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Yu-Chieng Liou

Abstract

The errors produced by a least squares type single-Doppler velocity retrieval scheme based on variational analysis are studied. With proper simplifications of the retrieval formulation, it can be found that the strength of the retrieved radial wind is comparable to the true one. By contrast, the retrieved azimuthal component is, in most cases, underestimated. For a given radar site, this underestimation is directly related to the discrete nature of the radar observations. It occurs when the time period between two radar scans, Δt, is greater than Δx/u, where Δx is the radar's spatial resolution and u is the speed of the observed weather phenomenon. This condition unfortunately is often true for today's Doppler radar operational modes. As a result, an underestimation of the retrieved wind speed becomes inevitable. Retrieval work performed on an optimized moving frame of reference can reduce the aforementioned error in the retrieved azimuthal component of wind. The experiment also demonstrates that the search for this moving reference frame can be achieved as long as Δt is less than λ/2u, where λ is the wavelength of the weather phenomenon. This condition is somewhat relaxed, and it can be fulfilled without much difficulty by the current operational Doppler radars. The results predicted by the theoretical analyses are confirmed by a real case study.

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Yu-Chieng Liou

Abstract

A thermodynamic retrieval scheme has been developed by which one can derive the pressure and potential temperature perturbation fields from wind observations detected by remote sensing devices such as Doppler radar. In this method, the technique of variational analysis is applied to seek a set of optimal solutions for the pressure and potential temperature perturbations that, in the least squares sense, will simultaneously satisfy three momentum equations and the thermodynamic equation. The products of the retrieval are the three-dimensional absolute potential temperature fluctuations and the pressure perturbation gradients in any direction. Using artificial datasets generated by a numerical model, a series of experiments is conducted to test the proposed algorithm against various types of degraded input data. These primarily include finite difference approximations of the local temporal derivatives, random errors embedded in velocity observations with significant magnitudes, as well as incomplete data coverage. Improvements in the retrievals are found to be possible if, within a short period of time, wind data are available at multiple time levels. Overall, it has been demonstrated that the absolute potential temperature field and the pressure gradients can be determined with sufficient accuracy in a three-dimensional space. Such a capability is believed to be particularly useful in many meteorological applications.

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Yu-Chieng Liou

Abstract

The moving frame of reference technique is modified so that the unobserved cross-beam wind components can be retrieved, with high resolution, from data measured by either single-Doppler or conventional radar. In this modified algorithm the reflectivity fields detected by consecutive radar scans are used to find a moving frame of reference for which the reflectivity measurements are as stationary as possible. After interpolating all of the observational data onto this optimal moving frame and assuming that the wind field is in a steady state for several radar scans, one can formulate a cost function that contains the following weak constraints: 1) conservation of reflectivity; 2) a geometric relationship between the radial velocity V r and its Cartesian components u, υ, w; 3) incompressibility; and 4) small vertical vorticity. By minimizing this cost function, a complete three-dimensional wind field can be constructed. Using simulated data to test this method against the original moving-frame technique, it is found that the retrieval results are improved significantly. The modified method can sustain different sources of errors. This property is needed if the application of this method to real Doppler radar datasets is desired. When only reflectivity data are available, the modified method can still catch the principal feature embedded in the true wind field, which implies that the utility of a conventional radar—if equipped by this modified method—might be promoted further. Finally, the computation is economical, which is important for operational purposes. Overall, the modification proposed in this study substantially increases the moving-frame technique’s applicability.

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Yu-Chieng Liou
and
Ya-Ju Chang

Abstract

A multiple–Doppler radar synthesis method is developed to recover the three-dimensional wind field. In this method the solutions are obtained by variationally adjusting the winds to satisfy a series of constraints in weak formats. Among them, the primary ones are multiple-radar radial velocity observations, the anelastic continuity equation, the vertical vorticity equation, the background wind, and spatial smoothness terms. The retrieved wind products are at two time levels, and can be readily applied to deduce the information about the pressure and temperature through the use of the thermodynamic retrieval algorithm, in which the temporal derivatives of the wind fields are required.

Experiments using model-simulated data are conducted, from which two major findings are obtained. First, the wind field along and near the radar baseline can still be recovered. This is a major advantage over the traditional approach. Therefore, the proposed method is capable of providing uninterrupted observations of a weather system as it passes the baseline. This allows for more flexibility when designing the radar deployment in field experiments. Second, if the winds are applied to infer the thermodynamic fields using the traditional dynamic retrieval method, and an extra sounding (e.g., radiosonde or dropsonde) is combined in order to specify the horizontal average of the thermodynamic perturbations, the preferable place to release this sounding is within the region of weak, rather than strong, convection.

In additional to the aforementioned findings, with this method there is no need to prescribe the top or bottom boundary conditions for the vertical velocities in the traditional sense. Since the computation is performed without explicit vertical integration of the continuity equation, the problem of error accumulation due to inappropriate boundary conditions for the vertical velocities is prevented. These finding are consistent with some previous publications. Furthermore, the instability that occurs during traditional iterative dual-Doppler wind synthesis based on a Cartesian coordinate can also be avoided. Finally, data from any number of radars can be easily added to the computation.

This method is also tested using the radar datasets collected during the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX), which was conducted from May to June 2008 in Taiwan, and reasonable results are obtained.

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Yu-Chieng Liou
and
Ing-Shiang Luo

Abstract

The moving-frame single-Doppler radar wind retrieval technique is investigated using field experimental data observed during the 1987 Taiwan Area Mesoscale Experiment intensive observation period 2. Emphasis is placed on studying the impact of the geometric position of the radar in relation to the quality of the retrievals. Experiments show that this technique is capable of recovering the missing cross-beam wind components, but their magnitude is always underestimated. As a consequence, when the unobserved tangential components are smaller than the observable radial components, the best results are produced. By contrast, if the unknown cross-beam winds considerably exceed the radial winds because of a disadvantageous relationship to the radar observation site, the retrievals become less reliable. However, even without a priori knowledge of the true flow structure, which is always the case in reality, this single-Doppler retrieval scheme demonstrates its ability to distinguish which component (radial or azimuthal) is greater. In other words, when the tangential component completely dominates the radial winds, this message can be correctly delivered through the retrieval algorithm to alert the users so that the radar data and these single-Doppler-retrieved results will be interpreted and used with caution.

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Yu-Chieng Liou
and
Yung-Lin Teng

Abstract

It has been long recognized that in the retrieved thermodynamic fields using multiple-Doppler radar synthesized winds, an unknown constant exists on each horizontal level, leading to an ambiguity in the retrieved vertical structure. In this study, the traditional thermodynamic retrieval scheme is significantly improved by the implementation of the Equation of State (EoS) as an additional constraint. With this new formulation, the ambiguity of the vertical structure can be explicitly identified and removed from the retrieved three-dimensional thermodynamic fields. The only in situ independent observations needed to perform the correction are the pressure and temperature measurements taken at a single surface station. If data from multiple surface stations are available, a strategy is proposed to obtain a better estimate of the unknown constant. Experiments in this research were conducted under the observation system simulation experiment (OSSE) framework to demonstrate the validity of the new approach. Problems and possible solutions associated with using real datasets and potential future extended applications of this new method are discussed.

Open access
Yu-Chieng Liou
,
Tai-Chi Chen Wang
, and
Pei-Yu Huang

Abstract

This study documents observational changes in the eyewall of Typhoon Fanapi (2010) after landfall in Taiwan. The observations indicate that Fanapi’s eye and eyewall disappeared on the eastern side of Taiwan’s Central Mountain Range (CMR) after landfall, but reemerged on the western side of CMR. The cyclonic circulation, increasing wind speed, a low-level low pressure and high temperature zone, the associated updrafts and downdrafts, and surface pressure and rainfall measurements all support the existence of a reintensified eyewall. The storm slowed down during the redeveloping stage, thus prolonging the rainfall duration over Taiwan.

On the western side of CMR a northwest–southeast-oriented rainband formed at an earlier stage, possibly due to the large-scale interaction between Fanapi’s remnant flow and the environment. However, the subsequent reintensification might be attributed to the interaction between the circulation and topography. This is supported by the finding that adjacent to CMR, strong wind develops vertically from lower levels, indicating that the reintensification appears to be initiated through a bottom-up process. A vorticity budget analysis shows that at lower layers the stretching mechanism plays a leading role in increasing positive vorticity, followed by the contributions from tilting and horizontal advection. The horizontal advection plays a comparable role to the vertical advection in increasing low- to midlevel vorticity. The vertical advection aloft is responsible for transporting the vorticity upward. Finally, this research provides a relatively rare documentation of the vortical hot towers (VHTs) over terrain using ground-based radars, in contrast to most previous studies focusing on maritime VHTs using simulations or aircraft measurements.

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Wei-Yu Chang
,
Wen-Chau Lee
, and
Yu-Chieng Liou

Abstract

Dual-Doppler, polarimetric radar observations and precipitation efficiency (PE) calculations are used to analyze subtropical heavy rainfall events that occurred in southern Taiwan from 14 to 17 June 2008 during the Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX) field campaign. Two different periods of distinct precipitation systems with diverse kinematic and microphysical characteristics were investigated: 1) prefrontal squall line (PFSL) and 2) southwesterly monsoon mesoscale convective system (SWMCS). The PFSL was accompanied by a low-level front-to-rear inflow and pronounced vertical wind shear. In contrast, the SWMCS had a low-level southwesterly rear-to-front flow with a uniform vertical wind field. The PFSL (SWMCS) contained high (low) lightning frequency associated with strong (moderate) updrafts and intense graupel–rain/graupel–small hail mixing (more snow and less graupel water content) above the freezing level. It is postulated that the reduced vertical wind shear and enhanced accretional growth of rain by high liquid water content at low levels in the SWMCS helped produce rainfall more efficiently (53.1%). On the contrary, the deeper convection of the PFSL had lower PE (45.0%) associated with the evaporative loss of rain and the upstream transport of liquid water to form larger stratiform regions. By studying these two events, the dependence of PE on the environmental and microphysical factors of subtropical heavy precipitation systems are investigated by observational data for the first time. Overall, the PE of the convective precipitation region (47.9%) from 14 to 17 June is similar to past studies of convective precipitation in tropical regions.

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Yu-Chieng Liou
,
Tai-Chi Chen Wang
, and
Kao-Shen Chung

Abstract

A newly designed retrieval scheme based on three-dimensional variational analysis is used to extract the thermodynamic field of a weather system from Doppler wind measurements. As compared with the traditional retrieval method, with this formulation the proposed scheme is able to find a set of optimal solutions for the pressure and buoyancy perturbations that, in the least squares sense, will simultaneously satisfy three momentum equations and a simplified thermodynamic equation. Therefore, the products of the retrieval are the complete thermodynamic fields in three dimensions. To test the performance of this method in real cases, it is applied to the analysis of a subtropical squall line. The required wind data were synthesized by two C-band Doppler radars during the 1987 Taiwan Area Mesoscale Experiment (TAMEX). The emphasis of this study is devoted to an examination of the validity of the retrieved thermodynamic structure, especially along the vertical direction. The results indicate that the distributions of the retrieved thermodynamic parameters are consistent with the kinematic structure and can be reasonably explained by the conceptual model of a squall line. Evidence is collected that strongly supports the validity of the derived thermodynamic structure. Thus, the applicability of this new retrieval scheme is demonstrated.

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Yu-Chieng Liou
,
Shao-Fan Chang
, and
Juanzhen Sun

Abstract

This study develops an extension of a variational-based multiple-Doppler radar synthesis method to construct the three-dimensional wind field over complex topography. The immersed boundary method (IBM) is implemented to take into account the influence imposed by a nonflat surface. The IBM has the merit of providing realistic topographic forcing without the need to change the Cartesian grid configuration into a terrain-following coordinate system. Both Dirichlet and Neumann boundary conditions for the wind fields can be incorporated. The wind fields above the terrain are obtained by variationally adjusting the solutions to satisfy a series of weak constraints, which include the multiple-radar radial velocity observations, anelastic continuity equation, vertical vorticity equation, background wind, and spatial smoothness terms. Experiments using model-simulated data reveal that the flow structures over complex orography can be successfully retrieved using radial velocity measurements from multiple Doppler radars. The primary advantages of the original synthesis method are still maintained, that is, the winds along and near the radar baseline are well retrieved, and the resulting three-dimensional flow fields can be used directly for vorticity budget diagnosis. If compared with the traditional wind synthesis algorithm, this method is able to merge data from different sources, and utilize data from any number of radars. This provides more flexibility in designing various scanning strategies, so that the atmosphere may be probed more efficiently using a multiple-radar network. This method is also tested using the radar data collected during the Southwest Monsoon Experiment (SoWMEX), which was conducted in Taiwan from May to June 2008 with reasonable results being obtained.

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