NASA Technical Memorandum 104566, Vol. 10

SeaWiFS Technical Report Series

Stanford B. Hooker and

Elaine R. Firestone, Editors

Volume 10, Modeling of the SeaWiFS

Solar and Lunar Observations

Robert H. Woodward, Robert A. Barnes, Charles R. McClain,

Wayne E. Esaias, William L. Barnes, and Ann T. Mecherikunnel

May 1993
NASA Technical Memorandum 104566, Vol. 10

SeaWiFS Technical Report Series

Stanford B. Hooker, Editor

NASA Goddard Space Flight Center

Greenbelt, Maryland

Elaine R. Firestone, Technical Editor

General Sciences Corporation

Laurel, Maryland

Volume 10, Modeling of the SeaWiFS

Solar and Lunar Observations

Robert H. Woodward

General Sciences Corporation

Laurel, Maryland

Robert A. Barnes

CHEMAL, Inc.

Wallops Island, Maryland

Charles R. McClain, Wayne E. Esaias,

WilliamL. Barnes, and Ann T. Mecherikunnel

NASA Goddard Space Flight Center

Greenbelt, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

1993
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Abstract

Post-launch stability monitoring of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) will include periodic

sweeps of both an onboard solar diffuser plate and the moon. The diffuser views will provide short-term

checks and the lunar views will monitor long-term trends in the instrument’s radiometric stability. Models of

the expected sensor response to these observations were created on the SeaWiFS computer at the National

Aeronautics and Space Administration’s (NASA) Goodard Space Flight Center (GSFC) using the Interactive

Data Language (IDL) utility with a graphical user interface (GUI). The solar model uses the area of intersecting

circles to simulate the ramping of sensor response while viewing the diffuser. This model is compared with

preflight laboratory scans of the solar diffuser. The lunar model reads a high resolution lunar image as input.

The observations of the moon are simulated with a bright target recovery algorithm that includes ramping and

ringing functions. Tests using the lunar model indicate that the integrated radiance of the entire lunar surface

provides a more stable quantity than the mean of radiances from centralized pixels. The lunar model is compared

to ground-based scans by the SeaWiFS instrument of a full moon in December 1992. Quality assurance and

trend analyses routines for calibration and for telemetry data are also discussed.

1. INTRODUCTION

This document describes analytical prototypes for postlaunch lunar and solar diffuser observations, plus quality

control and trend analysis routines for data related to instrument calibrations and engineering. The lunar and solar

diffuser observations do not provide an absolute calibration

traceable to National Institute of Standards and Technology (NIST) standards and are correctly viewed only as

stability checks. However, they are closely coupled to an

understanding of the temporal changes in instrument calibration relative to the sun, and thus the terms “calibration” and “observations” are nearly synonymous.

All the software routines were developed on the Seaviewing Wide Field-of-view Sensor (SeaWiFS) Calibration/

Validation (CALVAL) SGI 440 workstation. It is expected

that these modeling tasks will add to the understanding of

the calibration operations as well as to the understanding

of potential problems. Many of the routines developed for

this task may either be directly ported to the SeaWiFS

operational environment or may provide the groundwork

for future software development.

The observation models and simulated input data are

designed to be as realistic as possible. Solar irradiances are

integrated to the SeaWiFS bands and are read as input for

both the diffuser and lunar models. A high resolution lunar

image is also read as input in the lunar model. Laboratory simulations of the diffuser observations are compared

to the solar model, and ground-based lunar scans by the

SeaWiFS instrument are compared to the lunar model.

Most of the software routines discussed in this document were implemented using the Interactive Data Language (IDL) software package. This utility is an interpreted/compiled language which is designed for statistical

analysis and display of large multidimensional arrays or

images. IDL is used for the calibration task since much of

the data related to this task will be ingested and analyzed

as images. IDL also provides a graphical user interface

(GUI) allowing easy manipulation of models.

2.0 ONBOARD CALIBRATIONS

Lunar and solar on-orbit measurements are intended

for the monitoring of changes in the radiometric sensitivity of the SeaWiFS instrument. These measurements

will complement interchannel gain and time delay integration (TDI) checks, which also track changes in the sensor.

For solar measurements, the instrument has two diffuser

surfaces—the solar flight diffuser and a nearly identical

surface on the back of the solar flight diffuser cover. The

sequence of measurements will include the monitoring of

changes in the reflectance of the diffuser cover and the exposure of the flight diffuser with the removal of the cover.

Early in the mission, there will be more calibrations to

provide an accurate baseline for further assessment.

Many of the onboard calibration related activities will

occur while the platformis over the South Pole or in backorbit, minimizing interference with ocean data collection.

Lunar measurements will involve scanning the moon at 1–

3 month intervals when the moon is within 7◦ of full. The

solar diffuser will be scanned at shorter intervals between

lunar measurements to provide complete temporal coverage.

It is expected that the diffuser will degrade with time

as contaminants condense on the surface. In contrast, the

lunar surface is assumed to maintain stable reflective properties. Lunar observations will therefore provide anchor

points for calculating trends in the calibrations. The calibration and instrument telemetry data will undergo quality control and time series analyses prior to being stored in

the CALVAL archive. These analyses will include screening for outliers and discerning trends in the measurements.

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Modeling of the SeaWiFS Solar and Lunar Observations

For a complete description of the calibration activities see

McClain et al. (1992).

2.1 Calibration Background

Lunar measurements are the single source of information for monitoring the long-term drift in the radiometric

sensitivity of the SeaWiFS instrument. The sun and the

surface of the moon are considered as stable, non-changing

light sources. Variations can be accounted for in the incident solar flux due to changes in the Earth-sun distance

by using (Gordon et al. 1983):

F0 = F0



1 + e cos

2π(D − 3)

365 2

(1)

where D is the sequential day of the year, e is orbit eccentricity (0.016), and F0 is the mean solar irradiance. In a

similar manner, variations in the reflectance of the moon,

due to small differences in the lunar phase angle and due

to small changes resulting from lunar libration, can also be

removed by calculation. With these corrections, changes in

measurements of the lunar reflectance can be used directly

to detect changes in the sensitivity of the instrument.

For solar measurements with the diffuser, it is not possible to separate changes in instrument sensitivity from

changes in the reflectance of the diffuser plate in an a priori fashion. All that can be derived fromthese measurements is the product of the change in the instrument and

the change in the diffuser. However, there is an assumption that can tie diffuser and lunar measurements together.

Basically, the change in the reflectance of the diffuser is assumed to be essentially linear over periods of one month,

or so. Over longer periods, e.g., periods of one to several

years, the change may turn out to be exponential, with

gradually decreasing changes over time. However, this exponential change can be treated as a series of many linear segments. Experience with diffusers on previous satellite instruments has led to the assumption that diffuser

degradation has been caused by the coating of the diffuser

with solarized organic materials that have outgassed from

the spacecraft. This accumulation process does not cause

sharp step changes in the diffuser’s reflectance.

Using nearly simultaneous lunar and solar diffuser measurements, it is possible to separate changes in the sensitivity of the instrument (from the lunar measurements) from

changes in the reflectance of the diffuser. The time series of diffuser values will be normalized by lunar measurements. It is then possible to use the assumption of a linear

change in diffuser reflectivity to identify step changes in

instrument sensitivity between lunar measurements. Step

changes were found in measurements with the Coastal Zone

Color Scanner (CZCS), SeaWiFS’ predecessor.

The initialization phase of on-orbit calibration operations, approximately the first two months after the instrument is turned on, has been designed to provide a statistically significant endpoint for the time series of SeaWiFS

calibration measurements. This is primarily the endpoint

for the time series of changes in the radiometric sensitivity of the sensor. The drafting of this schedule at a point

approximately six months before the launch of the instrument reduces the schedule to a “strawman,” since on-orbit

factors—primarily the rate of change of the reflectance of

the diffuser cover—may force a modification of the schedule of events.

The following sequence provides a schedule of the calibration initialization phase of instrument operations.

1. With the solar diffuser cover on:

Take a solar diffuser measurement at the first,

safe opportunity.

Take an interchannel measurement immediately

thereafter. (This can be done at any point on

orbit.)

If possible, take a TDI measurement at the next

available safe opportunity on the orbit following the diffuser measurement. Operationally, the

TDI check will be about equal to a second solar diffuser measurement (see the section on TDI

checks, below).

Repeat this sequence for every downlink (twice

per day) for one week. This gives 14 sets of

measurements as a baseline for instrument operation. This also gives a data set to check for

large changes in the reflectance of the solar diffuser cover. (Large-scale changes in the diffuser

measurements will show degradation of the diffuser surface. Large-scale changes in instrument

sensitivity during initial operation on orbit will

be shown in measurements of the oceans.)

2. At the first full moon:

Take a lunar measurement at a lunar phase angle

of about 7◦, going into the full moon.

If lunar phase angles and instrument power permit, take a second lunar measurement at the same

lunar phase angle coming out of the full moon.

(Power restrictions may limit the measurements

to one per full moon, without regard to the opportunity for a second measurement.)

Repeat this sequence monthly for a minimum of

3–4 months. From these data, a minimum practical interval (in months) for lunar measurements

for the remainder of the mission can be determined .

3. When the solar diffuser cover is removed:

Take a solar diffuser measurement, using the diffuser cover, on one orbit.

Take a solar diffuser measurement on the next orbit. Remove the diffuser cover during the middle

of this measurement.

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R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Using the flight diffuser, take a solar diffuser measurement on the next orbit, followed by an interchannel gain check and a TDI check.

Make a lunar measurement at the next available

opportunity. It is anticipated that the solar diffuser cover will be removed one day before a lunar

measurement.

Take a solar diffuser measurement once per downlink (twice per day) for one week to monitor any

changes in the freshly exposed flight diffuser.

4. For routine operations:

With the sequence of one every downlink, take

solar diffuser measurements, TDI checks, and interchannel gain checks. This sequence can be

changed to once per week, if the stability of the

instrument permits.

Take lunar measurements monthly. This can be

changed to every other month or quarterly, if the

stability of the instrument permits.

2.2 Solar Diffuser Calibration

Solar diffusers, such as the one designed for SeaWiFS,

have been used several times on previous remote sensing

satellite instruments. The series of diffuser measurements

with the Solar Backscatter Ultraviolet (SBUV) spectrometer on the NIMBUS-7 satellite, and with the SBUV/2 spectrometers on the National Oceanic and Atmospheric Administration’s NOAA-9 and NOAA-11 satellites, a history

of the development of this technique is provided. Changes

in the reflectance of the diffuser on the NIMBUS-7 SBUV

were calculated using an on-orbit experiment, based on

changes of the exposure rate of the diffuser for extended

periods on orbit. This experiment gave an empirical model

that separated changes in the SBUV spectrometer from

changes in the instrument’s diffuser (Cebula et al. 1988).

After several years of apparently successful observations

by the SBUV, it became apparent that most of the longtermchanges in stratospheric ozone indicated by the instrument were not geophysical, but were instead a calibration drift within the instrument (World Meteorological Organization, 1990). The drift was determined to result from

the empirical model for the diffuser reflectance. It was also

found that alternate models for diffuser plate degradation

could be applied to the results of the on-orbit experiment

(Herman et al. 1990), with different models giving different

long-termchanges in stratospheric ozone.

The SBUV/2 instruments on NOAA-9 and NOAA-11

were equipped with a lamp that could be viewed either directly by the spectrometer or indirectly using the surface

of the diffuser assembly (Frederick et al. 1986). By taking

a series of alternating measurements of these two sources,

it is possible to obtain a ratio that gives the reflectance

of the diffuser. Problems with the design of the lamp on

NOAA-9 prohibited the collection of long-termreflectance

measurements of its diffuser. However, corrections to the

design of the NOAA-11 SBUV/2 have allowed long-term

measurements of these diffuser changes. A similar, but

more complicated scheme for monitoring diffuser changes

has been proposed for the Moderate Resolution Imaging

Spectrometer (MODIS) instrument on the Earth Observing Satellite (EOS) AM platform.

The SeaWiFS diffuser plate will be affixed to the SeaStar platformsuch that it faces opposite to the usual velocity vector. Sunlight will reflect off the plate for about

80 seconds as the platformpitches 5◦ while passing over

the South Pole. For the duration of the calibration, the

instrument assembly will be tilted 20◦ aft and the sensor

will scan the diffuser plate for about 10–20 pixels along the

back-scan (Fig. 1).

The solar diffuser response can be characterized by the

bidirectional reflectance distribution function (BRDF) of

the diffuser assembly. This function ranges above and below the nominal overall reflectance of the diffuser and is

used to describe the angular dependent reflective response

of the diffuser plate to incident light. The SeaWiFS diffuser BRDF can be translated to a three-dimensional table

representing the spacecraft pitch, spacecraft yaw, and the

instrument scan angle. It is assumed that the solar flux at

the input of the diffuser assembly remains constant. The

BRDF of the diffuser assembly will probably change with

time as contaminants condense on the reflecting surface.

To account for this change, lunar measurements are required.

The SeaWiFS instrument has eight bands with each

band having four detectors. Each of the 32 detectors has

its own photodiode, current-to-voltage converter, gain selection, and analog-to-digital converter. For each detector,

there will be an electronic calibration pulse at the output of the current-to-voltage converter. The pulse will be

recorded for about 100 pixels as part of the data stream

following the diffuser plate portion of the scan. The electronic calibration pulse will have an amplitude near the

maximum number of counts (1,024 counts for the 10-bit

SeaWiFS data). The pulse provides a measure of interchannel gains and eliminates the need for scanning Earth

targets for gain measurements. The calibration voltage

for the pulse will be summed with the output from the

detector’s current-to-voltage converter. Since the pulse is

applied while the instrument is viewing the black, inner

surface of the instrument housing, the output from the

detector should be zero. However, small changes in the

detector output can be removed by referencing the output fromthe calibration pulse to “zero” values fromthe

readings that immediately precede and follow the pulse.

It is possible to control combinations of the detectors

used in each SeaWiFS band, i.e., froma single detector,

to pairs of detectors, to a combination of all four. For

test purposes on orbit, each detector for individual bands

can be viewed independently. Table 1 gives the five possible TDI configurations. During the initial gain checks,

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Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 1. Scanning angles of SeaWiFS instrument for solar calibrations.

the stability of the calibration voltage can be checked by

cycling through the gain sequence (gi) shown in Table 2.

The set of g1 values before and after each other gain gives

a check of the constancy of the calibration voltage over the

measurement period. For this type of check of relative values, a constant input value (or a well-characterized, slowly

changing value) is necessary. Knowledge of the absolute

value of the input is not required.

Table 1. TDI configurations with the corresponding detector arrangements.

Configuration Detector Arrangement

1 Det1 + Det2 + Det3 + Det4

2 Det1 summed with itself 4 times

3 Det2 summed with itself 4 times

4 Det3 summed with itself 4 times

5 Det4 summed with itself 4 times

Table 2. Gain sequences for TDI configurations.

Start and stop times are in seconds.

Configuration Gain Sequence Start Stop

1 g1, g2, g1, g3, g1, g4, g1 0 7

2 g1, g2, g1, g3, g1, g4, g1 7 14

3 g1, g2, g1, g3, g1, g4, g1 14 21

4 g1, g2, g1, g3, g1, g4, g1 21 28

5 g1, g2, g1, g3, g1, g4, g1 28 35

1 g1, g2, g1, g3, g1, g4, g1 35 42

2 g1, g2, g1, g3, g1, g4, g1 42 49

3 g1, g2, g1, g3, g1, g4, g1 49 56

4 g1, g2, g1, g3, g1, g4, g1 56 63

5 g1, g2, g1, g3, g1, g4, g1 63 70

1 g1, g2, g1, g3, g1, g4, g1 70 77

The scan in the solar calibration mode will produce a

data streamidentical in formto a typical SeaWiFS (high

resolution) Local Area Coverage (LAC) scan. Fig. 2 shows

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R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 2. Response of SeaWiFS channels 5 and 6 during an experimental solar calibration.

the response of two of the SeaWiFS channels for an experimental solar calibration. The diffuser is viewed in the

sensor response for about 400 pixels fromstart to finish,

and the calibration pulse follows about 100 pixels downstream. The anomalously high readings in the first few

hundred pixels (before scanning the diffuser) are a result

of possible solar reflectance contamination from the small

gap between the diffuser and the telescope housings. The

portion of the scan that views the diffuser exhibits a nearly

linear ramping to and from a maximum plateau. The ramp

occurs as the instrument scans from deep space, onto the

diffuser and then onto the black, inner-surface of the back

of the instrument. As can also be seen in Fig. 2, the calibration pulse produces a curved signal as it transitions to

the maximum value around pixel number 700 and again

as it transitions to the background value around pixel 840.

This curved response is a result of a bandwidth reduction

which is applied to reduce high frequency noise in the signal.

2.2.1 Diffuser Calibration Model

The solar calibration model is designed to simulate the

LAC data streamof a solar calibration for various test scenarios. Solar irradiances fromNeckel and Labs (1984) for

selected channels are read into the model from a database

on CALVAL. The irradiance data are integrated to the SeaWiFS bands using a full-width at half-maximum (FWHM)

approximation. The model simulates a diffuser scan by

considering the intersection area of two circles which are

in relative movement. The circles represent the instantaneous field-of-view (IFOV) of the sensor and of the aperture covering the solar diffuser plate. In the algorithm, the

circles are aligned such that the y locations of the circle

centers are identical, and the initial x locations of the circle centers are set by the user. The IFOV circle is then

moved in a stepwise fashion in the x direction relative to

the aperture circle and the intersection area is computed

for each step. The intersection area Ai is defined as follows

(see also Fig. 3):

Ai = r1

2(θ1 − sin θ1)

2 +

r2

2(θ2 − sin θ2)

2 , (2)

where r1 is the radius of circle one, r2 is radius of circle

two, θ1 is the intersection angle of circle one, and θ2 is

intersection angle of circle two.

The normalized intersection area is obtained by dividing Ai by the area of the smaller circle, which defines the

maximum intersection area. The normalized areas of intersection for each step are translated to ramping coefficients, i.e., the ratio of the sampled value to the actual

value, which are then applied as multiplicative factors to

each pixel in succession along the scan. This intersection

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Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 3. The area of intersecting circles, Ai.

Fig. 4. The initial GUI for the solar calibration model.

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R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

algorithm produces a symmetric pattern for a scan with

quasi-linear ramp-up and ramp-down intervals bracketing

a period of fixed maximum output. A simulated calibration pulse may also be inserted in the modeled signal following the above diffuser pattern. The simulated pulse produces a stepwise jump in the signal and, therefore, does not

accurately model the curved response produced by bandwidth reduction in the transition to maximum and again

to background (see Fig. 2).

Fig. 4 shows the solar calibration model GUI. These

input values may be adjusted to simulate various calibration scenarios for selected SeaWiFS channels (CHANNEL).

For instance, the lengths and amplitudes of both the sensor response to the diffuser and the calibration pulse can

be adjusted by modifying the input values on the GUI. The

center of the intersecting circles (X CENTER OF IFOV and

X CENTER OF APERTURE), the sizes of the circles (RADIUS

OF IFOV and RADIUS OF APERTURE), and the scan movement (INCREMENT OF IFOV) determine the lengths of the

ramp-up, maximum, and ramp-down intervals for the simulated diffuser measurement. ENTER FACTOR modifies the

ramping coefficients by applying multiplicative factors to

the coefficients determined by the above circle intersection algorithm. In addition, the value entered in ALBEDO

OF DIFFUSER is applied as a multiplicative factor and can

therefore be used to simulate diffuser degradation.

ZENITH ON DIFFUSER and AZIMUTH ON DIFFUSER refer

to the angle of the incident sunlight on the diffuser and are

used for retrieving BRDF values froma three-dimensional

lookup table. The third dimension in this table is linked

to the scan angle of the sensor. This value is a function

only of pixel number and is computed automatically in

the algorithm. The calibration pulse can be modeled using MAGNITUDE OF CALIBRATION PULSE % which sets the

maximum value for a pulse by applying a percentage of the

Neckel and Labs (1984) irradiance for the given channel.

START OF CALIBRATION PULSE and END OF CALIBRATION

PULSE assigns start and end pixel numbers for the pulse

within the scan.

2.2.2 Diffuser Calibration Model Results

Figs. 5–7 show three representations of the modeled

instrument response of a solar calibration for the criteria

listed in Fig. 4 and a flat BRDF field, i.e., all BRDF values set to unity. In this example, X CENTER OF IFOV, X

CENTER OF APERTURE, and INCREMENT OF IFOV are chosen in such a manner as to produce about a 375 pixel startto-finish response of the diffuser induced signal. The simulated calibration pulse is modeled to be 150 pixels wide

with a maximum amplitude equal to the saturation radiance value. The total calibration is simulated to span 82.4

seconds which corresponds to 494 SeaWiFS scans. Additional ramping to phase in and out of the lunar sweep is

also modeled using intersecting circles producing a total of

592 scans. Fig. 5 shows a nearly linear ramping to maximum and back for the diffuser portion of a single scan

agreeing in general with the laboratory results shown in

Fig. 2. Also included in this figure is the simulated calibration pulse.

In Fig. 6, a two-dimensional representation of the calibration is shown with the x coordinate representing the

instrument scan and the y coordinate representing time. A

three-dimensional representation of the same output is provided in Fig. 7. Fig. 8 shows the same calibration, except

with a randomBRDF field applied as a three-dimensional

lookup table. The three dimensions on the diffuser represent the incident solar zenith angle, the incident solar

azimuth angle, and the pixel number (viewing angle of

the sensor). The prelaunch BRDF measurements from the

Hughes/Santa Barbara Research Center (SBRC) will be

substituted as input to the solar model when testing is

completed. The addition of this information to the model

will prove useful in tracking post-launch diffuser and sensor

performance.

2.3 Lunar Calibration

Observations of the diffuser assembly will not be used

to monitor long-term changes in the instrument’s radiometric sensitivity. Rather, for this purpose, the instrument will make a series of measurements of the surface of

the moon during the lifetime of the SeaWiFS mission. It is

assumed that the lunar surface has stabilized over geologic

time and that the reflectance of the surface will not change

over the 5-year mission of SeaWiFS. It is also assumed that

the solar irradiance will be known fromsources outside of

the SeaWiFS measurement. Solar diffuser measurements

will be used to fill in the gaps between lunar measurements,

which cannot be made more often than once per month.

The diffuser measurements will be normalized to the lunar

values at the measurement times.

To maintain consistency, lunar calibrations can occur

only about once a month when the lunar phase angle is

within 7◦ of full phase. When this criterion is satisfied

on selected orbits, the SeaStar platformwill undergo a

360◦ tilt maneuver on the back-orbit allowing the sensor to

produce a standard LAC data streamof the lunar surface.

Given a nominal SeaStar pitch rate of about 0.15◦ s−1, it is

expected that the moon will encompass about 7 SeaWiFS

pixels at the lunar equator and about 20 SeaWiFS scan

lines fromlunar pole-to-lunar pole.

2.3.1 Lunar Calibration Model Description

The lunar calibration model simulates the sensor response of a SeaWiFS lunar viewing for varying instrument

and spacecraft conditions. Table 3 provides a synopsis of

the user interfaces for the model. The means and standard deviations for both the integrated scanned moon and

the scanned central nine pixels are written to a specified

output file which is used for subsequent statistical analysis. An output display is also produced, consisting of the

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Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 5. A single scan of the solar diffuser measurement (including a calibration pulse) produced by the

solar calibration model.

Fig. 6. A two-dimensional representation of the solar diffuser measurement (including a calibration

pulse) produced by the solar calibration model.

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R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 7. A three-dimensional representation of the solar diffuser measurement (including a calibration

pulse) produced by the solar calibration model.

Fig. 8. The same as Fig. 7 except with a random BRDF field read as input for the solar calibration

model.

9
Modeling of the SeaWiFS Solar and Lunar Observations

original lunar image and the output following each model

step listed in Table 3 (scanned image, scanned image with

bright-to-dark response, and scanned image with brightto-dark and dark-to-bright response).

Table 3. User interfaces for the lunar calibration

model.

Interface Function Inputs

SCANMOON Simulates the Image size,

image of the Scan resolution,

moon recorded Scan position,

for a lunar Channel,

calibration. Sensor degradation,

Gain, and

Output filename.

DRK2BRT Simulates the Ringing and

dark-to-bright Ramp-up factors.

response of

the sensor.

BRT2DRK Simulates the Ringing and

bright-to-dark Ramp-down factors.

response of

the sensor.

Fig. 9 shows the initial GUI of the lunar calibration

model. The size of the input image is specified with X

IMAGE SIZE and Y IMAGE SIZE, respectively. The scan

pixel size and scan line sampling are adjustable by setting

SCANSIZE and SCANSTEP, respectively. Initial pixel and

line position are determined by START X SCAN and START

Y SCAN. The simulated SeaWiFS pixels are constructed by

computing the mean of all input image pixels within a

square of size SCANSIZE × SCANSIZE. The corner of each

square is determined by pointers incremented in the x direction by SCANSIZE and in the y direction by SCANSTEP.

This separation of x and y pointer movement allows oversampling or subsampling in the y direction, thus permitting the modeling of platform rotation rates.

Variance in pixel registration can be tested using START

X SCAN and START Y SCAN to initialize the pointer to a

pixel and line on the input image. Loss of instrument

sensitivity can be simulated using SENSOR DEGRADATION,

which applies the specified percent decrease in range to

the input image. Selecting CHANNEL initiates a query to

the CALVAL database to obtain the wavelength dependent solar irradiance fromNeckel and Labs (1984). A gain

factor can be input to the model by entering a value in the

ENTER GAIN prompt.

The user interfaces shown in Figs. 10 and 11 provide

inputs to routines for simulating the dark-to-bright and

bright-to-dark target responses of the instrument. The

ramp-up and ramp-down factors are specified by the ENTER

FACTOR prompts. A ringing response is triggered when the

absolute value of the difference in successive values exceeds

THRESHOLD. This ringing will last for N PERIOD pixels and

has a damped periodic function specified in ENTER PERIOD

and AMPLITUDE. For example, the following events occur if

the values shown in Fig. 10 are chosen:

1. If the difference in successive pixels exceeds the

value of THRESHOLD, ramping occurs over the

subsequent five pixels. These pixels are factored by 0.3, 0.85, 0.95, 0.98, and 1.00 (ENTER

FACTOR), respectively, simulating the response to

a bright target. If THRESHOLD is not exceeded,

then the five pixels are factored by the quantity:

FACTOR/(∆P/THRESHOLD), where ∆P is the difference in successive pixels. If this value exceeds

1.00 it is set equal to 1.00.

2. If the difference in successive pixels exceeds the

value of THRESHOLD, a delayed ringing response

is triggered. The ringing commences when successive downstreampixels remain equal or decrease in magnitude. The ringing occurs for 6

pixels (N PERIOD) employing a periodic wave of

8π rad. (ENTER PERIOD) with wave amplitude

specified as 1 mW cm−2 μm−1 sr−1 (AMPLITUDE).

The wave function is characterized by a damped

sine wave using a sin(x)/x function, where x is

the pixel number within the scan line.

The user can adjust the frequency, amplitude, and duration of the ringing by altering the input values for the

lunar model. Fig. 12 shows the modeled ringing of a single

scan for four selected scenarios. High amplitude and low

amplitude ringing are shown in panels a) and b), respectively; variations in the ringing periodicity are shown in

panels c) and d).

2.3.2 Lunar Calibration Model Results

A high resolution (16 bit) lunar image at 3◦ phase

(Kieffer, pers. comm.) was read as input for the lunar calibration model. Fig. 13 shows an example of the display

output obtained fromthe model. The upper left panel

shows the original Kieffer moon, the lower left shows the

scanned moon, the upper right shows the scanned moon

with the dark-to-bright response applied, and the lower

right shows the scanned moon with both the dark-to-bright

and the bright-to-dark responses applied. In this example,

the model input values were adjusted such that the scanned

moon was 7 pixels wide and 22 scan lines high. The total

integrated mean of the moon and the mean of the central

nine pixels are also displayed for each model step.

A test was performed using the lunar calibration model

to determine the effects on the calibration of variable pixel

registration of the lunar surface. A total of 15 runs were

produced in which x pixel positions (along scan lines) were

moved at one-fourth SeaWiFS pixel increments while holding the y pixel position (scan lines) constant; and y pixel

positions were then moved at one-twelfth pixel increments

while holding the x pixel position constant. For this series

of runs, an extreme case of ringing was applied. The initial

10
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 9. Initial GUI for the lunar calibration model.

11
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 10. GUI for the dark-to-bright instrument response in the solar calibration model.

12
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 11. GUI for the bright-to-dark instrument response in the solar calibration model.

13
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 12. Ringing fromthe lunar calibration model for a) high amplitude ringing, b) low amplitude

ringing. Note: the dashed line is the target and the solid line is the response.

14
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 12. (cont.) Ringing fromthe lunar calibration model for c) high frequency ringing, and d) low

frequency ringing.

15
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 13. Display output fromthe lunar calibration model.

16
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 14. Stability of the lunar measurements as a function of pixel registration for the integrated lunar

mean (solid line) and the central 9-pixel mean (dashed line).

Fig. 15. Stability of the lunar measurements as a function of the number of scan lines for the integrated

lunar mean (solid line) and the central 9-pixel mean (dashed line).

17
Modeling of the SeaWiFS Solar and Lunar Observations

amplitude of the ringing was set to 1 mW cm−2 μm−1 sr−1,

and the ringing period was set to 8π rad. The results were

tabulated for each step of the model for both the integrated

image mean and the central 9-pixel (3×3) mean (Table 4).

Standard deviations (σ) of the model output over the runs

were computed for each model step as a measure of stability. Fig. 14 shows the retrieved mean radiances for both

the mean integrated image and the mean central 9 pixels

as a function of pixel registration. These results indicate

the retrieved radiances fromthe lunar calibration are more

stable, as indicated by the standard deviations, for the integrated mean than the central 9-pixel mean. The relative

instability of the central 9-pixel mean among calibrations

is most likely a result of variable lunar reflectance as the

3 × 3 sampling box changes position with regard to the

lunar surface.

Another test, using the lunar calibration model, was

conducted to determine the effects of varying the number of scan lines across the moon. This test illustrates

the impact of variable platform rotation rates upon lunar

calibrations. The results are tabulated in Table 5 and displayed in Fig. 15. The integrated mean is again found to

be more stable than the central 9-pixel mean in tracking

lunar reflectance.

These modeling studies can be compared to a groundbased sweep of the moon by the SeaWiFS instrument at

Goleta, California on December 9, 1992. On this date,

the moon was sampled shortly after a lunar eclipse giving

a very small lunar phase angle. Fig. 16 shows the Kieffer

moon, the modeled lunar scan, and four observed sweeps of

the moon. The observed lunar scans were not corrected for

atmospheric interference, which possibly accounts for the

discrepancies between the observations and the modeled

scan. The scan at 1922 Pacific Standard Time (PST) was

scanned fromthe top to the bottomproducing an upsidedown view in comparison to the other images in the figure.

An important consideration for the solar and lunar observation data is the potential for ghost images in the optical path of the instrument. These artifacts occur around

bright targets and are a result of reflections off of the polarization scrambler, which is the third component in the

SeaWiFS optical path (Fig. 17). The light reflected off the

polarization scrambler exhibits two artificial images on either side of pixels in the direction perpendicular to the

scan (Holmes, pers. comm.) as shown in Fig. 18. These

artifacts contain about 3% of the signal and are confined

to about 4 pixels of the target edge. In Fig. 16, the observed lunar scans exhibit little or no evidence of ghost

images. Fig. 19 shows a three-dimensional representation

of the lunar sweep fromopposite perspectives at 1922 PST

for channel 6. In this figure, the natural logarithmof SeaWiFS counts has been plotted as the vertical coordinate.

There appears to be some elevated values in the direction

perpendicular to the scan frompixels 9–15.

Side-to-side differences in the half-angle mirror (Fig. 17)

will be characterized at SBRC before launch. There may

be changes in the side-to-side characteristics of the halfangle mirror during the course of the mission. The change

in the average for the two mirror sides cannot be determined independently on orbit and must be part of the

long-termsensitivity of the instrument. The average is

an inherent part in the 20 scans that cover the surface

of the moon and in the 480 scan lines of a diffuser measurement. The magnitude of the side-to-side differences

in the half-angle mirror, however, can be tracked during

standard measurements of the instrument’s diffuser. During each diffuser measurement, there are 240 side1-side2

pairs of half-angle differences to be used for calculations.

These differences transforminto scan line-to-scan line differences in the ocean measurements. The magnitude of

the scan-to-scan differences will be tracked in the onboard

calibration information although, strictly speaking, these

differences are not part of the radiometric calibration for

the instrument.

2.3.3 Additional Considerations

Several factors are likely to impact the measured lunar

reflectance with the SeaWiFS instrument. One of these

factors is the eccentricity of the lunar orbit. The lunar orbit places the moon 356,410 km from the Earth at perigee,

and 406,697 kmat apogee. Over the course of a lunar orbit, the Earth-moon distance (ξEM) can be expressed as

(Duffett-Smith 1979):

ξEM = a(1 − e2)

1 + e cos[M

m + 6.289 sin(Mm)] (3)

where a is the semi major axis, e is the eccentricity, and

M

m is the corrected mean anomaly, which is a function of

date, and refers to an imaginary moon in a circular orbit.

Assuming an inverse square distance relationship for

the observed lunar reflectance, the amount of lunar radiance measured by SeaWiFS can vary by as much as 30%

over all possible full moon orbital positions. Observed lunar radiance may also be dependent, to a lesser extent, on

the moon-sun distance. Lunar observations will therefore

require normalization to account for the variable Earthmoon and sun-moon distances. In addition to the variable radiance, pixel registration will vary as a result of the

change in distance between the sensor and the moon. This

latter consideration may be allayed by using the integrated

lunar surface for the SeaWiFS observations, as discussed

in Section 2.3.2. Additional functionality will be added

to the lunar calibration model to simulate the potential

effects of an elliptical orbit.

Libration is another possible source of uncertainty for

the SeaWiFS lunar observations. The major motions of

the Earth-moon system allow observers on Earth, over a

period of time, to view 59% of the lunar surface, even

though the same side of the moon is always facing the

Earth. Longitudinal libration occurs because the moon

18
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Table 4. Lunar observation model results for testing calibration stability as a function of variable pixel registration.

All units are in mW cm−2 μm−1 sr−1. As a measure of stability, standard deviations (σ) of the model output over the

runs are reported.

x Pixel y Pixel Integrated Central Nine

Offset Offset Scan Dark-Bright Bright-Dark Scan Dark-Bright Bright-Dark

0 0 3.71 2.83 2.33 5.02 5.19 4.17

1/4 0 3.76 2.86 2.31 5.16 5.25 3.80

2/4 0 3.81 2.86 2.30 5.01 4.45 5.26

3/4 0 3.76 2.74 2.26 4.88 5.21 4.71

0 1/12 3.76 2.89 2.37 5.00 5.24 4.14

0 2/12 3.76 2.87 2.24 4.98 4.96 4.23

0 3/12 3.71 2.84 2.32 4.45 4.89 4.15

0 4/12 3.71 2.81 2.32 5.03 5.22 4.18

0 5/12 3.76 2.88 2.37 5.01 5.15 4.15

0 6/12 3.76 2.87 2.36 4.98 4.99 4.24

0 7/12 3.72 2.84 2.33 4.96 4.97 4.17

0 8/12 3.76 2.86 2.32 4.93 4.84 4.18

0 9/12 3.71 2.83 2.33 5.01 5.17 4.16

0 10/12 3.69 2.90 2.36 4.99 5.00 4.25

0 11/12 3.76 2.89 2.36 4.96 4.92 2.21

Column σ 0.03 0.04 0.04 0.06 0.14 0.33

Table 5. Lunar observation model results for testing calibration stability as a function of a variable number of scan

lines. All units are in mW cm−2 μm−1 sr−1. As a measure of stability, standard deviations (σ) of the model output

over the runs are reported.

Number of Integrated Central Nine

Scan Lines Scan Dark-Bright Bright-Dark Scan Dark-Bright Bright-Dark

1 3.60 3.12 3.22 4.36 4.52 4.52

2 4.24 3.47 3.29 4.96 5.34 5.34

4 4.18 3.21 3.16 5.31 5.42 5.51

6 3.60 2.93 2.86 5.43 5.71 5.75

8 3.81 3.05 3.02 4.90 5.05 5.08

10 3.64 3.05 3.02 4.96 4.96 5.18

12 3.64 3.04 3.02 4.10 5.26 5.27

14 3.82 3.14 3.09 4.91 5.35 5.37

16 3.73 3.08 3.06 4.98 5.08 5.10

18 3.71 3.12 3.05 5.01 5.22 5.26

20 3.70 3.10 3.03 5.02 5.26 5.30

22 3.75 3.13 3.06 4.96 5.08 5.13

24 3.72 3.12 3.06 4.98 5.12 5.16

26 3.72 3.12 3.08 5.01 5.22 5.30

28 3.77 3.14 3.08 4.98 5.03 5.05

30 3.70 3.05 3.01 4.97 5.01 5.04

Column σ 0.18 0.11 0.10 0.22 0.26 0.26

19
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 16. Comparison of modeled lunar scan to ground-based measurements.

20
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 17. A schematic of the SeaWiFS optical layout.

Fig. 18. Ghost images induced by the polarization scrambler.

21
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 19. A three-dimensional representation of a) the lunar sweep at 1922 PST for channel 6 and b)

the same scene from the opposite perspective (180◦ difference).

22
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

Fig. 20. GUI for the calibration data and instrument telemetry quality control routines.

23
Modeling of the SeaWiFS Solar and Lunar Observations

Fig. 21. GUI for the calibration data and instrument telemetry trend analysis routines.

24
R. Woodward, R. Barnes, C. McClain, W. Esaias, W. Barnes, and A. Mecherikunnel

rotates on its axis at a constant rate but travels around

the Earth at varying velocities due to the elliptical orbit.

Latitudinal libration is a result of the 6.7◦ tilt in the lunar

axis with regards to the Earth ecliptic. The obvious effect

of libration is that the sensor will not always be viewing

the same complete face of the moon. To correct for this

effect, a database of lunar observations can be populated

with respect to libration.

3.0 QUALITY CONTROL

Quality control routines will be essential for ensuring

the integrity of the calibration data. It is anticipated that

most of this activity will be activated in an automated

fashion. However, user intervention routines can be implemented using interfaces such as the prototype presented in

Fig. 20. Statistics are generated by using this interface to

check for outliers or unusual patterns in the data. The user

can select from three types of data average: mean, mode,

and median. The standard deviation can be generated to

check for unexpected variance in the data. Outliers can be

determined by selecting for the minimum and maximum

value.

The user can also choose to specify a valid range of

data. Unusual or unexpected patterns in the data can be

checked by selecting the histogramoption. The example

in Fig. 20 shows a histogramapplied to radiances froma

simulated lunar calibration.

4.0 TREND ANALYSIS

Trends in both the calibration and instrument telemetry data will require analysis, since patterns in these data

may display drift or periodicity. An accurate resolution

of these effects will allow corrective techniques to be applied to the data. For example, polynomial or periodic

functions may be implemented to compensate for any observed trends.

Fig. 21 shows a prototype interface for trend analysis.

The selections activate routines that are designed to both

characterize and compensate for trends in the instrument

calibration and telemetry data. In the example from this

figure, a simulated degradation in the lunar calibration

has been plotted as a function of day. Since a calibration

reading may be composed of the mean of several pixels,

the user can also track the trend of calibration scatter by

plotting the standard deviation as a function of time.

Periodicity in the data can be analyzed by selecting

the AUTOCORRELATION AND SPECTRAL ANALYSIS and MEM

- PERIODICITY options. The maximum entropy method

(MEM) is used to deduce periodicity when data are not

evenly spaced in time. Regressions and cross-correlations

can be generated to check for relationships among calibration or telemetry parameters. Finally, trends in the data

can be removed through the use of polynomial fitting algorithms.

5.0 RECOMMENDATIONS

Modeling results fromthe lunar calibration indicate the

integrated mean of the entire lunar surface is a more stable measure than the mean of a central grouping of pixels.

This conclusion was reached by considering possible uncertainties in the pixel registration and platformrotation

rates. In addition, there may be some evidence of optical artifacts, i.e., ghost images, in the SeaWiFS signals.

The magnitude of these artifacts is small in comparison to

the lunar signals, but the impact on calibrations remains

uncertain. More analysis of ghost images may be required.

Another consideration is to use the prelaunch sensor

characterizations, when available fromthe SBRC, to modify the solar and lunar models. The models can be made

to conformto the new data and to test the transfer of

prelaunch data to orbit. An additional enhancement to

the models will include the input of the actual BRDF table fromSBRC. Following launch, the models can be used

to evaluate the actual performance of the sensor-diffuser

system.

Acknowledgments

The authors would like to thank Watson Gregg for use of the

solar irradiance data integrated to SeaWiFS bands.

Glossary

BRDF Bidirectional Reflectance Distribution Function

CALVAL Calibration/Validation

CZCS Coastal Zone Color Scanner

EOS Earth Observing Satellite

FWHM Full-Width at Half-Maximum

GSFC Goddard Space Flight Center

GUI Graphical User Interface

IDL Interactive Data Language

IFOV Instantaneous Field-Of-View

LAC Local Area Coverage

MEM Maximum Entropy Method

MODIS Moderate Resolution Imaging Spectrometer

NASA National Aeronautics and Space Administration

NIMBUS Not an acronym—a series of NASA experimental

weather satellites containing a wide variety of atmosphere, ice, and ocean sensors.

NIST National Institute of Standards and Technology

NOAA National Oceanic and Atmospheric Administration

PST Pacific Standard Time

SBRC (Hughes) Santa Barbara Research Center

SBUV Solar Backscatter Ultraviolet Sensor

SeaWiFS Sea-viewing Wide Field-of-view Sensor

SGI Silicon Graphics, Incorporated

TDI Time Delay Integration

25
Modeling of the SeaWiFS Solar and Lunar Observations

Symbols

a Semi-major axis of the Earth’s orbit.

Ai The intersection area.

D Sequential day of the year.

e Orbit eccentricity of the Earth.

F0 Solar irradiance corrected for the Earth-sun distance.

F0 Mean solar irradiance.

M

m The corrected mean orbit anomaly of the Earth,

which is a function of date, and refers to an imaginary moon in a circular orbit.

r1 The radius of circle one.

r2 The radius of circle two.

x The pixel number within a scan line.

∆P The difference in successive pixels.

θ1 The intersection angle of circle one.

θ2 The intersection angle of circle two.

ξEM The distance between the Earth and the moon.

σ Standard deviation of a set of data values.

References

Cebula, R.P., H. Park, and D.F. Heath, 1988: Characterization

of the Nimbus-7 SBUV radiometer for the long term monitoring of stratospheric ozone, J. Atmos. Ocean. Technol.,

5, 215–227.

Duffett-Smith, P., 1979: Practical astronomy with your calculator, Cambridge University Press, New York, NY, 129 pp.

Frederick, J.E., R.P. Cebula, and D.F. Heath, 1986: Instrument characterization for detection of long-term changes in

stratospheric ozone: An analysis of the SBUV/2 radiometer, J. Atmos. Ocean. Technol., 3, 472–480.

Gordon, H.R., D.K. Clark, J.W. Brown, O.B. Brown, R.H.

Evans, and W.W. Broenkow, 1983: Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determination and CZCS estimates, Appl.

Opt., 22, 20–36.

Herman, J.R., R.D. Hudson, and G.N. Serafino, 1990: An

analysis of the 8 year trend in ozone depletion from alternate models of SBUV instrument degradation, J. Geophys.

Res., 95, 7,403–7,416.

McClain, C.R., W.E. Esaias, W. Barnes, B. Guenther, D. Endres, S. Hooker, G. Mitchell, and R. Barnes, 1992: Calibration and validation plan for SeaWiFS, NASA Tech.

Memo. 104566, Vol. 3, S.B. Hooker and E.R. Firestone,

Eds., 41 pp.

Neckel, H. and D. Labs, 1984: The solar radiation between 3300

and 12500  ̊A, SolarPhys., 90, 205–258.

World Meteorological Organization, 1990: Report of the International Ozone Trends Panel, 1988: World Meteorological Organization Global Ozone Research and Monitoring

Project, Report No. 18, 2 Vols., Geneva, Switzerland.

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 Unclassified Unclassified Unclassified Unlimited

 SeaWiFS, Oceanography, Modeling, Solar Observations, Lunar Observations, 26

 Calibration

Robert H. Woodward and Elaine R. Firestone: General Sciences Corporation, Laurel, Maryland;

Robert A. Barnes: CHEMAL, Inc., Wallops Island, Virginia

Report is available from the Center for AeroSpace Information (CASI),

7121 Standard Drive, Hanover, MD 21076–1320; (301)621-0390

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Subject Category 48

13. ABSTRACT (Maximum 200 words)

National Aeronautics and Space Administration

Washington, D.C. 20546–0001 TM–104566, Vol. 10

Laboratory for Hydrospheric Processes

Goddard Space Flight Center 93B00085

Greenbelt, Maryland 20771

6. AUTHOR(S)

 Robert H. Woodward, Robert A. Barnes, Charles R. McClain, Wayne E. Esaias,

 William L. Barnes, and Ann T. Mecherikunnel

 Series Editors: Stanford B. Hooker and Elaine R. Firestone

Post-launch stability monitoring of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) will include periodic sweeps of

both an onboard solar diffuser plate and the moon. The diffuser views will provide short-term checks and the lunar views

will monitor long-term trends in the instrument's radiometric stability. Models of the expected sensor response to these

observations were created on the SeaWiFS computer at the National Aeronautics and Space Administration's (NASA)

Goodard Space Flight Center (GSFC) using the Interactive Data Language (IDL) utility with a graphical user interface

(GUI). The solar model uses the area of intersecting circles to simulate the ramping of sensor response while viewing the

diffuser. This model is compared with preflight laboratory scans of the solar diffuser. The lunar model reads a high

resolution lunar image as input. The observations of the moon are simulated with a bright target recovery algorithm that

includes ramping and ringing functions. Tests using the lunar model indicate that the integrated radiance of the entire lunar

surface provides a more stable quantity than the mean of radiances from centralized pixels. The lunar model is compared to

ground-based scans by the SeaWiFS instrument of a full moon in December 1992. Quality assurance and trend analyses

routines for calibration and for telemetry data are also discussed.