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Heiner Lange and Tijana Janjić

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.

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Volker Wulfmeyer and Tijana Janjić

Abstract

Shipborne observations obtained with the NOAA high-resolution Doppler lidar (HRDL) during the 1999 Nauru (Nauru99) campaign were used to study the structure of the marine boundary layer (MBL) in the tropical Pacific Ocean. During a day with weak mesoscale activity, diurnal variability of the height of the convective MBL was observed using HRDL backscatter data. The observed diurnal variation in the MBL height had an amplitude of about 250 m. Relations between the MBL height and in situ measurements of sea surface temperature as well as latent and sensible heat fluxes were examined. Good correlation was found with the sea surface temperature. The correlation with the latent heat flux was lower, and practically no correlation between the MBL height and the sensible heat and buoyancy fluxes could be detected. Horizontal wind profiles were measured using a velocity–azimuth display scan of HRDL velocity data. Strong wind shear at the top of the MBL was observed in most cases. Comparison of these results with GPS radiosonde data shows discrepancies in the wind intensity and direction, which may be due to different observation times and locations as well as due to multipath effects at the ship’s platform. Vertical wind profiles corrected for ship’s motion were used to derive vertical velocity variance and skewness profiles. Motion compensation had a significant effect on their shape. Normalized by the convective velocity scale and by the top of the mixed layer zi, the variance varied between 0.45 and 0.65 at 0.4z/zi and decreased to 0.2 at 1.0z/zi. The skewness ranged between 0.3 and 0.8 in the MBL and showed in almost all cases a maximum between 1.0z/zi and 1.1z/zi. These profiles revealed the existence of another turbulent layer above the MBL, which was probably driven by wind shear and cloud condensation processes.

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Zavisa Janjic, Tijana Janjic, and Ratko Vasic

Abstract

Starting from three Eulerian second-order nonlinear advection schemes for semi-staggered Arakawa grids B/E, advection schemes of fourth order of formal accuracy were developed. All three second-order advection schemes control the nonlinear energy cascade in case of nondivergent flow by conserving quadratic quantities. Linearization of all three schemes leads to the same second-order linear advection scheme. The second-order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by modifying the advected quantity while still preserving consistency. Tests with linear advection of a cone confirm the advantage of the fourth-order scheme. However, if a localized, large amplitude and high wavenumber pattern is present in initial conditions, the clear advantage of the fourth-order scheme disappears.

The new nonlinear fourth-order schemes are quadratic conservative and reduce to the Arakawa Jacobian for advected quantities in case of nondivergent flow. In case of general flow the conservation properties of the new momentum advection schemes impose stricter constraint on the nonlinear cascade than the original second-order schemes. However, for nondivergent flow, the conservation properties of the fourth-order schemes cannot be proven in the same way as those of the original second-order schemes. Therefore, demanding long-term and low-resolution nonlinear tests were carried out in order to investigate how well the fourth-order schemes control the nonlinear energy cascade. All schemes were able to maintain meaningful solutions throughout the test.

Finally, the impact was examined of the fourth-order momentum advection on global medium-range forecasts. The 500-hPa anomaly correlation coefficient obtained using the best performing fourth-order scheme did not show an improvement compared to the tests using its second-order counterpart.

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Tijana Janjić and Stephen E. Cohn

Abstract

Observations of the atmospheric state include scales of motion that are not resolved by numerical models into which the observed data are assimilated. The resulting observation error due to unresolved scales, part of the “representativeness error,” is state dependent and correlated in time. A mathematical formalism and algorithmic approach has been developed for treating this error in the data assimilation process, under an assumption that there is no model error. The approach is based on approximating the continuum Kalman filter in such a way as to maintain terms that account for the observation error due to unresolved scales. The two resulting approximate filters resemble the Schmidt–Kalman filter and the traditional discrete Kalman filter.

The approach is tested for the model problem of a passive tracer undergoing advection in a shear flow on the sphere. The state contains infinitely many spherical harmonics, with a nonstationary spectrum, and the problem is to estimate the projection of this state onto a finite spherical harmonic expansion, using observations of the full state. Numerical experiments demonstrate that approximate filters work well for the model problem provided that the exact covariance function of the unresolved scales is known. The traditional filter is more convenient in practice since it requires only the covariance matrix obtained by evaluating this covariance function at the observation points. A method for modeling this covariance matrix in the traditional filter is successful for the model problem.

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Tijana Janjić, Dennis McLaughlin, Stephen E. Cohn, and Martin Verlaan

Abstract

This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a nonnegativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

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Lars Nerger, Tijana Janjić, Jens Schröter, and Wolfgang Hiller

Abstract

In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

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Tijana Janjić, Lars Nerger, Alberta Albertella, Jens Schröter, and Sergey Skachko

Abstract

Ensemble Kalman filter methods are typically used in combination with one of two localization techniques. One technique is covariance localization, or direct forecast error localization, in which the ensemble-derived forecast error covariance matrix is Schur multiplied with a chosen correlation matrix. The second way of localization is by domain decomposition. Here, the assimilation is split into local domains in which the assimilation update is performed independently. Domain localization is frequently used in combination with filter algorithms that use the analysis error covariance matrix for the calculation of the gain like the ensemble transform Kalman filter (ETKF) and the singular evolutive interpolated Kalman filter (SEIK). However, since the local assimilations are performed independently, smoothness of the analysis fields across the subdomain boundaries becomes an issue of concern.

To address the problem of smoothness, an algorithm is introduced that uses domain localization in combination with a Schur product localization of the forecast error covariance matrix for each local subdomain. On a simple example, using the Lorenz-40 system, it is demonstrated that this modification can produce results comparable to those obtained with direct forecast error localization. In addition, these results are compared to the method that uses domain localization in combination with weighting of observations. In the simple example, the method using weighting of observations is less accurate than the new method, particularly if the observation errors are small.

Domain localization with weighting of observations is further examined in the case of assimilation of satellite data into the global finite-element ocean circulation model (FEOM) using the local SEIK filter. In this example, the use of observational weighting improves the accuracy of the analysis. In addition, depending on the correlation function used for weighting, the spectral properties of the solution can be improved.

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Yuefei Zeng, Tijana Janjić, Alberto de Lozar, Stephan Rasp, Ulrich Blahak, Axel Seifert, and George C. Craig

Abstract

Different approaches for representing model error due to unresolved scales and processes are compared in convective-scale data assimilation, including the physically based stochastic perturbation (PSP) scheme for turbulence, an advanced warm bubble approach that automatically detects and triggers absent convective cells, and additive noise based on model truncation error. The analysis of kinetic energy spectrum guides the understanding of differences in precipitation forecasts. It is found that the PSP scheme results in more ensemble spread in assimilation cycles, but its effects on the root-mean-square error (RMSE) are neutral. This leads to positive impacts on precipitation forecasts that last up to three hours. The warm bubble technique does not create more spread, but is effective in reducing the RMSE, and improving precipitation forecasts for up to 3 h. The additive noise approach contributes greatly to ensemble spread, but it results in a larger RMSE during assimilation cycles. Nevertheless, it considerably improves the skill of precipitation forecasts up to 6 h. Combining the additive noise with either the PSP scheme or the warm bubble technique reduces the RMSE within cycles and improves the skill of the precipitation forecasts, with the latter being more beneficial.

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George C. Craig, Andreas H. Fink, Corinna Hoose, Tijana Janjić, Peter Knippertz, Audine Laurian, Sebastian Lerch, Bernhard Mayer, Annette Miltenberger, Robert Redl, Michael Riemer, Kirsten I. Tempest, and Volkmar Wirth

Abstract

Prediction of weather is a main goal of atmospheric science. Its importance to society is growing continuously due to factors such as vulnerability to natural disasters, the move to renewable energy sources, and the risks of climate change. But prediction is also a major scientific challenge due to the inherently limited predictability of a chaotic atmosphere, and has led to a revolution in forecasting methods as we have moved to probabilistic prediction. These changes provide the motivation for Waves to Weather (W2W), a major national research program in Germany with three main university partners in Munich, Mainz, and Karlsruhe. We are currently in the second 4-year phase of our planned duration of 12 years and employ 36 doctoral and post-doctoral scientists. In the context of this large program, we address what we have identified to be the most important and challenging scientific questions in predictability of weather, namely upscale error growth, errors associated with cloud processes, and probabilistic prediction of high impact weather. This paper presents some key results of the first phase of W2W and discusses how they have influenced our understanding of predictability. The key role of interdisciplinary research linking atmospheric scientists with experts in visualization, statistics, numerical analysis, and inverse methods will be highlighted. To ensure a lasting impact on research in our field in Germany and internationally, we have instituted innovative programs for training and support of early career scientists, and to support education, equal opportunities, and outreach, which are also described here.

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Clemens Simmer, Gerhard Adrian, Sarah Jones, Volkmar Wirth, Martin Göber, Cathy Hohenegger, Tijana Janjic´, Jan Keller, Christian Ohlwein, Axel Seifert, Silke Trömel, Thorsten Ulbrich, Kathrin Wapler, Martin Weissmann, Julia Keller, Matthieu Masbou, Stefanie Meilinger, Nicole Riß, Annika Schomburg, Arnd Vormann, and Christa Weingärtner

Abstract

In 2011, the German Federal Ministry of Transport, Building and Urban Development laid the foundation of the Hans-Ertel Centre for Weather Research [Hans-Ertel-Zentrum für Wetterforschung (HErZ)] in order to better connect fundamental meteorological research and teaching at German universities and atmospheric research centers with the needs of the German national weather service Deutscher Wetterdienst (DWD). The concept for HErZ was developed by DWD and its scientific advisory board with input from the entire German meteorological community. It foresees core research funding of about €2,000,000 yr−1 over a 12-yr period, during which time permanent research groups must be established and DWD subjects strengthened in the university curriculum. Five priority research areas were identified: atmospheric dynamics and predictability, data assimilation, model development, climate monitoring and diagnostics, and the optimal use of information from weather forecasting and climate monitoring for the benefit of society. Following an open call, five groups were selected for funding for the first 4-yr phase by an international review panel. A dual project leadership with one leader employed by the academic institute and the other by DWD ensures that research and teaching in HErZ is attuned to DWD needs and priorities, fosters a close collaboration with DWD, and facilitates the transfer of fundamental research into operations. In this article, we describe the rationale behind HErZ and the road to its establishment, present some scientific highlights from the initial five research groups, and discuss the merits and future development of this new concept to better link academic research with the needs and challenges of a national weather service.

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