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Ying-Hwa Kuo
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Jian-Wen Bao
and
Ying-Hwa Kuo

Abstract

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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Ying-Hwa Kuo
and
Yong-Run Guo

Abstract

This paper presents results from a series of observing system simulation experiments (OSSEs), designed to test a dynamic initialization procedure for continuous assimilation of observations from a hypothetical network of profilers. A 40-km adiabatic mesoscale model was used to generate a set of simulated observations from a network of 77 wind profilers over the continental United States with a station separation of 360 km. These observations were then assimilated into an 80-km model during a 12-h preforecast integration through a Newtonian nudging technique.

We found that dynamic initialization by nudging can successfully assimilate the time-continuous wind profiler observations into the model. The profiler data assimilation is effective in recovering mesoscale circulations which are not properly resolved by the observing network (due to inadequate horizontal resolution), while at the same time controlling the error growth for large-scale circulations. The impact is particularly significant in the divergence field, which is crucial for an accurate precipitation forecast. The improved initial state leads to further improvement in the subsequent forecast, demonstrating the value of the time-continuous profiler observations on short-range numerical weather prediction.

Assimilation of the wind field is found to be considerably more effective than assimilation of the temperature field. Specifically, wind assimilation leads to improvement in both the temperature and the wind fields, while temperature assimilation produces little improvement in the wind field. The best results are obtained when both temperature and wind fields are assimilated.

The proposed demonstration network of 31 profiles is likely to have a positive impact on short-range numerical weather prediction, though mainly confined over the localized region covered by the profiler network. Further expansion of the profiler network to increase its spatial resolution and its areal coverage is needed if improved prediction is expected over a larger area.

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Ying-Hwa Kuo
and
Simon Low-Nam

Abstract

A series of 14 numerical experiments were conducted using the Pennsylvania State University/National Center for Atmospheric Research mesoscale model on nine cases of explosive marine cyclogenesis. The main objective was to identify key factors that are important to short-range prediction of explosive cyclones.

We found that the intensity and structure of the simulated cyclones were sensitive to the details of precipitation parameterization. The grid-resolvable-scale precipitation associated with the mesoscale slantwise ascent in the vicinity of the warm front was crucial for rapid development. The upright convective precipitation played a relatively unimportant role. Surface energy fluxes had little effect on the development during the 24-h period of rapid cyclogenesis. The pattern of upward and downward fluxes while the storms were in progress was not favorable for storm intensification.

Small case-to-case variation was found among the nine-case ensemble in the resulting deepening due to changes in physical parameterizations or in horizontal and vertical resolutions; however, a substantial variation existed in the fundamental characteristics of these storms. Some storms were more dynamically driven, while others were more diabatically forced. Some cyclones were more sensitive to uncertainties in the initial conditions, and were therefore less predictable, than others.

Averaged over the nine cases, the model components crucial for short-range (0–24 h) prediction of rapid deepening—in order of decreasing importance—were: 1) initial conditions, 2) horizontal grid resolution, 3) precipitation parameterization, and 4) lateral boundary conditions. The parameterization of the surface energy fluxes and the vertical resolution generally had lesser impacts.

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Ying-Hwa Kuo
and
Richard J. Reed

Abstract

A series of nine experiments were conducted using a version of the Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) mesoscale model. Objectives were: 1) to test the ability of a high resolution limited-area model to simulate an extraordinary cyclogenesis that occurred in the eastern Pacific in November 1982; 2) to examine the effects of various physical processes on the storm development and 3) to determine the reasons for the failure of the operational Limited-area Fine-mesh Model (LFM) to forecast the event. Six of the experiments employed a 40 km grid and three employed an 80 km grid. Initial data for seven of the experiments consist of fields interpolated from the National Meteorological Center (NMC) operational analysis supplemented by subjective soundings created by Reed and Albright. The supplementary data were withheld in two of the experiments. Principal findings are:

1) The control experiment, which utilized the supplementary dataset, a 40 km grid and an explicit moisture scheme, simulated a mejor cyclone with a central pressure of 969 mb and a deepening rate of 31 mb per 24 h (observed values were 950 mb and 48 mb per 24 h). The path of the cyclone was well predicted, as were several features of the storm that could be verified by satellite and aircraft observations.

2) A vertical cross section taken immediately ahead of the storm center at the time of rapid deepening revealed a symmetrically neutral or slightly unstable state in and near the warm frontal zone and a narrow, sloping sheet of rapidly ascending air (w > 50 cm s−1) at the frontal boundary. Low-level convergence exceeded 1.0×10−4 s−1 as the air approached the zone. Vorticity grew from near zero to 6–7 f in only a few hours.

3) Moist processes were essential to the rapid development. Dry simulations produced deepenings of only 13–15 mb in the 24 hour period, implying that roughly half the intensification in the control experiment can be ascribed to dry baroclinicity and half to latent beat release and its interactions with baroclinicity.

4) Surface energy fluxes had no significant impact on the development during the 24 hour period of rapid deepening.

5) An experiment with parameterized convective and nonconvective precipitation yielded essentially the same final pressure as the control experiment. However, the time of most rapid deepening was delayed in the simulation with parameterized convection. The delay was related to differences in the vertical heating profile in the two experiments.

6) Reduction of the grid size from 80 km to 40 km had only a minor effect on the central pressure, suggesting that further reduction would not eliminate the 19 mb error in the predicted central pressure.

7) A considerably weaker cyclone (982 mb vs 971 mb central pressure) resulted when the supplementary data were withheld in an experiment conducted on the 80 km grid.

8) An experiment designed to match most closely the conditions of the LFM forecast yielded the weakest development of all. It is speculated that the absence of development in the LFM forecast stemmed from short-comings of the initial analysis.

9) A possible cause of the failure of the present experiments to fully capture the storm intensity is the deficiency of middle and upper-level observations, and the attendant uncertainties in the upper-level analyses, in the prestorm period.

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Ying-Hwa Kuo
and
Richard A. Anthes

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.

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Ying-Hwa Kuo
and
Richard A. Anthes

Abstract

The effect midlatitude organized onvection on its environment is diagnosed through the calculation of mesoscale heat and moisture budgets over a region during the 10–11 April 1979 AYE-SESAME case. The noise level or error at individual points is about 5°C day−1 for the heat budget and 2 g kg−1 day−1 for the moisture budget, consistent with the sensitivity tests discussed by Kuo and Anthes in a related paper. However, when averaged over an area bigger than the observational scale, the noise level is considerably reduced. The general agreement between the observed rainfall rate and the vertically integrated apparent heat sources and moisture sinks, together with the temporal continuity shown by the budgets at the nine analysis times, supports the credibility of the area-averaged budget results. The vertical structure of convective heating diagnosed from this organized midlatitude convection shows significant differences from those structures diagnosed in the tropics on much larger temporal and spatial scales; in particular, the maximum at about 350 mb is greater, little heating occurs below 650 mb, and strong cooling is diagnosed in the upper troposphere. High correlation exists between large-scale moisture convergence and observed rainfall rate. However, there is a time lag of several hours between the moisture convergence and the rainfall rate. Their phase relationship is similar to that observed in previous studies on the easterly waves, and suggests a strong relationship between the large-scale and the convective systems.

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Ying-Hwa Kuo
and
Richard A. Anthes

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.

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Qiu-Shi Chen
and
Ying-Hwa Kuo

Abstract

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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Qiu-Shi Chen
and
Ying-Hwa Kuo

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.

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