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Solar irradiation and asimuth calculation sheet
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22.00 1 2010 Lokbatan Shikhzairli D M Y Long Lat Intensity MeanDistance,km Intensity Distance,km Intensity Distance, km 19.00 11 1981 456 29 49 40.5 5 3.8 77 4.7 45 4.3 6122.00 12 2000 528 10 54.8 39.5 7.4 4.6 435 4.4 493 4.5 46422.00 3 1879 528 131 47.6 39.2 6.5 4.4 214 4.6 187 4.5 20016.00 9 1989 384 21 51.6 40.4 6.5 4.9 161 4.4 215 4.6 188
4.00 11 1946 96 64 54.5 39.8 7.5 4.8 405 4.6 462 4.7 4333.00 8 1832 72 178 48.6 40.6 5.4 4 99 5.3 44 4.7 729.00 8 1828 216 182 48.4 40.7 5.7 4.2 117 5.3 59 4.7 88
20.00 6 1990 480 20 49.3 37 7.4 4.8 369 4.8 389 4.8 3797.00 8 1875 168 135 48.7 40.7 5.4 4.1 95 5.6 38 4.8 66
27.00 1 1963 648 47 49.8 41.1 6.2 5.2 102 5.1 108 5.1 10519.00 2 1924 456 86 48.6 39.4 6.6 5.1 155 5.2 146 5.1 151
7.00 6 1911 168 99 50.5 41 6.4 5.3 111 4.9 141 5.1 12611.00 6 1859 264 151 48.5 40.7 5.9 4.6 110 5.8 52 5.2 8128.00 1 1872 672 138 48.7 40.6 5.7 4.6 90 6.3 32 5.5 61 b 18.00 9 1961 432 49 50.2 41.1 6.6 5.6 114 5.3 133 5.5 123
8.00 7 1895 192 115 53.7 39.5 8.2 6.1 349 5.9 406 6 37825.00 11 2000 600 10 50 40.2 6.2 7 32 5.5 85 6.3 5925.00 11 2000 600 10 49.9 40.2 6.4 6.5 55 5.6 94 6 7413.00 2 1902 312 108 48.6 40.7 6.9 6.2 103 7.5 46 6.9 75 a b
1800 1850 1900 1950 2000 20500
2
4
6
8
10
12
Column HMoving average (Column H)
Resource Description
a Ais Aliyevetal. [2002],
G&F is Guliyevand Feizullayev[1995], GSI is Geological Survey of Indian (2005, available at http://www.gsi.gov.in/ mudvol.htm), B&E is Baciuand Etiope[2005], Dis Delisleetal. [2002]C&T is Chigiraand Tanaka[1997]. NatGeo National Geografic
Earthquake locations are from Kondorskayaand Shebalin[1982]when availableotherwise, they are from the NEIC. Historical earthquakes without locations (indicated by a dash) were not found in the available catalogs. Depths of earthquakes are shallow or assumed shallow except for the 1977 Romania event (90 km). b Distance was calculated to the nearest rupture rather than the epicenter. B04304 MELLORS ET AL.: EARTHQUAKES AND MUD VOLCANO ERUPTIONS 2of 11 B04304
Table 1. Earthquakes and Closely Related Mud Volcano Eruptions as Compiled From Various Sourcesa Region Earthquakes Mud Volcano Eruptions
C&T
Latitude Chart for Major Cities of the World
City State Latitude
35° N
Alaska 61° NAtlanta Georgia 34° N
Boston 42° NChicago Illinois 42° NCleveland Ohio 41° NDallas Texas 33° NDenver Colorado 40° NDetroit Michigan 42° NHonolulu Hawaii 21° N
Jackson 32° N
Missouri 39° N
Nevada 36° N
Arkansas 35° N
California 34° NMiami Florida 26° N
Wisconsin 46° N
Nashville 36° N
Louisiana 30° NNew York New York 41° N
Oklahoma 35° N
40° NPhoenix Arizona 33° NPortland Oregon 46° N
Richmond Virginia 37° N
Utah 41° N
Texas 29° N
Latitudes of major cities around the world are listed below. To determine the latitude of a location not listed on the chart, locate the
Northern hemisphere observers (N): If your location is over 70 miles (110 km) north of the listed
Southern hemisphere observers (S): If your location is over 70 miles north of the listed
UNITED STATES
Albuquerque
New Mexico
Anchorage
Massachusetts
Mississippi
Kansas City
Las Vegas
Little Rock
Los Angeles
Milwaukee
Tennessee
New Orleans
Oklahoma City
Philadelphia
Pennsylvania
Salt Lake City
San Antonio
California 33° N
California 38° N
Seattle 47° N
39° NWichita Kansas 38° N
EUROPE
City Country Latitude
52° NAthens Greece 38° N
Bern 47° N
Denmark 56° NDublin Ireland 53° NFrankfurt Germany 50° NGlasgow Scotland 56° NHelsinki Finland 60° NLisbon Portugal 39° NLondon England 51° NMadrid Spain 40° NOslo Norway 60° NParis France 49° NRome Italy 42° N
Sweden 59° NVienna Austria 48° NWarsaw Poland 52° N
City State LatitudeAsuncion Paraguay 25° SBrasilia Brazil 24° S
Argentina 35° S
Uruguay 35° SSantiago Chili 34° S
City State LatitudeBeijing China 40° N
Seoul 37° NTaipei Taiwan 25° NTokyo Japan 36° N
San Diego
San Francisco
Washington
Washington
District of Columbia
Amsterdam
Netherlands
Switzerland
Copenhagen
Stockholm
SOUTH AMERICA
Buenos Aires
Montevideo
ASIA
South Korea
Victoria 23° N
City State LatitudeCairo Egypt 30° N
34° SRabat Morocco 34° NTunis Tunisia 37° N
Windhoek Namibia 23° S
City State Latitude
Adelaide 35° S
Brisbane 27° S
Canberra 35° S
24° SHobart Tasmania 43° S
Perth 32° S
Sydney 34° S
Victoria 38° S
Hong Kong
AFRICA
Cape Town
South Africa
AUSTRALIA
South Australia
Queensland
New South Wales
Alice Springs
Northern Territory
Western Australia
New South Wales
Melbourne
of major cities around the world are listed below. To determine the latitude of a location not listed on the chart, locate the city closest to you and then follow the procedure below:
If your location is over 70 miles (110 km) north of the listed city, add one degree for every 70 miles. If it is over 70 miles south of the listed
If your location is over 70 miles north of the listed city, subtract one degree for every 70 miles. If it is over 70 miles south of the listed
closest to you and then follow the procedure below:
, add one degree for every 70 miles. If it is over 70 miles south of the listed city, subtract one degree per 70 miles.
, subtract one degree for every 70 miles. If it is over 70 miles south of the listed city, add one degree per 70 miles.
aS E
Solar Surface aS/E
Material Absorption ratio
Silver, Highly polished 3 Marks (1)
Gold, Highly polished 3 Marks (1)
Barium Sulphate with Polyvinyl Alcohol 0.06 0.88 0.07
Aluminum polished 0.09 0.03 3 ?
Magnesium Oxide Paint 0.09 0.9 0.1
Magnesium/Aluminium Oxide Paint 0.09 0.92 0.1
Aluminum quarts overcoated 0.11 0.37 0.3 ?
Aluminum, Highly polished 3 Marks (1)
Snow, Fine particles fresh 0.13 0.82 0.16 ?
Zinc Orthotitanate with Potassium Silicate 0.13 0.92 0.14
Aluminum anodized 0.14 0.84 0.17 ?
Aluminum foil 0.15 0.05 3 ?
Potassium Fluorotitanate White Paint 0.15 0.88 0.17
Zinc Oxide with Sodium Silicate 0.15 0.92 0.16
Paint, White zinc oxide 0.16 0.93 0.17 ?
GSFC White Paint NS-74 0.17 0.92 0.18
Titanium Oxide White Paint with Potassium Silicate 0.17 0.92 0.18
Zerlauts Z-93 White Paint 0.17 0.92 0.18
Cromium 0.026666667 0.08 3 Marks (1)
Cromium 0.086666667 0.26 3 Marks (1)
Dow Corning White Paint DC-007 0.19 0.88 0.22
GSFC White Paint NS43-C 0.2 0.92 0.22
Titanium Oxide White Paint with Methyl Silicone 0.2 0.9 0.22
Zerlauts S-13G White Paint 0.2 0.9 0.22
Light colored paints, firebrick, clay, glass 0.04 - 0.40 0.9 0.24
Biphenyl-White Solid 0.23 0.86 0.27
P764-1A White Paint 0.23 0.92 0.25
Zirconium Oxide with650 Glass Resin 0.23 0.88 0.26
Solec LO/MIT selective surface paint 0.21 - 0.26 1.38
Catalac White Paint 0.24 0.9 0.27
Hughson White Paint Z-202 0.25 0.87 0.29
Hughson White Paint Z-255 0.25 0.89 0.28
Hughson White Paint Z-255 0.25 0.89 0.28
3M-401 White Paint 0.25 0.91 0.27 ?
Hughson White Paint A-276 0.26 0.88 0.3
Hughson White Paint V-200 0.26 0.89 0.29
OSO-H White Paint 63W 0.27 0.83 0.33
Opal Glass 0.28 0.87 0.32
Sherwin Williams White Paint (A8W11) 0.28 0.87 0.32
Mautz White House Paint 0.3 0.9 0.33
Snow, Ice granules 0.33 0.89 0.37 ?
GSFC White Paint NS44-B 0.34 0.91 0.18
Sperex White Paint 0.34 0.85 0.4
Dupont Lucite Actylic Lacquer 0.35 0.9 0.39
GSFC White Paint NS-37 0.36 0.91 0.4
Sherwin Williams F8WJ2030 w Polasol V6V241 0.36 0.87 0.41
Sherwin Williams White Paint (F8WJ2030) 0.39 0.82 0.48
Tedlar White Paint 0.39 0.87 0.45
Hughson White Paint Z-202+1000 0.4 0.87 0.46
Aluminum paint (bright) 0.30 - 0.50 0.8
Hughson White Paint A-276+1O36 0.44 0.88 0.5
Dull brass, copper, galv. steel, aluminum 0.40 - 0.65 2.1
Colored paints, brick, light brick, 0.50 - 0.70 0.67
Concrete 0.6 0.88 0.68 ?
Galvanized metal new 0.65 0.13 5 ?
Brick, red (Purdue) 0.65 0.93 0.68 ?
Concrete and stone, dark 0.65 - 0.80 0.81
Galvanized metal weathered 0.8 0.28 2.9 ?
Metal, plated Black chrome 0.87 0.09 9.7 ?
Anodize Black 0.88 0.88 1
Martin Black Velvet Paint 0.91 0.94 0.97
Solec Solkote selective surface paint 0.88 - 0.94 2.36
Metal, plated Nickel oxide 0.92 0.08 11 ?
Metal, plated Black sulfide 0.92 0.1 9.2 ?
Pyramil Black on Beryllium Copper 0.92 0.72 1.28
Metal, plated Cobalt oxide 0.93 0.3 3.1 ?
Polyethylene Black Plastic 0.94 0.92 1.01
Martin Black Paint N-150-1 0.94 0.94 1
Tedlar Black Plastic 0.94 0.9 1.04
Iron and Steel, strongly oxidized 0.95 3 Marks (1)
Hughson Black Paint L-300 0.95 0.84 1.13
Paladin Black Lacquer 0.95 0.75 1.27
Black Crystal 0.92 - 0.98 5.76
Crystal Clear 0.95 - 0.97 8.35
Carbon Black Paint NS-7 0.96 0.88 1.09
Carbon Black Paint 0.96 0.88 1.09
Chemglaze Black Paint Z3O6 0.96 0.91 1.05
Absorptivity & Emissivity table 1 plus others.
Emissivity
Comments
Reference
0.02 - 0.030.02 - 0.04
The Fridge
The Fridge
The Fridge
0.04 - 0.06
The Fridge
Aluminum foil gets very hot because of this high ratio.
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
U of Miss
The Fridge
The Fridge
The Fridge0.15 - 0.19
LO/MIT I/II products are low Solec
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge0.40 - 0.60 U of Miss
The Fridge0.20 - 0.30 U of Miss0.85 - 0.95 U of Miss
0.85 - 0.95 U of Miss
The Fridge
The Fridge0.28 - 0.49
SOLKOTE HI/SORB-II is an Solec
This is stainless steel heated
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge0.08 - 0.25
Thermafin's Black Crystal Selective Thermafin0.09 -
0.14
Thermafin's Crystal Clear Selective Thermafin
The Fridge
The Fridge
The Fridge
Delrin Black Pastic 0.96 0.87 1.1
GSFC Black Silicate MS-94 0.96 0.89 1.08
GSFC Black Paint 313-1 0.96 0.86 1.12
Hughson Black Paint H322 0.96 0.86 1.12
Velesat Black Plastic 0.96 0.85 1.12
Solchrome 0.94 - 0.98 8
Ebanol C Black 0.97 0.73 1.33
Ebanol C Black-384 ESH* UV 0.97 0.75 1.29
3M Black Velvet Paint 0.97 0.91 1.07
Parsons Black Paint 0.98 0.91 1.08
Flat black paint 0.97 - 0.99 1
Paint, Black (Parsons) 0.98 0.98 1 ?
Selective surfaces
Solec LO/MIT selective surface paint 0.21 - 0.26 1.38
White paint 0.23 - 0.49
Solec SOLKOTE selective surface paint 0.88 - 0.94 2.36
Copper, aluminum, or nickel plate with CuO coating 0.08 - 0.93 3.37
Black Crystal 0.92 - 0.98 5.76
0.87 0.13 6.69
Solchrome 0.94 - 0.98 8
Crystal Clear 0.95 - 0.97 8.35
Metal, plated Black sulfide 0.92 0.1 9.2 ?
Metal, plated Black chrome 0.87 0.09 9.7 ?
Metal, plated Nickel oxide 0.92 0.08 11 ?
The Fridge
The Fridge
The Fridge
The Fridge
The Fridge0.10 - 0.14
Solchrome Systems India Solchrome
The Fridge
The Fridge
The Fridge
The Fridge0.97 - 0.99 U of Miss
I understand this is lamp
0.15 - 0.19
LO/MIT I/II products are low Solec
U of Miss0.28 - 0.49
SOLKOTE HI/SORB-II is an Solec0.09 -
0.21 U of Miss0.08 - 0.25
Thermafin's Black Crystal Selective Thermafin
Copper treated with NaCIO2 and NaOH U of Miss0.10 - 0.14
Solchrome Systems India Solchrome0.09 -
0.14
Thermafin's Crystal Clear Selective ThermafinThis is stainless steel heated
NELSPRUIT EFFECTIVE AS OF 19 JANUARY 2009
950
GALVANISEDMETRE MASS PRICE /M SQ.METRE EXCL
/TON KG/M EXCL. IBR 10.5 W/m2 Length width DayHours Price
0.40mm ISQ 300 Z160 344 2.907 47.03 68.55 61.70 0.725 0.205 3.95 141.1938 7.2 0.762195 774.8438 6 4649.063 14.4 1,012.84 0.50mm ISQ 550 Z160 274 3.650 57.57 83.93 75.53 0.725 0.92 9.2 633.65 7.2 0.762195 3477.348 6 20864.09 14.4 1,239.98 0.50mm ISQ 550 Z275 275 3.636 59.76 87.12 78.40 0.725 0.87 9.7 599.2125 7.2 0.762195 3288.361 6 19730.17 14.4 1,287.08 0.58mm ISQ 300 Z275 237 4.219 67.46 98.34 88.51 0.725 0.92 11 633.65 7.2 0.762195 3477.348 6 20864.09 14.4 1,452.92 0.80mm ISQ 230 Z275 172 5.814 89.83 130.95 117.85 0.725 0.205 3.95 141.1938 7.2 0.762195 774.8438 6 4649.063 14.4 1,934.68
237 4.219 79.00 115.16 103.64 0.725 0.205 3.95 141.1938 7.2 0.762195 774.8437 6 4649.062 14.4 1,701.41 172 5.814 103.23 150.49 135.44 0.725 0.205 3.95 141.1938 7.2 0.762195 774.8438 6 4649.063 14.4 2,223.42
-
CHROMADEK
METRE MASS PRICE /M SQ.METRE EXCL
/TON KG/M EXCL. IBR 10.5 0.50mm ISQ 550 Z200 275 3.636 80.07 116.73 105.05 0.87 0.09 9.7 74.385 3.6 0.762195 204.1052 6 1224.6310.58mm ISQ 300 Z200 237 4.219 88.75 129.37 116.44 0 4.6 0.762195 0 7 00.80mm ISQ 230 Z200 172 5.814 115.42 168.26 151.43 0 5.6 0.762195 0 8 00.50mm ISQ 550 Z275 275 3.636 0.58mm ISQ 300 Z275 237 4.219
0.80mm ISQ 230 Z275 172 5.814
0.1 0.92
0.09 0.87
ZINCALUME AZ150
METRE MASS PRICE /M SQ.METRE EXCL
0.08 0.92/TON KG/M EXCL. IBR 10.5
0.47mm 300 3.333 75.69 110.34 99.30 0.53mm 265 3.774 87.21 127.14 114.42 1200x0.55mm f/feed 188 5.306 118.24 172.37 155.13
COLORBOND METRE MASS PRICE /M SQ.METRE EXCL /TON KG/M EXCL. IBR 10.5
0.47mm 297 3.367 90.74 132.28 119.05 0.53mm 263 3.802 100.39 146.35 131.71 1200x0.55mm f/feed 188 5.306 131.08 191.09 171.98
8.5/76 CORRUGATED METRE MASS PRICE 8.5 CORR GALVANISED /TON KG/M METRE SQ.METRE
0.30mm ISQ 550 Z100 514 1.946 30.11 49.35 0.50mm ISQ 550 Z275 283 3.534 Withdrawn
Galvanized metal AVG
Total Energy W/3.6m
Requirement-m
0.58mm ISQ 300 Z6000.80mm ISQ 230 Z600
Metal, plated Black chrome
Metal, plated Black sulfide
Metal, plated Black chrome
Metal, plated Nickel oxide
Hello, Hello,
sorry, I missed the first request. Attached what I use to calculate sorry, I missed the first request. Attached what I use to calculate
your rollerblinds. That how I did it. your rollerblinds. That how I did it.
Longitude 26Latitude 24
K 0.01745365.3422 30.4451833333333
08/Apr/23 12:36
2023099daycountl 45025.03 #daycountl = (month-1)*30 + date + 0.5deklin 14.9878150757083 #deklin = -23.45*cos(K*360*(daycount+10)/365)timediff 1.33333333333333 #timediff = hour + minute/60 - (15.0-longitude)/15.0 - 12x 0.934457699399226 #x = sin(K*latidute)*sin(K*deklin) +
#NAME? cos(K*latidute)*cos(K*deklin)*Math.cos(K*15*timediff)#sunhight 65.2408269216558 #sunhight = x/K + 0.25*x*x*x/K (ARCSIN-approximated through polynom)
#NUM!(ARCSIN-approximated through polynom)use vars ('$altitude', '$SolZen'); use vars ('$altitude', '$SolZen');
my $tageszahl 98.50
14.98781507570831.33333333333333
; $config_parms{longitude}) / 15 - 12;0.934457699399226
cos(KValue*15*$zeitdiff);65.2408269216558
-0.142257038896788
sqrt(1 - $x * $x), $x)));-8.18001562044577
0}
SolZen is the direction of the sun (0 is north) SolZen is the direction of the sun (0 is north)altitude is the hight of the sun. (0 is she is half down the hoizont) altitude is the hight of the sun. (0 is she is half down the hoizont)
To trigger actions I use the following vars: To trigger actions I use the following vars:my $Sonne_NO = 0; my $Sonne_NO = 0;my $Sonne_NW = 0; my $Sonne_NW = 0;my $Sonne_SO = 0; my $Sonne_SO = 0;my $Sonne_SW = 0; my $Sonne_SW = 0;
$altitude >=30 && $altitude <=90) ? 1 : 0; $altitude >=30 && $altitude <=90) ? 1 : 0;
$altitude >=30 && $altitude <=90) ? 1 : 0; $altitude >=30 && $altitude <=90) ? 1 : 0;$Sonne_NW = ($SolZen >= 275 && $SolZen <= 150 && $Sonne_NW = ($SolZen >= 275 && $SolZen <= 150 &&$altitude >=30 && $altitude <=90) ? 1 : 0; $altitude >=30 && $altitude <=90) ? 1 : 0;
Of course you have to change the values in the round brackets to your needs. Of course you have to change the values in the round brackets to your needs.
KR KR
the azimuth (direction) and the elevation (hight over the horizon) of the azimuth (direction) and the elevation (hight over the horizon) ofthe sun. If you estimate for each front of your house for which angles the sun. If you estimate for each front of your house for which anglesthe sun is shinig on the front you can do the appropriate actions with the sun is shinig on the front you can do the appropriate actions with
Sorry, code is in German, but you should get the idea. Sorry, code is in German, but you should get the idea.
# Source: http://www.jgiesen.de/SME/tk/index.htm # Source: http://www.jgiesen.de/SME/tk/index.htmDate above in "Julian" format, with a four-digit year
(2007174)
if ($New_Minute || $Reload || $Startup || state_changed $Anwesend eq OFF) { if ($New_Minute || $Reload || $Startup || state_changed $Anwesend eq OFF) { my $tageszahl = ($Month - 1) * 30 + $Mday + 0.5; my KValue = 0.01745;
my deklin my deklin = -23.45 * cos( KValue * 360 * ($daycount + 10) / 365); my $zeitdiff = my $zeitdiff = $Hour + $Minute / 60 - (15 -
my $x = my $x = sin(KValue * $config_parms{latitude}) * sin(KValue * deklin) + cos(KValue * $config_parms{latitude}) * cos(KValue * deklin) *
$altitude = $altitude = $x/KValue + 0.25*$x*$x*$x/KValue; my $y = my $y = -(sin(KValue * $config_parms{latitude}) *$x - sin(KValue * deklin)) /
(cos(KValue * $config_parms{latitude}) * sin(atan2(
$SolZen = $SolZen = atan2( sqrt(1- $y * $y), $y) / KValue; $SolZen = $SolZen = 360 - $SolZen if ($Hour > 12);
$Sonne_SO = ($SolZen >= 95 && $SolZen <= 250 && $Sonne_SO = ($SolZen >= 95 && $SolZen <= 250 &&
$Sonne_NO = ($SolZen >= 0 && $SolZen <= 130 && $Sonne_NO = ($SolZen >= 0 && $SolZen <= 130 &&
1.1 Beam radiationF 33 1.566939 Anglof roof or object(more or less tracking the sun or staticS 56.779005292 1.981961 Flat on horizon ie level
1 1.9819611767
1367.0000 W.m-2
-1 FltincAnlge
1322.5022 FltincAnglewhere:
e = 0.9674
-3j’ = 85.1029 4948.396 =j
-4
1130.4672587
-0.8662
-5m= -0.000251809
0.00024335798
-6
1.9822045347 h0ref
m = -0.000258283
given elevation z [m] 1.981961
-7
exp -0.000235
for m <= 20:
-8
0.10333070985for m > 20 0.0845805574
-9
0.08458055735
-10
1036.2494606
-11
870.716903or
-12
1036.2494606
-22
-101.153523
-23
-0.042014457
-24
1.8204797619
-25
0.3203280121
-0.052362929
2.0431251574
-1.330098394
Outside the atmosphere, at the mean solar distance, the beam irradiance, also known as the solar constant (I0),
I0 =
G0 = I0 e
G0 =
e = 1 + 0.03344 cos (j’ - 0.048869) (2)
the day angle j’ is in radians:
j’ = 2 p j/365.25
and j is the day number which varies from 1 on January 1st to 365 (366) on December 31st.
The beam irradiance normal to the solar beam B0c [W.m-2], is attenuated by the cloudless atmosphere, and calculated as follows:
B0c = G0 exp {-0.8662 TLK m dR(m)}
B0c = The term -0.8662 TLK is the air mass 2 Linke atmospheric turbidity factor [dimensionless] corrected by Kasten (1996).
TLK
m = (p/p0)/(sin h0ref + 0.50572 (h0
ref + 6.07995)-1.6364)
where h0ref is the corrected solar altitude h0 (an angle between the sun and horizon) in degrees by the atmospheric refraction component Dh0
ref:
Dh0ref=0.061359 (0.1594+1.123 h0 + 0.065656 h0
2)/(1 + 28.9344 h0 + 277.3971 h02)
Dh0ref=
h0ref = h0 + Dh0
ref
h0ref =
The p/p0 component in equation (5) is correction for given elevation z [m]:
m = (p/p0)/(sin h0ref + 0.50572 (h0
ref + 6.07995)-1.6364)
p/p0 = exp (-z/8434.5)
p/p0 =
The parameter dR(m) in equation (4) is the Rayleigh optical thickness at air mass m and is calculated according to the improved formula by Kasten (1996) as follows:
dR(m) = 1/(6.6296 + 1.7513 m - 0.1202 m2 + 0.0065 m3 - 0.00013 m4)
dR(m) =
dR(m) = 1/(10.4 + 0.718 m)
dR(m) =
The beam irradiance on a horizontal surface Bhc [W.m-2] is then calculated as:
Bhc = B0c sin h0
Bhc =
where h0 is the solar altitude angle given by equation (13).
The beam irradiance on an inclined surface Bic [W.m-2] is calculated as:
Bic = B0c sin dexp
Bic =
Bic = Bhc sin dexp/sin h0
Bic =
where dexp is the solar incidence angle measured between the Sun and an inclined surface (equation 17).1.2 Diffuse radiation [top of the page]
As the cloudless sky becomes more turbid, the diffuse irradiance increases while the beam irradiance decreases. The estimation of the diffuse component on a horizontal surface Dhc [W.m-2] is made as a product of the normal extraterrestrial irradiance G0, a diffuse transmission function Tn dependent only on the Linke turbidity factor TLK, and a diffuse solar altitude function Fd dependent only on the solar altitude h0 (Scharmer and Greif 2000):
Dhc = G0 Tn(TLK) Fd(h0)
Dhc =
The estimate of the transmission function Tn(TLK) gives a theoretical diffuse irradiance on a horizontal surface with the Sun vertically overhead for the air mass 2 Linke turbidity factor. The following second order polynomial expression is used:
Tn(TLK) = -0.015843 + 0.030543 TLK + 0.0003797 TLK2
Tn(TLK) =The solar altitude function is evaluated using the expression:
Fd(h0) = A1 + A2 sin h0 + A3 sin2 h0
Fd(h0) =
where the values of the coefficients A1, A2 and A3 are only depended on the Linke turbidity TLK defined in the following expressions:
A1' = 0.26463 - 0.061581 TLK + 0.0031408 TLK2
A1' =
A1 = 0.0022/Tn(TLK) if A1' Tn(TLK) < 0.0022
A1 =
A1 = A1’ if A1' Tn(TLK) >= 0.0022
A2 = 2.04020 + 0.018945 TLK - 0.011161 TLK2
A2 =
A3 = -1.3025 + 0.039231 TLK + 0.0085079 TLK2
A3 =
The model for estimating the clear-sky diffuse irradiance on an inclined surface Dic [W.m-2] distinguishes between sunlit, potentially sunlit and shadowed surfaces. The equations are as follows (Muneer 1990):
a) for sunlit surfaces and non-overcast sky (h0 in radians):
-26
6251.580767
-27
5025.9017639where
-28
-72.69258825
-72.69258825-72.69258825
-78.97577356
-66.40940294
-66.40940294
-29
41.085889842
-30
20.729916572
-31
0.3001613173and value of N for surfaces in shadow is 0.25227. For sunlit surfaces under clear sky the term N is calculated as:
-32N = -7.165495108
-33
3.4320238956
-34
301.93538628
203.60541341-35 where:
-36
0.9805396424
-37
1038.2314218Albedo= 0.2
-13 sin h0 = xC31 cos T + xC33sin h0 = -0.925106277
cos A0 = (xC11 cos T + xC13)/((xC22 sin T)2+ (xC11 cos T + xC13)2)1/2cos A0 = 0.0805780534
where:
-14 xC11 = sin j cos dxC11 = -0.352302882
xC13 = -cos j sin dxC13 = 0.332868379
xC22 = cos dxC22 = 0.9331560423
xC31 = cos j cos dxC31 = -0.864096568
xC33 = sin j sin dxC33 = -0.135714564
-150.3677015359
-16 T = 0.261799 (t - 12)T = 0.4188784
-17
if h0 >= 0.1 (i.e. 5.7°)
Dic = Dhc {F(gN) (1 - Kb) + Kb sin dexp/sin h0}
Dic =
if h0 < 0.1
Dic = Dhc {F(gN) (1 - Kb) + Kb sin gN cos ALN/(0.1 - 0.008 h0)}
Dic = Dic = Dhc {F(gN) (1 - Kb) + Kb sin gN cos ALN/(0.1 - 0.008 h0)}
A*LN = A0 - AN
A*LN =
if -p <= A*LN <= p ALN = A*LN
ALN =
if ALN > p ALN = A*LN - 2p
ALN =
if A*LN < -p ALN = A*LN + 2p
ALN =
ALN =
b) for surfaces in shadow (dexp < 0 and h0 >= 0):
Dic = Dhc F(gN)
Dic =
where F(gN) is a function accounting for the diffuse sky irradiance that may be calculated by the following equation (gN in radians):
F(gN) = ri(gN) + (sin gN - gN cos gN - p sin2 (gN/2)) N
F(gN) =
where ri(gN) is a fraction of the sky dome viewed by an inclined surface [dimensionless]:
ri(gN) = (1 + cos gN)/2
ri(gN) =
N = 0.00263 – 0.712 Kb – 0.6883 Kb2
The Kb is a measure of the amount of beam irradiance available (proportion between beam irradiance and extraterrestrial solar irradiance on a horizontal surface):
Kb = Bhc/G0h
Kb =
where G0h [W.m-2] is calculated as:
G0h = G0 sin h0
G0h =1.3 Ground reflected radiation [top of the page]
The estimation of the clear-sky ground reflected irradiance for inclined surfaces (Ri) relies on an isotropic assumption. The ground reflected clear-sky irradiance received on an inclined surface [W.m-2] is proportional to the global horizontal irradiance Ghc, to the mean ground albedo rg and a fraction of the ground viewed by an inclined surface rg(gN) (Muneer 1997):
Ri = rg Ghc rg(gN)
Ri =
rg(gN) = (1 - cos gN)/2
rg(gN) =
and global irradiance on a horizontal surface Ghc [W.m-2] is given as a sum of its beam and diffuse component:
Ghc = Bhc + Dhc
Ghc =
In Scharmer and Greif (2000, page 141) typical albedo values for a variety of ground surfaces are listed. In general the values of 0.2 or 0.15 are mostly used.
1.4 Position of the Sun [top of the page]
The position of the Sun with respect to a horizontal surface is given by the two co-ordinates – solar altitude h0 (an angle between the Sun path and a horizontal surface), and solar azimuth A0 (horizontal angle between the Sun and meridian - measured from East), and is calculated as follows (Krcho 1990, Jenèo 1992):
The Sun declination d [rad] is computed according to Gruter (1984):
d = arcsin (0.3978 sin (j’ - 1.4 + 0.0355 sin (j’ - 0.0489)))d =
where the calculation of the day angle j’ [radians] is explained in equation (3). The hour angle T [rad] is calculated from the local solar time t expressed in decimal hours on the 24 hour clock as:
The position of the Sun with respect to an inclined surface (the solar incidence angle) is defined by the angle dexp (Krcho 1990, Jenèo 1992). If an inclined surface is defined by the inclination angle gN and the azimuth (aspect) AN (an angle between the projection of the normal on the horizontal surface and East) then:
sin dexp = yC31 cos (T - l’) + yC33
sin dexp = -0.75651328where:I' = 1.9819611767
-18
-0.935696595
0.0982883308and:
-190.6755059066
-6.310157531
-20 cos Thr,s = -xC33/xC31cos Thr,s = -0.157059488
-21 cos (Tir,s - l’) = -yC33/yC31.cos (Tir,s - 0.1050429501
-38
953
953
1038.2314218
-39
0.9179071062
-40
-18.60542486
190.6
Dhs/Ghs 0.8
-41
762.4
190.6
-42
-7.537058301
0.1839325445
yC31 = cos j’ cos d
yC31 =
yC33 = sin j’ sin d
yC33 =
sin j’ = - cos j sin gN cos AN+ sin j cos gN
sin j’ =
tg l’ = - (sin gN sin AN)/(sin j sin gN cos AN+ cos j cos gN).tg l’ =
The hour angle of the time of sunrise/sunset over a horizontal surface Thr,s can be calculated then as:
The hour angle of the time of sunrise/sunset over an inclined surface Tir,s can be calculated by analogy:
2 Computing real-sky radiation [top of the page]
The real-sky irradiance/irradiation are calculated from clear-sky raster maps by the application of a factor parameterizing the attenuation of cloud cover. Examples of explicit calculations of this parameter can be found in Becker (2001), Kitler and Mikler (1986). However, the cloudiness observation by a meteorological service routine is usually prone to subjective errors and does not describe sufficiently the physical nature and dynamic spatial-temporal pattern of different types of cloud cover. Therefore, a simpler parameter has to be used. The solutions for horizontal and inclined surfaces are slightly different.
For the assessment of global irradiance/irradiation on a horizontal surface under overcast conditions Gh the clear-sky values Ghc are multiplied by clear-sky index kc (Beyer et al 1996, Hammer et al 1998, Rigollier et al. 2001):
Gh = Ghc kc
Gh =
The index kc represents the atmospheric transmission expressed as a ratio between horizontal global radiation under overcast and clear-sky conditions. For a set of ground meteorological stations the clear-sky index can be calculated from measured global radiation Ghs and computed values of clear-sky global radiation Ghc:
Ghs
Ghc
kc = Ghs/Ghc
kc =
As an alternative the kc can be derived also from other climatologic data (e.g. cloudiness, cf. Kasten and Czeplak 1980). The raster maps of kc must be then derived by spatial interpolation. The kc can be calculated directly as a raster map from short-wave surface irradiance measured by satellites. This method is based on the complementarity between the planetary albedo recorded by the radiometer and the surface radiant flux (Cano et al 1986, Beyer et al 1996, Hammer et al 1998).
To compute the overcast global irradiance/irradiation for inclined surfaces, Gi the diffuse Dh and beam Bh components of overcast global radiation and of the clear-sky index kc have to be treated separately as follows from the equations (26), (27), (29) and (37):
Dh = Dhc kdc
Dh =
Bh = Bhc kbc
Bh =
The ratio of diffuse to the global radiation Dh/Gh for clear and overcast skies changes according to the cloudiness. In Europe the Dh/Gh values are typically in interval 0.3-1.0 (Kasten and Czeplak 1980). The underlying physical processes are quite complicated and computationally represented only by empirical equations (cf. Scharmer and Greif, 2000, Kasten and Czeplak 1980, Hrvo¾ 1991). However, for many meteorological stations, besides the global horizontal radiation Ghs, the diffuse component Dhs is either measured or calculated from cloudiness, sunshine or other climatologic data. The raster map of Dhs/Ghs can be derived from the point values by spatial interpolation. Consecutively, the raster maps of diffuse and beam components of the clear sky index can be computed:
Dh = Gh Dhs/Ghs
Dh =
Bh = Gh – Dh
Bh =
kdc = Dh/Dhc
kdc =
kbc = Bh/Bhc
kbc =
where subscript s is meant to distinguish data measured on meteorological stations Bhs and Dhs from the estimated values Bh, and Dh.
3 Implementation in GRASS GIS [top of the page]
The presented solar radiation model is a substantial improvement of the older version (Hofierka 1997), which application was limited only to small areas and clear-sky beam radiation. The new model provides a solution for all three components of global solar radiation under clear-sky or overcast conditions. Large areas can be modelled accurately using spatially variable parameters, and shadowing effects of terrain can be modelled by new effective shadowing algorithm.
The r.sun works in two modes. In the mode 1 - for the instant time - it calculates a solar incident angle [degrees] and solar irradiance values [W.m-2]. In the mode 2 the daily sum of solar irradiation [Wh.m-2.day-1] and duration of the beam irradiation are computed within a given day. By scripting the two modes can be used separately or in a combination to provide estimates for any desired time steps or intervals. The model accounts for a sky obstruction by local relief features using an optional shadowing parameter. Details of the command (synopsis, description, notes) can be found on r.sun manual page.
3.1 Model inputs [top of the page]
The model requires only a few mandatory input parameters – digital terrain model (elevation, slope, aspect – elevin, slopein, aspin), day number day (for mode 2), and additionally a local solar time time (for mode 1). However, several other parameters can be set to fit the specific user needs. These parameters have default values that are used unless they are overridden by user settings as a single value or a name of the raster. The table 1 presents a list of all input parameters.
Type Units
name of inputelevin raster elevation 1, 2 meters 0 – 8900aspin raster 1, 2 0 – 360
slopein raster 1, 2 0 – 90
linkein raster 1, 2
single value 1, 2
albedo raster 1, 2 0 – 1
single value 1, 2 0 – 1
latin raster latitude 1, 2 -90 – 90
single value latitude 1, 2 -90 – 90
coefbh raster 1, 2 0 – 1
coefdh raster 1, 2 0 – 1
day single value 1, 2 0 – 366
declin single value 1, 2 radians
single value 1 0 – 24
step single value 2 0.01 – 1.0
single value 1, 2 0.1 – 2.0
Description Mode Units
nameincidout 1
1
diff_rad 1
refl_rad 1
insol_time 2 min.
beam_rad 2
diff_rad 2
refl_rad 2
Parameter
Description
Mode Interval of values
aspect (solar panel azimuth)
decimal degrees
slope (solar panel inclination)
decimal degrees
Linke atmospheric turbidity
dimensionless
0 - »7
lin Linke atmospheric turbidity
dimensionless
0 - »7
ground albedo
dimensionless
alb ground albedo
dimensionless
decimal degrees
lat decimal degrees
clear-sky index for beam component
dimensionless
clear-sky index for diffuse component
dimensionless
day number
dimensionless
solar declination
-0.40928 – 0.40928
time local (solar) time
decimal hours
time step decimal hours
dist sampling distance coefficient for shadowing
dimensionless
Table 1: r.sun input parameters
Solar declination is computed internally using equation (15) and day number unless an explicit value of declin is used. In the case that user’s data are localised in GRASS location with defined projection, r.sun uses internal GRASS function to get geograp
3.2 Model outputs [top of the page]
According to the setting of output parameters the model automatically recognises between modes 1 and 2. When calculating in mode 1 the solar incident angle incidout, and solar irradiance raster maps beam_rad, diff_rad and refl_rad are computed. Calculation in mode 2 gives the sums of solar irradiation within a specified day for selected components of global irradiation beam_rad, diff_rad and refl_rad. A raster map showing duration of beam irradiation insol_time can be computed as well.
Besides clear-sky irradiances/irradiations, the model can calculate overcast radiation on conditions that coefbh and coefdh input raster maps are defined, expressing the beam and diffuse components of clear-sky index (equations 42).
The incidence angle and irradiance/irradiation maps can be computed without considering the terrain shadowing by default or with shadowing effects by setting the flag -s. In mountainous areas this can lead to very different results especially at low sun altitudes. The value of a shadowed area is written to the output maps as zero. The table 2 presents a list of all output raster maps.
Besides output raster maps, the model stores basic solar radiation parameters used in the computation in r.sun_out.txt local text file. Currently it contains day number, solar constant, extraterrestrial irradiance, solar declination, interval of latitude, times of sunrise and sunset, time step, interval of used Linke turbidity and ground albedo.
Solar radiation modeling for periods longer or shorter than one day can be done using UNIX shell scripting within GRASS GIS environment. The example can be found in the book by Neteler and Mitasova (p. 326).
Parameter
solar incidence angle
decimal degrees
beam_rad beam irradiance
W.m-2
diffuse irradiance
W.m-2
ground reflected irradiance
W.m-2
duration of the beam irradiation
beam irradiation
Wh.m-
2.day-
diffuse irradiation
Wh.m-
2.day-1
ground reflected irradiation
Wh.m-
2.day-1
δ azimuth
nadir An extreme state of adversity; the lowest point of anythingalbedo
diurnal Having a daily cycle or occurring every dayξ Declination
β Tilt angle tilt angle of the collectorsangle between surface normal and solar ray
Zzenith
Penumbra A fringe region of partial shadow around an umbraγ Latitude An imaginary line around the Earth parallel to the equatorφ local latitude
θLongitude
ω solar hour angle(1 - 8760) H The angular distance along the celestial equator from the observer's meridian to the hour circle of a given celestial body(astronomy) the angular distance of a celestial point measured westward along the celestial equator from the zenith crossing; the right ascension for an observer at a particular location and time of day
365.3422 Solar Year The time for the earth to make one revolution around the sun, measured between two vernal equinoxesVernal Equinox(Nhem) 22 March 2009 South 2009
0 Vernal Equinox Mar. 21/22 0 22 3/22/2009
23.5 Summer Solstice Jun. 21/22 -23.5 22 3/22/2009
0 Autumnal Equinox Sept. 21/22 0 22 3/22/2009
-23.5 Winter Solstice Dec. 21/22 23.5 22 3/22/20099/20/2009
Solstice Either of the two times of the year when the sun is at its greatest distance from the celestial equator
A collector widthD north-south spacing between collectorsd D/H
beam insolation (Wh/m2)
diffuse insolation (Wh/m2) H h eight ( β sin A H = ) (meters)L collector length ( meters) l L/H Q annual energy received (kWh)
angle between surface normal and solar ray
γ solar azimuthδ solar declination angle Ψ also inclination ψ1sin(360(T/365.25)) ξ relative shaded areaη screening angle
Solar Constant Beam irradiance 1367
Extra terrestrial irradiancee correction factor for solar irradiationj' Day angle in radians
Beam irradiance normal to solar beam
Normal (geometry) forming a right angle
The azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian
The point below the observer that is directly opposite the zenith on the imaginary sphere against which celestial bodies appear to be projected
(astronomy) the angular distance to a point on a celestial object measured north or south from the celestial equator; expressed in degrees; used with right ascension to specify positions on the celestial sphere
The point above the observer that is directly opposite the nadir on the imaginary sphere against which celestial bodies appear to be projected
cos-1 (sinφ sin δ + cosφ cosδ cosω (H))
An imaginary great circle on the surface of the earth passing through the north and south poles at right angles to the equator15o x (Time (hours past noon)
I b
I d
θ ς
Io W.m2
Go Io after correction with e W.m2
Boc
TLK
1 cm = 28.35 pointsPoints cm
0 01719 60.63492 0 28.35
0 0860.25 30.34392 28.35
Cities Label Lat Long Zone Justify Selected[location 1] Amsterdam 52.5 5 NET 11 no[location 2] Ankara 40 32.7 TUR 11 no[location 3] Bangkok 13.7 100.7 THA 0 no[location 4] Beijing 40 117 CHN 12 yes[location 5] Berlin 52.5 13 GER 1 no[location 6] Bombay 19 72.8 IND 0 yes[location 7] Buenos Aires -35 -58 ARG 1 no[location 8] Cape Town -34 18.3 SOU 2 yes[location 9] Carradale 55.5 -5.4 UNK 12 yes[location 10] Colombo 7 80 SRL 0 no[location 11] Hong Kong 22.5 114 CHN 1 no[location 12] Islamabad 33.7 73 PAK 11 no[location 13] Jerusalem 32 35 ISR 2 no[location 14] Ngodwana -25.57 30.68 SOU 1 no[location 15] Karachi 24.9 67 PAK 12 yes[location 16] London 51.3 0 UNK 2 no[location 17] Los Angeles 34 -118 USA6 0 yes[location 18] Mexico City 19.5 -99 MEX1 0 no[location 19] Montreal 45.5 -73.5 CAN2 11 no[location 20] Moscow 55.8 37.5 RUS2 10 yes[location 21] Muscat 23.5 58.2 OMA 2 no[location 22] New Delhi 28.7 77.2 IND 1 yes[location 23] New York 41 -74 USA1 1 yes[location 24] Paris 49 2.3 FRA 1 no[location 25] Quito 0 -78 ECU 0 yes[location 26] Reykjavik 63.8 -22.5 ICE 2 no[location 27] Santiago -33 -72 CHI 2 no[location 28] Sao Paolo -24.03333 -47 BRA1 11 no[location 29] Seoul 37.5 127 KOR 0 no[location 30] Singapore 1.3 103.8 SGP 0 no[location 31] Stockholm 59 18 SWE 0 no[location 32] Sydney -34 151 AUS1 2 yes[location 33] Tokyo 36 140 JAP 1 no[location 34] Washington DC 39 -77 USA1 12 elected=no[location 35] Wellington -41.5 174.8 NEZ 2 no[location 36] Stavanger 58.95 5.72 NOR 2 no[location 37] Aberdeen 57.2 -2.1 UNK 2 no[location 38] Madisonville 30.45 -90.12 USA3 2 no[location 39] Abu Dhabi 24.5 54.37 UAE 2 no[location 40] Perth -32.2 116 AUS6 2 no[location 41] Rio de Janeiro -23 -43 BRA1 2 yes[location 42] Houston 29.7 -95.4 USA3 2 no[location 43] Bogota 2 -72 COL 0 no[location 44] justify=0 selected=no 14.5 lat=50.000000 zone=CZE label=Prague
References country Name Latitude Longitude (Hour) M Date Leap D M Y Distance, km Latx 30.35 LongY 60.64 1 cm 860.25 1719 = 28.35 points
G&F Azerbaijan 40.6 N 48.6 E 4.6 24/09/1848 24 9 1848 50 < A 236.09083333 1091.565G&F S. Caspian 39.5 N 53.7 E 8.2 07/08/1895 07 08 1895 50 < A 241.34791667 1115.9175 Points cmG&F Azerbaijan 40.7 N 48.6 E 6.9 02/13/1902 02 13 1902 50 < A 235.61291667 1091.565 0G&F Azerbaijan 40.7 N 48.6 E 6.9 02/13/1903 02 13 1902 50 < A 235.61291667 1091.565
Italy Messina 45 N 10 E 6.8 1/6/1908 6 1 1908 215.0625 907.25 0New Ginea Cracataua 15 S 140 E 9.9 4/5/1913 5 4 1913 501.8125 1528China Gansu 2 12 N 122 E 6.5 1/6/1920 6 1 1920 100 372.775 1442.05 0.168444444444444Japan Kanto 12 N 23 E 7 1/6/1923 6 1 1923 100 372.775 969.325 585.7825China Tangshan 12 N 24 E 7 6/6/1976 6 6 1926 100 372.775 974.1 860.4225China Gansu 1 12 N 25 E 7 1/6/1932 6 1 1932 100 372.775 978.875
B&E Makran 24.5 N 63 E 8 11/28/1945 28 11 1945 313.03541667 1160.325B&E Ormara 25.2 N 64.2 E 11/28/1945 28 11 1945 50 < b D 309.69 1166.055
Turkmenistan Ashgabat 40 N E 8 6/6/1948 6 6 1948 100 238.95833333 859.5C&T Japan 41.8 N 144.1 E 8.1 04/03/1952 3 4 1952 230.35583333 1547.5775C&T Niikappu N E 8.1 04/03/1952 3 4 1952 100 < b 430.125 859.5ONL Chile S of San Tiago 35 S 72 W 9.5 4/6/1960 4 1 1960 90 597.39583333 515.7
S W 6 3/5/1964 3 1 1964 430.125 859.5Peru Lima/Gayaquil 5 N 78 W 5 6/6/1970 6 1 1970 90 406.22916667 487.05
G&F Azerbaijan 40.6 N 48.7 E 5.7 01/28/1872 28 1 1972 50 < A 236.09083333 1092.0425G&F Azerbaijan 41 N 49 E 01/28/1872 28 1 1972 50 < A 234.17916667 1093.475
China Quinghai 90 N 49 E 6.5 6/6/1926 1 6 1926 100 0 1093.475GSI Romania 45.77 N 26.76 E 7.2 04/03/1977 3 4 1977 90 d 211.38254167 987.279GSI Baciu 45.32 N 26.76 E 6.71 04/03/1977 3 4 1977 213.53316667 987.279
Italy Cologne 35 N 15 E 7 6/6/1980 6 1 1980 262.85416667 931.125C&T Japan Japan 42.16 N 142.36 E 6.5 03/21/1982 21 3 1982 228.63533333 1539.269C&T Japan Niikappu 42.16 N 142.36 E 03/21/1982 21 3 1982 34 228.63533333 1539.269
Armenia Azerbajan N E 7 6/6/1988 6 1 1988 100 430.125 859.5California Loma Prieta 33 N 117 W 9 6/6/1989 6 1 1989 100 272.4125 300.825
C&T Japan Japan 40.45 N 143.49 E 7.7 12/28/1994 28 12 1994 236.80770833 1544.66475C&T Japan Niikappu 40.45 N 143.49 E 8 12/28/1994 28 12 1994 150 b 236.80770833 1544.66475
LAX North Ridge N W 6.8 12/28/1994 28 12 1994 100 430.125 859.5Russia Kuril Isands N E 7 1/6/1994 1 1 1994 100 430.125 859.5Japan Hokkaido 42 N 143.49 E 7 1/6/1994 1 1 1994 100 229.4 1544.66475Japan Kobe N E 7 1/6/1995 1 1 1995 100 430.125 859.5Turkey Instanbul 41.9701776667 N 28.867011 E 7.5 1/8/11999 1 1 1999 229.5425259 997.33997752Turkey instanbul + 50km E 40.9701776667 N 27.867011 E 7 1/11/1999 1 1 1999 100 234.32169257 992.56497752Taiwan Taipei 24 N 120 E 7 1/6/1999 1 1 1999 100 315.425 1432.5
B&E Japan Japan 41.77 N 143.9 E 8.3 09/26/2003 09 26 2003 230.49920833 1546.6225B&E Japan Niikappu 42.3 N 142.4 E 09/26/2003 09 26 2003 100 b 227.96625 1539.46
Iran Bam 25 N 25 E 8 1/6/2003 1 2 2003 100 310.64583333 978.875G&F Andaman 25 N 95.8 E 9 12/26/2004 12 26 2004 50 < A 310.64583333 1316.945G&F Marazy 40.56 N 48.97 E 6 12/26/2004 12 26 2004 50 < A 236.282 1093.33175G&F Kalamaddyn 40.27 N 48.85 E 6 12/26/2004 12 26 2004 50 < A 237.66795833 1092.75875G&F Shikhzairli 40.49 N 49.05 E 6 12/26/2004 12 26 2004 50 < A 236.61654167 1093.71375G&F Shikhlairli 40.49 N 49.05 E 6 12/26/2004 12 26 2004 50 < A 236.61654167 1093.71375G&F Bozakhtarma 40.51 N 49.14 E 6 12/26/2004 12 26 2004 50 < A 236.52095833 1094.1435G&F Livanova Bank 39.8 N 52.1 E 6 12/26/2004 12 26 2004 140 239.91416667 1108.2775GSI Baratang 12.2 N 115 E 6 12/26/2004 12 26 2004 90 b 371.81916667 1408.625
Japan Niigata 42.3 N 140 E 7 1/6/2004 1 2 2004 100 227.96625 1528Africa Lake Tanganyika 7 S 29 E 7 6/6/2005 6 2 2005 600 463.57916667 997.975indonesia Sumatra 10 S 160 E 9.2 26/12/2004 26 12 2004 477.91666667 1623.5Pakistan Kasmir N E 7 6/6/2005 6 2 2005 100 430.125 859.5Caribean Haitti 15 N 60 W 8.7 15/1/2010 15 1 2010 358.4375 573Caribean Haitti 14 N 60 W 6 19/1/2010 19 1 2010 363.21666667 573? ? S W 9.8 3/5/2012 3 2 2012 430.125 859.5Lokbatan Lokbatan 40.5 N 49 E 5 19/11/1981 19.00 11 1981 45 77 3.8 236.56875 1093.475Lokbatan Lokbatan 39.5 N 54.8 E 7.4 22/12/2000 22.00 12 2000 493 435 4.6 241.34791667 1121.17Lokbatan Lokbatan 39.2 N 47.6 E 6.5 22/3/1879 22.00 3 1879 187 214 4.4 242.78166667 1086.79Lokbatan Lokbatan 40.4 N 51.6 E 6.5 16/9/1989 16.00 9 1989 215 161 4.9 237.04666667 1105.89Lokbatan Lokbatan 39.8 N 54.5 E 7.5 4/11/1946 4.00 11 1946 462 405 4.8 239.91416667 1119.7375Lokbatan Lokbatan 40.6 N 48.6 E 5.4 3/8/1832 3.00 8 1832 44 99 4 236.09083333 1091.565Lokbatan Lokbatan 40.7 N 48.4 E 5.7 9/8/1828 9.00 8 1828 59 117 4.2 235.61291667 1090.61Lokbatan Lokbatan 37 N 49.3 E 7.4 20/6/1990 20.00 6 1990 389 369 4.8 253.29583333 1094.9075Lokbatan Lokbatan 40.7 N 48.7 E 5.4 7/8/1875 7.00 8 1875 38 95 4.1 235.61291667 1092.0425Lokbatan Lokbatan 41.1 N 49.8 E 6.2 27/1/1963 27.00 1 1963 108 102 5.2 233.70125 1097.295Lokbatan Lokbatan 39.4 N 48.6 E 6.6 19/2/1924 19.00 2 1924 146 155 5.1 241.82583333 1091.565Lokbatan Lokbatan 41 N 50.5 E 6.4 7/6/1911 7.00 6 1911 141 111 5.3 234.17916667 1100.6375Lokbatan Lokbatan 40.7 N 48.5 E 5.9 11/6/1859 11.00 6 1859 52 110 4.6 235.61291667 1091.0875Lokbatan Lokbatan 40.6 N 48.7 E 5.7 28/1/1872 28.00 1 1872 32 90 b 4.6 236.09083333 1092.0425Lokbatan Lokbatan 41.1 N 50.2 E 6.6 18/9/1961 18.00 9 1961 133 114 5.6 233.70125 1099.205Lokbatan Lokbatan 39.5 N 53.7 E 8.2 8/7/1895 8.00 7 1895 406 349 6.1 241.34791667 1115.9175Lokbatan Lokbatan 40.2 N 50 E 6.2 25/11/2000 25.00 11 2000 85 32 7 238.0025 1098.25Lokbatan Lokbatan 40.2 N 49.9 E 6.4 25/11/2000 25.00 11 2000 94 55 6.5 238.0025 1097.7725Lokbatan Lokbatan 40.7 N 48.6 E 6.9 13/2/1902 13.00 2 1902 46 103 a b 6.2 235.61291667 1091.565Shikhzairli Shikhzairli 40.5 N 49 E 4.7 19/11/1981 19.00 11 1981 45 61 3.8 236.56875 1093.475Shikhzairli Shikhzairli 39.5 N 54.8 E 4.4 22/12/2000 22.00 12 2000 493 464 4.6 241.34791667 1121.17Shikhzairli Shikhzairli 39.2 N 47.6 E 4.6 22/3/1879 22.00 3 1879 187 200 4.4 242.78166667 1086.79Shikhzairli Shikhzairli 40.4 N 51.6 E 4.4 16/9/1989 16.00 9 1989 215 188 4.9 237.04666667 1105.89Shikhzairli Shikhzairli 39.8 N 54.5 E 4.6 4/11/1946 4.00 11 1946 462 433 4.8 239.91416667 1119.7375Shikhzairli Shikhzairli 40.6 N 48.6 E 5.3 3/8/1832 3.00 8 1832 44 72 4 236.09083333 1091.565Shikhzairli Shikhzairli 40.7 N 48.4 E 5.3 9/8/1828 9.00 8 1828 59 88 4.2 235.61291667 1090.61Shikhzairli Shikhzairli 37 N 49.3 E 4.8 20/6/1990 20.00 6 1990 389 379 4.8 253.29583333 1094.9075Shikhzairli Shikhzairli 40.7 N 48.7 E 5.6 7/8/1875 7.00 8 1875 38 66 4.1 235.61291667 1092.0425Shikhzairli Shikhzairli 41.1 N 49.8 E 5.1 27/1/1963 27.00 1 1963 108 105 5.2 233.70125 1097.295Shikhzairli Shikhzairli 39.4 N 48.6 E 5.2 19/2/1924 19.00 2 1924 146 151 5.1 241.82583333 1091.565Shikhzairli Shikhzairli 41 N 50.5 E 4.9 7/6/1911 7.00 6 1911 141 126 5.3 234.17916667 1100.6375Shikhzairli Shikhzairli 40.7 N 48.5 E 5.8 11/6/1859 11.00 6 1859 52 81 4.6 235.61291667 1091.0875Shikhzairli Shikhzairli 40.6 N 48.7 E 6.3 28/1/1872 28.00 1 1872 32 61 b 4.6 236.09083333 1092.0425Shikhzairli Shikhzairli 41.1 N 50.2 E 5.3 18/9/1961 18.00 9 1961 133 123 5.6 233.70125 1099.205Shikhzairli Shikhzairli 39.5 N 53.7 E 5.9 8/7/1895 8.00 7 1895 406 378 6.1 241.34791667 1115.9175Shikhzairli Shikhzairli 40.2 N 50 E 5.5 25/11/2000 25.00 11 2000 85 59 7 238.0025 1098.25Shikhzairli Shikhzairli 40.2 N 49.9 E 5.6 25/11/2000 25.00 11 2000 94 74 6.5 238.0025 1097.7725Shikhzairli Shikhzairli 40.7 N 48.6 E 7.5 13/2/1902 13.00 2 1902 46 75 a b 6.2 235.61291667 1091.565[location 1] Amsterdam 52.5 N 5 E 179.21875 883.375[location 2] Ankara 40 N 32.7 E 238.95833333 1015.6425[location 3] Bangkok 13.7 N 100.7 E 364.65041667 1340.3425[location 4] Beijing 40 N 117 E 238.95833333 1418.175[location 5] Berlin 52.5 N 13 E 179.21875 921.575[location 6] Bombay 19 N 72.8 E 339.32083333 1207.12[location 7] Buenos Aires 35 S 58 W 597.39583333 582.55[location 8] Cape Town 34 S 18.3 E 592.61666667 946.8825[location 9] Carradale 55.5 N 5.4 W 164.88125 833.715[location 10] Colombo 7 N 80 E 396.67083333 1241.5[location 11] Hong Kong 22.5 N 114 E 322.59375 1403.85[location 12] Islamabad 33.7 N 73 E 269.06708333 1208.075[location 13] Jerusalem 32 N 35 E 277.19166667 1026.625[location 14] Ngodwana 25.57 S 30.68 E 552.32829167 1005.997[location 15] Karachi 24.9 N 67 E 311.12375 1179.425[location 16] London 51.3 N 0 E 184.95375 859.5[location 17] Los Angeles 34 N 118 W 267.63333333 296.05[location 18] Mexico City 19.5 N 99 W 336.93125 386.775[location 19] Montreal 45.5 N 73.5 W 212.67291667 508.5375[location 20] Moscow 55.8 N 37.5 E 163.4475 1038.5625[location 21] Muscat 23.5 N 58.2 E 317.81458333 1137.405[location 22] New Delhi 28.7 N 77.2 E 292.96291667 1228.13[location 23] New York 41 N 74 W 234.17916667 506.15[location 24] Paris 49 N 2.3 E 195.94583333 870.4825[location 25] Quito 0 N 78 W 430.125 487.05[location 26] Reykjavik 63.8 N 22.5 W 125.21416667 752.0625[location 27] Santiago 33 S 72 W 587.8375 515.7[location 28] Sao Paolo 24.03333 S 47 W 544.98428963 635.075[location 29] Seoul 37.5 N 127 E 250.90625 1465.925[location 30] Singapore 1.3 N 103.8 E 423.91208333 1355.145[location 31] Stockholm 59 N 18 E 148.15416667 945.45[location 32] Sydney 34 S 151 E 592.61666667 1580.525[location 33] Tokyo 36 N 140 E 258.075 1528[location 34] Washington DC 39 N 77 W 243.7375 491.825[location 35] Wellington 41.5 S 174.8 E 628.46041667 1694.17[location 36] Stavanger 58.95 N 5.72 E 148.393125 886.813[location 37] Aberdeen 57.2 N 2.1 W 156.75666667 849.4725[location 38] Madisonville 30.45 N 90.12 W 284.599375 429.177[location 39] Abu Dhabi 24.5 N 54.37 E 313.03541667 1119.11675[location 40] Perth 32.2 S 116 E 584.01416667 1413.4[location 41] Rio de Janeiro 23 S 43 W 540.04583333 654.175[location 42] Houston 29.7 N 95.4 W 288.18375 403.965[location 43] Bogota 2 N 72 W 420.56666667 515.7
ψ 23.5Hemisphere S N or S
21 Mar 2009 20 Sep 2009 20 Sep 2009
δ = ψψ1sin(360(T/365.25))
δ = -6.32φ = 334.4159
= 25.5841 S
θ = 30.67493 E
θ = 360
0.996861788294597#VALUE!
0.962114742025866
The dot product of this vector with the unit normal is
cos(ψ)cos(φ)cos(θ) + sin(ψ)sin(φ)-0.04413957176859
365.34 SolarYear88.4590683928667
13.60 Time time lat Angle of incidenceFict Date 8-Apr-23 0 4947.829 -180 -6.271996 -0.897183 0.999811 -63.7902 -70.11059 2.57 153.7902
Latitude 25.50 ψ 1 4947.871 -165 -6.288224 -0.838237 0.999783 -56.95438 -63.27476 2.02 146.9544Radian 57.295779513 0.017453 2 4947.912 -150 -6.304448 -0.722029 0.999708 -46.22225 -52.54263 2.44 136.2222
T = 10 + 21 + 4/24 = 31.167 3 4947.954 -135 -6.320669 -0.556497 0.999508 -33.8139 -40.13429 2.29 123.8139
4948.39556666667 4 4947.996 -120 -6.336886 -0.352948 0.998778 -20.66776 -26.98815 2.88 110.6678
ψ = 23.5°sin(360(31.167/365.25)) = 23.5sin(30.719°) = 12.00° 5 4948.037 -105 -6.353101 -0.125287 0.990312 -7.197312 -13.5177 2.49 97.19731
1.7461504884667 6 4948.079 -90 -6.369312 0.110937 0.98765 6.369312 0.048924 1.48 83.63069
θ = 360(4/24) = 60° 24 7 4948.121 -75 -6.38552 0.339585 0.99868 19.8516 13.53121 0.56 70.1484
0.017453292519943 8 4948.162 -60 -6.401724 0.545039 0.999487 33.02736 26.70697 0.06 56.97264
cos(φ) = cos(45°) = 0.7071 9 4948.204 -45 -6.417925 0.713265 0.999701 45.50116 39.18078 0.02 44.49884
0.902585284349861 10 4948.246 -30 -6.434123 0.832769 0.99978 56.38422 50.06383 1.70 33.61578
11 4948.287 -15 -6.450318 0.895388 0.99981 63.55826 57.23787 0.80 26.44174
0.836563615457436 12 4948.329 0 -6.466509 0.896843 0.999811 63.74614 57.42575 0.61 26.25386
0.99978237386823 13 4948.371 15 -6.482697 0.837034 0.999783 56.82828 50.50789 1.25 33.17172
14 4948.412 30 -6.498882 0.720047 0.999706 46.05836 39.73797 0.54 43.94164
90° - cos-1(0.836563615457436) 15 4948.454 45 -6.515063 0.553871 0.999504 33.63299 27.31261 0.67 56.3670190 - 0.579816 * 57.29578 16 4948.496 60 -6.531241 0.349858 0.998756 20.47861 14.15823 0.07 69.52139
= 17 4948.537 75 -6.547416 0.121943 0.989775 7.004225 0.683838 0.84 82.99577= 90 - 58.273 90 - 33.22099 18 4948.579 90 -6.563587 -0.114306 0.988366 -6.563587 -12.88397 1.86 96.56359
= Angle of incidence 31.73° 56.779 19 4948.621 105 -6.579755 -0.342749 0.998704 -20.04446 -26.36485 2.78 110.0445851.685079377563 303.221 20 4948.662 120 -6.59592 -0.547783 0.999492 -33.21503 -39.53542 2.89 123.215
5/14/2023 1:17 21 4948.704 135 -6.612081 -0.7154 0.999702 -45.67599 -51.99638 2.99 135.67622 4948.746 150 -6.628239 -0.834151 0.999781 -56.52749 -62.84788 1.59 146.527523 4948.787 165 -6.644393 -0.895922 0.99981 -63.62708 -69.94747 2.41 153.627124 4948.829 180 -6.660544 -0.896494 0.99981 -63.70092 -70.0213 2.48 153.7009
n = (x/r)i + (y/r)j + (z/r)k
= cos(φ)cos(θ)i + cos(φ)sin(θ)j + sin(φ)
cos(ψ)i + sin(ψ)k.
This is the cosine of the zenith angle so the angle of elevation η is given by:
η = 90° - cos-1[cos(φ)cos(ψ)cos(θ)+sin(ψ)sin(φ)]
The elevation angle η of the sun at 4 P.M. on April 21st at latitude 45° is found, assuming the spring equinox occurs at noon 00 P.M. on March 21:
η = 90° - cos-1[(0.7071)cos(12°)cos(60°)+sin(12°)sin(60°)]1 2 3 4 5 6 7 8 9 1
011
12
13
14
15
16
17
18
19
20
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23
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-90
-70
-50
-30
-10
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90
Column I
Column J
Column K
Column L
Column M
Column N
Column O
Column P
Column Q
Column R
absorption.
absorption band.
acquisition.
albedo.
alignment data
altitude.
analog-to-digital conve
angular velocity.
angle of drift.
anomaly.
aperture.
apogee.
ascending node.
at-aperture-radiance.
attenuation.
attitude.
azimuth.
background.
band sequential.
band, spectral.
BCH.
black body.
brightness value.
calibration data.
ETC
(1) Image captured by satellite sensor. (2) The process of searching for and locking onto a received signal.
The angle between the heading of the axis of a craft and its ground track.
A deviation from the norm.
The point in the orbit of a heavenly body, especially of a manmade satellite, at which it is farthest from the Earth.
The point at which the orbit of an earth satellite intersects the plane of the equator going from south to north.
The radiance at the aperture of the sensor.
The process by which electromagnetic radiation (EMR) is assimilated and converted into other forms of energy, primarily heat. Absorption takes place only on the EMR that enters a medium. A substance that absorbs EMR may also be a medium of refraction, diffraction, or scattering; however, these processes involve no energy retention or transformation and are distinct from absorption.
A range of wavelengths (or frequencies) of electromagnetic radiation that is assimilated by the atmosphere or other substance.
(1) The ratio of the amount of electromagnetic energy reflected by a surface to the amount of energy incident upon it, often expressed as a percentage. (2) The reflectivity of a body as compared to that of a perfectly diffusing surface at the same distance from the Sun, and normal to the incident radiation. Albedo may refer to the entire solar spectrum or merely to the visible portion.
. Angular measurement of the physical position of the optical axis with respect to the primary space vehicle reference axes.
Height above a datum, the datum usually being mean sea level. Refers to point above the Earth's surface rather than those on it (elevation).
The process of sampling continuous analog signals in order to convert them into a stream of digital values. ETM+ data undergo such a conversion prior to downlinking. Abbreviated as A/D conversion.
Also called rotational velocity, it is the amount of rotation that a spacecraft undergoes per unit time. For Landsat 7 it is equal to 1.059 mrad/sec ((233 paths/cycle * 2*pi*1000 mrad/path) / (16 days/cycle * 86400 sec/day)).
An opening that admits electromagnetic radiation to a detector or film. An example would be the lens diaphragm opening in a camera.
The reduction in the intensity of radiation with distance from its source due to atmospheric absorption and/or scattering. It does not include the inverse-square decrease of intensity of radiation with distance from the source.
The angular orientation of a spacecraft as determined by the relationship between its axes and some reference line or plane or some fixed system of axes. Usually, Y is used for the axis that defines the direction of flight, x for the crosstrack axis, perpendicular to the direction of flight, and z for the vertical axis. Roll is the deviation from the vertical (the angle between the z-axis of the vehicle and the vertical axis, or angular rotation around the y-axis). Pitch is the angular rotation around the x-axis. Yaw is rotation around the z-axis.
The arc of the horizon measured clockwise from the north point to the point referenced. Expressed in degrees. Azimuth indicates direction, not location.
B
An error detection and correction scheme named after its inventors Bose, Chanduri, and Hochergan.
C
D
Any effect in a sensor or other apparatus or system above which the phenomenon of interest must manifest itself before it can be observed.
A format that arranges the data by band such that all of the data from band 1 followed by all of the data from band 2, etc.
An interval in the electromagnetic spectrum defined by two wavelengths, frequencies, or wave numbers. With Landsat, bands designate the specific wavelength intervals at which images are acquired.
An ideal body which, if it existed, would be a perfect absorber and a perfect radiator, absorbing all incident radiation, reflecting none, and emitting radiation at wavelengths. In remote sensing, the exitance curves of black bodies at various temperatures can be used to model naturally occurring phenomena like solar radiation and terrestrial emmitance.
In Landsat parlance, a number in the range of 0-255 that is related to the amount of planetary radiance striking a sensor's detector.
In remote sensing, measurements pertaining to the spectral or geometric characteristics of a sensor or radiation source. Calibration data are obtained through the use of a fixed energy source such as a calibration lamp, a temperature plate, or a geometric test pattern. The application of calibration data to restore measurements to their true values is called rectification.
coherent noise. The noise associated with periodic signals arising from power supplies, transmitters and clock signal typically.
color. That property of an object which is dependent on the wavelength of the light it reflects or, in the case of a luminescent body, the wavelength of the light it emits. If, in either case, this light is of a single wavelength, the color seen is a pure spectral color, but, if the light of two or more wavelengths is emitted, the color will be mixed. White light is a balanced mixture of all the visible spectral colors.
color composite. A color image produced by the combination of three individual monochrome images in which each is assigned a given color. For ETM+ data, if blue is assigned to band 1, green assigned to band 2, and red assigned to band 3, a true color image will result.
cubic convolution. A high-order resampling technique is which the brightness value of a pixel in a corrected image is interpolated from the brightness values of the 16 nearest pixels around the location of the corrected pixel.
data capture. The receipt and storage of return link mission data at the CADU level.
data continuity. A NASA requirement to ensure that Landsat 7 data are compatible to those obtained by earlier Landsat satellites.
E
data granule. The increment of image data stored in the archive, i.e. an interval, swath, or WRS scene.
data loads. Data and command transfers from the MOC to the onboard computer.
dark shutter image data. The image data obtained from ETM+ detectors when the calibration shutter obscures the detectors from incident electromagnetic radiation.
descending node. The point at which the orbit of an earth satellite intersects the plane of the equator going from north to south.
detector. The composite circuitry supporting the development of a single output data sample.
detector sample. The process of determining the transfer characteristics (detector mean output as a function of incident exposure) for each detector element.
digital terrain elevation data (DTED). Digital information produced by DMA which provides a uniform matrix of terrain elevation values. DTED is commonly used to terrain correct Landsat data.
distortion. A change in scale from one part of an image to another.
dwell time. Refers to the momentary time interval during which a detector is able to, or allowed to, sense incoming electromagnetic radiation within its intended instantaneous field of view.
dynamic range. The ratio of the maximum signal to the smallest measurable signal.
EDC. Earth Resources Observation System Data Center is a national archive, production, distribution and research facility for remotely sensed data and other geographic information. (see EROS)
electromagnetic radiation. Energy emitted as result of changes in atomic and molecular energy states and propagated through space at the speed of light.
electromagnetic spectrum. The system that classifies, according to wavelength, all energy (from short cosmic to long radio) that moves, harmonically, at the constant velocity of light.
elevation. Vertical distance from the datum, usually mean sea level, to a point or object on the Earth's surface.
emission. With respect to electromagnetic radiation, the process by which a body emits electromagnetic radiation as a consequence of its kinetic temperature only.
emissivity. Ratio of radiation emitted by a surface to the radiation emitted by a black body at the same temperature under similar conditions. May be expressed as total emissivity (for all wavelengths), spectral emissivity (as a function of wavelength), or goniometric emissivity (as a function of angle).
Enhanced Thematic Mapper Plus (ETM+). The ETM+ is a fixed-position nadir viewing whisk-broom instrument. The viewing swath is produced by means of an oscillating mirror system that sweeps across track as the sensor field of view moves forward along-track due to satellite motion.
ETM+ scene. A set of ETM+ observations that covers 170 km in width by 185 km in length and is centered about a WRS vertex.
Evcuated tube Collector
F
G
engineering data. All data available on-board about health, safety, environment or status of the platform and instruments.
ephemeris. A set of data that provides the assigned places of a celestial body (including a manmade satellite) for regular intervals. Ephemeris data help to characterize the conditions under which remote sensing data are collected and may be used to correct the sensor data prior to analysis.
EROS. The Earth Resources Observation System was established in the early 1970Õs under the Department of InteriorÕ U.S. Geological Survey, to receive, process and distribute data from the United StatesÕ Landsat satellite sensors and from airborne mapping cameras.
field-of-view. The solid angle through which an instrument is sensitive to radiation. See effective resolution element, instantaneous field of view, resolution.
focal length. In a camera, the distance measured along the optical axis from the optical center of the lens to the plane at which the image of a very distant object is brought into focus.
focal plane. In a sensor, the plane occupied by the detectors, and on which the radiances sensed are incident.
frame. For Landsat 7, a frame is one Virtual Channel Data Unit with a frame synchronizer pattern (frame marker) attached. This is the same as a Channel Access Data Unit (CADU).
geocentric. Any coordinate frame whose origin is relative to the Earth's center of mass.
geometric correction. The transformation of image data, such as Landsat data, to match spatial relationships as they are on the Earth. Includes correction for band-to-band offsets, line length, Earth rotation, and detector-to-detector sampling delay. For ETM+ data, a distinction is made between data that have been geometrically corrected using systematic, or predicted, values and data that have been geometrically corrected using precise ground control point data and elevations models.
geodetic coordinates. Quantities which define the position of a point on the spheroid of reference (for example, the Earth) with respect to the planes of the geodetic equator and of a reference meridian. Commonly expressed in terms of latitude and longitude.
geodetic accuracy. A measure of how closely a point on the Earth can be located relative to its true absolute location.
geosynchronous. An Earth satellite orbit in which the satellite remains in a fixed position over a geographic location on Earth.
Global Position System (GPS). A constellation of satellites that can be used to determine accurately the orbit data of satellites.
H
I
ground control point (GCP). A geographic feature of known location that is recognizable on images and can be used to determine geometric correction functions for those images.
ground track. The vertical projection of the actual flight path of a plane or space vehicle onto the surface of the Earth.
ground truth. Data which are acquired from field checks, high-resolution remote sensing data, or other sources of known data. Ground truth is used as the basis for making decisions on training areas and evaluating classification results.
housekeeping data. All data available onboard about health, safety, environment, or status of the platform and instruments.
hue. The attribute of a color that differentiates it from gray of the same brilliance and that allows it to be classed as blue, green, red, or intermediate shades of these colors.
image. The recorded representation of an object produced by optical, electro-optical, optical-mechanical, or electronic means. It is the term generally used when the electromagnetic radiation emitted or reflected from a scene is not directly recorded on photographic film.
image enhancement. Any one of a group of operations which improves the interpretability of an image or the detectability of targets or categories in the image. These operations include contrast enhancement, edge enhancement, spatial filtering, image smoothing, and image sharpening.
image restoration. A process by which a degraded image is restored to its original condition. Image restoration is possible only to the extent that the degradation transform is mathematically invertable.
image-to-image registration. The registration between images taken at different times.
image transformation. A function or operator which takes an image as input and produces an image as its output. Depending on the transform chosen, the input and output images may appear entirely different and have different intrepretations. Fourier, Hadamard, and Karhunen-Love transforms as well as various spatial filters, are examples of frequently used image transformation procedures.
infrared. Pertaining to energy in the 0.7 - 100 µm wavelength region of the electromagnetic spectrum. For remote sensing, the infrared wavelengths are often subdivided into near infrared (0.7 - 1.3 µm), middle infrared (1.3-3.0 µm), and far infrared (7.0 - 15 µm). Far infrared is sometimes referred to as thermal or emissive infrared.
instantaneous field of view (IFOV). The solid angle through which a detector is sensitive to radiation. In a scanning system this refers to the solid angle subtended by the detector when the scanning motion is stopped. Instantaneous field of view is commonly expressed in milliradians. IFOV also refers to the ground area covered by this solid angle.
international ground station (IGS). Any Landsat ground station not belonging to the United States.
J
K
L
M
interval. Is a scheduled ETM+ image period along a WRS path, and may be from 1 to 90 full scenes in length.
irradiance. The measure, in units of power, of radiant flux incident on a surface.
jitter. Small rapid variations in a variable (such as a waveform) due to deliberate or accidental electrical or mechanical disturbances or to changes in the supply of voltages, in the characteristics of components. Jitter effects arising from the oscillating mirrors and other movable parts aboard the Landsat spacecraft are often a cause of certain anomalies in the image data received and must be compensated for by the ground processing software.
K-band. A radio frequency band extending from approximately 12.5 to 36 gigahertz.
kernel. In the spatial domain, a kernel is a MxM operator which can be used in the convolution or multiplication with a NxN image to accentuate certain features or properties of an image. A kernel can also be represented in the frequency domain as a Fourier transform.
L-band. A radio frequency band extending from approximately 1.0 to 2.0 gigahertz.
Landsat 7. Consists of the spacecraft and the ETM+ payload.
level 0. Space vehicle or instrument data at full space-time resolution with space-to-ground communication artifacts removed.
light, transmitted. Light that has traveled through a medium without being absorbed or scattered.
long term acquisition plan. The tasking of the sensor using cloud predictions to optimize the acquisition of cloud free scenes.
lookup table. An array of values from which functions corresponding to a given argument can be obtained.
major frame. For ETM+, a major frame period is one complete scan of the ETM+ scan mirror (either direction), which includes not only the period during a scan but also the turnaround interval when the scan mirror changes direction for the next scan.
map projection. Any systematic arrangement of meridians and parallels portraying the curved surface of a sphere or spheroid upon a plane.
N
metadata. An archived set of descriptive information about a scene and the parent sub-interval that provides a user with geographic coverage, date of acquisition, sun angles, could cover, gain states, and other quality measurements.
minor frame. For ETM+ major frames are partitioned into minor frames which is the most fundamental element of the data stream structure in which specific data measurands (e.g. imagery, PCD, time codes) are extracted.
mirror scan correction data. This data includes scan start time, first half scan time error, second half scan time error, scan direction, and any other data which is required to perform mirror scan correction.
modulate. To vary, or control, the frequency, phase, or amplitude of an electromagnetic wave or other variable.
modulation transfer function (MTF). The modulation transfer function of an imaging system measures the spatial frequency modulation response of the system. As an imaging system processes or records an image, the contrast modulation of the processed or recorded image is different from the input image. The MTF can be thought of as a curve, indicating for each spatial frequency the ratio of the contrast modulation of the output image to the contrast modulation of the input image. It is formally defined as the magnitude of the Fourier transform of the line spread function of the imaging system.
mosaic. An image made by piecing together individual images covering adjacent areas.
multiplexer. An electronic device which permits the transmission of multiple messages simultaneously on one communication channel.
multispectral. Generally denotes remote sensing in two or more spectral bands, such as visible and infrared.
nadir. That point on the celestial sphere vertically below the observer, or 180° from the zenith.
narrowband data. The data includes the command or forward ranging in the narrowband forward link, and the telemetry or return ranging in the narrowband return link.
near infrared. The preferred term for the shorter wavelengths in the infrared region extending from about 0.7 µm (visible red) to about 3 µm. The longer wavelength end grades into the middle infrared. Sometimes called solar infrared, as it is only available for use during the daylight hours. Also known as the shortwave infrared (SWIR).
node. Either of the two points at which the orbit of a heavenly body intersects a given plane, especially the plane of ecliptic. With respect to Landsat, the orbital nodes occur at the equator, one on the descending, or daylight, track of the orbit and the other on the ascending, or nighttime, track.
noise. Any unwanted disturbance affecting a measurement (as of a frequency band), especially that which degrades the information-bearing quality of the data of interest.
Nyquist interval. The maximum time interval between equally spaced samples of a signal that will enable the signal waveform to be completely determined. The Nyquist interval is equal to the reciprocal of twice the highest frequency component of the sampled signal.
Nyquist's theorem: A theorem, developed by H. Nyquist, which states than an analog signal waveform may be uniquely reconstructed, without error, from samples taken at equal time intervals. The sampling rate must be equal to, or greater than, twice the highest frequency component in the analog signal.
O
P
optical transfer function (OTF). A mathematical statement that describes the relationship between the input and the output of an imaging system. When the transfer function operates on the input, the output is obtained. Given any two of these three entities, the third can be obtained.
orbit adjust. The adding to or taking away of orbital velocity. This is normally done to maintain altitude or orbit phasing relationships.
orbital period. The interval in time between successive passages (orbits) of a satellite through a reference plane.
orthorectified. Describing an image in which terrain relief distortions have been removed.
panchromatic. A single band covering a broad range of wavelengths; usually used in context of collecting information from the whole visible spectrum.
parallax. The apparent change in the position of one object, or point, with respect to another, when viewed from different angles.
path. The longitudinal center line of a Landsat scene of a Landsat scene, corresponding to the center of an orbital track. Sequential numbers from east to west are assigned to 233 nominal satellite tracks for Landsat 7. Path numbers are used with row numbers to designate nominal scene center points.
payload. That part of a spacecraft (e.g. ETM+) that is separate from the equipment or operations necessary to maintain the spacecraft in orbit.
payload correction data. Image support data imbedded in the wideband data stream. Includes satellite attitude, ephemeris, time, angular displacement sensor (ADS) data and payload state.
perigee. The point in the orbit of a heavenly body (e.g. satellite) at which it is nearest the Earth.
pixel. Picture element provided by a single detector scene sample output.
pitch. The rotation of a spacecraft about the horizontal axis normal to its longitudinal axis (in the along-track direction) so as to cause a nose-up or nose-down attitude.
polar stereographic. An azimuthal stereographic projection commonly used with Landsat data acquired about 65° latitude. In this projection, the meridians are straight lines converging at the pole (central point), and lines of latitude are concentric circles about this point. Like the UTM projection, the polar stereographic is a conformal projection, meaning that angular relationships are preserved.
pole wander. The apparent motion in the poles of the Earth relative to inertial coordinate system. Changes in moments of inertia are due to changes in moments of density due primarily to tides and liquid mass. The National Imager and Mapping Agency (NIMA) generates pole wander data which are used by the Landsat 7 system in the conversion of downlinked ephemeris from inertial to fixed reference, during Level 0R processing.
Q
R
S
precision correction. Post-processed geometric correction of satellite data using ground control points to correlate the spacecraft's predicted position with its actual geodetic position.
prime meridian. Meridian of longitude 0 degrees, used as the origin for measurements of longitude. The meridian of Greenwich, England, is the internationally accepted prime meridian on most charts.
quantization level. The number of numerical values used to represent a continuous quantity.
quaternion. A vector of four components; the position is contained in the first three components and an associated scalar rater is located in the last component of this four element vector.
radian. The angle subtended by an arc of a circle equal in length to the radius of the circle: 57.3°
radiance. Measure of the energy radiated by an object. In general, radiance is a function of viewing angle and spectral wavelength and is expressed as energy per solid angle.
Rayleigh scattering. Selective scattering of light in the atmosphere by particles that are small compared with the wavelength of light.
reflectance. The ratio of the radiant energy reflected by a body to that incident upon it. In general, reflectance is a function of the incident angle of the energy, viewing angle of the sensor, spectral wavelength and bandwidth, and the nature of the object.
registration. The process of geometrically aligning two or more sets of image data such that resolution cells for a common ground area can be digitally or visually superimposed.
roll. The rotation of a spacecraft about its longitudinal axis (in the along-track direction) so as to cause a side-up or side-down attitude. The roll axis is referred to as the y axis.
row. The latitudinal (nominal) center line of a Landsat scene. Row 1 is at latitude 80° 47'N, row 60 is at the equator, and row 122 is at latitude 81° 51'S. In total there are 248 rows.
sampling rate. The number of samples taken per unit time, i.e., the rate at which signals are sampled for subsequent use, such as for modulation, coding, and quantization.
saturation. The condition where energy flux exceeds the sensitivity range of a detector.
S band. A radio frequency band extending from approximately 2.0 to 4.0 gigahertz.
T
sidelap. The extent of lateral overlap between images acquired over adjacent ground tracks.
signal-to-noise ratio. The ratio of the level of the information-bearing signal power to the level of the noise power. More precisely, the signal-to-noise ratio of the mean DN to the standard deviation in DN. This is a temporal noise definition in that the mean DN is the time averaged value and the standard deviation in DN is the standard deviation in the time series.
space oblique mercator. A variation on the basic mercator map projection based on the dynamics of satellite motion. The movements of the satellite, sensor, and the Earth, expressed as functions of time, are used to calculate which latitudes and longitudes on the Earth correspond to locations in the projection plane.
spectral band. An interval in the electromagnetic spectrum defined by two wavelengths, frequencies, or wave numbers.
spectral response. The response of a material as a function of wavelength to incident electromagnetic energy, particularly in terms of the measurable energy reflected from and emitted by the material.
spectral signature. The quantitative measurement of the properties of an object at one or several wavelength intervals. Spectral signature analysis techniques use the variation in the spectral reflectance or emittance of objects as a method of identifying the objects.
steradian. A unit of measure of solid angles. Formally, it is the angle subtended at the center of the sphere by a portion of the surface whose area is equal to the square of the radius of the sphere. There are 4 pi steradians in a sphere.
subinterval. Is a contiguous segment of raw wideband data received during a Landsat 7 contact period. Subintervals are caused by breaks in the wideband datastream due to communication dropouts and/or the inability of the spacecraft to transmit a complete observation (interval) within a single Landsat 7 contact period. The largest possible subinterval is 35 full scenes long with a partial scene preamble and postamble. The smallest possible subinterval is a single ETM+ scene.
sun elevation angle. The angle of the Sun above the horizon.
solar zenith angle. Reciprocal of the sun elevation angle.
sun synchronous. An Earth satellite orbit in which the orbital plane remains at a fixed angle with respect to the Sun, precessing through 360° during the period of a year.
swath. Refers to the 185 kilometer wide ETM+ imaging ground track.
telemetry. The science of measuring a quantity, transmitting the measured value to a distant station, and there, interpreting or recording the quantity measured.
temporal. Pertaining to, concerned with, or limited by time.
temporal resolution. The expected repeat time between measurements over the same location.
thermal band. A general term for intermediate and long wavelength infrared-emitted radiation, as contrasted to short wavelength reflected infrared radiation. In practice, generally refers to infrared radiation emitted in the 3-5 µm and 9-14 µm atmospheric windows.
U
V
thermal infrared. The preferred term for the middle wavelength ranges of the infrared region extending roughly from 3 µm at the end of the near infrared, to about 15 or 20 m where the far infrared commences. In practice the limits represent the the envelope of energy emitted by the Earth behaving as a graybody with a surface temperature around 290 K. Seen from space, the radiance envelope has several brighter bands corresponding to windows in the atmospheric absorption bands. The thermal band most used in remote sensing extends from 8 to 15 µm.
time, Greenwich mean. Mean solar time of the meridian of Greenwich, England (longitude 0), used by most navigators and adopted as the prime basis of standard time throughout the world. Abbreviated GMT.
time, mean Sun. The mean Sun time at a given location on the Earth is determined by the distance in longitude from the Greenwich meridian. The mean Sun time at any location is determined by dividing the difference in longitude from Greenwich (in degrees, moving east) by 15 and adding the result to the current GMT. This will be mean Sun time relative to Greenwich, expressed in hours.
transmittance. The ratio of the energy per unit time per unit area (radiant power density) transmitted through an object to the energy per unit time per unit area incident on the object. In general, transmittance is a function of the incident angle of the energy, viewing angle of the sensor, spectral wavelength and bandwidth, and the nature of the object.
ultraviolet radiation. Electromagnetic radiation of shorter wavelength than visible radiation but longer than X-rays; roughly, radiation in the wavelength interval between 10 and 4,000 angstroms.
umbra. The complete or perfect shadow of an opaque body, as a planet, where the light from the source of illumination is completely cut off.
universal transverse mercator. A widely used map projection employing a series of identical projections around the world in the intermediate latitudes, each covering 6 degrees of longitude and oriented to a meridian. The UTM projection is characterized by its property of conformality, meaning that it preserves scale and angular relationships well, and by the ease with which it allows a useful rectangular grid to be superimposed on it. The UTM projection is most commonly used with landsat data.
UT1-UTC time correction data. Universal Time (UT) 1 is determined from observations of stellar transits to determine local mean sidereal time corrected to remove the effects of polar motion. Universal Time Coordinated (UTC) is defined to be equal to that of the International System used for atomic time, but it is kept with .9 seconds of UT1 by periodic leap-second adjustments.
virtual channel data unit (VCDU). The CCSDS protocol data unit consisting of a fixed length data structure. It is used for bidirectionally space/ground communications on a CCSDS virtual channel.
visible radiation. Electromagnetic radiation of the wavelength interval to which the human eye is sensitive; the spectral interval from approximately 0.4 to 0.7 µm.
W
X
Y
Z
wavelength. Wavelength = 1/frequency. In general, the mean distance between maximums (or minimums) of roughly periodic pattern. Specifically, the shortest distance between particles moving in the same phase of oscillation in a wave disturbance.
world geodetic system (WGS). The reference Earth model used by the Landsat 7 system.
worldwide reference system. A global indexing system for Landsat data which is based on nominal scene centers defined by path and row coordinates.
X-band. A radio frequency band extending from approximately 8.0 to 12.5 gigahertz.
yaw. The rotation of a spacecraft about its vertical axis so as to cause the spacecraft's longitudinal axis to deviate left or right from the direction of flight. The yaw axis is referred to as the z axis.
zenith. The point in the celestial sphere that is exactly overhead.
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ψ 23.5Hemisphere S N or S
21 Mar 2009 20 Sep 2009 20 Sep 2009
δ = ψψ1sin(360(T/365.25))
δ = -6.32φ = 334.415916666667
= 25.584083333333 S
θ = 30.6749333333333 E
θ = 360
0.996861788294597
0.962114742025866
The dot product of this vector with the unit normal is
cos(ψ)cos(φ)cos(θ) + sin(ψ)sin(φ)-0.04413957176859
365.34220000 SolarYear88.4590683928667
13.60 TimeFict Date 8-Apr-23Latitude 25.50Radian 57.295779513 0.017453
T = 10 + 21 + 4/24 = 31.1674948.39556666667
ψ = 23.5°sin(360(31.167/365.25)) = 23.5sin(30.719°) = 12.00°1.7461504884667
θ = 360(4/24) = 60° 24
0.017453292519943
cos(φ) = cos(45°) = 0.70710.902585284349861
0.836563615457436
0.99978237386823
90° - cos-1(0.836563615457436)90 - 0.579816 *
=
n = (x/r)i + (y/r)j + (z/r)k
= cos(φ)cos(θ)i + cos(φ)sin(θ)j + sin(φ)
cos(ψ)i + sin(ψ)k.
This is the cosine of the zenith angle so the angle of elevation η is given by:
η = 90° - cos-1[cos(φ)cos(ψ)cos(θ)+sin(ψ)sin(φ)]
The elevation angle η of the sun at 4 P.M. on April 21st at latitude 45° is found, assuming the spring equinox occurs at noon 00 P.M. on March 21:
η = 90° - cos-1[(0.7071)cos(12°)cos(60°)+sin(12°)sin(60°)]
= 90 - 58.273 90 -
= 31.73° 56.779303.221
0.0174530.01745357.29578 114.591559026165000000000000000000
3.142857
#VALUE!
time lat0 4947.8289 -180 -6.271996 -0.8971831 4947.87056666667 -165 -6.288224 -0.8382372 4947.91223333333 -150 -6.304448 -0.722029
3 4947.9539 -135 -6.320669 -0.556497
4 4947.99556666667 -120 -6.336886 -0.352948
5 4948.03723333333 -105 -6.353101 -0.125287
6 4948.0789 -90 -6.369312 0.110937
7 4948.12056666667 -75 -6.38552 0.339585
8 4948.16223333333 -60 -6.401724 0.545039
9 4948.2039 -45 -6.417925 0.713265
10 4948.24556666667 -30 -6.434123 0.832769
11 4948.28723333333 -15 -6.450318 0.895388
12 4948.3289 0 -6.466509 0.896843
13 4948.37056666667 15 -6.482697 0.837034
14 4948.41223333333 30 -6.498882 0.720047
15 4948.4539 45 -6.515063 0.55387157.29578 16 4948.49556666667 60 -6.531241 0.349858
17 4948.53723333333 75 -6.547416 0.121943
at 4 P.M. on April 21st at latitude 45° isfound, assuming the spring equinox occurs at noon 00 P.M. on March 21:
33.22099 18 4948.5789 90 -6.563587 -0.114306
19 4948.62056666667 105 -6.579755 -0.34274920 4948.66223333333 120 -6.59592 -0.54778321 4948.7039 135 -6.612081 -0.715422 4948.74556666667 150 -6.628239 -0.83415123 4948.78723333333 165 -6.644393 -0.89592224 4948.8289 180 -6.660544 -0.896494
Angle of incidence0.999811 -63.7902 -70.11059 2.57 153.79020.999783 -56.95438 -63.27476 2.02 146.95440.999708 -46.22225 -52.54263 2.44 136.2222
0.999508 -33.8139 -40.13429 2.29 123.8139
0.998778 -20.66776 -26.98815 2.88 110.6678
0.990312 -7.197312 -13.5177 2.49 97.19731
0.98765 6.369312 0.048924 1.48 83.63069
0.99868 19.8516 13.53121 0.56 70.1484
0.999487 33.02736 26.70697 0.06 56.97264
0.999701 45.50116 39.18078 0.02 44.49884
0.99978 56.38422 50.06383 1.70 33.61578
0.99981 63.55826 57.23787 0.80 26.44174
0.999811 63.74614 57.42575 0.61 26.25386
0.999783 56.82828 50.50789 1.25 33.17172
0.999706 46.05836 39.73797 0.54 43.94164
0.999504 33.63299 27.31261 0.67 56.367010.998756 20.47861 14.15823 0.07 69.521390.989775 7.004225 0.683838 0.84 82.99577
0.988366 -6.563587 -12.88397 1.86 96.56359
0.998704 -20.04446 -26.36485 2.78 110.04450.999492 -33.21503 -39.53542 2.89 123.2150.999702 -45.67599 -51.99638 2.99 135.6760.999781 -56.52749 -62.84788 1.59 146.5275
0.99981 -63.62708 -69.94747 2.41 153.62710.99981 -63.70092 -70.0213 2.48 153.7009
ψ 23.53/21/2009
δ = ψψ1sin(360(T/SolarYear))
δ = -14.35φ = 334.497778
=
θ = 30.911
θ = 360
1.02865475187437
-1.05998732197382
The dot product of this vector with the unit normal is
cos(ψ)cos(φ)cos(θ) + sin(ψ)sin(φ)-0.99917058826205
88.1515713211881
16Fict Date 21-Apr-08
45.00Radian 57.2957795130823
T = 10 + 21 + 4/24 = 31.167-333.833333333333
ψ = 23.5°sin(360(31.167/365.25)) = 23.5sin(30.719°) = 12.00°12.1203113983079
θ = 360(4/24) = 60° 60
0.0174532925199433
cos(φ) = cos(45°) = 0.70710.707106781186548
0.527507459516846
-0.755483349980339
90° - cos-1(0.527507459516846)90 - 1.015132 * 57.29578
== 90 - 58.273 90 - 58.1628
= 31.73° 31.8372
n = (x/r)i + (y/r)j + (z/r)k
= cos(φ)cos(θ)i + cos(φ)sin(θ)j + sin(φ)
cos(ψ)i + sin(ψ)k.
This is the cosine of the zenith angle so the angle of elevation η is given by:
η = 90° - cos-1[cos(φ)cos(ψ)cos(θ)+sin(ψ)sin(φ)]
The elevation angle η of the sun at 4 P.M. on April 21st at latitude 45° is found, assuming the spring equinox occurs at noon 00 P.M. on March 21:
η = 90° - cos-1[(0.7071)cos(12°)cos(60°)+sin(12°)sin(60°)]
