Since radar observations are highly dense in spatial and temporal resolutions, they have been often used to improve short‐term numerical weather prediction (NWP) by means of detailed model ...verification and 3D radar data assimilation. However, the observed quantities are not directly comparable to the prognostic variables of NWP models (e.g. hydrometeor densities, wind vector, temperature, pressure, etc.), so a common approach to facilitate this comparison is to derive synthetic radar observations from model variables; this is the so‐called ‘radar forward operator’. In the present article, a new Efficient Modular VOlume scanning RADar Operator (EMVORADO) for Doppler velocity and reflectivity is introduced. Although it has been developed in the COSMO model framework, it can be also coupled online to any other NWP model. Comprehensive physical aspects of radar measurements (e.g. beam bending/broadening/shielding, Doppler velocity with fall speed and reflectivity weighting, attenuated reflectivity, detectable signal, etc.) have been implemented in a modular way, using state‐of‐the‐art methods with different levels of approximation and numerical costs that can be optionally chosen. The reflectivity derivation from the prognostic model variables is as ‘model consistent’ as possible and carefully honours the uncertainties associated with partially melted particles. Efficiency and applicability on supercomputers (MPI‐parallelism) is a major design criterion, which allows us to simulate entire networks of 3D volume‐scanning meteorological radars within one model run and makes EMVORADO well suited for operational applications. This article aims to give a thorough description of the EMVORADO and to provide a first insight to the performance of different modules by some selected case‐studies.
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.
Radar data assimilation has been operational at the Deutscher Wetterdienst for several years and is essential for generating accurate precipitation forecasts. The current work attempts to further ...enhance the radar data assimilation by improving the latent heat nudging (LHN) scheme and by reducing the observation error (OE) caused by the representation error of the efficient modular volume radar operator (EMVORADO). First of all, a series of hindcasts for a one-month convective period over Germany are performed. Compared with radar reflectivity and satellite observations, it is found that the LHN scheme that implicitly adjusts temperature performs better, and the beam broadening effect and the choice of the scattering schemes in EMVORADO are important. Moreover, the Mie scheme with the new parameterization to reduce the brightband effect not only proves to be the best in hindcasts but also that it results in the smallest standard deviations and the shortest horizontal correlation length scales of the OE in data assimilation experiments.
In the present work, we investigate the impacts on the observation error (OE) statistics due to different types of errors in the forward operator (FE) for both radar reflectivity and radial wind ...data, in the context of convective-scale data assimilation in the summertime. A series of sensitivity experiments were conducted with the Efficient Modular VOlume RADar Operator (EMVORADO), using the operational data assimilation system of the Deutscher Wetterdienst (DWD, German Weather Service). The investigated FEs are versatile, including errors caused by neglecting the terminal fall speed of hydrometeor, the reflectivity weighting, and the beam broadening and attenuation effects, as well as errors caused by different scattering schemes and formulations for melting particles. For reflectivity, it is found that accounting for the beam broadening effect evidently reduces the standard deviations, especially at higher altitudes. However, it does not shorten the horizontal or along-beam correlation length scales. In comparison between the Rayleigh and the Mie schemes (with specific configurations), the former one results in much smaller standard deviations for heights up to 4 km, and aloft, slightly larger standard deviations. Imposing the attenuation to the Mie scheme slightly reduces the standard deviations at lower altitudes; however, it largely increases the standard deviations at higher altitudes and it also leads to longer correlation length scales. For radial wind, positive impacts of considering the beam broadening effect on standard deviations and neutral impacts on correlations are observed. For both reflectivity and radial wind, taking the terminal fall speed of hydrometeor and the reflectivity weighting into account does not make remarkable differences in the estimated OE statistics.
Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance ...matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations are assimilated and for assignment of the OE covariance matrix that can be diagonal or full and correlated.
For convective clouds and precipitation, model uncertainty in cloud microphysics is considered one of the most significant sources of model error. In this study, samples for model microphysical ...uncertainty are obtained by calculating the differences between simulations equipped with two‐ and one‐moment schemes during a one‐month training period. The samples are then added to convective‐scale ensemble data assimilation as additive noise and combined with large‐scale additive noise based on samples from climatological atmospheric background error covariance. Two experiments, including the combination and large‐scale error only, are conducted for a one‐week convective period. The results reveal that the simulation with a two‐moment scheme triggers more convection and has larger ice‐phase precipitation particles, which produce a stronger signal in the melting layer. During data assimilation cycling, although more water is introduced to the model, it is shown that the combination performs better for both background and analysis and significantly improves short‐term ensemble forecasts of radar reflectivity and hourly precipitation.
Plain Language Summary
One of the main difficulties hindering the improvements of weather forecasts is correct representation of uncertainties in clouds and precipitation in the numerical weather prediction models. The goal of this work is to improve the representation of this uncertainty when combining our prediction with observations. This way, we would obtain better initial condition for our model and better prediction of convection. Here, we obtain the samples for model error by computing the differences between simulations that use two cloud microphysical schemes in the model. Then such obtained samples for model microphysical uncertainty are combined with large‐scale error and incorporated into data assimilation. To evaluate the performance of this method, two experiments are carried out in a one‐week period over Germany. We find that the combination indeed achieves significant improvement of short‐term forecasts of radar reflectivity and hourly precipitation.
Key Points
Model simulations with two microphysical schemes are used to represent uncertainty in clouds and precipitation during data assimilation
In data assimilation, including the combination of microphysical and large‐scale uncertainty improves the performance
The improvement is also significant for short‐term ensemble forecasts of radar reflectivity and hourly precipitation
The ensemble Kalman filter algorithm can produce negative values for non‐negative variables. To mitigate this sign problem and to simultaneously maintain the mass conservation, a new concept of ...combining weak constraints on mass conservation and non‐negativity has been introduced in this work, with a focus on hydrometeor variables in convective‐scale data assimilation. We modify the local ensemble transform Kalman filter with weak constraints on mass conservation for each hydrometeor variable and adopt the assimilation of clear‐air reflectivity data as a weak constraint on non‐negativity. We examine the concept by a series of sensitivity experiments using an idealized setup. Results show that both weak constraints successfully improve the mass conservation property in analyses and both reduce the biased increase in integrated mass‐flux divergence and vorticity. Furthermore, the least biased increase is obtained by combining both constraints, and the best forecasts are also achieved by the combination.
Plain Language Summary
Often physical properties of a system that we are modeling dictate plausible values of the initial conditions of our numerical models. Unfortunately, by using modern data assimilation techniques to obtain these initial conditions, physical property of non‐negativity is frequently violated. On the other hand, algorithms that are able to preserve the non‐negativity usually would break mass conservation. Here, we propose a fast, easy to implement modification of the existing algorithm (local ensemble transform Kalman filter) that is able to weakly preserve both properties of mass conservation and non‐negativity. In idealized experiments that assimilate radar data in non‐hydrostatic, convection‐permitting numerical model and update hydrometeor values, we show the benefit of the proposed approach on prediction of atmospheric water variables.
Key Points
A weakly constrained LETKF for mass conservation and non‐negativity is introduced and examined in convective‐scale data assimilation
Combining both constraints results in the least biases in total mass of hydrometeors and in mass‐flux divergence and vorticity in analyses
Best forecasts are also achieved by the combination
Numerical discretization schemes have a long history of incorporating the most important conservation properties of the continuous system in order to improve the prediction of the nonlinear flow. The ...question arises whether data assimilation algorithms should follow a similar approach. To address this issue, we explore the conservation properties during data assimilation using perfect model experiments with a 2D shallow‐water model preserving important properties of the true nonlinear flow. The data assimilation scheme used here is the Local Ensemble Transform Kalman Filter with varying observed variables, inflation, localization radius and thinning interval. It is found that, during the assimilation, the total energy of the analysis ensemble mean converges with time towards the nature run value. However, enstrophy, divergence and the energy spectra are strongly affected by the data assimilation settings. Having in mind that the conservation of both the kinetic energy and enstrophy by the momentum advection schemes in the case of non‐divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we test the effects on the prediction depending on the type of error in the initial condition. During the assimilation, we assess the downward nonlinear energy cascade through a scalar, domain‐averaged noise measure. We show that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction.
For numerical discretization schemes, the violation of enstrophy conservation causes a systematic and unrealistic energy cascade towards high wave numbers. The same occurs in data assimilation ...schemes, where the total energy, enstrophy and divergence could be strongly affected. In this article, we construct an ensemble data assimilation algorithm that conserves mass, total energy and enstrophy. The algorithm uses B‐spline functions for localization and sequential quadratic programming to solve nonlinear constrained minimization problem. Idealized experiments are performed using a 2D shallow‐water model, with selected contraints derived from the nature run. It is found that all experiments exhibit comparable root‐mean‐square errors, with a slight advantage for those that include the conservation constraint on the globally integrated enstrophy. However, the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of the rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14 day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts.
Unphysical noise can be generated by assimilating data. We construct an ensemble‐type Kalman filter algorithm that enforces the conservation of mass, total energy and enstrophy as equality constraints. Experiments with the enstrophy constraints E_BSP_Es and E_BSP_EnEs (the latter additionally imposing total energy conservation) avoid the spurious energy cascade of the rotational part, thereby suppressing noise and improving the quality of a 14 day free forecast, compared with experiments without the enstrophy constraints E_BSP_NO and E_BSP_En.
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