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Ulrich Blahak

Abstract

To obtain statistically stable reflectivity measurements by meteorological radars, it is common practice to average over several consecutive pulses during which the antenna rotates at a certain angular velocity. Taking into account the antenna’s continuous motion, the measured reflectivity is determined by an effective beam weighting function, which is different from a single-pulse weighting function—a fact that is widely ignored in applications involving beam weighting. In this paper, the effective beam weighting function is investigated in detail.

The theoretical derivation shows that the effective weighting function is essentially a simple moving sum of single-beam weighting functions. Assuming a Gaussian shape of a single pulse, a simple and easy-to-use parameterization of the effective beam weighting function is arrived at, which depends only on the single beamwidth and the ratio of the single beamwidth to the rotational angular averaging interval. The derived relation is formulated in the “radar system” (i.e., the spherical coordinate system consisting of azimuth and elevation angles) that is often applied in practice. Formulas for the “beam system” (two orthogonal angles relative to the beam axis) are also presented.

The final parameterization should be applicable to almost all meteorological radars and might be used (i) in specialized radar data analyses (with ground-based or satellite radars) and (ii) for radar forward operators to calculate simulated radar parameters from the results of NWP models.

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Martin Löffler-Mang and Ulrich Blahak

Abstract

In this paper, a method for the estimation of radar reflectivity from measured snow particle size distributions is presented based on earlier works of Marshall and Gunn and of Smith. During two snowfalls, the method was applied to estimate the equivalent reflectivity factor from measured snow size distributions obtained by the Particle Size and Velocity (PARSIVEL) optical disdrometer. The results are compared with the data of conventional C-band Doppler radar. Here, two snowfalls are presented as case studies. In addition, a comparison during one rainfall is included, which shows good agreement between the two instruments. In the case of snow, the calculation of the equivalent reflectivity factor from the PARSIVEL data is based on a relation between the mass and the size of the snow particles. In this study, a mass–size relation for graupel-like snow was used for all snowfalls. Because this is a crude description of naturally occurring snow, which can be of any other type (e.g., dendrites), the differences with the radar-measured reflectivities here are strongly dependent on the snow particle type. Nevertheless, in one case, the snowfall was fairly homogeneous in time, space, and snow type, and so the agreement was reasonably good, with a relatively constant underestimation (3–5 dB) of the radar data by PARSIVEL and a low variance of the differences. This underestimation could be due to non-graupel-like particles or the tendency of PARSIVEL to underestimate the reflectivities, as outlined in the text. The other snowfall was convective, with strong spatial and temporal variations in precipitation intensity and snow type. The instrument differences in this case ranged from −6 to 16 dB because of changing snow types, but both instruments showed the same qualitative variations. The agreement can be improved by an advanced signal processing of PARSIVEL in which the snow type is determined automatically and a proper mass–size relation is used.

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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
Axel Seifert, Alexander Khain, Ulrich Blahak, and Klaus D. Beheng

Abstract

The effects of the collisional breakup of raindrops are investigated using the Hebrew University Cloud Model (HUCM). The parameterizations, which are combined in the new breakup scheme, are those of Low and List, Beard and Ochs, as well as Brown. A sensitivity study reveals strong effects of collisional breakup on the precipitation formation in mixed-phase deep convective clouds for strong as well as for weak precipitation events. Collisional breakup reduces the number of large raindrops, increases the number of small raindrops, and, as a consequence, decreases surface rain rates and considerably reduces the speed of rain formation. In addition, it was found that including breakup can lead to a more intense triggering of secondary convective cells. But a statistical comparison with observed raindrop size distributions shows that the parameterizations might systematically overestimate collisional breakup.

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Yuefei Zeng, Ulrich Blahak, Malte Neuper, and Dorit Jerger

Abstract

Simulation of radar beam propagation is an important component of numerous radar applications in meteorology, including height assignment, quality control, and especially the so-called radar forward operator. Although beam propagation in the atmosphere depends on the refractive index and its vertical variation, which themselves depend on the actual state of the atmosphere, the most common method is to apply the 4/3 earth radius model, based on climatological standard conditions. Serious deviations from the climatological value can occur under so-called ducting conditions, where radar beams at low elevations can be trapped or propagate in a waveguide-like fashion, such that this model is unsuitable in this case. To account for the actual atmospheric conditions, sophisticated methods have been developed in literature. However, concerning the practical implementation of these methods, it was determined that the description in the literature is not always complete with respect to possible pitfalls for practical implementations.

In this paper, a revised version of an existing method (one example for the above-mentioned “pitfall” statement) is introduced that exploits Snell’s law for spherically stratified media. From Snell’s law, the correct sign of the local elevation is a priori ambiguous, and the revised method explicitly applies (i) a total reflection criterion and (ii) another ad hoc criterion to solve the problem.

Additionally, a new method, based on an ordinary differential equation with respect to range, is proposed in this paper that has no ambiguity.

Sensitivity experiments are conducted to investigate the properties of these three methods. The results show that both the revised and new methods are robust under nonstandard conditions. But considering the need to catch an elevation sign ambiguity in the revised method (which cannot be excluded to fail in rare instances), the new method is regarded as more robust and unproblematic, for example, for applications in radar forward operators.

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Alessandro Battaglia, Elke Rustemeier, Ali Tokay, Ulrich Blahak, and Clemens Simmer

Abstract

The performance of the laser-optical Particle Size Velocity (PARSIVEL) disdrometer is evaluated to determine the characteristics of falling snow. PARSIVEL’s measuring principle is reexamined to detect its limitations and pitfalls when applied to solid precipitation. This study uses snow observations taken during the Canadian Cloudsat/Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) Validation Project (C3VP) campaign, when two PARSIVEL instruments were collocated with a single two-dimensional disdrometer (2-DVD), which allows more detailed observation of snowflakes. When characterizing the snowflake size, PARSIVEL instruments inherently retrieve only one size parameter, which is approximately equal to the widest horizontal dimension (more accurately with large snowflakes) and that has no microphysical meaning. Unlike for raindrops, the equivolume PARSIVEL diameter—the PARSIVEL output variable—has no physical counterpart for snowflakes.

PARSIVEL’s fall velocity measurement may not be accurate for a single snowflake particle. This is due to the internally assumed relationship between horizontal and vertical snow particle dimensions. The uncertainty originates from the shape-related factor, which tends to depart more and more from unity with increasing snowflake sizes and can produce large errors. When averaging over a large number of snowflakes, the correction factor is size dependent with a systematic tendency to an underestimation of the fall speed (but never exceeding 20%).

Compared to a collocated 2-DVD for long-lasting events, PARSIVEL seems to overestimate the number of small snowflakes and large particles. The disagreement between PARSIVEL and 2-DVD snow measurements can only be partly ascribed to PARSIVEL intrinsic limitations (border effects and sizing problems), but it has to deal with the difficulties and drawbacks of both instruments in fully characterizing snow properties.

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Roland Potthast, Klaus Vobig, Ulrich Blahak, and Clemens Simmer

Abstract

We investigate the assimilation of nowcasted information into a classical data assimilation cycle. As a reference setup, we employ the assimilation of standard observations such as direct observations of particular variables into a forecasting system. The pure advective movement extrapolation of observations as a simple nowcasting (NWC) is usually much better for the first minutes to hours, until outperformed by numerical weather prediction (NWP) based on data assimilation. Can nowcasted information be used in the data assimilation cycle? We study both an oscillator model and the Lorenz 63 model with assimilation based on the localized ensemble transform Kalman filter (LETKF). We investigate and provide a mathematical framework for the assimilation of nowcasted information, approximated as a local tendency, into the LETKF in each assimilation step. In particular, we derive and discuss adequate observation error and background uncertainty covariance matrices and interpret the assimilation of nowcasted information as assimilation with an H 1-type metric in observation space. Further, we show numerical results that prove that nowcasted information in data assimilation has the potential to significantly improve model based forecasting.

Open access
Martin Rempel, Peter Schaumann, Reinhold Hess, Volker Schmidt, and Ulrich Blahak

Abstract

A wealth of forecasting models is available for operational weather forecasting. Their strengths often depend on the lead time considered, which generates the need for a seamless combination of different forecast methods. The combined and continuous products are made in order to retain or even enhance the forecast quality of the individual forecasts and to extend the lead time to potentially hazardous weather events. In this study, we further improve an artificial neural network based combination model that was recently proposed in a previous paper. This model combines two initial precipitation ensemble forecasts and produces exceedance probabilities for a set of thresholds for hourly precipitation amounts. Both initial forecasts perform differently well for different lead times, whereas the combined forecast is calibrated and outperforms both initial forecasts with respect to various validation scores and for all considered lead times (+1h to +6h). Moreover, the robustness of the combination model is tested by applying it to a new dataset and by evaluating the spatial and temporal consistency of its forecasts. The changes proposed further improve the forecast quality and make it more useful for practical applications. Temporal consistency of the combined product is evaluated using a flip-flop index. It is shown that the combination provides a higher persistence with decreasing lead times compared to both input systems.

Free access
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.

Open access
Pavel Khain, Reuven Heiblum, Ulrich Blahak, Yoav Levi, Harel Muskatel, Elyakom Vadislavsky, Orit Altaratz, Ilan Koren, Guy Dagan, Jacob Shpund, and Alexander Khain

Abstract

Shallow convection is a subgrid process in cloud-resolving models for which their grid box is larger than the size of small cumulus clouds (Cu). At the same time such Cu substantially affect radiation properties and thermodynamic parameters of the low atmosphere. The main microphysical parameters used for calculation of radiative properties of Cu in cloud-resolving models are liquid water content (LWC), effective droplet radius, and cloud fraction (CF). In this study, these parameters of fields of small, warm Cu are calculated using large-eddy simulations (LESs) performed using the System for Atmospheric Modeling (SAM) with spectral bin microphysics. Despite the complexity of microphysical processes, several fundamental properties of Cu were found. First, despite the high variability of LWC and droplet concentration within clouds and between different clouds, the volume mean and effective radii per specific level vary only slightly. Second, the values of effective radius are close to those forming during adiabatic ascent of air parcels from cloud base. These findings allow for characterization of a cloud field by specific vertical profiles of effective radius and of mean liquid water content, which can be calculated using the theoretical profile of adiabatic liquid water content and the droplet concentration at cloud base. Using the results of these LESs, a simple parameterization of cloud-field-averaged vertical profiles of effective radius and of liquid water content is proposed for different aerosol and thermodynamic conditions. These profiles can be used for calculation of radiation properties of Cu fields in large-scale models. The role of adiabatic processes in the formation of microstructure of Cu is discussed.

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