Minimum Forcing Research Articles

The dynamical response of the middle atmosphere to the tropospheric solar signal

To assess a possible solar modulation of the planetary waves, the 300 hPa geopotential height of the two major reanalysis data sets, NCEP/NCAR and ERA40, is studied for the difference between years of solar maximum and minimum activity for three solar cycles in the period 1963–1999. We find a significant positive difference over the North Pacific ocean for December through February which resembles that found in sea level pressures in earlier studies. Furthermore, there are statistically significant amplitude differences in the climatological state of the first two planetary waves extracted from the geopotential heights. We also perform a model study of the middle atmospheric response to the tropospheric solar signal. The 300 hPa geopotential height is used as the lower boundary in a middle atmosphere model which is run with a constant solar cycle minimum radiative forcing, so that only the lower boundary is forcing the middle atmosphere. The zonal wind and temperature at 300–0.01 hPa from the model experiment are studied in boreal winter for the same years that were studied in the geopotential height analysis. Differences of the means of the two data sets reproduce the structure and amplitude seen in observations and in reanalysis data. Whether this is a direct effect of the solar forcing of the troposphere or a feedback coupling of the solar forcing of the stratosphere is not presently clear, but the modulation of the tropospheric planetary waves seems to be important for the observed solar modulation of the stratosphere.

Deglaciating the snowball Earth: Sensitivity to surface albedo

The accepted values for both snow and ice albedo cover a large range, which is reflected in the values used in models studying the Neoproterozoic snowball Earth. The variation in these parameters can have a significant impact on modeling results and are often not explored within the modelling studies. Here we attempt to quantify the relative sensitivity of different surface albedos, using the University of Victoria's Earth System Climate Model, to deglaciating the snowball Earth. We investigate the sensitivity of ice, snow, and land albedo on the minimum CO2 greenhouse forcing required for deglaciating the Neoproterozoic snowball Earth. We find that the amount of CO2 forcing required for deglaciation can vary by nearly an order of magnitude within accepted albedo ranges.

Locomotor-respiratory coordination dynamics and metabolic cost during walking at different stride frequencies

Human locomotion has been modeled as a force-driven harmonic oscillator (FDHO). The minimum forcing function in locomotion has been shown to occur at the resonant frequency of the FDHO and results in the suggestion that oxygen cost may be considered an optimality criterion for locomotion. The purposes of this study were twofold: first, to determine the relationship between stride frequency and shock attenuation, and second, to determine whether shock attenuation may also be considered an optimality criterion. Ten healthy young adult males served as subjects in this study. Each subject's preferred running speed and preferred stride frequency (PSF) were determined. In addition to the PSF, they ran at stride frequencies corresponding to −20%, −10%, +10%, and +20% of the PSF at the preferred running speed. Metabolic data as well as leg and head acceleration data were collected during a steady state run at each of the stride frequency conditions. The metabolic data produced a U-shaped curve hypothesized by the FDHO model. Spectral analysis on the leg and head acceleration data were used to develop transfer functions for each of the stride frequency conditions. Analysis of the transfer function indicated that there was a gain at the low frequencies and an attenuation at the higher frequencies. The transfer function at the higher frequencies indicated that the impact shock signal was attenuated as it passed through the body. However, the transfer functions appeared to vary according to the amount of shock input to the system with the result that the head accelerations remained constant. It would appear that impact (high frequency) shock attenuation increases with stride frequency and thus does not fit the FDHO model as an optimization criterion. At all stride frequencies, regardless of the impact shock, head accelerations were maintained at a constant level.

Seasonal Variation of Aerosol Direct Radiative Forcing and Optical Properties Estimated from Ground-Based Solar Radiation Measurements

The surface direct radiative forcing and optical properties of aerosols have been analyzed from a groundbased solar radiation measurement, which was made under clear-sky conditions in Tsukuba, Japan, over two years from April 1997 to March 1999. The global and diffuse irradiances in the total and near-infrared (NIR) solar spectral regions were simultaneously measured by using two sets of the total-band and NIR-band pyranometers, respectively. The visible (VIS)-band irradiances were estimated by taking differences between the totalband and NIR-band irradiances. Spectral aerosol optical thicknesses (AOTs) in the air column were also measured, using a sun photometer. By combining the spectral AOTs and the surface diffuse irradiances, a retrieval algorithm for simultaneously estimating the effective aerosol size distribution and imaginary index of refraction ( mi) was developed. Seasonal variations of the broadband surface radiative forcings and retrieved optical properties of the columnar aerosols have been studied. A close correlation was found among these parameters with similar features of seasonal variations. In winter the columnar aerosols exhibit the minimum surface radiative forcing and a minimum AOT, but the maximum mi value of 0.04. The opposite is true in summer, when the minimum mi value of 0.02 was estimated. The surface radiative forcing in the VIS band was estimated to be almost 4 times larger than in the NIR band. The total-band aerosol forcing efficiency is defined as the change in the surface radiative forcing in the total band due to a unit increase of AOT at 500 nm. This has its largest magnitude of 2 219 Wm 22 in winter and its smallest magnitude of 2 150 Wm 22 in summer. The results suggest that the correlated seasonal variations between the aerosol radiative forcing and the optical properties may result from seasonal changes in the dominant aerosol components.

The minimum forcing number for the torus and hypercube

Let G be a graph with a perfect matching M. Define the forcing number of M in G to be the smallest size of a subset S⊂ M that is in no other perfect matching. In this paper, we present a property of bipartite graphs G that acts as a lower bound on the forcing number of perfect matchings in G. We then apply this to the torus and the hypercube, proving that the minimum forcing number of a perfect matching on a 2 m×2 n torus with m⩾ n is 2 n, and that the minimum forcing number on an n-dimensional hypercube is 2 n /4 if n is even.

Geological evaluation of multiple general circulation model simulations of Late Jurassic palaeoclimate

General circulation models (GCMs) are currently used to predict future global change. However, the robustness of GCMs should be evaluated by their ability to simulate past climate regimes. Their success in ‘retrodiction’ can then be assessed by reference to the geological record. Geological evidence provides a database that can be used in the estimation of sea surface temperatures, orography and other proxy data useful in palaeoclimatic studies. These data can then be used to refine the prescribed boundary conditions for running GCMs themselves. Results from a series of modelling experiments, run with Late Jurassic (Kimmeridgian) boundary conditions, and using the UK University Global Atmospheric Modelling Programme (UGAMP) GCM and the UK Meteorological Office GCM are presented. Simulations from these two quite independently generated models, although subtly different, confirm a generally warmer Jurassic Earth with arid zones over the Tethys and SW USA, parts of Gondwana dominated by ‘monsoonal’ systems and convective rainfall generally higher over the oceans than at present. Circum-polar wetlands are also indicated. These results generally conform well to the distributions of known facies in these regions. Modelled cloudiness is also higher in the Jurassic, and although unconfirmed geologically, such conditions would have contributed to greenhouse conditions at high latitudes and could have influenced both terrestrial biomes and marine ecosystems. Using one of the GCMs (UGAMP) we have also investigated the role of orbital parameters for high latitude climate. At times of ‘minimum seasonal forcing’ (comparable with an orbital geometry affecting the Earth at 115 ka BP) parts of Antarctica could have sustained a modest ice sheet over areas exceeding 1 km elevation, but such modelled sheets would have been ephemeral features and very dynamic in character.

Shock attenuation and stride frequency during running

Human locomotion has been modeled as a force-driven harmonic oscillator (FDHO). The minimum forcing function in locomotion has been shown to occur at the resonant frequency of the FDHO and results in the suggestion that oxygen cost may be considered an optimality criterion for locomotion. The purposes of this study were twofold: first, to determine the relationship between stride frequency and shock attenuation, and second, to determine whether shock attenuation may also be considered an optimality criterion. Ten healthy young adult males served as subjects in this study. Each subject's preferred running speed and preferred stride frequency (PSF) were determined. In addition to the PSF, they ran at stride frequencies corresponding to −20%, −10%, +10%, and +20% of the PSF at the preferred running speed. Metabolic data as well as leg and head acceleration data were collected during a steady state run at each of the stride frequency conditions. The metabolic data produced a U-shaped curve hypothesized by the FDHO model. Spectral analysis on the leg and head acceleration data were used to develop transfer functions for each of the stride frequency conditions. Analysis of the transfer function indicated that there was a gain at the low frequencies and an attenuation at the higher frequencies. The transfer function at the higher frequencies indicated that the impact shock signal was attenuated as it passed through the body. However, the transfer functions appeared to vary according to the amount of shock input to the system with the result that the head accelerations remained constant. It would appear that impact (high frequency) shock attenuation increases with stride frequency and thus does not fit the FDHO model as an optimization criterion. At all stride frequencies, regardless of the impact shock, head accelerations were maintained at a constant level.

Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank

Experiments are described on surface gravity-capillary waves in a 70 cm × 2.8 cm rectangular tank undergoing small vertical oscillations. The large aspect ratio of the tank permits study of several neighbouring two-dimensional wave modes; their onset, hysteresis and instability. Two water depths, close to one and two centimetres, are investigated in detail. Thresholds are determined for wave onset from a flat surface and the hysteretic return to a flat surface from finite-amplitude waves. Also, conditions at which a pure standing wave becomes unstable to other modes are established. Our finding of hysteresis below the minimum forcing for linear wave-onset suggests that nonlinear forcing and nonlinear damping are both significant, as recently suggested by Miles (J. Fluid Mechanics 248 (1993) 671.) A theoretical model, incorporating these effects, is analysed and the corresponding hysteresis boundaries established. These are broadly consistent with our experimental results.

Modelling Late Jurassic Milankovitch climate variations

Abstract Although largely circumstantial in character, evidence for orbitally-forced (Milankovitch) climate changes in Jurassic microrhythmic successions, such as those of the Lias and Kimmeridgian, is becoming more persuasive. We present here the results of experiments, using a general circulation model, testing ways in which orbitally-induced variations in solar energy might be translated into a Jurassic climate response. In particular, we address the problem of the 100 ka (eccentricity-forced) cycle. This is generally considered to have only a small direct effect on solar input. It would be expected to have little impact on an ice-free Earth (commonly assumed for the Jurassic). Nonetheless, this weak signal is claimed to have been recognized in many Jurassic successions. Our results simulate, for the Late Jurassic, the possible effects at the ‘minimum’ and ‘maximum’ extremes of seasonal forcing (i.e. comparable with those affecting the Earth at 115 and 9 ka bp , respectively). Model predictions are critically evaluated against the geological database. At times of ‘minimum seasonal forcing’ there is a significant expansion in the area of the Northern hemisphere monsoon. In the tropics, changes in precipitation predominate over changes in temperature, whereas at high southern latitudes there are very large seasonal variations in temperature, and heavy winter snows. During these times the model is close to predicting a modest, but significant, Jurassic ice-cap in the Antarctic. Ice build-up is particular larly likely over uplands. Such an ice-cap disappears at times of ‘maximum seasonal forcing’. Waxing and waning of ice may thus provide the elusive mechanism for metre-scale sea-level changes. It is argued that apparently similar microrhythms (e.g. limestone-shale) might be the sedimentary response to different climatic signals in different climate zones, cause and effect being exactly the opposite in some circumstances.

Well-behaved dynamics in a parametrically damped pendulum.

Well-behaved dynamical properties have been found in a parametrically damped pendulum. For various dampings, all minimum forcing amplitudes E for chaos to occur are at the forcing frequency \ensuremath{\Omega}=1.66, and all minimum E for a stationary solution to be unstable are identical (E=2) and at \ensuremath{\Omega}=2 in the \ensuremath{\Omega}-E state space. Between these two frequencies, the variation to chaos along stability boundaries (where the stationary solution becomes unstable) is solely \ensuremath{\Omega} dependent and insensitive to dampings. These two frequencies separate parameter regions with distinct dynamical behaviors. For \ensuremath{\Omega}1.66, the route to chaos is due to an inverse boundary crisis while for \ensuremath{\Omega}>1.66, it is associated with period doubling. For \ensuremath{\Omega}2 the transition from stationary solution to periodic solution is a jump, while for \ensuremath{\Omega}>2 it is a Hopf bifurcation.