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Kirstin Kober and George C. Craig

Abstract

Stochastic perturbations allow for the representation of small-scale variability due to unresolved physical processes. However, the properties of this variability depend on model resolution and weather regime. A physically based method is presented for introducing stochastic perturbations into kilometer-scale atmospheric models that explicitly account for these dependencies. The amplitude of the perturbations is based on information obtained from the model’s subgrid turbulence parameterization, while the spatial and temporal correlations are based on physical length and time scales of the turbulent motions. The stochastic perturbations lead to triggering of additional convective cells and improved precipitation amounts in simulations of two days with weak synoptic forcing of convection but different amounts of precipitation. The perturbations had little impact in a third case study, where precipitation was mainly associated with a cold front. In contrast, an unphysical version of the scheme with constant perturbation amplitude performed poorly since there was no perturbation amplitude that would give improved amounts of precipitation during the day without generating spurious convection at other times.

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Tobias Selz, Lotte Bierdel, and George C. Craig

Abstract

Research on the mesoscale kinetic energy spectrum over the past few decades has focused on finding a dynamical mechanism that gives rise to a universal spectral slope. Here we investigate the variability of the spectrum using 3 years of kilometer-resolution analyses from COSMO configured for Germany (COSMO-DE). It is shown that the mesoscale kinetic energy spectrum is highly variable in time but that a minimum in variability is found on scales around 100 km. The high variability found on the small-scale end of the spectrum (around 10 km) is positively correlated with the precipitation rate where convection is a strong source of variance. On the other hand, variability on the large-scale end (around 1000 km) is correlated with the potential vorticity, as expected for geostrophically balanced flows. Accordingly, precipitation at small scales is more highly correlated with divergent kinetic energy, and potential vorticity at large scales is more highly correlated with rotational kinetic energy. The presented findings suggest that the spectral slope and amplitude on the mesoscale range are governed by an ever-changing combination of the upscale and downscale impacts of these large- and small-scale dynamical processes rather than by a universal, intrinsically mesoscale dynamical mechanism.

Open access
Tobias Selz, Lucas Fischer, and George C. Craig

Abstract

The spatial scale dependence of midlatitude water vapor variability in the high-resolution limited-area model COSMO is evaluated using diagnostics of scaling behavior. Past analysis of airborne lidar measurements showed that structure function scaling exponents depend on the corresponding airmass characteristics, and that a classification of the troposphere into convective and nonconvective layers led to significantly different power-law behaviors for each of these two regimes. In particular, scaling properties in the convective air mass were characterized by rough and highly intermittent data series, whereas the nonconvective regime was dominated by smoother structures with weaker small-scale variability. This study finds similar results in a model simulation with an even more pronounced distinction between the two air masses. Quantitative scaling diagnostics agree well with measurements in the nonconvective air mass, whereas in the convective air mass the simulation shows a much higher intermittency. Sensitivity analyses were performed using the model data to assess the impact of limitations of the observational dataset, which indicate that analyses of lidar data most likely underestimated the intermittency in convective air masses due to the small samples from single flight tracks, which led to a bias when data with poor fits were rejected. Though the quantitative estimation of intermittency remains uncertain for convective air masses, the ability of the model to capture the dominant weather regime dependence of water vapor scaling properties is encouraging.

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Stephan Rasp, Tobias Selz, and George C. Craig

Abstract

Air parcel ascent in midlatitude cyclones driven by latent heat release has been investigated using convection-permitting simulations together with an online trajectory calculation scheme. Three cyclones were simulated to represent different ascent regimes: one continental summer case, which developed strong convection organized along a cold front; one marine winter case representing a slantwise ascending warm conveyor belt; and one autumn case, which contains both ascent types as well as mesoscale convective systems. Distributions of ascent times differ significantly in mean and shape between the convective summertime case and the synoptic wintertime case, with the mean ascent time being one order of magnitude larger for the latter. For the autumn case the distribution is a superposition of both ascent types, which could be separated spatially and temporally in the simulation. In the slowly ascending airstreams a significant portion of the parcels still experienced short phases of convective ascent. These are linked to line convection in the boundary layer for the wintertime case and an elevated conditionally unstable layer in the autumn case. Potential vorticity (PV) modification during ascent has also been investigated. Despite the different ascent characteristics it was found that net PV change between inflow and outflow levels is very close to zero in all cases. The spread of individual PV values, however, is increased after the ascent. This effect is more pronounced for convective trajectories.

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Stephan Rasp, Tobias Selz, and George C. Craig

Abstract

The statistical theory of convective variability developed by Craig and Cohen in 2006 has provided a promising foundation for the design of stochastic parameterizations. The simplifying assumptions of this theory, however, were made with tropical equilibrium convection in mind. This study investigates the predictions of the statistical theory in real-weather case studies of nonequilibrium summertime convection over land. For this purpose, a convection-permitting ensemble is used in which all members share the same large-scale weather conditions but the convection is displaced using stochastic boundary layer perturbations. The results show that the standard deviation of the domain-integrated mass flux is proportional to the square root of its mean over a wide range of scales. This confirms the general applicability and scale adaptivity of the Craig and Cohen theory for complex weather. However, clouds tend to cluster on scales of around 100 km, particularly in the morning and evening. This strongly impacts the theoretical predictions of the variability, which does not include clustering. Furthermore, the mass flux per cloud closely follows an exponential distribution if all clouds are considered together and if overlapping cloud objects are separated. The nonseparated cloud mass flux distribution resembles a power law. These findings support the use of the theory for stochastic parameterizations but also highlight areas for improvement.

Open access
Mirjam Hirt, Stephan Rasp, Ulrich Blahak, and George C. Craig

Abstract

Kilometer-scale models allow for an explicit simulation of deep convective overturning but many subgrid processes that are crucial for convective initiation are still poorly represented. This leads to biases such as insufficient convection triggering and late peak of summertime convection. A physically based stochastic perturbation scheme (PSP) for subgrid processes has been proposed (Kober and Craig) that targets the coupling between subgrid turbulence and resolved convection. The first part of this study presents four modifications to this PSP scheme for subgrid turbulence: an autoregressive, continuously evolving random field; a limitation of the perturbations to the boundary layer that removes artificial convection at night; a mask that turns off perturbations in precipitating columns to retain coherent structures; and nondivergent wind perturbations that drastically increase the effectiveness of the vertical velocity perturbations. In a revised version, PSP2, the combined modifications retain the physically based coupling to the boundary layer scheme of the original scheme while removing undesirable side effects. This has the potential to improve predictions of convective initiation in kilometer-scale models while minimizing other biases. The second part of the study focuses on perturbations to account for convective initiation by subgrid orography. Here the mechanical lifting effect is modeled by introducing vertical and horizontal wind perturbations of an orographically induced gravity wave. The resulting perturbations lead to enhanced convective initiation over mountainous terrain. However, the total benefit of this scheme is unclear and we do not adopt the scheme in our revised configuration.

Free access
Kevin Bachmann, Christian Keil, George C. Craig, Martin Weissmann, and Christian A. Welzbacher

Abstract

We investigate the practical predictability limits of deep convection in a state-of-the-art, high-resolution, limited-area ensemble prediction system. A combination of sophisticated predictability measures, namely, believable and decorrelation scale, are applied to determine the predictable scales of short-term forecasts in a hierarchy of model configurations. First, we consider an idealized perfect model setup that includes both small-scale and synoptic-scale perturbations. We find increased predictability in the presence of orography and a strongly beneficial impact of radar data assimilation, which extends the forecast horizon by up to 6 h. Second, we examine realistic COSMO-KENDA simulations, including assimilation of radar and conventional data and a representation of model errors, for a convectively active two-week summer period over Germany. The results confirm increased predictability in orographic regions. We find that both latent heat nudging and ensemble Kalman filter assimilation of radar data lead to increased forecast skill, but the impact is smaller than in the idealized experiments. This highlights the need to assimilate spatially and temporally dense data, but also indicates room for further improvement. Finally, the examination of operational COSMO-DE-EPS ensemble forecasts for three summer periods confirms the beneficial impact of orography in a statistical sense and also reveals increased predictability in weather regimes controlled by synoptic forcing, as defined by the convective adjustment time scale.

Free access
Marlene Baumgart, Paolo Ghinassi, Volkmar Wirth, Tobias Selz, George C. Craig, and Michael Riemer

Abstract

Two diagnostics based on potential vorticity and the envelope of Rossby waves are used to investigate upscale error growth from a dynamical perspective. The diagnostics are applied to several cases of global, real-case ensemble simulations, in which the only difference between the ensemble members lies in the random seed of the stochastic convection scheme. Based on a tendency equation for the enstrophy error, the relative importance of individual processes to enstrophy-error growth near the tropopause is quantified. After the enstrophy error is saturated on the synoptic scale, the envelope diagnostic is used to investigate error growth up to the planetary scale. The diagnostics reveal distinct stages of the error growth: in the first 12 h, error growth is dominated by differences in the convection scheme. Differences in the upper-tropospheric divergent wind then project these diabatic errors into the tropopause region (day 0.5–2). The subsequent error growth (day 2–14.5) is governed by differences in the nonlinear near-tropopause dynamics. A fourth stage of the error growth is found up to 18 days when the envelope diagnostic indicates error growth from the synoptic up to the planetary scale. Previous ideas of the multiscale nature of upscale error growth are confirmed in general. However, a novel interpretation of the governing processes is provided. The insight obtained into the dynamics of upscale error growth may help to design representations of uncertainty in operational forecast models and to identify atmospheric conditions that are intrinsically prone to large error amplification.

Open access
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-yr phase of our planned duration of 12 years and employ 36 doctoral and postdoctoral 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.

Open access