The height of the sun above the earth. The height of the sun above the horizon: change and measurement

a) For an observer at the north pole of the Earth ( j = + 90°) non-setting luminaries are those with d-- i?? 0, and non-ascending are those with d--< 0.

Table 1. Altitude of the midday Sun at different latitudes

The Sun has a positive declination from March 21 to September 23, and a negative declination from September 23 to March 21. Consequently, at the north pole of the Earth, the Sun is a non-setting luminary for approximately half the year, and a non-rising luminary for half the year. Around March 21, the Sun here appears above the horizon (rises) and, due to the daily rotation of the celestial sphere, describes curves close to a circle and almost parallel to the horizon, rising higher and higher every day. In a day summer solstice(around June 22) The sun reaches maximum height h max = + 23° 27 " . After this, the Sun begins to approach the horizon, its height gradually decreases, and after the autumn equinox (after September 23) it disappears under the horizon (sets). The day, which lasted six months, ends and the night begins, which also lasts six months. The sun, continuing to describe curves almost parallel to the horizon, but below it, sinks lower and lower, on the day winter solstice(around December 22) it will drop below the horizon to a height h min = - 23° 27 " , and then will begin to approach the horizon again, its height will increase, and before the spring equinox the Sun will again appear above the horizon. For an observer at the Earth's south pole ( j= - 90°) the daily movement of the Sun occurs in a similar way. Only here the Sun rises on September 23, and sets after March 21, and therefore when it is night at the North Pole of the Earth, it is day at the South Pole, and vice versa.

b) For an observer at the Arctic Circle ( j= + 66° 33 " ) non-setting luminaries are those with d--i + 23° 27 " , and non-ascending - with d < - 23° 27". Consequently, in the Arctic Circle the Sun does not set on the summer solstice (at midnight the center of the Sun only touches the horizon at the north point N) and does not rise on the day of the winter solstice (at noon the center of the solar disk will only touch the horizon at the point south S, and then drops below the horizon again). On the remaining days of the year, the Sun rises and sets at this latitude. Moreover, it reaches its maximum height at noon on the day of the summer solstice ( h max = + 46° 54"), and on the day of the winter solstice its midday height is minimal ( h min = 0°). In the southern polar circle ( j= - 66° 33") The sun does not set on the winter solstice and does not rise on the summer solstice.

The northern and southern polar circles are the theoretical boundaries of those geographical latitudes where polar days and nights(days and nights lasting more than 24 hours).

In places beyond the polar circles, the Sun remains a non-setting or non-rising luminary the longer, the closer the place is to the geographic poles. As you approach the poles, the length of the polar day and night increases.

c) For an observer in the northern tropic ( j--= + 23° 27") The sun is always a rising and setting luminary. On the summer solstice it reaches its maximum height at noon. h max = + 90°, i.e. passes through the zenith. On the remaining days of the year, the Sun culminates at noon south of the zenith. On the day of the winter solstice its minimum midday height is h min = + 43° 06".

In the southern tropics ( j = - 23° 27") The sun also always rises and sets. But at its maximum midday height above the horizon (+ 90°) it occurs on the day of the winter solstice, and at its minimum (+ 43° 06 " ) - on the day of the summer solstice. On the remaining days of the year, the Sun culminates here at noon north of the zenith.

In places lying between the tropics and the polar circles, the Sun rises and sets every day of the year. Half a year is the length of the day here longer duration nights, and for six months the night is longer than the day. The midday altitude of the Sun here is always less than 90° (except in the tropics) and more than 0° (except in the polar circles).

In places lying between the tropics, the Sun is at its zenith twice a year, on those days when its declination is equal to the geographical latitude of the place.

d) For an observer at the Earth's equator ( j--= 0) all luminaries, including the Sun, are rising and setting. At the same time, they are above the horizon for 12 hours, and below the horizon for 12 hours. Therefore, at the equator, the length of the day is always equal to the length of the night. Twice a year the Sun passes at its zenith at noon (March 21 and September 23).

From March 21 to September 23, the Sun at the equator culminates at noon north of the zenith, and from September 23 to March 21 - south of the zenith. The minimum noon altitude of the Sun here will be equal to h min = 90° - 23° 27 " = 66° 33 " (June 22 and December 22).

13.1 The values ​​of the height of the sun above the horizon are given in Table 13.1.

Table 13.1

Appendix b (informative) Methods for calculating climatic parameters

The basis for the development of climate parameters was the Scientific and Applied Reference Book on the Climate of the USSR, vol. 1 - 34, parts 1 - 6 (Gidrometeoizdat, 1987 - 1998) and observation data at meteorological stations.

Average values ​​of climatic parameters (average monthly temperature and air humidity, average monthly precipitation) are the sum of the average monthly values ​​of members of a series (years) of observations, divided by their total number.

Extreme values ​​of climatic parameters (absolute minimum and absolute maximum air temperature, daily maximum precipitation) characterize the limits within which the values ​​of climatic parameters are contained. These characteristics were selected from extreme observations during the day.

The air temperature of the coldest day and the coldest five-day period was calculated as the value corresponding to the probability of 0.98 and 0.92 from the ranked series of air temperatures of the coldest day (five-day period) and the corresponding probability for the period from 1966 to 2010. The chronological data series was ranked in descending order of meteorological magnitude values. Each value was assigned a number, and its security was determined using the formula

where m is the serial number;

n is the number of members of the ranked series.

The air temperature values ​​of the coldest day (five days) of a given probability were determined by interpolation using the integral temperature distribution curve of the coldest day (five days), built on a probabilistic retina. A retinal double exponential distribution was used.

Air temperatures of different levels of probability were calculated based on observational data for eight periods for the whole year for the period 1966-2010. All air temperature values ​​were distributed into gradations of 2°C and the frequency of values ​​in each gradation was expressed through the frequency of occurrence of the total number of cases. The availability was calculated by summing the frequency. Security refers not to the middle, but to the boundaries of the gradations, if they are calculated according to distribution.

The air temperature with a probability of 0.94 corresponds to the air temperature of the coldest period. Uncertainty of air temperature exceeding the calculated value is equal to 528 hours/year.

For the warm period, the calculated probability temperature of 0.95 and 0.99 was adopted. In this case, the lack of air temperature exceeding the calculated values ​​is 440 and 88 hours/year, respectively.

Average maximum air temperature is calculated as the monthly average of daily maximum air temperatures.

The average daily amplitude of air temperature was calculated regardless of cloudiness as the difference between the average maximum and average minimum air temperatures.

Duration and average temperature air periods with average daily temperature air equal to or less than 0°C, 8°C and 10°C characterize a period with stable values ​​of these temperatures; individual days with an average daily air temperature equal to or less than 0°C, 8°C and 10°C are not taken into account .

Relative air humidity was calculated using series of average monthly values. Average monthly relative humidity during the day, calculated from observations during the daytime (mainly at 15:00).

The amount of precipitation is calculated for the cold (November - March) and warm (April - October) periods (without correction for wind underestimation) as the sum of average monthly values; characterizes the height of the layer of water formed on a horizontal surface from rain, drizzle, heavy dew and fog, melted snow, hail and snow pellets in the absence of runoff, seepage and evaporation.

The daily maximum precipitation is selected from daily observations and characterizes the largest amount of precipitation that fell during a meteorological day.

The frequency of wind directions is calculated as a percentage of the total number of observation cases, excluding calms.

The maximum of the average wind speeds by bearings for January and the minimum of the average wind speeds by bearings for July are calculated as the highest of the average wind speeds by bearings for January, the frequency of which is 16% or more, and as the smallest of the average wind speeds by bearings for July , the repeatability of which is 16% or more.

Direct and diffuse solar radiation on surfaces of various orientations under cloudless skies was calculated using a method developed in the laboratory of construction climatology of the NIISF. In this case, actual observations of direct and diffuse radiation under cloudless skies were used, taking into account the daily variation of the sun's height above the horizon and the actual distribution of atmospheric transparency.

Climatic parameters for stations of the Russian Federation marked with "*" were calculated for the observation period 1966 - 2010.

* When developing territorial building codes (TSN), climatic parameters should be clarified taking into account meteorological observations for the period after 1980.

Climatic zoning was developed on the basis of a complex combination of average monthly air temperature in January and July, average wind speed for three winter months, average monthly relative humidity in July (see Table B.1).

Table B.1

The map of humidity zones was compiled by NIISF based on the values ​​of the complex indicator K, which is calculated according to the ratio of the monthly average for the frost-free period of precipitation on a horizontal surface, relative air humidity at 15:00 of the warmest month, the average annual total solar radiation on a horizontal surface, the annual amplitude of monthly averages ( January and July) air temperatures.

In accordance with the complex indicator K, the territory is divided into zones according to the degree of humidity: dry (K less than 5), normal (K = 5 - 9) and wet (K more than 9).

The zoning of the northern construction-climatic zone (NIISF) is based on the following indicators: absolute minimum air temperature, the temperature of the coldest day and the coldest five-day period with a probability of 0.98 and 0.92, the sum of average daily temperatures for heating season. According to the severity of the climate in the northern construction-climatic zone, areas are distinguished as severe, least severe and most severe (see Table B.2).

A map of the distribution of the annual average number of air temperature transitions through 0°C was developed by the State Geophysical Observatory based on the number of average daily air temperature transitions through 0°C, summed up for each year and averaged over the period 1961-1990.

Table B.2

φ = 90° - North Pole

Only at the pole day and night last for six months. On the day of the vernal equinox, the Sun describes a full circle along the horizon, then every day it rises higher in a spiral, but not higher than 23°27 (on the day of the summer solstice). After this, turn by turn, the Sun again descends to the horizon. Its light is reflected many times from ice and hummocks. On the day of the autumn equinox, the Sun once again circles the entire horizon, and its next turns very gradually go deeper and deeper under the horizon. The dawn lasts for weeks, even months, moving all 360°. The White Night gradually darkens, and only near the winter solstice does it become dark. It is the middle of the polar night. But the Sun does not fall below the horizon below 23°27 The polar night gradually brightens and the morning dawn lights up.

φ = 80° - one of the Arctic latitudes

The movement of the Sun at latitude φ = 80° is typical for areas located north of the Arctic Circle, but south of the pole. After the vernal equinox, the days grow very quickly, and the nights shorten, the first period of white nights begins - from March 15 to April 15 (1 month). Then the Sun, instead of going beyond the horizon, touches it at the north point and rises again, goes around the sky, moving all 360°. The daily parallel is located at a slight angle to the horizon, the Sun culminates above the point of the south and descends to the north, but does not go beyond the horizon and does not even touch it, but passes above the point of the north and again makes another daily revolution across the sky. So the Sun rises in a spiral higher and higher until the summer solstice, which marks the middle of the polar day. Then the turns of the daily movement of the Sun descend lower and lower. When the Sun touches the horizon at the north point, the polar day will end, which lasted 4.5 months (from April 16 to August 27), and the second period of white nights will begin from August 27 to September 28. Then the length of the nights quickly increases, the days become shorter and shorter, because... the points of sunrise and sunset rapidly shift to the south, and the arc of the daily parallel above the horizon shortens. On one of the days before the winter solstice, the Sun does not rise above the horizon at noon, and the polar night begins. The sun, moving in a spiral, goes deeper and deeper below the horizon. The middle of the polar night is the winter solstice. After it, the Sun again spirals towards the equator. In relation to the horizon, the turns of the spiral are inclined, so when the Sun rises to the southern part of the horizon, it becomes light, then dark again, and a struggle between light and darkness occurs. With each revolution, the daytime twilight becomes lighter and, finally, the Sun appears for a moment above the southern (!) horizon. This long-awaited ray marks the end of the polar night, which lasted 4.2 months from October 10 to February 23. Every day the Sun lingers longer and longer above the horizon, describing an ever larger arc. The greater the latitude, the longer the polar days and polar nights, and the shorter the period of daily alternation of days and nights between them. In these latitudes there is a long twilight, because... The sun goes below the horizon at a slight angle. In the Arctic, the Sun can rise at any point on the eastern horizon from north to south, and also set at any point on the western horizon. Therefore, a navigator who believes that the Sun always rises at the point of the east and sets at the point risks being off course by 90°.

φ = 66°33" - Arctic Circle

Latitude φ = 66°33" is the maximum latitude separating the areas in which the Sun rises and sets every day from the areas in which merged polar days and merged polar nights are observed. At this latitude in the summer, the points of sunrise and sunset shift in “broad steps” from the points of east and west by 90° to the north, so that on the day of the summer solstice they meet at the point of north. Therefore, the Sun, having descended to the northern horizon, immediately rises again, so that two days merge into a continuous polar day (June 21 and 22 Before and after the polar day, there are periods of white nights. The first is from April 20 to June 20 (67 white nights), the second is from June 23 to August 23 (62 white nights). On the day of the winter solstice, the sunrise and sunset points meet at the point south. There is no day between two nights. The polar night lasts two days (December 22, 23). Between the polar day and polar night, the Sun rises and sets every day, but the length of days and nights changes quickly.

φ = 60° - latitude of St. Petersburg

The famous white nights are observed before and after the summer solstice, when “one dawn hastens to replace another,” i.e. At night the sun descends shallowly below the horizon, so its rays illuminate the atmosphere. But the residents of St. Petersburg are silent about their “rainy days,” when the Sun on the day of the winter solstice rises at noon only 6°33" above the horizon. White nights (navigational twilight) of St. Petersburg are especially good in combination with its architecture and the Neva. They begin around May 11 and last 83 days until August 1. Most daylight hours- the middle of the interval - around June 21. Over the course of a year, the sunrise and sunset points shift along the horizon by 106°. But white nights are observed not only in St. Petersburg, but along the entire parallel φ = 60° and to the north up to φ = 90°, to the south of φ = 60° the white nights become shorter and darker. Similar white nights are observed in the Southern Hemisphere, but at the opposite time of year.

φ = 54°19" - latitude of Ulyanovsk

This is the latitude of Ulyanovsk. The movement of the Sun in Ulyanovsk is typical for all mid-latitudes. The radius of the sphere shown in the figure is so large that in comparison with it the Earth looks like a point (symbolized by the observer). Geographic latitude φ is given by the height of the pole above the horizon, i.e. angle Pole (P) - Observer - Point North (N) in the horizon. On the day of the vernal equinox (21.03) the Sun rises exactly in the east, rises across the sky, moving to the south. Above the south point is the highest position of the Sun on a given day - the upper culmination, i.e. midday, then it descends “downhill” and sets exactly in the west. The further movement of the Sun continues below the horizon, but the observer does not see this. At midnight, the Sun reaches its lowest point below the north point, then rises again to the eastern horizon. On the day of the equinox, half of the daily parallel of the Sun is above the horizon (day), half is below the horizon (night). On the next day, the Sun does not rise exactly at the point of the east, but at a point slightly shifted to the north, the daily parallel passes above the previous one, the height of the Sun at noon is greater than on the previous day, the setting point is also shifted to the north. Thus, the daily parallel of the Sun is no longer divided in half by the horizon: most of it is above the horizon, the smaller part is below the horizon. The summer half of the year is coming. The points of sunrise and sunset are increasingly shifting to the north, an increasing part of the parallel is above the horizon, the midday height of the Sun increases and on the day of the summer solstice (21.07 -22.07) in Ulyanovsk reaches 59°08". At the same time, the points of sunrise and sunset are shifted relative to the points of the east and west to north by 43.5°. After the summer solstice, the daily parallels of the Sun descend to the equator. On the day of the autumn equinox (23.09) the Sun again rises and sets at the points of the east and west, passes along the equator. Subsequently, the Sun gradually day after day descends under the equator. At the same time, the points of sunrise and sunset shift to the south until the winter solstice (December 23) also by 43.5°. Most of the parallels in winter time is below the horizon. The midday altitude of the Sun decreases to 12°14". The further movement of the Sun along the ecliptic occurs along parallels, again approaching the equator, the sunrise and sunset points return to the points of the east and west, the days increase, spring comes again! It is interesting that in Ulyanovsk the sunrise points shift along the eastern horizon at 87°. Sunset points accordingly “walk" along the western horizon. The sun rises exactly in the east and sets exactly in the west only twice a year - on the days of the equinoxes. The latter is true on the entire surface of the Earth, except for the poles.

φ = 0° - Earth's equator

The movement of the Sun above the horizon in different times year for an observer located in mid-latitudes (left) and at the Earth's equator (right).

At the equator, the Sun passes through the zenith twice a year, on the days of the spring and autumn equinoxes, i.e. There are two “summers” at the equator, when we have spring and autumn. Day at the equator is always equal to night (12 hours each). The points of sunrise and sunset shift slightly from the points of east and west, no more than 23°27" towards the south and the same amount towards the north. There is practically no twilight, a hot bright day abruptly gives way to black night.

φ = 23°27" - Northern Tropic

The sun rises steeply above the horizon, very hot during the day, then drops steeply below the horizon. Twilight is short, nights are very dark. The most characteristic feature is that the Sun reaches its zenith once a year, on the summer solstice, at noon.

φ = -54°19" - latitude corresponding to Ulyanovsk in the Southern Hemisphere

Just like throughout the southern hemisphere, the Sun rises on the eastern horizon and sets on the western horizon. After sunrise, the Sun rises above the northern horizon at noon and sinks below the southern horizon at midnight. Otherwise, the movement of the Sun is similar to its movement at the latitude of Ulyanovsk. The movement of the Sun in the southern hemisphere is similar to the movement of the Sun at the corresponding latitudes in the northern hemisphere. The only difference is that from the east the Sun moves towards the northern horizon rather than the southern one, culminates over the north point at noon and then also sets on the western horizon. Seasons in the northern and southern hemispheres opposite.

φ = 10° - one of the latitudes of the hot zone

The movement of the Sun at a given latitude is typical for all places located between the northern and southern tropics of the Earth. Here the Sun passes through the zenith twice a year: on April 16 and August 27, with an interval of 4.5 months. The days are very hot, the nights are dark and starry. Days and nights differ little in duration, there is practically no twilight, the Sun sets below the horizon and it immediately becomes dark.