Importance of cross-channel bathymetry and eddy viscosity parameterisation in modelling estuarine flow

For a proper understanding of flow patterns in curved tidal channels, quantification of contributions from individual physical mechanisms is essential. We study quantitatively how such contributions are affected by cross-channel bathymetry and three alternative eddy viscosity parameterisations. Two models are presented for this purpose, both describing flow in curved but otherwise prismatic channels with an (almost) arbitrary transverse bathymetry. One is a numerical model based on the full three-dimensional shallow water equations. Special feature of this diagnostic model is that assumptions regarding the relative importance of particular physical mechanisms can be incorporated in the computations by switching corresponding terms in the model equations on or off. We also present an idealized model that provides semi-analytical approximate solutions of the shallow water equations for all three considered alternative eddy viscosity parameterisations. It forms an aid in explaining and theorising about results obtained with the numerical model. Observations regarding Chesapeake Bay serve as a reference case for the present study. We find that the relative importance of both along-channel advective forcing and transverse diffusive forcing depends on local characteristics of the cross-sectional bottom profile rather than global ones. In our reference case, tide-residual along-channel flow induced by these forcings is not small compared to the total tidal residual. Building on this observation, we present an indicative test to judge whether advective processes should be included in leading order in modelling tide-dominated estuarine flow. Furthermore, depending on the applied eddy viscosity parameterisation (uniformly or parabolically distributed over the vertical), we find qualitatively different spatial patterns for the along-channel advective forcing.     

Time-varying storm surges on Lorentz’s Wadden Sea networks

We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-water equations in a channel are combined in an algebraic system for the network. The velocity scale that is used for the linearized friction coefficient is determined iteratively. The hindcast of the storm surge of 5 December 2013 produces credible time-varying results. The effects of storm and basin parameters on the peak surge elevation are the subject of a sensitivity analysis. The formulation in the frequency domain reveals which modes in the external forcing lead to the largest surge response at coastal stations. There appears to be a minimum storm duration, of about 3–4 h, that is required for a surge to attain its maximum elevation. The influence of the water levels at the North Sea inlets on the Wadden Sea surges decreases towards the shore. In contrast, the wind shearing generates its largest response near the shore, where the fetch length is at its maximum.     

A note on multiple flow equilibria

A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admitN steady solutions, whereN is a positive odd integer and where at least (N–1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem.     

20世纪温度变化中自然变率和人为因素的影响:基于耦合气候模式的归因模拟

本文基于中国科学院大气物理研究所大气科学和地球流体力学国家重点实验室(LASG/IAP)发展的气候系统模式FGOALS_gl对近百年气温变化的模拟,讨论了自然变率和人为因素对20世纪全球变暖的相对贡献.数值试验结果表明,在自然和人为因子的共同强迫作用下,耦合模式能够合理再现20世纪全球平均气温随时间的演变;仅在自然因子作用下,模式不能再现1970年以后的全球变暖.自然因素对20世纪第一次变暖的作用是显著的,但温室气体是20世纪后期变暖的主要原因.在这一定性结论基础上,进一步对近百年变化中自然和人为因素的相对贡献做定量的归因分析,结果表明,除赤道中东太平洋和北大西洋外,人为因素对近百年的增暖起决定性作用.对全球、半球及大陆尺度而言,外强迫可以解释平均气温变化的70%以上,而内部变率贡献较小;但对于区域尺度而言,多数地区内部变率的贡献大于外强迫,区域尺度气温变化的机制较全球、半球尺度要复杂.对中国地区而言,20世纪早期的气温变化受自然变率影响,但20世纪后期的变暖主要是温室气体增加的结果.中国东部气温变化的空间分布表明,自然因素对近50年及近百年中国地区的变暖趋势贡献较小.在自然和人为因子共同作用下,模式能够再现近50年中国东部气温变化冬春两季增暖的特征、但没有模拟出夏季长江中下游地区及淮河流域的降温趋势;自然因子试验的结果表明,太阳活动对该区域的变冷有贡献,但模式无法再现该地区气温的季节变化特征.     

Air temperature feedback and its contribution to global warming

Air temperature feedback results from the thermal-radiative coupling between the atmosphere and the surface and plays an important role in surface energy balance. This paper reveals the contribution of air temperature feedback to the global warming from 1980 to 2000. The air temperature feedback kernel, evaluated using the ERA-Interim reanalysis data, is used to discuss the physical mechanism for air temperature feedback, the dependency of the strength of air temperature feedback on the climatological spatial distributions of air temperature, water vapor and cloud content, and the contributions of air temperature feedback to rapid global warming. The coupling between temperature feedback and each of the external forcings and individual feedback processes will amplify the anomaly of direct energy flux convergence at the surface induced by the external forcings and individual processes. The air temperature feedback amplifies the initial surface warming due to the increase in CO₂ concentration, ice and snow melting, increase in water vapor, and change in ocean heat storage. It also amplifies the surface warming due to the longwave radiaitve forcing associated with the increase in cloud cover, which acts to suppress the cooling of the shortwave effect of cloud forcing. Overall, temperature feedback plays an important role in the global warming from 1980 to 2000, as the net positive contribution to the perturbation of global mean energy flux at the surface from the air temperature feedback is larger than the net negative contribution from external forcing and all non-temperature feedbacks.     

Nonhydrostatic Atmospheric Normal Modes on Beta-Planes

--To facilitate the understanding of nonhydrostatic effect in global and regional nonhydrostatic models, the normal modes of a nonhydrostatic, stratified, and compressible atmosphere are studied using Cartesian coordinates on midlatitude and equatorial #-planes. The dynamical equations without forcing and dissipation are linearized around the basic state at rest, and solved by using the method of separation of variables. An eigenvalue-eigenfunction problem is formulated, consisting of the horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as "equivalent height," appear in both the horizontal and vertical characteristic equations as a coupled problem, unlike the hydrostatic case. Therefore, the nonhydrostatic equivalent height depends not only on the vertical modal scale, as in the hydrostatic case, but also on the zonal and meridional modal scales. Numerical resu lts on the dispersion relations are presented for an isothermal atmosphere. Three kinds of normal modes, namely acoustic, gravity, and Rossby modes, are solved and compared with the corresponding global solutions. Nonhydrostatic effects are studied in terms of normal modes in a wide range of wavelengths from small to planetary scales. It is demonstrated that Rossby modes are hardly affected by nonhydrostatic effects regardless of wavelengths. However, nonhydrostatic effects on gravity modes become significant for smaller horizontal and deeper vertical scales of motion. The equivalent height plays a particularly important role in evaluating nonhydrostatic effects of normal modes on the equatorial #-plane, because the equivalent height appears in the scaling of meridional distance variable of the eigenfunctions. The implementation of nonhydrostatic normal mode analysis on high-resolution numerical modeling is also discussed.     

Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space

Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the global stiffness matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the global stiffness matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.     

Solitary Rossby Waves in Zonally Varying Jet Flows

The dynamics of solitary Rossby waves (SRWs) embedded in a meridionally sheared, zonally varying background flow are examined using a non-divergent barotropic model centered on a midlatitude g -plane. The zonally varying background flow, which is produced by an external potential vorticity (PV) forcing, yields a modified Korteweg-de Vries (K-dV) equation that governs the spatial-temporal evolution of a disturbance field that contains both Rossby wave packets and SRWs. The modified K-dV equation differs from the classical equation in that the zonally varying background flow, which varies on the same scale as the disturbance field, directly affects the disturbance linear translation speed and linear growth characteristics. In the limit of a locally parallel background flow, equations governing the amplitude and propagation characteristics of SRWs are derived analytically. These equations show, for example, that a sufficiently large (small) translation speed and/or a sufficiently weak (strong) background zonal shear favor transmission (reflection) of the SRW through (from) the jet. Conservation equations are derived showing that time changes in the domain averaged amplitude ("mass") or squared amplitude ("momentum") are due to zonal variation in both the linear, long-wave phase speed and linear growth; dispersion and nonlinearity do not affect the "mass" or "momentum". Provided (1) the background PV forcing is sufficiently small, or (2) the background PV forcing is meridionally symmetric and the disturbance is a SRW, the dynamics of the disturbance field is Hamiltonian and mass and energy are thus conserved. Numerical solutions of the K-dV equation show that the zonally varying background flow yields three general classes of behavior: reflection, transmission, or trapping. Within each class there exists SRWs and Rossby wave packets. SRWs that become trapped within the zonally localized jet region may exhibit the following behaviors: (1) an oscillatory decay to a steady state at the jet center, (2) the creation of additional SRWs within the jet region, or (3) a steady-state wherein the solution has a smoothed step-like structure located downstream along the jet axis.     

Correcting circulation biases in a lower-resolution global general circulation model with data assimilation

In this study, we aim at developing a new method of bias correction using data assimilation. This method is based on the stochastic forcing of a model to correct bias by directly adding an additional source term into the model equations. This method is presented and tested first with a twin experiment on a fully controlled Lorenz ’96 model. It is then applied to the lower-resolution global circulation NEMO-LIM2 model, with both a twin experiment and a real case experiment. Sea surface height observations are used to create a forcing to correct the poorly located and estimated currents. Validation is then performed throughout the use of other variables such as sea surface temperature and salinity. Results show that the method is able to consistently correct part of the model bias. The bias correction term is presented and is consistent with the limitations of the global circulation model causing bias on the oceanic currents.     

On the upper bounding approach to thermal convection at moderate rayleigh numbers

Abstract

Two upper bounding problems for thermal convection in a layer of fluid contained between perfectly conducting stress-free boundaries are treated numerically. Since the Euler equations resulting from this variational approach are simpler than the Navier-Stokes equations, they allow numerical calculations to be carried out economically to fairly large values of the Rayleigh number. The upper bounding problem formulated by Howard (1963), which yields a Nusselt number independent of Prandtl number, diverges from the correct behavior as the Rayleigh number increases. In hopes of coming closer to results of previous investigations of the Boussinesq equations of motion, a more restrictive upper bounding problem is formulated. For large Prandtl numbers the momentum equation is linearized and is used as an explicit side constraint on the variational problem, thereby forcing the solutions to more closely resemble the solutions of the Boussinesq equations. Numerical calculations at values of the Rayleigh number up to 1.5 × 10⁵ indicate that the additional constraint decreases the upper bound on the Nusselt number; it appears that this upper bound differs by only a multiplicative factor from that calculated from solutions of the full equations of motion and may be a reasonable approximation for large Rayleigh numbers.     

Phase synchronization of slips by periodical (tangential and normal) mechanical forcing in the spring-slider model

In the present study, the character of slip regimes under weak external periodical (tangential and normal) mechanical forcing has been investigated in a laboratory spring-slider system. We report the experimental evidence of phase synchronization in a slip dynamics, induced by the external periodic mechanical impact. At certain conditions, we have a stick-slip effect in the spring-slider system. To describe this effect, we can use rate-and state-dependent friction law. In our experiments, the slip events are distinguished by acoustic emission bursts, which are generated by slider displacement. In addition to drag, the weak variable mechanical forcing was superimposed either tangential or normal to the slip plane. With increasing external forcing one can see increasing phase synchronization of the first arrivals (onsets) of stick-slip generated acoustic pulses. The grouping of the onsets in a certain phase of the external periodic forcing is considered as a hallmark of the phase synchronization. The onsets of stick-slip pulses in the case of normal mechanical forcing are shifted relative to onsets in the case of tangential forcing.     

Stability of weak solutions to climate dynamics model with effects of topography and non-constant external force

In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L~1-stability of weak solutions to the atmospheric equations.     

Long-range forecasts of River Po discharges based on predictable solar activity and a fuzzy neural network model / Prévisions à long terme des débits du Fleuve Pô basées sur l’activité solaire prévisible et sur un modèle de réseau de neurones flou

Abstract

Abstract Is it possible to make seasonal and interannual forecasts of hydrological variables if one cannot predict next week’s rainfall? Contrary to common view, some scientists support the hypothesis that variations in mean global temperature and precipitation are controlled more by external forcing (solar variability and volcanic eruptions) than by increasing atmospheric concentration of greenhouse gases. Temperature and precipitation are connected with special phases of the 11-year sunspot cycle, which coincide with significant accumulation of energetic solar eruptions. Because of the possibility of identifying years with many solar eruptions, the attractive prospect emerges of the long-term hydrological forecasting based on cycles of solar activity. Starting from this assumption, an expert system was built based on a fuzzy neural network model for seasonal and interannual forecasting of the Po River discharge. It was found that indices of solar activity and of global circulation are sufficient to yield useful forecasts of hydrological variables.     

对流层强迫与平流层暴发性增温

采用平流层准地转－β通道近似下的波流相互作用模型，考虑大气行星波１和波２与流的相互作用，以平流层底部边界强迫波波１和波２的振幅作为参数，对该模型的分岔特性进行了研究．结果表明，系统具有稳态解支Ａ，Ｂ，Ｃ，在某些参数范围内，多种稳态解同时存在．解支Ａ对应于平流层冷冬状态，解支Ｃ对应于平流层增温状态．由于参数变化系统在稳态解Ａ和Ｃ之间发生灾变是冬季平流层暴发性增温的原因．文中给出了二维参数空间中的分岔集，它表明了对流层顶的波动对平流层暴发性增温的控制作用，能很好地解释观测事实．     

Evolution mechanism of the western Pacific subtropical high

Ever since Charney et al.[1] studied the multiple equilibrium states in atmosphere with highly truncated spectral method in 1979, many Chinese researchers, such as Li Maicun et al. (1983)[2], Liu Chongjian et al. (1983)[3], Miu Jinhai et al. (1985)[4] and…     

On the interaction between a radiatively damped planetary wave and the zonally averaged circulation in the middle atmosphere

The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small).A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes.An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed.     

Stochastic partial differential equations in groundwater hydrology

Many problems in hydraulics and hydrology are described by linear, time dependent partial differential equations, linearity being, of course, an assumption based on necessity.Solutions to such equations have been obtained in the past based purely on deterministic consideration. The derivation of such a solution requires that the initial conditions, the boundary conditions, and the parameters contained within the equations be stipulated in exact terms. It is obvious that the solution so derived is a function of these specified, values.There are at least four ways in which randomness enters the problem. i) the random initial value problem; ii) the random boundary value problem; iii) the random forcing problem when the non-homogeneous part becomes random and iv) the random parameter problem.Such randomness is inherent in the environment surrounding the system, the environment being endowed with a large number of degrees of freedom.This paper considers the problem of groundwater flow in a phreatic aquifer fed by rainfall. The goveming equations are linear second order partial differential equations. Explicit form solutions to this randomly forced equation have been derived in well defined regular boundaries. The paper also provides a derivation of low order moment equations. It contains a discussion on the parameter estimation problem for stochastic partial differential equations.     

Periodic forcing in composite aquifers

Observations of periodic components of measured heads have long been used to estimate aquifer diffusivities. The estimations are often made using well-known solutions of linear differential equations for the propagation of sinusoidal boundary fluctuations through homogeneous one-dimensional aquifers. Recent field data has indicated several instances where the homogeneous aquifer solutions give inconsistent estimates of aquifer diffusivity from measurements of tidal lag and attenuation. This paper presents new algebraic solutions for tidal propagation in spatially heterogeneous one-dimensional aquifers. By building on existing solutions for homogeneous aquifers, comprehensive solutions are presented for composite aquifers comprising of arbitrary (finite) numbers of contiguous homogeneous sub-aquifers and subject to sinusoidal linear boundary conditions. Both Cartesian and radial coordinate systems are considered. Properties of the solutions, including rapid phase shifting and attenuation effects, are discussed and their practical relevance noted. Consequent modal dispersive effects on tidal waveforms are also examined via tidal constituent analysis. It is demonstrated that, for multi-constituent tidal forcings, measured peak heights of head oscillations can seem to increase, and phase lags seem to decrease, with distance from the forcing boundary unless constituents are separated and considered in isolation.     

Numerical study of seasonal circulation and variability over the inner shelf of the northern South China Sea

This study examines seasonal circulation, hydrography, and associated spatial variability over the inner shelf of the northern South China Sea (NSCS) using a nested-grid coastal ocean circulation model. The model external forcing consists of tides, atmospheric forcing, and open boundary conditions based on the global ocean circulation and hydrography reanalysis produced by the Hybrid Coordinate Ocean model. Five numerical experiments are conducted with different combinations of external forcing functions to examine main physical processes affecting the seasonal circulation in the study region. Model results demonstrate that the monthly mean circulation in the study region features the Guangdong Coastal Current (GCC) over coastal waters and the South China Sea Warm Current (SCSWC) in the offshore deep waters. The GCC produced by the model flows nearly southwestward in winter months and northwestward in summer months, which agrees with previous studies. The SCSWC flows roughly northeastward and is well defined in summer months. In winter months, by comparison, the SCSWC is superseded by the southwestward strong wind-driven currents. Analysis of model results in five different experiments demonstrates that the monthly mean circulation over coastal and inner shelf waters of the NSCS can be approximated by barotropic currents forced by the southwestward monsoon winds in winter months. In summer months, by comparison, the monthly mean circulation in the study region is affected significantly by baroclinic dynamics associated with freshwater runoff from the Pearl River and advection of warm and saline waters carried by the SCSWC over the NSCS.     

Future wave climate over the west-European shelf seas

In this paper, we investigate changes in the wave climate of the west-European shelf seas under global warming scenarios. In particular, climate change wind fields corresponding to the present (control) time-slice 1961–2000 and the future (scenario) time-slice 2061–2100 are used to drive a wave generation model to produce equivalent control and scenario wave climate. Yearly and seasonal statistics of the scenario wave climates are compared individually to the corresponding control wave climate to identify relative changes of statistical significance between present and future extreme and prevailing wave heights. Using global, regional and linked global–regional wind forcing over a set of nested computational domains, this paper further demonstrates the sensitivity of the results to the resolution and coverage of the forcing. It suggests that the use of combined forcing from linked global and regional climate models of typical resolution and coverage is a good option for the investigation of relative wave changes in the region of interest of this study. Coarse resolution global forcing alone leads to very similar results over regions that are highly exposed to the Atlantic Ocean. In contrast, fine resolution regional forcing alone is shown to be insufficient for exploring wave climate changes over the western European waters because of its limited coverage. Results obtained with the combined global–regional wind forcing showed some consistency between scenarios. In general, it was shown that mean and extreme wave heights will increase in the future only in winter and only in the southwest of UK and west of France, north of about 44–45° N. Otherwise, wave heights are projected to decrease, especially in summer. Nevertheless, this decrease is dominated by local wind waves whilst swell is found to increase. Only in spring do both swell and local wind waves decrease in average height.