Local stability and estimation of uncertainty for solutions to inverse problems

 We present a method for studying local stability of a solution to an inverse problem and evaluate the uncertainty in determining true values of particular observables. The investigation is done under the assumption that only the Gaussian part of fluctuations about the local minimum of the cost (likelihood) function is essential. Our approach is based on the spectral analysis of the Hessian operator associated with the cost function at its extremal point, and we put forward an effective iterative algorithm suitable for numerical implementation in the case of a computationally large problem. Received: 16 May 2001 / Accepted: 22 October 2001     

Experimental investigation of free (downward) convection near horizontal cold spots

To explain the conditions for dew and pollutant precipitation during still-weather radiative cooling of the Earth’s surface, attention is paid to the role of surface temperature inhomogeneities and convective air flows appearing near them. To understand how convection forms near cold spots, schematic cylinders with adiabatic walls and a cold bottom are considered. The results of this consideration agree with the results obtained in previous calculations and experimental studies, namely, the Nusselt number depends on the Rayleigh number to the power 1/5 with the proportionality coefficient γ. The quantitative characteristics were experimentally investigated by measuring the vertical temperature profiles and observing tracer motion near circular cold water surfaces about 30 cm and 10 m in size. As a result, it is found that, for isolated planar spots, the temperature difference between the spot surface and the environment decreases in accordance with the exponential law and air motions from the center of the spot toward its edges are of a laminar character. For the Rayleigh numbers that use the ratio of the area of the spot to the half of its perimeter as the characteristic size, the mean values of the coefficient γ are 1.1 for an isolated spot with Ra = 10⁶ and 0.7–0.8 for spots with Ra = 10⁶?5 × 10¹⁰ located at one level with the surrounding surface. For deepened spots, the processes of heat exchange significantly slow down and the character of temperature profiles changes depending on the material of the surrounding walls. The process of establishing the equilibrium temperature of an isolated spot that is caused by radiative cooling and the convective inflow of heat and moisture is considered in the Appendix. A method for preventing radiation fog by air drying during convection near the surrounding cold surfaces is proposed, and the principles of the intensification of the condensed-moisture collection are formulated.     

The Mitigation of Multipath Errors by Strobe Correlators in GPS/GLONASS Receivers

An effective method of decreasing multipath errors in GPS or GPS/GLONASS receivers by changing delay lock loop correlator reference signal is discussed. Unlike other approaches, this method does not lead to apparatus complication, power comsumption increase, or augmentation of digital processor load. This method eliminates the multipath error completely if the difference in delays of direct and reflected signal is more than 30 m, and decreases this error for smaller delays. The cost of such decrease is that the noise error is decreased. However, the noise error is much less dangerous than the multipath one because of its smaller value and much shorter correlation interval. Calculated and experimental data for the method are given for multipath and noise errors. ? 1998 John Wiley & Sons, Inc.     

A new formula for saturated water steam pressure within the temperature range −25 to 220°C

Instead of approximation formula ln(E(t)/E(0)) = [(a ? bt)t/(c + T)] commonly used at present for representing dependence of pressure of saturated streams of liquid water E upon temperature we suggested new approximation formula of greater accuracy in the form ln(E(t)/E(0)) = [(A ? Bt + Ct ²)t/T], where t and T are temperature in °C and K respectively. For this formula with parameters A = 19.846, B = 8.97 × 10^?3, C = 1.248 × 10^?5 and E(0) = 6.1121 GPa with ITS-90 temperature scale and for temperature range from 0°C to 110°C relative difference of approximation applying six parameter formula by W. Wagner and A. Pruß 2002, developed for positive temperatures, is less than 0.005%, that is approximately 15 times less than accuracy obtained with the firs formula. Increase of temperature range results in relative difference increasing, but for even temperature range from 0°C to 220°C it does not higher than 0.1%. For negative temperatures relative difference between our formula and a formula of D. M. Murphy and T. Koop, 2005, is less than 0.1% for temperatures higher than ?25°C. This paper also presents values of coefficients for approximation of Goff and Grach formula recommended by IMO. The procedure of finding dew point T _d for known water steam pressure e _n based on our formula adds up to solving an algebraic equation of a third degree, which coefficients are presented in this paper. For simplifying this procedure this paper also includes approximation ratio applying a coefficient A noted above, in the form T _d (e _n ) = \(\frac{{AT_0 }}{{A - \varepsilon }}\) + 0.0866?² + 0.0116?^10/3, where ? = ln(e _n /E(T ₀)). Error of dew point recovery in this ratio is less than 0.005 K within the range from 0 to 50°C.     

Statistical significance and climatic role of the Global Atmospheric Oscillation

The statistical significance of Global Atmospheric Oscillation (GAO), whose main element is the well-known El Niño–Southern Oscillation in the equatorial Pacific, was assessed from monthly mean atmospheric pressure data at sea level at the nodes of a regular 5° × 5° grid covering the entire surface of the Earth. The data were collected in 1920–2012. It was found that statistically reliable GAO signals cover almost the entire tropical zone and they also appear at mid- and high latitudes of both hemispheres.     

New seismic array solution for earthquake observations and hydropower plant health monitoring

We present the novel fusion of seismic safety monitoring data of the hydropower plant in Chirkey (Caucasus Mountains, Russia). This includes new hardware solutions and observation methods, along with technical limitations for three types of applications: (a) seismic monitoring of the Chirkey reservoir area, (b) structure monitoring of the dam, and (c) monitoring of turbine vibrations. Previous observations and data processing for health monitoring do not include complex data analysis, while the new system is more rational and less expensive. The key new feature of the new system is remote monitoring of turbine vibration. A comparison of the data obtained at the test facilities and by hydropower plant inspection with remote sensors enables early detection of hazardous hydrodynamic phenomena.     

Triplications for the converted wave in transversely isotropic media with a tilted symmetry axis

In seismic data processing, serious problems could be caused by the existence of triplication and need to be treated properly for tomography and other inversion methods. The triplication in transversely isotropic medium with a vertical symmetry axis has been well studied and concluded that the triplicated traveltime only occurs for S wave and there is no triplication for P and converted PS waves since the P wave convexity slowness always compensates the S wave slowness concavity. Compared with the vertical symmetry axis model, the research of the triplication in transversely isotropic medium with a tilted symmetry axis is still keeping blank. In order to analyse the triplication for the converted wave in the tilted symmetry axis model, we examine the traveltime of the triplication from the curvature of averaged P and S wave slowness. Three models are defined and tested in the numerical examples to illustrate the behaviour of the tilted symmetry axis model for the triplicated traveltime with the change of the rotation angle. Since the orientation of an interface is related to the orientation of the symmetry axis, the triplicated traveltime is encountered for the converted wave in the tilted symmetry axis model assuming interfaces to be planar and horizontal. The triplicated region is influenced by the place and level of the concave curvature of the P and S wave slowness.     

Atmospheric and Coupled Model Intercomparison in Terms of Amplitude—Phase Characteristics of Surface Air Temperature Annual Cycle

1. Introduction In spite of the progress achieved in global climatemodelling during the last few decades, the models stillshow considerable errors even for the surface air tem-perature ?eld (Covey et al., 2000; IPCC, 2001; Lam-bert and Boer, 2001). As i…     

Comparison of Bayesian estimates of peak ground acceleration (<Emphasis Type="Italic">A</Emphasis>max) with PSHA in Iran

Bayesian probability theory is an appropriate and useful method for estimating parameters in seismic hazard analysis. The analysis in Bayesian approaches is based on a posterior belief, also their special ability is to take into account the uncertainty of parameters in probabilistic relations and a priori knowledge. In this study, we benefited the Bayesian approach in order to estimate maximum values of peak ground acceleration (A_max) also quantiles of the relevant probabilistic distributions are figured out in a desired future interval time in Iran. The main assumptions are Poissonian character of the seismic events flow and properties of the Gutenberg-Richter distribution law. The map of maximum possible values of A_max and also map of 90% quantile of distribution of maximum values of A_max on a future interval time 100 years is presented. According to the results, the maximum value of the A_max is estimated for Bandar Abbas as 0.3g and the minimum one is attributed to Esfahan as 0.03g. Finally, the estimated values in Bayesian approach are compared with what was presented applying probabilistic seismic hazard (PSH) methods based on the conventional Cornel (1968) method. The distribution function of A_max for future time intervals of 100 and 475 years are calculated for confidence limit of probability level of 90%.     

Influence of a tropical cyclone on the upper ionosphere according to tomography sounding data over Sakhalin Island in November 2007

Tomography sounding data for the first half of November 2007 are presented. The sounding was conducted over three points located at the same meridian—Yuzhno-Sakhalinsk (47° N, 143° E), Poronaisk (49° N, 143° E), and Nogliki (51° N, 143° E)—in order to find the possible influence of a tropical cyclone on the upper ionosphere. A change in the foF2 parameter by on average no more than 10–20% is a possible response of the upper ionosphere localized over the tropical cyclone (TC) zone (in the given case, 25°–30° northward and 5°–20° eastward) at a distance of approximately 3800–5500 km from it. A decrease or, vice versa, an increase in foF2 is related to the delay of the measurement moment relative to the beginning of the TC action. The complexity of a morphological analysis of the given event is that a tropical cyclone is a “wideband” (in the longitudinal and, to a lesser degree, in the latitudinal directions) and lasting disturbance source.