Monthly Archives: May 2014

Description of the Ionospheric Layers

Sounder Measurement Method. In any discussion of the ionospheric electron density distribution, it is important to recognize that many experimental methods have been used to arrive at our current understand­ing. The major ones include ground-based vertical-incidence sounding (VIS), topside sounding using satellite platforms, incoherent backscatter radar, the Faraday rotation and signal delay of satellite signals, and in situ measurements using rocket probes and satellites. The VIS method, which employs the high-frequency (HF) band, was the earliest method and has provided the most comprehensive picture of the lower ionosphere and its worldwide distribution. The ionospheric D layer is an exception, and special methods are needed to determine the electron densities in that region. Much of the current nomenclature involving ionospheric structure and phenomena is a carryover from early VIS investigations. As a consequence we shall briefly examine the VIS method. For a discussion of other methods, the reader is referred to Hunsucker (10).

The plasma frequency associated with an electron gas, f p (a natural resonant frequency), is proportional to the square root of the electron density of the gas:

where f p is in hertz and Ne is in electrons per cubic meter.

It may be shown that a radio wave, propagating vertically upward into the ionosphere, will penetrate the region until it reaches a point at which the sounding frequency matches the plasma frequency. All frequencies less than this value will be reflected back to ground. An ionospheric sounder is essentially a radar, which maps out the height-dependent ionospheric electron concentration versus transmission frequency, where the probing frequency is typically a stepwise increasing function of time. A plot of signal echo time delay versus transmission frequency is called an ionogram. A typical ionogram and the corresponding ionospheric profile are given in Figure 6. If Nmax is the maximum electron density of a layer, then we define a so-called critical frequency of reflection, fc, which is the maximum plasma frequency within the layer. If the sounder transmission frequency exceeds f c, then the signal is not reflected and penetrates the layer. There are as many critical frequencies in the ionosphere as there are layers or regions. A more complete treatment of the theory of radio propagation in the ionosphere shows that a magnetoionic medium supports two modes of propagation, the ordinary (O mode) and the extraordinary (X mode). These modes encounter slightly different indices of refraction and thus travel with slightly different velocities and directions. As a consequence, each ionogram consists of two traces, corresponding to O – and X-mode echoes. These traces may be closely aligned over a large portion of their respective propagation bands but can depart significantly at their respective critical frequencies, with the X mode supporting somewhat higher-frequency signal reflections. By convention, the O-mode trace is used for conversion of ionogram critical frequencies into maximum electron densities. The following convenient

Fig. 6. Typical vertical-incidence ionosonde recording (i. e., ionogram) and the corresponding plasma frequency profile fp(h). The electron density profile is related to the plasma frequency profile by the Eq. 9 in the text. [This ionogram was derived from U. S. Government web site (http://www. ngdc. noaa. gov/stp/), and the instrument was developed by University of Massachusetts-Lowell for the U. S. Air Force.]

expression is used:

where fO is the ordinary-ray critical frequency (MHz) and Nmax is the maximum electron density of the given layer (e/m3). Equation (10) is equivalent to Eq. (9).

From a historical perspective, it is interesting to note that the concept of radar detection of aircraft derived from the early work of ionospheric specialists who were already using ionospheric sounders as a means to detect ionospheric layers.

The D Region. The D region is responsible for most of the absorption encountered by HF signals, which exploit the sky-wave mode. In most instances, D-region absorption is a primary factor in the determination of the lowest frequency, which is useful for communication over a fixed sky-wave circuit. In addition, the D region supports long-wave propagation at very low frequency (VLF) and low frequency (LF), and the medium is exploited in certain legacy navigation systems and strategic low-rate communication systems. The sounder method as described in the previous section is not useful for measurement of the D region, since the elec­tron densities are relatively low. Details of D-region electron concentration are sketchy in comparison with information available about the E and F regions, principally because of the difficulty in making diagnostic measurements. Moreover, analysis is hampered because many photochemical processes with poorly defined reaction rates take place in the D region. Over 100 reactions have been compiled.

Table 1 shows that the D region lies between 70 km and 90 km. In fact, the upper and lower levels are not precisely defined. It is evident that more than one source of ionization gives rise to the D-region electron density distribution. Sources include solar radiation at the upper levels and galactic cosmic rays at lower levels. In addition, relatively rare polar-cap absorption (PCA) events are characterized by highly energetic solar protons that provide an additional source for ionization of the lower D region within the polar cap. Some investigators place the lower boundary of the D region at 50 km to allow for the contribution of galactic cosmic rays in the neighborhood of 50 km to 70 km. This altitude regime, termed the C region, is not produced by solar radiation. It exhibits different characteristics from the region between 70 km and 90 km. Specifically, a minimum in electron concentration is observed during solar-maximum conditions for the lower portion (viz., region C), while the reverse is true in the upper portion (viz., region D). This can be explained if we assume that the galactic cosmic rays are partly diverted from the earth by an increase in the interplanetary magnetic field (IMF), which occurs during solar maximum conditions.

The E Region. In an (a) Chapman layer for which photochemical equilibrium has been established, the following equation represents the electron density distribution as a function of reduced height г:

where a is the recombination coefficient, x is the solar zenith angle, and q0 is the maximum production rate in the layer. Recall that a is the recombination coefficient (see the section “The Continuity Equation and Equilibrium Processes” above). The quantity q0/a is dependent upon the sunspot number and is specific to the region involved, in this case the E region. The maximum rate of electron production q0 occurs only for the overhead sun. However, it may be shown that actual maxima for other zenith angles are simply related by this expression:

It may be shown that the ordinary-ray critical frequency for the E region, which is directly related to the E-region maximum electron density through Eq. (10), may be found from Eq. (11), and is given by

where к is a constant of proportionality, which is dependent upon the sunspot number. The exponent n tends to a value 0.25 for long-term seasonal behavior, and in compliance with Chapman theory, but some workers have found that a value for n « 0.3 better represents the diurnal dependence. The constant of proportionality к ranges between about 3 MHz and 4 MHz, bearing in mind that Eq. (13) represents a climatological median value.

The solar-activity dependence of the ratio of peak production to the effective loss (recombination) coeffi­cient has been studied by a number of workers, and the results enable values of foE to be deduced. There have also been direct measurements of foE using vertical incidence sounders. While there is some variability to be considered, it is possible to develop a relationship connecting the median value of foE, the solar zenith angle, and the 12-month running-mean sunspot number. A generally accepted candidate for the daytime E-region critical frequency is

foE = 3.31(1 + 0.008fi12) cos /]025 MHz (14)

where R12 is the running 12-month sunspot number, which may range between roughly 10 and 150.

Equation (14) provides excellent agreement with observation during the daytime, but alternative ex­pressions are found to be more appropriate during the nighttime hours (3). Moreover, it has been found that

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Fig. 7. (a) Depiction of the local-time (LST) and latitude dependence of foE for solar-maximum conditions in summer [from Davies (1)](b) Contours of foE at Fort Belvoir, Virginia, in 1958 (solar maximum), showing seasonal variations. The contours are in megahertz.

Eq. (14) is inaccurate in the very high latitudes, where other means of electron production become important, invalidating the Chapman hypothesis. Internationally adopted relations for monthly median foE are due to Muggleton (18); and an alternative relation, specific to the European region, has been published (15).

Figure 7(a) contains an E-region critical-frequency map for summer solstice conditions in 1958, a period of high solar activity (i. e., R12 large). The contours are representative of median conditions as a function of

geographic latitude and local time. It is seen that the E-region critical frequencies (and consequently the electron densities) are vanishingly small in regions devoid ofsolar illumination. This summer solstice behavior is consistent with Eq. (14), and other seasons have been shown to behave in conformance with (cos x)0 25 as well.

Figure 7(b) shows the monthly variation of foE for one station (Ft. Belvoir, Virginia) for the year 1958. The solar control is obvious in the median data plotted.

The F1 Region. The F1 region is not unlike the E region in the sense that it obeys many of the predictions of Chapman theory. We look for a relation for the ordinary-ray critical frequency that is formally similar to Eq. (13). A relation patterned after Chapman principles may be expressed as

Like the E region, the F1 region exhibits more complicated behavior than that expressed by such a simple formula. Specifically, it has been found that the geomagnetic latitude tends to exhibit some control over the F1-region electron densities. The function fs in Eq. (15) depends upon sunspot number and magnetic latitude. It is also observed that the F1 region disappears (i. e., merges with the F2 region) at values of the solar zenith angle exceeding a certain maximum that itself depends upon both the sunspot number and the geomagnetic latitude. The Radio Sector of the International Telecommunications Union (ITU-R, previously the CCIR) has developed a method for computing foF1 taking all these factors into account (18). The internationally adopted monthly median foF1 formulation is based on the work of Ducharme et al. (19). The relation due to Davies (3) gives a convenient but approximate expression for the F1-layer critical frequency:

Figure 8 shows the solar-zenith-angle control of foF1 under sunspot maximum and minimum conditions.

The height of the F1 ledge, hF1, is taken to be between 180 km and 210 km. From Chapman theory we anticipate that hF1 will be lower in summer than in winter and will be higher at midlatitudes than at low latitudes. Unfortunately, the reverse is true. Explanations for this behavior may be found in a detailed study of scale-height gradients, a nonvanishing movement term (as expressed in the continuity equation), or gradients in upper atmospheric chemistry.

The F2 Region. The F2 region is the most prominent layer in the ionosphere, and this significance arises as a result of its height (it is the highest of all the component layers) and of course its dominant electron density. It is also characterized by large ensembles of irregularity scales {AL} and temporal variations {AT}. The F2 region is a vast zone, which eludes prediction on the microscale (A L < 1 km) and mesoscale (1 km < AL < 1000 km) levels, and even provides challenges to forecasters for global and macroscale (AL > 1000 km) variations. This is largely because of the elusive transport term in the continuity equation. There are also a host of so-called anomalous variations to consider, and these are the subjects of a succeeding section.

As in the E and F1 regions, we may conveniently specify the behavior of the F2 region in terms of equivalent plasma frequency rather than the electron density. For the peak of ionization we have

where foF2 is the ordinary-ray critical frequency.

While foF2 exhibits solar-zenith-angle, sunspot-number, and geomagnetic-latitude dependences, simple algebraic algorithms do not characterize these relationships. As a consequence, mapping methods are used to describe the F2 region electron density patterns.

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Fig. 8. Depiction of the local-time and latitudinal variation of foF1 for two different solar activity conditions: (a) solar minimum, June 1954; (b) solar maximum, June 1958. The contours are in megahertz. [From Jursa (8).]

The CCIR published its CCIR Atlas of Ionospheric Characteristics, which includes global maps of F2-layer properties for sunspot numbers of 0 and 100, for every month, and for every even hour of Universal Time (20). Figure 9 is an illustration of the global distribution of foF2 for a sunspot number of 100. Such maps are derived from coefficients based upon data obtained from a number of ionosonde stations for the years 1954-1958 as well as for the year 1964. This set of coefficients is sometimes identified by an ITS prefix, but is known more

Fig. 9. Map of foF2 showing the worldwide distribution under the following conditions: 15 November, Sunspot Number = 135, Time = 0000 UTC. The countours of foF2 are developed using the URSI set of ionospheric coefficients. Curves similar to this are found in the Atlas of Global Ionospheric Coefficients (20). [By permission, Radio Propagation Services, November 2000.]

generally as the CCIR coefficients. Because of the paucity of data over oceanic areas, a method for improving the basic set of coefficients by adding theoretically derived data points was developed. As a result, a new set of coefficients has been sanctioned by International Union of Radio Science (URSI), and this is termed the URSI coefficient set. Many communication prediction codes, which require ionospheric submodels, allow selection of either set of ionospheric coefficients.

Anomalous Features of the Ionospheric F Region. The F2 layer of the ionosphere is probably the most important region for many radio-wave systems. Unfortunately, the F2 layer exhibits the greatest degree of unpredictable variability because of the transport term in the continuity equation. As indicated previously, this term represents the influences of ionospheric winds, diffusion, and dynamical forces. The Chapman description for ionospheric behavior depends critically upon the unimportance of the transport function. Consequently, many of the attractive, and intuitive, features of the Chapman model are not observed in the F2 region. The differences between actual observations and predictions derived on the basis of a hypothetical Chapman description have been termed anomalies. In many instances, this non-Chapman-like behavior is not anomalous at all, but rather typical.

The following list represents the major forms of anomalous behavior in the F2 layer: diurnal, Appleton, December, winter, and the F-region trough. A few comments are provided for each major form.

The Diurnal Anomaly. The diurnal anomaly refers to the situation in which the maximum value of ionization in the F2 layer occurs at a time other than at local noon as predicted by Chapman theory. On a statistical basis, the actual maximum occurs typically in the temporal neighborhood of 1300 to 1500 LMT. Furthermore, there is a semidiurnal component that produces secondary maxima at approximately 1000 to 1100 LMT and 2200 to 2300 LMT. Two daytime maxima are sometimes observed (one near 1000 and the other near 1400), and these may cause the appearance of a minimum at local noon. This feature, when observed, is called the midday biteout.

Appleton Anomaly. This feature is symmetric about the geomagnetic equator and goes by a number of other names, including the geographic anomaly, the geomagnetic anomaly, and the equatorial anomaly. The Appleton anomaly is associated with the significant departure in the latitudinal distribution of the maximum electron concentration within 20° to 30° on either side of the geomagnetic equator. Early in the morning a single ionization peak is observed over the magnetic equator. However, after a few hours the equatorial F region is characterized by two distinct crests of ionization that increase in electron density as they migrate poleward. This phenomenon is described as an equatorial fountain initiated by an E x B plasma drift (termed a Hall drift), where E is the equatorial electrojet electric field and B is the geomagnetic field vector. This drift is upwards during the day, since the equatorial electric field E is eastward at that time. As the electrojet decays, the displaced plasma is now subject to downward diffusion when the atmosphere begins to cool. This diffusion is constrained along paths parallel to B, which map to either side of the geomagnetic equator. The poleward extent of the anomaly crests is increased if the initial Hall-drift amplitude is large. This anomalous behavior accounts for the valley in the parameter foF2 (with peaks on either side) seen at the geomagnetic equator in Figure 9. There are significant day-to-day, seasonal, and solar-controlled variations in the onset, magnitude, and position of the anomaly. There are also asymmetries in the anomaly crest position and electron density. Asymmetries in the electron density in the anomaly crests appear to be the result of thermospheric winds that blow across the equator from the subsolar point. The effect of magnetic activity on the anomaly is to constrain the electron density and latitudinal separation of the crests. Magnetic activity is monitored worldwide, and the quasilogarithmic index Kp is used to represent the level of worldwide activity (21). When Kp> 5 (on a scale from 0 to 9), the anomaly disappears.

The December Anomaly. This term refers to the fact that the electron density at the F2 peak over the entire earth is 20% higher in December than in June, even though the solar-flux change due to earth eccentricity is only 5% (with the maximum in January).

The Winter (Seasonal) Anomaly. This is the effect in which the noontime peak electron densities are higher in the winter than in the summer despite the fact that solar zenith angle is smaller in the summer than it is in the winter. This effect is modulated by the 11-year solar cycle and virtually disappears at solar minimum.

The F-Region (High-Latitude) Trough. This is representative of a number of anomalous features that are associated with various circumpolar phenomena, including particle precipitation, the auroral arc formations, etc. The high-latitude trough is a depression in ionization, occurring mainly in the nighttime sector, and it is most evident in the upper F region (22). It extends from 2° to 10° equatorward of the auroral oval, an annular region of enhanced ionization associated with optical aurora (see the section “The High-Latitude Ionosphere”). The trough region is associated with a mapping of the plasmapause onto the ionosphere along geomagnetic field lines (see Fig. 17). The low electron density within the trough results from a lack of replenishment through candidate processes such as antisunward drift, particle precipitation, or the storage effect of closed field lines. The latitudinal boundaries of the trough may be sharp, especially the poleward boundary with the auroral oval. A model of the trough is due to Halcrow and Nisbet (23).

Irregularities in the Ionosphere. In addition to the various anomalous features, irregularities in the electron density distribution may be observed throughout the ionosphere. The size, intensity, and location of these irregular formations are dependent upon a number of factors, including geographical area, season, time of day, and levels of solar and magnetic activity. The traveling ionospheric disturbance (TID; see the subsection “Short-Term Variations” and the section “Ionospheric Predictions” below) belongs to a special class of irregular formations that are generally associated with significant changes in the electron density (more than a few percent) over large distances (> 10 km). The remaining irregularities, loosely termed ionospheric inhomo­geneities, typically develop as the result of ionospheric instability processes and are not directly associated
with TIDs. On the other hand, TIDs have been shown to be a possible catalyst in the formation of ionospheric inhomogeneities, especially in the vicinity of the Appleton anomaly. Relatively small-scale ionospheric inho­mogeneities are important, since they are responsible for the rapid fading (scintillation) of radio signals from satellite communication and navigation systems. Such effects may introduce performance degradations or outages on systems operating at frequencies between 100 MHz and several gigahertz. Models of radiowave scintillation have been developed, and these are based upon a basic understanding of the global morphology of ionospheric inhomogeneities.

There are inhomogeneities in all regions of the ionosphere, but the equatorial and high-latitude regions are the most significant sources. Hunsucker and Greenwald (24) have reviewed irregularities in the high-latitude ionosphere, and Aarons (25) has examined the equatorial environment.

Equatorial inhomogeneities tend to develop following sunset and may persist throughout the evening, but with decreased intensity after local midnight. The irregularities are thought to be the result of an instability brought about by a dramatic change in F-region height at the magnetic equator following sunset. The scale lengths of the irregularities may range between roughly a meter and several kilometers, and the spectrum of the irregularities has been observed to exhibit a power-law distribution. There is a tendency for the irregularities to be field-aligned with an axial ratio of roughly 20 to 1. In addition, the irregularities are organized in distended patches. Though the situation is variable, the patch sizes range between ~100 km and several thousand kilometers in the upper F region, and average ~100 km in the lower F region. The equatorial irregularities tend to be more intense and widespread at the equinoxes and at solar maximum, but magnetic activity tends to suppress the growth of the irregularities.

High-latitude irregularities exist within the polar cap and the auroral zone, with the latter being primarily associated with the bottomside F region. The high-latitude F region is quite variable, and unlike midlatitudes, it may have an electron density less than the E-region during nocturnal hours. In the wintertime, structured auroral arcs may migrate within the polar cap, and the electron density enhancements within these formations may be several orders of magnitude greater than the normal background, especially during elevated solar activity. During disturbed geomagnetic conditions, structured electron density patches have been observed to travel across the polar cap in the antisunward direction. These irregularities may have a significant effect on communication systems. For both the auroral zone and the polar cap, increased geomagnetic activity has a dramatic influence on the growth of irregular ionospheric formations. Moreover, for large and sustained values of Kp, it has been observed that the high-latitude irregularity patterns tend to migrate equatorward, replacing the background midlatitude properties (see the section “The High-Latitude Ionosphere”).

Blood Gas Monitoring

Blood gas always means the oxygen and carbon dioxide con­tents of the blood. Because most of the oxygen in the blood exists in combination with hemoglobin, the oxygen content of the blood can be expressed in terms of the ratio of the amount of oxyhemoglobin to that of total hemoglobin; this ratio is called the oxygen saturation. A small amount of oxygen, usu­ally less than 1%, remains in the plasma as dissolved oxygen, and its amount is expressed in terms of oxygen partial pres­sure. Although there is a relationship between oxygen satura­tion and oxygen partial pressure, this relationship is nonlin­ear so that saturation increases steeply with increasing oxygen partial pressure when the latter lies in the range 20 to 40 mm Hg (2.7 to 5.3 kPa), but tends to saturate when the oxygen partial pressure reaches above 60 mm Hg (8 kPa). In normal arterial blood, oxygen saturation is above 98%, and oxygen partial pressure is approximately 100 mm Hg (13.3 kPa). The main purpose of monitoring oxygen level is to con­firm the oxygen transport which sustains metabolic demand.

Carbon dioxide is highly soluble in body fluids, and it is also converted, reversibly, to bicarbonate ions. Therefore, blood plasma as well as interstitial fluids have an apparently large storage capacity for carbon dioxide. However, changes in the carbon dioxide content of the body fluids causes a change in the acid-base balance of those body fluids, which is expressed by pH. Thus, it is important to maintain an ade­quate carbon dioxide level in the body fluids. It is therefore monitored by measuring the partial pressure of carbon diox­ide of arterial blood.

Blood gas levels can be measured by taking a blood sample and analyzing it using a blood gas analyzer which provides information about the partial pressures of oxygen and carbon dioxide, and about the pH of the blood. However, in a patient whose respiration is unstable, blood gas values may fluctuate so that frequent measurement is required, and hence continu­ous blood gas monitoring is preferred.

Arterial blood oxygen saturation can be monitored nonin – vasively using a pulse oximeter (15). Due to the difference in the spectral absorption of oxyhemoglobin and reduced hemo­globin, the oxygen saturation of a particular blood sample can be determined by absorption measurements at two wave­lengths, typically in a red band between 600 nm and 750 nm and in an infrared band between 850 nm and 1000 nm. How­ever, the tissue in vivo contains both arterial and venous blood, and hence light absorption occurs by both components. To obtain the arterial component selectively, the pulsatile component is extracted. As shown in Fig. 6(a), light absorp­tion is usually measured in a finger. Two light-emitting di­odes of different wavelengths, for example 660 nm and 910 nm, are operated alternately, and the transmitted light is de­tected by a photocell. The pulsatile components of both wave­lengths are then extracted by a bandpass filter. Arterial oxy­gen saturation is determined from the ratio of these two components.

Although the pulse oximeter is reliable enough and has been used successfully for patient monitoring in most cases, measurement sites of the transmittance measurement are limited, and thus a reflection-type pulse oximeter in which

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backscattered light is measured has been developed (16). In back-scattered light measurement, a difficulty arises due to the fact that the optical pathlength may vary when absorp­tion is varied, although it is not changed as much in transmis­sion measurement. In principle, this difficulty can be solved by using more than three wavelengths, however, a reflection – type pulse oximeter with comparable performance to the transmission-type oximeter has not yet been developed. In some applications, the reflection-type oximeter is highly ap­preciated. For example, it is applied to fetal monitoring dur­ing labor in which the sensor is applied to the skin of the fetal head (17).

The oxygen content in arterial blood can also be measured continuously and noninvasively with the aid of a transcutane – ous oxygen electrode (18,19). The configuration of the probe is shown in Fig. 6(b). The principle employed is that of polaro – graphic measurement, by which current drains proportionally to the amount of oxygen that reaches the cathode by diffusion through the oxygen permeable membrane. Because the oxy­gen flux is determined by the gradient in oxygen partial pres­sure at the membrane, and the oxygen partial pressure at the electrode surface is reduced to zero by the electrode reaction; the current that results from the oxygen flux depends upon the oxygen partial pressure on the outside of the membrane. When the probe is used for measuring arterial oxygen partial pressure, the electrode body is heated to approximately 42 or 43 °C. At this temperature, arteriovenous shunts in the skin tissue fully open, thus allowing large amounts of blood to flow through the tissue, far more than is required nutritionally, so that the venous blood has almost the same oxygen content as that of the arterial blood. Consequently, the oxygen partial pressure in the tissue reaches almost the same level as that of the arterial blood, and thus the arterial oxygen partial pressure can be measured transcutaneously.

Both the pulse oximeter and the transcutaneous oxygen electrode can be used for monitoring blood oxygenation; how­ever, each method has advantages and disadvantages. The pulse oximeter is safe, easy to use, inexpensive, and sensitive at lower partial pressures. However, for higher oxygen partial pressure where oxygen saturation is almost 100%, a pulse oxi­meter can not detect any change in oxygen partial pressure. Higher oxygen partial pressures may occur during, for exam­ple, oxygen therapy. In such a condition, oxygen partial pres­sure may vary in wider range, and thus a transcutaneous oxy­gen electrode can be a good monitor of gas exchange in the lung.

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Carbon dioxide partial pressure in the blood can also be measured transcutaneously using a heated carbon dioxide electrode, similar to the transcutaneous oxygen electrode. The carbon dioxide electrode consists of a pH electrode covered with a carbon dioxide permeable membrane (20). This type of electrode has been used for neonatal monitoring. The com­bined oxygen and carbon dioxide electrode which consists of a transcutaneous carbon dioxide electrode and a transcutane – ous oxygen electrode is also available (21).

The Continuity Equation and Equilibrium Processes

The equation that expresses the time rate of change of electron concentration, Ne, is the continuity equation:

where Ne is the electron density, L(Ne) is the loss rate, which is dependent upon the electron density, div stands for the vector divergence operator, and V is the electron drift velocity.

The divergence of the vector in Eq. 6 is the transport term, sometimes conveniently called the movement term. The continuity equation says that the time derivative of the electron density within a unit volume is equal to the number of electrons that are generated within the volume (through photoionization processes) minus the number that are lost (through chemical recombination or attachment processes), and finally adjusted for those electrons that exit or enter the volume (as expressed by the transport term). To first order, the only derivatives of importance in the divergence term are in the vertical direction, since horizontal Ne gradients are generally smaller than vertical ones. In addition, there is a tendency for horizontal velocities to be small in comparison with vertical drift velocities. Consequently, we may replace div (Ne V) by (d/dh) (Ne Vh), where Vh is the scalar

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Fig. 5. Curve illustrating the rate of electron production as a function of reduced height (h — h0) and for selected values of the solar zenith angle. [From Davies (1).]

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i? k=q-L(Ne)-^-(NcVh) at dh


Table 2: Types of Equilibrium Processes Photochemical equilibrium (production balanced by loss):

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L(Ne) < —(NeVh) ___________________ dh

Now let us look at some special cases. If Vh = 0 (no movement), then the time variation in electron concentration is controlled by a competition between production q and loss L. At nighttime, we may take q = 0, and this results in

In principle, there are two mechanisms to explain electron loss: attachment of electrons to neutral atoms (in the upper ionosphere), and recombination of electrons with positive ions (in the lower ionosphere). The attachment process is proportional to Ne alone, while recombination depends upon Ne with Nj, where N is the number of ions. Attachment involves radiative processes and has an extremely low cross section (probability of occurrence). We may ignore it in many practical situations and take recombination as the major source for electron loss. Since Ne = Ni, the recombination process obeys the equation L = a ■ Ne2, where a is the recombination coefficient. Recombination is very rapid in the D and E regions, the process being accomplished in a time on the order of seconds to minutes. Attachment, the electron loss process for the upper ionosphere, has a time constant on the order of hours. This is the primary reason that the ionosphere does not entirely disappear overnight. Another reason is that there exists a second source of electrons associated with the plasmasphere. This reservoir of ionization is built up during the daytime through vertical drift, but bleeds into the ionosphere during nocturnal hours.

In the vicinity of local noon, dNJdt = 0 and we may analyze the quasiequilibrium conditions suggested by Eq. (7) when the left-hand side of the equation equals 0. The two main types of equilibrium processes are given in Table 2.

The equilibrium processes identified in Table 2 are the dominant possibilities during daytime when photoionization is significant. During nocturnal hours, equilibrium is seldom achieved at F-region heights, although it is approached in the period before sunrise.

While the continuity equation appears quite simple, the generic terms (i. e., production, loss, and transport) represent a host of complex photochemical and electrodynamic processes, which exhibit global variations and are influenced by nonstationary boundary conditions within the atmosphere and the overlying magnetosphere. Notwithstanding these complications, the equation provides a remarkably clear view of the basic processes that account for ionospheric behavior. In fact, the relative contributions of terms in the continuity equation will account for the majority of the anomalous ionospheric properties; that is, those ionospheric variations that depart from a Chapman-like characteristic. This is especially true for the F2 layer, within which the movement term attains paramount status. In the E and F1 regions, where the movement term is small compared with production and loss (through recombination), photochemical equilibrium exists in the neighborhood of midday. All of this has had a significant bearing on the development of ionospheric models and prediction methods.

Indeed, as it relates to the F region of the ionosphere, it may be said that the existence of a nonvanishing divergence term in the continuity equation has been the primary impetus for the development of statistical modeling approaches. Nevertheless, efforts to account for all terms in the continuity equation through physical modeling are ongoing.

The underlying assumptions used by Chapman in his theory of layer production are in substantial disagreement with observation. The Chapman layer was based upon an isothermal atmosphere, and it is well known that the atmosphere has a scale height, kT/mg, which varies with height. Moreover, the basic theory assumes a monochromatic source for photoionization and a single constituent gas. Corrections and extensions to the early Chapman theory have led to better agreement with observation, and to this day the Chapman layer provides a fundamental baseline for ionospheric profile modeling.

Respiratory Monitoring

Respiratory monitoring involves monitoring of ventilation and respiratory gases. While ventilation of the lung can be as­sessed by observing movements of the thorax, it can be mea­sured quantitatively by either gas flow in the airway or vol­ume changes of the lung. During anesthesia or under artificial ventilation where the patient is intubated, gas flow in the airway can be monitored by inserting a flowmeter be­tween the endotracheal tube and the breathing circuit. Many different types of flowmeters such as a rotameter, pneumota­chograph, hot-wire anemometer, ultrasound flowmeter, and vortex flowmeter have been used. Most of them provide in­stantaneous gas flow rates. Tidal volume can be obtained by integrating the flow rate for the inspiratory or expiratory phase. Under artificial ventilation using a volume-limit type of mechanical ventilator, tidal volume is determined simply by presetting the ventilator.

Spontaneous breathing in unintubated patients can be monitored by the respiratory motion of the thorax and abdo­men. A simple method of monitoring such motion is to mea­sure the circumferential length or cross-sectional area of the thorax and abdomen. A flexible belt containing a zigzag-fash­ioned wire can be used as a transducer. When it is attached to the thorax or abdomen so as to form a single-turn coil, its inductance changes with respiratory motion, and tidal volume can be obtained with considerable accuracy (11). A commer­cial model of this type is currently available (Respitrace, AMI Inc., Sedona, Arizona).

Lung volume change can also be monitored by measuring the electrical impedance across the thorax (12). Impedance is measured by placing electrodes at both sides of the thorax, applying an ac current, and detecting the voltage that devel­ops between the electrodes. Although thoracic impedance de­pends largely upon electrode position, the size and shape of the body, and body fluid distribution, it can be a quantitative monitor of lung volume changes when it is calibrated ade­quately using a spirometer.

Respiratory gas is also a common parameter that is used for patient monitoring; monitoring the level of carbon dioxide in expired air is especially important during anesthesia and in intensive care where artificial ventilation is performed. In physiological conditions, the carbon dioxide content in the body fluids, particularly in the arterial blood, is always main­tained within a narrow range by the regulatory mechanism of respiration, but it may vary largely under artificial ventila­tion when the setting of the ventilator is inadequate. The ar­terial carbon dioxide partial pressure is related to the carbon dioxide content in expired air and especially to the value at the end of the expiratory phase. Carbon dioxide in the expired air can be monitored beat-by-beat by a carbon dioxide ana­lyzer, called a capnometer, in which carbon dioxide content is measured by infrared absorption (13). There are two types of capnometer: the side-stream capnometer and the mainstream capnometer. In the side-stream capnometer, the sensor is lo­cated in the main unit, and a small amount of gas flow branched from the patient’s airways is pumped continuously to it through a fine tubing. In the mainstream capnometer, a cuvette with an infrared source and a detector is inserted be­tween the endotracheal tube and the breathing circuit as shown in Fig. 5. Although the mainstream capnometer has the advantage of no time delay, it has disadvantages, such as the condensation of water vapor to the window and loading a weight to the connector.

The mass spectrometer has also been used for continuous respiratory gas monitoring (14). It can be used to analyze many gasses simultaneously, not only physiological gasses such as oxygen, carbon dioxide, and nitrogen but also anes­thetic gas such as nitrous oxide, halothane, enflurane, and isoflurane. In addition, many patients can be monitored with the aid of a mass spectrometer by using an inlet select unit. In fact, a single mass spectrometer system is capable of ser-

IR source

vicing up to sixteen patients (Lifewatch Monitor, Perkin-El – mer Co., Pomona, California).

Multisensor Fusion (8,14,15)

Research has been conducted on multisensor fusion for target recognition. Some of the motivating factors of such research are increased target illumination, increased coverage, and increased information for recognition. Significant improvement in target recognition performance has been reported (8) when multiple radar sources are utilized using sensor fusion approaches. Tenney and Sandell (14) developed a theory for obtaining the distributed Bayesian decision rules. Chair and Varshney (15) presented an optimal fusion structure given that

Multisensor Fusion (8,14,15)

Fig. 8. A typical data fusion approach for target recognition. [Adapted from Heuter et al. (8)].

detectors are independently designed. The target recognition using multiple sensors is formulated as a two – stage decision problem in Ref. 8. A typical radar target recognition approach using data fusion is illustrated in Fig. 8. After the prescreening, single-source classifications are performed first; then the fusion of decision are performed.

The data fusion problem is treated as an m-hypothesis problem with individual source decisions being the observations. The decision rule for m-hypothesis is written as

Decide wi if g1 (u) > gj(u) for all j ф і і 30 j

For Bayes’ rule, gi(u) is a posterior probability. That is,

Since the prior probability and the distribution of features cannot be estimated accurately, a heuristic function is used (8). It is a direct extension of Bayesian approach introduced by Varshney (16), and the function gi(-) is generalized to include the full threshold range:

where P0 and P1 are prior probabilities; ^1 and are the sets of all i such that {gi(u) > Ti} and {gi(u) < Ti}, respectively, with Ti being the individual source threshold for partitioning decision regions; and the proba­bilities Pfi and Pdi are false alarm rates and probabilities of detections of each local sensor. The probabilities Pf i and Pdi are defined by the cumulative distribution functions (CDF) for each decision statistic. In practice, the CDFs are quantized and estimated from training on the individual sensor’s classifier error probabilities. In a distributed scenario, the weighting can be computed at each sensor and transmitted to the fusion center, where they will be summed and compared to the decision threshold. In 8, the data fusion approach is applied to multiple polarimetric channels of a SAR image, and substantially improved classification performance is reported.

Summary

In radar target recognition, different types of radar are employed for different applications. In this article, radar target recognition approaches for different radar systems are discussed.

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering Copyright © 1999 John Wiley & Sons, Inc.