Nimbus 7 solar irradiance values have been made available to the scientific community through the open literature (e.g., Hickey et al., 1988) and through NASA data centers. A comparison of these measurements to the Solar Maximum Mission/Active Cavity Radiometer Irradiance Monitor (SSM/ACRIM) time series indicated differences which might be caused in part by the method of converting the Nimbus 7 raw data counts to solar irradiance values. In an effort to see if the derivation of the solar irradiance could be improved, the raw counts were extracted from the tapes and analyzed to see how a new algorithm could be constructed. The basic form of the calibration remains the same as in the previous solar irradiance derivations. However, the input values to the equation differ from what was used before. In particular, improved values of the Earth-sun distance are incorporated and new temperature sensitivities were derived. Several problems with the instrument were uncovered which previously had not been noticed. The sun did not appear to cross the center of field of the radiometer but was systematically off by 1.5 to 2.5 degrees. The analog to digital convertor changed its properties in July 1980. The gain of the electronics apparently increased by 0.03 percent in September 1987. Applying these and other changes in the processing, the day to day variations appear much more like the SMM observations. In fact, the Nimbus 7 observations are sufficiently stable that a problem with the SSM observations in the spin mode period of 1981 to 1984 can be detected when the two time series are compared

Hoyt, Douglas V.

Kyle, H. Lee

English

NASA Technical Reports Server

AN ALTERNATIVE DERIVATION OF THE NIMBUS 7 
TOTAL SOLAR IRRADIANCE VARIATIONS 
Douglas V. Hoyt 
Research and Data Systems, Corp. 
7855 Walker Drive, Suite 460 
Greenbelt, MD 20770 
and 
H. Lee Kyle 
Goddard Space Flight Center 
Greenbelt, MD 20771 
Abstract. Nimbus 7 solar irradiance values have been made 
available to the scientific community through the open literature 
(e.g., Hickey et al., 1988) and through NASA data centers. A 
comparison of these measurements to the SMM/ACRIM time series 
indicated differences which might be caused in part by the method 
of converting the Nimbus 7 raw data counts to solar irradiance 
values. In an effort to see if the derivation of the solar 
irradiance could be improved, the raw counts were extracted from 
the tapes and analyzed to see how a new algorithm could be 
constructed. The basic form of the calibration remains the same as 
in the previous solar irradiance derivations. However, the input 
values to the equation differ from what was used before. In 
particular, improved values of the Earth-sun distance are 
incorporated and new temperature sensitivities were derived. 
Several problems with the instrument were uncovered which 
previously had not been noticed: 1) The sun did not appear to cross 
the center of field of the radiometer but was systematically off by 
1.5 to 2.5 degrees. 2) The AID convertor changed its properties in 
July 1980. 3) The gain of the electronics apparently increased by 
0.03% in September 1987. Applying these and other changes in the 
processing, the day to day variations appear much more like the SMM 
observations. In fact, the Nimbus 7 observations are sufficiently 
stable that a problem with the SMM observations in the spin mode 
period of 1981-84 can be detected when the two time series are 
compared. 
https://ntrs.nasa.gov/search.jsp?R=19910003183 2020-03-24T06:54:44+00:00Z
1. Introduction 
The major highlights of the method of reducing the instrument 
influences upon the measurements are described in section 2. 
Because of space limitations some of these descriptions will be 
limited. A paper describing these techniques in more detail is now 
being prepared for publication in the refereed literature. The 
third section provides a comparison of some of the newly derived 
Nimbus 7 solar irradiance values to the SMM/Acrim measurements. 
The final section sums up our present status in understanding the 
instrument. 
2. The Removal of Instrument Influences 
The basic equation used to convert counts to irradiance is: 
0.998 12 (csun-cs~ce) 1 
1.3013 cos (G) [I. +A(T-22)  1 
where 1.3013 is the calibration constant, 0.998 is a correction 
constant to account for spurious reflections from the baffles into 
the cavity, r is the Earth-sun distance, C,,, is the mean on-sun 
counts, C, ,,, is the mean space look counts, A is the coefficient 
for the eemperature sensitivity of the radiometer, T is the 
temperature of the radiometer in degrees Celsius, and G is the 
offset angle between the normal vector to radiometer cavity and the 
vector to the sun. This equation is an attempt to remove all the 
portions of the counts signal which arises from the instrument and 
geometry so that only a pure signal arising from solar behavior 
remains. 
If the Nimbus 7 radiometer had no pointing problems, then each 
time the sun drifted across its field of view it would pass through 
the center of the radiometer's field of view. Unfortunately, the 
sun normally appears to drift through the field of view on an off 
center cord or path. The angle between the radiometer-sun vector 
and the normal vector of the plane of the detector is known as the 
off-axis angle. 
The off-axis angle is generally assumed to be measured by 
taking the difference between the so-called beta and gamma angles. 
The beta angle is angle between the plane of the satellite's orbit 
and the plane defined by the ecliptic. The beta angle is measured 
by the Digital Solar Aspect Sensor (DSAS). The gamma angle, on the 
other hand, is the angle between the axis of the solar telescope 
and the orbital plane and it can be varied only in one degree 
steps. If the two angles are equal, then the radiometer is assumed 
to be on-axis. In most cases the difference between these two 
angles is measured as less than one degree. The difference in the 
two angles provides a measure of the off-axis angle. If these off- 
axis angles are kept less than 0.5 degrees, then the cosine of 
these angles will be very close to one so the pointing correction 
will be negligible (e.g., 0.05 watts per square meter or less). 
To derive what the off-axis angle really is, it is assumed 
that the solar constant and radiometer properties remain stable 
just before and just after the gamma angle change. It follows then 
that the ratio of the counts, corrected to one astronomical unit, 
will equal the ratio of the cosine of the off-axis angle prior to 
the change to the cosine of that angle plus one degree after the 
change. The only unknown is the off-axis angle, G, which can be 
solved for, using the following equation: 
where C, is the mean on-sun counts prior to the gamma angle change 
and C? IS the mean on-sun count after the gamma angle change. In 
practice, we use 5, 6, 7, 8, or 9 orbits prior and after to form 
the two means of the counts. These five determinations are 
averaged together to derive an average off-axis angle. In effect, 
the observations closest to the gamma angle changes are more 
heavily weighted. 
D e l t a  Beta P o i n t i n g  Er ro r s  I 
v i t h  no smoothing 
0 
- 1 
- 2  
- 
VI -3  
a, 
" Cn
- 4 S 
Y 0
" - 5 
" I 
W 
s - 6 I 
r( 
4 
C 
.A 0
- 7 
0 8  
I 
I 
! 
-8  
I 
- 9 I 
i 
-10 I I 
7 8 . 9 3  79 .94  8 0 . 0 1  81. 94 82.  82 83 .94  84.94 85.84 86.  80 87 .80  93 5 9  83 22 
year  I 
Figure 1. The off-axis angle vs. time using the change in gamma 
angles and change in counts to calculate the off-axis angle. The 
individual values show considerable scatter due to the limited 
resolution of the AID convertor, the limited number of useful 
measurements on each side of the gamma angle change, and spurious 
influences caused by high solar activity. An 81 point running mean 
is drawn through the points. 
Figure 1 shows the 236 determinations of the off-axis angle. 
An 81 point running mean is drawn through the points which shows 
the slow component of the off-axis angle variations. There is 
considerable scatter in the raw values but a systematic off-axis 
angle slowly comes closer to the zero as the experiment precedes. 
The scatter in Figure 1 is reduced by forming a running mean 
of values. This procedure is justified since any individual off- 
axis angle is uncertain due to 1) the limited resolution of the AID 
convertor, 2) possible variations in the solar irradiance during 
each determination, and 3) some small changes in radiometer 
temperature. Various lengths for the running mean were tried, but 
a length of 81 points was chosen since there are about 20 gamma 
angle changes per year and 81 covers 4 years reducing any signal 
from an annual variation. The radiometer's gamma angle was 
systematically too low by about 2.5 degrees early in the 
measurement period, but more recently it is off by only about 1.5 
degrees. 
Because the AID convertor provides only a 0.7 watt per square 
meter resolution for any one measurement, when looking at space to 
determine the offset of the instrument, a large number of 
measurements is required to accurately determine the offset. It 
was decided that large blocks of time, usually one year's worth of 
data could be used to provide a measure of the offset. This 
procedure considerably reduces the day to day scatter in the solar 
irradiance measurements. 
On July 20, 1980 the AID convertor changed its properties such 
that it tended to round off its count values to the next higher 
digit more frequently than it would if this bias had not developed. 
Because both the on sun and zero counts were equally effected, the 
result is not readily evident in most derivations. However, if we 
use large blocks of time to measure the zero offset, the zero 
offset must be determined for the period January 1 to July 20 and 
from July 21 to December 31, 1980 separately. otherwise, an 
artificial trend could be introduced into the solar irradiance 
values for 1980. 
Assuming the calibration constant of channel 10c remained 
unchanged throughout the mission and calculating the solar 
irradiance, it varies smoothly except for an upward jump of 0.03% 
in irradiance on September 26, 1987. The change in sensitivity is 
confirmed by the electrical calibrations, so its effect is removed 
by having a new calibration constant after this date. 
The radiometer is slightly sensitive to temperature since the 
cavity sees the field-of-view limiters which have different 
temperatures for each solar irradiance measurement. The 
temperature sensitivity can be determined by two techniques: 1) 
Assume the solar irradiance is a constant and the unexplained 
variations arise from the radiometer temperature variations and 2) 
use the space look observations and the temperature measurements 
and derive a fit between the counts and the temperature. Both 
techniques werea tried and gave nearly the same answers. The 
coefficient in the calibration is found to be 0.001998 for 
temperatures above 18 C, 0.0002713 for temperatures between 15 and 
18 C, and 0.0003086 for temperatures below 15 C based upon the 
first technique and using all observations between November, 1978 
and December, 1988. Using the second technique, the temperature 
sensitivity above 18 C for 1988 is 0.000196. The second technique 
is actually less accurate than the first technique, because of the 
limited resolution of the A/D convertor. Theref ore, the 
temperature coefficients from the first technique are used. 
Previously published solar irradiance measurements assumed a 
single value of 0.000524 for temperatures of the radiometer. This 
value was based upon a few determinations in 1978 and 1979. Smith 
et al. (1983) previously pointed out that a linear relationship of 
the radiometer is not valid since the transfer of radiation from 
the field-of-view limiters to the cavity is done radiatively and is 
thus proportional to the blackbody flux which depends upon 
temperature raised to the fourth power. By using a linear 
relationship and splitting it into three ranges, much of this non- 
linearity is captured. However, there are several methods which 
may be used to derive the temperature sensitivity of the instrument 
and the problem continues to be studied. Future studies may 
improve our understanding of the temperature sensitivity of the 
instrument. 
Finally, the derived solar irradiance measurements were 
improved by using more precise Earth-sun distance calculations. 
This distances are now accurate to eight significant figures and 
are calculated for each orbit rather than for each day as was 
previously done. 
3. A Comparison to the SMM/ACRIM Measurements 
Daily solar irradiance values from the SMM are available for 
the period February 1980 to December 1988 (e.g., Willson and 
Hudson, 1988). These independent solar irradiance measurements are 
numerous enough to provide a good comparison to the ~imbus 7 
measurements. Figure 2 shows the measurements for 1988. The 
correlation between these two measurements is 0.87 for this year. 
Overall these two independent sets of measurements show good 
agreement. This increases our confidence that the true solar 
behavior is being tracked. 
Figure 3 provides a plot of the Nimbus 7 and SMM monthly mean 
solar irradiance values. The two curves are quite similar with 
both instruments indicating a rise in solar irradiance in the 
latest cycle to a value less than that in the previous cycle. In 
Figure 4, the differences in monthly means is plotted. These 
differences are about 4 to 5 watts per square meter when the SMM 
pointing is known to be correct and slightly less than 4 watts per 
square meter during the period 1981 to 1984 when the SMM had. 
N-7 and SMM 1988 Solar lrradiances 
1 31 61 B1 121 151 181 211 241 271 301 331 361 
l l m e  In Day of Year. 1988 
Figure 2. A comparison of the Nimbus 7 and SMM solar irradiance 
values for 1988 on the same plot. Day to day variations have a 
correlation of 0.87 for this year. 
78 79 80 81 82 83 84 85 86 87 88 89 90 
Year 
Figure 3. The Nimbus 7 and SMM monthly means for 1978 to 1989. 
Both instruments are indicating similar solar behavior except for 
a few periods such as early 1980, late 1983, mid-1986, and late 
1988. 
pointing problems. During the quiet sun, the SMM radiometer has 
smaller month to month variations than does the Nimbus 7 
radiometer. This may indicate that some residual pointing errors 
still exist in the Nimbus 7 measurements. The rise in Nimbus 7 
measurements in August 1987, which does not occur in the SMM 
measurements, could be caused by an undetected 0.1 degree error in 
the Nimbus 7 pointing. Alternatively, since this rise was evident 
just after a special operations period, the Nimbus 7 radiometer's 
thermal properties may have changed for a time and relaxed back to 
normal after several months. In late 1988 there is a small 
divergence between the two measurements for as yet unknown reasons. 
Despite these divergences the agreement is still rather good. 
The correlation of the monthly means is 0.867 for 1980 to 1983, 
0.014 from 1984 to 1986 after the SMM pointing was restored but the 
sun remained quiet, and 0.816 in 1987-88 when solar activity 
resumed. The low correlation in 1984-86 arises because the 
variability in the solar irradiance became less than the noise in 
the measurements, particularly in the Nimbus 7 measurements. As a 
comparison, the older published Nimbus 7 irradiances had 
correlations with SMM of 0.863, 0.000, and 0.836 respectively for 
the three periods. Much of these correlations are arising from 
common long-term trends. Using daily values for 1988, the new 
algorithm has a 0.87 correlation with SMM whereas the old algorithm 
has a 0.75 correlation. 
I N-7 minus SMM Solar lrradiances 
Monthly Means 
78.00 79.00 80.00 81.00 82.00 8300 84.00 85.00 86.00 87.00 88.00 89 00 90.00 
Year 
Figure 4. The Nimbus 7 monthly mean solar irradiance minus the 
monthly mean SMM solar irradiance. Most differences are between 4 
and 5 watts per square meter except for 1981 to 1984 when the SMM 
had pointing problems. 
4. Concluding Remarks 
A new algorithm to derive the solar irradiance from the Nimbus 
7 raw data is reported upon here. The algorithm removes more of 
the instrumental and geometrical influences upon the measurements 
than did the old algorithm so that the true solar behavior becomes 
more apparent. Changes in the analysis include: 1) better Earth- 
sun distance determinations, 2) improved temperature sensitivity 
coefficients, and 3) re-calculated off-axis angles. These 
algorithm changes give substantially smoother day to day variations 
in the solar irradiance and a greater correlation with the SMM 
observations. The Nimbus 7 long-term trends in solar irradiance 
are different then previously calculated and now generally closer 
to the SMM observations. These changes increase our confidence 
that both satellites are measuring a real solar signal. Despite 
nearly equal solar activity for the last two solar cycles based 
upon Wolf sunspot numbers, the solar irradiance for the two cycles 
are not equal. Both the Nimbus 7 and SMM satellites appear to 
confirm this behavior. 
Considering that the SMM measurements suffered from pointing 
problems between 1981 and 1983, it is reasonable to suggest that 
the Nimbus 7 solar irradiances derived for this time period are a 
better measure of true solar behavior. Most of the differences 
between the two measurements in the 1981-83 time period may be 
arising from random errors in the SMM measurements which has a 
greater day to day variability than the Nimbus 7 measurements. 
Although some of the problems with the Nimbus 7 measurements 
are removed in this analysis, insufficient information exists to 
remove all the instrument influences on the solar irradiance 
determinations. In particular, the off-axis angle corrections 
remove the short-term and long-term variations in the off-axis 
angle, but the intermediate variations (months to two years) may 
not be fully removed. With the limited number of independent 
measurements of the off-axis angle (236) and the limited accuracy 
of each off-axis angle determination, it does not appear that 
these intermediate term variations can be removed completely. 
Hickey, J. R., B. M. Alton, H. L. Kyle, and D. V. Hoyt, 1988. 
Total solar irradiance measurements by ERB/Nimbus-7. A review 
of nine years. Sp. Sci. Rev., 48, 321-342. 
Smith, E. A., T. H. Vonder Haar, and J. R. Hickey, 1983. The 
nature of the short period fluctuations in solar irradiance 
received by the Earth. Climatic Change, 5, 211-236. 
Willson, R. C. and H. S. Hudson, 1988, Solar luminosity variations 
in solar cycle 21. Nature, 332, 810-812. 


An Alternative Derivation of the Nimbus 7 Total Solar Irradiance Variations

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