinetic energy spectra indicated that the reduction in error is related to analysis updates on all scales resolved by COSMO-DE.

Denotes Open Access content.

Corresponding author address: Heiner Lange, Meteorological Institute Munich, Theresienstrasse 37, 80333 Munich, Germany. E-mail: heiner.lange@lmu.de

1. Introduction

For more than two decades, operational numerical weather prediction (NWP) has benefited from aircraft observations. Typically transmitted by the Aircraft Meteorological Data Relay (AMDAR; WMO 2003), the aircraft observations provide the data assimilation (DA) systems with in situ measurements of the important dynamical variables of temperature and wind (Daley 1991). AMDAR data contain vertical profiles near airports and upper-air observations at flight level with cruising altitudes around 10 km above mean sea level (MSL), corresponding to a layer between 200 and 300 hPa.

A new aircraft data source has been introduced in de Haan (2011). It uses airport radars in the surveillance Mode-S to collect traffic control reports of commercial aircrafts from which observations of wind and temperature can be derived. de Haan (2011) has described this dataset of Mode-S Enhanced Surveillance (Mode-S EHS)1 and has found a quality comparable to AMDAR by comparing collocated measurements from the same aircrafts. de Haan and Stoffelen (2012) have assimilated Mode-S EHS observations from Schiphol Airport into the High Resolution Limited Area Model (HIRLAM) using the three-dimensional variational data assimilation (3DVar) algorithm. In the study, HIRLAM is run with a resolution of 10 km and Mode-S observations are assimilated in 3-hourly and 1-hourly intervals. The assimilation of Mode-S data has shown a reduction in wind forecast errors by approximately 5% (de Haan and Stoffelen 2012). Strajnar et al. (2015) also found benefits when assimilating Mode-S observations from a different data source in a limited-area model over Slovenia.

The present study aims to assimilate the Mode-S EHS data with the Kilometre-scale Ensemble Data Assimilation (KENDA) system (Schraff et al. 2016, hereafter SCH), which is being developed at Deutscher Wetterdienst (DWD). KENDA couples a local ensemble transform Kalman filter (LETKF; as in Bishop et al. 2001; Hunt et al. 2007) with a 40-member ensemble of the Consortium for Small-Scale Modeling (COSMO; Baldauf et al. 2011) model in the domain over Germany (COSMO-DE). COSMO-DE is a nonhydrostatic, convection-permitting model that runs operationally with a horizontal resolution of 2.8 km and 50 vertical levels. COSMO-KENDA provides a framework for convective-scale ensemble data assimilation of different observation types and aims to replace the previously used nudging scheme for observed model variables and the latent heat nudging scheme (Stephan et al. 2008).

The present study aims at using the Mode-S EHS aircraft data to improve in particular the estimates of temperature and wind, in order to provide better background forecasts for the assimilation of radar data (Bick et al. 2016). Past studies have assimilated observations from Doppler radars with an ensemble Kalman filter (EnKF) in order to forecast convective systems (e.g., Stensrud et al. 2009). Aksoy et al. (2010) and Stensrud and Gao (2010) stress the important dependence of convective forecasts on correct environmental profiles of wind and temperature, which are usually provided by radiosondes and aircraft observations. In the present study, NWP experiments with and without Mode-S EHS are performed (i.e., by supplementing the previously used AMDAR data or by replacing it). For verification purposes, radiosondes are not assimilated and used as fully independent observations.

Since the large amount of additional aircraft observations is expected to reduce the ensemble spread, it is tested how robust are the alleviating mechanisms of background covariance inflation (Zhang et al. 2004; Li et al. 2009) and adaptive covariance localization (Perianez et al. 2014). Further, estimates of the observation error are made following Desroziers et al. (2005). Thinning experiments are performed that gradually increase the amount of Mode-S EHS data to see whether the assimilation system reaches a point of saturation where no more additional benefit is taken from the observations. Forecasts with lead times up to 3 hours are computed to see how the error reduction of the Mode-S EHS data persists.

Since any error reduction is related to a change of the model state, a quantification of those model state modifications is of interest in this study, particularly with respect to the assimilated data amount. Using OSSEs of a regional EnKF system that assimilate datasets comparable to the present study, Zhang et al. (2006) and Meng and Zhang (2007) have investigated how the difference total energy grows for selected variables with and without data assimilation. They found that for vertical velocity and cloud variables, the growth of difference energy is mainly in the small scales, while for wind and temperature, the growth in difference is dominated by the larger scales. This was done using a localization radius of 900 km. In the present study, adaptive localization length scales of order 100 km are applied. The true state is not known, so a control experiment without data assimilation will be used as the reference state. It will be evaluated which scales of the horizontal kinetic energy are affected by the data assimilation experiments and how quickly the different scales will relax toward the control experiment during the 3-h forecasts.

Section 2 describes the conventional observations in COSMO-KENDA and the properties of the Mode-S EHS aircraft observations. Section 3 briefly introduces the forecast model COSMO-DE, describes how the LETKF and the adaptive algorithms of the DA system are set up, and how the observation errors are estimated. Section 4 describes the experimental period and the different configurations for the assimilation experiments. In section 5, the DA results during the continuous cycling and 3-h forecasts are evaluated. Section 6 discusses the observation error estimates and how the adaptive KENDA settings act when the Mode-S EHS data density is varied. Section 7 discusses the impact of Mode-S EHS data on the kinetic energy spectrum of the forecasts. Section 8 summarizes the results and discusses their implications on forecasts with COSMO-KENDA.

2. Observations

The conventional observations that are currently assimilated in the COSMO-KENDA system consist of surface pressure and 10-m wind observations from surface synoptic stations (SYNOP); upper-air observations of wind, temperature, and humidity from radiosondes (TEMP) and aircrafts; and wind profiler data (PROF). Figure 1 illustrates the amount and spatial distribution of the conventional dataset that is used in the experimental period from 7 to 12 May 2014. Most of the 30 radiosondes provide vertical soundings of wind, temperature, and relative humidity only at 0000 and 1200 UTC, some also at 0600 and 1800 UTC. The six wind profilers continuously sample with intervals between 5 and 30 min. Hourly assimilated surface data from SYNOP stations are located only in such land areas with a surface height below 100 m MSL and on the sea surface, due to a rigorous quality control (SCH). The amount of aircraft measurements of wind and temperature collected in the AMDAR format are illustrated in Fig. 2. While the bulk number of single observations in AMDAR is similar to the profiler category, the horizontal distribution is broader.

Fig. 1.
Fig. 1.

Domain extent of COSMO-DE with conventional observations. The circles indicate positions of the surface-based stations. The areas of the circles correspond to the average daily number of single observations of the wind variable per station. The average number of observations per day are 11 851 PROF, 5813 SYNOP, and 1571 TEMP.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

Fig. 2.
Fig. 2.

(a),(b) The horizontal density of assimilated aircraft observations of AMDAR and the full Mode-S EHS set per average day. The color scale in (b) is enhanced by a factor of 10 with respect to (a). (c),(d) The vertical density against longitude. Differences in the low-level distributions are due to highly frequented airports and are overly exaggerated by their color scales. (e),(f) The overall vertical density.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

de Haan (2011) first presented Mode-S EHS aircraft data as a meteorological observation source. In contrast to the actively submitted AMDAR reports from specially equipped planes, flight control messages of Mode-S EHS are collected by airport radars from all commercial aircrafts within a radius of 270 km every 4–20 s (depending on the purpose of the scanning radars) in the region of Mode-S EHS over Europe and are distributed in a postprocessed quality by the Royal Netherlands Meteorological Institute (KNMI).2 Therefore, this experimental dataset is limited to the range of the collecting airport radars (Fig. 2b). The horizontal extent in the COSMO-DE domain is, therefore, slightly smaller than for AMDAR, but the number of observations is roughly 15 times larger (Figs. 2e,f). The single Mode-S EHS report messages contain information on latitude/longitude, flight level, ground speed, airspeed, track angle, heading angle, and Mach number. As with AMDAR, the horizontal wind observations are derived from the vectors of airspeed with heading angle and ground speed with track angle. The reported Mach number has been computed by the board computer of the aircraft from the in situ temperature and airspeed. Reverting this calculation using the ideal gas law, the observed temperature is regained and bias corrected [see de Haan (2011) and de Haan and Stoffelen (2012) for details], whereas AMDAR reports contain the direct temperature measurement from the airplane thermometer. Relative humidity is not contained in the Mode-S EHS reports. The number of AMDAR reports that contain relative humidity is negligible in the present dataset.

de Haan (2011) further describes the postprocessing that is applied to the Mode-S EHS data (e.g., exclusion of observations with a large roll angle, magnetic heading offset corrections, and bias corrections for different aircraft types). In collocated comparisons with AMDAR data of the same airplane de Haan (2011) finds observation error standard deviations of comparable magnitude for wind and a slightly larger magnitude for the temperature in case of Mode-S EHS.

Along the flight tracks of single planes, the raw Mode-S EHS observations have been averaged in order to meet the criteria of AMDAR (WMO 2003; de Haan and Stoffelen 2012). During the ascending flight phase, the first nine observations are vertically 10 hPa apart and after that they are 50 hPa apart. On the flight level, consecutive observations are 60 s apart, resulting in a distance of approximately 15 km for a typical flight speed of 250 m s−1. In the descending flight phase, observations with p hPa are 50 hPa apart, for p hPa they are 10 hPa apart. The resulting horizontal distribution of Mode-S EHS within the observed region (Fig. 2b) is more homogenous than AMDAR (Fig. 2a), while the latter also contains profiles from airports outside of the Mode-S EHS coverage (Figs. 2c,d). In both AMDAR and Mode-S EHS, the cruising flight level between 200 and 300 hPa is relatively well observed. In middle levels, patterns of ascending and descending aircrafts become visible, which converge toward the locations of the airports, leaving horizontal data gaps in the low levels between 700 and 1000 hPa (Fig. 2). The ratio of flight level data compared to data at p 300 hPa is larger for Mode-S EHS than for AMDAR (Figs. 2e,f). This is because Mode-S EHS also observes a lot of aircrafts that are passing over the COSMO-DE model domain in flight level without ascending or descending. The number of available observations at different times of day depends on the flight activity, which is highest during the daytime between 0600 UTC and 2100 UTC and is lowest at night (de Haan and Stoffelen 2012).

3. Data assimilation with COSMO-KENDA

COSMO-DE (Baldauf et al. 2011) is a nonhydrostatic model, which is run operationally at DWD with a model domain of 461 by 421 grid points horizontally, covering Germany and parts of neighboring countries (Fig. 1). It has a 2.8-km horizontal grid resolution and 50 vertical layers. The data assimilation framework of KENDA has been developed at the DWD for operational use (SCH). It is an ensemble-based data assimilation system that uses the LETKF algorithm (Hunt et al. 2007). This section describes the settings of the KENDA system for the assimilation experiments with COSMO-DE of this study.

a. Local ensemble transform Kalman filter

COSMO-KENDA uses a 40-member ensemble to sample the background error covariance, in which each member i with state consists of the prognostic variables of wind, vertical velocity, temperature, pressure perturbation, specific humidity, and cloud water and ice. The prognostic variables of turbulent kinetic energy, rain, snow, and graupel are excluded from the analysis update (SCH). In this study, an analysis ensemble is computed every full hour using the observations from −1 to 0 h of the analysis time. Observations closer than 0.67° to the lateral boundaries are excluded so that the analysis update is only performed in the inner domain. All observations above 100 hPa are excluded and no analysis update is performed above 100 hPa in order to keep the state close to the model top (20 km, approximately 40 hPa) unchanged between background and analysis.

The LETKF calculations are done on a coarse analysis grid and the analysis weights are interpolated onto the model grid before the ensemble forecasts are started [see Yang et al. (2009) for details]. The coarse analysis grid is horizontally reduced by a factor of 3 with respect to the COSMO-DE model, resulting in a spacing of roughly 8 km (COSMO-DE: 2.8 km), and it has 30 vertical levels (COSMO-DE: 50 levels).

The boundary conditions (BCs) are provided by an LETKF-ensemble of the Icosahedral Nonhydrostatic (ICON) general circulation model (Zängl et al. 2015). This global LETKF system uses a 3-hourly cycle in which observations from surface stations, radiosondes, aircrafts, and satellites are assimilated (Fernandez et al. 2015, manuscript submitted to Mon. Wea. Rev.; SCH), using a localization radius of 1000 km. The ICON forecasts between the analyses of 0000, 0300, 0600, UTC are saved every hour and provide the BCs for the COSMO-DE-ensemble. Since the BCs of 0000, 0300, 0600, UTC are represented by global analyses, they contain information also from observations inside the COSMO-DE domain. Because of the lack of longer global forecasts, the local ensemble forecasts of this study have been limited to the 3 h of lead time between the global analyses to study only the internal error evolution within COSMO-DE.

b. Observation error statistics

The computation of analyses in the LETKF depends on a proper specification of the observation error statistics. Following Desroziers et al. (2005) and Li et al. (2009), the observation error covariance can be estimated from the differences between observations and background in the observation space (“DOB” in the plots) and between observations and analysis in observation space by using , where E denotes the expectation operator; H is the observation operator; and and are the ensemble means of analysis and background, respectively. Before the estimation, the means of and are subtracted to make the estimation unbiased. In COSMO-KENDA, only the diagonal of the estimated is used for the observation error covariance matrix. The cross covariances between different observations are neglected. The variance is estimated offline for every hourly cycle and then averaged over the 5-day period. The observation error standard deviation of the wind observations U and V is estimated from the wind speed . The term is evaluated for 100-hPa-tall bins of pressure height p. For SYNOP, PROF, and AMDAR, the estimates of the observational error statistics have been made in a previous study by SCH using the same approach and are denoted as .

The estimates obtained for Mode-S EHS should indicate the quality of the dataset compared to AMDAR. It will be tested if the estimated observation error standard deviations are the same or similar to the previously estimated values for AMDAR. Note, however, that this technique is based on the innovation statistics of the DA system and cannot replace the external comparison already done in de Haan (2011) for the estimation of the measurement error for Mode-S EHS and AMDAR.

c. Methods of accounting for model and sampling error

The background error covariance derived from the ensemble does not adequately represent the uncertainty of the background field due to sampling and model error. In KENDA, the methods of background covariance inflation, adaptive covariance localization, relaxation-to-prior-perturbation (RTPP), and random surface perturbations are implemented. These methods are briefly introduced here and their effects are presented in section 6.

The RTPP scheme of Zhang et al. (2004) relaxes the analysis ensemble perturbations of the LETKF toward the background ensemble perturbations at every grid point of the model. In KENDA, the relaxation is performed with a factor of , thus, limiting the maximum influence of the analysis to 25% of the maximum change. This helps to keep the analysis ensemble spread alive by acting as an inflation with both multiplicative and additive aspects, albeit in the space spanned by the ensemble only (Zhang et al. 2004; Whitaker and Hamill 2012). Harnisch and Keil (2015) showed its beneficial effects on ensemble forecasts with the COSMO-KENDA system.

Following Li et al. (2009), an adaptive multiplicative covariance inflation with factor ρ is applied separately for every coarse analysis grid point (SCH) and relaxed in time by mixing the current ρ estimate with the estimate of the previous cycle. The variable ρ is larger than 1 where the background ensemble spread in observation space is small in proportion to how much the magnitude of deviates from the specified observation error , expressed by the difference .

In the present KENDA setup based on SCH, the horizontal localization is adaptive to the number of observations in the vicinity of an analysis grid point (Perianez et al. 2014) so that the spatial influence is distributed differently between corresponding scales (Janjić et al. 2011, 2012). The horizontal localization length scale is defined here as the radius where the Gaussian-like covariance function [Eq. (5.1) from Gaspari and Cohn (1999)] goes down to . With lower and upper bounds of 50 and 100 km, is adaptively determined to contain 100 observations, which is 2.5 times the ensemble size of 40. The vertical localization length scale is fixed and ranges from 0.075 ln(p) at the surface to 0.5 ln(p) at the model top.

As described by SCH, the sea surface temperature (SST) and the soil moisture are randomly perturbed in every analysis by adding temporally and spatially correlated perturbation fields in order to enhance the spread near the model surface and in the boundary layer.

4. Experiments with varying aircraft datasets

The experiments of this study were performed from 7 to 12 May 2014. The meteorological situation was a west-wind period with passing cyclones. A warm front passage on 8 May caused stratiform precipitation and a cold front passage on 10 May caused predominantly convective precipitation with embedded thunderstorms and showers. The period was chosen because synoptically and locally forced convection was present and a convection-permitting model such as COSMO-DE is expected to produce more realistic weather systems than its driving global model.

The initial COSMO-DE ensemble, consisting of the downscaled global ICON-LETKF ensemble, is started at 0000 UTC 6 May. One day of cycled data assimilation is performed to spin up COSMO-DE and the time-relaxed adaptive covariance inflation. The resulting analysis ensemble and the covariance inflation field ρ at 0000 UTC 7 May are then used as initial conditions for all other experiments.

Table 1 summarizes the performed experiments for the chosen test period. The monitored observations (mon.) are not assimilated, therefore, their model equivalents are only influenced by the cross correlations calculated by the LETKF by the means of the assimilated observations (denoted by •). The control experiment NoDA is performed without data assimilation. All DA experiments assimilate the selected datasets in an hourly interval. The basic experiment Aconv assimilates conventional (SYNOP, PROF) and AMDAR observations. From Aconv, the Mconv experiment is derived by setting AMDAR to monitoring and assimilating Mode-S EHS. The experiment MAconv assimilates both AMDAR and Mode-S EHS datasets. In MAconvTh10 and MAconvTh50 the Mode-S EHS data are randomly thinned to 10% and 50% of the full density that is used in MAconv. The random thinning makes sure that the spatial and temporal distribution characteristics of the Mode-S EHS observation space are preserved, only with a lower density. The observation error standard deviation , which was preliminarily estimated for AMDAR, is used identically for the assimilation of Mode-S EHS. The observation operator is applied during the model integration of COSMO at the appropriate time of the respective observation. Therefore, the of a 1-h forecast is a collection of innovations along the temporal trajectory. In case of the 3-h forecasts, refers to the observations within the third hour of the forecast window.

Table 1.

Experiments (rows) performed with COSMO-KENDA. Observations with bullet points (•) are assimilated, and observations with “mon.” are monitored. In the case of “• x%,” only a random subset of x percent is assimilated.

Table 1.

The experimental results are evaluated separately in the observation spaces of each upper-air system (TEMP, AMDAR, Mode-S EHS) for wind speed, direction, and temperature. Where the results of the observation systems are qualitatively similar, only the radiosonde space is shown. The root-mean-square (RMS), the mean, and the standard deviation (STD) of are computed at every forecast step for every ensemble member and are averaged over the 5-day period. To test whether the ensemble is underdispersive, for every pressure level the consistency ratio (CR) is computed, which also takes the observation error variance into account, as in SCH:
e1
The CR should ideally be 1. For , the previously defined was used posterior to the experiments.

The profiles of RMS and mean of are tested for significant differences among the experiments. Using the Student’s t test, the null hypothesis that the results were identical shall be rejected on a confidence level of 95%. Since the experiments share the same model and boundary conditions and have a mutual subset of assimilated observations, the forecast errors are correlated among the experiments. Therefore, the t test is performed as a paired difference test in which the number of degrees of freedom n is reduced by half. In case of the 1-hourly cycling, the test is performed using the hourly profiles of RMS and mean of of the single members as the testing sample with n = (5 days × 24 cycles × 40 members) × 2−1 = 4800 × . In the case of the 3-h forecasts, two ensemble sets of profiles per day are tested between the experiments with .

5. Results

The RMS, mean, and STD of in the control experiment NoDA are shown in Figs. 3, 4, and 5, respectively. The wind speed STD of NoDA is largest at 300-hPa height (Figs. 5a,d,g), the largest STD in wind direction is close to the surface (Figs. 5b,e,h), and the largest temperature STD in NoDA is at 250 hPa (Figs. 5c,f,i). In the radiosonde space, a warm bias of the background exists in NoDA above 400 hPa and a cold bias exists around 700 hPa (Fig. 4c).

Fig. 3.
Fig. 3.

Mean RMS () of the ensemble members for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

Fig. 4.
Fig. 4.

Mean () of the ensemble members for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

Fig. 5.
Fig. 5.

STD of the ensemble and RMS of the ensemble mean for upper-air observations of (left) wind speed, (middle) wind direction, and (right) temperature throughout the 1-hourly cycling, for experiments NoDA, Aconv, Mconv, and MAconv. Where data are actively assimilated, the consistency ratio CR is computed using the estimated values of Fig. 9, and is scaled by the respective RMS to fit into the x axes of the plots.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

As a first diagnostic for the observation error, the RMS of NoDA is examined, under the assumption that the model equivalents in the upper-air observation spaces of all three systems are subject to the same forecast error characteristics. For wind speed, the observation systems TEMP, AMDAR, and Mode-S EHS behave similarly (Figs. 3a,d,g), which hints at comparable observation errors. For temperature (Figs. 3c,f,i), the NoDA RMS of Mode-S EHS in lower levels (Fig. 3i) is larger than for the other systems. For wind direction (Figs. 3b,e,h), the NoDA RMS of Mode-S EHS is much smaller. This difference in directional observation error could be a consequence of the heading correction in the postprocessing of Mode-S EHS (de Haan 2011), which is calibrated for different commercial aircraft models. According to WMO (2003), such a correction is not performed for AMDAR.

a. Results with AMDAR and Mode-S EHS observations

The main experiments Aconv, Mconv, and MAconv compare the usage of AMDAR and Mode-S EHS as the only assimilated aircraft observation types (Aconv and Mconv) and the combination of assimilating both (MAconv). In Fig. 3, the significance symbols are omitted because where the RMSs of DOB are reduced by adding additional data, the reductions are significant in all cases.

The RMS in the radiosonde space is continuously reduced with respect to NoDA for wind speed and temperature (Figs. 3a,c) and less so for wind direction (Fig. 3b) when AMDAR and additionally Mode-S EHS data are assimilated in the experiments Aconv and MAconv. Also, the STD is continuously diminished (Figs. 5a–c).

The RMS values of Mconv in AMDAR space and of Aconv in Mode-S EHS space show the influence of the datasets across the two aircraft observation spaces. The RMSs of wind speed (Figs. 3d,g) and temperature (Figs. 3f,i) are reduced across the spaces for Aconv and Mconv, while the cross-space RMSs in wind direction (Figs. 3e,h) are increased for levels below 700 hPa. This might again be a consequence of the heading correction of Mode-S EHS.

In Fig. 5, the ratio of the RMS and the STD give information about the consistency of background error and spread, assuming that the biases in DOB are small enough. The CRs of wind speed and temperature are close to 0.9 or 1 for all experiments, except close to the surface where values around 0.75 are reached.

b. Results with varying Mode-S EHS data coverage

As there are far more Mode-S EHS data than AMDAR data, it is tested how the forecasts depend on the amount of Mode-S EHS observations. In the experiments MAconvTh50 and MAconvTh10, the assimilated portion of the Mode-S EHS observations is randomly thinned to roughly 50% and 10% of the original set.

During the cycling, the wind speed RMS in the radiosondes (Fig. 6a) is significantly reduced going from 10% to 50% for all levels except 700 and 1000 hPa, while an increase from 50% to 100% does not yield benefits. For the wind direction (Fig. 6b), there is no significant RMS reduction when increasing the data amount. For temperature (Fig. 6c), the RMS is decreased going from 10% to 50% and from 10% to 100% for all levels except the surface. At 400 and 300 hPa, an improvement is also visible when going from 50% to 100% of Mode-S EHS. The wind and temperature STD in the radiosonde space is continuously reduced when adding more data (Fig. 7, AMDAR and Mode-S are analogous and not shown), but not in a linear dependence on the data amount.

Fig. 6.
Fig. 6.

As in Fig. 3, but for experiments NoDA, MAconvTh10, MAconvTh50, and MAconv. A two-colored diamond on a level means that the RMSs of the left experiment are significantly smaller than that of the right experiment.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for experiments NoDA, MAconvTh10, MAconvTh50, and MAconv.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

c. Results of the 3-h ensemble forecasts

The daily analysis ensembles at 0900 and 2100 UTC were saved and ensemble forecasts of 3 hours were initialized from all experiments, so that also the radiosondes launched at 1200 and 0000 UTC could be used for the verification. The forecast RMS of (third hour of the 3-h window) is shown in Fig. 8.

Fig. 8.
Fig. 8.

Forecast RMS of the Mode-S EHS thinning experiments and Aconv, evaluated for the last hour of the 3-h forecast windows from 0900 to 1200 UTC and 2100 to 0000 UTC. A two-colored diamond on a level means that the RMSs of the left experiment are significantly smaller than that of the right experiment. At levels where the RMS of an experiment is smaller than the RMS of NoDA, the difference is always significant and the diamonds are not plotted.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

For wind speed, significant reductions in forecast RMS between Aconv and MAconv take place at all levels except the surface. The clearest reduction is visible when using Mode-S EHS for the verification (Fig. 8g). The radiosonde space (Fig. 8a) is positively affected mainly in levels above 500 hPa. For AMDAR, additional Mode-S EHS data of MAconvTh10 and MAconvTh50 is beneficial at 700 hPa (Fig. 8d), which could be due to the shared observation spaces of the aircraft systems (Fig. 2). For wind direction RMS, the radiosonde space verification shows no significant improvement due to Mode-S EHS (Fig. 8b). Still, in AMDAR the wind direction forecast is improved on the flight levels (Fig. 8e), and in the Mode-S EHS space also the 700-hPa level is improved (Fig. 8h). For temperature RMS, an improvement due to additional Mode-S EHS data is visible for all three systems (Figs. 8c,f,i) from 700 to 200 hPa.

The 3-h forecast RMSs are, in some cases, improved by increasing the amount of assimilated Mode-S EHS. The wind speed RMS of MAconv is smaller than both Aconv and MAconvTh10 at 300 (Fig. 8a), 500, and 700 hPa (Fig. 8g). The 700-hPa wind direction is improved within Mode-S EHS going from MAconvTh10 to MAconv (Fig. 8h). For temperature, an improvement from MAconvTh10 to MAconv is visible from 700 to 200 hPa (Figs. 8c,f,i). An improvement from MAconvTh50 to MAconv appears only in the 300-hPa radiosonde wind speed (Fig. 8a). A deterioration of forecast RMS at 500 hPa is apparent in some cases when increasing the data amount from MAconvTh50 to MAconv (Figs. 8c,d,e).

6. Effects of adaptive KENDA settings

The settings used in KENDA affect the representations of both background and analysis error covariances. The specified values of the observation error are discussed first in section 6a. Second, the influence of the methods that account for model and sampling error in KENDA are examined in section 6b.

a. Results of the observation error estimation

The estimated error standard deviation of AMDAR and Mode-S EHS are depicted in Fig. 9 together with the initial error estimate of SCH that was used for the assimilation. The term for wind speed in AMDAR is lower than (Fig. 9a), which can be attributed to a different experimental period and a difference in the driving global ensemble.

Fig. 9.
Fig. 9.

Estimated observation error STD for AMDAR and Mode-S EHS observation spaces; is the initial error standard deviation value used as input for the LETKF for both AMDAR and Mode-S EHS for all experiments.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

The values are similar among the experiments that actively assimilate AMDAR (Aconv, MAconvTh10, MAconv). A lower estimate is reached (Fig. 9a) when Mode-S EHS observations are used that reduce the estimators and also across the AMDAR observation space. The estimated deviation for temperature in AMDAR (Fig. 9b) is close to between 700 and 400 hPa and much smaller in the lower levels.

For the wind speed of Mode-S EHS (Fig. 9c), is, within a range of 10% difference, quantitatively and qualitatively similar to the wind speed of AMDAR (Fig. 9a) in the case of the joint data experiment MAconv. For the Mode-S EHS temperature (Fig. 9d), follows the shape of on all levels and is larger for levels below 700 hPa where it reaches 1.2 K for Mode-S EHS in MAconv, but only 0.8 K for AMDAR in MAconv (Fig. 9b). This difference in low-level temperature errors is qualitatively consistent with the findings of de Haan (2011) and de Haan and Stoffelen (2012), although they diagnosed larger absolute error standard deviations.

The hypothesis that a feedback -input of the values estimated by MAconv (Fig. 9) would give better results during the cycling was tested with an iterated experiment MAconvR1 (not shown), which did not exhibit significant improvements with respect to MAconv.

b. Accounting for model and sampling error

Figure 10a shows the adaptive covariance inflation factor. It is almost continuously larger for experiments with more observations. One maximum lies between 300 and 200 hPa where the high data density of the flight level is situated (Fig. 2). Another maximum is between 700 hPa and the surface. This is caused by a spread deficiency in the lower levels (see CR in Fig. 5). While the adaptive inflation is set to counteract this deficiency, the RTPP factor of 0.75 limits the overall reduction and inflation of spread by the analysis update. As seen in Fig. 10b, the adaptive localization directly depends on the number of observations per level. In the horizontal snapshot of Fig. 10c, highly frequented airports (Amsterdam, the Netherlands; Frankfurt and Berlin, Germany) become visible.

Fig. 10.
Fig. 10.

(a) Adaptive covariance inflation factor, averaged over the experimental period on the pressure levels of the analysis grid. (b) Adaptive localization length scale. (c) Snapshot of the localization length scale at the surface level at 1200 UTC 8 May 2014. The plotted circles are centered on every eighth point of the coarse analysis grid, so the overlap of the local LETKF solutions is denser than in this illustration.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

7. Kinetic energy spectra of 3-h forecasts

One-dimensional kinetic energy spectra are derived from the analysis and forecast ensemble members as in Bierdel et al. (2012). Because of the predominant westerly flow, isotropy is not assumed and the energy spectra are calculated separately in longitudinal and latitudinal directions on levels with a constant height MSL. Since on the flight levels there are significant amounts of AMDAR and Mode-S EHS observations, an average over three heights of 10-, 11-, and 12-km height MSL is chosen for the investigation. The wind field of the ensemble was saved every 15 min throughout the previously mentioned 3-h forecasts and the corresponding spectra were calculated. Figure 11 shows the difference kinetic energy spectrum of Aconv, MAconvTh10, MAconvTh50, and MAconv with respect to the NoDA experiment. To enhance the relative differences, the energy of the difference wind field from the NoDA experiment is scaled by the absolute kinetic energy spectrum of NoDA. The evaluation presumes that during the three forecast hours the BCs are not dominant and the main part of the dynamical evolution is happening within the COSMO-DE domain itself.

Fig. 11.
Fig. 11.

Kinetic energy of the difference wind fields from NoDA (along latitudes between 10 and 12 km MSL), scaled by absolute kinetic energy of the NoDA wind field. The upper-air spectra are shown for the experiments (a) Aconv, (b) MAconvTh10, (c) MAconvTh50, and (d) MAconv.

Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0112.1

Starting from the analyses (forecast minute 0), the largest relative differences are present on the scales below the effective resolution of found for COSMO-DE (Bierdel et al. 2012). Between the wavelengths of 10 and 40 km, there is a level of relatively large difference energy, and above 40 km there is an almost steady drop. Among the series of Figs. 11a–d, the analysis states are subsequently farther away from NoDA when more data are assimilated. With the 10% of Mode-S EHS data in MAconvTh10, the characteristics are similar to Aconv. For MAconvTh50, a significant difference to Aconv becomes visible on all scales.

Throughout the three forecast hours, the relative difference energy on all scales is gradually decreasing, where a value of zero would express a wind field identical to NoDA. In all experiments, the spectrum of the relative forecast difference energy remains similar to the analysis of the respective experiment for up to 1 hour, especially on scales smaller than 200 km. After 1 hour, a drop in relative difference energy with respect to the analysis can be noted on all scales. As a consequence of pulling the states farther away from the attractor of COSMO-DE, the rate of convergence toward NoDA is higher when more data are assimilated. Although the experiments MAconvTh50 and MAconv are almost indistinguishable after 3 hours of forecast with respect to the forecast RMS (Fig. 8), the higher level of the relative spectra at 180 min in MAconv still indicates differences in the wind field. It can be concluded that the usage of 100% Mode-S data causes excessive modifications, possibly in the form of gravity wave noise (Houtekamer and Mitchell 2005), which are more extensive than necessary to actually improve the forecast.

8. Summary and discussion

To evaluate the benefit of additional aircraft in situ observations of wind and temperature that are collected by airport radars (Mode-S EHS), experiments were performed with the COSMO-KENDA system, which couples an LETKF to an ensemble of the nonhydrostatic model COSMO-DE. The Mode-S EHS observations are available within most of the domain of the COSMO-DE model over Germany. The amount of Mode-S EHS observations is 15 times larger than of the traditionally used AMDAR, with a similar observation density distribution. Cycled ensemble data assimilation was performed for a period of 5 days with a cycling interval of 1 h. Mode-S EHS data were assimilated in addition to AMDAR, assuming the same observation error. Using 100% of the Mode-S data improved the upper-air innovation RMSs during the 1-h cycling and in the verification of 3-h ensemble forecasts, in comparison to assimilating only AMDAR aircraft data. A comparable improvement was visible when assimilating 50% of Mode-S EHS instead of none. The 3-h forecasts that were started from the experiment with 100% Mode-S EHS data often had significantly lower errors than from the experiment with 10%. Still, using 100% Mode-S EHS instead of 50% degraded the 3-h forecasts in some cases. It is, therefore, concluded that a saturation of benefit exists between 50% and using 100% of Mode-S EHS.

By using innovation statistics in observation space, the observation error standard deviation of Mode-S EHS was estimated to be comparable to AMDAR in the wind variable. For temperature, the observation error of Mode-S EHS was diagnosed to be 50% larger for levels below 700 hPa. It must be noted that observation error standard deviations obtained by this method depend on the background ensemble spread of the cycling system, so the estimated observation errors can only be regarded as inherently compatible with the present DA system. Still, the current KENDA setting appeared mostly insensitive to slightly wrong prescribed observation errors.

The ensemble spread was generally consistent with the forecast errors, except near the surface due to a deficiency of small-scale error growth (SCH). KENDA contains mechanisms that maintain the ensemble spread, namely the RTPP scheme, adaptive covariance inflation, and adaptive localization. The effects of these methods were evaluated and it was concluded that they enable the assimilation system to use the larger number of aircraft observations without a collapse of the ensemble spread. The spread reduction exhibited a nonproportional dependence on the increasing number of observations. In the future, unified inflation methods such as those presented in Ying and Zhang (2015) could be helpful in further dealing with this issue.

The ability to benefit from a high observation density strongly depends on the RTPP relaxation parameter. With less relaxation toward the background ensemble than the currently used factor of 0.75, the resulting analysis ensemble could contain smaller errors because the observations are given more weight. In future experiments, also a more sophisticated thinning could be applied to reduce the observation density only where it is redundant or where saturation effects are apparent. The high temporal density of Mode-S EHS observations could be exploited in a 15-min cycling interval. An observation system that fills the low-level data gaps between airports could be useful for airport forecasts, especially for warnings of small-scale phenomena such as rapidly evolving gust fronts and downbursts. A wider usage of surface stations than in the present study could supplement the high density of upper-air observations, if provided with proper vertical localization.

Spectra of the difference kinetic energy with respect to a control experiment showed that the LETKF data assimilation affects all model scales. The amount of observation data in the experiments was reflected by the degree of modification of analysis and forecast states. A stronger modification caused a faster relaxation toward the attractor of the control experiment. In further studies, different regimes (dry/wet) or seasons (winter/summer) could be chosen to compare the influence of dense observation sets when error growth is dominated by either synoptic or local processes. The spectral difference energy of temperature and cloud fields could give insight on scale-dependent error growths (Zhang et al. 2007; Selz and Craig 2015).

It is planned to combine the present setup with the assimilation of observation sets with even higher resolutions, such as radial winds and reflectivity of convective systems from Doppler radar, and to verify their influences across the observation spaces [e.g., by using the techniques of Sommer and Weissmann (2014)]. Forecasts with longer lead times than 3 hours should be performed to evaluate if the Mode-S EHS benefit is persistent. A rigorous survey of the imbalances should be performed that are caused by possible overfitting and overly small localization lengths (Lange and Craig 2014), along with a test period longer than 5 days to improve the significance of the results.

Acknowledgments

We thank MUAC-EUROCONTROL and the Mode-S-group at KNMI for processing and providing the Mode-S EHS data, Christoph Schraff for the implementation of the Mode-S EHS input in COSMO, Hendrik Reich for his support of the basic cycling (BaCy) system of COSMO-KENDA, and Alexander Cress and Ana Fernandez for generating and providing the ICON BCs. This study was carried out in the Hans Ertel Centre for Weather Research. This research network of universities, research institutes, and the Deutscher Wetterdienst is funded by the BMVI (Federal Ministry of Transport and Digital Infrastructure). The first author is funded by the BMVI Forschungsvorhaben Nr. 50.0357-2013-L1.

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