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Within the progressive improvement in wave modeling we focus on the attenuation of swell waves by rain. Till now ignored, the process is shown to be relevant, especially for the correct estimate of swell. Following the practical impossibility of devoted field experiments, we exploit the global model results over a period of more than four years to extract the tiny signal associated to the attenuation by rain. A direct comparison of the ratio model by altimeter significant wave heights versus the encountered rain amount hints to a marked related dependence. A proper quantification of the related physical effect requires a multiple step procedure that we describe in detail. We check the reliability of the results, and we provide the related source function ready for implementation in operational wave models.

A Wave Boundary Layer Model (WBLM) is implemented in the third-generation ocean wave model SWAN to improve the wind-input source function under idealized, fetch-limited condition. Accordingly, the white capping dissipation parameters are re-calibrated to fit the new wind-input source function to parametric growth curves. The performance of the new pair of wind-input and dissipation source functions is validated by numerical simulations of fetch-limited evolution of wind-driven waves. As a result, fetch-limited growth curves of significant wave height and peak frequency show close agreement with benchmark studies at all wind speeds (5 ∼ 60 ms−1) and fetches (1 ∼ 3000 km). The WBLM wind-input source function explicitly calculates the drag coefficient based on the momentum and kinetic energy conservation. The modeled drag coefficient using WBLM wind-input source function is in rather good agreement with field measurements. Thus, the new pair of wind-input and dissipation source functions not only improve the wave simulation but also have the potential of improving air-sea coupling systems by providing reliable momentum flux estimation at the air-sea interface. This article is protected by copyright. All rights reserved.

Analytical upscaled models that can describe the depletion of dense nonaqueous phase liquids (DNAPLs) and the associated mass discharge are a practical alternative to computationally demanding and data-intensive multiphase numerical simulators. A major shortcoming of most existing upscaled models is that they cannot reproduce the nonmonotonic, multistage effluent concentrations often observed in experiments and numerical simulations. Upscaled models that can produce multistage concentrations either require calibration, which increases the cost of applying them in the field, or use dual-domain conceptual models that may not apply for spatially complex source zones. In this study, a new upscaled model is presented that can describe the nonmonotonic, multistage average concentrations emanating from complex DNAPL source zones. This is achieved by explicitly considering the temporal evolution of three source zone parameters, namely source zone projected area, the average of local-scale DNAPL saturations, and the average of local-scale aqueous relative permeability, without using empirical parameters. The model is evaluated for two real and twelve hypothetical centimeter-scale complex source zones. The proposed model captures the temporal variations in concentrations better than an empirical model and a dual-domain ganglia-to-pool ratio model. The results provide evidence that effluent concentrations downgradient of DNAPL source zones are controlled by the evolution of the aforementioned macroscopic parameters. This knowledge can be useful for the interpretation of field observations of effluent concentrations downstream of DNAPL source zones, and for the development of predictive upscaled models. Advances in DNAPL characterization techniques are needed to quantify these macroscopic parameters that can be used to guide DNAPL remediation efforts.

[1] Initial efforts toward developing a combined organic-inorganic sea spray source function parameterization for large-scale models made use of chlorophyll-a (Chl-a) and wind speed as input parameters to combine oceanic biology and atmospheric dynamics. These studies reported a modest correlation coefficient (0.55) between chlorophyll-a and organic matter (OM) enrichment in sea spray, suggesting that chlorophyll-a is only partially suitable for predicting organic enrichment. A reconstructed chlorophyll-a field of the North Atlantic Ocean from GlobColour reveals an improved correlation of 0.72 between the fractional mass contribution of organics in sea spray and chlorophyll-a concentration. A similar analysis, using colored dissolved and detrital organic material absorption and particulate organic carbon concentration, revealed slightly lower correlation coefficients (0.65 and 0.68). These results indicate that to date, chlorophyll-a is the best biological surrogate for predicting sea spray organic enrichment. In fact, considering the minimal difference between the correlation coefficients obtained with the three ocean color products, there is no reason to substitute chlorophyll-a, which is the most accurate parameter obtained from ocean color data, with other biological surrogates being generally affected by larger and less known errors. The observed time lag between chlorophyll-a concentration and organic matter enrichment in aerosol suggests that biological processes in oceanic surface waters and their timescales should be considered when modeling the production of primary marine organic aerosol.

[1] In this study we report the development of a time dependency of global dust source and its impact on dust simulation in the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model. We determine the surface bareness using the 8 km normalized difference vegetation index (NDVI) observed from the advanced very high resolution radiometer satellite. The results are used to analyze the temporal variations of surface bareness in 22 global dust source regions. One half of these regions can be considered permanent dust source regions where NDVI is always less than 0.15, while the other half shows substantial seasonality of NDVI. This NDVI-based surface bareness map is then used, along with the soil and topographic characteristics, to construct a dynamic dust source function for simulating dust emissions with the GOCART model. We divide the 22 dust source regions into three groups of (I) permanent desert, (II) seasonally changing bareness that regulates dust emissions, and (III) seasonally changing bareness that has little effect on dust emission. Compared with the GOCART results with the previously employed static dust source function, the simulation with the new dynamic source function shows significant improvements in category II regions. Even though the global improvement of the aerosol optical depth (AOD) is rather small when compared with satellite and ground-based remote sensing observations, we found a clear and significant effect of the new dust source on seasonal variation of dust emission and dust optical depth near the source regions. Globally, we have found that the permanent bare land contributes to 88% of the total dust emission, whereas the grassland and cultivated crops land contribute to about 12%. Our results suggest the potential of using NDVI over a vegetated area to link the dust emission with land cover and land use change for air quality and climate change studies.

A new combined differential-integral approach (CDI) has been developed, which is more accurate than commonly used pseudospherical models but not so complicated and computer time-consuming as a fully spherical model. The radiative transfer equation is solved in its integral form. The multiple-scattering source function is obtained by solving the integrodifferential radiative transfer equation in a pseudospherical atmosphere. Relative differences between the new model and the pseudospherical model for a variety of solar zenith angles, viewing angles, and azimuth angles for a set of wavelengths are presented. Furthermore, the GDI model is compared with a Gauss-Seidel spherical model (GSS) and with MODTRAN. The difference between GDI and GSS is found to be less than 2% and between GDI and MODTRAN up to 12%.

This paper presents a new radiative transfer model based on the correlated-k technique that is particularly suitable for applications associated with broadband infrared satellite remote sounding of the atmosphere. We describe new developments to the approach which improve the accuracy of correlated-k distribution radiative transfer calculations. These include methods to model an instrument response function, spectral line overlap for multiple gases, and the spectral variation of solar and thermal source functions. We also describe an approach to improving vertical spectral correlation along ray paths through a nonhomogeneous atmosphere. For a radiative transfer model to be efficient as the forward model of a retrieval scheme, the calculation of analytical Jacobians is particularly important. This is implemented in the model using a variation on the correlated-k approach. The application of the new model, RADCKD, is demonstrated with example calculations for the EOS Terra satellite Measurements of Pollution in the Troposphere (MOPITT) instrument.

In this study we present a new formulation for the nonlinear wave-wave interaction source function in finite water depth. The formulation, denoted the reduced integration approximation (RIA), is shown to compare well with published formulations, both for shallow water wave-wave interactions [Hertench and Hasselmann, 1980; Polnikov, 1997; Hashimoto et al., 1998; A. Masuda and K. Komatsu, manuscript in preparation, 1998] and also for the asymptotic deep water limit: (1) the Hamiltonian formulation proposed by Lin and Perrie [1997], by (2) Hasselmann and Hasselmann [1981], and (3) the line integral transformation of Webb [1978] and Resio and Ferne [1991]. Of these deep water formulations, that of Lin-Perrie generalizing the Hamiltonian representation of Zakharov [1968] to finite depth water, is notable for its simplicity, efficiency and its ability to apply to very shallow water (kh ≈ 0.3), and highly nonlinear (e≤0.3) interactions. RIA is based on an analysis of the main resonance domain, which reduces the six-dimensional integration to a quasi-line integral to minimize computational time. In terms of computational time, RIA is a thousand times faster than the EXACT-NL version formulated by Hasselmann and Hasselmann [1981], with similar accuracy. Thus RIA can be considered a candidate for operational forecasting in finite depth water, in the sense that the discrete interaction approximation was presented as a candidate for operational deep water wave forecasting by Hasselmann et al. [1988].

An analytical solution for the sound field in a resonant magma conduit with depth-dependent magma properties provides a versatile interpretative tool for the analysis of seismoacoustic signals generated by fluid processes in active volcanoes. Expressions are given for the acoustic field in the atmosphere and the seismic field in the ground radiated through the magma conduit vent and walls, respectively. A new source model allows the resonance in the conduit to be excited by the vertical fluid velocity at the bottom of the conduit. This source model represents acoustic excitation induced by low-frequency fluid oscillations or large volume fluctuations originating at depth. The magma conduit is modeled as a three-section duct, with each section having a different density, sound speed, viscosity, and dimension. The modal structure of the coupled resonant system is retained as the sound field in the conduit propagates into the surrounding bedrock and the overlying atmosphere. The source-time function permits estimates of the total mass injected or removed from the magmatic system, and the source spectrum acts as a band-pass filter on the resonant modes of the conduit. Theoretical or empirical source functions can be used to drive the seismoacoustic wave field, and the amplitude of the source velocity may be constrained by the ballistics of pyroclasts and the height of ash plumes. The acoustic properties of the melt may be predicted from the temperature, composition, and flow conditions of the magma as a function of depth. Comparisons of synthetic waveforms and spectra with those of seismic and acoustic signals recorded on active volcanoes permit estimates of the conduit geometry, density, sound speed, and attenuation properties of the melt, and characterize the temporal and spectral features of the source function. The ability to extract this information accurately and efficiently from seismic and acoustic data streams may permit near real time modeling of fluid-driven processes in active volcanoes.

In this paper we show that given prior information in terms of a lower and upper bound, a prior bias, and constraints in terms of measured data, minimum relative entropy (MRE) yields exact expressions for the posterior probability density function (pdf) and the expected value of the linear inverse problem. In addition, we are able to produce any desired confidence intervals. In numerical simulations, we use the MRE approach to recover the release and evolution histories of plume in a one-dimensional, constant known velocity and dispersivity system. For noise-free data, we find that the reconstructed plume evolution history is indistinguishable from the true history. An exact match to the observed data is evident. Two methods are chosen for dissociating signal from a noisy data set. The first uses a modification of MRE for uncertain data. The second method uses “presmoothing” by fast Fourier transforms and Butterworth filters to attempt to remove noise from the signal before the “noise-free” variant of MRE inversion is used. Both methods appear to work very well in recovering the true signal, and qualitatively appear superior to that of Skaggs and Kabala [1994]. We also solve for a degenerate case with a very high standard deviation in the noise. The recovered model indicates that the MRE inverse method did manage to recover the salient features of the source history. Once the plume source history has been developed, future behavior of a plume can then be cast in a probabilistic framework. For an example simulation, the MRE approach not only was able to resolve the source function from noisy data but also was able to correctly predict future behavior.

[1] Direct eddy covariance measurements of size-segregated sea spray aerosol fluxes over the open Atlantic Ocean are presented, along with a source function derived from them for a wind speed range of 4 to 18 m s−1 and a size range of 0.176 < R80 < 6.61 μm. This is in broad agreement with other recent estimates of the source function over this size range but shows a more rapid decrease with size above R80 = 2 μm than most other functions. The measurements were made during a 3 week cruise in the North Atlantic as part of the UK contribution to the international Surface Ocean–Lower Atmosphere Study (SOLAS) program. They utilized the new high-rate Compact Lightweight Aerosol Spectrometer Probe (CLASP), providing a 16-channel size spectrum (0.17

[1] A parameterization for the emission of sea-salt aerosol (SSA) particles is presented and its application in the SILAM dispersion modeling system for regional and global SSA simulations is discussed. The SSA production term is based on the parameterization of Monahan et al. and on experimental data from Martensson et al., and Clarke et al. The observational data were used to extend the Monahan et al. SSA emission flux to particles as small as 10 nm (dry particle diameter DP) and to account for water temperature and salinity. The result is an analytical formulation describing the SSA production fluxes for particles with Dp between 10 nm and 10 μm. This source function is implemented in the dispersion model SILAM and applied to compute the distribution of sea salt over the North Atlantic and Western Europe for the years 2000, 2003, 2007, 2009 and 2010, as well as globally for 2001 and 2008. The computed annual global production of SSA is between 6700 and 7400 Tg/year. Comparison of the SILAM near-surface SSA concentrations and its wet deposition with the in situ EMEP observations showed good agreement for summer periods while in winter time the model tends to under-estimate the wet deposition by a factor of ∼3. The underestimation is attributed to the coarse fraction (Dp > 10 μm) and the spume production mechanism, which were excluded from the analysis, to the wet deposition parameterization in SILAM and to the under-estimated precipitation amount in the input meteodata. The predicted vertically integrated aerosol optical depth (AOD) showed a close match with satellite observations over SSA-dominated areas.

[1] We identify a previously undetected link between the river network morphology and key recession curves properties through a conceptual-physical model of the drainage process of the riparian unconfined aquifer. We show that the power-law exponent, α, of −dQ/dt vs. Q curves is related to the power-law exponent of N(l) vs. G(l) curves (which we show to be connected to Hack's law), where l is the downstream distance from the channel heads, N(l) is the number of channel reaches exactly located at a distance l from their channel head, and G(l) is the total length of the network located at a distance greater or equal to l from channel heads. Using Digital Terrain Models and daily discharge observations from 67 US basins we find that geomorphologic α estimates match well the values obtained from recession curves analyses. Finally, we argue that the link between recession flows and network morphology points to an important role of low-flow discharges in shaping the channel network.

[1] We investigate regional variations in the Lg-wave quality factor (Q) in Northeast China and its vicinity with a tomographic method. Digital seismic data recorded at 20 broadband stations from 125 regional events are used to extract Lg-wave spectra. Tomographic inversions are independently conducted at 58 discrete frequencies distributed log evenly between 0.05 and 10.0 Hz. We simultaneously invert for the Lg-wave Q distribution and source spectra at individual frequencies without using any a priori assumption about the frequency dependence of the Q model and source function. The best spatial resolution is approximately 1° × 1° in well-covered areas for frequencies between 0.4 and 2.0 Hz. The Lg Q shows significant regional variations and an apparent relationship with regional geology. We use a statistical method to investigate the regional variations of Lg Q and their frequency dependence. The average Q0 (1 Hz Lg Q) in the entire investigated region is 414. Sedimentary basins are usually characterized by lower average Q0 values (from 155 to 391), while volcanic mountain areas have relatively high average Q0 values (from 630 to 675). Lg Q generally increases with increasing frequency. However, the frequency dependence has complex nonlinear features on a double-logarithmic scale, indicating that the commonly adopted power-law relationship may be oversimplified in a broad frequency band. The frequency dependence varies in different geological areas, with larger variations seen at lower frequencies.

[1] The study describes the development, testing and applications of site-specific tsunami inundation models (forecast models) for use in NOAA’s tsunami forecast and warning system. The model development process includes sensitivity studies of tsunami wave characteristics in the nearshore and inundation, for a range of model grid setups, resolutions and parameters. To demonstrate the process, four forecast models in Hawaii, at Hilo, Kahului, Honolulu, and Nawiliwili are described. The models were validated with fourteen historical tsunamis and compared with numerical results from reference inundation models of higher resolution. The accuracy of the modeled maximum wave height is greater than 80% when the observation is greater than 0.5 m; when the observation is below 0.5 m the error is less than 0.3 m. The error of the modeled arrival time of the first peak is within 3% of the travel time. The developed forecast models were further applied to hazard assessment from simulated magnitude 7.5, 8.2, 8.7 and 9.3 tsunamis based on subduction zone earthquakes in the Pacific. The tsunami hazard assessment study indicates that use of a seismic magnitude alone for a tsunami source assessment is inadequate to achieve such accuracy for tsunami amplitude forecasts. The forecast models apply local bathymetric and topographic information, and utilize dynamic boundary conditions from the tsunami source function database, to provide site- and event-specific coastal predictions. Only by combining a Deep-ocean Assessment and Reporting of Tsunami-constrained tsunami magnitude with site-specific high-resolution models can the forecasts completely cover the evolution of earthquake-generated tsunami waves: generation, deep ocean propagation, and coastal inundation. Wavelet analysis of the tsunami waves suggests the coastal tsunami frequency responses at different sites are dominated by the local bathymetry, yet they can be partially related to the locations of the tsunami sources. The study also demonstrates the nonlinearity between offshore and nearshore maximum wave amplitudes.

[1] In this paper we report on a laboratory study, the Spray Production and Dynamics Experiment (SPANDEX), conducted at the University of New South Wales Water Research Laboratory in Australia. The goals of SPANDEX were to illuminate physical aspects of spume droplet production and dispersion; verify theoretical simplifications used to estimate the source function from ambient droplet concentration measurements; and examine the relationship between the implied source strength and forcing parameters such as wind speed, surface turbulent stress, and wave properties. Observations of droplet profiles give reasonable confirmation of the basic power law profile relationship that is commonly used to relate droplet concentrations to the surface source strength. This essentially confirms that, even in a wind tunnel, there is a near balance between droplet production and removal by gravitational settling. The observations also indicate considerable droplet mass may be present for sizes larger than 1.5 mm diameter. Phase Doppler Anemometry observations revealed significant mean horizontal and vertical slip velocities that were larger closer to the surface. The magnitude seems too large to be an acceleration time scale effect. Scaling of the droplet production surface source strength proved to be difficult. The wind speed forcing varied only 23% and the stress increased a factor of 2.2. Yet, the source strength increased by about a factor of 7. We related this to an estimate of surface wave energy flux through calculations of the standard deviation of small-scale water surface disturbance, a wave-stress parameterization, and numerical wave model simulations. This energy index only increased by a factor of 2.3 with the wind forcing. Nonetheless, a graph of spray mass surface flux versus surface disturbance energy is quasi-linear with a substantial threshold.

The return flux (RF) sunspot model is applied to a round, unipolar sunspot observed by H. Kawakami (1983). Solving the magnetohydrostatic problem using the gas pressure deficit between the umbral and quiet-sun atmospheres as a source function, a distribution of electric current density in an untwisted, unipolar sunspot as a function of height and radial distance from the sunspot center is observed. Maximum electric current density is about 32 mA/sq m at the bottom of the sunspot.

[1] Short-wave directional distributions estimated using HF (high-frequency) radar are compared with model predictions. The short-wave directional distributions are estimated on the basis of HF radar using two- and four-parameter parametric models to describe short-wave directional distributions. The model-predicted short-wave directional distributions are computed using the energy balance equation. The nonlinear interaction source function in the energy balance equation is calculated from both the exact computation and the discrete interaction approximation (DIA). The predicted short-wave directional distributions from the exact computation and the DIA are compared with those estimated using HF radar. The energy balance equation is simplified by neglecting the propagation term, and the validity of the simplification is investigated. It is found that the four-parameter model is more accurate than the two-parameter model to estimate short-wave directional distribution using HF radar. The model-predicted mean short-wave directions with respect to wind directions are correlated with those estimated from the HF radar. The short-wave direction change associated with a sudden wind shift can be reproduced both from the exact computation and the DIA. The predicted second-order moments of short-wave directional distributions are also correlated with those estimated from the HF radar. This result shows that the model can reproduce transient short-wave directional distributions associated with changes of wind direction. The short-wave directional distributions predicted by the exact computation are narrower than those predicted by the DIA and estimated using the HF radar. The simplification of the energy balance equation is not the main source of the short-wave prediction error.

[1] A new approach to sea salt parameterization is proposed which incorporates wind-wave characteristics into the sea salt emission function and can be employed globally and under swell-influenced conditions. The new source function was applied into Navy Aerosol Analysis and Prediction System model together with predictions from the global wave model Wave Watch III. The squared surface wind velocity U10 and the wave's orbital velocity Vorb=πHs/TP are shown to be the key parameters in the proposed parameterization. Results of the model simulations are validated against multi-campaign shipboard measurements of the sea salt aerosol. The validations indicate a good correlation between Vorb and the measured surface concentrations. The model simulations with the new parameterization exhibit an improved agreement with the observations when compared to a wind-speed-only approach. The proposed emission parameterization has the potential to improve the simulations of sea salt emission in aerosol transport models.

[1] Sea-salt aerosol (SSA) is an important constituent of natural marine aerosol to which anthropogenic aerosols must be compared when assessing their climatic influence. Size distributions of particles, produced by bubbles from coastal oceanic breaking waves, were found to have sizes as small as 0.01 μm, with 60% smaller than 0.1 μm diameter. The thermal stability of these particles and their growth factor measured under increasing humidity indicate that most are sea salt. These SSA size distributions were used in conjunction with the measured number flux for bubbles from coastal breaking waves to develop a new sea-salt source function. This source function and the associated SSA flux compare favorably with previously published estimates available for sizes larger than 0.5 μm but extend the source function down to much smaller sizes. When this SSA flux is applied to oceanic whitecaps that have a highly nonlinear dependence on wind speed, it implies strong regional and temporal differences in the open ocean surface number flux. In marine regions with little continental impact we estimate that this SSA flux can contribute ∼5–90% of the marine cloud condensation nuclei (CCN), with the rest accounted for by the flux of aerosol entrained from the free troposphere. These two fluxes are large enough to account for commonly observed aerosol and CCN concentrations in the clean MBL without requiring a nucleation source in the MBL. These observations have significant implications for modeling marine aerosol concentrations and evolution.

[1] Convection in the Earth's outer core excites torsional oscillations in the fluid, which couple to rigid-body motion of the inner core and mantle. The torsional oscillations are detected as time variations of the magnetic field, whereas the motion of the mantle is observed as changes in the length of day. We develop a model for the motion of the core-mantle system using a Green's function for the impulse response to a localized source of excitation. The response to a source which is distributed in both space and time is obtained by convolving the Green's function with the appropriate source function. The Green's function is constructed by summing the normal modes of the system. We derive an orthogonality condition for the normal modes and use it to determine the coefficients of the normal mode expansion. Examples of the Green's function are presented for a variety of source locations. The predictions may be compared with observations to provide insights into the convective processes that excite the oscillations. It may also be possible to recover the physical properties that determine the period of the normal modes, including the structure of the magnetic field inside the outer core and the nature of coupling at the fluid boundaries. We outline a strategy for inverting the observations and identify potential difficulties due to the nonuniqueness of the inverse problem.

[1] Measurements from three spectral instruments, the Solar Spectral Flux Radiometer (SSFR), the Rotating Shadowband Spectrometer (RSS), and the Solar Ultraviolet Spectroradiometer (SUV), are compared to results from the Santa Barbara Moderate Resolution Radiative Transfer Model (SBMOD). SSFR data are from the SHEBA experiment of May–June 1998. RSS and SUV data are from Barrow, Alaska, April 1999. SBMOD is a recently developed model utilizing the correlated-k method of computing gaseous absorption and convolves the solar source function and the instrument's filter function during computations. Comparisons indicate that absorption of ozone, water vapor, oxygen, and the O2-O2 absorption complexes are well characterized by the model. There does not appear to be any significant unexplained absorption between 0.4 and 1.0 microns, as evidenced by comparisons between SBMOD and both SSFR and RSS data. However, a more absorptive aerosol was required to reach agreement between SBMOD and RSS diffuse fields than we anticipated. Data from the RSS and SUV possess similar structure over their entire shared spectral range from 400 to 600 nm, and the RSS and SSFR possess similar structure between 500 and 1000 nm. However, below 500 nanometers, measurements from all three instruments diverge noticeably from model results. The residual between the SUV and RSS measurements and SBMOD are similar to those presented in prior studies, suggesting that there may be errors in several widely used representations of the solar spectrum between 400 and 500 nm. The shape of the SSFR's data in this region has yet to be fully explained; aspects of its calibration and operation may be the main source of uncertainty.

[1] A parameterization of a sea-salt source function for both sub- and super-micron particles was developed based on the semi-empirical formulation of Monahan et al. [1986]. This new parameterization extends the range of Monahan's equation to below 0.2 μm in diameter where it has been found to overestimate submicron sea-salt aerosols, especially the sea-salt number concentrations. The new parameterization was used in a one-dimensional (1-D) column model to predict the number size distributions and compared with reasonable agreement to the observed distributions at various wind speeds reported by O'Dowd et al. [1997]. A global 3-D sea-salt simulation with this parameterization was also made and a much better dependence of sea-salt on surface wind speed was predicted than other schemes compared to observations. For an indirect impact assessment of sea-salt aerosols on climate where submicron particles may have a dominant contribution to aerosol-cloud interactions, this scheme provides the most realistic number flux of sea-salt particles between ocean and atmosphere.

[1] We present new solutions of the pitch-angle-averaged transport equation of pick-up ions in the heliosphere. These solutions supplement those available so far for the case of a vanishing momentum diffusion. A general solution is derived for nonvanishing momentum diffusion. This solution, which is valid for a simple spatial power law behavior of the solar wind plasma and for arbitrary source functions, is applied to the stochastic acceleration of pick-up ions and generalizes earlier solutions. Based on this, we present several asymptotic phase space integrals for the outer heliosphere and solve them analytically for a standard pick-up ion source function. Numerical calculations for interstellar neutral hydrogen yield phase space distributions depending sensitively on the underlying turbulence and its dependence on heliocentric distance.

[1] The dry deposition velocity for a uniform surface source of particles, such as sea-salt aerosol, is shown to be fundamentally different than that for a source of particles from above or upwind. An expression for the deposition velocity for a uniform surface source of particles and an improved expression for the deposition velocity when the source is from above (upwind) is derived. The equilibrium method of deriving the sea-salt source function from an aerosol concentration, measured at a reference height, and the deposition velocity, is shown to be of little value for particles smaller than about 5 to 10 μm in radius for two reasons: (1) The time to establish equilibrium between the source and loss by dry deposition is much longer than the typical lifetime of small particles determined by precipitation scavenging. (2) It is difficult, if not impossible, to correct for the effect of synoptic-scale vertical velocities and the effect of mixing between the marine boundary layer and the free troposphere. A sea-salt aerosol source function that combines the Monahan et al. [1986] formulation at radii smaller than about 10 μm with the modified Smith et al. [1993] formulation at radii larger than 10 μm is proposed.

A model is developed for simulating the two-dimensional radiative transfer of resonance line emissions in auroras. The method of solution utilizes Fourier decomposition of the horizontal dependence in the intensity field so that the two-dimensional problem becomes a set of one-dimensional problems having different horizontal wavenumbers. The individual one-dimensional problems are solved for using a Feautrier-type solution of the differential-integral form of the radiative transfer equation. In the limit as the horizontal wavenumber becomes much larger than the local line-center extinction coefficient, the scattering integral becomes considerably simplified, and the final source function is evaluated in closed form. The two-dimensional aspects of the model axe tested against results for nonresonance radiative transfer studies, and the resonance line part of the model is tested against results of existing plane-parallel resonance line radiative transfer codes. Finally, the model is used to simulate the intensity field of OI 1304 A for hard and soft auroras of various Gaussian horizontal widths. The results demonstrate the importance of considering the effects of two-dimensional radiative transfer when analyzing auroral resonance line data.

We determine the importance of V-V transitions in the radiative cooling by the CO2 15 μm band near the mesopause where the maximum error in cooling rate by two-level model is expected to occur. It is shown that the effect of including V-V transitions is to locally smooth the source functions for different sub-bands toward a single mean value. This effect allows the changes in cooling rate for each sub-band to partially cancel each other, so the total change in cooling rate for the whole band is not very significant. It is found that the maximum error in cooling rate around the mesopause is ∼0.5°K day−1. We have also examined errors in the cooling rate of the CO2 15-μm band for an equivalent two-level model suggested by Zhu (1990). The maximum error in cooling rate for the equivalent two-level model is ∼1.3°K day−1 around the summer mesopause. Present calculations confirm that the equivalent two-level model can be used in GCMs to calculate the CO2 15-μm band cooling rate.

Two statistical equilibrium models are compared to analyze the departure from local thermodynamic equilibrium (LTE) in the vibration-rotation bands of ozone in the middle atmosphere. The bands that emit in the 9-11 {mu}m spectral interval depart from LTE due to chemical pumping, spontaneous emission, radiative absorption, and photochemical reaction. The diurnal variation in the {nu}{sub 1} and {nu}{sub 3} fundamental band source functions is determined by the diurnal changes in the rate of photolysis of ozone by solar radiation. The hot band source functions ({nu} > 2) are invariant above 85 km due to the diurnal invariance in the chemical pumping process. The magnitude of the hot-band source functions is uncertain because of the lack of understanding of the chemical pumping process. Collisional quenching of vibrationally excited ozone by atomic oxygen may reduce the magnitude of the {nu}{sub 3} and {nu}{sub 1} fundamental source functions by 10% near 100 km.

As part of a larger joint effort by the Defense Advanced Research Project Agency and the Department of Energy to study the seismic source problem, a comprehensive reevaluation of the 1964 Salmon and 1966 Sterling nuclear explosions in dome salt was carried out. The Sterling source function originally estimated by Springer et al. (1968) conveys the impression that the cavity was badly overdriven; on reexamination this does not appear to be the case. The work of Glenn et al. (1987) on the Sterling free-field data is expanded upon, confirming that the cavity response was close to the theoretical expectation. Sterling's source function is estimated and is found to be comparable to Patterson's (1966) slightly weakened salt model. A source model for Salmon is derived from the Sterling source model and the five seismic stations that recorded both events. The new source model has a reduced displacement potential ψ∝ of about half that previously estimated. A temporary nonlinear two-wave system developed during the Salmon explosion as the compressional wave evolved from a shock wave; the separation of these two waves resulted in a high-frequency roll-off of the reduced velocity potential of ω−3. In addition, it is shown that the comer frequency is much higher and is created much closer to the cavity than the eigenfrequency. For both Salmon and Sterling the radial stresses are approximately a low-passed damped sinusoid superimposed on a small step function. The decoupling value of 72 obtained by Springer et al. (1968) is confirmed. A revision of Patterson's (1966) partial decoupling curve shows that the value for full decoupling in a shot-generated cavity would be only slightly higher. Contrary to previous studies, decoupling as a function of frequency for the surface waves is found to be the same as for the P waves. A new definition of decoupling appropriate to threshold test-ban treaty monitoring is also proposed.

We have constructed a vertically and zonally averaged model of the troposphere which calculates photochemical interactions and diffusive North-South transport of trace species. The model can be used to calculate the latitudinal distribution of the source function of a species if its concentration distribution is known. We have applied this procedure to carbon monoxide and find large sources outside the industrialized belt in the Northern Hemisphere.

An empirically fitted function describes surface Pacific Ocean tritium concentrations as varying exponentially with latitude, the r.m.s. fit to observations is 18%. The oceanic tritium concentration maximum in the North Pacific, which resulted from nuclear weapons testing, lagged the rain data by two to three years occurring in 1965--66. Tritium-salinity correlations are consistent with climatology. Tritium-longitude correlations are consistent with surface water circulation.

Methods are described for estimating the quantity and dispersion on a global scale of the material injected into the stratosphere by a violent volcanic eruption by using a combination of lidar measurements of stratospheric aerosols and a previously described two-dimensional atmospheric dispersion model with the initial volcanic cloud as the ‘source function’ (Cadle et al., 1976). The technique involves comparing the lidar data with model predictions normalized by using data of various kinds obtained after the Gunung Agung eruption in Bali in 1963. In this paper we show that the estimates for the Fuego eruption of 1974 can be made equally well by comparing model and lidar measurements of peak stratospheric concentrations or the total masses within a range of altitudes in a column above the place where the lidar measurements were made. The lidar data previously reported have been extended to several months following the eruption of Augustine volcano in Alaska during January and February 1976. The results indicate that the Augustine eruption must have injected no more than one fiftieth of the amount of material into the stratosphere that was injected by Agung and confirm the previous finding (Cadle et al., 1976) that Fuego injected one fifth of the amount injected by Agung.

EUV spectra (530-1500A) of the day airglow in up, down and horizontal aspect orientations have been obtained with 6.5A resolution and a limiting sensitivity of 5R from a rocket experiment. Below 834A the spectrum is rich in previously unobserved OII transitions connecting with 4S(0), 2D(0), and 2P(0) states. Recent broad-band photometric observations of geocoronal HeI 584A emission in terms of the newly observed OII emissions are shown. The OI 989A and OI 1304A emissions exhibit similar dependence on altitude and viewing geometry with the OI 989A brightness 1/15 that of OI 1340. Emission at 1026A is identified as geocoronal HI Lyman beta rather than OI multiplet emission and observed intensities agree well with model estimates. An unexpectedly high NI 1200/NI 1134A brightness ratio is evidence of a significant contribution from photodissociative excitation of N2 to the NI 1200A source function.

Source depth effects are examined for five 115-kg trinitrotoluene (TNT) explosions buried at depths ranging from the optimum cratering depth of 1.8 m to the fully contained depth of 11.5 m. Data were recovered at near source ranges from 17 to 228 m. The waveforms are dominated by P and SV-Rayleigh energy. Depth effects are evident in the increase of P to SV-Rayleigh amplitude ratios and in the twofold increase of high-frequency energy for the deeper sources. Theoretical propagation depth effects are modeled by Green's functions calculated for a velocity gradient which approximates the velocity structure of the experimental site. The effects of depth on the explosion source function are predicted using the scaling laws of Mueller and Murphy (1971). These models did not reproduce the observed twofold increase of high-frequency energy. The discrepancy between the model and observations is attributed to increased coupling of high frequency P wave energy for fully contained sources. Energy calculations confirm that the shallowest event coupled 40% and the fully contained event 80% of the total seismic energy into the P wave. Source coupling efficiencies ranged from 0.7∼1.0% for the near surface source to 1.5∼2.9% for the fully contained explosion.

The dynamical processes affecting the evolution of a random internal wave field are considered. If the statistical properties of the internal wave field vary slowly with space and time, these dynamical processes can be treated as small perturbations about the local steady state of the free linear field. The time evolution of the wave field is then governed by a radiative transfer equation describing changes in the action density spectrum of the wave field along wave group trajectories. The source function describing these changes is determined by the superposition of all processes governing the generation, transfer, and dissipation of wave energy. Some terms of the source function, those corresponding to expansible processes, can be derived rigorously by using weak interaction concepts. Other terms, corresponding to nonexpansible processes which are governed locally by strongly nonlinear dynamics, cannot be determined completely. For the case where the internal wave field can adequately be described in the WKBJ approximation, a rather complete list of source terms is presented. The evaluation of these source terms is difficult partly because of their complicated functional structure and partly because the geophysical fields involved are not sufficiently known. Those source terms which have been evaluated in detail are briefly reviewed, and their implications on the energy balance of the internal wave field are discussed.

We present a model from which the angular and depth dependent atmospheric γ rays can be derived in the energy range of 0.3–10 MeV at λ = 40°. The model consists of an isotropic source function which depends on depth and energy expressed in the form S(E, x) = S0(E)[1 + b(E)x + c(E)x²]e−x/p(E) photons/(g air s MeV) and is determined semiempirically. We determined source strengths for 38 predicted atmospheric γ ray lines and for 10 different energies in the continuum. For the continuum a diffuse cosmic flux, consistent with the Apollo 15/16 data, is assumed in order to fit the measured data above 10 g/cm². Total and directional fluxes are computed at two different atmospheric depths. The computed flux compares well with other measurements and theoretical calculations.

Variation in the eddy diffusion coefficient constitutes a momentum source. This variation near the turbopause affects both the composition and the wind and temperature fields of the thermosphere. Two types of calculations are carried out, for horizontal winds considered self-consistently in a three-dimensional dynamic model and horizontal winds artificially suppressed to simulate a one-dimensional model. Momentum transfer associated with variations in eddy diffusion coefficients represents the source function in the analysis presented. It is shown that for long-term variations in the thermosphere, the compositional dependence on variations in eddy diffusion coefficients can be entirely different in one and three dimensional models with horizontal winds included. Horizontal winds can greatly reduce the effects of eddy diffusion in general and the ratio between He and O amplitudes in particular.

The present discussion is based on a study of the magnetic field data obtained with the aid of the magnetic field satellite Magsat, deployed in October 1979, over most of the earth during a 7.5-month mission. Inversions using spherical harmonic coefficients are considered along with the inversion of residual fields. In order to perform the correct operation, it is necessary to add on to the source function produced by the inversion process a magnetization function which has no external field. Such a function is known as an annihilator. The use of the annihilator for Pacific Ocean anomalies is discussed. Attention is given to models of oceanic crustal magnetization, and continental long-wavelength anomalies. It is found that in continental regions the annihilator is also useful if induced magnetizations are thought to be responsible for the long-wavelength anomaly.

Some field-geometric features of relevance to particle trapping in the inner magnetosphere and polar-cap regions of Jupiter are described using an internal-field model that includes terms up to the order of n equals 3 (octupole). Adiabatic particle parameters for detectors on Pioneers 10 and 11 during their flights through Jupiter's inner magnetosphere are determined along with the configuration of the intersections of particle drift shells with the planetary ionosphere. Possible correlations between drift-shell contours and the planet-locked characteristics of Jovian decametric radio emission are investigated, and longitudinal asymmetries of the ionospheric plasma source function are analyzed. It is shown that if the ionosphere is the main source of magnetospheric plasma, the latitude dependence of the plasma source function should have a considerable effect on the longitudinal asymmetry of the corotating plasma.

The thermal maps of Murray and his collaborators have been analyzed statistically into solar effects, latitude variations, and limb darkening. Seeking a pole position for minimum residual variance leads to α = 7.4 ± 2.0°, δ = −68.1 ± 0.9°. The solar effect is opposite to the simple expectation of an increasing temperature from antisolar to subsolar point; this suggests that the main deposition of solar energy takes place somewhat below the levels relevant to the measured emission. Inversion of the limb-darkening curves yields a source function which, if interpreted as a thermal source function, indicates an increasing temperature with depth and cold polar regions, in agreement with microwave data. Finally, analysis of the terminator position indicates a very deep and variable scattering layer and gives some support to a predominantly scattering source function in the 10-μ region.

The source functions of 53 shocks of the circum-Pacific belt were obtained by a method of equalization applied to Rayleigh waves in the period range of 35 sec to 150 sec recorded at the Seismological Laboratory, Pasadena. The source function was interpreted in terms of the direction of forces at the source. The interpretation was checked by additional information concerning the earthquake as well as by an error analysis. The horizontal forces deduced from the source function showed a systematic geographic distribution, which favors Benioff's hypothesis on the circum-Pacific tectonics. The vertical forces are found to be mostly directed upward on the oceanic side.

A differential equation of transport is written for protons losing energy in an atmosphere but not scattering. It is solved under the approximation that a proton loses a negligible amount of energy while it drifts once around the earth in longitude. Three cases are treated: the equilibrium, solution with input and loss rates equal; the solution for impulsive injection at t = 0, the intensity then dying away; and the solution for the intensity zero initially, the input mechanism being turned on at t = 0. No numerical work bearing on the geometry of the source function is included. The treatment is an improvement over previous ones in that it adequately treats the particles as moving along their actual trajectories. A detailed comparison with observations over South Africa shows that the altitude dependence of intensity is roughly consistent with the view that the particles seen by the unshielded Geiger tube on 1958e are protons supplied by a weak source (for example, by decay of albedo neutrons) which are lost to the detector when their energy is reduced below the detection threshold by absorption. The atmosphere required has a temperature of about 2000°K at 400 km if it is pure dissociated nitrogen. At some height between about 1100 and 1300 km the scale height sharply increases in a way consistent with the view that at this height the composition changes to pure dissociated hydrogen. Only relative intensities are used in these comparisons.

The source functions of three earthquakes in the western Pacific are obtained from Rayleigh waves recorded at many IGY stations over the world. The method of interpreting the source function, which was proposed in a previous paper, is applied to these source functions. It is found that the pattern of the force at the source is quadrant for all three earthquakes, in accordance with the model adopted in the fault plane studies. One of the two nodal lines is found to be nearly parallel to the trend of the seismic zone for each of these earthquakes, and if we take this nodal line as the actual fault, the slip directions are right hand for all of them. The result from the recent Chilean shocks also supports the hypothesis that right-hand strike-slip prevails along the circum-Pacific earthquake belt.

Theoretical wave forms for the first cycle and a half are calculated for Romney's experimental recordings of underground nuclear explosions Blanca, Logan, and Tamalpais at distances of 96 to 714 km. Models of the crust are constructed from travel times. Zvolmskii s near-front approximation is used to form the basis of amplitude calculations which include head coefficients, geometrical spreading, and corrections for superposed layers. The source function is scaled from measurements made of the Rainier shot. The effects of attenuation and instrument response are included. By convolving these factors, theoretical displacement amplitudes are calculated in millimicrons for the first half-cycle which agree with the experimental measurements of Logan and Bianca from 300 to 600 km within +4 to −16 per cent. A single-layer crustal model with a Q of about 400 is indicated by the amplitude calculations. The amplitudes of later half-cycles are influenced by the reflection or interaction at the surface of the Rainier mesa. Additional data and calculations indicate that the surface reflection or interaction is nonlinear and has an amplitude about three times that expected on an elastic basis.

A step-by-step display of the theoretical P-wave amplitude spectrum of shallow (focal depth ≤ 40 km) earthquakes with mb values ranging from 5.9 to 6.3 and underground explosions of comparable magnitudes as the signal propagates from source to receiver indicates that the factors most influential in shaping the respective spectra are the source crust transfer function, which includes the focal depth effect, and the source function. The results, although not unequivocal, favor a peak in the amplitude spectrum of the teleseismic P coda of earthquakes rather than a flat spectrum at low frequencies. The effect of focal depth appears to have more influence than the effect of source parameters on the peak frequency f0 in the spectra of earthquakes, whereas the source function is the important parameter for shallow underground nuclear explosions. For shallow seismic events of comparable mb the f0 of earthquake spectra is smaller than the f0 of explosion spectra by approximately an order of magnitude. The pronounced minimum (hole) at about 0.1 Hz in the long-period spectrum of earthquakes is associated with the focal depth effect and can be identified for several events. However, theoretically predicted holes starting at about 0.5 Hz in the short-period spectrum of assumed unilateral faulting earthquakes are due to the extended source effect and are not identifiable on any of the experimental spectra. For short-period records of Longshot and Milrow, Haskell's analytic formulation of the Werth and Herbst displacement potential, in conjunction with the outlined theory, predicts fairly accurately the increase (approximately 0.15 sec) in the duration of the first half-cycle with increasing yield. For the corresponding long-period records of Milrow his formulation predicts a value smaller than a mean of the measured values by about 15% (0.32 sec). Haskell's equations, together with the rest of the theory, appear to predict fairly accurately the variation in mb with yield for these two events when amplitude measurements are restricted to the first half-cycle.

Relative shear-wave excitation equivalent to large Nevada Test Site underground explosions was detected for the Amchitka Island test Milrow. Use of Milrow Love waves as match filters enabled detection of these waves on Longshot and Milrow collapse recordings as well. Mechanisms other than tectonic strain release must have produced the Love waves. The Rayleigh waves from the collapse were oppositely polarized relative to Milrow and were delayed by a time increment approximately equal to the expected free-fall time through the postexplosion cavity. A small delay (1 to 2 sec) in the initial phase of long-period components of the source function was detected for Milrow relative to Longshot. A Rayleigh-wave amplitude ratio for Milrow and Longshot was precisely determined by match filtering; this ratio agreed almost exactly with amplitude scaling proportional to the cube root of yield.

Rayleigh waves and Love waves are used for the study of the earthquake mechanism by the application of a method of phase equalization. In this method, an impulse response is computed from known phase-velocity data and instrument characteristics, and is cross-correlated with an actual record. A comparative study of Love waves from Kern County aftershocks of 1952 and those from Nevada shocks of 1954 strongly supports the hypothesis of a pair of couples rather than a single couple for the earthquake source. Source functions for five Kern County aftershocks are derived from the Rayleigh waves recorded at Weston and Palisades. It was found that the sense of principal motion in the source function is in agreement with the fault-plane solution obtained from the P-wave data. Mantle Rayleigh waves are found to be useful for this purpose also.

The radiation patterns of Love and Rayleigh waves from three nuclear explosions (Hardhat, Haymaker, and Shoal) are studied to determine the nature of the asymmetry of radiation and the mechanism of Love wave generation. From a comparative study of different explosions it is reasoned that the Love waves are generated at the source of the explosion. The source function, represented as the superimposition of an isotropic dilatational component due to the explosion and a multipolar component due to the release of tectonic strain energy, is consistent with the observed radiation patterns and the amplitude spectrums. The amount of seismic energy due to the strain release is computed. In some cases (Haymaker and Shoal) it is found that this energy may be due to the relaxation of the pre-stressed medium by the explosion-formed cavity. In the case of Hardhat it is concluded that the explosion must have triggered some other strain release mechanism, such as an earthquake. The amplitude equalization method is applied to surface waves from an earthquake to determine the source parameters. From only the amplitude spectrums and radiation patterns of Love and Rayleigh waves, the source functions, source depth, strike and dip of the fault plane, and the rake of displacement are determined for the July 20, 1964, Fallon earthquake.

Rayleigh waves from underground nuclear explosions which are accompanied by high levels of tectonic strain release are observed to be reversed and time delayed relative to Rayleigh waves from “normal” underground explosions. The “time delays” can be explained as an interference effect between the explosion and tectonic source time functions which magnifies the true phase difference between the source functions. The phase of the explosion source time function is advanced relative to the phase of the tectonic source function, and the magnitude of the time advance is directly related to the amount of overshoot in the explosion source time function. The phase distortion is more complex than a simple time delay, and may appear as a constant phase shift with no linear trend. Apparent time advances are also possible; however because of small differences between the excitation functions of the explosion and tectonic sources at shallow depths, the phase shift will appear more frequently as an apparent time delay. Observations of Rayleigh wave phase shifts from underground explosions at the Soviet East Kazakh test site recorded at SRO stations are in very good agreement with simulated phase shifts derived from synthetic calculations.