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Chungu Lu and Yuanfu Xie

Abstract

The computational modes associated with a centered finite-differencing scheme in space are studied. The existence and impact of these computational modes in a numerical solution are demonstrated with the use of theoretical analyses and numerical experiments.

The results show that the computational modes due to a spatial discretization can have a detrimental effect on the numerical solution in situations where flows are evolved near shock (or having large spatial derivative). The numerical diffusion can reduce the impact of the computational modes, but can also impose an adverse effect on the physical modes.

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Yuanfu Xie, Chungu Lu, and Gerald L. Browning

Abstract

Three-dimensional variational data assimilation (3DVAR) analysis is an important method used at many operational and research institutes in meteorology, for example, the National Centers for Environmental Prediction (NCEP) and the European Centre for Medium-Range Weather Forecasts (ECMWF). In 3DVAR analysis, different forms of cost functions and constraints (e.g., geostrophic balance) have been used. However, the impacts of these different forms of cost functions, covariances, and constraints on the 3DVAR solutions have not been completely analyzed due to their complexity. Using the Fourier analysis where the Fourier transformation is applicable, the impacts of different forms of cost functions and some commonly used physical constraints are demonstrated. In the particular case of geostrophic balance as the constraint, the large-scale motion of a 3DVAR analysis could be in geostrophic balance, but the mesoscale solution may be nearly unchanged if the penalty terms and the forms of J b (terms related to the background field in 3DVAR cost functions) and J o (related to the observation field) are chosen properly. This conclusion shows that the penalization of geostrophic imbalance can be used for mesoscale data assimilation without serious damage to the mesoscale features. More important for constructing a 3DVAR system, this paper also demonstrates that some formulations of J b can produce physically unexpected solutions. The theory is illustrated using numerical experiments.

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Zoltan Toth, Steve Albers, and Yuanfu Xie

No abstract available.

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Wei Li, Yuanfu Xie, Shiow-Ming Deng, and Qi Wang

Abstract

In recent years, the Earth System Research Laboratory (ESRL) of the National Oceanic and Atmospheric Administration (NOAA) has developed a space and time mesoscale analysis system (STMAS), which is currently a sequential three-dimensional variational data assimilation (3DVAR) system and is developing into a sequential 4DVAR in the near future. It is implemented by using a multigrid method based on a variational approach to generate grid analyses. This study is to test how STMAS deals with 2D Doppler radar radial velocity and to what degree the 2D Doppler radar radial velocity can improve the conventional (in situ) observation analysis. Two idealized experiments and one experiment with real Doppler radar radial velocity data, handled by STMAS, demonstrated significant improvement of the conventional observation analysis. Because the radar radial wind data can provide additional wind information (even it is incomplete: e.g., missing tangential wind vector), the analyses by assimilating both radial wind data and conventional data showed better results than those by assimilating only conventional data. Especially in the case of sparse conventional data, radar radial wind data can provide significant information and improve the analyses considerably.

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Alexander E. MacDonald, Yuanfu Xie, and Randolph H. Ware

Abstract

In recent years techniques have been developed to obtain integrated water vapor along slant paths between ground-based Global Positioning System (GPS) receivers and the GPS satellites. Results are presented of an observing system simulation (OSS) to determine whether three-dimensional water vapor fields could be recovered from a high-resolution network (e.g., with 40-km spacing) of GPS receivers, in combination with surface moisture observations and a limited number of moisture soundings. The paper describes a three-dimensional variational analysis (3DVAR) that recovers the moisture field from the slant integrated water vapor and other observations. Comparisons between “nature” moisture fields taken from mesoscale models and fields recovered using 3DVAR are presented. It is concluded that a high-resolution network of GPS receivers may allow diagnosis of three-dimensional water vapor, with applications for both positioning and mesoscale weather prediction.

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Steven E. Koch, Randolph Ware, Hongli Jiang, and Yuanfu Xie

Abstract

This study documents a very rapid increase in convective instability, vertical wind shear, and mesoscale forcing for ascent leading to the formation of a highly unusual tornado as detected by a ground-based microwave radiometer and wind profiler, and in 1-km resolution mesoanalyses. Mesoscale forcing for the rapid development of severe convection began with the arrival of a strong upper-level jet streak with pronounced divergence in its left exit region and associated intensification of the low-level flow to the south of a pronounced warm front. The resultant increase in stretching deformation along the front occurred in association with warming immediately to its south as low-level clouds dissipated. This created a narrow ribbon of intense frontogenesis and a rapid increase in convective available potential energy (CAPE) within 75 min of tornadogenesis. The Windsor, Colorado, storm formed at the juncture of this warm frontogenesis zone and a developing dryline. Storm-relative helicity suddenly increased to large values during this pretornadic period as a midtropospheric layer of strong southeasterly winds descended to low levels. The following events also occurred simultaneously within this short period of time: a pronounced decrease in midtropospheric equivalent potential temperature θ e accompanying the descending jet, an increase in low-level θ e associated with the surface sensible heating, and elimination of the capping inversion and convective inhibition. The simultaneous nature of these rapid changes over such a short period of time, not fully captured in Storm Prediction Center mesoanalyses, was likely critical in generating this unusual tornadic event.

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Xiangjun Tian, Hongqin Zhang, Xiaobing Feng, and Yuanfu Xie

Abstract

The En4DVar method is designed to combine the flow-dependent statistical covariance information of EnKF into the traditional 4DVar method. However, the En4DVar method is still hampered by its strong dependence on the adjoint model of the underlying forecast model and by its complexity, maintenance requirements, and the high cost of computer implementation and simulation. The primary goal of this paper is to propose an alternative approach to overcome the main difficulty of the En4DVar method caused by the use of adjoint models. The proposed approach, the nonlinear least squares En4DVar (NLS-En4DVar) method, begins with rewriting the standard En4DVar formulation into a nonlinear least squares problem, which is followed by solving the resulting NLS problem by a Gauss–Newton iterative method. To reduce the computational and implementation complexity of the proposed NLS-En4DVar method, a few variants of the new method are proposed; these modifications make the model cheaper and easier to use than the full NLS-En4DVar method at the expense of reduced accuracy. Furthermore, an improved iterative method based on the comprehensive analysis on the above NLSi-En4DVar family of methods is also proposed. These proposed NLSi-En4DVar methods provide more flexible choices of the computational capabilities for the broader and more realistic data assimilation problems arising from various applications. The pros and cons of the proposed NLSi-En4DVar family of methods are further examined in the paper and their relationships and performance are also evaluated by several sets of numerical experiments based on the Lorenz-96 model and the Advanced Research WRF (ARW) Model, respectively.

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Zoltan Toth, Mark Tew, Daniel Birkenheuer, Steve Albers, Yuanfu Xie, and Brian Motta
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Zhongjie He, Yuanfu Xie, Wei Li, Dong Li, Guijun Han, Kexiu Liu, and Jirui Ma

Abstract

A recursive filter or parameterized curve fitting technique is usually used in a three-dimensional variational data assimilation (3DVAR) scheme to approximate the background error covariance, which can only represent the errors of an ocean field over a predetermined scale. Without an accurate flow-dependent error covariance that is also local and time dependent, a 3DVAR system may not provide good analyses because it is optimal only under the assumption of an accurate covariance. In this study, a sequential 3DVAR (S3DVAR) is formulated in model grid space to examine if there is useful information that can be extracted from the observation. This formulation is composed of a series of 3DVARs, each of which uses recursive filters with different length scales. It can provide an inhomogeneous and anisotropic analysis for the wavelengths that can be resolved by the observation network, just as with the conventional Barnes analysis or successive corrections. Being a variational formulation, S3DVAR can deal with data globally with an explicit specification of the observation errors; explicit physical balances or constraints; and advanced datasets, such as satellite and radar. Even though the S3DVAR analysis can be viewed as a set of isotropic functions superpositioned together, this superposition is not prespecified as in a single 3DVAR approach but is determined by the information that can be resolved by observation. The S3DVAR is adopted in a global sea surface temperature (SST) data assimilation system, into which the shipboard SSTs and the 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder daily SSTs are assimilated, respectively. The results demonstrate that the proposed S3DVAR works better in practice than a single 3DVAR.

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N. C. Privé, Yuanfu Xie, Steven Koch, Robert Atlas, Sharanya J. Majumdar, and Ross N. Hoffman

Abstract

High-altitude, long-endurance unmanned aircraft systems (HALE UAS) are capable of extended flights for atmospheric sampling. A case study was conducted to evaluate the potential impact of dropwindsonde observations from HALE UAS on tropical cyclone track prediction; tropical cyclone intensity was not addressed. This study employs a global observing system simulation experiment (OSSE) developed at the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL) that is based on the NOAA/National Centers for Environmental Prediction gridpoint statistical interpolation (GSI) data assimilation system and Global Forecast System (GFS) model. Different strategies for dropwindsonde deployment and UAS flight paths were compared. The introduction of UAS-deployed dropwindsondes was found to consistently improve the track forecast skill during the early forecast up to 96 h, with the caveat that the experiments omitted both vortex relocation and dropwindsondes from manned flights in the tropical cyclone region. The more effective UAS dropwindsonde deployment patterns sampled both the environment and the body of the tropical cyclone.

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