Final Report NO AA Grant 04-8-MO March 1 , 1 978 to December 31 ,1979 Use of Environmental Satellite Data for Input to Energy Balance Snowmelt Models Washington, DC December 1980 U.S. DEPARTMENT OF Commerce National Oceanic and Atmospheric Administration National Earth Satellite Service USE OF ENVIRONMENTAL SATELLITE DATA FOR INPUT TO ENERGY BALANCE SNOWMELT MODELS Principal Investigator Jeff Dozier Final Report NOAA Grant 04-8-MO March 1, 1978 to December 31, 1979 Computer Systems Laboratory University of California Santa Barbara, CA 93106 Report TR-CSL-8001 ABSTRACT This document describes the tasks completed during the tenure of the grant. Accomplishments include development of solar and longwave radia- tion models for alpine snout covered terrain, tech- niques for atmospheric correction of satellite radiometric data and for snow albedo determination from satellite, a very fast solution to the ter- rain horizon problem, investigations of the use of NOAA satellite data for snow surface temperature mapping, and work on canopy cover measurements from satellite for use in solar and longwave radi- ation models. USE OF ENVIRONMENTAL SATELLITE DATA FOR INPUT TO ENERGY BALANCE SNOWMELT MODELS Principal Investigator Jeff Dozier Final Report NOAA Grant 04-8-MO March 1, 1978 to December 31, 1979 Computer Systems Laboratory University of California Santa Barbara, CA 93106 Report TR-CSL-8001 Samiils Accpmpu$*wq"lfy 1. An instrument system for ground truth data collection for satellite snow studies has been developed and installed. One essential component of this system is a remote micrometeorological station which we have operated as a satellite data collection platform. Per- formance of the system under isolated alpine conditions has been satisfactory. 2. Models for clear sky solar and longwave radiation have been developed and tested. 3. The clear sky solar radiation model has been extended to calculate the necessary corrections for satellite radiometric data over rugged terrain. 4. A method for satellite determination of snow albedo has been developed and tested. 5. A very fast (order N) algorithm for computing horizon profiles over a digital terrain grid has been developed. 6. Comparisons of field temperature data with the thermal channel of TIROS-N indicate that satellite mapping of snow surface temperature is feasible. 7. Extensive point measurements of forest canopy densities have been made during both winter and summer condi- tions. These will be extended over the study area by correlation to satellite brightness data. This infor- mation will then be used to model the effect of canopy - 2 - cover on the snow surface radiation budget. Tns 1979* A solar radiation model for a snow surface in mountainous terrain* in Proceedings / Model- ing of Snow Cover Runoff * S. C. Colbeck and M. Ray* edi- tors* U.S. Army Cold Regions Research and Engineering Laboratory* pp. 144-153. 2. Marks* D. * 1979* An atmospheric radiation model for general alpine application* in Proceedings * Modeling of Snow Cover Runoff * S. C. Colbeck and M. Ray* editors* U.S. Army Cold Regions Research and Engineering Labora- tory* pp. 167-178. 3. Marks* D. * and Dozier* J.* 1979* A clear-sky longwave radiation model for remote alpine areas* Ar c h i v fur Meteorologie Geoohusik und Biok 1 imatoloa ie > ser. B. » 27* 159-187. 4. Doz,ier* J.* A clear-sky spectral solar radiation model for snow-covered mountainous terrain* Water Resources Research * 16. 709-718. The following manuscripts have been accepted for publi- cation. Copies of the abstracts are included below* but copies of the papers themselves have not been included as part of the final report. When they actually appear in print* five copies of each shall be furnished to the Techni- cal Monitor. - 4 - 1. Dozier* J. * Bruno, J. » and Downey. P., A faster solu- tion to the horizon problem/ to appear in Computers and Qeosc iences . We develop an algorithm for calculating the horizons for each point in a digital terrain grid in order N iterations* whereas all previous methods seem to be of order N squared time complexity. The new method makes horizon computations reasonable* and ought to improve the accuracy of surface climate models in rugged ter- rain. 2. Frampton* M. F. * and Marks* D. * Mapping snow surface temperature from thermal satellite data in the Southern Sierra Nevada* Proceedings of the 1980 Western Snow Conference * to appear. Mapping snow surface temperature over a large alpine area is a useful tool for snowmelt runoff investiga- tions. Tiros-N satellite data are used to measure snow surface temperature over a large area. These measure- ments have been corrected for atmospheric and terrain effects* and are used to calibrate an energy balance snowmelt model under development. The satellite data are calibrated with micrometeorological data from two remote stations in the southern Sierra Nevada* and from active field measurement of snow surface temperature using a radiant thermometer. Data products from the satellite temperature measurements include a tempera- ture grid for wind flow modeling* temperature contour- ing and a quantitative measure of snow surface tempera- ture regimes* and thermal inertia data for remote determination of average snow density. 3. Marks* B. * and Marks* D. « Areal determination of the influence of a forest canopy on the surface radiant energy exchange* Proceedings of the 1980 Western Snow Conference * to appear. To accurately model the energy balance of an alpine snowpack* the influence of a vegetation canopy on the surface radiant energy exchange must be known. A number of studies have been conducted to determine the shading effects of a canopy at a point. This paper presents a new method of estimating canopy cover den- sity which can be extended over a large area. Canopy shading functions* developed from photographic tech- niques* describe the proportion of the hemisphere sur- rounding a point which is partially obscured by vegeta- tion. A general diffuse shading function* and a beam shading function which accounts for changes in solar zenith are presented. Both functions account for changes in canopy cover density with variations in snow depth. A combination of Landsat satellite data and - 5 - field measurements are used to extend the estimated canopy densities over a large ava of the southern Sierra Nevada. The shading functions can then be used in areal models of solar and terrestrial radiation. The following manuscripts have been completed* but have not yet been accepted for publication in the refereed literature. Copies are included as part of this final report. 1. Dozieri J. » and Frew* J. E. » Atmospheric corrections to satellite data over rugged terrain* submitted to Remote Sensing of Environment. 2. Freui/ J. * Remote sensing of snoui surface albedo* M. A. thesis* University of California. Software A useful product of our research has been the develop- ment of an extensive system of programs for integrating numerous types of satellite data and NCIC digital terrain data with models of surface processes. The programs and functions have been written and tested on a small computer* a PDP-11/45 with Unix operating system* and most of them have been transferred to a VAX-1 1/780 under Version 7 of Unix. All routines are in the C language. The widespread utility and portability of these pro- grams is limited at present. The C language is available on only a few machines* although a portable compiler has been written (but not yet released). Its major advantages are that it allows the user to write efficient* readable* struc- tured code and that it virtually eliminates the need for the ordinary user to resort to assembly language. In the future* as the Unix system and the C language become more widely available and as operational installations acquire more advanced and more efficient interactive operating sys- tems* the distribution of these programs will be useful. It is worth noting that Amdahl has developed a Unix system for their in-house machine* and that IBM is working on a micro-processor interface so that Unix can be installed on their new 4300 series computers. Unfinished Projects 1. We have not fully investigated the implications of snow surface temperature and its relation to snowmelt run- off. Due to the late delivery of Tiros-N data* and to the fact that the West Coast data were available only in field station format* our work on this phase pro- ceeded far more slowly than we expected. In particu- lar* the geometric rectification and registration of the data using ground control points was time- - 6 - consuming. 2. We have not examined the differences in measured snow reflectance due to scale differences in Landsat MSS vs NOAA satellite data. 3. Me have made only an initial start to using thermal satellite data as part of a terrain wind model. Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/useofenvironmentOOunit ATMOSPHERIC CORRECTIONS TO SATELLITE RADIOMETRIC DATA OVER RUGGED TERRAIN Jeff Dozier and James Frew Department of Geography University of California Santa Barbara, CA 93106 for Remote Sensing of Environment 1- Abstract Radiometric measurements from satellites in the solar por- tion of the electro-nagnetic spectrum can be converted to meas- urements of surface exitance. Over rugged terrain* the satellite image must be precisely registered to a terrain data set. For small areas a first-order polynomial interpolation scheme is gen- erally satisfactory for the geometric rectification. Because of the widespread existence of saturated pixels* a nearest-neighbor procedure is used for the interpolated satellite radiance numbers. Path radiance and path transmission are calculated with a simple spectral model/ which requires an estimate of the water vapor and aerosol content of the atmosphere. -2- Notation a/Re absorp tance/ref lee tance ratio for atmospheric aerosols EO solar constant Ed diffuse irradiance Es direct (beam) irradiance E' irradiance scattered out of incoming beam do ozone absorption coefficient (.u uater vapor absorption coefficient L radiance ft exitance M' surface exitance which is subsequently scattered ma optical air mass (03) atmospheric ozone content (mm) P air pressure (Pa) r earth-sun radius vector RN satellite radiance number u precipi table uater vapor (mm) z altitude (m) Z solar zenith angle * Angstrom turbidity exponent Angstrom turbidity coefficient X wavelength P surface diffuse reflectance to direct irradiance p' surface diffuse reflectance to diffuse irradiance oA aerosol attenuation coefficient 3> Tabulated data for the solar constant EOCX] are available from Makarova and Kharitinov (1972) and Willson (1978); Rayleigh scattering coefficients (7) pCz23 - f$C03 exp C-SxlO"* z23 (8) Hence the transmission function for the scattered radiation is: YCX3 - exp -C-CkoCX3 (03)Cz2t3 + kwCX3 wCz2t3 + ol (9) pCz23 X* / (1 + l/(a/Re)>3> If a/Re = 0/ the last term/ for aerosol absorption/ is omitted. Tabulated values for the absorption coefficients are available for ozone (koCX3) from Inn and Tanaka (1953) and Leighton (1961)/ and for water vapor (kwCX3) from Gates (1960) and Gates and Har- rop (1963). 15- Combining equations (4) and (9) leads to the path radiance: LfCXlpath =0.5 cos^Z E'C\3 YCX3 / w (10) The first term (Robinson* 1966) accounts for the portion of the radiation scattered upward. For a given solar zenith angle and atmospheric attenuation parameters* the path radiance is a function of surface elevation. Hence the integrals over the wavelength range of interest can be calculated for a range of elevations within the area of interest* and the path radiance nay then be interpolated for each pixel* provided that each pixel's elevation is known. Sensitivity of path radiance to altitude and atmospheric aerosol content at two different solar zenith angles is shown in Figure 3. The highest Angstrom § value used is 3500* compared to our highest measured values (in the southern Sierra) of 4500. The lower (S value used is 50; ue have measured values below 10. The Figure demonstrates that path radiance is quite sensitive to altitude* solar angle* and atmospheric aerosols. Moreover* because of the dependence on altitude* it is likely that a single haze correction factor for an entire scene (e.g. Otterman and Fraser* 1976) will be incorrect for areas of rugged terrain. Figure 4 illustrates dependence of path radiance on precipitable water vapor. Because water vapor absorption is important chiefly beyond 855 nm» the scales on both axes are different than in Fig- ure 3. -16- - 3 c I uj" o z < "1 — I — I — I — | — i — i — I — t— i — I — I — I — i — | — i — i — I — r 500 1000 1500 WAVELENGTH, nm 2000 500 1000 1500 2000 WAVELENGTH, nm t°.3 E c N E lJ o z < ~i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — r c 500 1000 1500 WAVELENGTH, nm 2000 -r 3 E c N E o z < or 1 1 1 1 | 1 1 I 7 1 i i i 1 1 i i i - I) 1 >. I."'- S v (■■■:■ / '•-. V \ : J \l - ' 1 **' "-^L i i/ /' "nj i . L< i ■ ■ , ■*■ 1 1 5 , XiH, .1-4 t ■ i-_^i. i 500 1000 1500 2000 WAVELENGTH, nm 5c 1 1 1 1 1 1 1 1 1 1 r .10 E ' v, % " i 1 „ M / UJ o i i |.05 - Lt/ o » < or 800 1000 1200 1400 1600 1800 2000 WAVELENGTH, nm 800 1000 1200 1400 1600 1800 2000 WAVELENGTH, nm Figure 3. --See page 29. -17- Path Transmissio n Algorithm In order to determine path transmission with a satellite radiometer measuring upwelling space radiance in broad wavelength band(s)/ we must make some assumptions about the spectral reflec- tance of the surface. This does not mean that we need to know the surface albedo (indeed if we did we would hardly need the satellite to measure surface characteristics) but we must have some idea of the relative spectral response. Lacking any infor- mation whatever about the surface/ we might assume the spectral response to be flat across a wavelength range of measurement* but if we have some information about the nature of the surface we can use it. For example/ for a snow surface we know that the reflectance is similar to the curves/ which represent varying snow ages, shown in Figure 5. As the snow ages* the reflectance decreases in all wavelengths/ but the relative decrease has no strong wavelength dependence (O'Brien and Munis/ 1975). For a snow sur- face/ then/ we can calculate path transmission by first calculat- ing the surface irradiance and exitancei using the algorithm in Dozier (1980) and equation (4)/ assuming the reflectance curve is like that in Figure 5 and taking into account any solar angle dependencies. -18- .010 O05 < o < LC 800 1000 1200 1400 1600 1800 2000 WAVELENGTH, nm Figure 4. — See page 29. i.o i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r u .6 - o UJ d A UJ .2 t — i — i — r Q L_J I I I I I 1 1 I I I 1 1 L 500 1000 1300 WAVELENGTH, nm 2000 Figure 5. --See page 30. -19- As this radiation leaves the surface it is scattered and absorbed. The total amount scattered is: M'CX3 - MCX3surf il - expC-( + (11) cfRCX3 PCz3/PC03>3> As before/ this scattering takes place on the average from the level PCz3/2i so the scattered surface exitance which reaches space is: LtCX3sc =0.5 YCX3 M'CX3 / ir (12) The surface exitance which is neither scattered nor absorbed before reaching space is: LfCX3direct ■ MCX3surf ?CX3misc exp C-(koCX3 (03)Czt3 + (13) kwCX3 wCzt3 + ponential term (Gates and Harrop* 1963). Hence equation (2) for monochromatic space radiance may be re-phrased : L*CX3space ■ LtCX3path + L+CX3sc + L*CX3direct (14) This equation does not help us much/ because our space measure- ments are of Ltspace integrated over some aX. However* if we -20- have correctly specified the general form of p'CXD and pCX3/ then our calculations of HCXUsurf, LtCXDsc, and Lt C X 3d ir ec t at least have the correct relative values. Hence if we integrate these over the desired aX and drop the wavelength designation: r = tt (Ltsc + Ltdirect) / Mtsurf (15) The values of r vary uith altitude so the simulation has to be carried out for a range of altitudes in the area of interest. Then for any pixel of known altitude* T can be found by interpo- lation. Calculation of Surface Ex itance By the methods presented in the two previous sections, integrated values for Ltpath and f can be found for any wavelength range for any pixel of known elevation. By re- arranging equation (1) the surface exitance is: Mtsurf = tt (Ltspace - Ltpath) / t (16) In Figure 6 ue show how Ltspace/ Ltpath. and Mtsurf /tt vary with altitude/ atmospheric aerosol content/ and precipitable water vapor. From the Figure it is evident that all three variables *re sensitive to altitude and aerosols/ so that ad. hoc techniques (such as band-rat ioirg ) for estimating surface exitance will not work satisfactorily over a wide range of parameters. For the near-infrared wavelengths where water vapor absorption is the -21- .10 ^.05 < < a: 1 1 1 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 - A " kicA 1 \ V> \ \ - - I'vA V X. - 1 I / I 1 IT — i--3^1t =r T 1 — -K- 1 1 1 1 i - 500 1000 1500 2000 WAVELENGTH, nm 500 1000 1500 2000 WAVELENGTH, nm Figure 6. — See page 30. -22- frajor attenuation factor* corrections for path radiance can prob- ably be ignored. Conclusion Path radiance and path transmission vary with the altitude of the surface* atmospheric aerosol and water vapor content* and the nature of the spectral reflectance of the surface. The vari- ations involved are not trivial* and must be calculated expli- citly if we are to derive surface exitance data from space-borne radiometers. Figure 7 shows* for the area in Figure 2* the difference between Ltspace and Mtsurf/ir in MSS band 5* for 13 February 1977* when field measurements of solar radiation in two wavelength ranges (280-2800 nm and 700-2800 nm) indicated a value of 1100 and 14 mm precipitable water vapor. For this band (and for band 6) none of the differences are negative. This indicates that the increased brightness of the image due to path radiance more than compensated for the atmospheric attenuation of the surface signal. This is not true* however* for similar ana- lyses we made for MSS bands 4 and 7* where some of the differ- ences were negative. -23- Figure 7. --See page 30. ■24- REFERENCES Angstrom, A., (1961) Techniques for determining the turbidity of the atmosphere* Tellus , 13: 214-223. Angstrom, A. , (1964) Parameters of atmospheric turbidity, Tellus , 16: 64-75. Bernstein, R. , and Ferneyhough, D. 0. jr., (1975) Digital image processing, Photoqramm . Enqro . Remote Sens . * 41: 1465-1476. Dozier, J., (1980) A clear-sky spectral solar radiation model for snow-covered mountainous terrain, Mater Resour . Res . , (to appear ). Dozier, J. , and Outcalt, S. I. , (1979) An approach toward energy balance simulation over rugged terrain, Qeoo . Analusis , 11: 65-85. Gates, DM, (1960) Near infrared atmospheric transmission to solar radiation, J. Opt . Soc . Amer . , 50: 1299-1304. Gates, D. M. , and Harrop, W. J. , (1963) Infrared transmission of the atmosphere to solar radiation, App 1 . Optics , 2: 887-898. Holkenbrink, P. F. , (1978) Manual on characteristics of Landsat computei — compatible tapes produced by the EROS Data Center digital image processing system, User Services Section, U.S. Geological Survey, EROS Data Center, Sioux Falls, SD. 25 Inn* E. C. Y. » and Tanaka* Y. * (1953) Absorption coefficient of ozone in the ultraviolet and visible regions* J. Opt. Soc. Amer . * 43: 870-873. Kasten* F. » (1966) A new table and approximation formula for the relative optical air mass* Arch . Meteorol . Geoohus. Bioklim . * ser. B» 14: 206-223. Kirby, M. # and Steiner* D. , (1978) The appropriateness of the affine transf or.ration in the solution of the geometric base problem in Landsat data* Can , jj. Remote Sens . » 4: 32-43. Kreuger* A. J. * and Minzner* R. A. * (1974) A mid-latitude ozone model for the U. S. standard atmosphere* NASA Goddard Space Flight Center* report no. X-912-74-291* 17 pp. Landgrebe* D. A. * et al. , (1974) A study of the utilization of ERTS-1 data from the Wabash River Basin* final report con- tract no. NAS5-21773* NASA Goddard Space Flight Center* 337 PP- Leckner* B. » (1978) The spectral distribution of solar radiation at the earth's surface — elements of a model* Solar Enerau * 20: 143-150. Leighton* P. A. , (1961) Photochemistru of Air Pollution * Academic Press* New York* pp. 6-103. Makarova, Ye. A. * and Kharitinov* A. V. * (1972) Distribution of energy in the solar spectrum and the solar constant* NASA TT F-803* 245 pp. • 26- Mack/ M. L. / (1977) Rectification and registration of digital images and the effect of cloud detection* in 1977 Mach ine Processing of Remotel y Sensed Data Sumposium > LARS/ Purdue University/ West Lafayette* IN/ pp. 12-23. NASA (1976) Landsat data users handbook/ NASA Goddard Space Flight Center/ document no. 76SDS4258, O'Brien/ H. U. / and Munis/ R. H. / (1975) Red and near-infrared spectral reflectance of snoui in Workshop on Operational Application s of Satel lite Snoiucover Observations / (Rango/ A./ Ed.)/ NASA SP -391/ pp. 319-334. Otterman/ J. > and Fraser/ R. S. / (1976) Earth-atmosphere system and surface reflectivities in arid regions from Landsat MSS data/ Remote Sens . Environ . / 5: 247-266. Penndorf/ R. / (1957) Tables of the refractive index for standard air and the Rayleigh scattering coefficient for the spectral region between 0.2 and 20.0 microns and their application to atmospheric optics/ J. Qot . Soc . Amer . / 47: 176-182. Potter/ J. F. / (1977) The correction of Landsat data for the effects of haze/ sun angle/ and background reflectance/ in Sunposiun &n Mach ine Processing of Remotelu Sensed Data / LARS/ Purdue University, West Lafayette/ IN/ pp. 24-31. Robinson/ N. / Ed./ (1966) Solar Radiation / Elsevier* Amsterdam/ pp. 29-160. -27- Taber, J. E. , (1973) Evaluation of digitally corrected ERTS images/ Third ERTS- 1 Sumoosium , vol. 1-B. pp. 1837-1844. Thomas* V. L. i (1975) Generation and physical characteristics of Landsat 1 and 2 I1SS computer compatible tapes* NASA Goddard Space Flight Center/ report no. X-563-75-233/ 70 pp. Van Wiez P./ and Stein. M. / (1976) A Landsat digital image rec- tification system/ in Sumposium on Machine Processing of Remotelu Sensed Data / LARS/ Purdue University/ West Lafay- ette/ IN/ pp. 4A18-4A26. Uillsom R. C. / (1978) Accurate solar 'constant' determinations by cavity pyrhel iometers/ J. Geophus . Res . / 83: 4003-4007. Uong/ K. W. / (1975) Geonetric and cartographic accuracy of ERTS-1 imagery. Photoqramm . Enqrq . Remote Sens . / 41: 621-635. Yamamoto/ G. / (1949) Average vertical distribution of water vapour in the atmosphere/ Tohuku Univ . Sc i . Rep . / ser. 5/ 1: 76-79. -;28 FIGURE CAPTIONS 1. Shaded relief map (left) and Landsat image with sys- tematic distortions removed (right). The area is approximately a 15-minute quadrangle in the Kearsarge Pass - Bullfrog Lake region of the southern Sierra Nevada, in the Kings River drainage. South Fork. 2. The Landsat image from Figure 1 corrected to terrain, so that each pixel corresponds to a known coordinate on a digital terrain tape. On the right is a mask of saturated pixels. Unsa- turated radiances in the image range from to 17.5 W m"~^sr~ (integrated from 600 to 700 nm). 3. Sensitivity of path radiance to altitude/ solar angle, and atmospheric aerosols. (A) is for 3000 m elevation. (B)* uhose ordinate scale is the same* is for sea level. In each graph the solid lines represent May 30 at latitude 36.5 deg N; the dashed lines represent December 21 at the same latitude. In both cases the time of day is that corresponding to the Landsat overpass* about 9:37 a.m. For each date the upper curve represents path radiance for ■ 3500; the lower curve represents path radiance for § * 50. Both the magnitude and the spectral distribution of path radiance are sensitive to altitude* solar angle* and aerosols. 4. Sensitivity of path radiance to precipitable water vapor. The analysis is for May 30 at the location and time of day corresponding to Figure 3. The upper (solid) curve is for w = 10 mm* the lower curve (dashed) is for w = 40 mm. Because •29- water vapor absorbs some of the light which has been scattered upward, increased water vapor will decrease the path radiance/ in contrast to the situation shown in Figure 3. 5. Snow reflectance vs wavelength. The top curve represents new snow. The lower curves represent the degradation in reflectance that occurs as the snow ages. 6. Sensitivity of surface upwelling radiance Mtsurf/rr (solid line), space radiance Ltspace (dashed line), path radiance Lfpath (dotted line), and the transmitted signal Ltspace - Ltpath (dot-dashed line), to altitude, atmospheric aerosols, and precip- itable water vapor. (A) is for 3000 m elevation, 10 mm water vapor, and (3 = 50. (5) where i is the age of the snouipack in days. Values for a and b uhich reproduce the curves in figure (1) are: a b accumulation ablation . 78 1. 05 . 069 . 07 Of course/ these values are site-specific and cannot be used in a predictive fashion. The usefulness of equation (5) lies in its description of the general form of albedo decay over time. Theoretical models of snow albedo indicate that the primary parameter governing changes in reflectance at a given wavelength is the change in size of the individual snow grains as the pack metamorphoses. Dunkle and Bevans (1956)/ Oiddings and LaChapelle (1961), and Bergen (1975) modelled snow albedo based on the assumption that snow is a diffusing medium. In these models, light entering the snowpack proceeds in a random-walk fashion governed by its interactions with individual snow grains. As grain size increases, so does the probability that an incident light bean will be either transmitted or scattered for- ward. Figure (2) presents plots of snow spectral albedo from the Dunk le-Bevans model, showing the effect of vary- ing the grain size parameter. Unfortunately/ no simple analytic relationship has been developed between snowpack age and snow grain size; indeedi under some circumstances snow grain size may ac- tually decrease over time (Perla and Martinelli* 1975). For shallow snowpacks* melt-induced metamorphism will be much more rapid as radiation penetrates to the ground surface, is absorbed/ and is then conducted and/or re- radiated back into the pack/ accelerating the melt rate (U3ACE/ 1956; O'Neill and Gray. 1973). Also, an increase in snow density by gravitational compaction can have an effect on albedo similar to an increase in grain size (Bergen/ 1975). It is thus inappropriate to extrapolate the decay of snow albedo solely by means of an empirical function of elapsed time. In the remainder of this pa- per/ the "aging" of a snowpack will refer to the collec- tion of processes acting to reduce the snow surface al- - 10- bedo. Similarly, the "age" of a snouipack will be a di- mensionless index of the status of these albedo-reducing processes/ rather than an actual elapsed time. 3. 1_. 2. Spectral Characteristics The most comprehensive spectral measurements of snow reflectance available to date are those by O'Brien and Munis (1975). The measurements were made in a cold la- boratory/ using barium sulfate as a reflectance standard. Their "typical" spectral reflectance curve for new snow is shown in figure (3). The most striking feature of this curve is the rapid decrease in spectral reflectance in the infrared wavelengths (> 700 nrn), as opposed to the familiar/ uniformly high reflectance in the visible por- tion of the spectrum. As O'Brien and Munis note/ this can be almost entirely ascribed to the variation in the spectral absorption coefficient of pure ice (see figure (4); data from Irvine and Pollack/ 1968; Hobbs/ 1974). Theoretical albedo models whose snow transmissivity functions are driven by these spectral absorption data (Dunkle and Bevans/ 1956; Giddings and LaChapellei 1961; Choudhury and Chang/ 1979) yield curves that quite close- ly agree with the O'Brien and Munis "reference" curve/ 11- for snou grain sizes which are reasonable for new snow (Choudhury and Chang/ 1979). Moreover/ by increasing the grain size/ the albedo is decreased at all wavelengths in a manner similar to that observed by O'Brien and Munis for naturally aged snow. It is important to note that in both the models and the measurements/ the ratio of the spectral reflectances for any two wavelengths remains constant/ while the absolute reflectance decreases at all wavelengths. In fact/ when the O'Brien and Munis curve is multiplied by d imensionless/ constant "aging factors"/ a family of new curves is generated (see figure (5)) which are quite similar to those generated by the theory-based models when their grain-size parameters are varied (see figure (2)). 3. 1.. 3. Diffuse and Specular Components Although for most purposes snow is assumed to be a diffuse (Lambertian > reflector/ in reality it is well known that there is a significant specular component in snow reflectance. Measurements by Hubley (1955)/ the Corps of Engineers (1956)/ and Dirmhirn and Eaton (1975)/ using global pyranometers/ all show a pronounced increase in albedo at large (typically > 60 deg) solar zenith an- 12- gles. If the specular component is assumed to behave ac- cording to Fresnel 's law (Feynman et al, 1963)/ then its relative insignificance at lesser zenith angles is under- standable. Figure (6) is a graph of the Fresnel reflec- tance of pure ice as a function of the angle of incidence of the beam irradiance. A model of directional reflectance from snow was developed by Middleton and Mungall (1952) from extensive in situ measurements with a portable goniophotometer The directional component of the reflectance was ade- quately explained by a Fresnel model. Their observation that for beam irradiance* the angle of reflection tended to be slightly larger than the angle of refraction/ was explained by considering the snow surface to consist of myriad small/ randomly oriented reflecting surfaces. The rapid rise in the Fresnel reflectance cur\/e at large an- gles of incidence thus disproportionately favors those surfaces oriented nearer to parallel with the incoming beam. Snow reflectance of beam irradiance actually con- sists of two components/ the direct/ Fresnel component . The precision of the MSS data/ for all bands and all Landsats/ is better than 1 W m**-2 sr**-l» which is more than adequate for energy balance studies. Conversion of MSS digital radiance numbers (RNs) to target spectral ra- diance (LfspaceCbandl )* is accomplished using the thres- hold and saturation radiances from table (1) in the fol- lowing linear transform: Lf spacetbandJ = (RNCbandD / RNmax Cband 3 > * (8) (LsatCbandl - Lthresh Cband 1 ) + LthreshCband 3 The accuracy of the MSS data cannot be readily determined. The specifications call for an absolute ac- curacy of ±5 percent. Prelaunch tests indicate a poten- tial accuracy of ±1. 5 to 6 percent/ varying by band (Ad - 17- Hoc Advanced Imagers and Scanners Working Group- 1973). In-flight detector calibration is effected by exposing each individual detector to an on-board standard lamp/ and statistically deriving the coefficients of a two- parameter linear correction from the observed variation in detector response (NASA; 1976). This correction has not been entirely successful in removing interdetec tor response variations (visually apparent as "striping" in MSS imagery); as a result; NASA has modified the linear correction described above to include additional multi- plicative and additive correction factors derived from cumulative analysis of the existing corpus of MSS data (NASA. 1977). In spite of these efforts* interdetector response variations persist in MSS data. It thus appears that the present combination of internal and historical calibra- tion is not entirely adequate. 3. 3. 2. Spat ial Characteristics The spatial characteristics of MSS data that most concern this investigation are pixel resolution and image geometry. Pixel resolution refers to the earth surface area corresponding to a single MSS pixel; while image - 18- geometry refers to inter-pixel positional relationships. Pixel resolution or "size" is determined primarily by the IFOV of the MSS and the altitude of the satellite platform. The nominal values of these parameters (0.036 mr and 919 km, respectively) yield a pixel size of 79 m (on a side, since the detector aperture is square) at the nadir. Variations in this value of at most ± 2 m are caused by changes in satellite altitude, and by panoramic effects towards the ends of the scan lines. This resolution is quite compatible with the nominal grid spacing of the DTTs. In fact, Landsat MSS data are the only readily available spaceborne radiometric measure- ments possessing resolution to this order of magnitude. Although MSS data are logically organized as a grid of pixels forming an image, the actual earth surface po- sitional relationships of these pixels are quite complex. The factors which produce these distortions (in the sense of the departure of the image from an orthonormal grid of equally spaced lines and samples) are both systematic (i.e., predictable) and random. The most prominent sys- tematic distortions, and their approximate magnitudes, are (based on data from NASA, 1976): - 19- earth rotation: The rotation of the earth beneath the MSS during the scan retrace causes each succes- sive scan swath (a group of six adjacent scan lines acquired on the same scan half-cycle) to be dis- placed to the east of the previous swath. The resulting effect is a horizontal skew, variable with latitude/ whose maximum is about 35 m per swath at the equator. scan skew: The forward motion of the satellite dur- ing a single scan results in a fairly constant cross-scan skew of about 240 m from one end of a line to the other. sampling delay: The six detectors per band which make up a scan swath are sampled sequentially. Scan mirror motion during the interval between samples causes a fixed displacement of about 4m between corresponding samples in adjacent lines in the same swath. oversamp 1 ing : The electronic sampling rate of the MSS yields 1.41 samples per IFOV. This results in an along-scan pixel overlap with a nominal sample spacing of 56 mi while maintaining the nominal 79 m line spacing. panorama and earth curvature: The object plane of the MSS is essentially a cylinder whose axis is the spacecraft orbit and whose radius is the spacecraft altitude. The projection of the object plane onto the surface of the earth causes the earth distance between samples to increase as a function of the tangent of the scan nadir angle* yielding a maximum positional error of about 400 m at either end of a scan line (Kirby and Steiner* 1978; see figure (7>). scan nonl inear ity : The acceleration/deceleration of the MSS scan mirror during an active (scanning) half-cycle introduces a sinusoidal displacement of samples along the scan line. The maxima of this ef- fect occur at about one-quarter and three-quarters of the way through the scan, with magnitudes of about +400 m and -400 m, respectively (Thomas, 1975). - 20- The above distortion sources do not account for all of the positional error in the MSS data. It was origi- nally suggested by NASA that spacecraft attitude changes (yaw* pitch/ roll) could introduce up to 674 m of essen- tially random positional error/ owing to the poor resolu- tion of the on-board attitude sensors (NASA* 1971). Although subsequent investigations suggest that these er- rors may in fact be much less (Wong/ 1975)/ they must still be accounted for. Given that geometric correction to this level of accuracy is almost always for the pur- pose of registering the MSS data to an existing geograph- ic database/ the most common procedure for removing ran- dom distortions is a polynomial transform whose coeffi- cients are derived by analyzing the displacement between the coordinates of control points which are identifiable in both the MSS data and in the target database. The combination of systematic and random distortion models can generally achieve geometric registration accuracies to within 1 pixel (Bernstein and Ferneyhough/ 1975). Given mathematical models of the above distortion processes/ it is then possible to adjust the line and sample coordinates of the individual pixels so that they - 21- refer to a coordinate space in which the distortions are not present. In practicei this procedure is usually ap- plied in reverse; that is« an "empty" image is created whose regular grid is assumed to be free of any geometric distortions/ and inverse distortion models are evaluated at each "empty" location to find the coordinates of the original image pixel to place there (Van Wie and Stein* 1976; Bernstein and Ferneyhough* 1975). The original im- age coordinates so derived are unlikely to be integral; therefore/ an interpolation or resampling rule is re- quired to compute an RN value to assign to the corrected grid The simplest of these/ requiring no interpolation at all/ is nearest-neighbor assignment (i.e./ the origi- nal image coordinates are rounded to the nearest integral value). The most effective tradeoff between radiometric accuracy and computational speed appears to be a third- order/ "cubic convolution" interpolator/ which computes a new RN from a 4x4 kernel in the original image (Taber/ 1973). 3. 3. 3. Spec tral Characteristics The four spectral bands of the Landsat MSS are de- fined as follows (for historical reasons/ they are num- - 22- bered 4 through 7): band 4 5 6 7 500 - 600 nm 600 - 700 nm 700 - 800 nm 800 - 1100 nm In the absence of any documentation of the wi thin-band spectral responses of the MSS# they are assumed to be flat: although this is surely not the case. As can be seen from the O'Brien - Munis spectral re- flectance curve (figure (3))i bands 4 and 5 contain largely redundant information. Bands 7 and (to a lesser extent) 6 span the spectral window where the transition from very high visible to very low infrared reflectance occurs. In the case of band 7, it would be desirable to have finer spectral resolution over an equivalent window, especially in view of the pronounced water vapor effects in this band (Dozier, 1979). It is additionally unfor- tunate that band 7, where most of the snow reflectance information is contained* has the least radiometric pre- cision (6 bits/ versus 7 bits for bands 4 through 6) and, historically* the least accuracy of the four MSS bands (NASA, 1977). The combined spectral window of the MSS does not permit the discrimination of snow from clouds (Alfoldi» - 23- 1976)* which can be a problem over a remote mountainous area where highly variable local weather conditions may not be well knoun. A satellite designed for snow moni- toring would doubtless -include a band further into the infrared (around 1600 nm)# where the almost non- reflectance of snow contrasts w* th the highly-reflective water-droplet clouds (Barnes and Smallwood* 1975). The saturation ceiling of the bands in the visible portion of the spectrum would also need to be increased. 3. 3. 4. Temporal Characteristics A single Landsat satellite will pass over most earth locations once every 18 days. If two Landsats are operating! their orbits are usually staggered so that the effective overpass interval is reduced to 9 days (howev- er, as of this writing* only Landsat 3 is still operat- ing). In itselfi this interval is insufficient for snowpack albedo monitoring* for the following reasons: - A single day's snow fall between overpasses can drastically increase the albedo of an existing snowpack. Conversely, a light snowfall just before the satellite overpass may deceptively increase both the albedo of the existing pack as well as its ap- parent spatial extent* only to disappear entirely days before the next overpass. - 24- During the ablation season/ the change in albedo at the margins of a snowpack can be quite rapid (McGinnis* et al, 1975)* especially in cases where decreasing depth causes the ground surface albedo to become significant. For these reasons, supplementary information on the state of the snoupack is required. Extrapolation from a feu spatially isolated field measurements over a complex topographic surface is inherently unsound. It may be possible* though/ to monitor high-temporal-frequency events from sensors with significantly lower spatial resolutionsi such as are carried by the NOAA/TIROS satel- lites (Algazi and Suki 1975)/ and use these data to up- date the albedo model between MSS overpasses. 3- £• Atmo sp heric Effects in Irradiance and Exitance The earth's atmosphere acts as a spectrally* spa- tially* and temporally variable filter to solar radia- tion. The two principal processes involved are absorp- tion and scattering. Both processes will cause beam ra- diation to be attenuated. In addition* scattering intro- duces a diffuse radiation component* with entirely dif- ferent geometric and spectral properties. With respect to the albedo model* atmospheric effects must be evaluat- ed in converting the solar constant to surface irradi- - 25- ance/ and in deriving surface exitance from satellite ra- ti iometry. 3. 4. 1_. Irradiance The beam component of surface irradiance may be thought of as the product of the solar constant (i.e., the beam irradiance outside the earth's atmosphere) and an atnospheric transmission function. This transmission function is a composite of the optical behavior of both individual chemical compounds (e.g., water vapor; ozone)/ and atmospheric mixtures (e. g. , Rayleigh and aerosol scattering). These individual transmission functions all vary with wavelength and atmospheric path length (which varies with the solar zenith angle and the elevation of the surface). Some of these transmission functions also vary because the atmospheric components whose behavior they describe are spatially and temporally variable. A model developed by Dozier (1979) employs transmission functions for ozone, water vapor, Rayleigh scattering, aerosol scattering, and miscellaneous gases. The spec- tral significance of each of these functions, for a "typ- ical" set of atnospheric conditions* is shown in figure (8). - 26- The diffuse component of irradiance derives from two sources: radiation which is scattered downward out of the incoming beam* and radiation which is reflected from the surface and subsequently "back-scattered* 1 (Dozier, 1979). Downward scattering may be computed from the same transmission functions required for computing beam irra- diance. Computations of backscatter ing require some in- formation on the reflectance characteristics of the sur- face. The distinctive spectral reflectance of snow some- what simplifies this problem (Dozier/ 1979)* for the pur- poses of the albedo model. 3.- £L- §.• Exitance There are two principal atmospheric effects in the composite earth-atmosphere signal which is measured by a spaceborne radiometer: - path transmission: The atmosphere attenuates the surface upwelling radiance (i.e./ the exitance in the direction of the satellite) in a manner similar to its effect on beam irradiance. path radiance: Due to scattering of beam and re- flected solar radiation* there is a significant dif- fuse component in the direction of the satellite. The conbined effects of path radiance and transmission may be expressed as: 27- LtspaceCXD = LtpathCXD + rCXD (Msurf CX3 / w) (9) Some of the problems inherent in determining path radiance and transmission are (Dozier and Frew* 1980): - The Landsat MSS has a spectral resolution which is coarser than the spectral variations in both atmos- pheric attenuation and in snow surface reflectance. This makes it rather difficult to apply atmospheric corrections to MSS data. Both path transmission and path radiance vary with atmospheric parameters and with the elevation of the surface. In addition, path radiance will vary with the solar angle. - With path transmission there is the problem of scattering in the upward direction/ causing "smear- ing" of the radiance from one pixel over adjacent p ixels. 4. Imp lementat ion of the Albedo Model In this section the implementation of a surface al- bedo model according to the steps outlined in section 2.3 is discussed The resulting model is applied to a test site in the southern Sierra Nevada of California. i- 1- Bullfrog Lake Test Site The test site selected for this investigation is a geodetic quadrangle centered on Bullfrog Lake* in the Bubbs Creek drainage of the South Fork of the Kings River 28- (see figure (?)). The Bull-Prog Lake area was selected for «he following reasons: - The area selected is small (approximately 7.5 minutes square)* yet contains both a wide range in elevations (2400 - 4200 m) and rugged topography. These properties yield a considerable variety of at- mospheric and geometric radiation effects. - Since most of the area is either a designated wild- erness or a national park* and is inaccessible to casual travelers during the snow season* there are feu artificial effects in the snow cover that need to be accounted for (e. g. * packing by skiers and snowmob i lers; air pollution; etc. >. - Kearsarge Pass (see figure (9)) affords relatively rapid (1-2 days) winter access to the study area by means of ski mountaineering. Teams of field in- vestigators are thus able to make frequent field ra- diation measurements. - Kings Canyon National Park has permitted the instal- lation of an automatic Data Collection Platform (DCP) at Charlotte Ridge* between Bullfrog and Char- lotte Lakes in the study area (see figure (9)). In- struments connected to the DCP include radiometers to obtain calibration data for the atmosphere models. The DCP consists of a solar battery* an analog-to-digital converter* a digital memory* and a programmable transmitter which samples and saves in- strument readings at hourly intervals. The contents of the memory are relayed via the GOES satellite every six hours to a database in Washington* DC* which is interrogated daily by telephone. 4. 2 . Terrain Database 29- 4. £. i. Elevation Data A terrain base for the study area was created by first extracting a grid of elevations from the DTT corresponding to the eastern half of the Fresno 1:250,000 quadrangle. Misalignment of the original north-south transects was corrected. The grid spacing was reset to 100 m in both directions/ both to cut down on the number of points required to cover the study area, and to filter out some of the h igh-f requei.vy random noise. The logical structure of the grid was changed to row-major with the origin in the northwest corner) to more closely correspond to the image organization. The positional and elevation errors of this data, and for others created for adjacent areas, were evaluated by Marks and Dozier (1979). For 30 points of known loca- tion and elevation, the RMS latitude, longitude, and elevation errors were all in the neighborhood of 50 - 60 Rii or about one-half the grid spacing. 4- 2. 2. Geom etric Radiation Calculations Various topographic factors influence the distribu- tion and flux density of irradiance (and therefore exi- - 30- tance). Beam irradiance is locally influenced by slope and aspect* and by whether or not the solar beam is ob- scured by adjacent terrain (i.e., the local horizon). Diffuse irradiance is influenced by the distribution of terrain versus sky in the hemisphere above the calcula- tion point **2)»*( 1/2) ) (10) aspect - arctan(Oz/3x> / Oz/9y)> (11) 3z/8x and 3z/3y are computed by finite-difference methods on the topographic grid/ with a correction for latitude variations. The horizon function is computationally complex but may be outlined as follows (after Dozier and Outcalt/ 1979): - Compare the current point Cm, n3 with every other point Ciz j3 in the grid. If zCi/ j3 <= zCm, n3 then Ci,j3 is not a potential horizon for Cm,n3; skip it. - 31- Compute the tangent of the horizon angle from Cm, n] to C it j3: tan(H) ■ (zCi,j3 - zCm,n3) / (12) ] (i.e./ the "pie slice", centered at Cm, n], in which Cii j] falls): bCi,jJ ■ int(arctan( ( j - n) / (i - m)) / w) (13) Compare the current tan(H) with the previous tan(H) CbCi/ j33. If it is greater, then Ci,j3 is the neu horizon for sector bCi,j3. When all grid points have been tested, convert all (tan (H)CbJ to zenith angles* and save them as a "horizon vector" for point Cm,n3. Regardless of the number of sectors (w) used to con- struct the horizon vector (this investigation used 96; subsequent tests indicate that 32 are sufficient for ra- diation geometry calculations (Dozier, et al, 1980))* the procedure outlined above is of order (N**2) in computa- tion time* since every grid point is compared to every other grid point. Even for small datasets this can lead to excessive computer time, since a considerable region outside the area of interest must be searched for possi- ble horizon obstructions. On the other hand* the horizon - 32- computations need only be done once/ and can be saved for any subsequent analyses. The terrain view factor (the fraction of the hem- isphere above a point which is obscured by terrain) is computed by integrating the horizon function over an az- imuth of 2ir. For a discrete horizon vectori an approxi- mation to this integral is given by (Dozier and Outcalt, 1979): VtCmi nl = cos**2 (mean of horizon vector Cm* nil ) (14) The sky view factor is then simply: VfCrn, n3 - 1 - VtCm, n3 (15) 4. 3. Space Rad iance Data The Bullfrog Lake study area falls in the southeast quadrant of Landsat path 45; row 34. The image used in this demonstration of the model was MSS frame 2753-1740000, acquired at 0940 PST on 13 February 1977. Coincident surface radiation measurements were obtained by a field party (Dozier et al, 1978a/ vol. 2). The computer-"compatible l, -tape (CCT) of the MSS image was re- - 33- formatted/ and a 256 line by 256 sample sub-image con- taining the test area was extracted (these dimensions are convenient for various display devices and are not an in- trinsic requirement of the model). 1 3- A. Reg i strat ion to Terrain Grid MSS image transformations may be divided into two classes: rectification and registration (Van Wie and Stein* 1976). Rectification entails transforming the MSS data into a coordinate system which is a map projection (i.e./ one which has a well-defined mathematical rela- tionship to the geoid). It is usually possible to con- struct an analytical mapping between a particular map projection and the perspective projection which results uhen the systematic errors are removed from the MSS im- age. The remaining "random" (i.e.; unexplained) error between inage and map coordinates should be slight. An accurate rectification/ demands accurate map coordinates for the control points. This is not inordi- nately difficult over artificial landscapes/ which typi- cally present an abundance of point features with known geographic locations (eg, field boundaries/ highway in- tersections/ small reservoirs/ etc. ). For remote wilder- 34- ness areas, map control points are much harder to obtain: - Maps/ when available* tend to be less accurate/ less frequently updated/ and of smaller scale than those of more populated areas. - Point features such as mountain peaks or stream junctions are imprecisely located. - In snou-covered areas/ point features visible on maps are often buried and therefore invisible on the image. For the particular application of this investiga- tion/ a rectfication procedure is inappropriate/ since control points in a map coordinate system are difficult to obtain for the test area. Instead/ the terrain grid is treated as an image to which the MSS data are re- gistered. In a registration/ or "rubber-sheeting"/ pro- cedure/ one image is declared the "target" (in this case/ the terrain image) and all subsequent data are transformed to fit this target. Any intrinsic errors in the target image are ignored. The procedure used to register the MSS data to the terrain grid may be outlined as follows: - Locate control points in the image and in the ter- rain grid. - Correct the image control point coordinates for selected systematic distortions. - 35- Conpute a linear regression model which maps terrain grid coordinates into corrected image coordinates. Evaluate the regression model/ followed by the in- verse of the systematic distortion models- at each terrain grid point/ yielding the image coordinates corresponding to that point. If the computed image coordinates do not correspond to an existing image location (which will almost certainly be the case)/ resample the image to assign an RN to those coordinates and thereby to the corresponding terrain grid point. Control points in the terrain grid were located by generating a terrain "image" (essentially a shaded-rel ief map)/ in which the brightness value at each point represents the cosine of the solar zenith angle at that point/ corrected for slope and aspect (Sellers; 1965): cos(Z') = cos(S)cos(Z) + sin(S)sin(Z)cos(A - A') (16) The resulting image is similar to a shaded-rel ief map. If Z and A are set to the solar zenith angle and az- imuth for the date and time of the MSS overpass/ then the resulting terrain image bears a close resemblance to the MSS image. The two images are then displayed simultane- ously on a video monitor/ and control points selected in- teractively by an addressable cursor. An effort was made to acquire an adequate number (20) of control points and - 36- to distribute then fairly evenly over the test aTeai in- cluding some outside it. to help compensate for other inaccuracies in the registration procedure. Figure (10) contains a terrain image of a superset of the test area along uith the MSS subimage of 13 February 1977 (which here has been subject to several systematic corrections, to facilitate the comparison). Once the control points were located, selected sys- tematic corrections were applied to their MSS coordi- nates. Of the systematic distortions mentioned in sec- tion 3.2.2. all but scan nonlinearity and sampling delay are continuous and linear over the entire image (or. in the case of panorama and earth curvature, over reasonably small subimages). These distortions were therefore not modelled. on the assumption that they would be easily compensated by the statistical transformation. and also because the spacecraft parameters required to compute them are imprecisely determined. For the test reported here, only a sampling delay correction was employed. The available scan nonlinearity models were developed for the (no longer operational) Landsat i MSS (Van Wie et al. 1975); and are of uncertain applicability to Landsat 2 (from uhich the test data were acquired). Remaining - 37- "random" distortions uere compensated by two first-order bivariate polynomials. whose coefficients were computed with the SAS "General Linear Models" multivariate regres- sion program (Helwig and Council, 1979). Resampling the MSS image presented severe problems due to the presence of numerous saturated pixels. These pixels cannot be included in a high-order interpolation kernels since they do not represent bounded values. To preserve radiometric fidelity! zero-order (nearest neigh- bor) resampling was used to produce the registered image. Unfortunately- this method (a simple rounding of the predicted image coordinates to the nearest integer) in- troduces the greatest positional error of any resampling technique (Nack/ 1977). Figure (11) shows a terrain im- age of the study area proper (a subset of the terrain im- age in Figure (10))/ with a registered MSS band 5 image. 4 4. Irrad iance Simulation The irradiance simulation model used in this inves- tigation is described in Dozier (1979). The model is quite involved; therefore/ only an overview of its work- ings is presented in this section. Both beam and diffuse irradiance are simulated. The model is monochromatic/ so - 38- for this applicationi the results were integrated over the wavelength ranges of the MSS bands. The irradiance sinulation is run prior to the surface exitance deriva- tion* because one of the by-products of the irradiance sinulation is a set of atmospheric parameters which the exitance model requires. 4. 5.- JL* Over view of the Irradiance Mode l Beam irradiance (on a surface normal to the solar beam) is computed by correcting the solar constant for the following: - earth-sun distance - atmospheric absorption (by ozone/ water vapor* aero- sols* and miscellaneous gases) - atmospheric scattering (Rayleigh and aerosol) Of the physical factors governing these effects* the fol- lowing atmospheric parameters cannot be determined a priori* and therefore must be derived from field measure- ments: - ozone content - precipitable water vapor - aerosol attenuation coefficient - 39- The aerosol attenuation coefficient is determined from the Angstrom turbidity function* which is governed by two parameters (oc and p). Of these, the p parameter is most sensitive to atmospheric aerosol content and is thus derived from field measurements. Diffuse irradiance is separated into scattered (out of the solar beam) and backscattered (from surface exi- tance) components. The amount of radiation scattered out of the solar beam can be determined from the previously- computed Rayleigh and aerosol scattering functions. If it is assumed that scattering takes place at a single al- titude (in this model* z such that PCz3 ■ PCsfc3 / 2). then the amount of the scattered radiation which reaches the surface can be determined from the previously- computed absorption functions. The respective quantities of these absorbers are corrected for the amount of atmos- phere between zCsfc3 and zCPCsf c 3/23. Backscattered irradiance is computed from the beam and scattered diffuse irradiances already derived* multi- plied by an assumed regional albedo. This is not to be confused uith the albedo of the point itself* and in fact the model is not very sensitive to this parameter. This - 40- invest igation used the O'Brien - Munis "reference" snoui reflectance curve for a regional albedo (see figure (3)). This computation yields a regional exitance which is corrected for attenuation on either branch of its round trip to the scattering level zCPCsfc3/23. The necessary absorption and scattering functions have at this point already been computed. Finallyi in regions of high relief such as the test area of this investigation* there is significant diffuse irradiance due to reflection from adjacent terrain. Re- flected diffuse radiation is computed by multiplying the regional exitance by the terrain view factor. Diffusely-reflected beam radiation is obtained by averag- ing calculations for each sector in the horizon vector for the point. Specularly-reflected beam radiation from adjacent terrain is not considered. To do so would add greatly to the computational complexity of the model; and in any case the likelihood of the ocurrence of the par- ticular orientation of the sun and the two opposing slopes required to achieve a significant specular reflec- tance, is intuitively quite small (see section 4.6). The "unknowns" in the model (atmospheric ozone con- - 41- tent/ precipitable water vapor* Angstrom p coefficient) are derived from field measurements/ taken at different times during the day so as to include differing atmos- pheric path lengths for the beam irradiance. Since there are three unknowns/ at least three measurements are re- quired/ with four or more being preferred to obtain the redundancy needed for estimating measurement error. The measurements are assumed to be the output of the simula- tion model/ which is then solved inversely for those values of the unknown coefficients which would have gen- erated the observed irradiances. These parameters may then be used to run the model for any specific time (or integrated time interval) during that day. Figure (12) is an irradiance "image" generated on the test area terrain grid for MSS band 5/ for the time of the Landsat overpass on 13 February 1977. 4. 5 Surface. Exjtance Derivation By applying equation (8) to the registered MSS data, a space upwelling radiance value is obtained for each terrain grid point/ for up to four MSS bands (many points uill have less than four bands of information due to sa- turation). The conversion of the values into surface ex- - 42- itance requires corrections for the atmospheric path ra- diance and transmission effects described in section 3. 4. 2. Procedures for computing these corrections are developed in Dozier and Frew (1980)/ and are outlined briefly below. Path radiance is computed by essentially the same method as scattered diffuse irradiancei since they both derive from scattering of the solar beam (assumed to oc- cur at zCPtsf c 3/23 > . In the case of path radiance, the absorption functions are evaluated from the scattering altitude up to the top of the atmosphere/ rather than down 'to the surface as was the case in the diffuse irra- diance simulation. The resulting value is a diffuse at- mospheric exitancez which is converted to radiance by multiplying by ir. Figure (13> shows path radiance as a function of uavelength for different atmospheric aerosol and water vapor contentsi respectively. The four curves in each graph represent two different dates each evaluated for tuo different altitudes. The significance of the path radiance correction/ especially over rugged terrain/ should be apparent. - 43- The path transmission correction requires some knowledge of the relative spectral reflectance of the surface. For a snowpack, the O'Brien - Munis curve (fig- ure (3)) is used* since spectral signature of snout is fairly constant over time. By combining this postulated surface reflectance. the previously simulated irradi- ances. and equation (9). a surface exitance can be com- puted uhich is spectrally, although not rad iometr ical ly. correct. This "pseudo-ex itance" is subject to scattering at zCPCsf c 3/23. The sum of the portion uhich is not scattered* and the fraction of the scattered portion uhich reaches space. constitutes the surface exitance component of the signal uhich is perceived at the MSS. Equation (9) may thus be rewritten: YCXa = r(LtscCX3 + LtdirectCXD/Msurf CX3 (17) Integrating with respect to X over the spectral range of an MSS band causes the radiometric units to cancel, leav- ing a rCbandl uhich is basically a function of altitude. Combining path radiance and transmission gives the following equation for surface exitance: - 44- MCband3surf - Tr(LtspaceCband 3 - LtpathCband 3 ) /rCband 3 ( 18) This was implemented as a pointwise algebraic combination of images of space radiance. path radiance* and path transmission* generated for the date and time of the Landsat overpass. Figure (14) contains path radiance and transmission images for MSS band 5. Compare these with the pseudo-relief terrain image in figure (11)* and note the variations of both phenomena with altitude. 4. 6. Per iv a tion of Surface Albedo Components In section 3. 1. 3* it was noted that the albedo of a snow-covered surface has three components (f* p* and p')* which must each be known if the surface energy balance is to be calculated from irradiance and albedo alone. This section presents methods for calculating these com- ponents. It can be shown geometrically (see figure (15)) that the surface exitance derived from MSS data will not in- clude a measurable specular reflectance. Instead* specu- lar reflectance is computed by using the index of refrac- tion for ice (approximately 1.3 for solar wavelengths* from Irvine and Pollack. 1968)* and averaging the result- - 45- ing plane- and cross-polar i red Fresnel reflectances (Sellers, 1965): f ■ . 5( (sin**2(Z ' - ar )/sin**2(Z ' + ar) + tan**2(Z' - ar )/tan**2(Z ' + ar ) ) (19) where ar = arcsin(sin(-Z ' ) /ir ) ; ir = 1.3 (20) Note that f is strictly a function of the angle of in- cidence of the beam irradiance. Figure (6) contains a graph of f versus Z» note that at all but very large zen- ith angles, f is insignificant. The surface exitance derived from MSS data is relat- ed to surface reflectance by: M = p'Ed + pCZDEs (21) The omission of X here is deliberate/ since the MSS data are integrated over a fairly broad range of wavelengths. A result of this integration over the differing spectral distributions of Ed and Es is that p' is not the same as pCQDz for a given MSS band. However, since the transmis- sion functions which govern the spectral distributions of - 46- Ed and Es are -functions of elevation, we can postulate the following relationship: pC03/p' - Es/Ed = CCz3 (22) CCz] is determined for the range of elevations in the test area as follows: - Collect values of p' for a range of elevations by ratioing exitance and irradiance in areas shaded by terrain from beam irradiance. At these same elevations, select locations which are exposed to the solar beam. The difference in exi- tance will be due to ptl'l, which can be corrected to pC03 using a variation of equation (6). - Compute and save C values for these elevations. At other elevations/ find C by interpolation. Combining equations (6), (21)/ and (22) gives the following expression for p': p' - (M - Es(gCZ3 + fCZD) / (Ed + EsCCzDU - gCZ3))(23> Figure (16) contains images of p' for MSS bands 5 and 7. The apparently incongruous black spots were saturated pixels in the original MSS data. - 47- 4. 7. Spectral Albedo Extension The procedure derived above cannot be applied directly if e>itance information is unavailable due to saturation of the MSS data. This problem ranges from severe in bands 4 and 5 to negligible in band 7 (see fig- ure (16)>» as might be predicted from prior knowledge of the spectral reflectance characteristics of snow. What is needed is a method of indirectly deriving the albedo in the saturated bands. The spectral extension method depends on the fact that, because of band 7, there is at least one spectral band of exitance (and therefore albedo) information for the entire image. Recall from section 3.1.2 that natural variations in the overall albedo of snow can be closely approximated by a multiplicative adjustment of a spec- trally correct reflectance curve (e. g. * figure (3)). For example/ if a monochromatic reflectance measurement (pCXD) is made of a "patch" of snow, the factor by which the reference spectral reflectance curve must be multi- plied to yield the measured value is given by: K * pCmeasured D/pCref erencel (24) - 48- This K value may then be applied to any pCX3 on the reference curve to yield a best estimate of the actual reflectance that would have been measured at that wavelength. For a spectrally broadband reflectance measurement! such as is derived from the MSS data* the measured re- flectance is ratioed with the integrated value of the reference curve for the same wavelength interval: K - pCbandJ/pCref erence] dX (25) The K-value thus computed has twofold utility. Firsti it may be used outside the spectral range for which immediate measurements are available, as long as it is within the range of the reference curve from which it was derived. Second* the K-value is a unique determinant of spectral reflectance of a given snow-covered point* and thus is the only value which need be saved* as long as the reference curve is available to reconstruct the reflectances. This represents up to a 4x data reduction* which can be quite significant for large areas. Figure (17) shows an MSS band 5 image with the sa- 49- turated values reconstructed from K-values computed from band 7 exitances and the O'Brien - Munis reference snow spectral reflectance curve. i. Analysis and Cone lusion In this section/ each phase of the albedo model will be examined with respect to potential sources of error which could contribute to the accuracy of the final results. 5. L- Terrain data The inaccuracies inherent in the digital terrain data distributed as DTTs have already been discussed. The general effect of these errors would be to introduce isolated singularities in the derived terrain data. For example< the misplacing of a cliff by one grid point would cause the derived parameters in that immediate neighborhood to be grossly inaccurate. While such errors tend to cancel out in the context of an energy balance model evaluated over tens or hundreds of thousands of points/ they car* cause errors in situations where point- specific data are disproportionately critical. Two in- stances of this are registration control points and loca- - 50- tions of field measurements Errors in registration control point locations can be alleviated by using an excessive number of points to derive the registration transformation. If the position- al errors of the points are not systematic* this should cause cost of the errors to cancel out. Wildly inaccu- rate control points* such as might result from a mis- placed mountain peak, can usually be detected by "cross- checking" (Van Wie et al, 1975). This entails predicting the location of each control point using a model derived from the remaining control points. A poorly located point uill be indicated by large absolute or standard er- rors in its estimated location. Errors in locating field measurements arise due to the various locational transformations they undergo (a measurement made in the field is marked on a map; its geodetic coordinates are manually measured; the geodetic coordinates are used to derive an Cx*y3 location in the terrain grid). These errors can be reduced by visually inspecting the terrain grid neighborhood of the derived field location, by means of a pseudo-relief image, a numeric printout of the elevation grid, and/or a contour - 51- nap. Persons familiar with the field area can usually recognize sufficient cues from such displays to "fine tune : ' the measurement locations. §.• 2 . Landsat MSS Data Use of Landsat MSS data in this model is subject to the following errors: - inaccurate space radiance values due to calibration errors in the MSS system. - positional errors due to resampling. - spectral averaging by the relatively broad MSS bands. - spatial averaging of subp i xel-f requency terrain ef- fects. The absolute calibration of the MSS system is plain- ly inadequate/ as can be qualitatively deduced from the striping uhich appears in almost all MSS imagery. Some idea of the magnitude of this variation may be gained from table (2). which shows the mean values for all of the detectors/ organized by band/ for the raw MSS subim- age from uhich the registered data used in this investi- gation were extracted. The maximum mean within-band in- terdetector variation observed was 1.47 RNs in band 6. - 52- The positional inaccuracy of nearest neighbor resam- pling, mandated by the occurrence of saturated pixels, doubtless leads tc some mismatch of MSS data with terrain and irradiance information. Although* ideally, the ex- tent of this error is no more than ± one-half pixel* in practice nearest-neighbor resampling tends to magnify any errors in the registration transformation (Taber. 1973). Spectral averaging refers to the masking of sharp fluctuations in the spectral response of the surface and/or atmosphere, by the relatively broad spectral range over uhich a single MSS band is integrated. Examination of typical curves for snout spectral reflectance (figure (3)) and atmospheric spectral transmission (figure (8)) show that spectral averaging is most significant in band 7. This is due in part to the fact that this band has three times the spectral range of the other MSS bands* but mainly to the rapid change in snow albedo at these wavelengths and the atmospheric water vapor absorption bands. Compounding this problem is that for portions of a snow-covered scene, only band 7 will be unsaturated, so this band will be relied on more than the others. The effective IFOV of the MSS translates to about 56 53- by 79 m at the surface (about 1. 1 acre). Any changes in surface parameters which occur at a higher spatial fre- quency uill be confused (aliased) by the MSS system. An example of this situation is the mistaking of patches of snou interspersed with bare ground or rock/ for a uniform "dark" snou cover. Furthermore/ the surface area per pixel increases uith the slope of the surface/ so that phenomena uhose spatial frequency approaches the resolu- tion limits of the MSS may affect "steep" pixels more than "level" ones. 5. 3. Atmospheric Corrections Errors in the irradiance simulation and in the sur- face exitance derivation may result from improperly specified atmospheric parameters. These in turn result from errors in the field measurements/ and from spatial variations in atmospheric parameters assumed constant. Field measurements have presented some problems in this investigation. The portable radiometers carried into the back country by the investigators have yielded sone plainly erroneous measurements/ such as irradiances uhich increase uith increasing solar zenith angle/ or ii — radiances in excess of the solar constant. The portion 54- of the irradiance model which derives the atmospheric parameters from these measurements can cope with some de- gree of measurement error* but in several cases the field measurments have proven unusable. The most accurate and reliable results have been obtained from Eppleg pyranome- ters running continuously and unattended at the DCP. Even with usable mobile field measurements* only a small portion of the test area can be covered for a given satellite overpass. It is assumed that the principal at- mospheric parameters being derived (water vapor absorp- tion and aerosol scattering) have a predictable variation vertically and no variation horizontally. For the Sullfrog Lake test area this assumption is valid* owing to the high elevation of the area and its remoteness from any sources of artificial air pollution. Indeed, the most significant impact on the assumption of spatial in- variance would occur in cases of fires in or near the study area. Fortunately* such events are quite rare in the snow season. - 55- 5. 4. Surface Conditions Errors in this category constitute a catch-all of possible violations of the fundamental assumption of the model; namely/ that every point in the terrain grid is covered exclusively with a reasonable depth of snow. In a mountainous area this is almost certainly not true, if for no other reason than that some slopes will be too steep to sustain a snowpack. The model presented here does not address itself to this class of problems; rath- er* the assumption is made that separate mechanisms exist to determine which grid points are snow-covered and which ar& not. In fairness to the model/ it should be noted that the the errors involved in calculating a snow albedo for a non-snow point are significant mainly in subsequent energy-balance calculations/ and will not cause severe error propagation within the model itself. This is due to the relative insensitivity of those calculations which rely on regional rather than point reflectances. A more subtle problem arises when the surface con- sists not of smooth snow (or smooth non-snow mistaken for snow)/ but instead of a mixture of snow and trees. Such a mixture is significant since it radically affects the - 56- radiation geometry of a neighborhood of grid points. A simple means of avoiding the problem would be to prepare a mask (based on. say* classified summer MSS imagery) showing for each grid point the presence or absence of sufficiently dense vegetation to affect the model. 2.. 5. Conclusions and Further Work The model developed in this investigation is compu- tationally complex but not prohibitively so; and the in- formation it yields is otherwise unavailable. A detailed check of its overall accuracy has not been performed; however? its principal components have been demonstrated to perform adequately. The overall strategy of the model is based on fundamental physical principles (i.e. it is deterministic rather than statistical). The model's principal limitation is its pervasive reliance on the known spectral characteristics of the surface* which* uhile an acceptable approach for snow* may be more diffi- cult to apply over spectrally heterogeneous surfaces. The field measurements required are kept to an absolute minimum. The model is not intrinsically dependent on Landsat MSS data; indeed* it would doubtless benefit from spaceborne radiometry with wider dynamic range* narrower - 57- and better-defined spectral bands, less geometric distor- tion* and more frequent overpasses. The other data in- puts are similarly general in that they can be upgraded to state-of-the-art as desired. Further development of the model should include a field test of its accuracy. The two major factors which have so far prohibited such a test are the remoteness of the study area, and the infrequency of Landsat over- passes. The mountaineering skill required to enter the study area in the winter, combined with the limited load a person on skis can carry, has effectively limited the number of people and instruments which can be on-site during a satellite overpass. Moreover, it is neither feasible nor desirable to remain in the study area for the 18 days between Landsat overpasses, while the cost of frequent separate trips becomes prohibitive. A field test could possibly be implemented using NGAA satellite data and a more accessible test area. Work is currently in progress to integrate AVHRR data into the terrain/radiation database scheme described in this paper. The daily coverage afforded by the NOAA AVHRR (Advanced Very High Resolution Radiometer) would - 58- alloui the field investigators the option of remaining at a particular site for several consecutive overpasses, or moving to different sites for each overpass* thus sam- pling a maximum variety of surface conditions. The coarse spatial resolution of the AVHRR (900 m) would probably require a test area with less relief than the current one. so that spatial averaging effects would not be immediately blamed for any inaccuracies in the model. Techniques such as spectral analysis of the digital ter- rain database may prove useful in recognizing areas where the spatial frequency of surface relief would lead to significant averaging or aliasing errors. - 59- REFERENCES Ad Hoc Advanced Imagers and Scanners Working Group (1973) Advan ced Scanner s and I mag inq Sustems for Earth Observations . Washington. D. C. : NASA SP-335. 604 PP- Alfoldi, Thomas T. (1976) Digital analysis of Landsat MSS imagery for snow mapping applications. Canada Centre for Remote Sensing. 21 pp. Algazi. v". Ralph; Suk. Minsoo (1975) An all-digital ap- proach to snow areal mapping and snow modeling. In: Rangoi Albert (ed. ) Operational AppI icat ions of Satel lite Snowcover Observations . Washington. DC : NASA SP-391. pp. 249-257. Anderson. Eric A. (1976) A point energy and mass balance model of a snow cover. Washington. DC : NOAA Tech. Rept. NWS-19. 150 pp. Barnes. James C. ; Smallwood. Michael D. (1975) Synopsis of current satellite snow mapping techniques, with emphasis on the application of near-infrared data. In: Rango. Albert (ed. ) Operational Appl icat ions of Satellite Snowcover Observations . Washington. DC : NASA SP-391. pp. 199-213. Bergen. James D. (1975) A possible relation of albedo to the density and grain size of a natural snow cover. Water Resources Research 11: 5. 745-746. Bernstein. Ralph; Ferneyhough. Dallam G. . Jr. (1975) Di- gital image processing. Photoqramm . Enqr . 41: 12. 1465-1476. Choudhury. B. J. ; Chang. A. T. C. (1979) Two-stream theory of the spectral reflectance of snow. IEEE Trans . Geosc ience Electronics GE-17: 3. 63-68. - 60- Dirmhirn/ Inge; Eaton* Frank D. (1975) Some characteris- tics of the albedo of snow. Jour . Add 1 . Meteorol . 14: 3, 375-379. Dozier, Jeff; Davis. Robert; Frew* James; Gold* Caryn; Keith/ Sandra; Marks/ Danny (1978a) Remote sensing applications to hydrologic modeling in the southern Sierra Nevada and portions o-f the San Joaquin Valley (2 vols. ) (final report, NASA grant NSG-5155). University of California/ Santa Barbara/ CA : Department of Geography. Dozier/ Jeff; Davis/ Robert; Frew/ James; Marks/ Danny (1978b) Calibration of satellite data for input to distributed parameter hydrologic models. University of California/ Santa Barbara/ CA : Computer Systems Laboratory Technical Report TR-CSL-7808. Dozier/ Jeff (1979) A solar radiation model for a snow surface in mountainous terrain. In: Colbeck/ S. C. (ed. ) W orkshop on Model inq Snow Cover Runoff . Hano- ver/ NH : U.S. Army Cold Regions Research and En- gineering Laboratory. Dozier/ Jeff; Outcalt/ Sam I. (1979) An approach toward energy balance simulation over rugged terrain. Geographical Analusis 11: 1/ 65-85. Dozier, Jeff; Bruno/ John; Downey/ Peter (1980) A faster solution to the horizon problem. Computers and Geosciences/ in press. Dozier/ Jeff; Frew/ James (1980) Atmospheric corrections to satellite radiometric data over rugged terrain. University of California/ Santa Barbara/ CA : Com- puter Systems Laboratory Technical Report no. TR- CSL-7909, 35 pp. Dunkle/ Robert V. ; Bevansz J. T. (1956) An approximate analysis of the solar reflectance and transmittance of a snow cover. Jour. Meteorol. 13: 212-216. - 61- Feynmam Richard P. ; Leighton, Robert B. > Sands, Matthew (1963) Ihe. Feunman Lectures o_n_ Phusics/ vol. 1. Reading< Mass. Add ison-Wes ley Giddings/ J.C.J LaChapelle, E. (1961) Diffusion theory applied to radiant energy distribution and albedo of snow. Jour . Qeoohus . Res . 66: 1/ 181-189. Helwig/ Jane T. ; Council; Kathryn A. (eds. ) (1979) SAS User 's Guide . Raleigh/ NC : SAS Institute/ Inc. 494 pp. Hobbs/ Peter V. (1974) Ice Phusics . London : Oxford University Press. 837 pp. Hubley/ Richard C. (1955) Measurements of diurnal varia- tions in snou albedo on Lemon Creek Glacier/ Alaska. Jour . Glaciol . 2: 18/ 560-563. Irvine* William M. ; Pollack/ James B. (1968) Infrared optical properties of water and ice spheres. Icarus 8: 2/ 324-360. Kirbyz M. » Steiner/ D. (1978) The appropriateness of the affine transformation in the solution of the geometric base problem in Landsat data. Canad ian Jour . Rem . Sens . 4: 1/ 32-43. Marks; D. ; Dozier/ J. (1979) A clear-sky longwave radia- tion model for remote alpine areas. Arch . Meteorol . Qeophus . Bioklim . / Ser. B 27: 159-187. HcOinnis/ David F. / Jr. i McMillan/ Michael C. j Uiesnet, Donald R. (1975) Factors affecting snow assessment from Landsat data. NASA Earth Resources Surveu Sumoosium 1-D: 2661-2668. Middleton, W. E. K. ; Mungall. A. G. (1952) The luminous directional reflectance of snow. Jour . Opt . Soc . Amer. 42: 8/ 572-579. - 62- Nack# ML. (1976) Rectification and registration of di- gital images and the effect of cloud detection. Sumoos ium on Machine Processing of Remotelu Sensed Data , pp. 12-23. West Lafayette, IN : LARS/ Purdue University. NASA (1971) ERTS Data Users Handbook GSFC Document no. 71SD4249. Greenbelt/ MD NASA (1976) Landsat Data Users Handbook . GSFC Document no. 76SDS4258. Greenbelt/ MD NASA (1977) Radiometric calibration of Landsat 2 MSS da- ta. Landsat Newsletter 15: 1-2. O'Brien/ Harold W. ; Munis/ Richard H. (1975) Red and near-infrared spectral reflectance of snow. Hano- ver/ NH : U.S. Army Cold Regions Research and En- gineering Laboratory Research Report 332. 18 pp. O'Neill/ A.D.J./ Gray/ Don M. (1973) Spatial and tem- poral variations of the albedo of prairie snoupack. The Role of Snow and Ice in Hudroloqu 1: 176-186. Geneva/ Switzerland : International Association of Hydrologic Sciences. Paltridge/ C. W. ; Piatt, C. M. R. (1976) Radiative Proces s es in Meteoroloqu and Climatoloau . Amsterdam Elsevier Scientific. Perla, Ronald I Handbook , book 489. ; Martinelli/ M. Washington/ DC : 238 pp. (1975) Avalanche USDA Agriculture Hand Petzold, D. E. (1977) surface albedo. 11 pp. An estimation technique for snow McGill Univ . Climatol . Bull . 21: Sellers/ William D. (1965) Phusical Climatoloau . Chi- cago/ IL : University of Chicago Press. 272 pp. - 63- Taber/ John E. (1973) Evaluation of digitally corrected ERTS images. Third ERTS- 1 Sumposium 1-B: 1837-1844. Thomas- Valerie L (1975) Generation and physical characteristics of Landsat 1 and 2 MSS computer com- patible tapes. Greenbelt, MD : NASA/GSFC X-563-75-233, 28 pp. U.S. Army Corps of Engineers (1956) Snou Hudroloqu . Portland/ OR : 437 pp. U.S. Geological Survey (1979) Landsat Data Users Handbook ) revised edition . Arlington! VA. Van Wie, P.; Stein, M. ; Puccinelli, E. ; Fields, B. (1975) Landsat Digital Image Rectification System preliminary documentation. Greenbelt, MD : GSFC In- formation Extraction Division. Van Wie, Peter; Stein, Maurice (1976) A Landsat digital image rectification system. Sumposium on Mach ine Processing of Remote-lu Sensed Data , pp. 4al8-4a26 West Lafayette, IN : LARS, Purdue University. Uiesnet, Donald R ; McGinnis, David F. ; McMillan, Michael C. (1974) Evaluation of ERTS-1 data for certain hy- drologic uses (final report, NASA contract no. 432-641-14-04-03). Greenbelt, MD : Goddard Space Flight Center. U'ong, Kam W. (1975) Geometric and cartographic accuracy of ERTS-1 imagery. Photoqramm . Enqr . 41: 5, 621-635 • 64- • 10 12 14 AGE Of SNOW SURFACE, OAVS VARIATION IN ALBEDO WITH TIME 20 Figure 1 ; temporal decay in snowpack albedo, from in-situ measure- ments (U.S. Army Corps of Engineers, 1956). -65- o e to 4-> <-> .5 CD t — i — i — i — i — i — i — i — r i — i — i — i — r 2SO SOO lOOO 1SOO 3000 2SOO wavelength Figure 2 : snow spectral reflectance generated for various grain sizes (model from Dunkle and Bevans, 19$6). -66- 150 500 lOOO 1SOO 2000 2SOO wavelength Figure 3 : "typical" measured spectral reflectance of new snow, relative to BaSO, (data from O'Brien and Munis, 1975). -67- >P — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — JT1 — I — I — TT O) U O) o <-> .5 4-» i- O oU I I I I I I L— L 2SO SOO lOOO J L_J I L—l I L 1SOO 2000 7 SOO wavelength Figure 4 : spectral absorption coefficient of ice (data from Irvine and Pollack, 1968; Hobbs, 1974). -68- u c U Qi 0) 2 SO SOO lOOO 1SOO 1QQQ 2SOO wavelength Figure 5 : simulated temporal decay in snow spectral reflectance, generated by multiplying the curve in Figure (3) by various constant values. -69- cu a c «o +-» u zenith angle (deg) Figure 6 : Fresnel (specular) reflectance of ice as a function of beam angle of incidence. -70- Figure 7 : Landsat MSS along-scan geometry, showing relation be- tween mirror scan angle and Earth surface distance (from Kirby and Steiner, 1978).. Parameters h = altitude of MSS 9 = MSS mirror scan angle (from nadir) = MSS object plane T = tangent plane E = Earth surface R = earth radius ■ geocentric angle resulting from a given 9 -71- 500 1000 1500 wavelength 2000 2500 Figure 8 : spectral absorption characteristics of various atmospheric constituents (Dozier, 1980). ozone Rayleigh atrotol water vapor miscellaneous gases -72- l/> fO *—* 4-> • O (O f"~ •r» Q. C S- 0) o > «♦- •r" •r - 4-> r— O «TJ O) <_> ex (/) A i. -o d) c z «o f0 *— s t- E s- o 4-> S- 3 > i- -a 3 3 o +■> +■> oo c o cu u -*: a _j • • CT» O) o QJ s- S~ «+- 3 r"~ C71 r- •r~ 3 U. CO -73- QJ fO -^ £ n QJ _j 4-» o> >> o (/> i- »4- S_ r— • O r— H- Z3 CO 00 c **- o 4-> >» O 4-> C i_ c •r— O O u •r- •r- 4J > JZ S_ 4-» O *♦- •f— +-> o 5 QJ n -a cr> fO tc» 0) E i_ •r - •r™ (O LO >» O ■0 f= CO 3 O CO ■M QJ S «/) a> QJ Ol m itJ > •t— TO ^— 3 QJ +■> J- CO 1 QJ QJ ^ •O fO CD • O i- •0 «♦- 13 ^— > 4-» •74- ■75' Figure 12 : image of surface irradiance in MSS band 5, 13 Feb 77, 0937 PST. -76- § 500 1000 1500 2000 WAVELENGTH, nm A: elevation 3000 m B: sea level A and B 30 May - - - : 21 Dec upper : 3 = 3500 lower : e = 50 500 1000 1500 2000 WAVELENGTH, nm .010 E c CM 'e 8 005- g 800 1000 1200 1400 1600 1800 2000 WAVELENGTH, nm C: sea level; 30 May 10 nun H 2 40 mm H 2 Figure 13 : sensitivity of path radiance to elevation, solar angle, and atmospheric aerosols. 36.5 deg N latitude, 0937 local time. •77- CD o 3 CQ t- O *♦- • I— to CO QJ Q- Z3 r— r^* (O CO > en o >> 4-> A •r" r^ > r-* •p— CO -Q CO OJ •r— u. cz CO ro C i—i 03 S- •» ■♦-> 03 CD JZ S_ 4-> > •o 4- ZJ O 4-> co O OJ r™~ 01 r-^ OJ r^ u c -Q 03 OJ •r— Lo- -a 03 co L- i— • JC n -M 03 o3 OJ O. i_ 03 «4- O >> •a OJ 3 en -t-> 03 co E •r - OJ JX. m • • _i "3- t— ( en o OJ i_ i- «4- 3 r— cr i •f— 3 u. CQ ■78- MSS Sun Figure 15 : diagram showing lack of specular reflectance component in MSS signal. The angles were chosen to maximize any specular component and represent a "worst case" situation (on edge of MSS frame with sun on horizon). Parameters Z = maximum apparent zenith angle of MSS (5.78 deg) Z = maximum possible solar zenith angle (90 deg) V = solar zenith angle relative to slope (47.89 deg) S = slope, chosen to reflect beam towards MSS (42.11 deg) From the Fresnel reflectance equation, the Fresnel reflectance under the above conditions is computed to be 0.03. Since this maximum possible value is insignificant, the possibility of the MSS signal being "contaminated" by specular reflectance is discounted. -79- ... S7»10K C o> s- o CD U"l S . fW> O) E CL 1- O) 4-> (O i- 4J fO «/> cn c •r~ 4-> u •a e a c a ra Q. U) CO •a c .a to CO 3 CO h- CO ■ o_ •o oo C CT> . a ro A3 ai s- > •o CO o -80- Figure 17 : image of surface p' for MSS band 5, 13 Feb 77, 0937 PST. Locations for which space radiance data were not available due to detector saturation have been assigrea values extrapolated from the corresponding p' in MSS band 7. -81- MULTISPECTRAL SCANNER BANDS 4 - 7 iLANDSAT 1) BAND MAXIMUM RADIANCE ifllilllwatS cnV - »i As Bind 8 is a thermal sensor, its response char- acteristics are not quoted m terms ol energy. The re- lation ot sensor response (voltage) to scene-apparent- temperature is being inves- tigated and will be provid- ed when determined. LOW GAIN HIGH GAIN 4 2 48 083 5 2.00 67 6 1 76 N A ; 4 00 N A 8' MULTISPECTRAL SCANNER BANOS 4 - 7 (LANDSAT 2| BAND LOW GAIN' HIGH GAIN R Mm Rita R Mm Rita 4 10 2.10 .06 .80 s .07 1.56 .04 55 e .07 1.40 ' Prior to July 16. 1975 ' Alter July 16. 1975 i 14 4.15 LOW GAIN'' 4 .08 2.63 5 .06 1 76 6 .06 1 52 7 11 3.91 MULTISPECTRAL SCANNER BANDS 4 - 7 (LANDSAT 3) BANDS LOW GAIN' HIGH GAIN R Mm RMai R Mm R Mai 4 04 2.20 01 .85 5 .03 1 75 .01 65 6 .03 1.45 Prior to June 1. 1978 2 After June 1. 1978 7 .03 4.41 LOW GAIN'' 4 04 2.59 5 .03 1.79 6 03 1.49 7 OJ }83 Table 1 : Landsat MSS saturation and threshold radiances (only Landsat-3 is currently operational; from U.S. Geological Survey, 1979). •82- detector band 4 band 5 band 6 band 7 55.4 64.7 63.2 23.2 1 55.8 64.6 63.4 22.7 2 56.6 65.0 64.4 23.3 3 56.8 65.5 64.4 23.3 4 56.0 64.3 64.2 22.8 5 56.0 64.5 63.0 22.9 Table 2 : mean radiance numbers (RNs) for all MSS detectors, computed for the uncorrected image from which the registered space radiance data were extracted. 1>U.S. GOVERNMENT PRINTING OFFICE: 1981-340-997/1508 .<< °' c % s C P^7