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- Author or Editor: Ying-Hwa Kuo x
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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.
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.
Abstract
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 
Abstract
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
Abstract
This paper examines further the problem of deducing the wind field from vorticity and divergence over a limited area with prescribed winds at the boundary. An earlier work showed that the wind field in a limited area can be partitioned into internal divergent, internal rotational, and harmonic wind components. Because the harmonic wind is both nondivergent and irrotational, it is demonstrated in this paper that the two harmonic wind components at the boundary must satisfy a consistency condition. Based on this properly, a direct method is developed to solve two Laplace equations with the prescribed two harmonic wind components at the boundary. If the prescribed harmonic wind components at the boundary satisfy the consistency condition, the solution of the two Laplace equations must be nondivergent and irrotational. The direct method is shown to be highly accurate and efficient. If the prescribed wind at the boundary does not satisfy the consistency condition, this implies a mismatch between the interior vorticity and divergence and the prescribed winds at the boundary. This inconsistency must be removed before the wind field can be reconstructed. A method to remove this inconsistency is discussed.
A harmonic-cosine series expansion is also developed for a function over a limited area. The application of the harmonic-cosine series expansion to the wind-field partitioning and reconstruction problem has two distinct advantages compared with the harmonic-sine series expansion. The first is that the internal and harmonic winds can be more accurately determined at the boundary. The second is that the partitioning of the wind field into streamfunction and velocity potential can be obtained more efficiently and accurately through an iterative method.
Abstract
This paper examines further the problem of deducing the wind field from vorticity and divergence over a limited area with prescribed winds at the boundary. An earlier work showed that the wind field in a limited area can be partitioned into internal divergent, internal rotational, and harmonic wind components. Because the harmonic wind is both nondivergent and irrotational, it is demonstrated in this paper that the two harmonic wind components at the boundary must satisfy a consistency condition. Based on this properly, a direct method is developed to solve two Laplace equations with the prescribed two harmonic wind components at the boundary. If the prescribed harmonic wind components at the boundary satisfy the consistency condition, the solution of the two Laplace equations must be nondivergent and irrotational. The direct method is shown to be highly accurate and efficient. If the prescribed wind at the boundary does not satisfy the consistency condition, this implies a mismatch between the interior vorticity and divergence and the prescribed winds at the boundary. This inconsistency must be removed before the wind field can be reconstructed. A method to remove this inconsistency is discussed.
A harmonic-cosine series expansion is also developed for a function over a limited area. The application of the harmonic-cosine series expansion to the wind-field partitioning and reconstruction problem has two distinct advantages compared with the harmonic-sine series expansion. The first is that the internal and harmonic winds can be more accurately determined at the boundary. The second is that the partitioning of the wind field into streamfunction and velocity potential can be obtained more efficiently and accurately through an iterative method.
Abstract
In this study, the impacts of Taiwan topography on the extreme rainfall of Typhoon Morakot and the predictability of this rainfall are examined with a high-resolution (4 km) ensemble simulation using the Advanced Research core of the Weather Research and Forecasting Model (WRF-ARW). Ensemble prediction with realistic topography reproduces salient features of orographic precipitation. The 24- and 96-h accumulated rainfall amount and distribution from the ensemble mean compare reasonably well with the observed precipitation. When the terrain of Taiwan is removed, the rainfall distribution is markedly changed, suggesting the importance of the orography in determining the rainfall structure. Moreover, the peak 96-h rainfall amount is reduced to less than 20%, and the total rainfall amount over southern Taiwan is reduced to less than 60% of the experiments with Taiwan topography. Further analysis indicates that Taiwan’s topography substantially increases the variability of rainfall prediction. Analysis uncertainties as reflected in the perturbed initial state of the ensemble are amplified due to orographic influences on the typhoon circulation. As a result, significant variability occurs in the storm track, timing, and location of landfall, and storm intensities, which in turn, increases the rainfall variability. These results suggest that accurate prediction of heavy precipitation at a specific location and at high temporal resolution for an event such as Typhoon Morakot over Taiwan is extremely challenging. The forecasting of such an event would benefit from probabilistic prediction provided by a high-resolution mesoscale ensemble forecast system.
Abstract
In this study, the impacts of Taiwan topography on the extreme rainfall of Typhoon Morakot and the predictability of this rainfall are examined with a high-resolution (4 km) ensemble simulation using the Advanced Research core of the Weather Research and Forecasting Model (WRF-ARW). Ensemble prediction with realistic topography reproduces salient features of orographic precipitation. The 24- and 96-h accumulated rainfall amount and distribution from the ensemble mean compare reasonably well with the observed precipitation. When the terrain of Taiwan is removed, the rainfall distribution is markedly changed, suggesting the importance of the orography in determining the rainfall structure. Moreover, the peak 96-h rainfall amount is reduced to less than 20%, and the total rainfall amount over southern Taiwan is reduced to less than 60% of the experiments with Taiwan topography. Further analysis indicates that Taiwan’s topography substantially increases the variability of rainfall prediction. Analysis uncertainties as reflected in the perturbed initial state of the ensemble are amplified due to orographic influences on the typhoon circulation. As a result, significant variability occurs in the storm track, timing, and location of landfall, and storm intensities, which in turn, increases the rainfall variability. These results suggest that accurate prediction of heavy precipitation at a specific location and at high temporal resolution for an event such as Typhoon Morakot over Taiwan is extremely challenging. The forecasting of such an event would benefit from probabilistic prediction provided by a high-resolution mesoscale ensemble forecast system.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
