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OPTICAL SYSTEMS GROUP
TECHNICAL NOTE NO. 219
3 1822 04429 6614
June 1990
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Offsite
(Annex-JON
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QC
974.5
. 143
no. 219
M
PRELIMINARY CLOUD ANALYSIS
CONCEPTS FOR APPLICATION TO
ASAT ENGAGEMENT SCENARIOS

T. L. Koehler
J. E. Shields
UNIVERSITY
OF
CALIFORNIA
SAN DIEGO
ERSITY
SMIN
.
..
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8981.)
...
The material contained in this note is to be considered
proprietary in nature and is not authorized for distribution
without the prior consent of the Marine Physical Laboratory.
SCRIPPS
INSTITUTION
"ON
OCEANOGRAPHY
MARINE PHYSICAL LAB San Diego, CA 92152-6400
OF

UNIVERSITY OF CALIFORNIA, SAN DIEGO
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3 1822 04429 6614
Preliminary Cloud Analysis Concepts
for Application to ASAT Engagement Scenarios
Contents
Introduction and Overview
Bullet Charts
Caveats for Demonstration Presentation
Demonstration Sequence - Unconditional Probabilities
Demonstration Sequence - Conditional Probabilities
Data Plots
Extracted One-Minute Image Format
Frequency Distribution: Start and End Position
Frequency Distribution: Arc Length
Cumulative Frequency of Arc Length
Conditional Cloud Free Arc Probability
Simulated Energy Matrix
Thresholded Energy Matrix
Simulated Percent Kill
Data Tables
Conditional CFARC Probability
Simulated Energy Matrix
Decision Matrix (Energy > 7000)
Appendices
Tech Memo AV90-074t, "25 May Meeting with Michelle Reed and Dick Newton"
Simulated Probability of Kill Computation Examples
Introduction and Overview
The attached plots are a sample calculation intended to demonstrate various cloud free
arc (CFARC) probabilities for use with an ASAT model (ref AV90-074t, attached).
Statistics have been extracted for a two week sample, for the arc shown in the first
figure. Bullet charts showing the resulting plots, and the appropriate caveats, are included.
Unconditional Probability Plots
The first plot gives the frequency distribution for start and end point of the longest
cloud free arc occurring along the selected arc within each image. Only those points which
are neither completely clear nor completely cloudy are included on the plot. (The
frequencies of clear and overcast cases are printed on the plot.) The shape of this curve is
appears reasonable; this may be discussed at the meeting.
The second plot on this page gives the frequency distribution for arc length. (Again,
clear and overcast are not included.) This is followed by a plot of the cumulative frequency
for arc length, both for the total sample, and for am (the 3 hours before local apparent
noon) and pm (the three hours after).
Unconditional Probability Interpretation
From the combined cumulative frequency plot, one can see that the 20% value
corresponds, for this sample, to an arc length of 45 degrees. Although these numbers
should not be trusted at this point (see the caveats bullet chart), they can be used for
illustrative purposes. In this sample, if one wishes an 80% success rate, one must be able
to input sufficient energy in 45 degrees. Note that the afternoon was considerably more
cloudy than the morning. In the morning one has over 60 degrees available, but in the
afternoon only 30 degrees are available, assuming a desired 80% success rate.
SAW
Conditional Probability Plot
The start point can also be quite critical in determinations of whether it is possible to
input enough energy. Therefore we also computed some conditional probabilities. One
can first compute the probability that the start point is a given position. Then for a given
start point, one can compute the conditional probability that the arc length is a given
amount. The application of this approach is illustrated in the remaining plots and tables.
The first plot and table show the arc length conditional probability, based on this
limited data sample, given the start pixel position shown. For illustration only, the arc has
been broken into 9 segments. These computations would normally be done at full
resolution.) Thus, for example, .7% of the cases had a start point within category 1 and
arc length within category 1 (roughly 0-12 degrees).
Application of the Conditional Probability
Once similar conditional probabilities are computed for sufficiently long periods, these
data could be used in the following way. The ASĀT model could be used to generate the
amount of energy which can be input for a given start point and arc length. This would be
computed for all combinations of start point and arc length. This has been done for a
simulated energy profile, in the figure labeled "Simulated Energy Matrix".
Heisa
If one knows the energy required for kill, the energy matrix is thresholded at this
known required energy. The resulting thresholded matrix is 0 if a given start point and arc
length do not yield sufficient energy. A sample thresholded energy matrix has been plotted
for a kill energy of 7000 relative units. This binary matrix is then multiplied by the
conditional cloud free arc length matrix shown earlier, to determine how often success is
achieved. The sum of this final matrix yields percent kill rate.
The final plot compares the resulting kill rate for the unconditional and conditional
probabilities. The unconditional probability gives a somewhat more conservative answer.
That is, for a given required kill energy, the unconditional probability will yield a slightly
lower success rate. For a required kill energy of 7000, the conditional probability predicts
a 2% higher success ratio.
For operational purposes, the important question is: how much will we overestimate
the energy output requirements of the GBL if we use unconditional probabilities.
Answering this directly requires multiple runs with different input energy profiles.
However we can approach the problem indirectly by asking a slightly different question:
what is the highest kill energy that could be achieved for a given fixed input energy. The
unconditional probability implies a kill energy of only 4700 units would be available on
target; the conditional probability implies that 7200 units of energy would be available, for
the same input profile. Thus in terms of energy, the conditional probability gives a much
more favorable answer.
Views
It should be noted that the stair-step nature of the unconditional percent kill vs. kill
energy plot is an artifact of the coarse arc length resolution used for the illustration of
concept in this sample. This artifact would disappear when the computations are made at
full resolution.
Summary
The cumulative frequency of arc length. i.e.. the unconditional probability of arc
length, yields a very convenient result. One can determine immediately the arc length in
which sufficient energy must be input. This is a very convenient format, as it uncouples
the cloud statistics from the ASAT model; these distributions may be run for as many cases
as desired, and input as distributions to the ASAT model.
The conditional probabilities also decoupled the cloud impact computations from the
ASAT computations That is, the cloud statistics may be determined independently from
many cases, and input as a distribution to the ASAT model. They also , in our opinion,
yield a somewhat more accurate result than the unconditional probabilities. They are not as
convenient to interpret however, because determination of the final percent kill rate requires
use of the an energy matrix from the ASAT model.
FUS
CAVEATS FOR DEMONSTRATION PRESENTATION
• SIMULATED ARC: ROW FROM IMAGE
• TWO WEEKS ONLY, 6 HRS, 1 MIN DATA
• PREVIOUSLY PROCESSED CLOUD DATA
• USED PRELIMINARY CLOUD ALGORITHM
• SIMULATED ARC LENGTH USING PIXEL EXTENT
.
.
MPL
DEMONSTRATION SEQUENCE UNCONDITIONAL PROBABILITIES
• START AND END POINT DISTRIBUTION
ARC LENGTH DISTRIBUTION
ARC LENGTH CUMULATIVE FREQUENCY (Total, AM, PM)
..
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DEMONSTRATION SEQUENCE CONDITIONAL PROBABILITIES
. ARC LENGTH VS START PIXEL MATRIX
SIMULATED ENERGY MATRIX
• THRESHOLDED ENERGY MATRIX
• RESULTING PROBABILITY OF KILL VS KILL ENERGY
.
.
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FIGURE 1
EXTRACTED ONE-MINUTE IMAGE FORMAT
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Conditional Probability of ARC length, for each given start point
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3260 5820 8820 11380
5090 8090 10650 12490
6630 9190 11030 12140
7070 8840 9950 10740
5950 7060 7940
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Summation of the product of the CFARC table with this table yields 22.8% Pk.
Addition of clear cases, 58.1%, yields net Pk = 80.9%
MARINE PHYSICAL LABORATORY, P-001
of the Scripps Institution of Oceanography
San Diego, California 92152-6400
AV90-0741
June 4, 1990
Technical Memorandum
To: R.W. Johnson
From: J.E. Shields
Subject: 25 May Meeting with Michelle Reed and Dick Newton
At your request, I will attempt to summarize the meeting with Michelle Reed and Dick
Newton, that took place at ASL in New Mexico. These are the people working with the
FEL laser site at Oro Grande. For this memo to make sense, I should first summarize the
18 April meeting, which also included Ken White of ASL and Ken Kosaka of TRW.
Overview of the Engagement Space Model
Dick Newton's work is in systems engineering for the anti-satellite, ASAT system.
Essentially, they are trying to predict engagement space for a variety of satellites. His
technical report TR90-001 summarizes the current state of the model. Essentially, the
characteristics of a the satellite, the atmosphere, and the ground-based laser, are input to
determine the irradiance that can be directed at the satellite by the laser as a function of
position of the satellite along a track. This, combined with the satellite angular velocity
along the track, yields a plot of the cumulative energy which can be deposited on the
satellite as a function of time. This is shown in the attached Fig 2.4 from their report.
Since the energy deposit rate is relatively low at larger zenith angles, the optimum initiation
time is somewhat after the first possible initiation time, as shown in Figure 2.5.
A sample output representative of their current model is in the form of Figure 4, which
shows the possible engagement space for a sample satellite. The line marked Pd is I
believe where the power density is sufficient to initiate burn. The "too late" curve is where
there is no longer time to cumulate enough energy for a burn. For example, in Fig 4 near
azimuth 180, if one needs to apply sufficient energy before reaching the Pd curve near the
bottom, one must start sufficiently above the Pd curve that the cumulative energy equals
that required for burn.
Dick N.'s report shows how this engagement space depends on satellite altitude,
shows the effects of regions which cannot be used (the "keep out zone"), and also shows
the curve within the engagement space which represents the optimum initiation time (based
on minimizing the required irradiation time).
The effect of a cloud can be rather large. As shown in his Figure 10, a cloud
represents another region through which significant energy cannot be directed. In order to
determine the engagement space, the user must back away from the cloud edge by the
amount of time required to deliver the burn energy. This gives a new "too late curve", as
shown in Fig 10.
AV90-0741
1 June 90
April comments regarding our contribution
At the time of the April meeting, they felt we could best help in several arenas.
a)
Their model gives them a total energy input, or fluence, for a given satellite and GBL.
They need to know how that fluence is degraded in the presence of clouds. In
particular they need the probability distribution for fluence between 0 and the max (no
cloud) case.
b)
They felt this could be done by running lots of cases with clouds through their model.
That is, input a specific cloud sample to their model, determine the resulting fluence
for that case, and continue with lots of specific cloud cases, to get a distribution of
fluence results.
They felt somewhat limited in their ability to handle lots of cases. They suggested
using the cloud images for noon for a period of one month. There was some
discussion of using hourly images. I got the impression that being able to run a finer
time scale would be difficult for them.
d)
They also wanted to know, in terms of clouds, what are the best and worst months.
e)
They were interested in knowing whether the inclination angle matters. By inclination
angle, they mean the angle of the satellite path with respect to a north-south line (this is
equivalent to azimuth if the satellite happens to pass overhead).
harland images, and input appropriate stausuu w.
I commented that it would be very helpful if we could de-couple the atmospherics from
the model. That is, rather than inputting specific cloud images to the model, and running
lots of cases to get a distribution of results, it would be very helpful if we could run
calculations on the cloud images, and input appropriate statistics to his model. This has the
advantage of letting us run lots of cases, to give them better distributions. It also makes
transport of the information easier, and means we don't have to get involved in classified
details of the model. At the time, he and Tom agreed, but none of us were sure how we
could decouple the cloud information from the engagement space model.
Decoupling the Clouds
At the May meeting, Dick N. proposed a plan for decoupling the cloud behavior from
the engagement space model. He suggests that he give us a couple bearings of interest, i.e.
a couple of possible satellite tracks. We would identify seasons of interest, such as the
least and most rainy seasons, and perhaps some average seasons. These would be based
on the data, not on the normal seasons. Similarly, there would be "seasons" of the day, or
periods of similar behavior. These could initially be am, noon, and pm. Suppose we
choose Aug-Sep, 2-4 pm as a sample.
We would process the data along 2 bearings, looking at CFARC. He suggested that
we just look at the longest CFARC for now. He also suggested putting the data into bins,
by choosing some angular interval, such as 10 degrees. The handwritten Fig 1 shows a
sample of 20 cases, with the longest CFARC indicated on each line, with start and end
positions indicated in terms of these angular bins. For this sample case, he computed the
average and STD for both start time and end time, yielding the plot in Fig 2.1. Then the
difference in the averages gives you the average arc length, and the RSS (root sum of
squares) can be used to derive the STD in arc length (I'm not sure how, but I'm sure Tom
can derive it).

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1 June 90
This gives you a mean and STD of arc lengths, as in Fig 2.2. For his model, he needs
to specify a Pk (probability of kill). Say he wants a Pk value of 80%. Then he needs to
determine from Fig 2.2 the minimum arc length that is found or exceeded 80% of the time.
In this case, the longest arc length was greater than or equal to 3.05 units (unit length
referring back to Fig 1) 80% of the time. So he needs to design his system such that he can
get enough energy on the satellite within 3.05 arc length units. In particular, he could enter
this mean arc length associated with the given Pk to his model, to compute new
engagement space diagrams.
He is not sure how limiting the atmosphere will actually be. He needs to design the
system for something like 80% Pk with an 80% confidence level (the numbers are yet to be
determined). He needs to know how much the atmosphere will limit him. For now, we
said we would try to make a sample run before the June meeting, and we would at least
think about this approach, but the method seemed reasonable.
Discussion of the Statistical Approach
Several other relevant comments were:
a) For our sample runs, we can limit the computations to 0 5 60°.
b) We discussed whether arcs with short breaks would be of interest. For example, we
could run the statistics for the longest arc with 100% clear, the longest with 95%
clear, and so on; this would be like an added dimension to the statistics. This is
because a long arc length with a short break in it might be useful. He felt that it would
be of interest some time, but since they do not have a good feel for the cooling rate (for
how much the satellite would cool during the short break), the 100% cloud free arc is
the most important case for now; this would give him the most conservative answer.
I suggested that they might later be interested in a conditional probability which
includes the start point. That is, we could give him the probability that a given
direction is clear, and the conditional probability for arc length, given that that start is
clear. This could be important, because the arc length required to input a given energy
depends strongly on the position of the start of the arc length. He seemed to feel this
would be a useful later addition.
d)
Sind
Since we are probably going to be limited more by Exabyte read time than by
processing time, I suggested that we might consider using a continuum in zenith angle,
rather than breaking things into 10 degree bins. I believe the binning is only to make
computations simpler, but for our automated processing, using the actual angle may be
simpler. I'm not aware of any statistical advantage in going with the bins, for this type
study. If we do use bins, he said the bin size would somehow be related to cloud size;
I suggested it could be based on the spatial coherence.
e)
Once they really get going, they will be very interested in a real time system at the site.
In the meantime, they are interested in the statistics for WSC, WSH, and maybe KAA.
Later CL4 may be of interest, as there is talk of a second site there.
.
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in d.
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pow. A. JIWW,
AV90-0740
1 June 90
f)
Viskas
I asked about time intervals. He's not sure what's best to use, although he agrees that
if the samples are too close together, they are no longer statistically independent.
Since he does not need persistence, the close time interval is not required. Perhaps 10
minute intervals would be reasonable, as it gets us away from the dependent sampling
problem a bit, and opens up more choices in tracks to use.
We would probably compute the distribution of arc length directly, rather than deriving
it from start and end statistics, since the latter probably requires assuming a standard
distribution.
h)
He says that over the next 5 years, they will probably want statistics for 12 satellites.
They might also want specific cloud images to try, perhaps as a prototype on how to
use the real time system results.
In general, they still feel that our data will answer a very crucial question for them.
They may or may not like the answer, but they need to know the answer.
Simulated Probability of kill Computation Examples
To demonstrate the use of the conditional cloud free arc (CFARC) values
in the probability of kill computations, a simple energy vs. pixel relationship
was assumed. The energy contribution per pixel started at 1 pixel 1 and
increased linearly to 122 at pixel 122. It then decreased linearly back to 1
at pixel 243. In these circumstances, a completely clear arc would yield a
total energy of 14884 energy units.
The following tables illustrate the probability of kill computations
for two cases. The first case employs a CFARC probability distribution that
is defined without considering the starting pixel position of the arc, and is
thus labelled the unconditional case. In the second case, a CFARC probability
distribution is defined for each start pixel location. This case is labelled
the conditional case. For illustration purposes, we have broken the 243 pixels
in the sample arc into 9 categories of 27 pixels each. In practice, the full
resolution could be used.
Unditional case. For:19.n. start pixel locatie
UNCONDITIONAL EXAMPLE
1
140
CFARC Length Category
2 3 4 5 6 7 8 9
890 2380 4590 7500 10390 12580 14030 14760
1. Simulated Energy
2. Decision Vector
(Energy > 7000)
0
0
0
0
1
1
1
1
1
4.1
3.6
3.9
3.6
5.1
4.5
4.5
3.6
3.2
3. Unconditional CFARC
Probability (%)
4. Line 2 times Line 3
0.0
0.0
0.0
0.0
5.1
4.5
4.5
3.6
3.2
Probability of kill = Sum of Line 4 + % of Completely Clear Cases
P.K.
=
20.9%
+
58.1%
=
79.0%
CONDITIONAL EXAMPLE
1. Simulated Energy
ܝܕ ܢܨ ܚ
3
ܩ ܟ
Start
Pixel
Category
CFARC Length Category
1 2 3 4 5 6 7 8 9
320 1420 3260 5820 8820 11380 13220 14320 14760
700 2530 5090 8090 10650 12490 13600 14150
1070 3630 6630 9190 11030 12140 12810
1450 4450 7070 88 40 9950 10740
1560 4120 5954 7060 7940
1210 3040 4151 4941
830 1940 2610
450 1010
140
ܗ ܢ
7
ܣ ܩ
2. Decision Matrix
(Energy > 7000)
3. Conditional CFARC Probability (%)
8
1.6
2.0
9
3.2
CFARC Length Category
1 2 3 4 5 6 7 8 9
1 000011111
2 0 0 0 1 1 1 1 1
3 0 0 0 1 1 1 1
Start 4 001111
Pixel 5 00011
Cat. 6 0000
7 000
8 00
9 0
1
0.7
0.5
0.4
0.3
0.2
0.4
0.5
0.6
0.5
2
0.8
0.2
0.3
0.2
0.4
0.5
0.3
0.9
CFARC Length Category
3 4 5 6 7
1.0 0.7 2.2 1.8 2.1
0.1 0.2 0.3 0.4 0.4
0.3 0.4 0.3 0.4 2.0
0.3 0.3 0.5 1.9
0.5 0.7 1.8
0.4 1.3
1.3
4. Elements of Matrix 3 times the corresponding elements of Matrix 4
8
1.6
2.0
9
3.2
1
2
3
4
:
2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
CFARC Length Category
3 4 5 6 7
0.0 0.0 2.2 1.8 2.1
0.0 0.2 0.3 0.4 0.4
0.0 0.4 0.3 0.4 2.0
0.3 0.3 0.5 1.9
0.0 0.7 1.8
0.0 0.0
0.0
Start
Pixel
Category
9
Probability of kill = Sum of Matrix 4 Elements + % of Completely clear Cases
P.K. = 22.8% + 58.18 = 80.98
* - The events that affect the conditional P.K., but not the unconditional
P.K. have been outlined.