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Atmospheric refraction depends on wind and the presence of layers of air various densities. The maximum contribution to this effect is usually made by the surface wind. Therefore, it is recommended to carry out field measurements of noise levels at a wind speed of no more than 5 m/s. It is also necessary to take into account the compass rose effect. Refraction is also affected by air temperature. In the daytime, at elevated air temperatures at the Earth’s surface and in a colder layer located above, sound wave spreads across the warm layer, reflecting upward, which reduces the noise level. At night, the opposite phenomenon occurs, resulting in increased noise. Typically this effect is noticeable at distances of up to 70 m from the road.
Due to atmospheric refraction, the Sun and Moon, when near the horizon (during sunrise or sunset), appear flattened in the vertical direction. Due to refraction, every luminary appears above the horizon even before the true exit and remains visible for some time after the true sunset.
The phenomena of atmospheric refraction make it difficult to carry out scientific research and application of a number optical methods solving technical problems.
In addition to atmospheric refraction, envelope earth's surface occurs due to diffraction of radio waves. However, in the shadow zone (beyond the horizon), the intensity of radio waves quickly drops due to losses in the underlying surface, which quickly increase with increasing frequency of the radio signal. Therefore, in long-range RNS, waves of the long-wave and ultra-long-wave ranges are used.
To provide correction for the influence of atmospheric refraction on the transmission of radio waves, models of average corrections to the refractive index have been proposed.
This phenomenon is called atmospheric refraction, and the angular displacement Af is called the refraction angle. The refraction angle Lsr is 0 for stars located at the zenith, and is maximum (Af 35) for stars located near the horizon.
Note that due to atmospheric refraction, the inclination angle that determines the direction to the stationary satellite will differ from the p value, which is determined from expression (2.6) or from Fig. 2.1, by the value of Ar. The latter depends on the atmospheric refractive index n and its change with height.
Atmospheric refraction has a significant influence on the propagation of the waves under consideration. Its effect is reduced to the curvature of the trajectories of radio waves, acquiring a curvilinear character with a convexity to the side, opposite surface land. Refraction is more pronounced the higher the content of water vapor in the air. IN recent years cases of ultra-long-range spread have been established ultrashort waves- at distances many times greater than the line of sight distance.
IN terrestrial conditions it depends on the coefficient of atmospheric refraction and especially on the conductivity of the surface along which the waves propagate.
If we take into account the so-called atmospheric refraction, the result will be even more unexpected. Refraction bends the path of rays in the air and thereby allows us to see the sunrise before its geometric appearance above the horizon. But with instantaneous propagation of light, refraction cannot occur, since refraction is caused by the difference in the speed of light in different media.
The refraction of radio waves or optical rays in the atmosphere, called atmospheric refraction, leads to a bend in the trajectory of their propagation.
It does not take into account that the apparent position of the Sun is influenced by atmospheric refraction even when the star is below the horizon. This cannot be assessed directly, since the Sun is invisible, but can be done indirectly - by the brightness of the dawn, calculated for the absence of refraction and measured in the presence of the latter.
Refraction astronomical
Refraction astronomical (atmospheric refraction) - refraction in the atmosphere of light rays from celestial bodies. Since the density of planetary atmospheres always decreases with height, the refraction of light occurs in such a way that its convexity of the curved beam is always directed towards the zenith. In this regard, refraction always “raises” the images of celestial bodies above their true position. Another visible consequence of refraction (more precisely, the difference in its values at different heights) is the flattening of the visible disk of the Sun or Moon on the horizon.
The actual position of the Sun below the horizon (yellow disk) and its apparent position (orange) during sunrise/sunset.
Refraction values
The magnitude of refraction strongly depends on the height of the observed object above the horizon and varies from 0 at the zenith to about 35 minutes of arc at the horizon. In addition, there is a dependence on atmospheric pressure and temperature: an increase in refraction value by 1% can be caused by an increase in pressure by 0.01 atm or a decrease in temperature by 3 degrees Celsius. There is also a dependence of the magnitude of refraction on the wavelength of light (atmospheric dispersion): short-wave (blue) light is refracted more strongly than long-wave (red), and at the horizon this difference reaches about 0.5 arc minutes.
The value of refraction at some altitudes (at a temperature of 10°C and a pressure of 760 mm Hg):
Thus, the refraction at the horizon is slightly greater than the apparent angular diameter of the Sun. Therefore, at the moment when it touches the horizon with the lower edge of the disk, we see it only thanks to refraction: if it were not there, the solar disk would already be entirely below the horizon. The same applies to the Moon.
Notes
Literature
Zharov V. E. 6.1. Refraction. Spherical astronomy. "Astronet" (2002). Archived from the original on October 27, 2012. Retrieved October 18, 2012.
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See what “Astronomical refraction” is in other dictionaries:
- (Refraction) the angle between the true and apparent directions to the celestial body, formed as a result of the refraction of a ray of light coming from the celestial body to the earth’s atmosphere. As a result of R.A., the apparent position of the luminaries is elevated above the horizon. The largest... ...Marine Dictionary
Refraction of light in the atmosphere [Late Lat. refractio - refraction, from lat. refractus - refracted (refringo - breaking, refracting)], an atmospheric optical phenomenon caused by the refraction of light rays in the atmosphere and manifested in the apparent... ...
astronomical refraction- Refraction of light in the atmosphere of the Earth or another planet, leading to a difference between the apparent and true directions of a celestial body. [Collection of recommended terms. Issue 79. Physical optics. Academy of Sciences of the USSR. Scientific and Technical Committee... ... Technical Translator's Guide
REFRACTION - (1) astronomical phenomenon refraction of light rays emanating from heavenly bodies when passing through the atmosphere; since the density of the atmosphere always decreases with height, the refraction of light occurs in such a way that its convexity... ... Big Polytechnic Encyclopedia
I Refraction of light in the atmosphere [Late Lat. refractio refraction, from lat. refractus refracted (refringo I break, refract)], an atmospheric optical phenomenon caused by the refraction of light rays in the atmosphere and manifested in the apparent... ... Great Soviet Encyclopedia- This term has other meanings, see Moon (meanings). Moon ... Wikipedia
It was not produced by the Russians before Peter the Great scientific works in astronomy. Peter the Great, visiting the observatories in Greenwich and Copenhagen, made his second visit to the first of them himself full definition position of Venus using the wall circle... Encyclopedic Dictionary F. Brockhaus and I.A. Efron
Atmospheric refraction
Atmospheric refraction is the deviation of light rays from a straight line as they pass through the atmosphere due to changes in air density with height. Atmospheric refraction near the Earth's surface creates mirages and can cause distant objects to appear to flicker, quiver, or appear above or below their true position. In addition, the shape of objects may be distorted - they may appear flattened or stretched. Term "refraction" The same applies to the refraction of sound.
Atmospheric refraction is the reason that astronomical objects rise above the horizon somewhat higher than they actually are. Refraction affects not only light rays but also for everything electromagnetic radiation, although in varying degrees. For example, in visible light, blue more affected by refraction than red. This can cause astronomical objects to blur into a spectrum in images with high resolution.
If possible, astronomers plan their observations when the celestial body passes the upper culmination point, when it is highest above the horizon. Also, when determining the coordinates of a ship, sailors will never use a luminary whose height is less than 20° above the horizon. If observing a star close to the horizon cannot be avoided, then the telescope can be equipped with control systems to compensate for the displacement caused by the refraction of light in the atmosphere. If dispersion is also an issue (in the case of using a broadband camera for high-resolution observations), then atmospheric refraction correction can be used (using a pair of rotating glass prisms). But since the degree of atmospheric refraction depends on temperature and pressure, as well as humidity (the amount of water vapor, which is especially important when observing in the mid-infrared region of the spectrum), the amount of effort required for successful compensation can be prohibitive.
Atmospheric refraction interferes with observations most strongly when it is not uniform, for example, in the presence of turbulence in the air. This is the reason for the twinkling of stars and the deformation of the visible shape of the sun at sunset and sunrise.
Atmospheric refraction values
Atmospheric refraction equal to zero at zenith, less than 1" (one minute of arc) at an apparent altitude of 45° above the horizon, and reaching a value of 5.3" at 10° altitude; refraction increases rapidly with decreasing altitude, reaching 9.9" at 5° altitude, 18.4" at 2° altitude, and 35.4" at the horizon (1976 Allen, 125); all values obtained at 10°C and atmospheric pressure 101.3 kPa.
At the horizon, the value of atmospheric refraction is slightly greater than the apparent diameter of the Sun. Therefore, when the full disk of the sun is visible just above the horizon, it is visible only due to refraction, since if there were no atmosphere, then not a single part of the solar disk would be visible.
According to the accepted convention, the time of sunrise and sunset is referred to as the time when the upper edge of the Sun appears or disappears above the horizon; standard value for the true height of the Sun is -50"...-34" for refraction and -16" for the half-diameter of the Sun (height celestial body usually given for the center of its disk). In the case of the Moon, additional corrections are necessary to take into account the horizontal parallax of the Moon and its apparent half-diameter, which varies depending on the distance of the Earth-Moon system.
Daily weather changes affect exact time rising and setting of the sun and moon (see the article "Refraction at the Horizon"), and for this reason it makes no sense to give the time of apparent sunset and sunrise of luminaries with an accuracy greater than a minute of arc (this is described in more detail in the book "Astronomical Algorithms", Jean Meeus, 1991, p. 103). More accurate calculations can be useful for determining day-to-day changes in sunrise and sunset times when using standard refractive index values, since it is clear that actual changes may differ due to unpredictable changes in refractive index.
Due to the fact that atmospheric refraction is 34" at the horizon, and only 29 minutes of arc at an altitude of 0.5° above the horizon, then at sunset or sunrise it appears to be flattened by about 5" (which is about 1/6 of its apparent diameter).
Calculation of atmospheric refraction
Rigorous calculation of refraction requires numerical integration using this method described in the paper by Auer and Standish Astronomical refraction: calculation for all zenith angles, 2000. Bennett (1982) in his article “Calculation of astronomical refraction for use in marine navigation” derived a simple empirical formula for determining the value of refraction depending on the apparent height of the luminaries, using the Garfinkel algorithm (1967) as a reference , If h a- this is the apparent height of the luminary in degrees, then refraction R in arc minutes will be equal to
The accuracy of the formula is up to 0.07" for altitudes from 0° to -90° (Meeus 1991, 102). Smardson (1986) derived a formula for determining refraction relative to the true height of the luminaries; if h- this is the true altitude of the luminary in degrees, then the refraction R in arc minutes will be
the formula agrees with the Bennett formula with an accuracy of 0.1". Both formulas will be correct at an atmospheric pressure of 101.0 kPa and a temperature of 10 ° C; for different pressure values R and temperature T the result of calculating refraction produced using these formulas should be multiplied by
(according to Meeus 1991, 103). Refraction increases by about 1% for every 0.9 kPa increase in pressure and decreases by about 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases by about 1% for every 3°C decrease in temperature and refraction decreases by about 1% for every 3°C increase in temperature.
Graph of refraction versus height (Bennett, 1982)
Random atmospheric effects caused by refraction
Atmospheric turbulence increases and decreases the apparent brightness of stars, making them brighter or fainter in milliseconds. The slow components of these oscillations are visible to us as flickering.
In addition, turbulence causes small random movements in the visible image of the star, and also produces rapid changes in its structure. These effects are not visible to the naked eye, but are easy to see even with a small telescope.
Atmospheric refraction is the deviation of light rays from a straight line as they pass through the atmosphere due to changes in air density with height. Atmospheric refraction near the earth's surface creates mirages and can cause distant objects to appear to flicker, quiver, or appear above or below their true position. In addition, the shape of objects may be distorted - they may appear flattened or stretched. Term "refraction" The same applies to the refraction of sound.
Atmospheric refraction is the reason that astronomical objects rise above the horizon somewhat higher than they actually are. Refraction affects not only light rays but also all electromagnetic radiation, although to varying degrees. For example, in visible light, blue is more affected by refraction than red. This can cause astronomical objects to blur into the spectrum in high-resolution images.
Whenever possible, astronomers plan their observations as they pass. heavenly body the highest point of culmination, when it is highest above the horizon. Also, when determining the coordinates of a ship, sailors will never use a luminary whose height is less than 20° above the horizon. If observing a star close to the horizon cannot be avoided, then the telescope can be equipped with control systems to compensate for the displacement caused by the refraction of light in the atmosphere. If dispersion is also an issue (in the case of using a broadband camera for high-resolution observations), then correction for light refraction in the atmosphere (using a pair of rotating glass prisms) can be used. But since the degree of atmospheric refraction depends on temperature and pressure, as well as humidity (the amount of water vapor, which is especially important when observing in the mid-infrared region of the spectrum), the amount of effort required for successful compensation can be prohibitive.
Atmospheric refraction interferes with observations most strongly when it is not uniform, for example, in the presence of turbulence in the air. This is the reason for the twinkling of stars and the deformation of the visible shape of the sun at sunset and sunrise.
Atmospheric refraction values
Atmospheric refraction equal to zero at zenith, less than 1" (one minute of arc) at an apparent altitude of 45° above the horizon, and reaching a value of 5.3" at 10° altitude; refraction increases rapidly with decreasing altitude, reaching 9.9" at 5° altitude, 18.4" at 2° altitude, and 35.4" at the horizon (1976 Allen, 125); all values obtained at 10°C and atmospheric pressure 101.3 kPa.
At the horizon, the value of atmospheric refraction is slightly greater than the apparent diameter of the Sun. Therefore, when the full disk of the sun is visible just above the horizon, it is visible only due to refraction, since if there were no atmosphere, then not a single part of the solar disk would be visible.
According to the accepted convention, the time of sunrise and sunset is referred to as the time when the upper edge of the Sun appears or disappears above the horizon; the standard value for the true height of the Sun is -50"...-34" for refraction and -16" for the half-diameter of the Sun (the height of a celestial body is usually given for the center of its disk). In the case of the Moon, additional corrections are necessary to take into account the horizontal parallax of the Moon and its apparent half-diameter, which varies depending on the distance of the Earth-Moon system.
Daily weather changes affect the exact times of sunrise and sunset of the sun and moon (), and for this reason it makes no sense to give the time of apparent sunset and sunrise of luminaries with an accuracy greater than a minute of arc (this is described in more detail in the book “Astronomical Algorithms”, Jean Meeus , 1991, p. 103). More exact calculations can be useful for determining day-to-day changes in sunrise and sunset times when using standard refractive values, since it is clear that actual changes may differ due to unpredictable changes in refractive value.
Due to the fact that atmospheric refraction is 34" at the horizon, and only 29 minutes of arc at an altitude of 0.5° above the horizon, then at sunset or sunrise it appears to be flattened by about 5" (which is about 1/6 of its apparent diameter).
Calculation of atmospheric refraction
Rigorous calculation of refraction requires numerical integration using this method described in the paper by Auer and Standish Astronomical refraction: calculation for all zenith angles, 2000. Bennett (1982), in his article “Calculation of astronomical refraction for use in marine navigation,” derived a simple empirical formula for determining the value of refraction depending on the apparent height of the luminaries, using Garfinkel’s algorithm (1967) as a reference, if h a- this is the apparent height of the luminary in degrees, then refraction R in arc minutes will be equal to
The accuracy of the formula is up to 0.07" for altitudes from 0° to -90° (Meeus 1991, 102). Smardson (1986) derived a formula for determining refraction relative to the true height of the luminaries; if h- this is the true altitude of the luminary in degrees, then the refraction R in arc minutes will be
the formula agrees with the Bennett formula with an accuracy of 0.1". Both formulas will be correct at an atmospheric pressure of 101.0 kPa and a temperature of 10 ° C; for different pressure values R and temperature T the result of calculating refraction made using these formulas should be multiplied by
(according to Meeus 1991, 103). Refraction increases by about 1% for every 0.9 kPa increase in pressure and decreases by about 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases by about 1% for every 3°C decrease in temperature and refraction decreases by about 1% for every 3°C increase in temperature.
Graph of refraction versus height (Bennett, 1982)
Random atmospheric effects caused by refraction
Atmospheric turbulence increases and decreases the apparent brightness of stars, making them brighter or fainter in milliseconds. The slow components of these oscillations are visible to us as flickering.
In addition, turbulence causes small random movements visible image star, and also produces rapid changes in its structure. These effects are not visible naked eye, but they are easy to see even with a small telescope.
Spatial inhomogeneities in refractive index values atmospheric air caused by spatial changes in it physical parameters, lead to deviations in linear propagation Sveta. This phenomenon is called refraction - the curvature of the trajectories of light rays in an inhomogeneous atmosphere. It is customary to divide refraction into a number of types: Astronomical refraction– the phenomenon of changes in the apparent position of extraterrestrial light sources relative to their true position on the celestial sphere.
Terrestrial (atmospheric) refraction - phenomena associated with a change in the apparent position of a light source (or object) located in the atmosphere when observed from the surface of the Earth or from another point in the atmosphere.
Cosmic refraction is the effect of changing the position of light sources when observed from space through earth's atmosphere. In the literature you can also find definitions of regular (normal) and random refraction. Regular refraction is due to smooth changes in atmospheric parameters and, accordingly, smooth changes in the refractive index. Random refraction is caused by relatively small-scale spatial variations in atmospheric parameters and refractive index.
These variations have different spatial scales - from centimeters to tens of meters. They are caused, for example, by turbulence in the atmosphere. Random refraction leads to good known phenomenon flickering of point light sources, for example, the twinkling of stars when observed from the surface of the Earth. Finally, let us note the phenomenon abnormal refraction - stable, long-term (up to several hours) deviations of the refractive index of air from its average value. The phenomena of refraction can be explained using the effect of light refraction at the boundaries of layers with different optical properties.
Let's consider the propagation of light from an extraterrestrial source - Fig. 4.10. Let us divide the atmosphere into several concentric layers, thin enough to be considered homogeneous, with a constant refractive index. Let us denote the refractive indices corresponding to these layers as n1, n2, n3, etc. The refractive index according to (4.1.12) is related to the air density, which decreases with height, therefore: n1< n2 < ….. Углы падения θ и преломления ψ на границе двух соседних слоев связаны законом Снеллиуса
From triangle 1O2, according to theorem of sines,
Where are the distances from points 1 and 2 to point O (the center of the Earth). Likewise for triangles 2O3, etc.
Multiplying the equalities in pairs we get 
Thus, at any point of the ray trajectory the relation is satisfied
where r is the distance to the center of the Earth, n (r) is the refractive index of air, θ is the zenith angle of the light beam. Equation (4.5.3) is the equation for the trajectory of a light ray in the atmosphere or the refraction equation. The constant in (4.5.3) is obviously equal to r 0 n sin θ 0 , where r 0 is the distance from the center of the Earth to upper limit atmosphere (where n≡1), θ 0 – angle of incidence of the beam on the upper boundary.
Astronomical refraction leads to the fact that all extraterrestrial light sources - the Sun, planets, stars - appear to be raised above the horizon by a certain angle. Important characteristic is the angle of astronomical refraction β - the angle between the true S and visible S" directions to the light source. The maximum angles of astronomical refraction are achieved at the moments of sunrise and sunset and at small negative altitude angles. Under average atmospheric conditions they reach values of 35", but at low temperatures And high blood pressure near the earth's surface, changes in the refractive index of air can become significant and the angles of refraction increase to 2–3 degrees. Due to this phenomenon, the length of the day (daylight hours) increases. At high latitudes, this increase can reach hours and days. Thus, at the pole, the duration of polar days (when the Sun does not set below the horizon) is 14 days longer than the duration of the polar night.
Rays of light from ground objects also spread across curvilinear trajectories. The angle of terrestrial refraction is the angle between the directions to the apparent and actual position of an object. The values of this angle depend on the distance to the observed object and the thermal stratification of the surface layer of air. Depending on the nature of the vertical temperature gradient (and, consequently, air density), which, according to (4.1.12), determines the gradient of the refractive index, rising and expanding or lowering and narrowing can occur in the surface layer of the atmosphere visible horizon. The consequence of this effect is an increase (with expansion) or decrease (with narrowing) of the geometric range of visibility of objects.
The development of space methods for measuring atmospheric parameters has made it relevant to consider refractive phenomena when observing extraterrestrial sources through the atmosphere from space. An important effect cosmic refraction is the refractive elongation of a beam element. At low altitudes of radiation propagation in the atmosphere, the refractive elongation can reach 5−15%, which must be taken into account when solving various atmospheric optical problems. When observing through the atmosphere of the disk of the Sun or the Moon, a change in the angle of refraction with the height of the beam leads to refractive divergence - a change in the angle between the rays emanating from different edges of the disk. This change can be quite significant if the observation point is sufficiently distant ( spacecraft) from the perigees of rays propagating through the atmosphere. In this case, the atmosphere can act as a scattering lens, which leads to a visible decrease in the brightness of the disk of the Sun (Moon). This is the phenomenon of refractive attenuation. The opposite situations of refractive enhancement are also possible, when the atmosphere acts as a collecting lens, reducing the angular dimensions of the Sun (Moon). These phenomena are especially strong when observed through the lower layers of the atmosphere.
Various distortions of the images of the Sun and Moon can occur there, including even their “breaks”. When observing the radiation of point sources (stars) during observations from space, which is caused by random variations in the refractive index of the atmosphere.
Various optical phenomena observed in the atmosphere have simple physical justifications. Twilight is understood as the entire complex of optical phenomena occurring in the atmosphere when the Sun rises or sets below the horizon. The lower the Sun is on the horizon, the more strongly it illuminates the upper, therefore less dense, layers of the atmosphere, therefore the weaker the scattered radiation reaching the surface. This is the reason for the smooth transition from day to night on Earth. If you look at the globe from space, it will appear to be surrounded by a wide strip of twilight penumbra, invariably covering from 20 to 25% of the earth's surface, depending on the state of the atmosphere. On one side of it, on 42–45% of the area globe, day reigns, on the other side 33–35% of the earth's surface is immersed in night. In the tropics, where the Sun descends steeper to the horizon, this time is shorter - about 10–15%, while at high latitudes it increases to 30–40% of the duration of the year, and in the polar regions in spring and autumn periods continuous twilight - white nights - last for weeks. Rainbow occurs when scattered sun rays on large drops rain.
For example, violet rays (0.40 µm) are more refracted than green rays (0.55 µm), and green rays are more refracted than red rays (0.76 µm).
Refractive index transparent optical environment, also called the refractive index, shows how many times the phase speed of light is less than the speed of light in a vacuum.
Complex The refractive index is used to quantify not only the phase change per unit length, but also (via its imaginary part) the optical gain or propagation loss (eg due to absorption).
The complex refractive index has the following physical interpretation:
A) real part complex refractive index determines the speed of light propagation in a dielectric
b) the imaginary part of the complex refractive index is responsible for the absorption of light in the medium.
In a standard atmosphere, the refractive index changes with height according to a linear law, and in a real atmosphere, the change in N with height on average occurs according to an exponential law.
The refractive index of the troposphere does not depend on frequency for waves more than 1 cm. For millimeter waves, losses have a significant effect, which is taken into account by introducing a complex dielectric constant air.
In practice, the value is more often used N = (n - 1) ×10 6, called the tropospheric refractive index, where n»Öe- refractive index of the troposphere.
On average N changes linearly with height, and for middle latitudes the gradient of change N with altitude in the standard troposphere is dN/dh = -40 1/km
IN real conditions There is often an irregular change in meteorological parameters, which leads to a complex relationship N from height.
Daily changes in the refractive index of the atmosphere are most significant in the lower kilometer layer and can reach 10 – 15N units. They are also due to the large daily variation in air temperature and humidity. Random fluctuations of the refractive index are associated with atmospheric turbulence and can reach a value of 10N - units.
Distortions of the Sun's disk at sunrise and sunset
Due to the refraction of the sun's rays at sunrise and sunset, several more optical phenomena occur. First of all, during sunrise and sunset, the shape of the solar disk is distorted. The usually round disk of the Sun, when approaching the horizon, flattens in the vertical direction, taking the shape of an egg with a horizontal long axis (Fig. 10.2). The flattening of the Sun is explained by the fact that its lower edge, touching the horizon, experiences stronger refraction than its upper edge, which is located at a height of 32" above the horizon, since the angular diameter of the Sun is 32". At in good condition atmosphere, the lower edge is raised by refraction by 35", and the upper edge by only 28". As a result, the solar disk is flattened by 7". At lower temperatures near the Earth's surface, for example, during winter anticyclones in Siberia or in the polar regions of the globe, the angle of refraction increases and the flattening of the solar disk can be more severe.
Let us emphasize the peculiarity of visual observation in comparison with photographing and obtaining television images. In good lighting (daytime) and sufficient angular dimensions observed objects (at least 20-30"), the threshold of contrast sensitivity of the human eye, as already mentioned, is equal to 2%, and sometimes even 1%; the thresholds of contrast sensitivity (i.e., the minimum resolved brightness contrasts) of photographic and television images are equal to 10, respectively -15 and 15-25%. Since the atmosphere makes its “mite” in reducing existing contrasts, especially between clouds and the Earth’s surface, the minimum contrast values necessary to confidently distinguish details on the Earth’s surface should be for visual observations and photography. and television images are at least doubled, i.e. must be at least 4, 30 and 50% respectively. Imagine how much better the human eye is at distinguishing the features and details of observed objects compared to photographs and television images! With the eye you can see what is not yet available to either photography or television images.
According to all astronauts, the visual picture of the earth's surface from space differs significantly from photographs and television images, primarily in its clarity. In photographs of the Earth's surface and cloud covers, there is always a veil or “mesh,” which is partly due to illumination by hard radiation present in space. The television image is weakened, in particular, by the atmosphere through which it must pass.
All astronauts easily recognized continents and oceans by their characteristic outlines. On the oceans they saw the movement of waves, swells, in deserts - sand dunes. They detected differences in the transparency of the atmosphere over certain areas of the earth's surface, cloud shapes, cyclones, thunderstorms and many other features of land, ocean and atmosphere. From a station altitude of 250-300 km, when looking down, objects 1-2 km in size, and sometimes smaller, about 500 m, are clearly visible.
2. Radio refraction
Radio refraction is the curvature of the trajectory of electromagnetic waves as they propagate in the atmosphere. The density of the real atmosphere decreases with height, so a radio beam directed upward from the earth's surface will move from the region with great value density in areas with low density values. If electromagnetic beam will propagate in a plane-layered atmosphere in which the refractive index changes gradually, a smooth curvature of the beam trajectory will occur. The radius of curvature will be determined by the magnitude of the refractive index gradient in accordance with the expression:
,(16)
where dn/dH is the gradient of the refractive index.
Of practical interest is the case of critical refraction, when the radius of curvature of a radio beam directed along the earth's surface is equal to the radius of the earth and the beam bends around the globe. The condition for critical refraction will be:
Normal radio refraction corresponds to refraction in a normal (standard) atmosphere having a refractive index gradient of –4·10-8 1/m. Radio refraction with refractive index gradient values from 0 to –4·10-8 1/m is called positive reduced refraction. Radio refraction at – 15.7·10-8 – 4·10-8 1/m is called positive increased refraction. At a gradient value = – 15.7·10-8 1/m, critical refraction is observed. When the refractive index gradient is less than – 15.7·10-8 1/m, overrefraction occurs. Beam curvature radius less than radius the globe, as a result of which the beam experiences multiple reflections from the earth's surface.
The movement of the atmosphere is, as a rule, turbulent, and consists of a set of disordered “vortices” various sizes and speeds. The largest vortices are formed as a result of instability of the main flow (their sizes L0 are comparable to the dimensions of the flow), when the Reynolds number Re=Vav⋅L0/ν is greater than the critical Recr, where Vav is the speed of the main flow, and ν is the kinematic viscosity. In turn, these vortices, due to their large number Reynolds, are destroyed and generate second-order, smaller disturbances. In this case, energy is transferred from disturbances larger size to smaller disturbances. The generation of vortices of smaller and smaller sizes l stops when the Reynolds number Re=V⋅l/ν of disturbances decreases to the critical number Recr, where V is the speed of movement of vortices of size l. Disturbances of minimal size are stable and do not decay further, and their energy is spent on overcoming friction forces and directly turns into heat.
In the case of stable stratification in the turbulence spectrum there is a transition of turbulence energy into potential energy stratification as a result of the work of vortices against Archimedean force sustainable stratification.
Unstable stratification leads to an increase in turbulence energy in a certain frequency range.
The existence of temperature inversion layers, as well as layers with a sharp drop in temperature, is accompanied by an increased value of turbulent energy.
Compared to propagation in a homogeneous atmosphere, in a heterogeneous atmosphere appear additional sources radiation, the intensity of which is completely determined by the primary field. Electromagnetic waves, which have experienced scattering by moving inhomogeneities of the refractive index, carry information about integral parameters air movements in the atmosphere.
As is known, the maximum attenuation of radio waves in rain is observed in the MM wavelength range. The attenuation is due to two mechanisms: absorption of wave energy in the volume of a raindrop and diffraction scattering of radiation from the droplet into external space.
Calculations of the attenuation and scattering coefficients of radio waves in rain show that the attenuation of millimeter waves in rain in equally is due to both the absorption of wave energy in the volume of drops and the diffraction scattering of the incident wave on drops, and this relationship (between absorption and scattering) practically does not depend on either the wavelength (in the IMF range), or on the intensity of the rain, or on the spectrum of droplet sizes .
In the SM wave range, on the contrary, attenuation is determined mainly by absorption, and the role of scattering decreases with increasing wavelength, with decreasing rain intensity and depends on the type of droplet size distribution.
Tropospheric refraction is one of the main sources of errors in GLONASS/GPS measurements. Phase speed wave front in the troposphere, the refractive index of which is greater than unity, is less than the speed of light in vacuum, as a result of which the “electromagnetic” length of the emitted electromagnetic signal of the NES becomes longer than the “geometric” one. Tropospheric refraction introduces an error in the pseudo-range measurement of the order of 2.0 - 2.5 m in the zenith direction and increases approximately with the cosecant of the elevation angle and can reach a value of 20 - 28 m at an elevation angle of the satellite satellite above the horizon of 5°. Therefore, to achieve acceptable accuracy of pseudo-range measurement by code and carrier phase, it is necessary to take into account and eliminate the influence of the troposphere in all types of measurements using GLONASS/GPS SRNS.
The troposphere is a non-dispersive medium, that is, the refractive index and the speed of propagation of the electromagnetic signal in the troposphere do not depend on the frequency of the electromagnetic signal, as a result of which tropospheric refraction does not depend on the carrier frequency, is not excluded by a combination of measurements at frequencies L1, L2 and equally affects the measurement of pseudorange and by code, and by carrier phase.
The dry atmosphere contributes approximately 90% of the total tropospheric refraction and can be modeled to within 0.05 m using surface pressure and temperature. Various models dry atmosphere are based on laws ideal gases; these models use spherical layers as the troposphere decomposition for the dry layer. The wet component is much more difficult to model, since water vapor cannot be accurately predicted and modeled. Even with normal conditions conditions of the troposphere there are limited sources of water vapor, often in the form liquid water. Therefore these water sources The vapor, along with turbulence in the lower atmosphere, causes variations in water vapor concentrations that cannot be correlated across time or space. These variations cannot be accurately predicted from surface measurements from Earth. Fortunately, the "wet" contribution is approximately equal to 10% of the total tropospheric refraction. Despite the variability of water vapor, there is a way to model it by creating an exponential vertical profile. The height of the wet layer is approximately 12 km. The wet delay is approximately 5 - 30 cm.
Through simulation, the average square error The definition of pseudorange is reduced to 2 - 5 cm. The combined models for dry and wet layers together predict the delay caused by the troposphere.
Radio signals, when propagating in the atmosphere, experience obstacles, as a result of which they are delayed and reach the Earth (the receiver) a little later. It is easy to say that the path of radio signals is determined by the formula:
S=∫cdt=∫c/vds=∫s(n) ds (5.1)
where S – electromagnetic range (pseudo-range), m; ds – elementary electromagnetic range, m; c – speed of light in vacuum, m/s; v – group speed of propagation of radio waves in the medium, m/s; n – refractive index. This electromagnetic range or pseudo-range is always greater than the geometric range.
The total delay of radio signals in the atmosphere consists of: ionospheric, tropospheric, time scale shift, systematic error And random error.
The reason for the delay of radio signals is that the atmosphere consists of layers with different physical characteristics Therefore, refraction of radio waves occurs all the time. From formula (5.1) it is clear that the electromagnetic range depends on the refractive index.
The tropospheric delay of radio signals is of greatest interest to meteorologists because it gives new opportunity obtaining information about the moisture content of the atmosphere. This chapter covers theoretical foundations and the use of radio signals received from GNSS satellites in the task remote sensing water vapor, as well as the possibility of implementing a new method of measuring water vapor using a network of GNSS receivers for the purpose of data assimilation into hydrodynamic forecast systems.
The following expression is true for the atmosphere:
where N is the refractive index in N-units; Nd is the refractive index in N-units for dry air; Nv is the refractive index in N-units for water vapor.
The refractive index in N-units for dry air can be calculated using the formula:
Nd=k1⋅P d /(T⋅Zd) (5.7)
where k1 is a certain coefficient, equal to 7.76·10 -1 K/Pa; P d – dry air pressure, Pa; T – dry air temperature, K; Zd is the compressibility factor of dry air.
The refractive index in N-units for water vapor can be calculated using the formula: Nv= ⋅Zv −1 (5.8)
where k2 is a certain coefficient, equal to 7.04·10 -1 K/Pa; k3 – a certain coefficient, equal to 3.776 10 -1 K 2 /Pa; e – partial pressure of water vapor, Pa; T – air temperature, K; Zd −1 – water vapor compressibility factor.
The compressibility factors of dry air and water vapor can be calculated from the following empirical formulas:
Zd −1 =1+Pd⋅
Zv −1 =1+e⋅⋅[−2.37321⋅10 −3 +2.23366T −1 −710.92T −2 +7.75141⋅10 4 T −3 ]
It is known that for any gas the following equality holds:
Pi=Zi⋅ri⋅Ri⋅Ti (5.11)
where Pi is the pressure of the i-th gas, Pa; Zi is the compressibility factor of the i-th gas; ri – density of the i-th gas, kg/m3; Ri – gas constant of the i-th gas, J/kg K; Ti – temperature of the i-th gas, K.
Vertical hydrostatic delay of radio signals shows how long radio signals are delayed in a vertical column of dry atmospheric air
From the description of the vertical wet delay of radio signals (5.34) it is clear that it is necessary to determine the average weighted temperature using the formula It is not difficult to understand that the average “weighted” temperature has a regional character, that is, it will be different for different regions. The average weighted temperature is obtained experimentally, namely, using radio sounding data and is expressed as follows: T m =a t +b t ⋅T 0 (5.43)
The vertical wet delay of radio signals is determined by the moisture content of water vapor in the atmosphere Therefore, the accuracy of its determination depends on the accuracy of determining the wet part of the radio signal delay. We discussed in Chapter 4 that the wet delay is only 10% of the tropospheric delay, and determining the hydrostatic delay of radio signals plays a large role in the accuracy of the wet delay. Figure 5.6 shows the contribution of each component of the total tropospheric delay. It can be seen that there is predominantly a hydrostatic delay, which mainly depends on pressure. It's not hard for us to see that maximum values wet delay corresponds to the maxima of the difference between the tropospheric and hydrostatic delays, which are clearly visible to us from Figure 5.7. The maximum wet delay of radio signals is over 14 cm, and the minimum is about 2 cm.
Having analyzed Figures 5.9, 5.10 and 5.11, we can say that the wet delay in to a greater extent depends on atmospheric pressure and partial pressure of water vapor, since the hydrostatic delay is determined mainly by surface pressure; therefore, the dependence of the wet delay on surface pressure is inverse.
From the analyzes performed, we can come to the conclusion that the method of remote sensing of water vapor using navigation receivers allows one to determine with good accuracy the integral amount of water vapor in the atmosphere. Therefore, it is of great practical importance, since knowledge of the integral amount of water vapor will be included in the quality of the initial data of hydrodynamic models, which clarifies the forecasts. This method is quick and has many advantages over other methods. This lies in the economic significance, in the simple implementation of water vapor measurement. And most importantly, it allows you to determine the integral amount of water vapor with a shorter time interval
