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Robert A. Dalrymple and Philip L-F. Liu

Abstract

The problem of water waves propagating over a mud bottom, characterized as a laminar viscous fluid, is treated in several ways. First, two complete models are present, each valid for different lower (mud) layer depths, and second, a boundary layer model is presented as an appendix for the case where the lower layer is thick with respect to the boundary layer.

These models are compared to the shallow water model and experimental results of Gade (1957, 1958) and agree well. The results show that extremely high wave attenuation rates are possible when the thickness of the lower layer is the same order as the internal boundary layer thickness and when the lower layer is thick.

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Qing Liu and Cornelius J. F. Schuurmans

Abstract

In this paper, the authors show that the effect of a tropical Pacific anomalous forcing can he primarily linear or nonlinear depending on its sign and longitudinal position. Using a nine-level steady-state model both the linear and nonlinear steady-state responses to tropical anomalous diabatic warming or cooling in the midtroposphere were computed. These sources were centered at 130°W and at the date line.

At 130°W the atmospheric response to tropical heating or cooling is primarily linear. The amplitudes are small and of opposite sign for heating and cooling. The response agrees well with the results of corresponding general circulation model (GCM) experiments. For a heating at the date line, the modification of the linear response by the nonlinear terms is substantial. The nonlinear response to the heating is much stronger than the linear response, whereas the nonlinear response to cooling is weaker. The main effect of the nonlinear terms is to modify the amplitudes; the structure of the response is only slightly adjusted. Both the linear and the nonlinear steady-state responses to tropical beating at the dale line result in an anti-Pacific-North American pattern. This is not in agreement with the results of corresponding GCM experiments.

The tropically forced stationary perturbations can have a substantial effect on the stability properties of the planetary-scale time-mean state. This may lead to strong nonlinear transient feedback effects and consequently a strong modification of the direct steady-state response. We have shown that the effect of a persistent heating or cooling at 130°W hardly affects the stability properties of the time-mean state. However, the effect of a heating at the date line is to strongly enhance the low-frequency variability. We hypothesize that this causes large additional transient feedback effects that substantially modify the character of the direct linear or nonlinear steady-state response. This may account for the discrepancy between the steady-state model and general circulation model results for the heating case at the date line.

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Han-Shou Liu and Benjamin F. Chao

Abstract

The wavelet time-frequency spectral analysis is applied to geological records that are proxies of paleoclimatic variations: δ 18O in sedimentary cores, atmospheric CO2 concentration, and a loess magnetic susceptibility stratigraphy within the past million years. These spectra are compared with those for the astronomically predicted variations of the earth’s orbital eccentricity, obliquity, precession, and their resultant variations of the incoming insolation. The latter has been known to be unable to explain the characteristics of the observed 100-kyr paleoclimatic cycles. Based on similarities between the wavelet spectra of the orbital variations and paleoclimatic cycles, the authors introduce a signal–noise resonance theory to understand the dynamics of climate response to the orbital forcing. It is shown that the observed 100-kyr cycles are mainly caused by the period variation in the obliquity, which amplifies the small orbital forcing. But the observed flickers within these cycles are induced by the amplitude variation of obliquity and precession, which are two major components of the Milankovitch insolation deviations.

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H-L. Liu, F. Sassi, and R. R. Garcia

Abstract

It has been well established that the atmosphere is chaotic by nature and thus has a finite limit of predictability. The chaotic divergence of initial conditions and the predictability are explored here in the context of the whole atmosphere (from the ground to the thermosphere) using the NCAR Whole Atmosphere Community Climate Model (WACCM). From ensemble WACCM simulations, it is found that the early growth of differences in initial conditions is associated with gravity waves and it becomes apparent first in the upper atmosphere and progresses downward. The differences later become more profound on increasingly larger scales, and the growth rates of the differences change in various atmospheric regions and with seasons—corresponding closely with the strength of planetary waves. For example, in December–February the growth rates are largest in the northern and southern mesosphere and lower thermosphere and in the northern stratosphere, while smallest in the southern stratosphere. The growth rates, on the other hand, are not sensitive to the altitude where the small differences are introduced in the initial conditions or the physical nature of the differences. Furthermore, the growth rates in the middle and upper atmosphere are significantly reduced if the lower atmosphere is regularly reinitialized, and the reduction depends on the frequency and the altitude range of the reinitialization.

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Philip L-F. Liu, Maarten W. Dingemans, and Jan K. Kostense

Abstract

The generation of long waves by short-wave groups propagating over a shear current is studied. The incident wave groups consist of two co-linear short waves with slightly different frequencies. These short waves are refracted by the shear currents. For certain angles of incidence caustics may exist and the short waves are reflected back by the shear current. Similarly, caustics could also appear in the wave envelope, which propagates in a different direction from that of the short waves. In the present paper, the treatment of caustics is not considered. In the region where the shear current vanishes, the short-wave groups are accompanied by locked long waves that propagate with the wave envelope of short waves at their group velocity. In the shear current region, the refraction effects not only separate the propagation directions of the short waves and the wave envelope but also generate free long waves, which propagate at the speed of.gh. The free long waves could also be trapped over the shear current region.

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Haixia Liu, Ming Xue, R. James Purser, and David F. Parrish

Abstract

Anisotropic recursive filters are implemented within a three-dimensional variational data assimilation (3DVAR) framework to efficiently model the effect of flow-dependent background error covariance. The background error covariance is based on an estimated error field and on the idea of Riishøjgaard. In the anisotropic case, the background error pattern can be stretched or flattened in directions oblique to the alignment of the grid coordinates and is constructed by applying, at each point, six recursive filters along six directions corresponding, in general, to a special configuration of oblique lines of the grid. The recursive filters are much more efficient than corresponding explicit filters used in an earlier study and are therefore more suitable for real-time numerical weather prediction. A set of analysis experiments are conducted at a mesoscale resolution to examine the effectiveness of the 3DVAR system in analyzing simulated global positioning system (GPS) slant-path water vapor observations from ground-based GPS receivers and observations from collocated surface stations. It is shown that the analyses produced with recursive filters are at least as good as those with corresponding explicit filters. In some cases, the recursive filters actually perform better. The impact of flow-dependent background errors modeled using the anisotropic recursive filters is also examined. The use of anisotropic filters improves the analysis, especially in terms of finescale structures. The analysis system is found to be effective in the presence of typical observational errors. The sensitivity of isotropic and anisotropic recursive-filter analyses to the decorrelation scales is also examined systematically.

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Yulan Hong, Guosheng Liu, and J.-L. F. Li

Abstract

Although it is well established that cirrus warms Earth, the radiative effect of the entire spectrum of ice clouds is not well understood. In this study, the role of all ice clouds in Earth’s radiation budget is investigated by performing radiative transfer modeling using ice cloud properties retrieved from CloudSat and CALIPSO measurements as inputs. Results show that, for the 2008 period, the warming effect (~21.8 ± 5.4 W m−2) induced by ice clouds trapping longwave radiation exceeds their cooling effect (~−16.7 ± 1.7 W m−2) caused by shortwave reflection, resulting in a net warming effect (~5.1 ± 3.8 W m−2) globally on the earth–atmosphere system. The net warming is over 15 W m−2 in the tropical deep convective regions, whereas cooling occurs in the midlatitudes, which is less than 10 W m−2 in magnitude. Seasonal variations of ice cloud radiative effects are evident in the midlatitudes where the net effect changes from warming during winter to cooling during summer, whereas warming occurs all year-round in the tropics. Ice cloud optical depth τ is shown to be an important factor in determining the sign and magnitude of the net radiative effect. Ice clouds with τ < 4.6 display a warming effect with the largest contributions from those with τ ≈ 1.0. In addition, ice clouds cause vertically differential heating and cooling of the atmosphere, particularly with strong heating in the upper troposphere over the tropics. At Earth’s surface, ice clouds produce a cooling effect no matter how small the τ value is.

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Y. Liu, Z. Liu, S. Zhang, X. Rong, R. Jacob, S. Wu, and F. Lu

Abstract

Ensemble-based parameter estimation for a climate model is emerging as an important topic in climate research. For a complex system such as a coupled ocean–atmosphere general circulation model, the sensitivity and response of a model variable to a model parameter could vary spatially and temporally. Here, an adaptive spatial average (ASA) algorithm is proposed to increase the efficiency of parameter estimation. Refined from a previous spatial average method, the ASA uses the ensemble spread as the criterion for selecting “good” values from the spatially varying posterior estimated parameter values; these good values are then averaged to give the final global uniform posterior parameter. In comparison with existing methods, the ASA parameter estimation has a superior performance: faster convergence and enhanced signal-to-noise ratio.

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Y. Liu, Z. Liu, S. Zhang, R. Jacob, F. Lu, X. Rong, and S. Wu

Abstract

Parameter estimation provides a potentially powerful approach to reduce model bias for complex climate models. Here, in a twin experiment framework, the authors perform the first parameter estimation in a fully coupled ocean–atmosphere general circulation model using an ensemble coupled data assimilation system facilitated with parameter estimation. The authors first perform single-parameter estimation and then multiple-parameter estimation. In the case of the single-parameter estimation, the error of the parameter [solar penetration depth (SPD)] is reduced by over 90% after ~40 years of assimilation of the conventional observations of monthly sea surface temperature (SST) and salinity (SSS). The results of multiple-parameter estimation are less reliable than those of single-parameter estimation when only the monthly SST and SSS are assimilated. Assimilating additional observations of atmospheric data of temperature and wind improves the reliability of multiple-parameter estimation. The errors of the parameters are reduced by 90% in ~8 years of assimilation. Finally, the improved parameters also improve the model climatology. With the optimized parameters, the bias of the climatology of SST is reduced by ~90%. Overall, this study suggests the feasibility of ensemble-based parameter estimation in a fully coupled general circulation model.

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F. J. Robinson, S. C. Sherwood, D. Gerstle, C. Liu, and D. J. Kirshbaum

Abstract

Moist convection is well known to be generally more intense over continental than maritime regions, with larger updraft velocities, graupel, and lightning production. This study explores the transition from maritime to continental convection by comparing the trends in Tropical Rainfall Measuring Mission (TRMM) radar and microwave (37 and 85 GHz) observations over islands of increasing size to those simulated by a cloud-resolving model. The observed storms were essentially maritime over islands of <100 km2 and continental over islands >10 000 km2, with a gradual transition in between.

Equivalent radar and microwave quantities were simulated from cloud-resolving runs of the Weather Research and Forecasting model via offline radiation codes. The model configuration was idealized, with islands represented by regions of uniform surface heat flux without orography, using a range of initial sounding conditions without strong horizontal winds or aerosols. Simulated storm strength varied with initial sounding, as expected, but also increased sharply with island size in a manner similar to observations. Stronger simulated storms were associated with higher concentrations of large hydrometeors. Although biases varied with different ice microphysical schemes, the trend was similar for all three schemes tested and was also seen in 2D and 3D model configurations. The successful reproduction of the trend with such idealized forcing supports previous suggestions that mesoscale variation in surface heating—rather than any difference in humidity, aerosol, or other aspects of the atmospheric state—is the main reason that convection is more intense over continents and large islands than over oceans.

Some dynamical storm aspects, notably the peak rainfall and minimum surface pressure low, were more sensitive to surface forcing than to the atmospheric sounding or ice scheme. Large hydrometeor concentrations and simulated microwave and radar signatures, however, were at least as sensitive to initial humidity levels as to surface forcing and were more sensitive to the ice scheme.

Issues with running the TRMM simulator on 2D simulations are discussed, but they appear to be less serious than sensitivities to model microphysics, which were similar in 2D and 3D. This supports the further use of 2D simulations to economically explore modeling uncertainties.

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