Modeling the QBO-Improvements resulting from higher-model vertical resolution

Using the NASA Goddard Institute for Space Studies (GISS) climate model, it is shown that with proper choice of the gravity wave momentum flux entering the stratosphere and relatively fine vertical layering of at least 500 m in the upper troposphere-lower stratosphere (UTLS), a realistic stratospheric quasi-biennial oscillation (QBO) is modeled with the proper period, amplitude, and structure down to tropopause levels. It is furthermore shown that the specified gravity wave momentum flux controls the QBO period whereas the width of the gravity wave momentum flux phase speed spectrum controls the QBO amplitude. Fine vertical layering is required for the proper downward extension to tropopause levels as this permits wave-mean flow interactions in the UTLS region to be resolved in the model. When vertical resolution is increased from 1000 to 500 m, the modeled QBO modulation of the tropical tropopause temperatures increasingly approach that from observations, and the "tape recorder" of stratospheric water vapor also approaches the observed. The transport characteristics of our GISS models are assessed using age-of-air and N₂O diagnostics, and it is shown that some of the deficiencies in model transport that have been noted in previous GISS models are greatly improved for all of our tested model vertical resolutions. More realistic tropical-extratropical transport isolation, commonly referred to as the "tropical pipe," results from the finer vertical model layering required to generate a realistic QBO.

Amplification of surface temperature trends and variability in the tropical atmosphere

The month-to-month variability of tropical temperatures is larger in the troposphere than at Earth's surface. This amplification behavior is similar in a range of observations and climate model simulations and is consistent with basic theory. On multidecadal time scales, tropospheric amplification of surface warming is a robust feature of model simulations, but it occurs in only one observational data set. Other observations show weak, or even negative, amplification. These results suggest either that different physical mechanisms control amplification processes on monthly and decadal time scales, and models fail to capture such behavior; or (more plausibly) that residual errors in several observational data sets used here affect their representation of long-term trends.

Global warming in the twenty-first century: an alternative scenario

A common view is that the current global warming rate will continue or accelerate. But we argue that rapid warming in recent decades has been driven mainly by non-CO(2) greenhouse gases (GHGs), such as chlorofluorocarbons, CH(4), and N(2)O, not by the products of fossil fuel burning, CO(2) and aerosols, the positive and negative climate forcings of which are partially offsetting. The growth rate of non-CO(2) GHGs has declined in the past decade. If sources of CH(4) and O(3) precursors were reduced in the future, the change in climate forcing by non-CO(2) GHGs in the next 50 years could be near zero. Combined with a reduction of black carbon emissions and plausible success in slowing CO(2) emissions, this reduction of non-CO(2) GHGs could lead to a decline in the rate of global warming, reducing the danger of dramatic climate change. Such a focus on air pollution has practical benefits that unite the interests of developed and developing countries. However, assessment of ongoing and future climate change requires composition-specific long-term global monitoring of aerosol properties.

Climate forcings in the industrial era

The forcings that drive long-term climate change are not known with an accuracy sufficient to define future climate change. Anthropogenic greenhouse gases (GHGs), which are well measured, cause a strong positive (warming) forcing. But other, poorly measured, anthropogenic forcings, especially changes of atmospheric aerosols, clouds, and land-use patterns, cause a negative forcing that tends to offset greenhouse warming. One consequence of this partial balance is that the natural forcing due to solar irradiance changes may play a larger role in long-term climate change than inferred from comparison with GHGs alone. Current trends in GHG climate forcings are smaller than in popular "business as usual" or 1% per year CO2 growth scenarios. The summary implication is a paradigm change for long-term climate projections: uncertainties in climate forcings have supplanted global climate sensitivity as the predominant issue.

A common-sense climate index: is climate changing noticeably?

We propose an index of climate change based on practical climate indicators such as heating degree days and the frequency of intense precipitation. We find that in most regions the index is positive, the sense predicted to accompany global warming. In a few regions, especially in Asia and western North America, the index indicates that climate change should be apparent already, but in most places climate trends are too small to stand out above year-to-year variability. The climate index is strongly correlated with global surface temperature, which has increased as rapidly as projected by climate models in the 1980s. We argue that the global area with obvious climate change will increase notably in the next few years. But we show that the growth rate of greenhouse gas climate forcing has declined in recent years, and thus there is an opportunity to keep climate change in the 21st century less than "business-as-usual" scenarios.

TRANSMISSION OF LIGHT BY WATER DROPS 1 TO 5 μ IN DIAMETER

The size of the drops formed when water vapour condenses is related to the work performed against the surface tension. For the determination of the size by optical methods, Mie's solution of the electromagnetic equations for the propagation of light of wave-length λ in a medium containing small spherical drops of radius a indicates that as the ratio α = 2πa/λ increases from 0 to 20, the intensity of the light received in the prolongation of the incident beam passes alternately through maximum and minimum values. At distances from the drops greatly exceeding λ, the first maximum lies close to α = 2π, the second is near α = 8.6, and the subsequent peaks are less distinct and tend to repeat themselves at α = (m + 3/4)π. As a result of these fluctuations the light seen through a cloud of particles with diameters greater than about 1 μ is coloured. The theory accounts for the cycles in the changes of colour observed when the diameter increases, and enables a determination of the radius of growing drops. With increasing radius, the influence of the index of refraction m decreases; for m = ∞ the positions and values of the peaks differ only slightly from those obtained with water.

SCATTERING OF LIGHT BY SMALL DROPS OF WATER

When very small drops of water increase in size until their diameter is one-fourth of the wave-length of the incident light (2a/λ = 1/4), they scatter the light essentially according to Rayleigh's law for non-conducting particles. But when the diameter increases from λ/4 to λ/2, the intensity of light scattered along directions that point toward the source decreases almost to zero, the change being most marked between 2a/λ = 1/4 and 2a/λ = 3/8. The sharp increase in the proportion of scattered light with an increase in size, according to the sixth power of the radius, continues however in the directions along which the main part of the scattered light is radiated by the particle. As the scattering begins to deviate from that given by Rayleigh's law, colours other than blue appear with great strength; the dispersion of the colours increases with increasing size of the particles until mainly red light remains.

ABSORPTION OF LIGHT BY SMALL DROPS OF WATER

When the extinction coefficient k in the attenuation formula I/I0 = (exp) — kz for a beam of radiations of initial intensity I0, and intensity I after travelling a distance z in water, changes from about 10−4, the value measured in the visible region, to 103, the value reached in some infrared absorption bands for water in bulk, the coefficient of extinction for water in very small drops, calculated according to Mie's theory, increases as long as the wavelength used is larger than the radius a of the particle. With larger drops, that is, when the wave-lengths are shorter than the radius, the coefficient for the extinction by water particles with strong absorption is smaller than that for perfectly transparent particles. However, the change does not exceed about 10% even where the absorption is strongest, and it is negligible when wavelengths smaller than one micron are considered. The main features of the coefficient of extinction per unit area of the drop remain unchanged by absorption; first there is a rapid increase with decreasing wave-lengths for particles of a given diameter until the ratio a/λ = 1/n (the reciprocal of the index of refraction) is reached, then follows a more gradual approach to a maximum, slightly less than 4πa2 as 2a/λ increases to unity, and finally, when λ is quite small, a decrease towards a constant value after a small number of fluctuations that reach their greatest amplitudes near the integer multiples of 2a/λ.

ABSORPTION OF LIGHT AND HEAT RADIATION BY SMALL SPHERICAL PARTICLES: II. SCATTERING OF LIGHT BY SMALL CARBON SPHERES

Spheres of carbon for which 2a/λ, the ratio between the diameter of the particle and the incident wave-length, is less than about [Formula: see text] scatter the light uniformly in all directions. The intensity of the scattered radiation for any angle is proportional to the square of the volume of the particle and inversely proportional to the fourth power of the wave-length. As the ratio 2a/λ increases from [Formula: see text] to [Formula: see text] and greater values, the diffused light collects more and more into a main beam that appears as a continuation of the incident ray and that decreases in width as 2a/λ increases. Blue light prevails in the scattered radiation. When the size of the particles is unknown, the intensity, distribution, and polarization of the scattered light give an at least approximate value for the radius.

ABSORPTION OF LIGHT AND HEAT RADIATION BY SMALL SPHERICAL PARTICLES: I. ABSORPTION OF LIGHT BY CARBON PARTICLES

From Mie's classical theory of the action of small spherical particles on plane waves of light, the expression giving the loss of light due to absorption and scattering is reduced to the formula involving only Bessel functions of orders given by half integral values. The result is used for calculating the absorption by small carbon particles whose diameter is comparable with the wave-length of the incident light, particles that can be measured only by interference methods. When the diameter is less than 0.2 μ the coefficient of absorption decreases toward the red end of the spectrum. The reverse is true for 0.3 and 0.4 μ particles.

DENSITY DIFFERENCES AT THE CRITICAL POINT ACCORDING TO R. PLANK'S EQUATION OF STATE

If R. Plank's equation of state is assumed to apply, the densities measured at two levels, 1 cm. apart, in a column of gas kept at the critical temperature, may differ by more than 5%. A large correction is therefore required for densities determined at the critical point unless the entire contents of the tube is vigorously stirred. Van der Waal's equation shows that the difference in level corresponding to a relative difference in density, (ρ – ρc)/ρc, is proportional to the third power of the relative difference; according to Wohl's equation it is proportional to the fourth, and according to Plank, to the fifth, power of the relative difference in density.

THE SOUND FIELD OF MEMBRANES AND DIAPHRAGMS: II. THE POWER EMITTED BY CIRCULAR MEMBRANES

Accurate formulas are presented showing the power radiated by a stretched circular membrane vibrating with small amplitudes and an arbitrary number of nodal circles or diameters. When the nodes are circular, the sound emitted is expressed as a sum of the products of simple functions of ka, J0(2ka), J1(2ka) by the definite integral of y2s/(κ2a2/k2a2 − 1 + y2)2 taken between the limits zero and unity. For values of ka = 2πa/λ between zero and two, where the radius a is taken as 10 cm., the membrane vibrating in its fundamental mode emits between three and four times as much power as the piston having the same maximum velocity at its centre. The first and second overtones have about the same strength as the corresponding fundamental frequencies, so the power radiated increases less rapidly with frequency than when nodes are absent.

THE BAROMETRIC FORMULA FOR REAL GASES AND ITS APPLICATION NEAR THE CRITICAL POINT

According to the theory of the continuity of liquid and gaseous states, as expressed for instance in van der Waals' equation, pronounced density differences may exist in a short column of fluid maintained, throughout its length, at the critical temperature. The point in the tube at which the density of the contents has decreased a given percentage from the critical value is the higher the larger the ratio of the critical temperature to molecular weight. For substances like neon the variations are so large that a measurable separation of isotopes may be expected at or near the critical point; for other substances the computed results are at least of the magnitude found by experiment. Also, according to the theory, in order to obtain, at or near the critical point, a column of gas of uniform density a temperature gradient must be allowed to exist along the column.

PROPAGATION OF ULTRASOUND IN SOLID CYLINDERS (TRANSVERSE WAVES)

The expression giving the phase velocity c with which flexural waves pass through long solid rods is deduced for frequencies varying between zero and over 1,000,000 cycles per sec. and rods of any diameter. As the frequency increases, the velocity c increases gradually from very low values toward c2 = mE/2s(m+1), reached when the wave-length is much smaller than the diameter of the rod. Published experimental results for transverse waves are in good agreement with the theory given. In general at least four effects enter into the propagation of ultrasound through solid cylinders: first, longitudinal waves, for which the phase velocity decreases toward c as the frequency increases; second, transverse waves, for which the phase velocity increases toward c as the frequency increases; third, pure radial waves at certain frequencies; fourth, resonance effects between the different types of waves, which, on account of the mechanical coupling existing between them, change the natural period of vibration of the rod without affecting the velocity.

ON THE SOUND FIELD IN THE NEIGHBORHOOD OF AN OSCILLATING PLANE DISK

With the aid of recent theories (H. Stenzel, N. W. McLachlan, H. Backhaus) the velocity potential and pressure distribution at points in the field of vibrating solid disks of 1 to 20 cm. diameter are calculated for a number of frequencies of practical importance. The graphs drawn from these values apply also to very high frequencies, but smaller disks (1 to 20 mm.). They illustrate the gradual transition from spherical distribution to directed transmission.

ON THE PROPAGATION OF LONGITUDINAL WAVES IN CYLINDRICAL RODS

The solution of the velocity equation obtained by Pochhammer on the basis of the mathematical theory of elasticity is determined for the propagation of longitudinal waves of any frequency in a long solid circular cylinder of any diameter. For a given frequency a large number of solutions may be obtained, but when the condition is imposed that for low frequencies the velocity must gradually assume the value found by experiment, a single value is obtained for each frequency. The velocity decreases with increasing frequency, so that, for a cylinder of finite length, the resonance frequencies come closer and closer together. It is also necessary to take into account, however, that in a solid rod longitudinal waves are accompanied by radial vibrations of the particles, and that a cylindrical rod has, regardless of its length, a series of natural frequencies for radial waves, so that for wave-lengths comparable with the diameter of the tube a coupled system of oscillations is set up. The resonant frequencies of such a system depend on the degree of coupling.