Topics in Practical Statistics

A practical knowledge of a core body of statistics is essential to any practising space scientist. Although the overall discipline is very extensive, it is surprising how a relatively small set of concepts can address the majority of situations. This chapter sets out to address statistical topics that are relevant in day-to-day data reduction and analysis. It also sets out to clarify aspects of statistical analysis that often appear to be confusing, and provide a quick and simple reference. It...

The requirements for remote sensing of the climate system

Much of the remote sensing for Earth system science is directed towards climate research, the main application considered in this chapter. Before discussing remote sensing methodology, therefore, it is useful to give an overview of the climate system, and to note how remote sensing can be used in the investigation of climate. The Earth's climate system (Figure 2.1) is complex and dynamic, involving the mutual interaction of the atmosphere, ocean, cryosphere, biosphere and land surface, as they...

Comets

Comets are the building blocks of the outer solar system. They formed at the low temperatures prevalent at these distances in the primordial nebula and they retain volatile material from the early solar system. They are relatively pristine bodies, making their study important. Some of them collided and coalesced to form the cores of the gas giants. From the orbits of comets we find that many 1012) were formed in the Uranus-Neptune region but were expelled to form the spherical (and theoretical)...

Quasiperpendicular Shock Upstream Shock Downstream

7 NOV 1977 I h 1111 ri n i r r- titttprr-rr 7 NOV 1977 I h 1111 ri n i r r- titttprr-rr ill n't Figure 4.10 (a) Field and flow structure in the vicinity of a quasi-perpendicular shock, at which the upstream magnetic field, Bu, is close to being perpendicular to the shock normal n. The flow speed decreases through the shock such that the density and magnetic field strength increase in the downstream region. A fraction of particles (e.g. as indicated by the grey trajectory) may be reflected at...

Corotating Interaction Regions CIRs

Corotating Interaction Region Cir

As discussed above, the dipole component of the Sun's magnetic field is drawn out radially and wound into a spiral at low latitudes by differential rotation. Between the opposite polarity hemispheres lies the heliospheric current sheet. At solar minimum the magnetic axis of the Sun is aligned with the rotation axis, but as the solar cycle progresses it tilts and eventually inverts. As a result of this tilt the high speed wind streams that are normally found at high latitudes can be brought down...

Louise Harra and Keith Mason

Space research is one of the most evocative and challenging fields of human endeavour. In the half-century that has elapsed since the beginning of the space age, we have been exposed to wonders beyond the imagination of even the most visionary of science fiction writers. We have peered deep into the Universe and studied physics that we can never duplicate on the Earth. We have begun to understand our own Sun, and the flow of energy outward through the Solar System that is fundamental to our...

The frozenin flux approximation

Frozen Magnetic Flux

Before looking in detail at various space plasma regimes, it is useful to recap one particular principle arising from MHD (see Chapter 9). The frozen-in flux approximation is a central tool for understanding a wide variety of space plasma applications which will be discussed in subsequent sections. We start from the MHD induction equation describing the evolution of the magnetic field in a plasma with conductivity a (a) The first term on the right hand side describes the convection of the...

Unified Quasar model

Quasars exhibit a number of observational characteristics many of which call be explianed in terms of (he 'unified' model illusfrated here. At the centre of a quasar is a supcrmassive black hole, with a mass al ieasl 1 million times thai of Sun. The luminosity ofthe quasar conies about hecausc the black hole is accreting matter from the surrounding galaxy, probably via some sort of accretion disk which is a few light days accross. X-ray emission comes from the inner part ofthe accretion disk,...

The Electromagnetic Spectrum

The quantum description of electromagnetic radiation emphasises its wave-particle duality. Thus energy is transferred in packets or quanta called photons and the energy of a photon of frequency v (Ev) is given by where h is Planck's constant, c is the velocity of light and A is the wavelength. When photons of high energy (short wavelength) are involved, the particle or photon nature of the radiation is most conveniently stressed. Alternatively, at long wavelength (low energy), the wave...

Lidia van Driel Gesztelyi

Since magnetic fields are ubiquitous in the universe, one cannot properly understand most of the physical processes in stars, planetary atmospheres, interplanetary space and galaxies without taking the effects of magnetic fields into account. Magnetohydrodynamics (MHD) is a branch of continuum mechanics, which studies the flow of electrically conducting fluid in the presence of an electromagnetic field. It is the marriage of fluid mechanics and electromagnetism, which created new physical...

Y BX BVB

It is noteworthy, however, that there is no net force along the magnetic field B. The magnitude of the plasma pressure p and magnetic pressure B2 2p0 are compared in the plasma-3 parameter, which is defined as 9.5.5 Force-free magnetic field conditions If 3 1, the pressure balance is determined by the plasma pressure distribution, and the influence of the magnetic field is negligible. However, for 3 1 the plasma pressure has virtually no influence and the slowly evolving magnetic field is...

The Solar Wind

In 1957 Chapman showed that the high thermal conductivity of the Sun's corona meant that it should extend out into interplanetary space rather than being confined near the surface like planetary atmospheres. In the following year Parker showed that in fact an inconsistency in Chapman's analysis meant that the corona actually expands outwards forming the solar wind. Thus the existence of the solar wind was predicted and Parker went on to show that the expansion was likely to have a velocity of...

Using Radar

Active radar instruments have antennas that send out pulses of microwave energy towards the Earth and detect the backscattered return pulses. Like passive microwave instruments they have the advantage of being able to observe the surface through cloud. They fall into three main types, namely scatterometers, synthetic aperture radars and radar altimeters. Scatterometers are designed to measure the radar backscatter from the surface or the atmosphere, with differences in return power...

Grazing incidence systems and multilayers

The concept of X-ray reflection at grazing incidence has already been discussed in Section 13.3.4, where we found that the value of critical angle for total external reflection depended on the X-ray wavelength A and on the atomic number (Z) of the reflector. Considering the photon-matter interaction in more detail, we find that when incoming X-rays, with energy greater than the binding energy of the outer electrons, impinge on a typical metal, they encounter a 'quasi-free' electron gas. The...

Higher energy photons EUV and Xray

A brief discussion of high energy X- and gamma-ray detection is included in Section 13.3.5 above. Here we will focus on the energy range of 0.03-10.0 keV. X-ray astronomy in particular has in the past relied on proportional counters and microchannel plates where, for Ev 1 keV, the former combined a measure of non-dispersive energy and position resolution (E AE 5 and Ax 200 m) while the latter provided no energy resolution but Ax 20 m. Proportional counters are disappearing from use while...

The solar wind and IMF

The solar wind is a supersonic flow of ionised solar plasma and an associated remnant of the solar magnetic field that pervades interplanetary space. It is a result of the huge difference in gas pressure between the solar corona and the interstellar space. This pressure difference drives the plasma outwards, despite the restraining influence of solar gravity. The existence of a solar wind was surmised in the 1950's on the basis that small variations measured in the Earth's magnetic field...

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Earth Visibility Absorption

Figure 2.3 (a) Schematic diagram of a typical near-polar LEO for remote sensing. Inclination angle i and ascending node A are shown (see text). (b) Four minutes of thermal infrared data from AVHRR in such a LEO, showing its wide swath. The satellite is travelling approximately northward across the warm (dark) Gulf Stream (bottom,) and east coast of the USA (top). The cool coastal waters and cold cloud appear light. Image from Cracknell and Hayes (1991). case the satellite is retrograde...

Radar altimetry

Radar Altimeter Footprint

The basic concept of radar altimetry is very simple. To a first approximation the height h of the satellite above the surface is given by h ct 2, where c is the speed of light and t is the round-trip time for a radar pulse to the surface at nadir and back. If the satellite orbit is accurately known (e.g. by using laser ranging from the Earth surface to the satellite), then the height of the reflecting surface can be found relative to some reference surface. The main uses for radar altimetry in...