Abstract

A three-dimensional variational (3DVAR) scheme is developed for retrieving three-dimensional moisture in the atmosphere from slant-path measurements of a hypothetical ground-based global positioning system (GPS) observation network. It is assumed that the observed data are in the form of slant-path water vapor (SWV), which is the integrated water vapor along the slant path between the ground receiver and the GPS satellite. The inclusion of a background in the analysis overcomes the under-determinedness problem. An explicit Gaussian-type spatial filter is used to model the background error covariances that can be anisotropic. As a unique aspect of this study, an anisotropic spatial filter based on flow-dependent background error structures is implemented and tested and the filter coefficients are derived from either true background error field or from the increment of an intermediate analysis that is obtained using an isotropic filter. In the latter case, an iterative procedure is involved.

A set of experiments is conducted to test the new scheme with hypothetical GPS observations for a dryline case that occurred during the 2002 International H₂O Project (IHOP_2002) field experiment. Results illustrate that this system is robust and can properly recover three-dimensional mesoscale moisture structures from GPS SWV data and surface moisture observations. The analysis captures major features in water vapor associated with the dryline even when an isotropic spatial filter is used. The analysis is further improved significantly by the use of flow-dependent background error covariances modeled by an anisotropic spatial filter.

Sensitivity tests show that surface moisture observations are important for the analysis near ground, and more so when flow-dependent background error covariances are not used. Vertical filtering is necessary for obtaining accurate analysis increments. The retrieved moisture field remains reasonably accurate when the surface moisture observations and GPS SWV data contain errors of typical magnitudes. The positive impact of flow-dependent background error covariances increases when the density of ground-based GPS receiver stations decreases.

Abstract

The 12–13 June 2002 convective initiation case from the International H₂O Project (IHOP_2002) field experiment over the central Great Plains of the United States is simulated numerically with the Advanced Regional Prediction System (ARPS) at 3-km horizontal resolution. The case involves a developing mesoscale cyclone, a dryline extending from a low center southwestward with a cold front closely behind, which intercepts the midsection of the dryline, and an outflow boundary stretching eastward from the low center resulting from earlier mesoscale convection. Convective initiation occurred in the afternoon at several locations along and near the dryline or near the outflow boundary, but was not captured by the most intensive deployment of observation instruments during the field experiment, which focused instead on the dryline–outflow boundary intersection point.

Standard and special surface and upper-air observations collected during the field experiment are assimilated into the ARPS at hourly intervals in a 6-h preforecast period in the control experiment. This experiment captured the initiation of four groups of convective cells rather well, with timing errors ranging between 10 and 100 min and location errors ranging between 5 and 60 km. The general processes of convective initiation are discussed. Interestingly, a secondary initiation of cells due to the collision between the main outflow boundary and the gust fronts developing out of model-predicted convection earlier is also captured accurately about 7 h into the prediction. The organization of cells into a squall line after 7 h is reproduced less well.

A set of sensitivity experiments is performed in which the impact of assimilating nonstandard data gathered by IHOP_2002, and the length and interval of the data assimilation are examined. Overall, the control experiment that assimilated the most data produced the best forecast although some of the other experiments did better in some aspects, including the timing and location of the initiation of some of the cell groups. Possible reasons for the latter results are suggested. The lateral boundary locations are also found to have significant impacts on the initiation and subsequent evolution of convection, by affecting the interior flow response and/or feeding in more accurate observation information through the boundary, as available gridded analyses from a mesoscale operational model were used as the boundary condition. Another experiment examines the impact of the vertical correlation scale in the analysis scheme on the cold pool analysis and the subsequent forecast. A companion paper will analyze in more detail the process and mechanism of convective initiation, based on the results of a nested 1-km forecast.

Abstract

Ensemble–variational data assimilation algorithms that can incorporate the time dimension (four-dimensional or 4D) and combine static and ensemble-derived background error covariances (hybrid) are formulated in general forms based on the extended control variable and the observation-space-perturbation approaches. The properties and relationships of these algorithms and their approximated formulations are discussed. The main algorithms discussed include the following: 1) the standard ensemble 4DVar (En4DVar) algorithm incorporating ensemble-derived background error covariance through the extended control variable approach, 2) the 4DEnVar neglecting the time propagation of the extended control variable (4DEnVar-NPC), 3) the 4D ensemble–variational algorithm based on observation space perturbation (4DEnVar), and 4) the 4DEnVar with no propagation of covariance localization (4DEnVar-NPL). Without the static background error covariance term, none of the algorithms requires the adjoint model except for En4DVar. Costly applications of the tangent linear model to localized ensemble perturbations can be avoided by making the NPC and NPL approximations. It is proven that En4DVar and 4DEnVar are mathematically equivalent, while 4DEnVar-NPC and 4DEnVar-NPL are mathematically equivalent. Such equivalences are also demonstrated by single-observation assimilation experiments with a 1D linear advection model. The effects of the non-flow-following or stationary localization approximations are also examined through the experiments.

All of the above algorithms can include the static background error covariance term to establish a hybrid formulation. When the static term is included, all algorithms will require a tangent linear model and an adjoint model. The first guess at appropriate time (FGAT) approximation is proposed to avoid the tangent linear and adjoint models. Computational costs of the algorithms are also discussed.

Abstract

In September–October 1988 and in April 1989 two 4-week cruises were organized to study the structure and dynamics of Gulf Stream meanders. The first one focused on an anticyclonic crest, and the second one on a cyclonic trough. One objective of this program was to conduct a high-resolution study of the upper-ocean velocity and vorticity field using a CTD and a continuously profiling acoustic Doppler current profiler (ADCP).

The cross-stream sections of velocity exhibit the typical pattern of a single velocity maximum with a narrow zone of cyclonic shear and a broad region of anticyclonic shear. The cyclonic velocity shear is larger and extends to greater depths in a crest than in a trough and can exceed 120% of the Coriolis parameter (f) at depths as great as 300 m. The vertically integrated transport to 250 m appears to be more symmetric in troughs than in crests. The computed sea level difference across the stream is about 0.46 m greater in the trough than the crest after seasonal correction and “normalization” to the same surface transport. The surface velocity vectors are divergent upstream and convergent downstream of a crest, consistent with upwelling and shingle formation, and entrainment/downwelling, respectively.

By combining the CTD observations of density with the velocity data, the cross-stream structure of the potential vorticity field and its components can be mapped. It is found that shear vorticity greatly enhances −(f/ρ)dρ/dz on the cyclonic side and weakens it to a distinct minimum in the center of the current at the crest. Although the database is not so extensive for the trough, the evidence suggests that the opposite is true: cyclonic shear is weakened and anticyclonic shear is strengthened resulting in a less asymmetric velocity and transport distribution. There was considerable “marbling” of the potential vorticity field by both the stratification and the shear vorticity field, but there is no evidence to suggest that the two fields are correlated in such a way as to reduce the marbling to less than what the component fields individually contribute.

Abstract

The development of an air pollution transport model that uses an expanding terrain-following coordinate with high resolution in analytic form near the surface and a high-order accurate transport algorithm is described. The model is designed to be internally consistent in the application of numerical methods, computationally efficient, and suitable for pollutant dispersion studies in complex terrain. The application of the time-splitting Warming–Kutler–Lomax advection scheme is examined in both rotational and deformational flows for its conservation and stability properties. It is found that the combination of this scheme with a short-wave filter makes the integration mass conserving and dispersion free. The model is applied to some hypothetical cases that represent the typical phenomena occurring over mountains. The model proves to be capable of simulating realistic planetary boundary layer structure and stability variation, hydrostatic mountain waves, thermally induced mountain–valley winds, and passive scalar dispersion over sloped surfaces reproducing features observed in field experiments.

Abstract

A wavelet-based algorithm is developed to detect tornadoes from Doppler weather radar radial-velocity observations. Within this algorithm, a relative region-to-region velocity difference (RRVD) is defined based on the scale- and location-dependent wavelet coefficients and this difference represents the relative magnitude of the radial velocity shear between two adjacent regions of different scales. The RRVD fields of an idealized tornado and a realistic tornado from a high-resolution numerical simulation are analyzed first. It is found that the value of RRVD in the tornado region is significantly larger than those at other locations and large values of RRVD exist at more than one scale. This characteristic forms the basis of the new algorithm presented in this work for identifying tornadoes. Different from traditional tornadic vortex signature detection algorithms that typically rely on the velocity difference between adjacent velocity gate pairs at a single spatial scale, the new algorithm examines region-to-region radial wind shears at a number of different spatial scales. Multiscale regional wind shear examination not only can be used to discard a nontornadic vortex signature to reduce the false alert rate of tornado detection but also has the ability of capturing tornadic signatures at various scales for improving the detection and warning. The potential advantage of the current algorithm is demonstrated by applying it to the radar data collected by Oklahoma City, Oklahoma (KTLX), Weather Surveillance Radar-1988 Doppler (WSR-88D) on 8 May 2003 for a central Oklahoma tornado case.

Abstract

The authors have developed a relatively simple, first-order closure, Eulerian diffusion model, in which turbulent coherent structures of the convective boundary layer are explicitly included as periodic velocities imposed on a stationary and horizontally homogeneous wind field. The dimensions of the convective updrafts and downdrafts are assumed to be inversely proportional to the ratio of their respective vertical speeds and are constant with height, and the updraft and downdraft areas are constant in the horizontal. Sinusoidal vertical velocity variations are specified with amplitudes proportional to the mean vertical velocity profiles for skewed distributions described by Weil. The horizontal velocity components of the coherent structures are calculated using the continuity equation. Model simulations for conditions on the afternoon of Wangara day 33 reproduce the major features of the complicated plume dispersion behavior observed in the water tank experiments and the CONDORS experiments. The model produces results comparable to those obtained by complex large-eddy simulation models and random walk Lagrangian models, but is computationally much less demanding. Sensitivity tests are presented that show that the model is insensitive to physically realistic ranges of the modeling parameters.

Abstract

Radar reflectivity (Z) data are either directly assimilated using 3DVar, 4DVar, or ensemble Kalman filter, or indirectly assimilated using, for example, cloud analysis that preretrieves hydrometeors from Z. When directly assimilating radar data variationally, issues related to the highly nonlinear Z operator arise that can cause nonconvergence and bad analyses. To alleviate the issues, treatments are proposed in this study and their performances are examined via observing system simulation experiments. They include the following: 1) When using hydrometeor mixing ratios as control variables (CVq), small background Z can cause extremely large cost function gradient. Lower limits are imposed on the mixing ratios (qLim treatment) or the equivalent reflectivity (ZeLim treatment) in Z observation operator. ZeLim is found to work better than qLim in terms of analysis accuracy and convergence speed. 2) With CVq, the assimilation of radial velocity (V _r ) is ineffective when assimilated together with Z data due to the much smaller cost function gradient associated with V _r . A procedure (VrPass) that assimilates V _r data in a separate pass is found very helpful. 3) Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can also avoid extremely large cost function gradient, and has much faster convergence. However, spurious analysis increments can be created when transforming the analysis increments back to mixing ratios. A background smoothing and a lower limit are applied to the background mixing ratios, and are shown to be effective. Using CVlogq with associated treatments produces better reflectivity analysis that is much closer to the observation without resorting to multiple analysis passes, and the cost function minimization also converges faster. CVlogq is therefore recommended for variational radar data assimilation.

Abstract

A hybrid ensemble–3DVar (En3DVar) system is developed and compared with 3DVar, EnKF, “deterministic forecast” EnKF (DfEnKF), and pure En3DVar for assimilating radar data through perfect-model observing system simulation experiments (OSSEs). DfEnKF uses a deterministic forecast as the background and is therefore parallel to pure En3DVar. Different results are found between DfEnKF and pure En3DVar: 1) the serial versus global nature and 2) the variational minimization versus direct filter updating nature of the two algorithms are identified as the main causes for the differences. For 3DVar (EnKF/DfEnKF and En3DVar), optimal decorrelation scales (localization radii) for static (ensemble) background error covariances are obtained and used in hybrid En3DVar. The sensitivity of hybrid En3DVar to covariance weights and ensemble size is examined. On average, when ensemble size is 20 or larger, a 5%–10% static covariance gives the best results, while for smaller ensembles, more static covariance is beneficial. Using an ensemble size of 40, EnKF and DfEnKF perform similarly, and both are better than pure and hybrid En3DVar overall. Using 5% static error covariance, hybrid En3DVar outperforms pure En3DVar for most state variables but underperforms for hydrometeor variables, and the improvement (degradation) is most notable for water vapor mixing ratio q _υ (snow mixing ratio q _s ). Overall, EnKF/DfEnKF performs the best, 3DVar performs the worst, and static covariance only helps slightly via hybrid En3DVar.

Abstract

Despite the well-known importance of background error covariance in data assimilation, not much study has been focused on its impact on the assimilation of radar reflectivity within a three-dimensional variational (3DVar) framework. In this study, it is shown that unphysical analysis increments of hydrometeors are produced when using vertically homogeneous background error variance. This issue cannot be fully solved by using the so-called hydrometeor classification in the reflectivity observation operator. Alternatively, temperature-dependent background error profiles for hydrometeor control variables are proposed. With such a treatment, the vertical background error profiles are specified to be temperature dependent, allowing for more physical partitioning of radar-observed precipitation information among the liquid and ice hydrometeors. The 3DVar analyses using our treatment are compared with those using constant background error or “hydrometeor classification” through observing system simulation experiments with a simulated supercell storm. Results show that 1) 3DVar with constant hydrometeor background errors produces unphysical rainwater at the high levels and unphysical snow at the low levels; 2) the hydrometeor classification approach reduces unphysical rainwater and snow at those levels, but the analysis increments are still unphysically spread in the vertical by the background error covariance when the vertically invariant background errors are used; and 3) the temperature-dependent background error profiles enable physically more reasonable analyses of liquid and ice hydrometeors from reflectivity assimilation.