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Ying-Hwa Kuo
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Xingqin Fang and Ying-Hwa Kuo

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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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David Jorgensen and Ying-Hwa(Bill) Kuo
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Ying-Hwa Kuo and Richard A. Anthes

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Observing systems simulation experiments were carried out to estimate the accuracy of temperatures diagnosed from the divergence equation when an army of nearly continuous (in time) wind observations is available. It was found that a useful estimate of temperature can be derived from high-resolution wind observations such as those obtainable from a network of wind profiling systems. Adding the divergence and vertical motion terms to the balance equation to form the complete divergence equation reduces the errors in derived temperatures and geopotential heights. Observations on an irregularly spaced grid lead to greater errors than those on a regularly spaced grid. Moderate errors are also introduced when large-scale errors in geopotential occur in the lateral boundary conditions. This suggests the need for some independent observations of temperature (from rawinsonde or temperature profiler) to prescribe the boundary conditions for the retrieval technique.

In a simulation of a possible operational system in which wind observations with random errors of 1 m s−1 are available on a 350 km grid and boundary values of geopotential height contain errors typical of a 12 h model forecast, the derived temperatures and heights on the interior of the grid contain root-mean-square errors of 1.55°C and 18.8 m, respectively.

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Ying-Hwa Kuo and Richard A. Anthes

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The accuracy of diagnostic heat and moisture budgets using the AVE-SESAME 1979 data is investigated through a series of observing system simulation experiments. The four-dimensional (including time) data set provided by a mesoscale model is used to simulate rawinsonde observations taken during the AVE-SESAME 1979 regional-scale experiment. Budget calculations using the simulated data set show that the average root-mean-square error is about 5°C day−1 for the heat budget and 2 g kg−1 day−1 for the moisture budget, on a spatial scale of 550 × 550 km and a temporal scale of 6 h. These magnitudes of error indicate difficulties in diagnosing the heating rate in weak convective systems. However, for strong convective systems, such as the 10–11 April 1979 case, the convective effects can be estimated with the AVE-SESAME data. The influences of observational frequency, objective analysis, observational density, vertical interpolation, and observational errors on the budget results are also studied. It is shown that the temporal and spatial resolution of the SESAME regional network is marginal for diagnosing the convective effects on a horizontal scale of 550 × 550 km, and so improved resolution in space and time is needed in future field programs in order to obtain improved budget results.

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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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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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David P. Chock and Ying-Hwa Kuo

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Results of the Cross-Appalachian Tracer Experiment have been used to compare the performance of three different wind models—a primitive-equation model a quasi-geostrophic model and a linear-interpolation model. The comparison shows that the primitive-equation model performed very well generally and should be a useful model when forecasting is required. The linear-interpolation model performed well in the absence of cold front passage, but less well in the presence of cold front passage. The quasi-geostrophic model performed well only if treatment for surface friction is incorporated; without the treatment it is the only model that revealed an observed stagnation.

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Peter A. C. Howells and Ying-Hwa Kuo

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A numerical case study of a Southerly Buster event that occurred on 1 December 1982 during the Southerly Buster Observational Program (SUBOP) is presented. Southerly busier refers to the leading edge of a coastally trapped gravity currentlike phenomenon that occurs over southeastern Australia during the passage of summertime cold fronts. The Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) mesoscale model has been used in a series of 36-hour experiments to determine the impact of orography, surface heating, boundary-layer physics and moist processes on the generation and maintenance of the broad features of the event. In addition, the effects of horizontal and vertical resolutions are examined. With 40 km grid separation, 15 vertical levels and a high-resolution boundary-layer formulation, the model captures the observed mesoscale flow pattern associated with the southerly busier event despite using coarse, although enhanced, U.S. National Meteorological Center global analyses for initialization.

The simulated southerly flow is a relatively shallow and narrow cold-air current. Adequate horizontal and vertical resolutions are very important for a simulation of this phenomenon. With 80 km grid spacing and 10 vertical levels, the model is unable to resolve the broad features of the event. This has strong implications for the operational prediction of these types of mesoscale disturbances.

Model sensitivity experiments indicate that strong gradients in physical properties associated with the land-sea contrast over southeastern Australia are responsible for the coastally enhanced flow. In particular, the synergy of orographic forcing and both differential surface friction and heating determines the structure of the current. It is shown that although the presence of the Great Dividing Range has a large influence on the events it does not seem to be essential for the development of the coastal jet in this particular study. This result contradicts most of the previous theories and hypotheses related to the dynamics of southerly busters.

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