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Equation (1.4.3) can be considered as an integral equation with respect to wa(£), where Planck's function BX[T(^)] is the core of Equation (1.4.2). Because of this the determination of the vertical distribution of specific humidity q(£) reduces to the simultaneous recovery of profiles wA(c) and T(c) according to measurements of emission in water vapour and C02 absorption bands, and to the subsequent transfer from wA(£) to q(c). Such a problem, as well as the problem of determination of the vertical temperature distribution, is ill-posed in the sense mentioned above. The difference is that instead of a solution for one integral equation, one has to solve a system of integral equations, which requires the additional use of a priori information about the structure of the humidity field in the atmosphere (say, an approximation of the vertical profile of humidity by some analytical expression). Next, because q(£) and wA(£) are related to each other by q(E) = (ps/g)_1 even small errors in the determination of wA(£) can result in serious distortions of the profile q(£). This last-mentioned fact places heavy demands when choosing the transmission function whose accuracy of definition leaves much to be desired because of the influence of aerosol attenuation on the emission transfer in the IR-range.

The obstacle can be overcome if we do not recover the profile q(£), but, instead, use the empirical dependence between the integral humidity content of the atmosphere and the specific humidity in the surface layer obtained, for example, from radiosonde measurements. The fact that such dependence really exists can be judged by the following arguments. It is known that the vertical distribution of specific humidity in the atmosphere is sufficiently well described by the relationship q/qs = where k is an empirical constant. Integrating this relationship over £ within the whole thickness of the atmosphere and using the definition of the integral water vapour content WK, we have qs = (k + l)(ps/f)~1 w\- The linear relationship between qs and WK is confirmed by data from radiosonde measurements at island stations and on ocean weather ships. According to Liu (1983) the standard deviation is only 0.78 g/kg.

It should be emphasized that in the presence of clouds satellite measurements of emission in the IR-range determine profiles and vvA(c) only in the atmosphere above the clouds, and that in such a situation there is only one recourse: to start measuring Ix in the microwave range. The procedure for reconstruction of qs remains the same: first the vertical profile of the temperature and integral water vapour content of the atmosphere are calculated from measurement data in C02 and water vapour absorption bands; next, using the relationship qs = (k + l)(Ps/0)_1 WK, one can find qs. Comparison of qs values obtained from three-monthly series of SEASAT

microwave measurements of Ix and from standard ship measurements in the Western North Atlantic, which provide better ship measurement data than do other parts of the ocean, show (see Liu, 1983) that the systematic error and root-mean-square error of satellite measurements of specific humidity in the surface atmospheric layer amount to 0.48 and 0.97 g/kg respectively.

Wind velocity

Depending on the type of usable satellite information one can single out the following five methods of determination of wind velocity:

1. by cloud motion;

2. by the brightness and dimensions of patches of sunlight;

3. by the reflected radiation in the microwave band;

4. by the echoes from short-pulse radiolocation signals;

5. by inverse scattering of electromagnetic waves in the centimetric band.

The first method basically reduces to the acquisition of tele- and photo images of fields of cloud, determination of velocity of cloud displacement and wind velocity at a fixed level in the surface layer. This procedure is used at present. Cloud fields serve as the initial information, and these are registered twice per day by a system of geostationary satellites (two American satellites of the GOES series, one European and one Japanese) located along the equator in such a way that the fields of view of cameras mounted on them cover 80% of the ocean area in the tropics.

The disadvantages of this method include, firstly, the fixation of the level of cloud displacement (cumulus clouds in the tropics are assumed to be transported by the wind at the base of the clouds) and, secondly, the necessity of prescribing the vertical shear of wind velocity in the subcloud layer. This last fact suggests a correlative relationship between wind velocities at the base of the cloud and in the surface layer. Considering that such a relationship is not invariable in space and time, then perhaps because of it, or in addition to it, the discrepancies between satellite estimates and data from ground-based observations turn out to be quite large and, according to Wylie and Hinton (1983), amount to ±2.1 m/s for velocity and +25° for wind direction.

The second method is based on the following simple considerations. If the ocean surface is smooth, then sunbeams are reflected from it at the identical angle so that a patch of sunlight remains small and sharply outlined (contrasting). In contrast, in the presence of waves, sunbeams are reflected from the ocean surface at different angles. This produces scattering of reflected light and, therefore, an increase in patches of sunlight and a decrease in their visibility. Further, because waves are the result of wind forcing, the existence of a relationship between the size and visibility of a patch of sunlight, on the one hand, and wind velocity, on the other, as well as between the shape of the patch of sunlight and wind direction, should not give rise to doubts. Thus, if such a relationship is set, and satellite images of the ocean surface are available, wind velocity and direction can be considered as known. For obvious reasons this method can be used only during the daytime and in the presence of sparse cloud. Its accuracy of estimation of wind velocity is ± 2.0 m/s; the accuracy of determination of wind direction is so low that this is not worth indicating.

We have already discussed the fact that the emission intensity in the microwave spectral range is controlled by the sea surface temperature, the vertical distribution of temperature, humidity and aerosols in the atmosphere, and the emissivity of the ocean. In its turn, the emissivity of the ocean depends on the state of the ocean surface and, hence, on wind velocity. This last fact, having been an obstacle in satellite indication of temperature acquires a new quality, being a prerequisite of the third (radiometric) method of wind velocity determination.

Its use presupposes that the extraneous effects created in this case by the vertical distribution of atmospheric parameters are excluded, and that the dependence between the ocean emission in the wavelength range of ~ 3 cm (here the emission is most sensitive to the state of the ocean surface) and wind velocity is known. The first condition is fulfilled by the simultaneous measurement of the emission intensity in various parts of the microwave band, and for this purpose a multichannel microwave radiometer is used; the second condition is fulfilled by taking account of a specific empirical relationship. Accuracy in determination of wind velocity by this method is ±1.9 m/s; wind direction cannot be estimated.

The fourth and fifth methods of determination of wind velocity are based on the use of active location of the ocean surface, and on registration of backward scattering of electromagnetic oscillations, presenting a combination of mirror reflection and so-called Bragg scattering. The meaning of the mirror reflection is obvious. As for the Bragg scattering, this needs to be explained.

With the above in mind we consider the propagation of a plane wave in a periodical structure, that is, in a structure where properties change in space according to a periodic law.

In the one-dimensional case the equation describing the propagation of a plane wave has the form where u is the surface elevation or current velocity; c is the phase velocity of the wave featuring properties of the environment; x is the spatial coordinate; t is time.

Assume that the environment has a periodic inhomogeneity along the direction of wave propagation, that is, c2 = Cq( 1 — ju cos Kx), where c0 is the phase wave velocity in the absence of inhomogeneity; K is the wave number of inhomogeneity defined by the distance between its neighbouring elements; fx « 1 is a small parameter (inhomogeneity is considered to be small).

Let us find the solution to Equation (1.4.4) in the form of u = A(x) exp(icoi), where co is the wave frequency. Then amplitude A must obey the equation

dx where k = co/c0 is the wave number of the plane wave in question.

We represent A as an expansion in powers of the small parameter /i and restrict ourselves to the first two terms of the expansion. We treat co similarly, thereby assuming that wave propagation in an inhomogeneous environment can be accompanied by dispersion. In other words we present A and co in the form

from which, and from the definition of k2, the equality follows:

Here we have ignored terms containing the ¡i parameter to powers higher than

Substituting (1.4.6) and (1.4.7) into (1.4.5) and gathering members containing parameter /i to powers of zero and one we find

The solution of Equation (1.4.8) has the form

A0 = Cx exp(ifc0x) + C2 exp( —i/c0x). (1.4.10) Its substitution in (1.4.9) yields

—+ koAx = —koCiftk! exp(i/c0x) + ^o exp[i(K + /c0)x]

+ 2^0 exp[ —i(K — /c0)x]} — k0C2{2k1 exp( —ik0x)

+ jk0 exp[ —i(K + fc0)x] + |fc0exp[i(X - k0)x]}. (1.4.11)

Let us define two possibilities: non-resonance (K 2k0) and resonance (K = 2k0) wave scattering by environmental inhomogeneities. In the first case the solution of Equation (1.4.11) is written in the form

A1 — cx exp(i/c0x) + c2 exp( — ik0x) + ik1x[C1 exp(ik0x) — C2 exp( —i/c0x)] k20

+ ^ expC-i^ - k0)x] + C2 exp[i(K - k0)x]}. (1.4.12)

As can be seen, there is a term on the right-hand side of (1.4.12) which increases linearly with x. Since we are interested only in waves with restricted amplitudes this term has to be set to zero; this is equivalent to = 0. Thus at K ^ 2k0 wave propagation in an inhomogeneous environment is not accompanied by a change in frequency (co = c0k0). But if K = 2k0 then Equation (1.4.11) will take the form

+ k%AX = -ko^iQ + y C^j exp(ik0x) - fco^Cj + y C, x exp(—ik0x) — y [C1 exp(3i/c0x) + C2 exp( — 3ifc0x)]. (1.4.13)

Its integration also results in the appearance of terms which increase linearly with x. For the solution to remain restricted it is necessary that the factors (2k1C1 + (k0/2)C2) and (2k1C2 + (/cq^Cj) before exp(±ik0x) become zero. In other words, it is necessary to demand that

These equalities form a system of algebraic equations with reference to Cl and C2. It has a non-trivial solution if k0/2 k0/2 2k!

Thus at K = 2k0 the frequency of wave propagation in an inhomogeneous environment is determined by the expression

This suggests that the dependence co = co(k0) at k0 = K/2 breaks and hence there is a forbidden frequency band of width A co = (n/2 )c0k0 such that waves belonging to it are quickly attenuated. This means that at K = 2k0 the incident wave is effectively reflected from inhomogeneities of the environment and its energy is transmitted to the wave propagating backward. The ratio K = 2k0 is called the condition of Bragg scattering. In the general case of an arbitrary incidence angle 6 calculated from the nadir, this condition is rewritten in the form K = 2k0 sin 9.

From the above discussion we draw the following conclusion: if the wavelength of wind waves is much greater than that of the signal, or if the angle of incidence of a radiated signal is close to zero the mirror reflection will dominate over the Bragg scattering; on the other hand, if wavelengths are comparable, or for oblique irradiation (at large angles of incidence), the Bragg scattering will dominate over the mirror reflection. In the fourth method of wind velocity determination (in this case registration of backward scattering is by a radiolocating altimeter) the first circumstance is realized; in the fifth method when a scatterometer is used the second circumstance is realized.

The intensity of backward scattering is characterized by an effective scattering cross-section a, defined as the ratio of backward scattering intensity to density of irradiation flux. The effective scattering cross-section has the dimensions of area. Dividing a by the geometrical area of the irradiated spot and designating the normalized effective backward scattering cross-section as <7°, we have that <r° has to be a function of the signal incidence, of the azimuthal angle k (the angle between the beam and wind direction), and of wind velocity wa in the surface atmospheric layer inducing the appearance of sea surface inhomogeneities (wind waves). When using altimeter measurements of a° from a subsatellite point the dependence a° = a0(6, k, ua) reduces to the form a = c°(wa). This facilitates the determination of ua but excludes the possibility of estimating wind direction. Scatterometric measurements of <7° are free from this disadvantage. The accuracy of determination of wind velocity and direction amounts to ±1.3m/s and ±16° in this case; the accuracy of altimeter measurements is ± 1.6 m/s (see Wylie and Hinton, 1983).

Net radiation flux at the upper atmospheric boundary This flux is not measured from a satellite. Only its separate components are registered: incident and reflected short-wave solar radiation, and long-wave emission of the atmosphere-underlying surface system into outer space (so-called outgoing emission). Recording of the first components is performed using a pyrheliometer and a spectrobolometer having the same sensitivity for different wavelengths from the short-wave spectrum range, and recording of the second and third components is performed using flat wide-angle and scanning narrow-angle radiometers (the scanning is performed along or across a satellite trajectory).

Flat wide-angle and scanning narrow-angle radiometers provide different information. Radiometers of the first kind measure upward radiation coming from the lower half-space. Therefore, their spatial resolution seems to depend only on the height of the satellite. Actually, not all parts of the visible disc of the Earth contribute equally to the formation of the field of upward radiation; the main contribution is from the vicinity of a subsatellite point. Therefore, the spatial resolution of a flat wide-angle radiometer at the altitude of a satellite orbit, about 600 km, will amount to ~ 10° or ~ 1000 km. Such spatial resolution allows us to gain information on the global distribution of the characteristics based on a minimum amount of data, but at the same time it makes for strong smoothing of the data.

On the other hand, a scanning narrow-angle radiometer measures the upward radiation coming from the lower half-space with a small but finite solid angle. Accordingly, its spatial resolution turns out to be thinner and varies in the range from 50 km in the nadir to 110 km at an angle of 40° from the nadir. But it should be remembered that the radiation recorded by such a radiometer does not meet all angular distributions but, rather, only some of them and, hence, it depends on zenithal and azimuthal angles of the satellite (in the case of short-wave radiation), and on the zenithal angle on the Sun. Because of this the use of scanning narrow-angle radiometers should provide for the assignment of some procedure correcting measurement data in order to take anisotropy (dependence on direction of propagation) of radiation into account. The last circumstance will inevitably entail the introduction of errors.

The current accuracy of satellite estimates of monthly averaged net radiation flux at the upper atmospheric boundary, according to Stephens et al. (1981), is of the order of 10 W/m2, that is, it is approximately equivalent to 3% accuracy in determining the solar constant.

Net radiation flux at the underlying surface Of all the components of net radiation flux, only the long-wave emission of the underlying surface can be measured directly. Other components are estimated using indirect methods. Let us discuss these methods, paying particular attention to their physical prerequisites. We start with the shortwave solar radiation flux assimilated by the underlying surface.

Its determination using data from satellite measurements is based on a number of assumptions and a priori information on the transmission functions of clouds and the atmosphere. One can distinguish two groups of methods. The distinctive feature of the first of them is the presetting of an empirical relation between data from satellite and ground-based measurements of the reflected solar radiation in the visible and near-IR-ranges. The distinctive feature of the second method is the interpretation of satellite measurement data in terms of the characteristics of reflection, absorption and scattering, appearing in the transfer equations for short-wave radiation, followed by the use of the values of these characteristics when integrating the transfer equations.

Both groups of methods have their own disadvantages. The disadvantages of the first group are the strong dependence on accuracy of calibration of the satellite data from ground-based measurements. Therefore, if the calibration relates to short time intervals then its application to other longer periods, strictly speaking, is not well founded. The disadvantages of the second group of methods relate to the restriction in application of transfer equations for the case of monochromatic radiation and, hence, the necessity of integrating over wavelengths and allowing for horizontal inhomogeneity of the characteristics of reflection, absorption and scattering of solar radiation. The relative error of the available methods of determination of short-wave solar radiation flux from satellite measurement data amounts to 10-15% for daily averaged values and 5-10% for monthly averaged values (see The Report of the Joint Scientific Committee, 1987). By the way, such large errors result not only from the reasons mentioned above but also from inadequate comparison: a satellite radiometer and ground pyranometer have different viewing areas.

The downward long-wave radiation flux consists of emission created by water vapour, other gases (including C02) active in terms of radiation, and also aerosols and cloud. To consider the dependence between the downward flux of long-wave emission and its determining parameters it is necessary to have at least some information about them; information which more often than not is unavailable. In particular, the altitude of the cloud base, under which the downward emission is formed, is not identified by satellite data. The only thing which can be reconstructed by their use is the height of the cloud top and the cloud type. But a problem arises in determining the height of the base, and changing from geometric to optical cloud thickness, or in general in refusing to use the height of the cloud base as the dependent variable. It is clear that in both cases one cannot do without additional assumptions and, hence, this means further deterioration in the quality of satellite information. According to The Report of the Joint Scientific Committee (1987), the root-mean-square error in determination of the downward flux of long-wave radiation from satellite measurement data amounts to at least 10-15 W/m2; in addition, very large deviations from ground-based measurement data will occur when the height of the cloud base undergoes strong variability.

Eddy fluxes of momentum, heat and moisture at the ocean-atmosphere interface These fluxes, like some components of net radiation flux, cannot be measured directly with the help of satellites. So there is only one recourse: to apply aerodynamic formulae connecting eddy fluxes with marine surface atmospheric layer parameters (temperature, humidity and wind velocity) determined by satellite measurement data. But one should not be under any illusion as to the simplicity and perfect nature of this tool, as explained below.

Meteorological and geophysical satellites functioning at present, and those planned for the future, have either solar-synchronous, precessing or geostationary orbits. Each of them is compiled with its own frequency of information-gathering. Solar-synchronous satellites receive information twice a day at the equator, always at the same local solar time and more often at high latitudes. This excludes the possibility of filtering out daily variations in the examined characteristics, especially where the measurements are obtained by one satellite. Information from precessing satellites is obtained at different times of the day, but it may not cover polar latitudes. Finally, geostationary satellites provide continuous information over time but only within the limits of the restricted part of the equatorial zone whose size depends on the scanning area of the measuring equipment.

Let us recall now that the density of measurements controls the possibility of reconstructing the spatial structure, and their time sampling controls the accuracy of monthly averaged local values of eddy fluxes. To provide support for these statements we refer to the results of the calculation of uncertainty in estimates of monthly averaged sensible and latent heat fluxes received from JASIN data in the North Sea and illustrated in Figure 1.5. In this diagram deviations of monthly averaged fluxes from their 'true' values corresponding to hourly sampling are plotted along the ordinate axis, and the sample interval of measurements in hours is plotted along the abscissa axis. As can be seen for 12-hour sampling an error in estimating latent heat amounts to ±2 W/m2, or about 10% of its 'true' value (21 W/m2). The same relative error in the determination of the monthly averaged sensible heat flux is obtained for three-hour sampling. In other words, 12-hour sampling turns out to be sufficient for more or less reliable estimation of latent heat flux but not of sensible heat flux.

Next, if measurements of one or other characteristic are taken using the same device the spatial correlation of measurement errors will be high. This entails a decrease in the amount of independent information, which leads to uncertainty in errors of interpolation and to distortions of the time-space variability of the characteristics examined.

These considerations should be kept in mind when estimating the possibilities of using satellite information. It should also be borne in mind that the specific cost of satellite information (cost of one observation) is not large as compared with the cost of conventional ships' measurements. For

Stick Man Assassinate
Figure 1.5 Uncertainty in estimating the monthly mean sensible and latent heat fluxes due to sampling at increased intervals as compared to hourly sampling, according to Taylor (1986): upper curve - latent heat flux; lower curve - sensible heat flux.

example, according to WMO data, the maintenance costs of one ocean weather ship, not counting other expenses, amounted to about half a million US dollars per year in the mid-1970s; this is not much less than the maintenance costs for one satellite including the costs of its equipment, launch and centres for receiving and processing the satellite information. But the operation of one satellite equals that of many ocean weather ships, so from the point of view of economy the advisability of using satellite information leaves no room for doubt. However, it is necessary not only to increase the accuracy of satellite information but also to interpret it in the correct way. Results achieved to date are encouraging.

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