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Erythemally Weighted Daily UV Exposures at the Earth's Surface
Introduction Release 1.0; August, 1996
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This CD-ROM contains one file for each day from November 1, 1978
to March 6, 1993 (with a few missing days). Each file contains data
representing the relative daily areal exposures of ultraviolet (UV)
radiation effective in causing skin irritation, computed at each
1 degree latitude by 1.25 degree longitude pixel, between latitudes
65S and 65N. These data were derived from measurements made by
NASA's Total Ozone Mapping Spectrometer (TOMS), which was flown
aboard the Nimbus-7 satellite.
Directory Structure & File Names
--------------------------------
The root directory (folder) of this CD-ROM contains a set of
subdirectories, y78, y79, ..., y93. Each subdirectory contains
a set of files with names of the form yymmdd.erx (e.g. the data
for November 1, 1978 are in the file called 781101.erx).
File Structure
--------------
Each data file has a three-line header, followed by 130 12-line
records. Each 12-line record contains the data for the 288 pixels
in a single latitude band. Each datum is represented by a 3-digit
number. The latitude of the midpoint of the band is given as the
last number in the twelfth line of each record. In all, each file
has 1563 lines and 117,495 bytes.
A sample header is shown here:
Day: 122 May 2, 1979 Production V70 NIMBUS-7/TOMS Erythemal Exposure
Longitudes: 288 bins centered on 179.375 W to 179.375 E (1.25 degree steps)
Latitudes : 130 bins centered on 64.5 S to 64.5 N (1.00 degree steps)
The first line of the header record contains the day number, the
date it corresponds to, using common 3-letter abbreviations for
month names, and the name of the data product.
The second and third lines of the header are the same for all files
in this product.
A sample 12-line record is shown here:
98101 93 99 90 85 77 77 87 83 88 96 97103104 93 91 93104119122121114114115
109115115110107 99101 95 74 54 44 47 44 53 56 51 65 67 70 72 72 70 82 97119
121118118116114110 95 94 95 93 92 84 37 14 21 29 48 74 91 77 75 84 84 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0140121112109110108106109114111113113
110119121125121114 88 64 77 87 88 85 84 87 93 71 29 34 63 74 88 99124109122
120119102103123118105 89101120125122125120112100105104107129129117126104101
98108115123122105118125154158158158157160160168168151148142118105101 95104
126136133106102126128109105100 99112107 95 70 33 20 27 21 19 25 44 78 82105
123130132118 78 83104104107131130130105115122106 99102 92 80 76 73 62 68 87
117117118112 98 95 97109108 89112120119119119118115 94 76 77 41 36 58 41 29
22 24 29 62109116143147153154154153150148147147130127123126107 44 66 88 97
97 89 90 90 83 86 85 79 91105 94105108 Lat= -29.5
This consists of 288 three-digit numbers followed by the latitude
at the band center. Southern latitudes are given by negative
numbers. The string of zeroes reflects a satellite orbit during
which either measurements were not made or the data were lost.
The following FORTRAN-77 code illustrates how the contents of an
entire file may be read into the array ERY.
INTEGER*4 ERY(288,130)
C...
OPEN(1, FILE='/CDROM/y79/790502.erx', FORM='FORMATTED')
READ(1,1) ERY
CLOSE(1)
C...
1 FORMAT(///129(11(1x,25i3,/),1x,13i3/),11(1x,25i3,/),1x,13i3)
When this code is executed, it will fill the array ERY in such a
way that ERY(ILON,ILAT) is the diurnal erythemal exposure per
unit area within the pixel centered at
longitude= -179.375 + (ILON-1)*1.25 and latitude= -64.5 + (ILAT-1),
with the convention that negative longitudes are West and negative
latitudes are South.
What the Data Mean
------------------
The data in this product have been computed from the NASA/GSFC
TOMS version 8, level 3 data. These consist of total column
ozone and scene reflectivities in the same latitude-longitude
pixels. (These data are available as separate products from
NASA/GSFC.) These are combined with the results of radiative
transfer calculations, terrain height data, and model action
spectrum of Caucasian erythemal susceptibility, to produce the
data in this product.
Since the action spectrum is defined up to an arbitrary multi-
plicative constant, its units are an arbitrary measure of poten-
tial erythemal damage per unit exposure; therefore the data in
this product, erythemal exposures, are also of arbitrary dimen-
sions. We have scaled the data to get the best dynamic range when
each datum is expressed as a three-digit decimal number. In order
to compute the numbers given in the files, the fluxes were in units
of nW/(m^2 nm); the action spectrum was calculated from the
expression given below, and scaled by the factor 16/(125 pi), or
about 0.004074 .
The definition of the action spectrum for a biological process
assumes a linear relation between the action spectrum-weighted
exposure and the quantitative biological response. Thus, a twofold
increase in the erythemal exposure corresponds to a twofold
increase in the potential incidence or severity of erythema.
How the Erythemal Exposures were Computed
-----------------------------------------
The Version-8 Level-3 Nimbus-7/TOMS data consist of total column
ozone and scene reflectivities derived from measurements of the
solar ultraviolet radiation that is backscattered from the
atmosphere. Ozone is determined from measurements of radiation
with wavelengths less than 318 nm, where ozone is strongly ab-
sorbing. The scene reflectivity is determined from the measurement
of radiation in a narrow band around 380 nm, where there is neg-
ligible absorption by any atmospheric constituents. Low pixel
reflectivities are associated with cloudless conditions, while high
reflectivities (greater than about 20%) are associated with either
cloudy conditions or snow and ice covered ground. Alone, TOMS is
unable to distinguish between cloud and snow cover; however,
climatological databases of surface reflectivity and snow/ice
cover have been used.
The spatial resolution of the Nimbus-7/TOMS does not permit one
to determine the nature of the clouds present in the scene; for
example, whether it is uniform, overcast, thin clouds, or a field
of broken, highly reflective cumulus clouds. For the purpose of
this computation, we modelled each pixel in which cloud cover is
implied by the TOMS measurement as a uniform overcast of cloud
with a putative optical thickness deduced from the 380 nm reflec-
tivity, homogeneously distributed in a slab between 700 mbar and
500 mbar. Since each pixel is measured only once for each day
for near noon conditions, no account is taken of diurnal variation
in cloudiness.
Detailed radiative transfer models were used to estimate the
spectral flux at the Earth's surface, given a column ozone amount,
TOMS-measured reflectivity, climatological surface reflectivity,
terrain height, and solar zenith angle, for a set of wavelengths
from 280 nm to 400 nm, which include the UV-B and UV-A regions.
The flux decreases sharply with decreasing wavelength shorter
than about 310 nm, due to absorption by ozone, while the action
spectrum for erythema decreases sharply with increasing wavelength
longer than 340 nm. Thus, using the wavelength range 280 nm to
400 nm ensures that all significant contributions to the erythemal
exposure have been included in the calculation.
The solar zenith angle as a function of time of day depends on the
latitude and solar declination angle. These were used to
accomplish the computation of the diurnally-integrated fluxes at
each wavelength in the set. The integrated fluxes were multiplied
by the model action spectrum values at each wavelength, and summed
to give the erythemal exposure.
Symbolically, we can write the erythemal exposure as the following
double integral
400nm sunset
/ /
Erythemal = C | dl w(l) S(l) | dt F(l, Oz, Robs, Rsurf, SZA(t), h)
Exposure / /
280nm sunrise
where
C = Arbitrary scaling constant (16/125/pi)
l = Wavelength (nm)
w(l) = Erythemal action spectrum. ([biological effect] J^(-1) m^2)
S(l) = Solar flux incident on the top of the atmosphere, corrected
for annual variation in the earth-sun distance.
(nW m^(-2) nm^(-1))
t = Time
F = Downward flux at the Earth's surface, corrected for
clouds, for unit incident solar flux at the top of the
atmosphere.
Oz = TOMS total column ozone
Robs = TOMS scene reflectivity
Rsurf = Climatological surface reflectivity
SZA(t) = Solar zenith angle (also depends on latitude, solar declination)
h = Terrain height
Some Additional Details
-----------------------
Wavelengths: All spectral quantities were calculated for all
wavelengths 280.0, 280.5, 281.0, ... , 400.0 nm
Solar spectrum: The extraterrestrial solar flux was measured by
the SOLSTICE instrument aboard the UARS satellite (data product
Version 8). The instrumental resolution was much finer than 0.5 nm,
so the spectrum was degraded by splining to the desired set of
wavelengths. The Earth-Sun distance varies annually by about 3.4%
due to the ellipticity of the Earth's orbit. An expression for
the Earth-Sun distance, provided in the Astronomical Almanac, was
used.
Action spectrum: The model erythemal action spectrum w(l) was
devised by Green, Sawada, and Shettle, and is
a c exp2
w(l) = ---------- + -----------
1 + exp1 2
1 + exp2
where
a= 0.04485
c= 3.9796
exp1= exp( (l - l1)/b )
exp2= exp( (l - l2)/d )
b= 3.13
d= 2.692
l1= 311.4
l2= 296.5
Total Column Ozone and Scene Reflectivity: The Version 8,
level-3 value from the Nimbus-7/TOMS instrument was used.
Terrain height: These values are based on a U.S. Department of
Defense geographical database, and were degraded to the grid
resolution. The height of the ocean surface was set to zero.
Solar Zenith Angle: The solar zenith angle is related to the
solar hour angle via the expression
SZA = cos(Lat - SDA) + [cos(Lat) cos(SDA)] [cos(SHA) - 1]
where
Lat = Latitude
SZA = Solar zenith angle
SHA = Solar hour angle
SDA = Solar declination angle
The hour angle is just the local apparent solar time, expressed as
an angle. The declination angle can be computed from the low-
precision formulae given in the Astronomical Almanac.
Normalized downward flux: These were calculated as the product of
a clear sky flux and a cloud correction factor. The clear-sky
fluxes were modelled by a function of the form
cos( gamma SZA ) exp( -alpha/cos( gamma SZA ) )
-----------------------------------------------
1 - Rsurf Sb
where alpha, gamma, and Sb values were fit to the results of
detailed radiative transfer calculations that used standard,
midlatitude ozone profiles and Bass & Paur ozone absorption
cross-sections, for each of the wavelengths required, total
column ozone amounts of 125 to 575 Dobson Units, and terrain
heights from 0 to 6 km.
The cloud correction factor was determined in two steps, using
the results of model radiative transfer calculations: First, a
putative cloud optical thickness was found as a function of the
three quantities, (SDA - Lat), Robs, and Rsurf. Next, the cloud
correction factor was determined as a function of wavelength,
putative cloud optical thickness, surface reflectivity, terrain
height, and solar zenith angle.
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Contacts:
Dr. Jay R. Herman
Code 916.0
NASA Goddard Space Flight Center
Greenbelt, Maryland 20771
herman@tparty.gsfc.nasa.gov
Dr. Edward A. Celarier
Software Corporation of America
Lanham, Maryland 20706
celarier@ozone.stx.com
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