Sheet9Absorptivity & Emissivity table 1 plus others.aSESolarSurfaceaS/EMaterialAbsorptionEmissivityratioCommentsReferenceSilver, Highly polished0.02 - 0.033Marks (1)Gold, Highly polished0.02 - 0.043Marks (1)Barium Sulphate with Polyvinyl Alcohol0.060.880.07The FridgeAluminum polished0.090.033?Magnesium Oxide Paint0.090.90.1The FridgeMagnesium/Aluminium Oxide Paint0.090.920.1The FridgeAluminum quarts overcoated0.110.370.3?Aluminum, Highly polished0.04 - 0.063Marks (1)Snow, Fine particles fresh0.130.820.16?Zinc Orthotitanate with Potassium Silicate0.130.920.14The FridgeAluminum anodized0.140.840.17?Aluminum foil0.150.053?Aluminum foil gets very hot because of this high ratio.Potassium Fluorotitanate White Paint0.150.880.17The FridgeZinc Oxide with Sodium Silicate0.150.920.16The FridgePaint, White zinc oxide0.160.930.17?GSFC White Paint NS-740.170.920.18The FridgeTitanium Oxide White Paint with Potassium Silicate0.170.920.18The FridgeZerlauts Z-93 White Paint0.170.920.18The FridgeCromium0.02666666670.083Marks (1)Cromium0.08666666670.263Marks (1)Dow Corning White Paint DC-0070.190.880.22The FridgeGSFC White Paint NS43-C0.20.920.22The FridgeTitanium Oxide White Paint with Methyl Silicone0.20.90.22The FridgeZerlauts S-13G White Paint0.20.90.22The FridgeLight colored paints, firebrick, clay, glass0.04 - 0.400.90.24U of MissBiphenyl-White Solid0.230.860.27The FridgeP764-1A White Paint0.230.920.25The FridgeZirconium Oxide with650 Glass Resin0.230.880.26The FridgeSolec LO/MIT selective surface paint0.21 - 0.260.15 - 0.191.38LO/MIT I/II products are low emissivity, non thickness dependent coatings.SolecCatalac White Paint0.240.90.27The FridgeHughson White Paint Z-2020.250.870.29The FridgeHughson White Paint Z-2550.250.890.28The FridgeHughson White Paint Z-2550.250.890.28The Fridge3M-401 White Paint0.250.910.27?Hughson White Paint A-2760.260.880.3The FridgeHughson White Paint V-2000.260.890.29The FridgeOSO-H White Paint 63W0.270.830.33The FridgeOpal Glass0.280.870.32The FridgeSherwin Williams White Paint (A8W11)0.280.870.32The FridgeMautz White House Paint0.30.90.33The FridgeSnow, Ice granules0.330.890.37?GSFC White Paint NS44-B0.340.910.18The FridgeSperex White Paint0.340.850.4The FridgeDupont Lucite Actylic Lacquer0.350.90.39The FridgeGSFC White Paint NS-370.360.910.4The FridgeSherwin Williams F8WJ2030 w Polasol V6V2410.360.870.41The FridgeSherwin Williams White Paint (F8WJ2030)0.390.820.48The FridgeTedlar White Paint0.390.870.45The FridgeHughson White Paint Z-202+10000.40.870.46The FridgeAluminum paint (bright)0.30 - 0.500.40 - 0.600.8U of MissHughson White Paint A-276+1O360.440.880.5The FridgeDull brass, copper, galv. steel, aluminum0.40 - 0.650.20 - 0.302.1U of MissColored paints, brick, light brick,0.50 - 0.700.85 - 0.950.67U of MissConcrete0.60.880.68?Galvanized metal new0.650.135?Brick, red (Purdue)0.650.930.68?Concrete and stone, dark0.65 - 0.800.85 - 0.950.81U of MissGalvanized metal weathered0.80.282.9?Metal, plated Black chrome0.870.099.7?Anodize Black0.880.881The FridgeMartin Black Velvet Paint0.910.940.97The FridgeSolec Solkote selective surface paint0.88 - 0.940.28 - 0.492.36SOLKOTE HI/SORB-II is an optical coating specifically formulated for solar thermal applications.SolecMetal, plated Nickel oxide0.920.0811This is stainless steel heated until the nickel oxidizes.?Metal, plated Black sulfide0.920.19.2?Pyramil Black on Beryllium Copper0.920.721.28The FridgeMetal, plated Cobalt oxide0.930.33.1?Polyethylene Black Plastic0.940.921.01The FridgeMartin Black Paint N-150-10.940.941The FridgeTedlar Black Plastic0.940.91.04The FridgeIron and Steel, strongly oxidized0.953Marks (1)Hughson Black Paint L-3000.950.841.13The FridgePaladin Black Lacquer0.950.751.27The FridgeBlack Crystal0.92 - 0.980.08 - 0.255.76Thermafin's Black Crystal Selective Surface Coating (apparently replaced with "Crystal Clear").ThermafinCrystal Clear0.95 - 0.970.09 - 0.148.35Thermafin's Crystal Clear Selective Surface Coating.ThermafinCarbon Black Paint NS-70.960.881.09The FridgeCarbon Black Paint0.960.881.09The FridgeChemglaze Black Paint Z3O60.960.911.05The FridgeDelrin Black Pastic0.960.871.1The FridgeGSFC Black Silicate MS-940.960.891.08The FridgeGSFC Black Paint 313-10.960.861.12The FridgeHughson Black Paint H3220.960.861.12The FridgeVelesat Black Plastic0.960.851.12The FridgeSolchrome0.94 - 0.980.10 - 0.148Solchrome Systems India Limited.SolchromeEbanol C Black0.970.731.33The FridgeEbanol C Black-384 ESH* UV0.970.751.29The Fridge3M Black Velvet Paint0.970.911.07The FridgeParsons Black Paint0.980.911.08The FridgeFlat black paint0.97 - 0.990.97 - 0.991U of MissPaint, Black (Parsons)0.980.981I understand this is lamp black mixed with spar varnish.?Selective surfacesSolec LO/MIT selective surface paint0.21 - 0.260.15 - 0.191.38LO/MIT I/II products are low emissivity, non thickness dependent coatings.SolecWhite paint0.23 - 0.49U of MissSolec SOLKOTE selective surface paint0.88 - 0.940.28 - 0.492.36SOLKOTE HI/SORB-II is an optical coating specifically formulated for solar thermal applications.SolecCopper, aluminum, or nickel plate with CuO coating0.08 - 0.930.09 - 0.213.37U of MissBlack Crystal0.92 - 0.980.08 - 0.255.76Thermafin's Black Crystal Selective Surface Coating (apparently replaced with "Crystal Clear").ThermafinCopper treated with NaCIO2 and NaOH0.870.136.69U of MissSolchrome0.94 - 0.980.10 - 0.148Solchrome Systems India Limited.SolchromeCrystal Clear0.95 - 0.970.09 - 0.148.35Thermafin's Crystal Clear Selective Surface Coating.ThermafinMetal, plated Black sulfide0.920.19.2?Metal, plated Black chrome0.870.099.7?Metal, plated Nickel oxide0.920.0811This is stainless steel heated until the nickel oxidizes.?

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Sheet8NELSPRUITEFFECTIVE AS OF 19 JANUARY 2009950GALVANISEDMETREMASSPRICE /MSQ.METRE EXCLGalvanized metal AVG/TONKG/MEXCL.IBR10.5W/m2LengthwidthTotal Energy W/3.6mDayHoursRequirement-mPrice0.40mm ISQ 300 Z1603442.90747.0368.5561.700.7250.2053.95141.193757.20.762195122774.8437564649.062514.41,012.840.50mm ISQ 550 Z1602743.65057.5783.9375.530.7250.929.2633.657.20.7621951223477.3475609756620864.085365853714.41,239.980.50mm ISQ 550 Z2752753.63659.7687.1278.400.7250.879.7599.21257.20.7621951223288.3612804878619730.167682926814.41,287.080.58mm ISQ 300 Z2752374.21967.4698.3488.510.7250.9211633.657.20.7621951223477.3475609756620864.085365853714.41,452.920.80mm ISQ 230 Z2751725.81489.83130.95117.850.7250.2053.95141.193757.20.762195122774.8437564649.062514.41,934.680.58mm ISQ 300 Z6002374.21979.00115.16103.640.7250.2053.95141.193757.20.762195122774.8437564649.062514.41,701.410.80mm ISQ 230 Z6001725.814103.23150.49135.440.7250.2053.95141.193757.20.762195122774.8437564649.062514.42,223.420.0CHROMADEKMETREMASSPRICE /MSQ.METRE EXCLMetal, plated Black chrome/TONKG/MEXCL.IBR10.50.50mm ISQ 550 Z2002753.63680.07116.73105.050.870.099.774.3853.60.762195122204.105182926861224.6310975610.58mm ISQ 300 Z2002374.21988.75129.37116.4404.60.7621951220700.80mm ISQ 230 Z2001725.814115.42168.26151.4305.60.7621951220800.50mm ISQ 550 Z2752753.6360.58mm ISQ 300 Z2752374.2190.80mm ISQ 230 Z2751725.8140.10.92Metal, plated Black sulfide0.090.87Metal, plated Black chromeZINCALUME AZ150METREMASSPRICE /MSQ.METRE EXCL0.080.92Metal, plated Nickel oxide/TONKG/MEXCL.IBR10.50.47mm3003.33375.69110.3499.300.53mm2653.77487.21127.14114.421200x0.55mm f/feed1885.306118.24172.37155.13COLORBONDMETREMASSPRICE /MSQ.METRE EXCL/TONKG/MEXCL.IBR10.50.47mm2973.36790.74132.28119.050.53mm2633.802100.39146.35131.711200x0.55mm f/feed1885.306131.08191.09171.988.5/76 CORRUGATEDMETREMASSPRICE 8.5 CORRGALVANISED/TONKG/MMETRESQ.METRE0.30mm ISQ 550 Z1005141.94630.1149.350.50mm ISQ 550 Z2752833.534Withdrawn

Sheet1Hello,Hello,sorry, I missed the first request. Attached what I use to calculatesorry, I missed the first request. Attached what I use to calculatethe azimuth (direction) and the elevation (hight over the horizon) ofthe azimuth (direction) and the elevation (hight over the horizon) ofthe sun. If you estimate for each front of your house for which anglesthe 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 withthe sun is shinig on the front you can do the appropriate actions withyour rollerblinds. That how I did it.your rollerblinds. That how I did it.Sorry, code is in German, but you should get the idea.Sorry, code is in German, but you should get the idea.Longitude26Latitude24K0.01745365.342230.445183333329/Sep/09 17:01# Source: http://www.jgiesen.de/SME/tk/index.htm# Source: http://www.jgiesen.de/SME/tk/index.htm20093187Date above in "Julian" format, with a four-digit year (2007174)daycountl0.00#daycountl = (month-1)*30 + date + 0.5deklin0#deklin = -23.45*cos(K*360*(daycount+10)/365)timediff5.75#timediff = hour + minute/60 - (15.0-longitude)/15.0 - 12x0#x = sin(K*latidute)*sin(K*deklin) +0cos(K*latidute)*cos(K*deklin)*Math.cos(K*15*timediff)#sunhight0#sunhight = x/K + 0.25*x*x*x/K (ARCSIN-approximated through polynom)0(ARCSIN-approximated through polynom)use vars ('$altitude', '$SolZen');use vars ('$altitude', '$SolZen');if ($New_Minute || $Reload || $Startup || state_changed $Anwesend eq OFF) {if ($New_Minute || $Reload || $Startup || state_changed $Anwesend eq OFF) {my $tageszahl269.50 my $tageszahl = ($Month - 1) * 30 + $Mday + 0.5; my KValue = 0.01745; my deklin0 my deklin = -23.45 * cos( KValue * 360 * ($daycount + 10) / 365); my $zeitdiff =5.75 my $zeitdiff = $Hour + $Minute / 60 - (15 -;$config_parms{longitude}) / 15 - 12; my $x =0 my $x = sin(KValue * $config_parms{latitude}) * sin(KValue * deklin) + cos(KValue * $config_parms{latitude}) * cos(KValue * deklin) *cos(KValue*15*$zeitdiff); $altitude =0 $altitude = $x/KValue + 0.25*$x*$x*$x/KValue; my $y =0 my $y = -(sin(KValue * $config_parms{latitude}) *$x - sin(KValue * deklin)) / (cos(KValue * $config_parms{latitude}) * sin(atan2(sqrt(1 - $x * $x), $x))); $SolZen =0 $SolZen = atan2( sqrt(1- $y * $y), $y) / KValue; $SolZen =0 $SolZen = 360 - $SolZen if ($Hour > 12);}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 $Sonne_SW = 0;$Sonne_SO = ($SolZen >= 95 && $SolZen = 95 && $SolZen =30 && $altitude =30 && $altitude = 0 && $SolZen = 0 && $SolZen =30 && $altitude =30 && $altitude = 275 && $SolZen = 275 && $SolZen =30 && $altitude =30 && $altitude = 0.0022A2 = 2.04020 + 0.018945 TLK - 0.011161 TLK2A2 =2.0431251574A3 = -1.3025 + 0.039231 TLK + 0.0085079 TLK2A3 =-1.3300983941The 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):if h0 >= 0.1 (i.e. 5.7)-26Dic = Dhc {F(gN) (1 - Kb) + Kb sin dexp/sin h0}Dic =6.8117714257if h0 < 0.1-27Dic = Dhc {F(gN) (1 - Kb) + Kb sin gN cos ALN/(0.1 - 0.008 h0)}Dic =7.5020792535Dic = Dhc {F(gN) (1 - Kb) + Kb sin gN cos ALN/(0.1 - 0.008 h0)}where-28A*LN = A0 - ANA*LN =-9.320168158if -p = 0):-29Dic = Dhc F(gN)Dic =-0.0503218119where F(gN) is a function accounting for the diffuse sky irradiance that may be calculated by the following equation (gN in radians):-30F(gN) = ri(gN) + (sin gN - gN cos gN - p sin2 (gN/2)) NF(gN) =1.000139198where ri(gN) is a fraction of the sky dome viewed by an inclined surface [dimensionless]:-31ri(gN) = (1 + cos gN)/2ri(gN) =0.9993672385and value of N for surfaces in shadow is 0.25227. For sunlit surfaces under clear sky the term N is calculated as:-32N = 0.00263 0.712 Kb 0.6883 Kb2N =-0.4096002667The Kb is a measure of the amount of beam irradiance available (proportion between beam irradiance and extraterrestrial solar irradiance on a horizontal surface):-33Kb = Bhc/G0hKb =0.1973715727where G0h [W.m-2] is calculated as:-34G0h = G0 sin h0G0h =-361.42591972031.3 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 =-0.0898929337-35where:-36rg(gN) = (1 - cos gN)/2rg(gN) =0.0062963005and global irradiance on a horizontal surface Ghc [W.m-2] is given as a sum of its beam and diffuse component:Ghc = Bhc + Dhc-37Ghc =-71.385516989Albedo=0.2In 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, Jeno 1992):-13sin h0 = xC31 cos T + xC33sin h0 =0.2536898342cos A0 = (xC11 cos T + xC13)/((xC22 sin T)2+ (xC11 cos T + xC13)2)1/2cos A0 =-0.3474493457where:-14xC11 = sin j cos dxC11 =-0.6180158425xC13 = -cos j sin dxC13 =-0.2800749619xC22 = cos dxC22 =0.9266705134xC31 = cos j cos dxC31 =-0.6904887102xC33 = sin j sin dxC33 =0.2506786294The Sun declination d [rad] is computed according to Gruter (1984):-15d = arcsin (0.3978 sin (j - 1.4 + 0.0355 sin (j - 0.0489)))d =-0.3853404671where 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:-16T = 0.261799 (t - 12)T =1.5751573167The position of the Sun with respect to an inclined surface (the solar incidence angle) is defined by the angle dexp (Krcho 1990, Jeno 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:-17sin dexp = yC31 cos (T - l) + yC33sin dexp =-0.1060000625where:I' =-0.0503148082-18yC31 = cos j cos dyC31 =-0.9545330049yC33 = sin j sin dyC33 =-0.110162758and:-19sin j = - cos j sin gN cos AN+ sin j cos gNsin j =0.7023042997tg l = - (sin gN sin AN)/(sin j sin gN cos AN+ cos j cos gN).tg l =0.0165714162The hour angle of the time of sunrise/sunset over a horizontal surface Thr,s can be calculated then as:-20cos Thr,s = -xC33/xC31cos Thr,s =0.3630452254The hour angle of the time of sunrise/sunset over an inclined surface Tir,s can be calculated by analogy:-21cos (Tir,s - l) = -yC33/yC31.cos (Tir,s - l) =-0.11541010892 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):-38Gh = Ghc kcGh =953The 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:Ghs953Ghc-71.385516989-39kc = Ghs/Ghckc =-13.350046903As 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):-40Dh = Dhc kdcDh =-24.5952715755Bh = Bhc kbcBh =190.6The 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, Hrvo 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:Dhs/Ghs0.8-41Dh = Gh Dhs/GhsDh =762.4Bh = Gh DhBh =190.6-42kdc = Dh/Dhckdc =82.8228679862kbc = Bh/Bhckbc =-2.6718926165where 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 mode2), and additionally a local solar time time (for mode1). 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 table1 presents a list of all input parameters.ParameterTypeDescriptionModeUnitsInterval of valuesnameof inputelevinrasterelevation1, 2meters0 8900aspinrasteraspect (solar panel azimuth)1, 2decimal degrees0 360slopeinrasterslope (solar panel inclination)1, 2decimal degrees0 90linkeinrasterLinke atmospheric turbidity1, 2dimensionless0 - 7lin single valueLinke atmospheric turbidity1, 2dimensionless0 - 7albedorasterground albedo1, 2dimensionless0 1alb single valueground albedo1, 2dimensionless0 1latinrasterlatitude1, 2decimal degrees-90 90lat single valuelatitude1, 2decimal degrees-90 90coefbhrasterclear-sky index for beam component1, 2dimensionless0 1coefdhrasterclear-sky index for diffuse component1, 2dimensionless0 1daysingle valueday number1, 2dimensionless0 366declinsingle valuesolar declination1, 2radians-0.40928 0.40928timesingle valuelocal (solar) time1decimal hours0 24stepsingle valuetime step2decimal hours0.01 1.0distsingle valuesampling distance coefficient for shadowing1, 2dimensionless0.1 2.0Table 1: r.sun input parametersSolar declination is computed internally using equation (15) and day number unless an explicit value of declin is used. In the case that users data are localised in GRASS location with defined projection, r.sun uses internal GRASS function to get geograp3.2 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 mode1 the solar incident angle incidout, and solar irradiance raster maps beam_rad, diff_rad and refl_rad are computed. Calculation in mode2 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).ParameterDescriptionModeUnitsnameincidoutsolar incidence angle1decimal degreesbeam_radbeam irradiance1W.m-2diff_raddiffuse irradiance1W.m-2refl_radground reflected irradiance1W.m-2insol_timeduration of the beam irradiation2min.beam_radbeam irradiation2Wh.m-2.day-diff_raddiffuse irradiation2Wh.m-2.day-1refl_radground reflected irradiation2Wh.m-2.day-1

1.2 Diffuse radiation [top of the page]1.3 Ground reflected radiation [top of the page]1.4 Position of the Sun [top of the page]2 Computing real-sky radiation [top of the page]3 Implementation in GRASS GIS [top of the page]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]Solar declination is computed internally using equation (15) and day number unless an explicit value of declin is used. In the case that users data are localised in GRASS location with defined projection, r.sun uses internal GRASS function to get geograp3.2 Model outputs [top of the page]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).

Symbols1azimuthThe azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridiannadirAn extreme state of adversity; the lowest point of anythingalbedoThe point below the observer that is directly opposite the zenith on the imaginary sphere against which celestial bodies appear to be projecteddiurnalHaving a daily cycle or occurring every dayDeclination(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 sphereTilt angletilt angle of the collectorsangle between surface normal and solar rayZzenithThe point above the observer that is directly opposite the nadir on the imaginary sphere against which celestial bodies appear to be projectedPenumbraA fringe region of partial shadow around an umbracos-1 (sin sin + cos cos cos (H))LatitudeAn imaginary line around the Earth parallel to the equatorlocal latitudeLongitudeAn imaginary great circle on the surface of the earth passing through the north and south poles at right angles to the equatorsolar hour angle(1 - 8760)15o x (Time (hours past noon)HThe 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 day365.3422Solar YearThe time for the earth to make one revolution around the sun, measured between two vernal equinoxesVernal Equinox(Nhem)01 March 2008South20080Vernal Equinox Mar. 21/220223/22/0823.5Summer Solstice Jun. 21/22-23.5223/22/080Autumnal Equinox Sept. 21/220223/22/08-23.5Winter Solstice Dec. 21/2223.5223/22/088/30/08SolsticeEither of the two times of the year when the sun is at its greatest distance from the celestial equatorAcollector widthDnorth-south spacing between collectorsdD/HI bbeam insolation (Wh/m2)I ddiffuse insolation (Wh/m2)H height ( sin A H = ) (meters)Lcollector length ( meters)l L/H Qannual energy received (kWh) angle between surface normal and solar raysolar azimuthsolar declination angle also inclination1sin(360(T/365.25))relative shaded areascreening angleIoSolar ConstantBeam irradiance1367W.m2GoExtra terrestrial irradianceIo after correction with eW.m2ecorrection factor for solar irradiationj'Day angle in radiansBocBeam irradiance normal to solar beamTLKNormal(geometry) forming a right angle

World

Sun Angle23.5HemisphereSN or S21 Mar 200820 Sep 200820 Sep 2008=1sin(360(T/365.25))=-16.80=334.4159=25.5841S=30.67493E=2160n = (x/r)i + (y/r)j + (z/r)k= cos()cos()i + cos()sin()j + sin()0.9968617883362.8828125cos()i + sin()k.0.4222593102The dot product of this vector with the unit normal iscos()cos()cos() + sin()sin()0.8666927105This is the cosine of the zenith angle so the angle of elevation is given by: = 90 - cos-1[cos()cos()cos()+sin()sin()]365.34SolarYear88.0229035239The elevation angle 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 21:18.02TimetimelatAngle of incidenceFict Date29-Sep-090373.8289-1803.4177767655-0.90097992750.9998123792-64.2871747779-81.08374318381.17154.2871747779Latitude25.501373.8705666667-1653.4344366262-0.88576953240.9998058805-62.3463694708-79.14293787670.93152.3463694708Radian57.29577951310.01745329252373.9122333333-1503.4510947232-0.81034255120.9997680627-54.1294131062-70.92598151222.06144.1294131062T = 10 + 21 + 4/24 = 31.1673373.9539-1353.4677510482-0.67982616410.9996704623-42.83006039-59.6266287962.83132.83006039374.57959444444373.9955666667-1203.4844055924-0.50309268670.9993982928-30.2048223126-47.00139071860.73120.2048223126 = 23.5sin(360(31.167/365.25)) = 23.5sin(30.719) = 12.005374.0372333333-1053.5010583475-0.29215644510.9982161241-16.9871034396-33.78367184562.64106.9871034396-2.65718465986374.0789-903.5177093047-0.06135704580.9598148596-3.5177093047-20.31427771070.2793.5177093047 = 360(4/24) = 6090.257374.1205666667-753.53435845560.17361543970.99495126859.9980953231-6.79847308292.0080.00190467690.01745329258374.1622333333-603.55100579170.39678710640.999032748123.3774780146.5809096081.7266.622521986cos() = cos(45) = 0.70719374.2039-453.56765130430.59298615310.999566883936.369202282219.57263387621.6853.63079771780.902585284310374.2455666667-303.58429498490.74887430140.999728426648.49296027631.69639187010.6741.507039724 = 90 - cos-1[(0.7071)cos(12)cos(60)+sin(12)sin(60)]11374.2872333333-153.6009368250.85385357730.999791097958.633312795641.83674438962.3531.3666872044-0.050293581512374.328903.6175768160.90078681010.999812298864.261683412247.46511500631.9225.73831658780.940387577213374.3705666667153.63421494940.88648286460.999806192762.434559135145.63799072912.0227.565440864914374.4122333333303.65085121670.8119136190.999768959454.28332074237.4867523360.7535.71667925890 - cos-1(-0.0502935815421485)15374.4539453.66748560930.68214793290.999672701643.011718963326.21515055740.0846.988281036790-1.621111135*57.295779513116374.4955666667603.68411811860.50600709330.999405203430.398228307213.60165990121.9959.6017716928=17374.5372333333753.70074873610.29546515930.998255841717.1854324460.388864040.9372.814567554=90 - 58.27390-92.882826155818374.5789903.71737745340.06483496690.9639851243.7173774534-13.07919095262.9886.2826225466=Angle of incidence31.73-2.882826155819374.62056666671053.7340042617-0.17020486780.9947470871-9.7997307138-26.59629911980.7199.79973071380.1921884104362.882826155820374.66223333331203.7506291527-0.39367580520.9990174014-23.1834129821-39.97998138811.84113.18341298219/29/09 18:1321374.70391353.7672521177-0.59038563810.9995630603-36.1843790274-52.98094743341.06126.184379027422374.74556666671503.7838731483-0.74696130230.9997270339-48.3278376686-65.12440607462.12138.327837668623374.78723333331653.8004922358-0.8527580270.9997905608-58.5129268811-75.30949528711.05148.512926881124374.82891803.8171093718-0.90058301930.9998122138-64.2348086605-81.03137706651.28154.2348086605

Sun Angle00373.82893.4177767655-0.90097992750.9998123792-64.2871747779-81.08374318381.1677591437154.2871747779373.87056666673.4344366262-0.88576953240.9998058805-62.3463694708-79.14293787670.9301452858152.3463694708373.91223333333.4510947232-0.81034255120.9997680627-54.1294131062-70.92598151222.0601132511144.1294131062373.95393.4677510482-0.67982616410.9996704623-42.83006039-59.6266287962.8261832429132.83006039373.99556666673.4844055924-0.50309268670.9993982928-30.2048223126-47.00139071860.7330263829120.2048223126374.03723333333.5010583475-0.29215644510.9982161241-16.9871034396-33.78367184562.6377952358106.9871034396374.07893.5177093047-0.06135704580.9598148596-3.5177093047-20.31427771070.268160721293.5177093047374.12056666673.53435845560.17361543970.99495126859.9980953231-6.79847308292.001391138280.0019046769374.16223333333.55100579170.39678710640.999032748123.3774780146.5809096081.718053025666.622521986374.20393.56765130430.59298615310.999566883936.369202282219.57263387621.6816603753.6307977178374.24556666673.58429498490.74887430140.999728426648.49296027631.69639187010.669928316741.507039724374.28723333333.6009368250.85385357730.999791097958.633312795641.83674438962.347842349131.3666872044374.32893.6175768160.90078681010.999812298864.261683412247.46511500631.918862243725.7383165878374.37056666673.63421494940.88648286460.999806192762.434559135145.63799072912.02126934527.5654408649374.41223333333.65085121670.8119136190.999768959454.28332074237.4867523360.749582801335.716679258374.45393.66748560930.68214793290.999672701643.011718963326.21515055740.076331146946.9882810367374.49556666673.68411811860.50600709330.999405203430.398228307213.60165990121.991492797359.6017716928374.53723333333.70074873610.29546515930.998255841717.1854324460.388864040.931487199472.814567554374.57893.71737745340.06483496690.9639851243.7173774534-13.07919095262.979175778386.2826225466374.62056666673.7340042617-0.17020486780.9947470871-9.7997307138-26.59629911980.712434957499.7997307138374.66223333333.7506291527-0.39367580520.9990174014-23.1834129821-39.97998138811.842034293113.1834129821374.70393.7672521177-0.59038563810.9995630603-36.1843790274-52.98094743341.0613671977126.1843790274374.74556666673.7838731483-0.74696130230.9997270339-48.3278376686-65.12440607462.1155830293138.3278376686374.78723333333.8004922358-0.8527580270.9997905608-58.5129268811-75.30949528711.0533584496148.5129268811374.82893.8171093718-0.90058301930.9998122138-64.2348086605-81.03137706651.2806849012154.2348086605

Sheet6absorption.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.absorption band.A range of wavelengths (or frequencies) of electromagnetic radiation that is assimilated by the atmosphere or other substance.acquisition.(1) Image captured by satellite sensor. (2) The process of searching for and locking onto a received signal.albedo.(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.alignment data. Angular measurement of the physical position of the optical axis with respect to the primary space vehicle reference axes.altitude.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).analog-to-digital conversion.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.angular velocity.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)).angle of drift.The angle between the heading of the axis of a craft and its ground track.anomaly.A deviation from the norm.aperture.An opening that admits electromagnetic radiation to a detector or film. An example would be the lens diaphragm opening in a camera.apogee.The point in the orbit of a heavenly body, especially of a manmade satellite, at which it is farthest from the Earth.ascending node.The point at which the orbit of an earth satellite intersects the plane of the equator going from south to north.at-aperture-radiance.The radiance at the aperture of the sensor.attenuation.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.attitude.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.azimuth.The arc of the horizon measured clockwise from the north point to the point referenced. Expressed in degrees. Azimuth indicates direction, not location.BMenubackground.Any effect in a sensor or other apparatus or system above which the phenomenon of interest must manifest itself before it can be observed.band sequential.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.band, spectral.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.BCH.An error detection and correction scheme named after its inventors Bose, Chanduri, and Hochergan.black body.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.brightness value.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.CMenucalibration data.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.DMenudata 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.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.EMenuEDC. 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.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 1970s under the Department of Interior U.S. Geological Survey, to receive, process and distribute data from the United States Landsat satellite sensors and from airborne mapping cameras.ETCEvcuated tube CollectorFMenufield-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).GMenugeocentric. 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.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.HMenuhousekeeping 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.IMenuimage. 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 m wavelength region of the electromagnetic spectrum. For remote sensing, the infrared wavelengths are often subdivided into near infrared (0.7 - 1.3 m), middle infrared (1.3-3.0 m), and far infrared (7.0 - 15 m). 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.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.JMenujitter. 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.KMenuK-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.LMenuL-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.MMenumajor 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.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.NMenunadir. 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 m (visible red) to about 3 m. 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.OMenuoptical 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.PMenupanchromatic. 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.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.QMenuquantization 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.RMenuradian. The angle subtended by an arc of a circle equal in length to the radius of the circle: 57.3radiance. 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.SMenusampling 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.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.TMenutelemetry. 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 m and 9-14 m atmospheric windows.thermal infrared. The preferred term for the middle wavelength ranges of the infrared region extending roughly from 3 m 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 m.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.UMenuultraviolet 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.VMenuvirtual 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 m.WMenuwavelength. 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.XMenuX-band. A radio frequency band extending from approximately 8.0 to 12.5 gigahertz.YMenuyaw. 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.ZMenuzenith. The point in the celestial sphere that is exactly overhead.

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Sheet723.5HemisphereSN or S21 Mar 200820 Sep 200820 Sep 2008=1sin(360(T/365.25))0.0174532925=-16.800.0174532925=334.415916666757.2957795131114.591559026165000000000000000000=25.5840833333S3.1428571429=30.6749333333E=2160n = (x/r)i + (y/r)j + (z/r)k= cos()cos()i + cos()sin()j + sin()0.9968617883362.8828125cos()i + sin()k.0.4222593102The dot product of this vector with the unit normal iscos()cos()cos() + sin()sin()0.8666927105This is the cosine of the zenith angle so the angle of elevation is given by: = 90 - cos-1[cos()cos()cos()+sin()sin()]365.34220000SolarYear88.0229035239The elevation angle 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 21:18.02TimetimelatAngle of incidenceFict Date29-Sep-090373.8289-1803.4177767655-0.90097992750.9998123792-64.2871747779-81.08374318381.17154.2871747779Latitude25.501373.8705666667-1653.4344366262-0.88576953240.9998058805-62.3463694708-79.14293787670.93152.3463694708Radian57.29577951310.01745329252373.9122333333-1503.4510947232-0.81034255120.9997680627-54.1294131062-70.92598151222.06144.1294131062T = 10 + 21 + 4/24 = 31.1673373.9539-1353.4677510482-0.67982616410.9996704623-42.83006039-59.6266287962.83132.83006039374.57959444444373.9955666667-1203.4844055924-0.50309268670.9993982928-30.2048223126-47.00139071860.73120.2048223126 = 23.5sin(360(31.167/365.25)) = 23.5sin(30.719) = 12.005374.0372333333-1053.5010583475-0.29215644510.9982161241-16.9871034396-33.78367184562.64106.9871034396-2.65718465986374.0789-903.5177093047-0.06135704580.9598148596-3.5177093047-20.31427771070.2793.5177093047 = 360(4/24) = 6090.257374.1205666667-753.53435845560.17361543970.99495126859.9980953231-6.79847308292.0080.00190467690.01745329258374.1622333333-603.55100579170.39678710640.999032748123.3774780146.5809096081.7266.622521986cos() = cos(45) = 0.70719374.2039-453.56765130430.59298615310.999566883936.369202282219.57263387621.6853.63079771780.902585284310374.2455666667-303.58429498490.74887430140.999728426648.49296027631.69639187010.6741.507039724 = 90 - cos-1[(0.7071)cos(12)cos(60)+sin(12)sin(60)]11374.2872333333-153.6009368250.85385357730.999791097958.633312795641.83674438962.3531.3666872044-0.050293581512374.328903.6175768160.90078681010.999812298864.261683412247.46511500631.9225.73831658780.940387577213374.3705666667153.63421494940.88648286460.999806192762.434559135145.63799072912.0227.565440864914374.4122333333303.65085121670.8119136190.999768959454.28332074237.4867523360.7535.71667925890 - cos-1(-0.0502935815421485)15374.4539453.66748560930.68214793290.999672701643.011718963326.21515055740.0846.988281036790-1.621111135*57.295779513116374.4955666667603.68411811860.50600709330.999405203430.398228307213.60165990121.9959.6017716928=17374.5372333333753.70074873610.29546515930.998255841717.1854324460.388864040.9372.814567554=90 - 58.27390-92.882826155818374.5789903.71737745340.06483496690.9639851243.7173774534-13.07919095262.9886.2826225466=31.73-2.882826155819374.62056666671053.7340042617-0.17020486780.9947470871-9.7997307138-26.59629911980.7199.7997307138362.882826155820374.66223333331203.7506291527-0.39367580520.9990174014-23.1834129821-39.97998138811.84113.183412982121374.70391353.7672521177-0.59038563810.9995630603-36.1843790274-52.98094743341.06126.184379027422374.74556666671503.7838731483-0.74696130230.9997270339-48.3278376686-65.12440607462.12138.327837668623374.78723333331653.8004922358-0.8527580270.9997905608-58.5129268811-75.30949528711.05148.512926881124374.82891803.8171093718-0.90058301930.9998122138-64.2348086605-81.03137706651.28154.2348086605

Sheet323.53/21/08=1sin(360(T/SolarYear))=23.22=334.497778==30.911=2160n = (x/r)i + (y/r)j + (z/r)k= cos()cos()i + cos()sin()j + sin()1.0286547519cos()i + sin()k.-1.059987322The dot product of this vector with the unit normal iscos()cos()cos() + sin()sin()-0.9991705883This is the cosine of the zenith angle so the angle of elevation is given by: = 90 - cos-1[cos()cos()cos()+sin()sin()]88.1515713212The elevation angle 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 21:16Fict Date21-Apr-0845.00Radian57.2957795131T = 10 + 21 + 4/24 = 31.16731.1666666667 = 23.5sin(360(31.167/365.25)) = 23.5sin(30.719) = 12.0012.0016142662 = 360(4/24) = 60600.0174532925cos() = cos(45) = 0.70710.7071067812 = 90 - cos-1[(0.7071)cos(12)cos(60)+sin(12)sin(60)]0.52590600190.669548948590 - cos-1(0.525906001927743)90-1.0170163595*57.2957795131==90 - 58.27390-58.270745097=31.7331.729254903