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Melinda S. Peng
and
Simon W. Chang

Abstract

Special Sensor Microwave/Imager (SSM/I) retrieved rainfall rates were assimilated into a limited-area numerical prediction model in an attempt to improve the initial analysis and forecast of a tropical cyclone. Typhoon Flo of 1990, which was observed in an intensive observation period of the Tropical Cyclone Motion Experiment-1990, was chosen for this study. The SSM/I retrieved rainfall rates within 888 km (8° latitude) of the storm center were incorporated into the initial fields by a reversed Kuo cumulus parameterization. In the procedure used here, the moisture field in the model is adjusted so that the model generates the SSM/I-observed rainfall rates. This scheme is applied through two different assimilation methods. The first method is based on a dynamic initialization in which the prediction model is integrated backward adiabatically to t = −6 h and then forward diabatically for 6 h to the initial time. During the diabatic forward integration, the SSM/I rainfall rates are incorporated using the reversed Kuo cumulus parameterization. The second method is a forward data assimilation integration starting from t = −12 h. From t = −6 h to t = 0, the SSM/I rainfall rates are incorporated, also using the reversed Kuo scheme. During this period, the momentum fields are relaxed to the initial (t = 0) analysis to reduce the initial position error generated during the preforecast integration. Five cases for which SSM/I overpasses were available were tested, including two cases before and three after Flo's recurvature. Forecasts at 48 h are compared with the actual storm track and intensifies estimated by the Joint Typhoon Warning Center. For the five cases tested, the assimilation of SSM/I retrieved rainfall rates reduced the average 48-h forecast distance error from 239 km in the control runs to 81 km in the assimilation experiments. It is postulated that the large positive impact was a consequence of the improved forecast intensity and speed of the typhoon when the SSM/I rain-rate data were assimilated.

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Melinda S. Peng
and
R. T. Williams

Abstract

A linear nondivergent barotropic model is developed to obtain the asymmetric circulation associated with a vortex moving on the β-plane. The total system is transformed to a coordinate system moving with the vortex. The direction and speed of movement is specified from full nonlinear model results. Two wavenumber one gyres are obtained from the asymmetric vorticity equation. The inner gyres move in the azimuthal direction whose maximum amplitude is located at the radius of maximum wind. These inner gyres are associated either with the unstable mode or the neutral mode depending on the resolution of the model. The outer gyres, whose orientations are always along the track direction specified by the movement, correspond to the β-gyres obtained in the nonlinear numerical model. The strength of the inner gyres is much larger than the strength of the outer gyres. For the steady state solution with high finite difference resolution, only the inner gyres are present. In a steady state solution, the outer β-gyres can be isolated by modifying the inner part of the basic wind profile or by reducing the resolution of the mode. In a time dependent solution, the inner gyres will not form if there is no discrete mode existing in the free model system. The outer β-gyres thus obtained have the correct orientation and magnitude when compared to the solutions of the full nonlinear model. These solutions can be used as a tool for bogusing the vortex into a numerical hurricane forecast model.

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Melinda S. Peng
and
Carolyn A. Reynolds

Abstract

Singular vector (SV) sensitivity, calculated using the adjoint model of the U.S. Navy Operation Global Atmosphere Prediction System (NOGAPS), is used to study the dynamics associated with tropical cyclone evolution. For each model-predicted tropical cyclone, SVs are constructed that optimize perturbation energy within a 20° by 20° latitude/longitude box centered on the 48-h forecast position of the cyclone. The initial SVs indicate regions where the 2-day forecast of the storm is very sensitive to changes in the analysis. Composites of the SVs for straight-moving cyclones and non-straight-moving cyclones that occurred in the Northern Hemisphere during its summer season in 2003 are examined. For both groups, the initial-time SV sensitivity exhibits a maximum within an annulus approximately 500 km from the center of the storms, in the region where the potential vorticity gradient of the vortex first changes sign. In the azimuthal direction, the composite initial-time SV maximum for the straight-moving group is located in the rear right quadrant with respect to the storm motion. The composite based on the non-straight-moving cyclones does not have a preferred quadrant in the vicinity of the storms and has larger amplitude away from the cyclones compared with the straight-moving storms, indicating more environmental influence on these storms. For both groups, the maximum initial sensitive areas are collocated with regions of flow moving toward the storm.

While the initial SV maximum is located where the potential vorticity gradient changes sign, the final SV maximum is located where the potential vorticity gradient is a maximum. Examinations of individual cases demonstrate how SV sensitivity can be used to identify specific environmental influences on the storms. The relationship between the SV sensitivity and the potential vorticity is discussed. The results support the utility of SVs in applications to phenomena beyond midlatitude baroclinic systems.

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Melinda S. Peng
and
R. T. Williams

Abstract

This note compares the error distributions for three transformation formulae between temporal growth rate and spatial growth rate with the linearized barotropic vorticity equation. The sech2 and the tanh basic-state profiles are used for illustration. The transformation which uses the phase velocity gives a moderate error which does not have a strong dependence on the growth rate. The formulae derived by Gaster, and later by Nayfeh and Padhye, which employ the group velocity, have errors that are a function of the ratio of the spatial growth rate to the wavenumber. The errors from their formulae are small when the ratio is small, but the errors increase with the ratio so that all three transformation formulae give similar errors when the ratio is of order one. Nayfeh and Padhye's formula is rederived for the barotropic vorticity equation with a procedure which shows that ratio of growth rate to wavenumber must be small for accuracy.

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Melinda S. Peng
and
R. T. Williams

Abstract

A two-scale expansion technique is used to study the barotropic instability of basic flows with slow streamwise variation. Disturbances in nonparallel flow possess properties that differ from those calculated from parallel flow theory. The difference, which is obtained at higher order in the parameter that measures the nonparallelism, depends on the first derivative of the parallel flow properties with respect to the streamwise direction. This higher order correction shifts the spatial growth rate profile for the nonparallel flow downstream relative to the spatial growth rate profile for parallel flow. These results are compared with a previous numerical study by Tupaz, Williams and Chang and some of their conclusions are modified.

Physically, the difference in the spatial instability for parallel and nonparallel flow is subject to two combined effects. The first is the lag effect discussed by Tupaz et al., which causes the disturbance structure to lag the parallel-flow solution structure in regions where the mean flow changes rapidly downstream. This causes the downstream shifting of the nonparallel growth rate profile. The second is related to the phase speed difference between the parallel and nonparallel flows. If the disturbance propagates faster than predicted by the parallel flow theory, the local spatial growth rate will be smaller than that calculated by the parallel flow and vice versa.

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Melinda S. Peng
and
R. T. Williams

Abstract

Spatial baroclinic instability in a mean flow with slow streamwise variation is studied with the quasi-geostrophic two-layer model. The two-scale expansion technique which was employed by Peng and Williams is used in this study. The zero-order terms give the local spatial instability solution. The next order terms determine the correction to the local solution due to the streamwise variation of the mean flow. It is found that this correction is not negligible when the β effect is large and the vertical shear is small. The results are explained with the lag effect, which was discussed by Peng and Williams. The lag effect occurs when the local solution changes its structure substantially in the streamwise direction. When the vertical shear is large or when the β effect is small, the ratio between the disturbances of the two layers is nearly uniform in the streamwise direction, even though the shear changes substantially. Thus, only a small lag effect is experienced by a disturbance as it propagates, and the streamwise effect is unimportant. The dependence of the vertical structure on the basic flow variation and other parameters is analyzed.

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Xuyang Ge
,
Tim Li
, and
Melinda S. Peng

Abstract

The genesis of Typhoon Prapiroon (2000), in the western North Pacific, is simulated to understand the role of Rossby wave energy dispersion of a preexisting tropical cyclone (TC) in the subsequent genesis event. Two experiments are conducted. In the control experiment (CTL), the authors retain both the previous typhoon, Typhoon Bilis, and its wave train in the initial condition. In the sensitivity experiment (EXP), the circulation of Typhoon Bilis was removed based on a spatial filtering technique of Kurihara et al., while the wave train in the wake is kept. The comparison between these two numerical simulations demonstrates that the preexisting TC impacts the subsequent TC genesis through both a direct and an indirect process. The direct process is through the conventional barotropic Rossby wave energy dispersion, which enhances the low-level wave train, the boundary layer convergence, and the convection–circulation feedback. The indirect process is through the upper-level outflow jet. The asymmetric outflow jet induces a secondary circulation with a strong divergence tendency to the left-exit side of the outflow jet. The upper-level divergence boosts large-scale ascending motion and promotes favorable environmental conditions for a TC-scale vortex development. In addition, the outflow jet induces a well-organized cyclonic eddy angular momentum flux, which acts as a momentum forcing that enhances the upper-level outflow and low-level inflow and favors the growth of the new TC.

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Weiwei Li
,
Zhuo Wang
, and
Melinda S. Peng

Abstract

Tropical cyclone (TC) forecasts from the NCEP Global Ensemble Forecasting System (GEFS) Reforecast version 2 (1985–2012) were evaluated from the climate perspective, with a focus on tropical cyclogenesis. Although the GEFS captures the climatological seasonality of tropical cyclogenesis over different ocean basins reasonably well, large errors exist on the regional scale. As different genesis pathways are dominant over different ocean basins, genesis biases are related to biases in different aspects of the large-scale or synoptic-scale circulations over different basins. The negative genesis biases over the western North Pacific are associated with a weaker-than-observed monsoon trough in the GEFS, the erroneous genesis pattern over the eastern North Pacific is related to a southward displacement of the ITCZ, and the positive genesis biases near the Cape Verde islands and negative biases farther downstream over the Atlantic can be attributed to the hyperactive Africa easterly waves in the GEFS. The interannual and subseasonal variability of TC activity in the reforecasts was also examined to evaluate the potential skill of the GEFS in providing subseasonal and seasonal predictions. The GEFS skillfully captures the interannual variability of TC activity over the North Pacific and the North Atlantic, which can be attributed to the modulation of TCs by the El Niño–Southern Oscillation (ENSO) and the Atlantic meridional mode (AMM). The GEFS shows promising skill in predicting the active and inactive periods of TC activity over the Atlantic. The skill, however, has large fluctuations from year to year. The analysis presented herein suggests possible impacts of ENSO, the Madden–Julian oscillation (MJO), and the AMM on the TC subseasonal predictability.

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Carolyn A. Reynolds
,
Melinda S. Peng
, and
Jan-Huey Chen

Abstract

Singular vectors (SVs) are used to study the sensitivity of 2-day forecasts of recurving tropical cyclones (TCs) in the western North Pacific to changes in the initial state. The SVs are calculated using the tangent and adjoint models of the Navy Operational Global Atmospheric Prediction System (NOGAPS) for 72 forecasts for 18 TCs in the western North Pacific during 2006. In addition to the linear SV calculation, nonlinear perturbation experiments are also performed in order to examine 1) the similarity between nonlinear and linear perturbation growth and 2) the downstream impacts over the North Pacific and North America that result from changes to the 2-day TC forecast. Both nonrecurving and recurving 2-day storm forecasts are sensitive to changes in the initial state in the near-storm environment (in an annulus approximately 500 km from the storm center). During recurvature, sensitivity develops to the northwest of the storm, usually associated with a trough moving in from the west. These upstream sensitivities can occur as far as 4000 km to the northwest of the storm, over the Asian mainland, which has implications for adaptive observations. Nonlinear perturbation experiments indicate that the linear calculations reflect case-to-case variability in actual nonlinear perturbation growth fairly well, especially when the growth is large. The nonlinear perturbations show that for recurving tropical cyclones, small initial perturbations optimized to change the 2-day TC forecast can grow and propagate downstream quickly, reaching North America in 5 days. The fastest 5-day perturbation growth is associated with recurving storm forecasts that occur when the baroclinic instability over the North Pacific is relatively large. These results suggest that nonlinear forecasts perturbed using TC SVs may have utility for predicting the downstream impact of TC forecast errors over the North Pacific and North America.

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Melinda S. Peng
,
James A. Ridout
, and
Timothy F. Hogan

Abstract

The convective parameterization of Emanuel has been employed in the forecast model of the Navy Operational Global Atmospheric Prediction System (NOGAPS) since 2000, when it replaced a version of the relaxed Arakawa–Schubert scheme. Although in long-period data assimilation forecast tests the Emanuel scheme has been found to perform quite well in NOGAPS, particularly for tropical cyclones, some weaknesses have also become apparent. These weaknesses include underprediction of heavy-precipitation events, too much light precipitation, and unrealistic heating at upper levels. Recent research efforts have resulted in modifications of the scheme that are designed to reduce such problems. One change described here involves the partitioning of the cloud-base mass flux into mixing cloud mass flux at individual levels. The new treatment significantly reduces a heating anomaly near the tropopause that is associated with a large amount of mixing cloud mass flux ascribed to that region in the original Emanuel scheme. In another modification, the selection of the updraft source level is changed in a manner that takes into consideration the assumed connection between updraft mass flux and parcel buoyancy at cloud-base level in the Emanuel scheme. Test results suggest that the modified scheme may in some cases better represent precipitation during the middle and latter stages of convective events. The scheme has also been modified to eliminate cloud-top overshooting. The parameterization changes are supported in part by diagnostic tests, including semiprognostic model tests using observed data and single-column model tests using cloud-resolving-scale simulation data. The modifications showed significant positive impacts in forecast experiments over the original designs and have been implemented into the operational NOGAPS.

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