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Ying-Hwa Kuo
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Xingqin Fang and Ying-Hwa Kuo

Abstract

In this paper, a modified probability-matching technique is developed for ensemble-based quantitative precipitation forecasts (QPFs) associated with landfalling typhoons over Taiwan. The main features of this technique include a resampling of the ensemble realizations, a rainfall pattern adjustment, and a bias correction. Using this technique, a synthetic ensemble is created for the purpose of rainfall prediction from a large-size (32 members), low-resolution (36 km) ensemble and a small-size (8 members), high-resolution (4 km) ensemble. The rainfall pattern is adjusted based on the precipitation distribution of the 36- and 4-km ensembles. A bias-correction scheme is then applied to remove the known systematic bias from the resampled 4-km ensemble realizations as part of the probability-matching procedure. The modified probability-matching scheme is shown to substantially reduce or eliminate the intrinsic model rainfall bias and to provide better QPF guidance. The encouraging results suggest that this modified probability-matching technique is a useful tool for the QPF of the topography-enhanced typhoon heavy rainfall over Taiwan using ensemble forecasts at dual resolutions.

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Xingqin Fang and Ying-Hwa Kuo

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The authors revisit the issue regarding the predictability of a flow that possesses many scales of motion raised by Lorenz in 1969 and apply the general systems theory developed by Selvam in 1990 to error diagnostics and the predictability of the fractal atmosphere. They then introduce a new generic method to quantify the scale predictability of the fractal atmosphere following the assumptions of the intrinsic inverse power law and the upscale cascade of error. The eddies (of all scales) are extracted against the instant zonal mean, and the ratio of noise (i.e., the domain-averaged square of error amplitudes) to signal (i.e., the domain-averaged square of total eddy amplitudes), referred to as noise-to-signal ratio (NSR), is defined as a measure of forecast skill. The time limit of predictability for any wavenumber can be determined by the criterion or by the criterion , where is the golden ratio and m is a scale index. The NSR is flow adaptive, bias aware, and stable in variation (in a logarithm transformation), and it offers unique advantages for model verification, allowing evaluation of different model variables, regimes, and scales in a consistent manner. In particular, an important advantage of this NSR method over the widely used anomaly correlation coefficient (ACC) method is that it could detect the successive scale predictability of different wavenumbers without the need to explicitly perform scale decomposition. As a demonstration, this new NSR method is used to examine the scale predictability of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) 500-hPa geopotential height.

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Clifford F. Mass and Ying-Hwa Kuo

During the past several years, regional numerical prediction efforts have proliferated as local computer power increased, mesoscale modeling systems became easier to use and more readily available, and model analyses and forecasts from national centers became increasingly accessible over the Internet. This paper surveys real-time numerical forecasting efforts around the country, reviews the conclusions of two recent workshops on the subject, evaluates the role of local real-time weather prediction, and suggests future cooperative efforts.

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Sergey Sokolovskiy, Ying-Hwa Kuo, and Wei Wang

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Assimilation into numerical weather models of the refractivity, Abel-retrieved from radio occultations, as the local refractivity at ray tangent point may result in large errors in the presence of strong horizontal gradients (atmospheric fronts, strong convection). To reduce these errors, other authors suggested modeling the Abel-retrieved refractivity as a nonlocal linear function of the 3D refractivity, which can be used as a linear observation operator for assimiliation. The authors of this study introduce their approach for the nonlocal linear observation operator, which consists of modeling the excess phase path, calculated along certain trajectories below the top of an atmospheric model. In this study (not aimed at development of an observation operator for any specific atmospheric model), both approaches are validated by assessing the accuracy of both linearized observation operators by numerical simulations with the high-resolution Weather Research and Forecasting (WRF) model and comparing them to the accuracy of interpretation of the Abel-retrieved refractivity as local. Improvement of the accuracy of about an order of magnitude is found with the nonlocal refractivity and further improvement is found with the excess phase path. The effect of horizontal resolution of an atmospheric model on the accuracy of modeling local and nonlocal linear observables is also investigated, and it is demonstrated that the nonlocal linear modeling of radio occultation observables is especially important for weather prediction models with sufficiently high horizontal resolution, grid size <100 km (mesoscale models).

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David Jorgensen and Ying-Hwa(Bill) Kuo
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Jian-Wen Bao and Ying-Hwa Kuo

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Numerical models that are used in four-dimensional data assimilation (FDDA) involve on-off switches associated with physical processes. Mathematically these on–off switches are represented by first-order discontinuous functions or step functions. In the development of the adjoint for the variational FDDA, the numerical models must be linearized. While insight has been gained into how to handle the on–off switches represented by first-order discontinuous functions, it is still unclear how to deal with the switches represented by step functions when the model equations are linearized. In this study, the calculus of variations is applied to under-stand how to treat step functions in the development of the adjoint. It is shown that in theory, if adding small perturbations to the initial state does not change the grid points in a forecast model where switching occurs, there is no difficulty in dealing with both first-order discontinuous points and the discontinuous points represented by step functions. However, in practice, first-order discontinuous points are much easier to deal with than those described by step functions.

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Qiu-Shi Chen and Ying-Hwa Kuo

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A harmonic-sine series expansion for a function in two-dimensional space is proposed to be a sum of two parts. The harmonic part is the solution of the Laplace equation with prescribed boundary values of this function. The inner part is the function from which the harmonic part has been subtracted; thus, it has zero boundary value and can be expanded by the double Fourier sine series. By using the harmonic-sine series expansion, it is shown that only simple operations are needed to solve the Laplace, Poisson, and Helmholtz equations with a given boundary condition.

The harmonic-sine series expansion is used to solve the wind partitioning and reconstruction problems in a limited area. The internal wind is computed from the inner parts of the streamfunction and the velocity potential. The harmonic wind is the difference between the observed wind and internal wind. In a limited region, the internal wind can be dealt with in the same way as the horizontal wind on the globe. The development of the vorticity and divergence in a limited area can be diagnosed from the inner parts of the streamfunction and velocity potential, and the corresponding internal rotational and divergent wind components. As long as the inner parts of the streamfunction and velocity potential are defined, the separation of the wind field into the internal rotational, the internal divergent, and the harmonic winds becomes completely definite. The harmonic wind is not only nondivergent but also irrotational in a limited region.

In both partitioning and reconstruction problems, the key is to solve the Laplace equations of the harmonic parts with the prescribed boundary value of the harmonic wind. The solution of the harmonic parts for the key problem is not unique, but the computed harmonic wind from the harmonic parts is. Based on this characteristic, an iterative method is developed. From a real-data example, it is demonstrated that the harmonic parts of the streamfunction and velocity potential and the computed harmonic wind can be accurately determined within 15 iterations. The iteration method by using harmonic-sine series expansion is very effective in solving the partitioning and reconstruction of problems in a limited region.

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Fang-Ching Chien and Ying-Hwa Kuo

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This paper describes an observational and numerical study of an intense wintertime cold front that occurred in Taiwan on 8 January 1996. The front was associated with rope clouds at the leading edge, and a broad area of stratiform clouds behind. The front was blocked by the Central Mountain Range of Taiwan and divided into two sections on each side of the mountain range. As the cold air moved southward along the east coast, the increasing westward Coriolis force induced a landward acceleration. After the cold air piled up against the mountains, a coastal pressure ridge developed. The cold air damming yielded a geostrophic balance between the westward Coriolis force and the eastward component of the pressure gradient force in the x direction, and a southward acceleration in the y direction mainly caused by the southward pressure gradient force component. Over the Taiwan Strait, southward pressure gradient forces increased when the low-level stable cold air was confined over the Taiwan Strait, leading to a southward acceleration of the cold air. The formation of a windward ridge off the northwest coast of Taiwan contributed to a large southward acceleration, resulting in the development of a coastal jet. Over the Taiwan Strait, the cold air moved southward the fastest due to the channeling effect. The air parcels along the east coast of Taiwan experienced a downgradient acceleration from the cold air damming and advanced at a slower speed. Those traveling over the western plains and the nearshore coast advanced at the slowest speed. Two sensitivity runs, one without Taiwan’s topography (flat land only) and the other without Taiwan’s landmass, demonstrated the influences of Taiwan’s terrain and water–land contrast on the airflow. The run with no surface fluxes showed that the ocean modified the low-level cold air by supplying surface heat and moisture fluxes. This weakened the front, reduced low-level stability, and increased forced shallow convection (formation of rope clouds) at the leading edge.

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Ying-Hwa Kuo and Richard A. Anthes

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Heat and moisture budgets associated with a midlatitude convective system (10–11 April 1979) are used to evaluate several versions of Kuo-type cumulus parameterization schemes on a semiprognostic basis.

It is shown that the observed rainfall rate is closely related to the large-scale vertical advection of moisture and to a lesser extent to the large-scale moisture convergence. Both the Kuo and the Anthes schemes show considerable skill in reproducing the convective heating profile (Q 1) when a moist adiabat is used to represent the cloud thermodynamic properties and the effect of eddy sensible heat flux is estimated by a steady-state cloud model. However, when a model cloud with a small radius is used to estimate the cloud's thermodynamic properties, both the Kuo and Authes schemes predict convective heating profiles with considerably lower levels of maximum heating than observed. This indicates that entrainment is not very important for the deep convection present in this case.

Anthes' scheme is revised to utilize the condensation profile and eddy moisture flux estimated by a steady-state cloud model. The revised scheme shows moderate skill in reproducing the convective drying profile (Q 2). The discrepancies between the observed and simulated profiles suggest that shallow convection and turbulent eddies transport substantial amounts of moisture from the subcloud layer to the cloud layer.

We find that the convective moistening profile (∂q/∂t) during the developing stage can be very well-simulated by a function of saturation mixing ratio as proposed by Anthes and others. The moistening profile cannot be reproduced by the cloud-environment moisture differences as proposed by Kuo.

These results suggest that it is possible to parameterize midlatitude organized convection in a large-scale numerical model because of the strong relationship between the convective rainfall rate, the convective heating profile, the convective moistening profile, and the large-scale variables.

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