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Nan Chen and Andrew J. Majda

Abstract

In this paper, a general conditional Gaussian framework for filtering complex turbulent systems is introduced. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the filter allows closed analytical formulas for updating the posterior states and is thus computationally efficient. An information-theoretic framework is developed to assess the model error in the filter estimates. Three types of applications in filtering conditional Gaussian turbulent systems with model error are illustrated. First, dyad models are utilized to illustrate that ignoring the energy-conserving nonlinear interactions in designing filters leads to significant model errors in filtering turbulent signals from nature. Then a triad (noisy Lorenz 63) model is adopted to understand the model error due to noise inflation and underdispersion. It is also utilized as a test model to demonstrate the efficiency of a novel algorithm, which exploits the conditional Gaussian structure, to recover the time-dependent probability density functions associated with the unobserved variables. Furthermore, regarding model parameters as augmented state variables, the filtering framework is applied to the study of parameter estimation with detailed mathematical analysis. A new approach with judicious model error in the equations associated with the augmented state variables is proposed, which greatly enhances the efficiency in estimating model parameters. Other examples of this framework include recovering random compressible flows from noisy Lagrangian tracers, filtering the stochastic skeleton model of the Madden–Julian oscillation (MJO), and initialization of the unobserved variables in predicting the MJO/monsoon indices.

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Minghang Chen and J. Ray Bates

Abstract

A series of 10-day forecast experiments has been carried out to investigate the sensitivity of a global semi-Lagrangian model to the value of the uncentering parameter ε, the magnitude of the time step for the dynamics, and the numerical treatment of the physical parameterizations (semi-Lagrangian versus Eulerian). The model has been run at a resolution of 2° latitude by 2.5° longitude with 20 vertical levels. Results from the experiments with values of ε ranging from 0 to 0.4 show that ε = 0.2 gives the best overall forecasts. The experiments with the time step for the dynamics varying from 15 to 60 min indicate that the forecasts are sensitive to the time step for the dynamics, even when the time steps for the physical parameterizations are held constant. The forecasts with the 60-min time step for the dynamics show the best overall objective skill scores. The two versions of the semi-Lagrangian model, one with Eulerian physics and the other with semi-Lagrangian physics, give similar forecast skill scores.

The semi-Lagrangian model is also compared with a corresponding Eulerian model. It is found that the forecasts from the two models have similar quality, even though the time step for the dynamics in the semi-Lagrangian model is 16 times as long as that in the Eulerian model and the physical parameterizations have been developed and tuned for the Eulerian model.

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Minghang Chen and J. Ray Bates

Abstract

Two parallel 5-year climate simulations have been carried out to assess the effect of changing from an Eulerian to a semi-Lagrangian formulation of a general circulation model's dynamical core with the physical parameterizations unchanged. It has been found that the change in formulation leads to significant differences in the simulated climates, both for fields determined mainly by the dynamics, such as sea level pressure, and for those determined mainly by the physics, such as precipitation. The differences result both directly from the changes in the dynamics and indirectly from the interactions of the dynamics with the physics. Compared to the simulation with the Eulerian model, the principal improvement with the semi-Lagrangian model is a significant reduction in, or even elimination of, the cold bias in the polar upper troposphere and lower stratosphere in both hemispheres. This improvement is evident in both the winter and summer seasons. It results from the more efficient poleward heat transport in the semi-Lagrangian model. The effect on other simulated fields can give results either closer to or farther from the corresponding analyses and observations.

The physical parameterizations used in the semi-Lagrangian model have been developed and tuned for the Eulerian model. To optimize the performance of the semi-Lagrangian model, it will be necessary to tune the physical parameterizations explicitly for this model.

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Nan Chen and Andrew J. Majda

Abstract

Lagrangian tracers are drifters and floaters that collect real-time information of fluid flows. This paper studies the model error in filtering multiscale random rotating compressible flow fields utilizing noisy Lagrangian tracers. The random flow fields are defined through random amplitudes of Fourier eigenmodes of the rotating shallow-water equations that contain both incompressible geostrophically balanced (GB) flows and rotating compressible gravity waves, where filtering the slow-varying GB flows is of primary concern. Despite the inherent nonlinearity in the observations with mixed GB and gravity modes, there are closed analytical formulas for filtering the underlying flows. Besides the full optimal filter, two practical imperfect filters are proposed. An information-theoretic framework is developed for assessing the model error in the imperfect filters, which can apply to a single realization of the observations. All the filters are comparably skillful in a fast rotation regime (Rossby number ). In a moderate rotation regime (), significant model errors are found in the reduced filter containing only GB forecast model, while the computationally efficient 3D-Var filter with a diagonal covariance matrix remains skillful. First linear then nonlinear coupling of GB and gravity modes is introduced in the random Fourier amplitudes, while linear forecast models are retained to ensure the filter estimates have closed analytical expressions. All the filters remain skillful in the regime. In the regime, the full filter with a linear forecast model has an acceptable filtering skill, while large model errors are shown in the other two imperfect filters.

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Tsing-Chang Chen and J. Shukla

Abstract

We examine diagnostically the structure and spectral energetics of an amplified persistent blocking ridge and trough pattern that occurred in one of the GLAS climate simulations. This particular model simulation was performed by Shukla and Bangaru (1979) to study the sensitivity of the quasi-stationary waves to the North Pacific sea surface temperature anomalies. The spectrally filtered Hovmöller diagram shows that wavenumbers 2 and 3 in the anomaly run become stationary near their climatological locations. The constructive interference of wavenumbers 2 and 3 forms two persistent blocking ridges: one in the west coast of North America and the other in western Europe.

Spectral energetics analysis of this blocking case shows that A 2I/ and A 3, the available potential energy of wavenumbers 2 and 3, are supplied by the conversion from zonal available potential energy. K 2 and K 3, the kinetic energy of thew two waves, are maintained by different processes: K 2 is maintained by conversion from A 2 to K 2, a baroclinic proem, while K 3 is mainly maintained by conversion from Kz, the zonal kinetic energy, to K 3, a barotropic process.

The model-simulated blocking episode is similar to the atmospheric circulation conditions in January 1963 and the 1976-77 winter. The spectral energetics for thew two periods are compared with those of the model simulation, and in most instances, are found to be quite similar.

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Nan Chen and Andrew J. Majda

Abstract

A new low-order nonlinear stochastic model is developed to improve the predictability of the Real-time Multivariate Madden–Julian oscillation (MJO) index (RMM index), which is a combined measure of convection and circulation. A recent data-driven, physics-constrained, low-order stochastic modeling procedure is applied to the RMM index. The result is a four-dimensional nonlinear stochastic model for the two observed RMM variables and two hidden variables involving correlated multiplicative noise defined through energy-conserving nonlinear interaction. The special structure of the low-order model allows efficient data assimilation for the initialization of the hidden variables that facilitates the ensemble prediction algorithm. An information-theoretic framework is applied to the calibration of model parameters over a short training phase of 3 yr. This framework involves generalizations of the anomaly pattern correlation, the RMS error, and the information deficiency in the model forecast. The nonlinear stochastic models show skillful prediction for 30 days on average in these metrics. More importantly, the predictions succeed in capturing the amplitudes of the RMM index and the useful skill of forecasting strong MJO events is around 40 days. Furthermore, information barriers to prediction for linear models imply the necessity of the nonlinear interactions between the observed and hidden variables as well as the multiplicative noise in these low-order stochastic models.

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Nan Chen and Andrew J. Majda

Abstract

The filtering and prediction of the Madden–Julian oscillation (MJO) and relevant tropical waves is a contemporary issue with significant implications for extended range forecasting. This paper examines the process of filtering the stochastic skeleton model for the MJO with noisy partial observations. A nonlinear filter, which captures the inherent nonlinearity of the system, is developed and judicious model error is included. Despite its nonlinearity, the special structure of this filter allows closed analytical formulas for updating the posterior states and is thus computationally efficient. A novel strategy for adding nonlinear observational noise to the envelope of convective activity is designed to guarantee its nonnegative property. Systematic calibration based on a cheap single-column version of the stochastic skeleton model provides a practical guideline for choosing the parameters in the full spatially extended system. With these column-tuned parameters, the full filter has a high overall filtering skill for Rossby waves but fails to recover the small-scale fast-oscillating Kelvin and moisture modes. An effectively balanced reduced filter involving a simple fast-wave averaging strategy is then developed, which greatly improves the skill of filtering the moisture modes and other fast-oscillating modes and enhances the total computational efficiency. Both the full and the reduced filters succeed in filtering the MJO and other large-scale features with both homogeneous and warm pool cooling/moistening backgrounds. The large bias in filtering the solutions by running the perfect model with noisy forcing is due to the noise accumulation, which indicates the importance of including judicious model error in designing filters.

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Ting-Chen Chen, M. K. Yau, and Daniel J. Kirshbaum

Abstract

Slantwise convection, the process by which moist symmetric instability is released, has often been linked to banded clouds and precipitation, especially in frontal zones within extratropical cyclones. Studies also suggest that the latent heat release associated with slantwise convection can lead to a spinup of surface frontogenesis, which can enhance the rapid intensification of extratropical cyclones. However, most of these studies considered only local areas or short time durations. In this study, we provide a novel statistical investigation of the global climatology of the potential occurrence of slantwise convection, in terms of conditional symmetric instability, and its relationship with precipitating systems. Using the 6-hourly ERA-Interim, two different indices are calculated, namely, slantwise convective available potential energy (SCAPE) and vertically integrated extent of realizable symmetric instability (VRS), to assess the likelihood of occurrence of slantwise convection around the globe. The degree of association is quantified between these indices and the observed surface precipitation as well as the cyclone activity. The susceptibility of midlatitude cyclones to slantwise convection at different stages of their life cycle is also investigated. As compared to the nonexplosive cyclone cases, the time evolution of SCAPE and VRS within rapidly deepening cyclones exhibit higher values before, and a more significant drop after, the onset of rapid intensification, supporting the idea that the release of symmetric instability might contribute to the intensification of storms.

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Yi-Leng Chen and Andrew J. Nash

Abstract

The high-resolution Portable Automated Mesonet data from the Hawaiian Rainband Project are used to document the circulation over the entire island of Hawaii for the first time. It is shown that the surface airflow and rainfall occurrences over the island are strongly modulated by the diurnal heating cycle.

Most areas over the island show daytime upslope and nighttime downslope components separated by morning and evening transitions. On the windward slope, the onset of the downslope (upslope) wind during the evening (morning) transition starts on the slopes and progresses downward. The effects of island blocking are also evident. On the windward slopes of Mauna Kea and Mauna Loa, the mean winds are weak (∼1 m s−1) due to flow deceleration. Flow splitting occurs in the Hilo Bay area as the trade winds are forced to move around the island. On the lee side, the trade winds are absent. For stronger trade-wind days, the island blocking is more significant with a higher surface pressure (0.2-0.5 hPa) on the windward slopes and lower pressure in the lee side than weak trade-wind days. Along the windward coast, it is much easier for the land breeze to overcome weaker trade winds. For weaker trade-wind days, the onset (cessation) of land breeze there is earlier (later) in the evening (morning).

At night, the area of maximum rainfall frequency is over the windward lowland west of Hilo. Most of the nocturnal precipitation there starts in situ. The effects of orographic lifting aloft are enhanced by the nighttime convergence west of Hilo due to the interaction between the katabatic-land-breeze flow and the trade winds. In the early morning, the rainfall frequency has a maximum along the windward coast due to the inland drifting of the frequently observed rainbands offshore.

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Jesse Norris, Gang Chen, and J. David Neelin

ABSTRACT

Projected changes in the frequency of major precipitation accumulations (hundreds of millimeters), integrated over rainfall events, over land in the late twenty-first century are analyzed in the Community Earth System Model (CESM) Large Ensemble, based on the RCP8.5 scenario. Accumulation sizes are sorted by the local average recurrence interval (ARI), ranging from 0.1 to 100 years, for the current and projected late-twenty-first-century climates separately. For all ARIs, the frequency of exceedance of the given accumulation size increases in the future climate almost everywhere, especially for the largest accumulations, with the 100-yr accumulation becoming about 3 times more frequent, averaged over the global land area. The moisture budget allows the impacts of individual factors—moisture, circulation, and event duration—to be isolated. In the tropics, both moisture and circulation cause large future increases, enhancing the 100-yr accumulation by 23% and 13% (average over tropical land), and are individually responsible for making the current-climate 100-yr accumulation 2.7 times and 1.8 times more frequent, but effects of shorter durations slightly offset these effects. In the midlatitudes, large accumulations become about 5% longer in duration, but are predominantly controlled by enhanced moisture, with the 100-yr accumulation (land average) becoming 2.4 times more frequent, and 2.2 times more frequent due to moisture increases alone. In some monsoon-affected regions, the 100-yr accumulation becomes more than 5 times as frequent, where circulation changes are the most impactful factor. These projections indicate that changing duration of events is a relatively minor effect on changing accumulations, their future enhancement being dominated by enhanced intensity (the combination of moisture and circulation).

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