FINDING CAUSES OF OUTLIERS IN MULTIVARIATE ENVIRONMENTAL DATA

Multivariate outliers in environmental data sets are often caused by atypical measurement error in a singlevariable.From a quality assurance perspective it is important to identify these variables efficiently so thatcorrective actions may be performed.We demonstrate a procedure for using two multivariate tests toidentify which variable‘caused’each outlier.The procedure is tested with simulated data sets that havethe same correlation structure as selected water chemistry variables from a survey of lakes in the WesternUnited States.The success rates are evaluated for three of the variables for sample sizes of 50 and 100,significance levels of 0.01 and 0.05 and various amounts of mean shift.The procedure works best forhighly correlated variables.     

Anthropogenic Sulfate and Nitrate Signals in Snow from Bogda Glacier, Eastern Tianshan

A 1.2 m snow pit was recovered on July 29th, 2009 from the Bogda Glacier, eastern Tianshan (天山). The sample site temperature of -9.6 ℃ indicates that the unique glaciochemical re-cord was well preserved and suitable for the reconstruction of air pollution levels in this previously un-explored region. Samples were analyzed for major ions (Na+, K+, Ca2+, Mg2+, NH4+, Cl-, SO42-, NO3-, HCOO-, and CH3COO-). NO3- and SO42- were characterized by significant high levels of pollution con-centration. Most air masses ...     

MHD model of magnetosheath flow: comparison with AMPTE/IRM observations on 24 October, 1985

We compare numerical results obtained from a steady-state MHD model of solar wind flow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevailed during this about 4 hour-long crossing. The magnetic shear at spacecraft entry into the magnetosphere was 15°. A steady density decrease and a concomitant magnetic field pile-up were observed during the 40 min interval just preceding the magnetopause crossing. In this plasma depletion layer (1) the plasma beta dropped to values below unity; (2) the flow speed tangential to the magnetopause was enhanced; and (3) the local magnetic field and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994). We model parameter variations along a spacecraft orbit approximating that of AMPTE/IRM, which was at slightly southern GSE latitudes and about 1.5 h postnoon Local Time. We model the magnetopause as a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We find that computed field and plasma profiles across the magnetosheath and plasma depletion layer match all observations closely. Theoretical predictions on stagnation line flow near this low-shear magnetopause are confirmed by the experimental findings. Our theory does not give, and the data on this pass do not show, any localized density enhancements in the inner magnetosheath region just outside the plasma depletion layer.     

Planetary ENA Imaging: Venus and a comparison with Mars

We present simulated images of energetic neutral atoms (ENAs) produced in charge exchange collisions between solar wind protons and neutral atoms in the exosphere of Venus, and make a comparison with earlier results for Mars. The images are found to be dominated by two local maxima. One produced by charge exchange collisions in the solar wind, upstream of the bow shock, and the other close to the dayside ionopause. The simulated ENA fluxes at Venus are lower than those obtained in similar simulations of ENA images at Mars at solar minimum conditions, and close to the fluxes at Mars at solar maximum. Our numerical study shows that the ENA flux decreases with an increasing ionopause altitude. The influence of the Venus nighttime hydrogen bulge on the ENA emission is small.     

Ion loss on Mars caused by the Kelvin-Helmholtz instability

Mars Global Surveyor detected cold electrons above the Martian ionopause, which can be interpreted as detached ionospheric plasma clouds. Similar observations by the Pioneer Venus Orbiter electron temperature probe showed also extreme spatial irregularities of electrons in the form of plasma clouds on Venus, which were explained by the occurrence of the Kelvin-Helmholtz instability. Therefore, we suggest that the Kelvin-Helmholtz instability may also detach ionospheric plasma clouds on Mars. We investigate the instability growth rate at the Martian ionopause resulting from the flow of the solar wind for the case where the interplanetary magnetic field is oriented normal to the flow direction. Since the velocity shear near the subsolar point is very small, this area is stable with respect to the Kelvin-Helmholtz instability. We found that the highest flow velocities are reached at the equatorial flanks near the terminator plane, while the maximum plasma density in the terminator plane appears at the polar areas. By comparing the instability growth rate with the magnetic barrier formation time, we found that the instability can evolve into a non-linear stage at the whole terminator plane but preferably at the equatorial flanks. Escape rates of O⁺ ions due to detached plasma clouds in the order of about 2×10²³-3×10²⁴ s^-1 are found. Thus, atmospheric loss caused by the Kelvin-Helmholtz instability should be comparable with other non-thermal loss processes. Further, we discuss our results in view of the expected observations of heavy ion loss rates by ASPERA-3 on board of Mars Express.     

The Kelvin–Helmholtz instability at Venus: What is the unstable boundary?

The Kelvin–Helmholtz instability gained scientific attention after observations at Venus by the spacecraft Pioneer Venus Orbiter gave rise to speculations that the instability contributes to the loss of planetary ions through the formation of plasma clouds. Since then, a handful of studies were devoted to the Kelvin–Helmholtz instability at the ionopause and its implications for Venus. The aim of this study is to investigate the stability of the two instability-relevant boundary layers around Venus: the induced magnetopause and the ionopause. We solve the 2D magnetohydrodynamic equations with the total variation diminishing Lax–Friedrichs algorithm and perform simulation runs with different initial conditions representing the situation at the boundary layers around Venus. Our results show that the Kelvin–Helmholtz instability does not seem to be able to reach its nonlinear vortex phase at the ionopause due to the very effective stabilizing effect of a large density jump across this boundary layer. This seems also to be true for the induced magnetopause for low solar activity. During high solar activity, however, there could occur conditions at the induced magnetopause which are in favour of the nonlinear evolution of the instability. For this situation, we estimated roughly a growth rate for planetary oxygen ions of about 7.6 × 10²⁵ s⁻¹, which should be regarded as an upper limit for loss due to the Kelvin–Helmholtz instability.     

Mass loss from “Hot Jupiters”—Implications for CoRoT discoveries, Part II: Long time thermal atmospheric evaporation modeling

We investigate the efficiency of the atmospheric mass loss due to hydrodynamic blow-off over the lifetime of the exoplanet HD209458b by studying numerically its hydrogen wind for host star X-ray and EUV (XUV) fluxes between 1 and 100 times that of the present Sun. We apply a time-dependent numerical algorithm which is able to solve the system of hydrodynamic equations straight through the transonic point of the flow including Roche lobe effects. The mass loss rates are calculated as functions of the absorbed energy in the thermosphere. Depending on the heating efficiency for a hydrogen-rich thermosphere the maximum temperature obtained in our study at 1.5R_pl by neglecting IR cooling is about 5000-10,000 K for heating efficiencies of 10% and 60%, respectively. We find that the upper atmosphere of HD209458b experiences hydrodynamic blow-off even at such low temperatures if one does not neglect gravitational effects caused by the proximity of the planet to its Roche lobe boundary. Depending on the heating efficiency, we find from the solution of the hydrodynamic equations of mass, momentum, and energy balance that energy-limited mass loss rate estimations overestimate the realistic mass loss rate at present time for HD209458b by several times. Using the maximum heating efficiency for hydrogen-rich atmospheres of 60% we find that HD209458b may experience an atmospheric mass loss rate at present time of about . The mass loss rate evolves to higher values for higher XUV fluxes expected during the early period of the planet's host star evolution, reaching values of several times . The integrated mass loss is found to be between 1.8% and 4.4% of the present mass of HD209458b. We found that the influence of the stellar tidal forces on atmospheric loss (the Roche lobe effect) is not significant at 0.045 AU. For a similar exoplanet, but at closer orbital distances , the combined effect of the Roche lobe and the high XUV radiation result in much higher thermal loss rates of about and even more for early stages. This leads to a total loss over 4 Gyr of 27.5% of the planetary mass.     

Deep Solar Activity Minimum 2007 – 2009: Solar Wind Properties and Major Effects on the Terrestrial Magnetosphere

We discuss the temporal variations and frequency distributions of solar wind and interplanetary magnetic field parameters during the solar minimum of 2007?–?2009 from measurements returned by the IMPACT and PLASTIC instruments on STEREO-A. We find that the density and total field strength were significantly weaker than in the previous minimum. The Alfvén Mach number was higher than typical. This reflects the weakness of magnetohydrodynamic (MHD) forces, and has a direct effect on the solar wind–magnetosphere interactions. We then discuss two major aspects that this weak solar activity had on the magnetosphere, using data from Wind and ground-based observations: i) the dayside contribution to the cross-polar cap potential (CPCP), and ii) the shapes of the magnetopause and bow shock. For i) we find a low interplanetary electric field of 1.3±0.9 mV?m^?1 and a CPCP of 37.3±20.2 kV. The auroral activity is closely correlated to the prevalent stream–stream interactions. We suggest that the Alfvén wave trains in the fast streams and Kelvin–Helmholtz instability were the predominant agents mediating the transfer of solar wind momentum and energy to the magnetosphere during this three-year period. For ii) we determine 328 magnetopause and 271 bow shock crossings made by Geotail, Cluster 1, and the THEMIS B and C spacecraft during a three-month interval when the daily averages of the magnetic and kinetic energy densities attained their lowest value during the three years under survey. We use the same numerical approach as in Fairfield’s (J. Geophys. Res. 76, 7600, 1971) empirical model and compare our findings with three magnetopause models. The stand-off distance of the subsolar magnetopause and bow shock were 11.8 R _E and 14.35 R _E, respectively. When comparing with Fairfield’s (1971) classic result, we find that the subsolar magnetosheath is thinner by ～1 R _E. This is mainly due to the low dynamic pressure which results in a sunward shift of the magnetopause. The magnetopause is more flared than in Fairfield’s model. By contrast the bow shock is less flared, and the latter is the result of weaker MHD forces.

     

ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS

In many environmental applications,such as exposure assessment and risk modelling,the desiredestimate is a random variable computed as the product of three independently distributed randomvariables.These variables may not necessarily have the same mean and variance.The method for findingthe 100(1-α)% confidence interval for the mean of the product random variable has been proposed bysome practitioners as the product of the 100(1-α)% confidence interval of the three means.In this paperwe show that the distribution of the product of three independent normal random variables is not normal.We find the mean and variance of the product distribution.Further,we show that although the meanof the product is equal to the product of the means,the product of the three confidence intervals is nota good approximation of the confidence intervals for the mean of the product variable.The confidenceinterval of the mean of the product variable may be estimated by computer simulation.An algorithmfor estimating the confidence interval for the mean of the product random variable is given.The programimplementing this algorithm is given as an appendix.