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Christoph Schär
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Christoph Schär

Abstract

The passage of a low-level baroclinic zone toward an elongated ridge is simulated in the limit of the nonlinear quasi-geostrophic dynamics of a uniform potential vorticity atmosphere. It is demonstrated that lee cyclogenesis can be realized for this combination of flow setting and idealized model. Moreover, the temporal growth rate, the spatial structure, the genesis region, and the subsequent movement of the cyclone bear comparison with observed features of Alpine lee cyclogenesis.

A series of numerical experiments serve to demonstrate the sensitivity of the lee event to external parameters and help to pinpoint its dynamical essence. In particular it is shown that the simulated development exhibits a two-stage character. The first phase is accompanied by growth rates that clearly exceed those of classical baroclinic instability and it is associated with the retardation, distortion, and frontogenetic development of the baroclinic zone as it impinges upon the orography. The resulting low-level perturbation is trapped in the close vicinity of the obstacle by effects due to localized baroclinicity. The second phase is a baroclinic development. It is characterized by the relative propagation of upper- and lower-level anomalies that result in the interaction of the preexisting upper-level vorticity strip and the incipient low-level vortex.

In relation to the various theories for lee cyclogenesis, it is noted that the horizontal scale of the first phase thermal perturbation is in agreement with the predictions of the baroclinic lee–wave theory, while the development in the second phase is more compatible to that of a type-B cyclogenesis than to an orographically modified modal baroclinic wave development.

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Christoph Schär

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The conservation of potential vorticity Q can be expressed as ∂(ρQ/∂t + ∇·J = 0, where J denotes the total flux of potential vorticity. It is shown that J is related under statistically steady conditions to the Bernoulli function B by
JθB
,where θ is the potential temperature. This relation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heating rates. In essence, it can be interpreted as a generalization of Bernoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem—valid for inviscid adiabatic and steady flows—states that the intersections of surfaces of constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux lines along which potential vorticity is transported.
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Christoph Frei and Christoph Schär

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A statistical framework is presented for the assessment of climatological trends in the frequency of rare and extreme weather events. The methodology applies to long-term records of event counts and is based on the stochastic concept of binomial distributed counts. It embraces logistic regression for trend estimation and testing, and includes a quantification of the potential/limitation to discriminate a trend from the stochastic fluctuations in a record. This potential is expressed in terms of a detection probability, which is calculated from Monte Carlo–simulated surrogate records, and determined as a function of the record length, the magnitude of the trend and the average return period (i.e., the rarity) of events.

Calculations of the detection probability for daily events reveal a strong sensitivity upon the rarity of events:in a 100-yr record of seasonal counts, a frequency change by a factor of 1.5 can be detected with a probability of 0.6 for events with an average return period of 30 days; however, this value drops to 0.2 for events with a return period of 100 days. For moderately rare events the detection probability decreases rapidly with shorter record length, but it does not significantly increase with longer record length when very rare events are considered. The results demonstrate the difficulty to determine trends of very rare events, underpin the need for long period data for trend analyses, and point toward a careful interpretation of statistically nonsignificant trend results.

The statistical method is applied to examine seasonal trends of heavy daily precipitation at 113 rain gauge stations in the Alpine region of Switzerland (1901–94). For intense events (return period: 30 days) a statistically significant frequency increase was found in winter and autumn for a high number of stations. For strong precipitation events (return period larger than 100 days), trends are mostly statistically nonsignificant, which does not necessarily imply the absence of a trend.

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Oliver Fuhrer and Christoph Schär

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Marginally unstable air masses impinging upon a mountain ridge may lead to the development of a nominally stratiform orographic cloud with shallow embedded convection. Rainfall amounts and distribution are then strongly influenced by the convective dynamics. In this study, the transition from purely stratiform orographic precipitation to flow regimes with embedded convection is systematically investigated. To this end, idealized cloud-resolving numerical simulations of moist flow past a two-dimensional mountain ridge are performed in a three-dimensional domain. A series of simulations with increasing upstream potential instability shows that the convective dynamics may significantly increase precipitation amounts, intensity, and efficiency, to an extent that cannot be replicated by two-dimensional simulations. Under conditions of uniform upstream flow, the embedded convection is of the cellular type. It is demonstrated that simple stability measures of the upstream profile are poor predictors for the occurrence and depth of embedded convection. A linear stability analysis is performed to understand the linear growth of the developing convective instabilities. Embedded convection results if the growth rates of convective instabilities are compatible with the advective time scale (the time an air parcel spends inside the orographic cloud) and the microphysical time scale (time for rain production and fallout). Individual convective updrafts are anchored to the mean flow. Additional simulations serve to demonstrate that the development of embedded convection and associated precipitation may strongly depend on small-amplitude upstream perturbations. Such perturbations enhance the efficacy of the convective circulations and lead to overall stronger precipitation. The potential implications of this result for the predictability of quantitative precipitation are also discussed.

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Urs Aebischer and Christoph Schär

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High-resolution numerical model simulations over the Alpine region are presented that reveal the presence of low-level elongated bands of potential vorticity (PV) downstream of high topography. These PV streamers (or PV banners) occur when the synoptic-scale wind turns into a direction across the Alps. Individual pairs of banners with anomalously positive and negative values of PV can be attributed to flow splitting, either on the scale of the whole of the Alps (primary banners), or on that of individual massifs and peaks of the model topography (secondary banners). The PV bands have amplitudes of up to −2.5 and +5 pvu, a width of 50–150 km, can attain a length of up to 1500 km, and extend in the vertical from the surface up to the 500-hPa level on occasions. The PV banners are associated with zones of enhanced horizontal wind shear. The analysis of daily output from the operational NWP model run of the Swiss Meteorological Institute also demonstrates that such PV streamers are a frequent feature and occur whenever there is appreciable flow past the Alps.

Low-level PV streamers may interact with the larger-scale flow, and thereby represent an intermediary between the (unbalanced) formation of an orographic vortex, and its (approximately balanced) interaction with the synoptic-scale environment. This process is analyzed for one particular case of Alpine lee cyclogenesis. Simulations show that PV streamers may wrap up and subsequently contribute to the low-level PV anomaly within the developing cyclone. It is suggested that the two phases of Alpine lee cyclogenesis can be interpreted in this way, that is, as the rapid formation of a low-level orographic vortex followed by its baroclinic and diabatic interaction with an approaching upper-level trough. To test this interpretation, sensitivity studies with dry dynamics, reduced surface friction, and idealized terrain are conducted.

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Christoph Schär and Nico Kröner

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Models are attractive tools to deepen the understanding of atmospheric and climate processes. In practice, such investigations often involve numerical experiments that switch on or off individual factors (such as latent heating, nonlinear coupling, or some climate forcing). However, as in general many factors can be considered, the analysis of these experiments is far from straightforward. In particular, as pointed out in an influential study on factor separation by Stein and Alpert, the analysis will often require the consideration of nonlinear interaction terms.

In the current paper an alternative factor separation methodology is proposed and analyzed. Unlike the classical method, sequential factor separation (SFS) does not involve the derivation of the interaction terms but, rather, provides some uncertainty measure that addresses the quality of the separation. The main advantage of the proposed methodology is that in the case of n factors it merely requires 2n simulations (rather than 2n for the classical analysis). The paper provides an outline of the methodology, a detailed mathematical analysis, and a theoretical intercomparison against the classical methodology. In addition, an example and an intercomparison using regional climate model experiments with n = 3 factors are presented. The results relate to the Mediterranean amplification and demonstrate that—at least in the particular example considered—the two methodologies yield almost identical results and that the SFS is rather insensitive with respect to design choices.

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Cathy Hohenegger and Christoph Schär

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While the benefits of ensemble techniques over deterministic numerical weather predictions (NWP) are now widely recognized, the prospects of ensemble prediction systems (EPS) at high computational resolution are still largely unclear. Difficulties arise due to the poor knowledge of the mechanisms promoting rapid perturbation growth and propagation, as well as the role of nonlinearities. In this study, the dynamics associated with the growth and propagation of initial uncertainties is investigated by means of real-case high-resolution (cloud resolving) NWP integrations. The considered case is taken from the Mesoscale Alpine Programme intensive observing period 3 (MAP IOP3) and involves convection of intermediate intensity. To assess the underlying mechanisms and the degree of linearity upon the predictability of the flow, vastly different initial perturbation methodologies are compared, while all simulations use identical lateral boundary conditions to mimic a perfectly predictable synoptic-scale flow.

Comparison of the perturbation methodologies indicates that the ensuing patterns of ensemble spread converge within 11 h, irrespective of the initial perturbations employed. All methodologies pinpoint the same meso-beta-scale regions of the flow as suffering from predictability limitations. This result reveals the important role of nonlinearities. Analysis also shows that hot spots of error growth can quickly (1–2 h after initialization) develop far away from the initial perturbations. This rapid radiation of the initial uncertainties throughout the computational domain is due to both sound and gravity waves, followed by the triggering and/or growth of perturbations over regions of convective instability. The growth of the uncertainties is then limited by saturation effects, which in turn are controlled by the larger-scale atmospheric environment.

From a practical point of view, it is suggested that the combined effects of rapid propagation, sizeable amplification, and inherent nonlinearities may pose severe difficulties for the design of EPS or data assimilation techniques related to high-resolution quantitative precipitation forecasting.

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Oliver Fuhrer and Christoph Schär

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Shallow orographic convection embedded in an unstable cap cloud can organize into convective bands. Previous research has highlighted the important role of small-amplitude topographic variations in triggering and organizing banded convection. Here, the underlying dynamical mechanisms are systematically investigated by conducting three-dimensional simulations of moist flows past a two-dimensional mountain ridge using a cloud-resolving numerical model. Most simulations address a sheared environment to account for the observed wind profiles. Results confirm that small-amplitude topographic variations can enhance the development of embedded convection and anchor quasi-stationary convective bands to a fixed location in space. The resulting precipitation patterns exhibit tremendous spatial variability, since regions receiving heavy rainfall can be only kilometers away from regions receiving little or no rain. In addition, the presence of banded convection has important repercussions on the area-mean precipitation amounts.

For the experimental setup here, the gravity wave response to small-amplitude topographic variations close to the upstream edge of the cap cloud (which is forced by the larger-scale topography) is found to be the dominant triggering mechanism. Small-scale variations in the underlying topography are found to force the location and spacing of convective bands over a wide range of scales. Further, a self-sufficient mode of unsteady banded convection is investigated that does not dependent on external perturbations and is able to propagate against the mean flow. Finally, the sensitivity of model simulations of banded convection with respect to horizontal computational resolution is investigated. Consistent with predictions from a linear stability analysis, convective bands of increasingly smaller scales are favored as the horizontal resolution is increased. However, small-amplitude topographic roughness is found to trigger banded convection and to control the spacing and location of the resulting bands. Thereby, the robustness of numerical simulations with respect to an increase in horizontal resolution is increased in the presence of topographic variations.

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Cathy Hohenegger and Christoph Schar

The limited atmospheric predictability has been addressed by the development of ensemble prediction systems (EPS) that are now routinely applied for medium-range synoptic-scale numerical weather prediction (NWP). With the increase of computational power, interest is growing in the design of high-resolution (cloud resolving) NWP models and their associated short-range EPS. This development raises a series of fundamental questions, especially concerning the type of error growth and the validity of the tangent-linear approximation. To address these issues, a comparison between perturbed medium-range (10 day) synoptic-scale integrations (taken from the operational ECMWF EPS with a horizontal resolution of about 80 km) and short-range (1 day) high-resolution simulations (based on the Lokal Modell of the Consortium for Small-Scale Modeling with a grid spacing of 2.2 km) is conducted. The differences between the two systems are interpreted in a nondimensional sense and illustrated with the help of the Lorenz attractor.

Typical asymptotic perturbation-doubling times of cloud-resolving and synoptic-scale simulations amount to about 4 and 40 h, respectively, and are primarily related to convective and baroclinic instability. Thus, in terms of growth rates, integrating a 1-day cloud-resolving forecast may be seen as equivalent to performing a 10-day synoptic-scale simulation. However, analysis of the prevailing linearity reveals that the two systems are fundamentally different in the following sense: the tangent-linear approximation breaks down at 1.5 h for cloud resolving against 54 h for synoptic-scale forecasts. In terms of nonlinearity, a 10-day synoptic-scale integration thus corresponds to a very short cloud-resolving simulation of merely about 7 h. The higher degree of nonlinearity raises questions concerning the direct application of standard synoptic-scale forecasting methodologies (e.g., optimal perturbations, 4D variational data assimilation, or targeted observations) to 1-day cloud-resolving forecasting.

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