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Initial Conditions for Convective-Scale Ensemble Forecasting Provided by Ensemble Data Assimilation FLORIAN HARNISCH Hans-Ertel Centre for Weather Research, Ludwig-Maximilians-Universit€ at, Munich, Germany
CHRISTIAN KEIL Meteorologisches Institut, Ludwig-Maximilians-Universit€ at, Munich, Germany (Manuscript received 23 June 2014, in final form 22 December 2014) ABSTRACT A kilometer-scale ensemble data assimilation system (KENDA) based on a local ensemble transform Kalman filter (LETKF) has been developed for the Consortium for Small-Scale Modeling (COSMO) limited-area model. The data assimilation system provides an analysis ensemble that can be used to initialize ensemble forecasts at a horizontal grid resolution of 2.8 km. Convective-scale ensemble forecasts over Germany using ensemble initial conditions derived by the KENDA system are evaluated and compared to operational forecasts with downscaled initial conditions for a short summer period during June 2012. The choice of the inflation method applied in the LETKF significantly affects the ensemble analysis and forecast. Using a multiplicative background covariance inflation does not produce enough spread in the analysis ensemble leading to a degradation of the ensemble forecasts. Inflating the analysis ensemble instead by either multiplicative analysis covariance inflation or relaxation inflation methods enhances the analysis spread and is able to provide initial conditions that produce more consistent ensemble forecasts. The forecast quality for short forecast lead times up to 3 h is improved, and 21-h forecasts also benefit from the increased spread. Doubling the ensemble size has not only a clear positive impact on the analysis but also on the short-term ensemble forecasts, while a simple representation of model error perturbing parameters of the model physics has only a small impact. Precipitation and surface wind speed ensemble forecasts using the high-resolution KENDA-derived initial conditions are competitive compared to the operationally used downscaled initial conditions.
1. Introduction Ensemble Kalman filters (EnKFs; Evensen 2003) are now widely used for data assimilation and initialization of numerical weather prediction (NWP) models for different applications ranging from the global (e.g., Houtekamer and Mitchell 2005; Szunyogh et al. 2008; Miyoshi et al. 2010) to the regional (e.g., Torn and Hakim 2008; Bonavita et al. 2010) and convective scales (e.g., Zhang et al. 2004; Aksoy et al. 2010). When running an ensemble prediction system (EPS), it is important to correctly sample the sources of forecast
Corresponding author address: Florian Harnisch, Meteorologisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 37, 80333 Munich, Germany. E-mail:
[email protected] DOI: 10.1175/MWR-D-14-00209.1 Ó 2015 American Meteorological Society
uncertainty that originate from the initial conditions and the model formulation. Since high-resolution EPSs are generally computed as limited-area models (LAMs) it is also necessary to consider uncertainty that stems from the lateral boundaries. This is usually accounted for by using an ensemble of lateral boundary conditions (LBCs), which is provided by a driving EPS with coarser resolution. Considering LBC uncertainty is crucial for a LAM EPS (e.g., Saito et al. 2012; Kunii 2014) and, especially for longer forecast lead times of 12 h or more, the LBC uncertainty can dominate over the initial condition uncertainty (e.g., Hohenegger et al. 2008; Kühnlein et al. 2014). An important contribution to the overall forecast error in high-resolution NWP models is the uncertainty related to the model formulation. There are different methods that try to account for model error in EPS
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forecasts at different resolution by using multimodel ensembles (e.g., Clark et al. 2011), multiphysics ensembles (e.g., Bowler et al. 2008; Gebhardt et al. 2011), or stochastic physics ensembles (e.g., Berner et al. 2011; Bouttier et al. 2012). How to represent initial condition uncertainty at the convective scales and to initialize EPSs with horizontal grid resolutions of the order of a few kilometers is still an open question. For coarser-resolution global NWP models, a number of different techniques have been developed and established to account for initial condition uncertainty and model error (e.g., Buizza et al. 2005; Leutbecher and Palmer 2008), but often assumptions made by these methods are not valid at convective scales, due to different predictability, error growth, and nonlinear effects at the higher model resolution (Hohenegger and Schär 2007a,b). However, initial condition perturbations for convective-scale EPS need to be included as they have a positive impact especially for the first few forecast hours, but in addition may also be important for longer forecasts depending on the weather situation (Vié et al. 2011; Kühnlein et al. 2014). A simple, but widely used approach to consider initial condition uncertainty is to downscale information from coarser-resolved NWP models to initialize the highresolution EPS forecast (e.g., Hohenegger et al. 2008; Peralta et al. 2012). In the downscaling approach, initial perturbations mostly affect mesoscale structures, while it is assumed that the model running at high resolution will create the initially missing small-scale perturbations during the forecast integration. The lack of small-scale initial ensemble perturbations may not be important since errors at scales of a few kilometers typically grow rapidly within the first few hours of the forecast and interact with larger mesoscale structures (e.g., Zhang et al. 2003; Hohenegger and Schär 2007a; Selz and Craig 2015). Kühnlein et al. (2014) demonstrated that the use of downscaled initial ensemble perturbations leads to improved results for convective-scale precipitation forecasts. Methods for explicitly perturbing small scales typically involve the generation of initial perturbations either from the ensemble forecasts themselves by applying ensemble transform techniques (e.g., Bishop et al. 2009; Bowler and Mylne 2009) or from running an EnKF data assimilation scheme (e.g., Zhang et al. 2004; Kunii 2014; Schwartz et al. 2014). An experimental kilometer-scale ensemble data assimilation (KENDA) system for the Consortium for Small-Scale Modeling (COSMO) forecast model has been developed at Deutscher Wetterdienst (DWD). KENDA-COSMO applies a local ensemble transform Kalman filter (LETKF; Hunt et al. 2007) to assimilate observations on convective scales [i.e., between 1 and 3 km; Reich et al. (2011); Schraff et al. (2014),
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manuscript submitted to Quart. J. Roy. Meteor. Soc.]. The LETKF data assimilation scheme produces an analysis ensemble, which gives a theoretical estimate of the analysis uncertainty of the COSMO model, and can be used to initialize a forecast ensemble. The impact of using KENDA-COSMO to initialize convective-scale ensemble forecasts is investigated in the present work. The main focus is on applying KENDACOSMO as a tool to provide ensemble initial conditions and performing a conceptual comparison of high-resolution ensemble forecasts using initial conditions derived from KENDA-COSMO and a downscaling method. A set of experiments has been computed to evaluate the influence of various inflation methods used in the LETKF, the ensemble size, and the use of perturbed values in model physics parameterization schemes. The outline of this study is as follows. The current operational convective-scale EPS at DWD, the KENDACOSMO system and the performed experiments are described in section 2. Section 3 evaluates data assimilation statistics and the impact of the LETKF derived initial conditions on forecasts of surface variables. A discussion of the improvements from the new LETKF initial conditions and a summary of the results are given in section 4.
2. Method and experimental setup a. The COSMO-DE ensemble prediction system COSMO-DE-EPS, a convective-scale LAM EPS, runs operationally at DWD. It is based on the highresolution COSMO-DE model (Baldauf et al. 2011), and 21-h forecasts using 20 ensemble members are performed in the operational setup used for this study. Forecasts are updated eight times per day every 3 h starting at 0000 UTC. The COSMO-DE model uses a rotated latitude–longitude grid that consists of 461 3 421 grid points with a horizontal grid resolution of 2.8 km and 50 vertical levels. Shallow convection is parameterized, while deep convection is resolved explicitly. The COSMO-DE domain (Fig. 1) covers Germany and parts of neighboring countries in central Europe. LBCs for COSMO-DE-EPS forecasts are provided by a four-member boundary condition EPS (BC-EPS) that uses a COSMO model version with 7-km horizontal grid resolution covering a larger domain over Europe. BCEPS is driven in turn by four global models and acts as an intermediate step to downscale information from coarser to finer scales (Gebhardt et al. 2011). In addition, BCEPS is used to derive four initial ensemble perturbations at 7-km grid resolution (Peralta et al. 2012). The perturbations are downscaled to the 2.8-km COSMO-DE grid and added to the operational deterministic COSMO-DE analysis, which assimilates radar data via latent heat
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FIG. 1. The COSMO-DE domain (black rectangle) covering central Europe. Political boundaries and coastlines are shown as gray solid lines.
nudging (Stephan et al. 2008). At initialization, each of the four different initial conditions is used for five ensemble members to create a 20-member ensemble. Each ensemble member receives the LBCs during the forecast from the BC-EPS member that corresponds to the member used to derive the initial conditions. For each ensemble subgroup with the same initial and lateral boundary conditions, five parameters of the model physics parameterizations are perturbed during the forecast. These parameters (Table 1) have been selected subjectively to produce the largest impact on the precipitation variance (Gebhardt et al. 2008, 2011). Operational ensemble forecasts of COSMO-DE-EPS, labeled as OPER, are used as reference, and the impact of the LETKF-derived initial conditions relative to the current operational downscaling method is evaluated.
b. Kilometer-scale ensemble data assimilation system The KENDA system using a LETKF (Hunt et al. 2007) has been developed for the COSMO model
(Reich et al. 2011; Schraff et al. 2014, manuscript submitted to Quart. J. Roy. Meteor. Soc.). KENDACOSMO provides a framework for convective-scale ensemble data assimilation of different observation types and aims to replace the latent heat nudging scheme that is presently used in COSMO to assimilate surface precipitation rates derived from radar reflectivity measurements (Stephan et al. 2008). Currently, only conventional observations can be assimilated with KENDA-COSMO (Sommer and Weissmann 2014). Further development of KENDA-COSMO is ongoing at DWD and in the Hans-Ertel Centre for Weather Research (Weissmann et al. 2014) including operators for Global Navigation Satellite System (GNSS) slant/zenith total delay, radar, and satellite measurements (Kostka et al. 2014). A first impact study assimilating satellitederived cloud information has shown promising results (Schomburg et al. 2015). An inflation procedure needs to be applied to account for unrepresented systematic errors in the LETKF such as model or sampling error. These systematic errors lead to an underestimation of the background ensemble variance, which subsequently decreases the weight given to the observations. If this discrepancy becomes too large it can happen that no weight is given to the observations at all and that they are essentially ignored. A number of procedures are developed to counteract this problem, mainly ad hoc procedures that inflate background or analysis covariances during each data assimilation cycle. These procedures can be separated into additive methods, which add some multiples of the identity matrix to the background or analysis covariances (Ott et al. 2004), and multiplicative methods, which multiply background or analysis covariances by a factor larger than 1 (e.g., Anderson and Anderson 1999; Hamill et al. 2001). In case each analysis member has a corresponding background member, relaxation methods can also be applied where the inflation relaxes the analysis
TABLE 1. Overview of perturbed model physics parameters that are selected following Gebhardt et al. (2011) and Peralta et al. (2012). Boldface parameters are also perturbed in the operational setup of COSMO-DE-EPS during 2012. The last column indicates the settings for each of the 20 ensemble members in KENDArsp. Parameter
Description 21
entr_sc q_crit rlam_heat
Entrainment rate for shallow convection (m ) Critical value for normalized oversaturation Scaling factor of the laminar boundary layer for heat
tur_len clc_diag mu_rain
Asymptotic mixing length of turbulence (m) Subscale cloud cover given grid-scale saturation in the turbulence scheme Gamma exponent of raindrop size distribution
cloud_num
No. concentration of cloud droplets (m3)
Actual
Perturbed
Members
0.0003 1.6 1.0 1.0 150 0.5 0.5 0.5 5.0 3 108 5.0 3 108
0.002 4.0 0.1 10 500 0.75 0 1.5 5.0 3 107 5.0 3 109
1, 11 2, 12 3, 13 4, 14 5, 15 6, 16 7, 17 8, 18 9, 19 10, 20
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ensemble back toward the background ensemble (Zhang et al. 2004; Whitaker and Hamill 2012). In KENDACOSMO, multiplicative covariance inflation and relaxation methods were implemented; these are described in the following.
(RTPS). The analysis ensemble standard deviation is relaxed back to the background values at each grid point: sa ) (1 2 a)sa 1 asb ,
1) MULTIPLICATIVE COVARIANCE INFLATION The multiplicative covariance inflation can be applied on either the background or the analysis covariance in each data assimilation cycle. It can be performed most easily on the analysis by multiplying the analysis perturbations in the weight space by an appropriate inflation factor r during the data assimilation step. Similarly the background ensemble can be inflated if the background perturbations are multiplied by some factor r before the data assimilation. In KENDA-COSMO, the inflation of the background covariance is done in the weight space before applying the observation operator, which is computationally more efficient (Hunt et al. 2007).
2) RELAXATION OF THE ANALYSIS ENSEMBLE An alternative approach to inflate the ensemble by relaxing the analysis ensemble toward the background ensemble was proposed by Zhang et al. (2004) and Whitaker and Hamill (2012). Zhang et al. (2004) relaxed the analysis ensemble perturbations back to the background values, and this method is usually referred to as relaxation to prior perturbations (RTPP). The analysis ensemble perturbations Xa are relaxed independently at each analysis grid point: Xa ) (1 2 a)Xa 1 aXb .
(1)
The analysis ensemble variance is increased in proportion to the amount that the assimilation has reduced the background ensemble variance. The analysis ensemble perturbation matrix Xa is defined as the column matrix of xak 2 xa (i.e., the deviation of the kth analysis ensemble member from the analysis ensemble mean). The background ensemble perturbation matrix Xb is defined analogously and a denotes a tunable relaxation factor. For values of a between 0 and 1, part of the analysis ensemble perturbations xak 2 xa are replaced by the background ensemble perturbations xbk 2 xb . The RTPP method combines both multiplicative inflation, the analysis ensemble is inflated by multiplication with (1 2 a), and additive inflation with perturbations added from the background ensemble. Whitaker and Hamill (2012) modified the relaxation approach and instead of relaxing the perturbations, the analysis ensemble spread is relaxed back to the background ensemble spread. They referred to this purely multiplicative method as relaxation to prior spread
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where
sa 5
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 (K 2 1)21 åK k51 (X )
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 21
(2) and
sb 5
(K 2 1) å denote the analysis and background ensemble standard deviation, respectively, and K is the ensemble size. Following Whitaker and Hamill (2012), Eq. (2) can be reformulated as K b 2 k51(X )
b s 2 sa 1 1 . Xa ) Xa a sa
(3)
For a given inflation factor a, the multiplicative inflation in the RTPS method is proportional to the amount of the ensemble spread being reduced by the assimilation of observations normalized by the analysis ensemble spread. The notation of a is used to represent the inflation factor for the RTPS and RTPP method since in both cases it represents a relaxation of the analysis ensemble to the background ensemble. The factor a is a tunable parameter and Whitaker and Hamill (2012) found an optimal value of 0.95 for the RTPS inflation and 0.755 for the RTPP inflation using a simple idealized global model, whereas Zhang et al. (2004) originally applied a smaller value of a 5 0.5 for the RTPP inflation.
c. Experimental setup The overall potential of convective-scale ensemble data assimilation to initialize subsequent ensemble forecasts is examined. A set of different KENDA-COSMO experiments was performed in order to investigate the impact of the inflation method, the ensemble size, and a simple representation of model uncertainty. The KENDA-COSMO system uses the COSMO-DE model (version 4.28) as a forecast model covering Germany and central Europe (Fig. 1) at a horizontal grid resolution of 2.8 km (Baldauf et al. 2011).
1) LATERAL BOUNDARY CONDITIONS LBCs were provided by global ECMWF EPS forecasts. The 20-member ensemble forecasts have been computed for a boreal summer period from 10 June to 28 June 2012 within the framework of a special project proposed by the Short Range Numerical Weather Prediction (SRNWP) working group on predictability and EPS. The ECMWF EPS forecasts were initialized twice per day at 0000 and 1200 UTC. Compared to the operational ECWMF EPS configuration, the ensemble
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FIG. 2. Schematic setup of KENDA-COSMO data assimilation cycle and ECMWF EPS LBCs. Note that only 4 out of 20 ensemble members are indicated because of readability. Thick black trajectories denote COSMO-DE ensemble forecasts up to 3-h forecast lead time. Gray trajectories represent the ECMWF EPS forecasts with gray labeled forecast lead times, and thick trajectories indicate forecast lead times when LBCs are provided for KENDA-COSMO analysis experiments. KENDA-COSMO analysis times are denoted at the bottom and the corresponding initialization times of ECMWF EPS forecasts are denoted at the top. ECMWF EPS forecasts are updated every 12 h and italic times denote ECMWF EPS forecasts initialized the previous day.
forecasts used here were calculated at an increased horizontal resolution of TL1279 (;16 km) with 62 vertical levels. The model version used was cycle 38R1 of the Integrated Forecast System (IFS). The initial ensemble perturbations were constructed as in the operational ECMWF EPS from a combination of singular vectors and an ensemble of data assimilations (EDA) uncertainty estimate. Model error was accounted for by tendency perturbations from the stochastic perturbed parameterization tendencies (SPPT) and stochastic kinetic energy backscatter (SKEB) schemes, similarly to the operational setup (Palmer et al. 2009; Buizza et al. 2010). A schematic overview of the LBCs derived from the ECMWF EPS forecasts and the application for the KENDA-COSMO experiments is given in Fig. 2. The LBCs for the KENDA-COSMO experiments were generated by ECMWF EPS forecasts with lead times ranging from 12 to 24 h to ensure that a reasonably large spread entered the COSMO-DE domain at the lateral boundaries. ECMWF EPS forecasts, which were updated every 12 h, were downscaled to the 2.8-km COSMO-DE grid and 1-hourly forecast fields with LBCs were available for upper-air, surface, and soil variables.
2) KENDA-COSMO EXPERIMENTS Two short periods during June 2012 were selected to perform a series of KENDA-COSMO analysis
experiments. The first period covers the time window from 1500 UTC 10 June to 0000 UTC 12 June 2012 and the second period from 0600 UTC 18 June to 1200 UTC 19 June 2012. Initial conditions for all KENDACOSMO analysis experiments were derived for 1200 UTC 10 June and 0300 UTC 18 June 2012 by downscaling ECMWF EPS forecasts, which also provided the LBCs. Although no large spinup effects occurred, the first data assimilation cycle during each period was neglected and evaluation started at 1500 UTC 10 June and 0600 UTC 18 June, respectively. All KENDA-COSMO experiments assimilated conventional observations of temperature, zonal and meridional wind, and relative humidity, which are measured by radio soundings (TEMP), wind profilers (PROF), aircraft reports (AIREP), and synoptic surface stations (SYNOP). The observations have a moderate temporal frequency and the data assimilation cycle was set to 3 h (i.e., the LETKF was started every 3 h using 3-h ensemble forecasts from the COSMO-DE model as background to assimilate these observations). Hence, 12 data assimilation cycles were performed for the first period and 11 data assimilation cycles were performed for the second period. On average there were around 7000 observations available within each assimilation cycle with a minimum number of about 5000 observations at night and a maximum number of about 8500 observations during the
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TABLE 2. Overview of performed KENDA-COSMO experiments and the abbreviations as used throughout the study. Two periods with 3-hourly data assimilation cycles are investigated and extended forecasts with a 21-h forecast lead time (FC) are computed for three selected cases. The 10 perturbed physics parameters are listed in Table 1. Abbreviation Inflation
Ensemble size Physics parameter perturbation
KENDAfcov
KENDAacov
KENDArtpp
KENDArtps
KENDArsp
Multiplicative covariance on first guess, r 5 1.5 20
Multiplicative covariance on analysis, r 5 1.5 20
Relaxation to prior perturbations, a 5 0.75 20
Relaxation to prior spread, a 5 0.95 20
Relaxation to prior spread, a 5 0.95 20 Yes, 10 parameters
Analysis cycle FC 0000 UTC 11 Jun FC 0000 UTC 12 Jun
Yes Yes Yes
Analysis cycle FC 1200 UTC 18 Jun
Yes Yes
Period 1: 1500 UTC 10 Jun–0000 UTC 12 Jun 2012 Yes Yes Yes Yes Yes Yes Yes Yes Yes Period 2: 0600 UTC 18 Jun–1200 UTC 19 Jun 2012 Yes Yes Yes Yes Yes Yes
daytime. No horizontal or vertical thinning of the observations was applied. For all experiments, the localization radius [i.e., the distance at which the localization function by Gaspari and Cohn (1999) becomes 0] was 365 km in the horizontal. In the vertical, the localization radius increased linearly from the model surface to the model top between values of 0.274 and 1.826 in units of logarithmic pressure. The settings of all KENDA-COSMO experiments performed are summarized in Table 2. As in the operational COSMO-DE-EPS, a horizontal grid resolution of 2.8 km was chosen for all KENDA-COSMO experiments and the ensemble size was 20 members unless stated otherwise. Two experiments were computed with multiplicative covariance inflation applied either to the background ensemble (KENDAfcov) or the analysis ensemble (KENDAacov). In KENDAacov, the effect of the inflation is apparent in the analysis ensemble, while in KENDAfcov the inflation is done during the data assimilation and does not directly affect the analysis ensemble. The same constant inflation factor of r 5 1.5 was chosen for both experiments. Two further experiments were conducted that used the relaxation inflation. Values for the inflation factor a were chosen to be 0.75 for the RTPP experiment (KENDArtpp) and 0.95 for the RTPS experiment (KENDArtps), respectively. The inflation factor a remained constant during the computation. An additional experiment (KENDArsp) using RTPS inflation was calculated that perturbed 10 parameters of the model physics parameterizations (Table 1) to account for model uncertainty. It provides a baseline of model error representation in KENDA-COSMO similar to the operational COSMO-DE-EPS, where the method has shown good results (Gebhardt et al. 2008, 2011). To investigate the dependence on the ensemble size and
KENDArtps40 Relaxation to prior spread, a 5 0.95 40
Yes Yes Yes
Yes
Yes Yes
Yes
estimate the benefit of a larger ensemble, a 40-member ensemble experiment was performed using RTPS inflation (KENDArtps40). A 40-member LBC ensemble was generated by taking the 20 default LBCs and deriving another 20 LBCs from time-lagged ECMWF EPS forecasts using the latest available forecasts with lead times from 0 to 12 h. In addition to the different KENDA-COSMO analysis experiments for the two periods, 21-h ensemble forecasts were initialized for three selected times during the first and second period to evaluate the impact of the ensemble initial conditions on the ensemble forecast beyond lead times of 3 h. LBCs for the extended forecasts were derived from ECMWF EPS forecasts with lead times from 12 to 33 h.
3) WEATHER SITUATION A snapshot of the weather situation during each of the two periods in June 2012 is displayed in Fig. 3. The first period was characterized by lower temperatures (T3.1 km # 228C) and southwesterly winds at lower- to midtropospheric levels (Figs. 3a,b). A weak disturbance was embedded into the southwesterly flow on 11 June which led to widespread precipitation over large parts of Germany (Figs. 3d,e). The precipitation was mainly triggered by large-scale forcing but convectively-driven precipitation also developed locally. Stronger southwesterly winds were found during the second period, which advected warm air masses (T3.1km $ 28C) over Germany (Fig. 3c). A low pressure system caused some precipitation in northern Germany during the day but large parts of the domain remained dry (Fig. 3f). In the late afternoon on 18 June a convectively-driven precipitation region developed in the Alps and propagated from Switzerland and Austria northeastwards across southern Germany during the night.
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FIG. 3. (a)–(c) COSMO-DE analysis for temperature (K; shaded) and wind speed (streamlines) at model level 30 (;3.1-km altitude). (d)–(f) The 3-hourly accumulated precipitation observations (mm) of the German radar network. White regions indicate where no data are available. The black solid rectangle marks the verification domain. Figures are valid at (a),(d) 0000 UTC 11 Jun; (b),(e) 1200 UTC 11 Jun; and (c),(f) 2100 UTC 18 Jun 2012.
3. Results a. Data assimilation statistics and evaluation of analysis Average observation numbers of assimilated measurements are given in Fig. 4a. PROF and SYNOP measurements are observed during the entire day and the observation numbers are constant between different analysis cycles amounting to about 3000 observations for PROF and 1500 for SYNOP. TEMPs are launched at fixed times and most data were assimilated at 0000 and 1200 UTC, with some soundings available at 0600 and 1800 UTC. AIREP observations show a typical diurnal cycle with the majority of the data collected during daytime. Figure 4b displays a snapshot of the spatial distribution of the observations across the COSMO-DE domain. The size of the bullets is proportional to the number of observations at the location. The spatial density of all observations is varying and the COSMO-DE
domain is not evenly covered with observations. SYNOP wind observations were only assimilated in northern Germany, where the topography is sufficiently flat, whereas SYNOP data in southern Germany were generally rejected (Fig. 4b). The different impact of the inflation methods is illustrated with a snapshot of background and analysis ensemble spread valid at 1200 UTC 11 June 2012 (Fig. 5), when a weak front propagated eastward across Germany and led to an extended region of precipitation (cf. Fig. 3e). The 3-h ensemble background forecasts of the KENDA-COSMO experiments show increased spread of zonal wind speed around the location of the front over western Germany (Figs. 5a–c). KENDAfcov exhibits a small analysis spread and a ‘‘hole’’-like pattern is found (Fig. 5d) that is mainly due to the geographical distribution of the observations and not to the underlying meteorological situation. The inflation in KENDAfcov acts on the ensemble background spread
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FIG. 4. (a) Average number of observations used in KENDArtps at each cycle during the first and second period. Deviations of observation numbers are shown as gray error bars. (b) Example observation coverage for analysis cycle at 1200 UTC 11 Jun 2012. The size of the colored dots scales with the observation numbers.
before the next data assimilation step and does not correct the present analysis spread. The analysis ensemble variance in KENDAacov is directly modified by the covariance inflation (Fig. 5e). The analysis ensemble spread is increased in the entire domain, but the general qualitative distribution with lower spread over Germany and larger spread at the corners of the domain (e.g., over the North Sea) is similar to KENDAfcov. The relaxation inflation also acts on the analysis ensemble and increases the analysis spread after the data assimilation step. However, the relaxation inflation is most active where the spread is strongly reduced during the assimilation and no ‘‘hole’’-like pattern in the analysis spread is found for KENDArtps (Fig. 5f) and KENDArtpp (not shown). The forecasts of KENDAacov (Fig. 5b) and KENDArtps (Fig. 5c) also possess a larger spread compared to KENDAfcov (Fig. 5a), with KENDAacov having large spread especially in sparsely observed regions. Note that the analysis spread in the relaxation and multiplicative analysis covariance inflation depends strongly on the choice of the inflation factor and rather large values were chosen. Observation departure statistics of all KENDACOSMO experiments confirm that the LETKF extracts information from the observations successfully. The standard deviation of the ensemble mean fit to the observations is reduced from the background to the analysis. Figure 6 displays an example of analysis and background departure statistics for zonal wind speed (Fig. 6a) and temperature (Fig. 6b) from AIREP observations. The analysis ensemble mean fit to the observations is significantly improved compared to the background at all vertical levels. Analysis departures of all 20-member ensemble experiments are generally similar. KENDAacov shows a slightly improved fit
compared to KENDArtps while KENDAfcov often has the worst fit among the different experiments, especially in the lower troposphere. The differences between the experiments become even smaller for the 3-h background forecasts, and the results of the ensemble mean background fit are similar with small differences between levels and variables. Increasing the ensemble size to 40 members has a clear positive impact on the analysis and background departures, and KENDArtps40 shows the best results. Improvements are largest for the analysis, but also apparent after 3-h lead time. This clearly demonstrates the advantage of a larger ensemble in producing a more accurate analysis using the LETKF.
b. Scales and growth rates of ensemble perturbations Energy spectra of ensemble perturbations were computed to investigate the differences in the scales of the initial perturbations derived from the LETKF in KENDA-COSMO and from the downscaling method. Spatial spectra of ensemble perturbations were calculated for horizontal wind with the ensemble perturbation defined as the difference between the individual ensemble member and the ensemble mean. Spectra were computed over a 419 3 379 gridpoint subdomain, where the outermost 21 grid points of the COSMO-DE domain were removed since these grid points are directly affected by the LBCs. Two-dimensional Fourier transforms were calculated for linearly detrended ensemble perturbation fields and Fourier coefficients were subsequently summed up over annuli in wavenumber space to derive one-dimensional spectra (Errico 1985). Spectra of the ensemble perturbations of the single ensemble members were averaged over all members.
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FIG. 5. Ensemble spread for zonal wind speed (m s21; shaded) at model level 30 (;3.1-km altitude) of (a)–(c) the background and (d)–(f) the analysis valid at 1200 UTC 11 Jun 2012. Results are for (a),(d) KENDAfcov; (b),(e) KENDAacov; and (c),(f) KENDArtps.
The initial ensemble perturbations in the operational COSMO-DE-EPS (hereafter denoted as OPER), which are based on the downscaled BC-EPS with 7-km horizontal grid resolution, have reduced energy on scales smaller than 100 km compared to all KENDA-COSMO experiments (Fig. 7a). Considering the ensemble perturbations at different forecast lead times, the majority of the missing small-scale signal is already restored after 1 h (Fig. 7b). Running the high-resolution forecast model leads to modifications on the small scales that enhance the perturbation energy at these scales. Since energy growth is assumed to be very rapid at small scales, the perturbation energy also grows quickly. For longer forecast lead times (Fig. 7c) the perturbation spectra do not vary considerably and are qualitatively similar for all KENDA-COSMO experiments and OPER even though some quantitative differences remain. The sharp decline in the perturbation energy at scales of 10–15 km is related to the effective horizontal resolution of the COSMO-DE model, which is around 4–5 times the grid resolution of 2.8 km (Bierdel et al. 2012).
The inflation modifies the ensemble variance and the choice of the inflation method has an impact on the energy of the ensemble perturbations. The energy of initial ensemble perturbations increases going from KENDAfcov to KENDArtpp, KENDArtps, and KENDAacov. The differences between all experiments decrease during the forecast and the perturbation energy converges (Figs. 7b,c), keeping the order between the experiments. The perturbations of KENDAacov still exhibit the largest perturbation energy after 3-h lead time (Fig. 7c). Note that the energy of the initial ensemble perturbations is controlled by the inflation factor chosen, and larger values lead to an increase of the initial perturbation energy. From the energy spectra of the ensemble perturbations E0 shown in Fig. 7, a relative growth rate of ensemble perturbations from time ti to ti11 can be derived:
relative growth rate 5
E0 (ti11 ) 2 E0 (ti ) . E0 (ti )
(4)
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FIG. 6. Standard deviation of observation minus background ensemble mean (dashed) and analysis ensemble mean (solid) departures, respectively. Results are for AIREP observations of (a) zonal wind speed and (b) temperature averaged over the first and second period.
A relative growth rate was computed from 0–1-, 1–2-, and 2–3-h forecast lead times to investigate the differences in the growth of ensemble perturbations in more detail (Fig. 8). After initialization (Fig. 8a), two growth rate maxima can be found for scales smaller than 25 km and larger than 500 km. The small-scale maximum results from upscale growth of forecast uncertainty, while the large-scale maximum is likely related to the perturbations of the LBCs. The magnitude of growth rates is significantly different among the KENDA-COSMO experiments. The growth rate is largest for KENDAfcov and KENDArtpp, which both exhibit the smallest energy initially. KENDArtps has small negative growth rates for scales from roughly 30 to 250 km in the first forecast hour and KENDAacov shows a negative growth for all scales except for the smallest scales (#25 km). One hour later (Fig. 8b), the growth rates of
KENDAfcov and KENDArtpp have decreased and the small-scale maximum has shifted upscale to scales between 50 and 100 km. In KENDArtps only large scales above 250 km show a growth of the ensemble perturbations while perturbations at smaller scales still decay. In KENDAacov, the growth rate is still negative for all scales except the largest scale around 1000 km. The growth rates of ensemble perturbations further converge at 2–3-h forecast lead time (Fig. 8c), and only scales larger than 25–50 km grow while the perturbations at the smaller scales appear to be saturated. The growth of perturbations is still bounded to scales larger than 500 km in KENDAacov and 250 km in KENDArtps, respectively. In general, experiments with initially smaller perturbation energy possess faster energy growth. Strongly inflating the analysis ensemble variance in KENDAacov and KENDArtps creates
FIG. 7. Power spectra of ensemble perturbations for horizontal wind at model level 30 (;3.1-km altitude) for (a) analysis time, (b) after 1 h, and (c) after 3-h forecast lead time averaged over the first and second period. OPER denotes the operational COSMO-DE-EPS.
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FIG. 8. Power spectra of relative growth rate [Eq. (4)] for horizontal wind at model level 30 (;3.1-km altitude) for (a) 0–1-, (b) 1–2-, and (c) 2–3-h forecast lead time averaged over the first and second period. OPER denotes the operational COSMO-DE-EPS.
perturbations with initially large energy that does not grow considerably during the first forecast hours. On the contrary, the initially small energy of the perturbations in KENDAfcov grows strongly during the first forecast hours and the absolute perturbation energy of the experiments converge. As stated earlier, the initial energy of the ensemble perturbations in OPER is reduced on scales below 100 km compared to KENDA-COSMO experiments, which leads to extremely large growth rates with values up to 20 at these scales (Fig. 8a). The energy on scales larger than 100 km does not grow at all and show a negative growth rate. Presumably, this is caused by adjustment processes early in the forecast since the ensemble forecasts are initialized with perturbations from BCEPS, which is driven by different global models. Similar to KENDAfcov and KENDArtpp, the perturbation growth shows a maximum around 50 km from 1 to 2 h (Fig. 8b), and the maximum shifts upscale toward larger scales one hour later (Fig. 8c).
c. Forecast quality of background ensemble forecasts Forecasts with 3-h lead time, which corresponds to the lead time of the background forecasts, were evaluated for both periods. For these short forecast lead times, the forecast uncertainty can be assumed to be dominated by the initial condition uncertainty and improvements of the initial ensemble perturbations should also be reflected in the skill of the ensemble forecast.
1) SPREAD SKILL Root-mean-square error (RMSE) and spread of 3-h forecasts for zonal wind speed, temperature, and specific humidity are displayed in Fig. 9. All experiments are underdispersive as the spread is overall smaller than the
RMSE. The difference between spread and RMSE decreases with increasing height especially for temperature (Fig. 9b) and humidity (Fig. 9c). The inflation method used has a large impact on the spread over the domain, similar to the ensemble perturbation energy (Fig. 7), and the smallest spread is found for KENDAfcov, which does not inflate the analysis ensemble. KENDAacov, where the analysis ensemble is inflated by a constant factor, has the largest spread due to the large spread values in the sparsely observed regions of the domain (cf. Fig. 5e). Considering only the interior of the domain over Germany reduces the average spread of KENDAacov considerably and it becomes comparable to the spread of KENDArtpp (not shown). The spread of the different relaxation experiments is bounded by KENDAfcov and KENDAacov, and increases going from KENDArtpp to KENDArtps40, KENDArtps, and KENDArsp. RMSE values for KENDArtpp, KENDArtps, KENDArsp, and KENDAacov are very similar and no consistent differences are found, which agrees with results for the background departures in Fig. 6. KENDAfcov has the largest RMSE for all levels and variables, which is more pronounced for wind speed and humidity in the lower to midtroposphere. Again the 40-member experiment KENDArtps40 exhibits the smallest RMSE for all levels and variables.
2) SURFACE WIND SPEED Ensemble rank histograms indicate how well the ensemble spread is able to represent the true uncertainty. The results for 3-h forecasts of 10-m wind speed are displayed in Fig. 10. Verification is against the deterministic COSMO-DE analysis, but the results are qualitatively similar when verified against SYNOP measurements. Results of the rank histograms for surface
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FIG. 9. Ensemble spread (dashed) and root-mean-square error (solid) of 3-h background ensemble forecasts for KENDA-COSMO experiments averaged over the first and second period. Results are for (a) zonal wind speed, (b) temperature, and (c) specific humidity. Verification is performed against deterministic COSMO-DE analysis over the model domain excluding the outermost 21 grid points that are given by the LBCs.
wind speed are similar to the spread-skill results for upper-level variables (cf. Fig. 9). All experiments are underdispersive and the ensemble spread is smaller than the true uncertainty estimated from the verifying model
analysis (Fig. 10). Multiplicative inflation of the analysis (KENDAacov) increases the spread considerably compared to inflating the background (KENDAfcov), and the shape of the rank histogram converges toward being
FIG. 10. Ensemble rank histogram for 10-m wind speed for 3-h forecast lead time averaged over the first and second period. Verification is performed against deterministic COSMO-DE analysis over the model domain excluding the outermost 21 grid points that are given by the LBCs. OPER denotes the operational COSMO-DE-EPS.
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flat in KENDAacov. The relaxation inflation method also increases the ensemble spread, with the spread being larger in KENDArtps than in KENDArtpp, but smaller in both experiments compared to KENDAacov. The model physics perturbations (KENDArsp) increase the ensemble spread of wind speed slightly, which leads to small further improvements in the rank histogram compared to KENDArtps. OPER is strongly affected by the use of only four different initial ensemble perturbations from the BC-EPS. This leads to a clustering of the ensemble members into four groups each with five members (Fig. 10). The extreme ranks in OPER are also populated more often than in all KENDA-COSMO experiments indicating that the KENDA-COSMO experiments are less underdispersive for surface wind speed. To assess the skill of the ensemble forecasts the continuous ranked probability score (CRPS) was computed. The CRPS evaluates the skill of the ensemble probability forecast in predicting the corresponding observation (Wilks 2011), and measures the difference between the cumulative density function provided by the ensemble and the location of the verifying observation. It is negative oriented (i.e., smaller values are better), and it equals the root-mean-square error when the ensemble forecast is replaced by a deterministic forecast. A bootstrap resampling method was applied to estimate the corresponding uncertainty of the CRPS results (Wilks 2011). The bootstrap was applied to resample the different initialization times with a sample size of 100. A Student’s t test was used to determine if differences between the experiments are statistically significant at the 95% confidence level. Synoptic surface measurements in Germany were used to verify ensemble forecasts of surface wind speed. In total, about 310–320 stations scattered over Germany were used for verification. Wind speed observations were quality controlled to avoid gross errors in the observations and only stations that had valid observations during all verification times were considered. All KENDA-COSMO experiments have a significantly improved CRPS compared to OPER for 3-h forecasts of 10-m wind speed (Fig. 11). Comparing the KENDA-COSMO experiments, KENDAfcov has the largest CRPS and the difference to all other experiments is statistically significant. No considerable differences are found between the relaxation experiments and KENDAacov. Adding the model physics parameter perturbations (KENDArsp) improves the CRPS for 10-m wind speed slightly. The smallest and best CRPS is achieved with the larger ensemble size in KENDArtps40, which outperforms all other experiments significantly expect KENDArsp.
FIG. 11. Continuous ranked probability score (CRPS) shown as gray diamonds and numbers at the bottom for 3-h forecasts for 10-m wind speed verified against SYNOP observations in Germany averaged over the first and the second period. A bootstrap resampling in time with sample size 100 is applied and box plots show the median together with the 25th and 75th percentiles, and whiskers denote the lower and upper adjacent values. Outliers are indicated as black crosses. OPER denotes the operational COSMO-DE-EPS.
3) PRECIPITATION The Brier score and its decomposition (Wilks 2011) were computed to assess the skill of the KENDA-COSMO experiments for precipitation forecasts. The results are presented in terms of the Brier skill score (BSS): BSS 5
‘‘Resolution’’ 2 ‘‘Reliability’’ . ‘‘Uncertainty’’
(5)
The uncertainty component here comes from the sample climatology of the period considered. Forecasts exhibit positive skill in terms of BSS (values between 0 and 1, with 1 being the best) if the absolute value of the resolution is larger than the absolute value of the reliability. Verification was done against precipitation observations derived from the measurements of the German radar network for the verification domain shown in Figs. 3d–f. DWD operates a radar network of 16 C-band Doppler radars in Germany and near-surface reflectivity scans are produced every 5 min with a spatial resolution of 1 km in range and 18 in azimuth (Stephan et al. 2008). Reflectivity measurements were converted to precipitation rates by using empirical reflectivity–rainfall relationships and various quality control checks were applied. For the verification, observation errors of precipitation were neglected. The BSS was calculated for different thresholds of 3-hourly accumulated precipitation: 0.1, 0.5, 1, and 2 mm. The larger accumulation time was chosen to avoid
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FIG. 12. Brier skill score for 3-hourly accumulated precipitation forecasts of 3-h forecast lead time in the verification domain (Figs. 3d–f) averaged over the first and second period. OPER denotes the operational COSMO-DE-EPS.
very rare events, which could lead to instabilities in the BSS. Larger thresholds are not shown here since there are only very few cases and the skill of all experiments drops to zero. For all different KENDA-COSMO experiments, 3-hourly accumulated precipitation forecasts are available for each data assimilation cycle providing a sample of 23 forecasts (12 for the first and 11 for the second period). The BSS of all forecasts is higher for smaller thresholds and drops off for larger thresholds of 1 and 2 mm (Fig. 12). Similarly to wind speed, KENDAfcov also has the lowest skill for precipitation. The qualitative evolution of the BSS is similar for all KENDA-COSMO experiments, but quantitative differences between the experiments are large (Fig. 12). Results of the relaxation experiments KENDArtpp, KENDArtps, and KENDArsp
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are comparable to each other, but KENDArtpp has a slightly higher BSS. The use of perturbed model physics parameters in KENDArsp leads to only a small increase of skill. KENDAacov outperforms the 20 ensemble member relaxation experiments in terms of BSS. However, the advantage of a larger ensemble size is considerable and KENDArtps40 produces the highest skill of all KENDA-COSMO experiments. Overall, OPER shows the highest skill and obtains the best performance for 3-h precipitation forecasts. The higher skill of OPER at 3-h forecast lead time results from the initial conditions being constructed around the deterministic COSMO-DE analysis, which is computed by assimilating radar derived precipitation information via a latent heat nudging algorithm. This initial knowledge of precipitation leads to a better performance of the ensemble at short forecast lead times. In contrast, no radar derived precipitation measurements or satellite observations are assimilated in the KENDA-COSMO experiments.
d. Forecast quality at longer forecast lead times The impact of KENDA-COSMO initial conditions on longer forecast lead times is investigated using three cases when 21-h ensemble forecasts with the COSMODE model were performed (Table 2).
PRECIPITATION The evolution of the observed hourly accumulated precipitation averaged over the verification domain together with the corresponding ensemble forecast of KENDArtps is shown in Fig. 13. Both 11 June (Fig. 13a) and 12 June (Fig. 13b) exhibit a similar diurnal cycle with a first maximum during the morning hours around 0600 UTC and a larger maximum in the afternoon. The precipitation during these two days is related to a weak
FIG. 13. 1-hourly accumulated precipitation (mm) averaged over the verification domain for radar observations and 21-h forecasts of KENDArtps initialized at (a) 0000 UTC 11 Jun, (b) 0000 UTC 12 Jun, and (c) 1200 UTC 18 Jun 2012.
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FIG. 14. Brier skill score for 3-hourly accumulated precipitation forecasts averaged over 3-, 6-, 9-, 12-, 15-, 18-, and 21-h forecast lead times in the verification domain (Figs. 3d–f). Forecasts are initialized at (a) 0000 UTC 11 Jun, (b) 0000 UTC 12 Jun, and (c) 1200 UTC 18 Jun 2012. OPER denotes the operational COSMO-DE-EPS.
front crossing Germany that causes widespread precipitation. In contrast, a different daily evolution is seen on 18 June (Fig. 13c). In the early morning hours a low pressure system passes to the north of Germany and leads to precipitation over parts of northern Germany at around noon. During the late afternoon, an isolated region with convectively driven precipitation develops in the Alps and crosses southern Germany at night. Results for the domain-averaged precipitation are similar for the different experiments, and here only KENDArtps is shown as example. Ensemble forecasts are in general able to capture the evolution of precipitation on 11 and 12 June (Figs. 13a,b), while on 18 June (Fig. 13c) none of the ensemble forecasts predicts the isolated precipitation region over southern Germany during the night (cf. Fig. 3f). To increase the sample size for the single cases, the BSS for 3-hourly accumulated precipitation forecasts was computed considering all forecast lead times up to 21 h together (Fig. 14). A considerably lower BSS is found on 11 June (Fig. 14a) for larger thresholds while for the 12 June (Fig. 14b) the BSS remains about the same level for different thresholds. Precipitation values larger than 1 mm occur more often on 12 June than on 11 June, which increases the sample uncertainty. This leads to a higher BSS as the Brier scores for both cases are similar for these thresholds. Overall, the impact of latent heat nudging in the initial conditions of OPER rapidly decreases for longer forecast lead times, and the BSS of OPER is reduced and becomes comparable or even lower than the BSS of the KENDA-COSMO experiments. The BSS results of the KENDA-COSMO experiments vary from case to case. KENDAfcov, using multiplicative covariance inflation on the background, has the lowest BSS except on 18 June. Results for KENDArtps and KENDArtpp are mixed. KENDArtpp shows slightly better results on 11
June for small thresholds (Fig. 14a), but has less skill compared to KENDArtps on 12 June (Fig. 14b) and 18 June (Fig. 14c). The perturbed parameter scheme (KENDArsp) has only a small impact and improves the BSS slightly on 11 June and 12 June (Figs. 14a,b), but leads to a small degradation 18 June (Fig. 14c). KENDAacov shows lower skill than the relaxation experiments on 11 June (Fig. 14a), but reaches a higher skill on 12 June (Fig. 14b) while the BSS results are similar on 18 June. The BSS of all ensemble forecasts is very low on 18 June (Fig. 14c) as none of the experiments predicts the convective precipitation in southern Germany at night. The impact of improving the initial condition is limited here and it seems that LBC and model errors were responsible for missing the nighttime precipitation event in the forecasts of all experiments. In contrast to OPER, the KENDA-COSMO experiments improve the precipitation forecast at least at some earlier lead times up to about 7 h (cf. Fig. 13c), which leads to the higher BSS compared to OPER here.
4. Discussion and summary KENDA-COSMO, a kilometer-scale ensemble data assimilation system based on a LETKF, has been developed at DWD within the COSMO model framework (Reich et al. 2011; Schraff et al. 2014, manuscript submitted to Quart. J. Roy. Meteor. Soc.). It provides a convective-scale data assimilation scheme for the COSMO model, but also produces an analysis ensemble that can be used to initialize high-resolution ensemble forecasts. The emphasis of this study was on the impact of KENDA-COSMO derived ensemble initial conditions for high-resolution ensemble forecasts and two short periods during June 2012 were evaluated. Various experiments were performed to investigate the influence of
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the inflation scheme, the ensemble size and a simple method accounting for model error. Results were compared against the operational COSMO-DE-EPS. In the future, it is envisaged to use the LETKFderived analysis ensemble to replace the current method to initialize COSMO-DE-EPS forecasts, which is based on downscaling coarser-resolved NWP model information onto the convective-scale grid. Downscaled ensemble initial conditions have shown a good performance for convective-scale ensemble forecasts of precipitation (Kühnlein et al. 2014), and it has to be assured that replacing the current downscaling method by using ensemble initial conditions from KENDA-COSMO can improve the forecast. Results confirmed that the lack of small-scale perturbations in the downscaled initial conditions is short lived and rapid growth of uncertainty at scales smaller than 100–200 km (Selz and Craig 2015) restored the initially missing small-scale perturbation energy during the first forecast hours. The LETKF-derived estimate of the analysis uncertainty will unavoidably underestimate the current uncertainty due to missing error sources such as sampling and model error (Whitaker and Hamill 2012), and different inflation methods were tested to account for unrepresented error sources in the LETKF. Multiplicative covariance inflation applied to the ensemble background before the data assimilation did not modify the analysis spread, leading to a significantly reduced analysis spread in densely observed areas. The estimated analysis uncertainty was strongly determined by the observation coverage and did not depend on the underlying meteorological situation. Even though the initial small spread grew during the forecast, the ensemble forecasts still suffered from the initial deficit. As an alternative, multiplicative covariance inflation can also be applied on the analysis ensemble. The observation density again determined the qualitative distribution of the analysis ensemble spread, but the spread could be increased to be sufficiently large. The larger analysis spread subsequently improved the performance of the ensemble forecasts. In addition, relaxation inflation methods (Zhang et al. 2004; Whitaker and Hamill 2012) that relax either the analysis ensemble perturbations (RTPP) or spread (RTPS) have been implemented. Relaxation methods act on the analysis ensemble after the data assimilation, which led to a significant increase in the analysis spread in the interior of the LAM domain. Results showed that an increased initial spread due to large inflation exhibited a slower growth rate during the first forecast hours and could even decay. The growth of RTPS ensemble spread was reduced during the forecast compared to RTPP, similarly to the results of Whitaker and Hamill (2012) for a primitive equation global model.
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In terms of forecast quality, no significant differences were detected between using initial conditions from the RTPP or RTPS inflation method. Applying multiplicative covariance inflation on the analysis led to similar or even slightly improved quality of the ensemble forecasts. Note that the presented results considered only a limited time period and conclusions might vary for different periods or ensemble data assimilation systems. The results did not support one best inflation method and the choice of the method may also depend on the application of the ensemble data assimilation system. Further improvements can be expected from using an adaptive inflation factor (Miyoshi and Kunii 2012) since the degree of inflation depends heavily on the observational network. Work is ongoing to include an adaptive inflation method, which aims to estimate a time- and space-dependent inflation factor based on the observation innovation statistics (Li et al. 2009). The results highlighted that it is important to have a sufficiently large initial ensemble spread inside the LAM domain at analysis time. The forecast spread at shorter forecast lead times (t # 3 h) was determined by its initial value and if the analysis spread was strongly underdispersive ensemble forecasts at later forecast times were also degraded (t . 3 h). The particular importance of initial condition perturbations for highresolution ensemble forecasts up to 12 h was also stressed in a study by Vié et al. (2011) for a Mediterranean heavy precipitating event. Kühnlein et al. (2014) found that the initial condition uncertainty dominates other sources of uncertainty for forecast lead times up to 6–9 h, but also that the impact of ensemble initial conditions on the forecast depends on the current weather situation. With longer forecast lead times, schemes to represent uncertainty in the model formulation have a growing impact on the ensemble forecasts (Bouttier et al. 2012). To represent model error, a multiphysics scheme perturbing subjectively chosen constants of the model physics parameterizations (Gebhardt et al. 2011) was tested. This scheme had a small positive effect on precipitation and wind speed. The impact for short forecast lead times may be small but any possible representation of model error should also be included in the data assimilation to ensure consistent perturbations between data assimilation and ensemble forecasts. Whitaker and Hamill (2012) found that combining inflation schemes with additional methods accounting for model error has a positive influence on ensemble forecasts and suggested treating different sources of unrepresented error by various methods. Increasing the ensemble size led to a more accurate analysis, where the analysis mean better fitted the assimilated observations. Ensemble forecasts at 3-h
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forecast lead time clearly benefited from both the larger ensemble and the analysis improvements, and the 40-member ensemble showed the highest forecast skill. However, even using a small ensemble with 20 members in KENDA-COSMO could improve ensemble forecasts compared to the operational COSMO-DE-EPS. Ongoing work on assimilation of geostationary satellite observations and radar measurements over Germany should help to further enhance the performance of KENDA-COSMO for ensemble forecasts. Acknowledgments. The authors are thankful to Hendrik Reich and Andreas Rhodin for providing code and support of the KENDA-COSMO system and Richard Keane for his remarks. Lateral boundary conditions used in this study were computed and provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). 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 authors thank the two anonymous reviewers for their helpful comments. REFERENCES Aksoy, A., D. C. Dowell, and C. Snyder, 2010: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part II: Short-range ensemble forecasts. Mon. Wea. Rev., 138, 1273–1292, doi:10.1175/2009MWR3086.1. Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 2741–2758, doi:10.1175/1520-0493(1999)127,2741: AMCIOT.2.0.CO;2. Baldauf, M., A. Seifert, J. Förstner, D. Majewski, M. Raschendorfer, and T. Reinhardt, 2011: Operational convective-scale numerical weather prediction with the COSMO model: Description and sensitivities. Mon. Wea. Rev., 139, 3887–3905, doi:10.1175/ MWR-D-10-05013.1. Berner, J., S.-Y. Ha, J. Hacker, A. Fournier, and C. Snyder, 2011: Model uncertainty in a mesoscale ensemble prediction system: Stochastic versus multiphysics representations. Mon. Wea. Rev., 139, 1972–1975, doi:10.1175/2010MWR3595.1. Bierdel, L., P. Friederichs, and S. Bentzien, 2012: Spatial kinetic energy spectra in the convection-permitting limited-area NWP model COSMO-DE. Meteor. Z., 21, 245–258, doi:10.1127/ 0941-2948/2012/0319. Bishop, C. H., T. R. Holt, J. Nachamkin, S. Chen, J. G. McLay, J. D. Doyle, and W. T. Thompson, 2009: Regional ensemble forecasts using the ensemble transform technique. Mon. Wea. Rev., 137, 288–298, doi:10.1175/2008MWR2559.1. Bonavita, M., L. Torrisi, and F. Marcucci, 2010: Ensemble data assimilation with the CNMCA regional forecasting system. Quart. J. Roy. Meteor. Soc., 136, 132–145, doi:10.1002/qj.553. Bouttier, F., B. Vié, O. Nuissier, and L. Raynaud, 2012: Impact of stochastic physics in a convection-permitting ensemble. Mon. Wea. Rev., 140, 3706–3721, doi:10.1175/MWR-D-12-00031.1.
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