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17 recordsLinked to original sources

arXiv1995

North Atlantic thermohaline circulation predictability in a coupled ocean-atmosphere model

Predictability of the North Atlantic thermohaline circulation (THC) variability as simulated in the GFDL coupled ocean-atmosphere general circulation model is established for a set of ensemble experiments. The ensembles consist of identical oceanic initial conditions underneath a model atmosphere chosen randomly from the model climatology. This experimental design is based on the separation in time scales present in the model which motivates the assumption that the predictability deduced from these ensembles provides an upper limit to the model's THC predictability. The climatology is taken from a multi-century model integration whose THC variability has power concentrated at the 40-60 year time scale. A linear stochastic perspective is shown to be generally consistent with the ensemble statistics. The linear theory suggests a natural measure of ensemble predictability as the time at which the ensemble variance becomes a subjectively defined fraction (0.5 used here) of the climatological variance. It is furthermore of interest to distinguish predictability of the rapidly de-correlating portion of the model's THC from the longer time correlated portion. The rapidly de-correlating portion shows predictability for $\approx 1.5$ years. The slower portion shows predictability for $\approx 5-7$ years. The linear stochastic framework provides for the straightforward construction of an optimal forecast of the model's THC variability and an understanding of why the optimal forecast is useless beyond a particular limit.

ao-sci↗

arXiv1995

Interpretation of TOVS Water Vapor Radiances Using a Random Strong Line Model

This study illustrates the application of a random strong line (RSL) model of radiative transfer to the interpretation of satellite observations of the upwelling radiation in the 6.3 micron water vapor absorption band. The model, based upon an assemblage of randomly overlapped, strongly absorbing, pressure broadened lines, is compared to detailed radiative transfer calculations of the upper (6.7 micron) tropospheric water vapor radiance and demonstrated to be accurate to within ~ 1.2 K. Similar levels of accuracy are found when the model is compared to detailed calculations of the middle (7.3 micron) and lower (8.3 micron) tropospheric water vapor radiance, provided that the emission from the underlying surface is taken into account. Based upon these results, the RSL model is used to interpret TOVS-observed water vapor radiances in terms of the relative humidity averaged over deep layers of the upper, middle, and lower troposphere. We then present near-global maps of the geographic distribution and climatological variations of upper, middle and lower tropospheric humidity from TOVS for the period 1981-1991. These maps clearly depict the role of large-scale circulation in regulating the location and temporal variation of tropospheric water vapor.

ao-sci↗

arXiv1995

Mechanisms of Seasonal - ENSO interaction

The mechanisms of interaction between the seasonal cycle and ENSO are investigated using the Zebiak and Cane ENSO prediction model. The most dominant seasonal effect is found to be due to the wind divergence field, as determined by the seasonal motion of the ITCZ, through its effect on the atmospheric heating. The next order seasonal effects are due to the seasonality of the background SST and ocean upwelling velocity, and the corresponding mechanisms are analyzed. It is suggested that the seasonal forcing has a first order effect on ENSO's dynamics. Important aspects of the seasonal forcing may be included in idealized delayed oscillator ENSO models by making the model background seasonally shift from stable to unstable states.

ao-sci↗

arXiv1995

Hadley circulations and large scale motions of moist convection in the two dimensional numerical model

As a tool for understanding the meridional circulation of the atmosphere, a two-dimensional ( latitude -- height ) numerical model is used to clarify the relationship between the Hadley circulation and large-scale motions associated with moist convection. The model is based on the primitive equations including the moist process, and two kinds of coordinates are used: the spherical coordinate and the Cartesian coordinate with a uniform rotation. The surface temperature is externally fixed and the troposphere is cooled by the radiation; unstable stratification generates large-scale convective motions. Dependencies on the surface temperature difference from north to south Delta T_s are investigated. The numerical results show that a systematic multi-cell structure exists in every experiment. If the surface temperature is constant (Delta T_s = 0 ), convective motions are organized in the scale of the Rossby deformation radius and their precipitation patterns have a periodicity of the advective time tau_D. As Delta T_s becomes larger, the organized convective system tends to propagate toward warmer regions. The convective cells calculated in the Cartesian coordinate model is very similar to those of the mid-latitudes in the spherical coordinate model. In particular, the Hadley cell can be regarded as the limit of the convective cells in the equatorial latitudes.

ao-sci↗

arXiv1995

A Stochastic Diffusion Model of Climate Change

We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled atmosphere-ocean model. The predictions of the model are supported by station records and paleoclimatic proxy data of temperature variations.

ao-sci↗

arXiv1996

Kardar-Parisi-Zhang model for the fractal structure of cumulus cloud fields

We model the ascent of warm, moist air in the Earth's atmosphere by turbulent convection and expansion with the KPZ equation, familiar in the physics literature on surface growth. Clouds form in domains where the interface between the rising air and its surrounding air achieves an elevation higher than that necessary for condensation. The model predictions are consistent with the perimeter fractal dimension and the cumulative frequency-size distribution of cumulus cloud fields observed from space.

ao-sci↗

arXiv1996

Analysis and modeling of scale-invariance in plankton abundance

The power spectrum, $S$, of horizontal transects of plankton abundance are often observed to have a power-law dependence on wavenumber, $k$, with exponent close to -2: $S(k)\propto k^{-2}$ over a wide range of scales. I present power spectral analyses of aircraft lidar measurements of phytoplankton abundance from scales of 1 to 100 km. A power spectrum $S(k)\propto k^{-2}$ is obtained. As a model for this observation, I consider a stochastic growth equation where the rate of change of plankton abundance is determined by turbulent mixing, modeled as a diffusion process in two dimensions, and exponential growth with a stochastically variable net growth rate representing a fluctuating environment. The model predicts a lognormal distribution of abundance and a power spectrum of horizontal transects $S(k)\propto k^{-1.8}$, close to the observed spectrum. The model equation predicts that the power spectrum of variations in abundance in time at a point in space is $S(f)\propto f^{-1.5}$ (where $f$ is the frequency). Time series analysis of local variations of phytoplankton and zooplankton yield a power-law power spectrum with exponents -1.3 and -1.2, respectively from time scales of one hour to one year. These values are roughly consistent with the model prediction of -1.5. The distribution of abundances is nearly lognormal as predicted. The model may be more generally applicable than for the spatial distribution of plankton. I relate the model predictions to observations of spatial patchiness in vegetation.

ao-sci↗

arXiv1996

Entropic "sound" in the atmosphere

It is shown that small, local disturbances of entropy in the atmosphere may give rise to "sound" waves propagating with a velocity which depends on the amplitude ratio of the local relative variations of temperature and volume. This velocity is much smaller than the mean molecular velocity and the usual, adiabatic sound velocity.

ao-sci↗

arXiv1996

Sub-Suns and Low Reynolds Number Flow

The phenomenon called the ``sub-Sun'' is the specular reflection of sunlight by horizontally oriented plates of ice. Although well-known in meteorological optics, the hydrodynamics of the orientation is not quantitatively understood. I review the theory of torques on objects at low Reynolds numbers, define coefficients $C_o$, $C_p$, and $C_ψ$ which describe the orienting torques on discs, rods, and hexagonal prisms, and report here the results of experiments to measure $C_o$ and $C_p$.

ao-sci↗

arXiv1995

Estimating the Attractor Dimension of the Equatorial Weather System

The correlation dimension and limit capacity serve theoretically as lower and upper bounds, respectively, of the fractal dimension of attractors of dynamic systems. In this paper, we show that estimates of the correlation dimension grow rapidly with increasing noise level in the time-series, while estimates of the limit capacity remain relatively unaffected. It is therefore proposed that the limit capacity be used in studies of noisy data, despite its heavier computational requirements. An analysis of Singapore wind data with the limit capacity estimate revealed a surprisingly low dimension (~2.5). It is suggested that further studies be made with comprehensive equatorial weather data.

chao-dyn↗

arXiv1995

Decaying Turbulence and the Dynamics of Diffusing Vortices with Conservation Laws

In this letter, I solve a model for the dynamics of vortices in a decaying two-dimensional turbulent fluid. The model describes their effective diffusion, and the merging of pairs of vortices of same vorticity sign, when they get too close. The merging process is characterized by the conservation of energy and of the quantity $Nr^n$, where $r$ is the mean vortex radius, and $N$ their number. $n=4$ corresponds to a constant peak vorticity, and $n=2$ to a constant kurtosis. I found the scaling laws for various physical quantities ($r$, enstrophy, kurtosis...), and for instance, it is shown that $N\sim (t/\ln(t))^{-\frac{2n}{3n-4}}$ for $n>2$, and $N\sim t^{-2}$ for $n=2$, in good agreement with extensive numerical simulations. I also discuss some recent experiments in view of these results.

cond-mat↗

arXiv1996

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.

comp-gas↗

arXiv1996

Interdecadal variability and oceanic thermohaline adjustment

Changes in the strength of the thermohaline overturning circulation are associated, by geostrophy, with changes in the east-west pressure difference across an ocean basin. The tropical-polar density contrast and the east-west pressure difference are connected by an adjustment process. In flat-bottomed ocean models the adjustment is associated with viscous, baroclinic Kelvin wave propagation. Weak-high latitude stratification leads to the adjustment having an interdecadal timescale. We reexamine model interdecadal oscillations in the context of the adjustment process, for both constant flux and mixed surface boundary conditions. Under constant surface flux, interdecadal oscillations are associated with the passage of a viscous Kelvin wave around the model domain. Our results suggest the oscillations can be self-sustained by perturbations to the western boundary current arising from the southward boundary wave propagation. Mixed boundary condition oscillations are characterized by the eastward, cross-basin movement of salinity-dominated density anomalies, and the westward return of these anomalies along the northern boundary. We suggest the latter is associated with viscous Kelvin wave propagation. Under both types of boundary conditions, the strength of the thermohaline overturning and the tropical-polar density contrast vary out of phase. We show how the phase relationship is related to the boundary wave propagation. The importance of boundary regions indicates an urgent need to examine the robustness of interdecadal variability in models as the resolution is increased, and as the representation of the coastal, shelf/slope wave guide is improved. (Abriged abstract)

ao-sci↗

arXiv1996

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia-gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow-water equations. Unlike the shallow-water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

chao-dyn↗

arXiv1995

A linear thermohaline oscillator driven by stochastic atmospheric forcing

The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (THC) is described and compared to the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe, and Stouffer (1993). The box model is placed in a linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of this state reveals one damped oscillatory THC mode in addition to purely damped modes. The variability of the model under a moderate amount of stochastic forcing, meant to emulate the random variability of the atmosphere affecting the coupled model's interdecadal THC variability, is studied. A linear interpretation, in which the damped oscillatory mode is of primary importance, is sufficient for understanding the mechanism accounting for the stochastically forced variability. Direct comparison of the variability in the box model and coupled GCM reveals common qualitative aspects. Such a comparison supports, although does not verify, the hypothesis that the coupled model's THC variability can be interpreted as the result of atmospheric weather exciting a linear damped oscillatory THC mode.

ao-sci↗

arXiv1995

A Scaling Theory for Horizontally Homogeneous, Baroclinically Unstable Flow on a Beta-Plane

The scaling argument developed by Larichev and Held (1995) for eddy amplitudes and fluxes in a horizontally homogeneous, two-layer model on an f-plane is extended to a beta-plane. In terms of the non-dimensional number x = U/(beta*lambda^2), where lambda is the deformation radius and U is the mean thermal wind, the result for the RMS eddy velocity V, the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets k, and the magnitude of the eddy diffusivity for potential vorticity D, in the limit x>>1, are as follows: V/U ~ x ; k*lambda ~ 1/x ; D/(U*lambda) ~ x^2. Numerical simulations provide qualitative support for this scaling, but suggest that it underestimates the sensitivity of these eddy statistics to the value of x. A generalization that is applicable to continuous stratification is suggested which leads to the estimates: V ~ 1/(beta T^2); k ~ beta*T; D ~ 1/{[beta^2][T^3]} where T is a time-scale determined by the environment; in particular, it equals lambda/U in the two-layer model and N/(fS) in a continuous flow with uniform shear S and stratification N. This same scaling has also been suggested as relevant to a continuously stratified fluid in the opposite limit, x<<1 (Held, 1980). Therefore, we suggest that it may be of general relevance in planetary atmospheres and in the oceans.

ao-sci↗

arXiv1995

The stability of a zonally averaged thermohaline circulation model

A combination of analytical and numerical techniques are used to efficiently determine the qualitative and quantitative behaviour of a one-basin zonally averaged thermohaline circulation ocean model. In contrast to earlier studies which use time stepping to find the steady solutions, the steady state equations are first solved directly to obtain the multiple equilibria under identical mixed boundary conditions. This approach is based on the differentiability of the governing equations and especially the convection scheme. A linear stability analysis is then performed, in which the normal modes and corresponding eigenvalues are found for the various equilibrium states. Resonant periodic solutions superimposed on these states are predicted for various types of forcing. The results are used to gain insight into the solutions obtained by Mysak, Stocker and Huang in a previous numerical study in which the eddy diffusivities were varied in a randomly forced one-basin zonally averaged model. Resonant stable oscillations with century scale periods are predicted with structures that compare favorably with those found in the previous study. In cases with large horizontal diffusivities, the two-cell pattern is also stable, which parallels cases in the previous study where large vacillations were seen between the three stable steady states. Further, in cases with large horizontal {\it and} large vertical diffusivities, no one-cell pattern can be realised and the only asymptotic behaviour found is the two-cell pattern.

ao-sci↗