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Распределение метеовеличин и коэффициента преломления воздуха в нижнем слое атмосферы летом

Язык: русский
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Оглавление

Введение

1. Радиофизические характеристики атмосферы и их связь с
метеопараметрами

2. Радиорефракция

2.1 Виды радиорефракции

2.2 Методы учета радиорефракции

2.2.1 Метод эквивалентного радиуса Земли

2.2.2 Метод приведенного коэффициента преломления

3. Исходные материалы и методика их обработки

4. Вертикальные профили радиометеорологических величин

4.1 Вертикальный профиль средней температуры июля

4.2 Вертикальные профили средней относительной влажности и средней
упругости водяного пара июля

4.3 Вертикальный профиль среднего показателя преломления воздуха в июле

4.4 Повторяемость различных видов рефракции в июле

Заключение

Список использованной литературы

Приложения

Введение

Влияние метеорологических условий на распространение радиоволн различных
диапазонов было установлено еще на заре современной радиофизики, однако
теоретическая сложность и экспериментальные трудности изучения этого
влияния в течение длительного времени ограничивали результаты
исследований лишь некоторыми, большей частью качественными выводами.

Широкое развитие технических средств радиолокации в годы войны и
последующее их применение в науке и технике, возникновение телевидения,
космической радиосвязи, телеуправления поставили исследователей перед
острой необходимостью изучить закономерности распространения радиоволн с
учетом влияния всех слоев атмосферы как среды с переменным показателем
преломления.

В применении к тропосфере это означало в первую очередь развитие широких
теоретических и экспериментальных исследований закономерностей
распространения ультракоротких волн (УКВ) в зависимости от
метеорологических условий. Поскольку в обычных условиях УКВ не
отражаются ионосферой, изменчивость характеристик принятого поля
объясняют изменчивостью условий их распространения в нижней атмосфере, в
частности вариациями показателя преломления воздуха.

Все существующие теории принимают показатель преломления за основной
параметр, определяющий особенности распространения УКВ в тропосфере.
Зависимость показателя преломления воздуха от высоты над земной
поверхностью вызывает искривление траектории волны, излученной
горизонтально. В нормальных условиях эта траектория искривляется в
направлении к Земле, и кривизна ее составляет около одной четверти
кривизны земной поверхности. При некоторых особых метеорологических
условиях энергия волны может быть сосредоточена в узких слоистых
областях вблизи поверхности Земли, так что далеко за пределами
радиогоризонта наблюдается аномально высокая напряженность поля. В
других условиях переходный слой между воздушными массами может вызвать
отражение энергии радиоволн. В дополнение к эффектам, связанным со
слоистостью, атмосфера всегда в большей или меньшей степени турбулентна,
что приводит к рассеянию радиоволн и уширению диаграмм направленности
антенн.

Изучение атмосферы с точки зрения влияния ее на распространение УКВ
является задачей радиометеорологии. Ее составными элементами являются
некоторые области радиофизики (распространение радиоволн, техника
сверхвысоких частот) и метеорология. Радиометеорологические исследования
активно проводятся несколько десятилетий. Однако до сих пор актуальными
являются исследования, посвященные пространственно-временным изменениям
коэффициента преломления (определяемого метеорологическими величинами) в
различных районах и на разных высотах в атмосфере [1].

Курсовая работа посвящена исследованию метеорологических величин и
коэффициента преломления, рассчитанного по данным о температуре воздуха,
влажности и атмосферному давлению, в нижнем слое атмосферы в городе
Хабаровск за июль. Целью данной работы является определение влияния
метеорологических условий в летний период на распространение УКВ в
выбранном районе.

1. Радиофизические характеристики атмосферы и их связь с
метеопараметрами

Радиофизическими характеристиками атмосферы являются диэлектрическая
проницаемость и коэффициент преломления, которые между собой однозначно
связаны. В общем случае диэлектрическая проницаемость и коэффициент
преломления являются величинами комплексными [2].

Предполагая выполнимость закона Дальтона о парциальных давлениях, можно
получить выражение для диэлектрической проницаемости
(picscalex10001000900000315010000020070000000000005000000020101000000050
000000102ffffff00050000002e0119000000050000000b0200000000050000000c02600
140011300000026060f001c00ffffffff0000060010000000c0ffffff260000000001000
0860100000b00000026060f000c004d61746854797065000030000500000009020000000
2050000001402000128001c000000fb0280fe00000000000090010100000100020010537
96d626f6c0000090c0a8578dd0600d89ff377e19ff3772020f577d40b6621040000002d0
1000009000000320a0000000001000000657900037000000026060f00d6004d617468547
970655555ca00050100040044534d543400001357696e416c6c4261736963436f6465506
167657300110554696d6573204e657720526f6d616e00110353796d626f6c001105436f7
572696572204e65770011044d5420457874726100120008212f458f442f4150f4100f475
f4150f21f1e4150f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f4
8f48f4100f4100f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c01000100010
202020200020001010100030001000400000a0100020484b5036500000b00000026060f0
00c00ffffffff01004c00000000001c000000fb021000070000000000bc02000000cc010
2022253797374656d0000d40b662100000a0021008a0100000000ffffffffe4e70600040
000002d01010004000000f0010000030000000000) смеси полярных и неполярных
газов. Для тропосферы необходим, в частности, учет влияния СО2, сухого
воздуха (неполярные молекулы) и водяного пара (полярные молекулы):
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, (1)

где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 – постоянные величины,
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 – давление
сухого воздуха,
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 – парциальное давление водяного
пара в гПа,
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 – парциальное
давление СО2,
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– температура в °К [1].

Значения диэлектрической проницаемости воздуха незначительно превышают
единицу. Для волн длиной более 1 см электропроводность нижней части
атмосферы (тропосферы) очень мала, и диэлектрическую проницаемость можно
считать величиной действительной [2].

При этом коэффициент преломления (n) определяется выражением:

picscalex1000100090000032e0200000700810000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c028002
00061300000026060f001c00ffffffff0000060010000000c0ffffffbaffffffc0050000
3a0200000b00000026060f000c004d617468547970650000600008000000fa0200000000
000000000002040000002d010000050000001402910189020500000013027701b0020500
000013022c020d030500000013024f0073030500000013024f00a60507000000fc020000
000000020000040000002d01010008000000fa0205000100000000000000040000002d01
02001a00000024030b0086028c01bb026a010d0301026c034600a6054600a60559007a03
590017032c0204032c02a60285018d029701040000002d01000005000000090200000002
050000001402c0013a051c000000fb0280fe000000000000900100000000000200105469
6d6573204e657720526f6d616e00d89ff377e19ff3772020f5772c0c66cb040000002d01
030009000000320a00000000010000002c790003050000001402c0013a001c000000fb02
80fe0000000000009001010000000002001054696d6573204e657720526f6d616e00d89f
f377e19ff3772020f5772c0c66cb040000002d01040004000000f001030009000000320a
00000000010000006e790003050000001402c0018a031c000000fb0280fe000000000000
9001010000010002001053796d626f6c0000d20b0a6c78dd0600d89ff377e19ff3772020
f5772c0c66cb040000002d01030004000000f00104000a000000320a0000000002000000
6d65d8000003050000001402c00154011c000000fb0280fe000000000000900100000001
0002001053796d626f6c0000d2040a9a78dd0600d89ff377e19ff3772020f5772c0c66cb
040000002d01040004000000f001030009000000320a00000000010000003d6500038100
000026060f00f8004d617468547970655555ec00050100040044534d543400001357696e
416c6c4261736963436f6465506167657300110554696d6573204e657720526f6d616e00
110353796d626f6c001105436f7572696572204e65770011044d54204578747261001200
08212f458f442f4150f4100f475f4150f21f1e4150f4150f4100f445f425f48f425f4100
f4100f435f4100f48f45f42a5f48f48f4100f4100f40f48f417f48f4100f412a5f445f45
f45f45f45f410f0c01000100010202020200020001010100030001000400000a01000200
836e000204863d003d03000a00000100020484bc036d020484b503650200822c00000b01
010000000b00000026060f000c00ffffffff01004c000000000008000000fa0200000000
000000000000040000002d01030007000000fc020000000000000000040000002d010500
1c000000fb021000070000000000bc02000000cc0102022253797374656d00002c0c66cb
00000a0021008a0100000000ffffffffe4e70600040000002d01060004000000f0010400
030000000000 (2)

где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 – магнитная проницаемость (для
воздуха ее полагают равной единице). Поскольку
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 (3)

можно использовать аппроксимацию:
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. (4)

В силу малости величины n – 1 коэффициент преломления удобно выражать в
N – единицах:
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, (5)

где К1, К2, К3, К4 – постоянные.

Постоянные коэффициенты равны [1]:

К1=77,607
picscalex100010009000003150100000200700000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c028001
60011300000026060f001c00ffffffff0000060010000000c0ffffffe6ffffff20010000
660100000b00000026060f000c004d617468547970650000200005000000090200000002
05000000140240013a001c000000fb0280fe000000000000900100000001000200105379
6d626f6c00002a0c0a3978dd0600d89ff377e19ff3772020f577cf046617040000002d01
000009000000320a0000000001000000b17900037000000026060f00d6004d6174685479
70655555ca00050100040044534d543400001357696e416c6c4261736963436f64655061
67657300110554696d6573204e657720526f6d616e00110353796d626f6c001105436f75
72696572204e65770011044d5420457874726100120008212f458f442f4150f4100f475f
4150f21f1e4150f4150f4100f445f425f48f425f4100f4100f435f4100f48f45f42a5f48
f48f4100f4100f40f48f417f48f4100f412a5f445f45f45f45f45f410f0c010001000102
02020200020001010100030001000400000a0100020486b100b100000b00000026060f00
0c00ffffffff01004c00000000001c000000fb021000070000000000bc02000000cc0102
022253797374656d0000cf04661700000a0021008a0100000000ffffffffe4e706000400
00002d01010004000000f0010000030000000000 0,13 °К/мб

К2=71,6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 8,5 °К/мб

К3=(3,747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 0,031) · 105 (°К)2/мб.

Итак, окончательное уравнение для показателя преломления, если
ограничиться для констант тремя значащими цифрами, имеет вид:
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(6)

Значения постоянных в этой формуле рекомендованы Смитом и Вейнтраубом
для вычисления N с точностью 0,5%.

Уравнение упрощается, если положить

P = Pd + e:
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. (7)

Для практического использования в радиометеорологии это соотношение
можно упростить, представив его в виде двучлена:
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, (8)

что дает значение N с точностью порядка 0,02% для интервала температур
от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 50°C до + 40°C.

Обычно уравнение (8) записывают в виде:
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. (9)

Значения коэффициента преломления, рассчитанные по формуле (9), зависят
от точности измерения метеорологических элементов. При радиозондировании
измеряется не парциальное давление (упругость водяного пара) е, а
относительная влажность f, которая легко может быть пересчитана в
парциальное давление е. Для этого используется следующая формула:
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, (10)

где t – температура в °C,

f – относительная влажность воздуха в % [1].

В реальной атмосфере вследствие изменений температуры, давления и
влажности происходят сложные пространственно – временные изменения
коэффициента преломления. Различают сезонные и суточные изменения
коэффициента преломления в тропосфере, а также случайные изменения,
обусловленные атмосферной турбулентностью. Сезонные изменения
обусловлены, главным образом, годовым ходом влажности с максимумом в
теплое полугодие. Наибольшие изменения коэффициента преломления имеют
место в нижнем трехкилометровом слое атмосферы, что обусловлено большими
изменениями в этом слое температуры и влажности. Суточные изменения
коэффициента преломления атмосферы наиболее значительны в нижнем
километровом слое и могут достигать 10 – 15N – ед. Они также обусловлены
большим суточным ходом температуры и влажности воздуха. Случайные
флюктуации коэффициента преломления связаны с атмосферной
турбулентностью и могут достигать значения 10N – ед.

Обычно учитывают изменение коэффициента преломления атмосферы только по
высоте, пренебрегая горизонтальной изменчивостью.

Для характеристики вертикальной изменчивости коэффициента преломления
пользуются понятием вертикального градиента:
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, (11)

или
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, (12)

где n1 и n2 – значения коэффициента преломления на нижней и верхней
границе слоя,

H1 и H2 – высоты нижней и верхней границ слоя.

Вертикальный градиент dn/dH имеет размерность 1/м, а градиент dN/dH – N
– ед/м. Из соотношения (11) следует, что реальной атмосфере, для которой
коэффициент преломления уменьшается с высотой, соответствуют
отрицательные значения градиента.

В радиометеорологии для решения ряда задач пользуются параметрами
стандартной, или нормальной, атмосферы. Нормальной считается атмосфера,
в которой имеют место линейное уменьшение температуры воздуха с высотой,
равное 6,5°C на 1 км, уменьшение давления по барометрическому закону:
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, (13)

и убывание влажности воздуха по эмпирическому соотношению:
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,(14)

где Р0 и РH – давление на нижнем и верхнем уровнях,

g – ускорение свободного падения,

R – универсальная газовая постоянная,

Т – температура столба воздуха между указанными уровнями,

H – высота в км,

q – удельная влажность в г/м3,

b, с – коэффициенты
(0,1112picscalex10001000900000315010000020070000000000005000000020101000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,2181;
0,0286picscalex100010009000003150100000200700000000000050000000201010000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сpicscalex1000100090000031
5010000020070000000000005000000020101000000050000000102ffffff00050000002
e0119000000050000000b0200000000050000000c02800140011300000026060f001c00f
fffffff0000060010000000c0ffffffe6ffffff00010000660100000b00000026060f000
c004d617468547970650000200005000000090200000002050000001402400134001c000
000fb0280fe0000000000009001000000010002001053796d626f6c000042070a0978dd0
600d89ff377e19ff3772020f5773f0866df040000002d01000009000000320a000000000
1000000a37900037000000026060f00d6004d617468547970655555ca000501000400445
34d543400001357696e416c6c4261736963436f6465506167657300110554696d6573204
e657720526f6d616e00110353796d626f6c001105436f7572696572204e65770011044d5
420457874726100120008212f458f442f4150f4100f475f4150f21f1e4150f4150f4100f
445f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f4100f40f48f417f4
8f4100f412a5f445f45f45f45f45f410f0c0100010001020202020002000101010003000
1000400000a01000204866422a300000b00000026060f000c00ffffffff01004c0000000
0001c000000fb021000070000000000bc02000000cc0102022253797374656d00003f086
6df00000a0021008a0100000000ffffffffe4e70600040000002d01010004000000f0010
0000300000000000,0375).

Удельная влажность с парциальным давлением водяных паров связана
соотношением:
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.(15)

В стандартной атмосфере коэффициент преломления изменяется с высотой по
линейному закону, а в реальной атмосфере изменение N с высотой в среднем
происходит по экспоненциальному закону [2].

2. Радиорефракция

Радиорефракцией называется искривление траектории электромагнитных волн
при распространении в атмосфере. Плотность реальной атмосферы убывает с
высотой, поэтому радиолуч, направленный с земной поверхности вверх,
будет переходить из области с большим значением плотности в области с
малыми значениями плотности.

Если электромагнитный луч будет распространяться в плоскослоистой
атмосфере, в которой коэффициент преломления изменяется постепенно, то
будет происходить плавное искривление траектории луча. Радиус кривизны
будет определяться величиной градиента коэффициента преломления в
соответствии с выражением:

picscalex1000100090000031f02000004008b0000000000050000000201010000000500
00000102ffffff00050000002e0119000000050000000b0200000000050000000c02e003
c0081300000026060f001c00ffffffff0000060010000000c0ffffffb8ffffff80080000
980300000b00000026060f000c004d617468547970650000c00008000000fa0200001300
000000000002040000002d0100000500000014020002ca03050000001302000262080500
00000902000000020500000014026e01b6051c000000fb0280fe00000000000090010000
00000002001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f5770906
6633040000002d01010009000000320a0000000001000000317900030500000014028c03
9e051c000000fb0280fe0000000000009001000000000002001054696d6573204e657720
526f6d616e00d89ff377e19ff3772020f57709066633040000002d01020004000000f001
010009000000320a00000000010000002f7900030500000014028c03e2031c000000fb02
80fe0000000000009001010000000002001054696d6573204e657720526f6d616e00d89f
f377e19ff3772020f57709066633040000002d01010004000000f00102000d000000320a
0000000004000000646e6448c000aa01c0000003050000001402600246001c000000fb02
80fe0000000000009001010000010002001053796d626f6c0000ee060a2b78dd0600d89f
f377e19ff3772020f57709066633040000002d01020004000000f001010009000000320a
000000000100000072790003050000001402600290011c000000fb0280fe000000000000
9001000000010002001053796d626f6c0000cb050a6178dd0600d89ff377e19ff3772020
f57709066633040000002d01010004000000f00102000a000000320a0000000002000000
3d2d2c0100038b00000026060f000c014d6174685479706555550001050100040044534d
543400001357696e416c6c4261736963436f6465506167657300110554696d6573204e65
7720526f6d616e00110353796d626f6c001105436f7572696572204e65770011044d5420
457874726100120008212f458f442f4150f4100f475f4150f21f1e4150f4150f4100f445
f425f48f425f4100f4100f435f4100f48f45f42a5f48f48f4100f4100f40f48f417f48f4
100f412a5f445f45f45f45f45f410f0c0100010001020202020002000101010003000100
0400000a0100020484c103720204863d003d02048612222d03000b000001000200883100
00010002008364000200836e000200822f0002008364000200834800000000000b000000
26060f000c00ffffffff01004c000000000008000000fa02000000000000000000000400
00002d0102001c000000fb021000070000000000bc02000000cc0102022253797374656d
00000906663300000a0021008a0100000000ffffffffe4e70600040000002d0103000400
0000f0010100030000000000,(16)

где dn/dH – градиент коэффициента преломления.

Представляет практический интерес случай критической рефракции, когда
радиус кривизны радиолуча, направленного вдоль земной поверхности, равен
радиусу Земли и луч огибает земной шар. Условием критической рефракции
будет:
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,(17)

где RЗ – радиус Земли.

2.1 Виды радиорефракции

Рассмотрим различные виды радиорефракции и соответствующие им значения
градиента коэффициента преломления. В зависимости от характера
искривления радиолуча различают три основных типа радиорефракции:

Отрицательную;

Нулевую;

Положительную.

Такое деление радиорефракции отражает ее влияние на дальность радиосвязи
в диапазоне СВЧ или на дальность радиолокационного наблюдения обьектов.

При нулевой рефракции (нулевое значение градиента коэффициента
преломления) радиолуч остается прямолинейным. Отрицательная рефракция
(вызывающая уменьшение дальности радиосвязи) имеет место, если луч
направлен выпуклостью вниз, т.е. луч из менее плотной среды переходит в
более плотную. Это может быть только при положительных значениях
градиента коэффициента преломления. Положительная рефракция возникает
при отрицательных значениях градиента коэффициента преломления и делится
в свою очередь на:

пониженную;

нормальную;

повышенную;

критическую;

сверхрефракцию.

Нормальная радиорефракция соответствует рефракции в нормальной
(стандартной) атмосфере, имеющей градиент коэффициента преломления
–4·10-8 1/м. Радиорефракция при значениях градиента коэффициента
преломления от 0 до –4·10-8 1/м называется положительной пониженной
рефракцией. Радиорефракция при – 15,7·10-8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 – 4·10-8 1/м называется положительной повышенной
рефракцией. При значении градиента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 – 15,7·10-8 1/м наблюдается критическая рефракция. При значениях
градиента коэффициента преломления менее – 15,7·10-8 1/м имеет место
сверхрефракция. Радиус кривизны луча меньше радиуса земного шара,
вследствие чего луч испытывает многократное отражение от земной
поверхности.

Критическая рефракция и сверхрефракция характеризуются сверхдальним
распространением радиоволн. Такое явление связывают с образованием так
называемых атмосферных волноводов, которые могут быть как приземными,
так и приподнятыми (отражение в этом случае имеет место не от земной
поверхности, а от слоя атмосферы, приподнятого над землей). Атмосферные
волноводы существенно повышают дальность радиосвязи на СВЧ и дальность
радиолокационного наблюдения объектов.

2.2 Методы учета радиорефракции

Явление рефракции в атмосфере приводит к ошибкам измерения координат
объектов радиотехническими и оптическими методами. Регулярную
составляющую таких ошибок можно учитывать путем введения соответствующих
поправок в результаты измерений. В зависимости от изменчивости
вертикального градиента коэффициента преломления различают два способа
введения поправок:

Метод эквивалентного радиуса Земли;

Метод приведенного коэффициента преломления.

2.2.1 Метод эквивалентного радиуса Земли

Он сводит задачу криволинейного распространения радиоволн к задаче с
прямолинейным распространением. Криволинейную траекторию луча
«разгибают», увеличивая радиус Земли до тех пор, пока траектория луча не
окажется прямолинейной. Радиус Земли, соответствующий прямолинейному
лучу, называют эквивалентным радиусом и используют для расчетов.
Эквивалентный радиус Земли будет равен:
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,(18)

где RЭ – эквивалентный радиус Земли,

KP – коэффициент пропорциональности,

RЗ – радиус Земли.

Коэффициент пропорциональности определяется формулой:
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,(19)

где n0 – значение коэффициента преломления на уровне земной поверхности.

Для нормальной атмосферы, полагая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 – 4·10-8 1/м, RЗ=6370·103 м, n0=1, получаем KP=1,33 и RЭ=8460 км.

При расчетах, связанных с обеспечением радиовидимости, следует
оперировать с эквивалентным радиусом Земли так же, как и с обычным
радиусом Земли при отсутствии рефракции.

2.2.2 Метод приведенного коэффициента преломления

Он состоит в том, что влияние кривизны земной поверхности (а
следовательно, и кривизны сферической слоистой атмосферы) заменяют
влиянием дополнительного значения коэффициента преломления атмосферы.
Для этого криволинейную траекторию луча вместе с земной поверхностью
«разгибают» до тех пор, пока сферическая поверхность Земли не
превратиться в плоскую, а луч при этом будет иметь другую кривизну.
Соответствующий новой рефракции коэффициент преломления атмосферы
называется приведенным коэффициентом преломления.

Приведенный коэффициент преломления равен:
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,(20)

или в N – единицах:
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.(21)

Приведенный коэффициент преломления используется так же, как и обычный
коэффициент преломления в задачах распространения над плоской Землей
[2].

3. Исходные материалы и методика их обработки

Для изучения закономерности распределения метеовеличин и показателя
преломления воздуха летом были использованы результаты, полученные в
июле 1977г. на высотной метеорологической мачте (ВММ) в городе Хабаровск
(данные были взяты из «Материалов высотных метеорологических наблюдений»
[3]). Эти результаты содержат данные измерений температуры и
относительной влажности атмосферы на ВММ (из справочника были взяты
средние за сутки значения температуры и относительной влажности на
высотах 0, 24, 40, 112, 180 м). Температура воздуха на этой мачте
регистрировалась термоградиентографом с погрешностью 0,2/0,3°C.
Влажность воздуха измерялась с помощью пленочного датчика с погрешностью
7%.

Данные по давлению были взяты из «Климатического атласа СССР» [4] для
уровня 0 м. Для остальных высот (24, 40, 112, 180 м) давление было
рассчитано по барометрической формуле:
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,(22
)

где P – давление на высоте z,

P0 – давление на исходном уровне,

g – ускорение свободного падения,

z – высота в м,

R – универсальная газовая постоянная (287, 05 Дж/кг·К),

T – температура в °K.

Обработка материалов велась с помощью процессора Exel. Данные вводились
по датам; для каждой даты значения температуры, влажности и давления
вводились на пяти высотах (0, 24, 40, 112, 180 м). Для того, чтобы
рассчитать показатель преломления N, еще были необходимы значения
упругости водяного пара на всех высотах по суткам. Парциальное давление
е было рассчитано по формуле (10). Далее были рассчитаны значения
показателя преломления N по формуле (9) и вертикальные градиенты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 по формуле (12) (см. приложение таблица 1).

После проведения расчетов были выполнены еще дополнительные действия:

Из общего массива данных через автофильтр находились отдельно данные по
каждой высоте за месяц; На этих высотах были посчитаны среднемесячные
значения t, f, e, P, N, dN/dH и их среднеквадратические отклонения (см.
приложение таблицы 2, 3, 4, 5, 6);

По среднемесячным значениям t, f, e, N на каждой высоте были построены
графики вертикальных профилей этих величин (см. анализ графиков и сами
графики в главе 4);

Была посчитана повторяемость различных видов рефракции по значениям
вертикального градиента dN/dH (см. таблицы 2,3).

После проведения всех расчетов, был сделан анализ полученных результатов
(см. главу 4).

4. Вертикальные профили радиометеорологических величин

Для изучения закономерности распределения метеовеличин и показателя
преломления воздуха в нижнем слое атмосферы летом был выбран город
Хабаровск. Он расположен в юго – восточной части нашей страны (48°35?
с.ш. и 135°в.д.). Хабаровск относится к умеренному климатическому поясу,
к области муссонного климата смешанных лесов Дальнего Востока. Средние
температуры июля и января составляют + 16°C и – 24°C соответственно [5].

Как уже было сказано раньше, по среднемесячным значениям t, f, e, N на
каждой высоте были построены графики вертикальных профилей этих величин
(таблица 1).

Таблица 1 – Среднемесячные значения радиометеорологических величин на
разных высотах

Высота, мСредняя t°CСредняя f%Средняя е, гПаСредний N, N –
ед/м021,98221,6355,424227820,83514023,17320,9349,411223,27220,6345,61802
1,56717,2331,7

Далее приведен анализ полученных графиков.

4.1 Вертикальный профиль средней температуры июля

В умеренном поясе на суше в северном полушарии самым теплым месяцем
является июль (именно этот месяц и был рассмотрен в данной работе).

Как уже известно, температура воздуха с высотой в среднем изменяется по
линейному закону:
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,(23)

где Th – абсолютная температура на верхней границе слоя,

T0 – абсолютная температура у основания слоя толщиной h,

gt – вертикальный градиент температуры.

Если принять в соответствии с международной стандартной атмосферой
температуру воздуха у земной поверхности (на «нулевой высоте») равной
15°C (288°K), а градиент температуры до высоты 11км равным 6,5°C на
километр подъема, то получится «стандартная» зависимость температуры от
высоты (в километрах):
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.(24)

С годовыми и суточными изменениями приземного значения температуры
связаны характер кривой высотного распределения температуры и градиенты
пограничного слоя тропосферы. Так, например, летом высотные зависимости
температуры от дня к ночи изменяют свой характер, а градиенты изменяют
знак с положительного (уменьшение t с высотой) на отрицательный (рост t
с высотой – инверсия). В этом смысле стандартное линейное падение
температуры с высотой не отражает процессов, происходящих в пограничном
слое тропосферы.

В летний период на высотах до 100 м существует (в среднем сезонном
профиле) инверсия температуры, являющаяся следствием ночных приземных
инверсий. Выше 100 м наблюдается убывание t с высотой [6].

В рассмотренном мною случае, в среднемесячном вертикальном профиле
температуры также имеется слой инверсии и слой падения t (см. рисунок
1).

Из графика видно, что инверсия наблюдается до высоты 80 м. В слое от 0
до 24 м слабо выраженная инверсия (градиент равен – 0,004°C/м). Выше 24
м идет резкое увеличение температуры с высотой и продолжается до 40 м
(градиент в этом слое составляет – 0,069°C/м). В слое от 40 до 80 м
наблюдается уменьшение интенсивности инверсии (градиент слоя равен –
0,005°C/м) – в этом слое инверсия практически такая же как и в слое от 0
до 40 м (различие составляет 0,001°C). На 80 м наблюдается максимальное
среднемесячное значение t = 23,3°C. Начиная с 80 м идет уменьшение
температуры с высотой (можно сказать, что на уровне 80 м происходит
изгиб кривой в сторону уменьшения температуры – это критическая точка).
В слое от 80 до 112 м идет слабое падение t (градиент составляет
0,003°C/м). А вот начиная со 112 м и до 180 м наблюдается резкое падение
температуры (здесь градиент равен 0,025°C/м). На 180 м наблюдается
минимальное среднемесячное значение t = 21,5°C.

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fffff00050000000902ffffff0005000000010200000000040000002d010700040000002
d010600040000002701ffff030000000000

Рисунок 1 – Вертикальный профиль средней температуры июля

4.2 Вертикальные профили средней относительной влажности и средней
упругости водяного пара июля

Как мы знаем, основной вклад в изменения коэффициента преломления вносят
изменения значений влажности. В тропосфере северного полушария
независимо от сезона года влажность воздуха уменьшается с высотой,
достигая минимумы вблизи тропопаузы. В стандартной атмосфере влажность
воздуха убывает с высотой по эмпирическому соотношению (14).

Среднегодовые и сезонные профили распределения влажности не отражают
«мгновенных», существующих в данный момент времени профилей.
«Мгновенные» профили обладают значительно более сложной конфигурацией с
различного рода изгибами и изломами и характеризуются большой
изменчивостью во времени [6].

Вертикальный профиль средней относительной влажности июля не имеет
больших изломов, а ведет себя довольно сглажено (см. рисунок 2). Падение
f с высотой совсем небольшое. В слоях от 0 до 40 м и от 112 до 180 м
более выраженное уменьшение влажности. А вот в слое от 40 до 112 м ее
падение практически не наблюдается. Вообще разница f между нулевым
уровнем и высотой 180 м составляет всего 15%.

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000000000000000250000000c00000005000000280000000c000000010000001b0000001
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000

Рисунок 2 – Вертикальный профиль средней относительной влажности июля

Вертикальный профиль средней упругости водяного пара июля практически
повторяет ход вертикального профиля f (см. рисунок 3). В слоях от 0 до
24 м и от 112 до 180 м наблюдается более выраженное падение, а в слое от
24 до 112 м изменений в упругости водяного пара практически не
наблюдается (отличие состоит в том, что относительная влажность
практически не меняется с 40 м, а упругость водяного пара с 24 м).
Разница е между нулевым уровнем и высотой 180 м составляет всего 4,4
гПа. Из графиков видно, что, действительно, среднемесячные профили
распределения влажности не отражают «мгновенных», существующих в данный
момент времени профилей.

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e00040000002d010600040000002d010100040000002d010900050000000102ffffff000
50000000902c0c0c000040000002c0100000700000016043801a8010000000008000000f
a0200000000000000000000040000002d01080004000000f001090005000000140215004
3000400000004010d000400000002010200050000001302f9004300040000002d0104000
50000001402f9004000050000001302f9004300050000001402e2004000050000001302e
2004300050000001402cb004000050000001302cb004300050000001402b400400005000
0001302b40043000500000014029e0040000500000013029e00430005000000140288004
000050000001302880043000500000014027100400005000000130271004300050000001
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500000014022c0040000500000013022c004300050000001402150040000500000013021
5004300050000001402f9004300050000001302f9001201050000001402fd00430005000
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d00050000001302f900cd00050000001402fd001201050000001302f9001201040000002
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0002d010400040000002d010100040000002d010800050000000102ffffff00050000000
902c0c0c000040000002c0100000700000016043301a40104000400040000002d0102000
40000002d010300040000002d010700040000002701ffff030000001e00040000002d010
400040000002d010100040000002d010800050000000102ffffff00050000000902c0c0c
000040000002c010000070000001604fe00190113004100040000002d010200040000002
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0002c010000070000001604fc0016011300410007000000fc02010000000000000004000
0002d01090004000000f001010008000000fa0200000100000000008000040000002d010
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900d600eb00d400e400d300de000e00000025030500d300de00d300da00d300d700d300d
200d300cb001400000025030800d300cb00d300c400d300bc00d300b100d400a600d3009
000d2008400d1007a001000000025030600d1007a00d0007000cd006600c8005300c1003
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80005000000090200008000050000000102000000000e00000024030500d900f700db00f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000320a04010b0102000000333007000700040000002d010200040000002d01030004000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Рисунок 3 – Вертикальный профиль средней упругости водяного пара июля

4.3 Вертикальный профиль среднего показателя преломления воздуха в июле

Вследствие большой изменчивости показатель преломления удобно
характеризовать средними (усредненными за определенный период времени)
величинами. Конкретные профили коэффициента преломления, полученные во
время одного зондирования, существенно отличаются от усредненных
высотных распределений N и от стандартной радиоатмосферы. Эти отличия
обусловлены нерегулярным характером высотного распределения температуры
и влажности, которое изменяется во времени и зависит от погоды и климата
[6].

Представление о закономерностях среднего изменения с высотой
коэффициента преломления атмосферы можно получить из анализа выражения
(9). Из этого выражения следует, что увеличение Р и е вызывает рост N, в
то время как увеличение Т приводит к уменьшению N. Если взять частные
производные соотношения (9) последовательно по Р, е и Т, то получится
выражение для оценки величины вклада, вносимого каждым метеорологическим
параметром в изменение N. Для средних летних условий это выражение
примет вид:
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,(25)

где ?T, ?P, ?e – приращения средних значений температуры, давления,
упругости водяного пара соответственно.

Из выражения (25) видно, что изменения величины N в одной точке в
основном зависят от изменения температуры и влажности, причем влияние
влажности заметно превосходит влияние температуры, т.к. величины ??e и
?T при выбранной системе единиц примерно одного порядка; влияние
давления в этом случае настолько мало, что им можно даже пренебречь [7].

По средним значениям N на высотах 0, 24, 40, 112, 180 м был построен
график вертикального профиля показателя преломления воздуха в июле (см.
рисунок 4). Из графика видно, что показатель преломления убывает с
высотой. Это происходит потому, что (если опять же анализировать
выражение (9) ) Р и е с высотой уменьшаются, а Т увеличивается до
определенного уровня, а потом уменьшается. В слое от 0 до 24 м идет
достаточно выраженное падение N (градиент здесь равен – 0,183 N – ед/м).
В слое от 24 до 40 м немного уменьшается интенсивность падения N, но не
сильно (градиент составляет – 0,100 N–ед/м). А вот от 40 до 112 м
наблюдается самое маленькое (незначительное) уменьшение N с высотой
(градиент слоя составляет всего – 0,053 N – ед/м). Начиная со 112 и до
180 м наблюдается самое сильное падение N с высотой (градиент здесь
самый большой и равен – 0,204 N – ед/м). Разница между нулевым уровнем и
высотой 180 м составляет 23,7 N – ед/м (такая небольшая разница скорее
всего обусловлена сглаженным среднемесячным ходом влажности – изменения
ее тоже очень маленькие по вертикали).

Данный, среднемесячный профиль N близок к стандартной линейной
зависимости. И поэтому можно аппроксимировать этот профиль линейной
зависимостью (на графике аппроксимация показана черной линией).

Уравнение этой линии выглядит следующим образом:
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,(26)

где у – значение N,

х – значение высоты.

Величина достоверности аппроксимации составляет: R2 = 0,9356.
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701ffff030000001e00040000002d010500040000002d010900040000002d01080005000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Рисунок 4 – Вертикальный профиль среднего показателя преломления воздуха
в июле

Видно, что эта характеристика составляет приблизительно 94%. Это говорит
о том, что аппроксимация вполне достоверна.

4.4 Повторяемость различных видов рефракции в июле

В ряде приложений широко применяются данные не о самом коэффициенте
преломления, а о величине его вертикального градиента. Для стандартной
атмосферы с нормальной (стандартной) рефракцией вертикальный градиент
равен: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 N – ед/м.
Однако в приземном слое градиенты, близкие к стандартному, наблюдаются
сравнительно редко вследствие большой изменчивости профиля N на этих
высотах. К стандартной величине градиента близки лишь средние значения
градиента в достаточно толстом слое воздуха – в слое 0 – 1000 м и более,
причем время усреднения тоже должно быть достаточно большим – усреднение
за месяц, за сезон и т.п.

Как и приземные значения показателя преломления, градиенты подвержены
сезонным изменениям, причем сезонный ход среднемесячных значений
градиента связан с сезонным ходом самого коэффициента преломления. С
увеличением высоты слоя воздуха сезонные колебания градиентов
уменьшаются, и на высотах более 600 м ими можно пренебречь [6].

Детальное рассмотрение многочисленных N – профилей, полученных в разную
погоду в разное время суток, показало в основном большинстве случаев
наличие критических и сверхкритических градиентов величины N в самом
нижнем 25 – метровом слое атмосферы. Для слоя 25 – 121 м – характерна
повышенная рефракция. Слой выше 120 м выглядит самым стабильным, он
приближается к стандартной атмосфере.

Как следует из выражения (9), появление больших градиентов N должно
иметь место в тех слоях атмосферы, где наиболее резко выражена инверсия
температуры и происходит падение с высотой абсолютной влажности воздуха.
Летом именно в слое до 100 м наиболее резко выражены ночные инверсии
температуры, а днем наблюдается значительное падение влажности с
высотой. Оба эти фактора и обусловливают сверхкритическую и повышенную
рефракции в нижнем 120 метровом слое атмосферы [7].

По полученным значениям N на разных высотах (во все дни июля)
определялись вертикальные градиенты dN/dH для слоев 0 – 24, 24 – 40,

40 – 112, 112 – 180 м. Градиенты были разбиты на 4 интервала:

1. Отрицательный
(picscalex100010009000003e2010000040083000000000005000000020101000000050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);

2. Пониженный
(picscalex100010009000003fb010000040093000000000005000000020101000000050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);

3. Повышенный
(picscalex1000100090000030f0200000400a0000000000005000000020101000000050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);

4. Сверхкритический
(picscalex100010009000003f6010000040090000000000005000000020101000000050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).

В соответствии с этой разбивкой для каждого вида рефракции были
посчитаны их повторяемости. (см. таблицы 2, 3).

Таблица 2 – Повторяемость различных видов рефракции в июле

Вид рефракцииЧисло случаевПовторяемость в
%Отрицательная2218Пониженная119Повышенная2419Сверхрефракция6754

Таблица 3 – Повторяемость различных видов рефракции в каждом слое

Слой, мОтрицательнаяПониженнаяПовышеннаяСверхрефракция0 – 245232124 –
408-51840 – 11289104112 – 1801-624

Отрицательная рефракция наблюдалась в общем случае за месяц всего в 18%
из 100%. Она была отмечена во всех слоях. От 0 – 24, 24 – 40, 40 – 112 м
чаще всего (повторяемость рефракции в этих слоях практически одинаковая,
но наблюдалась она в разные дни), и лишь 1 раз в слое 112 – 180 м (9
июля).

Положительная пониженная рефракция наблюдалась меньшее количество раз за
месяц и составила всего 9%. Была отмечена она в основном в слое

40 – 112 м, а вот в слое 0 – 24 м наблюдали ее всего 2 раза (16 и 24
июля).

За месяц чаще всего наблюдали положительную повышенную рефракцию и
сверхрефракцию, которые составили соответственно 19% и 54%. Повышенная
рефракция чаще отмечалась в слоях 24 – 40, 40 – 112,

112 – 180 м; меньше всего в слое 0 – 24 м (всего 3 раза). Полученные
результаты соответствуют выводам, сделанным в работе [7] о том, что для
слоя 25 – 121 м характерна повышенная рефракция. Сверхрефракция
составила самый большой процент повторяемости за месяц (наблюдалась она
во всех слоях). Наиболее часто она встречалась в слоях 0 – 24 и 112 –
180 м (повторяемость ее в этих слоях практически одинаковая). Меньше
всего раз сверхрефракция была отмечена в слоях 24 – 40 и 40 – 112 м. Это
так же соответствует выводам в работе [7] о том, что сверхрефракция в
большинстве случаев наблюдается в нижнем 25 – метровом слое.

Из полученных результатов можно сделать вывод о том, что наибольшую
повторяемость в июле повышенной и сверхкритической рефракций в нижнем
180 – метровом слое атмосферы обусловливают 2 фактора:

Резко выраженная инверсия температуры воздуха;

Падение с высотой влажности воздуха.

Заключение

В результате проделанной работы можно сделать следующие выводы:

В летний период в умеренном климатическом поясе на высотах до

80 м существует (в среднем месячном профиле) инверсия

температуры, являющаяся следствием ночных приземных инверсий.

Выше 80 м наблюдается убывание температуры с высотой;

Сглаженный ход (падение) среднемесячных вертикальных профилей
относительной влажности и упругости водяного пара обусловлен тем, что
эти профили распределения влажности не отражают «мгновенных»,
существующих в данный момент времени профилей, которые обладают
значительно более сложной конфигурацией с различного рода изгибами и
изломами и характеризуются большой изменчивостью во времени;

Изменения величины N в основном зависят от изменения температуры и
влажности, причем влияние влажности заметно превосходит влияние
температуры, влияние давления мало;

Показатель преломления убывает с высотой из – за того, что давление и
упругость водяного пара с высотой уменьшаются, температура увеличивается
до определенного уровня, а потом уменьшается;

Среднемесячный профиль N близок к стандартной линейной зависимости;

Наибольшую повторяемость летом повышенной (19%) и сверхкритической (54%)
рефракций в нижнем 180 – метровом слое атмосферы обусловливают 2
фактора:

резко выраженная инверсия температуры воздуха;

падение с высотой влажности воздуха;

Летом в умеренном климатическом поясе образуются весьма благоприятные
метеоусловия для появления сверхрефракции, которая в свою очередь
повышает (из – за волноводов) дальность радиосвязи на СВЧ и дальность
радиолокационного наблюдения объектов.

И в заключении можно сказать о том, что исследование вертикального
профиля показателя преломления радиоволн (и его градиентов), особенно в
нижнем слое атмосферы до высоты 300 – 500 м над поверхностью земли,
имеет большое значение для обеспечения надежной работы радиорелейных
линий, станций слежения за спутниками и некоторых других современных
радиосистем. Однако данных о пространственно – временном распределении
показателя преломления радиоволн в нижнем слое атмосферы явно
недостаточно – эта проблема остается очень актуальной в наше время.

Список использованной литературы

1. Бин Б.Р., Даттон Е.Дж. Радиометеорология: Пер. с англ. /Под ред. А.А.
Семенова. – Л.: ГМИ, 1971. – 363с.

2. Павлов Н.Ф. Аэрология, радиометеорология и техника безопасности. –
Л.: ГМИ, 1980. – 432с.

3. Материалы высотных метеорологических наблюдений – Часть 2, вып. 4. –
М.: ЦВГМО, 1978. – 195с.

4. Климатический атлас СССР/ Гл.ред. Т.П. Сидоренкова. – М.: ПКО
“Картография”, 1972. – 610с.

5. Атлас по географии России: (с компл. контур. карт) / Сост. и под. к
изд. ПКО “Картография” в 1996г.; Отв. ред. В.И. Щербакова. – Испр. в
1998г. – М-бы разн. – М.: Роскартография, 2000. – 1атл.(56с.)

6. Казаков Л.Я., Ломакин А.Н. Неоднородности коэффициента преломления
воздуха в тропосфере. – М.: Наука, 1976. – 168с.

7. Вяльцева Э.Е. Изменчивость коэффициента преломления атмосферы для УКВ
в пограничном слое // Метеорология и гидрология. – 1972. – №2. – С. 8 –
14.

Приложение

Таблица 1 – Среднесуточные значения радиометеорологических величин на
разных высотах

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N, N – едdN/dH, N
-ед/м1023,1811000,022,8359,0-0,1471242379997,322,1355,50,62314026,575995
,525,9365,4-0,167111224,375987,322,7353,4-0,222118022,570979,619,0338,32
021,7891000,023,0362,1-0,26522420,489997,221,3355,70,07024022,682995,422
,4356,80,009211222,784987,223,1357,5-0,298218020,376979,418,1337,23021,2
821000,020,6352,3-0,25632421,875997,219,5346,1-0,11234022,771995,419,534
4,3-0,033311223,369987,319,7342,0-0,294318020,860979,414,7322,04021,6781
000,020,1349,4-0,18542421,874997,219,3345,00,11344023,770995,420,5346,8-
0,133411223,764987,318,7337,3-0,205418021,360979,515,2323,35020,5921000,
022,1360,0-0,23152419,691997,220,7354,40,32054023,581995,423,4359,6-0,15
5511220,883987,220,3348,4-0,209518019,476979,317,1334,26021,9861000,022,
5359,6-0,19662422,381997,221,8354,90,83864026,577995,526,6368,3-0,177611
224,576987,323,3355,5-0,291618022,169979,518,3335,87022,8861000,023,8363
,6-0,2907242380997,322,4356,70,17374025,275995,524,0359,4-0,084711224,97
3987,322,9353,3-0,258718022,169979,518,3335,88024,1911000,027,3376,1-0,4
4582424,482997,325,0365,40,08884027,473995,526,6366,8-0,170811225,572987
,423,4354,6-0,203818024,267979,720,2340,89020891000,020,8354,8-0,2039241
9,288997,219,5349,9-0,1789402179995,419,6347,1-0,042911220,281987,119,13
44,00,092918019,592979,320,8350,310021,6811000,020,8352,8-0,202102421,17
9997,219,7347,9-0,074104022,474995,420,0346,70,0021011222,775987,220,634
6,9-0,2091018020,571979,417,1332,711018,3951000,019,9353,7-0,286112417,4
92997,218,2346,9-0,310114017,985995,317,4341,90,0141111218,387987,018,33
42,9-0,223111801777979,214,9327,812016,7841000,015,9338,4-0,322122416,37
7997,214,2330,7-0,121124016,774995,314,0328,7-0,0251211217,273987,014,33
27,0-0,1471218015,369979,012,0317,013017,2881000,017,2343,4-0,296132417,
181997,215,8336,3-0,246134017,177995,315,0332,40,0101311217,579987,015,8
333,1-0,1551318016,373979,113,5322,514020,6801000,019,4347,9-0,178142421
,474997,218,8343,6-0,199144021,970995,418,3340,4-0,0241411222,768987,218
,7338,7-0,1951418020,564979,415,4325,415023,7731000,021,3351,7-0,1581524
24,269997,320,8347,9-0,107154024,966995,520,7346,20,0051511225,965987,42
1,7346,6-0,2081518023,662979,618,0332,516024,6761000,023,5359,3-0,012162
425,374997,323,8359,0-0,129164026,270995,523,8356,9-0,0201611227,766987,
424,5355,5-0,3131618025,359979,719,0334,217022,5791000,021,5354,1-0,4391
72421,474997,218,8343,60,087174023,270995,419,9345,0-0,0021711224,468987
,320,7344,8-0,262171802359979,616,5327,018019,2891000,019,8351,6-0,27718
2418,984997,218,3345,0-0,265184019,578995,417,6340,70,0131811220,478987,
118,6341,6-0,227181801969979,315,1326,219022,1861000,022,8360,5-0,159192
42380997,322,4356,7-0,175194023,676995,422,1353,8-0,0181911224,474987,32
2,6352,5-0,252191802269979,518,2335,420027,2721000,025,9365,50,027202427
,871997,326,5366,2-0,271204028,367995,525,7361,80,0112011229,665987,526,
9362,6-0,3182018027,259979,921,2341,021023,5851000,024,6365,6-0,26721242
3,680997,323,2359,2-0,286214024,175995,422,5354,7-0,0242111224,873987,32
2,8352,9-0,2502118023,964979,618,9336,022023,8711000,020,9349,6-0,243222
425,263997,320,1343,8-0,217224025,560995,519,5340,3-0,219221122649987,41
6,4324,6-0,1402218025,245979,714,4315,123025,9811000,027,0372,1-0,067232
42680997,326,8370,5-0,319234026,575995,525,9365,4-0,0942311226,173987,42
4,6358,6-0,1672318025,269979,722,1347,324025,7801000,026,4369,7-0,029242
425,780997,326,4369,0-0,431244025,875995,524,9362,10,0502411226,776987,4
26,6365,7-0,2492418024,672979,722,2348,825026,2691000,023,4356,70,000252
426,768997,323,8356,7-0,352254026,565995,522,5351,1-0,0042511227,364987,
423,2350,8-0,2092518025,261979,719,5336,626019,3581000,013,0321,80,06026
2419,460997,213,5323,2-0,231264018,459995,412,5319,6-0,0472611220,154987
,112,7316,2-0,1142618018,252979,310,8308,427021,2701000,017,6339,30,0562
72421,571997,218,2340,6-0,246274021,867995,417,5336,7-0,0952711222,96098
7,216,7329,9-0,1752718021,854979,514,1318,028017,4891000,017,6345,00,108
282419,186997,219,0347,6-0,408284019,977995,417,8341,1-0,0072811219,8799
87,118,2340,6-0,1312818018,975979,316,3331,629022,3841000,022,6359,0-0,0
55292422,782997,322,6357,7-0,244294023,377995,422,0353,8-0,0582911223,17
6987,321,4349,7-0,193291802270979,518,5336,630023,6941000,027,3377,2-0,2
53302422,893997,325,7371,1-0,299304023,985995,425,2366,4-0,0803011224,28
1987,324,4360,6-0,2373018022,974979,620,6344,531018,7851000,018,3345,9-0
,490312418,873997,215,8334,2-0,163314019,469995,415,5331,6-0,0603111218,
370987,014,7327,3-0,1203118017,765979,213,1319,1

Таблица 2 – Значения радиометеорологических величин на высоте 0 м за
месяц

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N,
ед1023,1811000,022,8359,02021,7891000,023,0362,13021,2821000,020,6352,34
021,6781000,020,1349,45020,5921000,022,1360,06021,9861000,022,5359,67022
,8861000,023,8363,68024,1911000,027,3376,19020891000,020,8354,810021,681
1000,020,8352,811018,3951000,019,9353,712016,7841000,015,9338,413017,288
1000,017,2343,414020,6801000,019,4347,915023,7731000,021,3351,716024,676
1000,023,5359,317022,5791000,021,5354,118019,2891000,019,8351,619022,186
1000,022,8360,520027,2721000,025,9365,521023,5851000,024,6365,622023,871
1000,020,9349,623025,9811000,027,0372,124025,7801000,026,4369,725026,269
1000,023,4356,726019,3581000,013,0321,827021,2701000,017,6339,328017,489
1000,017,6345,029022,3841000,022,6359,030023,6941000,027,3377,231018,785
1000,018,3345,9Средние
значения21,9821000,021,6355,4Ср.квад.отклонение2,78,30,03,411,6

Таблица 3 – Значения радиометеорологических величин на высоте 24 м за
месяц

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N, N –
ед1242379997,322,1355,522420,489997,221,3355,732421,875997,219,5346,1424
21,874997,219,3345,052419,691997,220,7354,462422,381997,221,8354,9724238
0997,322,4356,782424,482997,325,0365,492419,288997,219,5349,9102421,1799
97,219,7347,9112417,492997,218,2346,9122416,377997,214,2330,7132417,1819
97,215,8336,3142421,474997,218,8343,6152424,269997,320,8347,9162425,3749
97,323,8359,0172421,474997,218,8343,6182418,984997,218,3345,019242380997
,322,4356,7202427,871997,326,5366,2212423,680997,323,2359,2222425,263997
,320,1343,823242680997,326,8370,5242425,780997,326,4369,0252426,768997,3
23,8356,7262419,460997,213,5323,2272421,571997,218,2340,6282419,186997,2
19,0347,6292422,782997,322,6357,7302422,893997,325,7371,1312418,873997,2
15,8334,2Средние
значения22,078997,220,8351,0Ср.квад.отклонение2,98,00,03,511,5

Таблица 4 – Значения радиометеорологических величин на высоте 40 м за
месяц

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N, N –
ед14026,575995,525,9365,424022,682995,422,4356,834022,771995,419,5344,34
4023,770995,420,5346,854023,581995,423,4359,664026,577995,526,6368,37402
5,275995,524,0359,484027,473995,526,6366,89402179995,419,6347,1104022,47
4995,420,0346,7114017,985995,317,4341,9124016,774995,314,0328,7134017,17
7995,315,0332,4144021,970995,418,3340,4154024,966995,520,7346,2164026,27
0995,523,8356,9174023,270995,419,9345,0184019,578995,417,6340,7194023,67
6995,422,1353,8204028,367995,525,7361,8214024,175995,422,5354,7224025,56
0995,519,5340,3234026,575995,525,9365,4244025,875995,524,9362,1254026,56
5995,522,5351,1264018,459995,412,5319,6274021,867995,417,5336,7284019,97
7995,417,8341,1294023,377995,422,0353,8304023,985995,425,2366,4314019,46
9995,415,5331,6Средние
значения23,173995,420,9349,4Ср.квад.отклонение3,16,30,03,912,5

Таблица 5 – Значения радиометеорологических величин на высоте 112 м за
месяц

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N, N –
ед111224,375987,322,7353,4211222,784987,223,1357,5311223,369987,319,7342
,0411223,764987,318,7337,3511220,883987,220,3348,4611224,576987,323,3355
,5711224,973987,322,9353,3811225,572987,423,4354,6911220,281987,119,1344
,01011222,775987,220,6346,91111218,387987,018,3342,91211217,273987,014,3
327,01311217,579987,015,8333,11411222,768987,218,7338,71511225,965987,42
1,7346,61611227,766987,424,5355,51711224,468987,320,7344,81811220,478987
,118,6341,61911224,474987,322,6352,52011229,665987,526,9362,62111224,873
987,322,8352,9221122649987,416,4324,62311226,173987,424,6358,62411226,77
6987,426,6365,72511227,364987,423,2350,82611220,154987,112,7316,22711222
,960987,216,7329,92811219,879987,118,2340,62911223,176987,321,4349,73011
224,281987,324,4360,63111218,370987,014,7327,3Средние
значения23,272987,320,6345,6Ср.квад.отклонение3,18,50,13,612,1

Таблица 6 – Значения радиометеорологических величин на высоте 180 м за
месяц

ЧислоВысота, мСредняя t°CСредняя f%Среднее P, гПаСредняя е, гПаСредний
N, N –
ед118022,570979,619,0338,3218020,376979,418,1337,2318020,860979,414,7322
,0418021,360979,515,2323,3518019,476979,317,1334,2618022,169979,518,3335
,8718022,169979,518,3335,8818024,267979,720,2340,8918019,592979,320,8350
,31018020,571979,417,1332,7111801777979,214,9327,81218015,369979,012,031
7,01318016,373979,113,5322,51418020,564979,415,4325,41518023,662979,618,
0332,51618025,359979,719,0334,2171802359979,616,5327,0181801969979,315,1
326,2191802269979,518,2335,42018027,259979,921,2341,02118023,964979,618,
9336,02218025,245979,714,4315,12318025,269979,722,1347,32418024,672979,7
22,2348,82518025,261979,719,5336,62618018,252979,310,8308,42718021,85497
9,514,1318,02818018,975979,316,3331,6291802270979,518,5336,63018022,9749
79,620,6344,53118017,765979,213,1319,1Средние
значения21,567979,517,2331,7Ср.квад.отклонение2,98,90,22,910,2

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