NASA Technical Memorandum 104566, Vol. 27

SeaWiFS Technical Report Series

Stanford B. Hooker, Elaine R. Firestone, and James G. Acker, Editors

Volume 27, Case Studies for SeaWiFS

Calibration and Validation, Part 3

James L. Mueller, Robert S. Fraser, Stuart F. Biggar, Kurtis J. Thome,

Philip N. Slater, Alan W. Holmes, Robert A. Barnes, Christian T. Weir,

David A. Siegel, David W. Menzies, Anthony F. Michaels,

and Guillermo Podesta

May 1995
NASA Technical Memorandum 104566, Vol. 27

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

James G. Acker, Technical Editor

Hughes STX, Lanham, Maryland

Volume 27, Case Studies for SeaWiFS Calibration

and Validation, Part 3

James L. Mueller

San Diego State University, San Diego, California

Robert S. Fraser

NASA Goddard Space Flight Center, Greenbelt, Maryland

Stuart F. Biggar, Kurtis J. Thome, and Philip N. Slater

University of Arizona, Tucson, Arizona

Alan W. Holmes

Santa Barbara Research Center, Goleta, California

Robert A. Barnes

ManTech Environmental Technology, Inc., Wallops Island, Virginia

Christian T. Weir, David A. Siegel, and David W. Menzies

University of California at Santa Barbara, Santa Barbara, California

Anthony F. Michaels

Bermuda Biological Station for Research, Ferry Reach, Bermuda

Guillermo Podesta

University of Miami, Miami, Florida

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

1995
Case Studies for SeaWiFS Calibration and Validation, Part 3

Preface

The scope of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Calibration and Validation Program

encompasses a broad variety of topics, as evidenced by the contents of two previous case studies volumes in

the SeaWiFS Technical Report Series—Volumes 13 and 19. Each case studies volume contains several chapters

discussing topics germane to the Calibration and Validation Program. Volume 27, the third collection of case

studies, further demonstrates both the breadth and complexity of the issues that the Program must address,

and provides further justification for a comprehensive calibration and validation effort.

The chapters in this volume present discussions of:

a) Results on the measurement of immersion coefficients for submersible radiometers;

b) The effect of oxygen absorption on the 765 nm SeaWiFS channel;

c) The results of the second SeaWiFS ground-based solar calibration experiment, which was performed

after the instrument was modified to reduce internal stray light;

d) Ship shadow effects on subsurface radiance and irradiance measurements; and

e) The definition of the SeaWiFS data day for level-3 data binning.

Greenbelt, Maryland — C. R. McClain

January 1995

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Table of Contents

Prologue .................................................................................................1

1. Comparison of Irradiance Immersion Coefficients for Several

Marine Environmental Radiometers (MERs) ........................................................3

1.1 Introduction ....................................................................................... 3

1.2 Method and Results ................................................................................4

1.3 Discussion ......................................................................................... 4

2. The Effect of Oxygen Absorption on Band-7 Radiance ............................................. 16

2.1 Introduction ...................................................................................... 16

2.2 Theory ........................................................................................... 16

2.3 Conclusion ....................................................................................... 19

3. Second SeaWiFS Preflight Solar Radiation-Based Calibration Experiment ......................... 20

3.1 Introduction ...................................................................................... 20

3.2 Experimental Method .............................................................................20

3.3 Results ........................................................................................... 21

3.4 Discussion ........................................................................................ 22

4. In Situ Evaluation of a Ship’s Shadow ............................................................ 25

4.1 Introduction ...................................................................................... 25

4.2 Experimental Methods ............................................................................26

4.3 Results ........................................................................................... 27

4.3.1 Simultaneous Comparison ........................................................................ 27

4.3.2 Multi-Distance Comparison .......................................................................28

4.4 Discussion ........................................................................................ 28

5. SeaWiFS Global Fields: What’s In a Day? ........................................................ 34

5.1 Introduction ...................................................................................... 34

5.2 Temporal Definition .............................................................................. 34

5.3 Spatial Definition .................................................................................35

5.3.1 Beginning of the Data Day ....................................................................... 36

5.3.2 Advantages of the Spatial Definition .............................................................. 38

5.3.3 An Alternative Explanation ...................................................................... 40

5.4 Other Issues ...................................................................................... 41

Glossary ...............................................................................................43

Symbols ................................................................................................ 43

References ............................................................................................ 43

The SeaWiFS Technical Report Series ............................................................ 44

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Abstract

This document provides brief reports, or case studies, on a number of investigations sponsored by the Calibration and Validation Team (CVT) within the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project.

Chapter 1 describes a comparison of the irradiance immersion coefficients determined for several different marine environmental radiometers (MERs). Chapter 2 presents an analysis of how light absorption by atmospheric

oxygen will influence the radiance measurements in band 7 of the SeaWiFS instrument. Chapter 3 gives the

results of the second ground-based solar calibration of the instrument, which was undertaken after the sensor

was modified to reduce the effects of internal stray light. (The first ground-based solar calibration of SeaWiFS

is described in Volume 19 in the SeaWiFS Technical Report Series.) Chapter 4 evaluates the effects of ship

shadow on subsurface irradiance and radiance measurements deployed from the deck of the R/V Weatherbird

II in the Atlantic Ocean near Bermuda. Chapter 5 illustrates the various ways in which a single data day of

SeaWiFS observations can be defined, and why the spatial definition is superior to the temporal definition for

operational usage.

Prologue

The purposes of the Sea-viewing Wide Field-of-view

Sensor (SeaWiFS) Project is to obtain valid ocean color

data of the world ocean for a five-year period, to process

that data in conjunction with ancillary data to meaningful biological parameters, and to make that data readily

available to researchers. The National Aeronautics and

Space Administration (NASA) Goddard Space Flight Center (GSFC) will develop a data processing and archiving

system in conjunction with the Earth Observing System

Data and Information System (EOSDIS), which includes

a ground receiving system; EOSDIS will oversee a calibration and validation effort which is designed to ensure the

integrity of the final products.

The Calibration and Validation Team (CVT) has three

main tasks:

1) Calibration of the SeaWiFS instrument;

2) Development and validation of the operational

atmospheric correction algorithm; and

3) Development and validation of the derived product algorithms, such as chlorophyll a concentration.

Some of this work will be done internally at GSFC, while

the remainder will be done externally at other institutions. NASA and the Project place the highest priority

on assuring the accuracy of derived water-leaving radiances globally, and over the duration of the entire mission.

If these criteria are met, the development of global and

regional biogeochemical algorithms can proceed on many

fronts. These various activities are discussed in detail in

The SeaWiFS Calibration and Validation Plan (McClain

et al. 1992).

Because many of the studies and other works undertaken with the Calibration and Validation Program are

not extensive enough to require dedicated volumes of the

SeaWiFS Technical Report Series, the CVT has decided to

publish volumes composed of brief, but topically specific,

chapters. Volume 13 was the first volume, and consists

primarily of contributions related to atmospheric correction methodologies, ancillary data sets required for level-2

processing of Coastal Zone Color Scanner (CZCS) and SeaWiFS data, laboratory techniques for instrument calibration relevant to calibration round-robins, and field observations designed for transferring the prelaunch calibration

to orbit, and in interpreting the on-orbit lunar calibration

data. The second case studies volume, Volume 19, contains chapters on atmospheric and glint corrections, solar-,

lunar-, and integrating sphere optical measurements, data

format considerations, and the use of ancillary data (including surface wind velocities) in SeaWiFS processing.

Volume 26 is the third in the set of such volumes. A short

synopsis of each chapter in this volume is given below.

1. Comparison of Irradiance Immersion

Coefficients for Several

Marine Environmental Radiometers (MERs)

This chapter describes how spectral immersion coefficients were measured experimentally for 12 irradiance collectors on underwater profiling radiometers. These coefficients are used to convert spectral radiance responsivity

calibration factors, measured in air, for use underwater.

At any given wavelength, the immersion coefficients typically had standard deviations between collectors ranging

from 3–5%. The total variations at some wavelengths were

as large as 10%. Repeated measurements on several of

the collectors showed that experimental uncertainty is not

greater than 1%. The primary conclusion of this study is

that accurate underwater radiometry absolutely requires

experimental characterization of each individual irradiance

collector, rather than assuming a value based solely on its

design and material specifications.

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Case Studies for SeaWiFS Calibration and Validation, Part 3

2. The Effect of Oxygen Absorption

on Band-7 Radiance

Atmospheric oxygen absorbs about 13% of the available

sunlight reflected from the Earth in band 7 of the SeaWiFS

instrument. If a correction is made for the average amount

of absorption, then the measured radiance would vary by

±0.004 for a two standard deviation (2σ) variability in the

amount of oxygen in a vertical column. For comparison,

the instrumental noise is about one-half, or 0.002, of this

variation. A correction based on the regional changes in

absorption as a function of season would not significantly

reduce the statistical variation in absorption.

3. Second SeaWiFS Preflight Solar

Radiation-Based Calibration Experiment

This paper describes the second solar radiation-based

calibration of SeaWiFS. The experiment was done on 1

November 1993 in the rock garden at the Santa Barbara

Research Center (SBRC). The results of the calibration

are presented, along with a comparison to the spherical

integrating source (SIS) calibration done at SBRC. The

estimated uncertainty of the SIS calibration is 2.8%, compared to the 4% estimated uncertainty for the solar-based

calibration. There is also an uncertainty in the value of the

exoatmospheric solar irradiance used to make this comparison, which is probably on the order of 1%. In addition, the integrated out-of-band blocking for SeaWiFS is

in the 1–3% range, which can introduce significant differences between the lamp- and solar-based calibrations. This

agreement is better than anticipated, and better than the

agreement achieved in March 1993 from the first experiment. The better agreement is probably due to a sphere

recalibration between the two experiments.

4. In Situ Evaluation of a Ship’s Shadow

In situ measurements of optical properties made from

a ship can be biased by the ship’s shadow. In an effort

to evaluate the ship shadow perturbation created by the

R/V Weatherbird II, profiles of downwelling irradiance,

Ed(z, λ); upwelling radiance, Lu(z, λ); and derived apparent optical properties (AOPs), were obtained at four

distances—1 m, 3 m, 6 m, and 20 m or more—off the ship’s

stern. Two statistical analyses of these data are explored.

The first analysis uses data from pairs of simultaneouslyobtained light profiles, one profile obtained at a distance

greater than 20 m from the stern of the ship, and the other

taken either 1 or 6 m off the stern. The second analysis compares the derived AOPs for each profiling distance

from the ship, using data obtained throughout the length

of the experiment. Significant differences are rare in comparisons of profiles obtained at least 3 m off the ship’s stern.

At 1 m off the stern, however, significant discrepancies are

intermittently observed. This work illustrates that the inherent sources of noise in determining radiative fluxes and

AOPs in the upper ocean are generally greater than the

effects incurred by the ship’s own shadow under optimal

conditions.

5. SeaWiFS Global Fields:

What’s In a Day?

This chapter defines the procedure to be employed to

delineate data corresponding to one day of SeaWiFS operation. The definition is required for data analysis with

minimal temporal aliasing in the same region of observation. The definition also allows proper assignment of data

into daily fields that will be used for the generation of

weekly and monthly average products.

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Chapter 1

Comparison of Irradiance Immersion Coefficients for Several

Marine Environmental Radiometers (MERs)

James L. Mueller

San Diego State University

San Diego, California

Abstract

Spectral immersion coefficients were measured experimentally for 12 irradiance collectors on underwater profiling radiometers. These coefficients are used to convert spectral irradiance responsivity calibration factors,

measured in air, for use underwater. All of the irradiance collectors were the same design, however, 11 were

made of PlexiglasR diffusing material and 1 was made of TeflonR. At any given wavelength, the immersion

coefficients typically had standard deviations between collectors ranging from 3–5%. The total variations at

some wavelengths were as large as 10%. The coefficients of the Teflon diffuser were well within the bounds

of one standard deviation from the sample mean. Repeated measurements on several of the collectors showed

that experimental uncertainty is not greater than 1% (one standard deviation, or 1σ). The primary conclusion of this study is that accurate underwater radiometry absolutely requires experimental characterization

of each individual irradiance collector, rather than assuming a value based solely on its design and material

specifications.

1.1 INTRODUCTION

The spectral responsivities of underwater (irradiance)

radiometers are calibrated in air using an FEL lamp, which

has a spectral irradiance scale traceable to the National Institute of Standards and Technology (NIST). The spectral

immersion coefficients for an underwater irradiance meter

represent the differences between the instrument’s spectral responsivities in air and in water. The responsivity

will change due to the fact that the refractive index of the

plastic (or TeflonR ) diffuser is smaller, relative to the refractive index of water, than it is relative to the refractive

index of air. Less incident light is reflected at the waterplastic interface, and therefore, more of the light reflected

from the collector’s inner surface escapes back into the

water. The net result is that a smaller fraction of incident

flux is transmitted through the irradiance collector in water and therefore, the instrument’s irradiance responsivity

is decreased.

At present, the practice of the oceanographic community is to experimentally characterize the spectral immersion coefficients of only a small sample of irradiance collectors in a given class of collectors (with the same materials and design specifications). These coefficients have

subsequently been associated with all collectors in that

class, which assumes negligible variability between individual items. In a previous report (Mueller 1994), this

assumption was tested by comparing irradiance immersion coefficients for several MER-series radiometers manufactured by Biospherical Instruments, Inc. (BSI) of San

Diego, California. The results of that preliminary comparison between measured spectral immersion coefficients for

six PlexiglasR diffusers of the same material and design

specifications show significant variations, with standard

deviations (σ) ranging from 3.2–3.5% and ranges (maximum minus minimum) as large as 9%. In this earlier

work, however, the immersion tests on each instrument

were not replicated, and thus, no estimates of the experimental uncertainty of the measurements could be made.

The conclusions were, therefore, only tentative.

This report presents results of an extended series of

immersion characterization experiments on an expanded

sample of irradiance collectors. The new series of characterization experiments were repeated two or more times,

at different lamp-to-collector distances, to provide an estimate of the uncertainty in this laboratory’s experimental

determinations of immersion coefficients. The new results

were then pooled with the earlier sample (Mueller 1994) to

analyze overall variability between individual collectors.

1.2 METHOD AND RESULTS

The laboratory procedure for determining an irradiance meter’s spectral immersion coefficients is described in

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Case Studies for SeaWiFS Calibration and Validation, Part 3

Mueller and Austin (1992). Immersion coefficients taken

from Mueller (1994) were each based on a single experimental measurement. Subsequently, a new set of experimental measurements were repeated 2–4 times on each of

seven irradiance collectors as a basis for uncertainty estimates. In each case, the immersion test (Mueller and

Austin 1992) was done first at one lamp-to-collector distance, and then the lamp was moved 12.5 cm toward the

collector and the test was repeated. In addition, the entire

procedure was repeated on different days for four of the

collectors, and for a fifth instrument [MER-1012f, Serial

Number (S/N) 8107] the single day results from this laboratory were combined with the results of an independent

immersion characterization by BSI.

Table 1. Immersion coefficients for several MERs

characterized at CHORS. The column headings denote the MER model number and irradiance type.

The data is extracted from Mueller (1994).

Wavelength MER-1048† MER-2040‡

[nm] Ed Eu Ed Eu

408 1.3686

410 1.4315 1.3882 1.3019

439 1.4289

440 1.4456

441 1.3846 1.3212

465 1.3751 1.3158

488 1.4138 1.3591 1.3012

489 1.4169

518 1.3841

519 1.3952

520 1.3470 1.2865

548 1.3822

550 1.3704

560 1.3693 1.3265 1.2695

589 1.3654 1.3699 1.3088 1.2557

632 1.3339

655 1.3425 1.2804 1.2332

671 1.3236 1.3344

683 1.3997

693 1.3724 1.3233

709 1.3389

† MER S/N 8302. ‡ MER S/N 8716.

Table 1 lists spectral irradiance immersion coefficients

for two MER instruments (i.e., four irradiance collectors)

characterized at the San Diego State University (SDSU)

Center for Hydro-Optics and Remote Sensing (CHORS)

during 1993 (Mueller 1994). Immersion coefficients for

seven additional collectors are listed in Tables 2–8, together with mean, standard deviation, and range for replicated tests at each wavelength. Spectral immersion coefficients from all collectors are illustrated in Fig. 1 (which

includes all data from Table 1, and mean coefficients from

Tables 2–8). Coefficients from replicate experiments, and

the experimental mean values, for each individual collector

(Tables 2–8) are illustrated in Figs. 2–8, respectively.

Linear regression analyses provide a reasonable fit for

many of the instrumental immersion coefficients, Fi, to an

equation of the form

Fi = a − bλ

104 (1)

where λ is the wavelength in nanometers. Regression coefficients a and b; residual standard deviations, sxy; and

squared linear correlation coefficients, R2; are compared

for these instruments in Table 9, and the regression lines

are illustrated in Figs. 2 and 4–8.

Mean, range, and σ of immersion coefficients for subsamples of different collectors were computed at selected

wavelengths and are presented in Table 10.

1.3 DISCUSSION

This report compares the experimentally determined

immersion coefficients for the irradiance collectors on nine

MER-series underwater radiometers manufactured by BSI.

There are 12 irradiance collectors involved in these experiments, all having the same basic design—11 have Plexiglas

diffusers and 1 (MER-2040 S/N 8738) has a Teflon diffusers

(Table 8 and Fig. 8).

The replicated experiments summarized in Tables 2–

8 show that, for the majority of channels tested, the 1σ

uncertainties in experimentally determined immersion coefficients are approximately 1% or less. The notable exceptions are the Ed(λ) channels at wavelengths greater than

550 nm of the MER-1012f S/N 8107 (Fig. 2 and Table 2)

and MER-1015 S/N 8205 (Fig. 3 and Table 3). It is suspected that these larger uncertainties may indicate nonlinearities in the responsivities of these channels. Nonlinearity may be due to a voltage discontinuity across a

gain change in replicated experiments at different lampto-collector distances.

The total range between the immersion coefficients of

the 12 collectors is as large as 15% at some wavelengths

(Fig. 1 and Table 10). The standard deviation of dispersion in immersion coefficients is generally between 3.5–5%,

at least at those wavelengths for which collector sample

sizes were large enough to estimate a reasonable standard

deviation (Table 10).

Immersion coefficients vary linearly with wavelength for

many of the diffusers (Table 9, and Figs. 2 and 4–8), with

residual standard deviation sxy × 100% ≤ 1% (except for

the MER-2040 S/N 8725, where sxy ×100% = 1.7%). The

immersion coefficients for the MER-1015 S/N 8205 are not

a well-behaved linear function of wavelength.

The dispersion in immersion coefficients between these

irradiance collectors (Fig. 1 and Table 10) is too large to

neglect, and the results of the replicated experiments indicate that only a small fraction of this variation can be

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Table 2. Immersion coefficients measured experimentally for the MER-1012f (S/N 8107). The data are presented here in order of decreasing lamp-to-collector distance.

Wavelength 24 June 1994 24 June 1994 17 March 1994† Immersion Coefficient

[nm] 144.5 cm 130.0 cm 106.3 cm μ σ Range

406.9 1.3510 1.3492 1.3512 1.3505 0.0009 0.0020

442.5 1.3673 1.3643 1.3685 1.3667 0.0018 0.0042

487.1 1.3499 1.3454 1.3501 1.3485 0.0022 0.0048

517.8 1.3383 1.3344 1.3391 1.3373 0.0020 0.0047

564.9 1.3178 1.3388 1.3195 1.3254 0.0095 0.0210

632.3 1.3130 1.2961 1.3246 1.3112 0.0117 0.0286

681.3 1.3044 1.2636 1.2807 1.2829 0.0167 0.0408

† Immersion coefficients calculated from experimental measurements by BSI.

Table 3. Immersion coefficients measured experimentally for the MER-1015 (S/N 8205).

Wavelength 1 September 1994 2 September 1994 Immersion Coefficient

[nm] 152.2 cm 137.8 cm 152.2 cm 137.8 cm μ σ Range

406.0 1.4159 1.4217 1.4233 1.4104 1.4178 0.0051 0.0130

438.5 1.4335 1.4473 1.4351 1.4398 1.4389 0.0054 0.0138

462.4 1.4253 1.4371 1.4309 1.4291 1.4306 0.0043 0.0118

485.5 1.4210 1.4248 1.4227 1.4177 1.4215 0.0026 0.0071

517.9 1.4031 1.4083 1.4071 1.4022 1.4052 0.0026 0.0060

536.8 1.3929 1.4004 1.3965 1.3930 1.3957 0.0031 0.0075

558.5 1.3843 1.3196 1.3879 1.3183 1.3525 0.0336 0.0696

588.4 1.3104 1.4189 1.3169 1.4171 1.3658 0.0522 0.1086

624.2 1.4494 1.4065 1.4448 1.3955 1.4240 0.0235 0.0539

673.3 1.4325 1.3993 1.4482 1.3861 1.4165 0.0249 0.0621

696.2 1.3846 1.3507 1.3730 1.3418 1.3625 0.0171 0.0428

762.4 1.3120 1.3131 1.3151 1.3109 1.3128 0.0016 0.0042

Table 4. Immersion coefficients measured experimentally for the MER-1032 (S/N 8301). The data are presented

here to allow comparison for similar lamp-to-collector distances.

Wavelength 30 December 1993 22 July 1992 26 July 1992 Immersion Coefficient

[nm] 120.0 cm 138.0 cm 123.5 cm 137.9 cm 123.5 cm μ σ Range

411.1 1.4053 1.4172 1.4136 1.4112 1.4037 1.4102 0.0057 0.0135

441.9 1.3946 1.4302 1.4016 1.4146 1.4005 1.4083 0.0143 0.0356

452.9 1.3897 1.4091 1.4129 1.4089 1.4096 1.4060 0.0093 0.0232

489.6 1.3754 1.3887 1.3918 1.3945 1.3925 1.3886 0.0077 0.0191

508.9 1.3795 1.3877 1.3854 1.3889 1.3819 1.3847 0.0039 0.0094

528.6 1.3529 1.3790 1.3753 1.3795 1.3735 1.3720 0.0110 0.0266

555.3 1.3451 1.3664 1.3618 1.3679 1.3622 1.3607 0.0091 0.0229

588.9 1.3329 1.3540 1.3450 1.3577 1.3490 1.3477 0.0096 0.0248

632.1 1.3071 1.3337 1.3271 1.3348 1.3280 1.3261 0.0112 0.0276

654.8 1.3013 1.3222 1.3153 1.3184 1.3151 1.3145 0.0079 0.0209

670.7 1.3032 1.3285 1.3232 1.3279 1.3219 1.3209 0.0103 0.0253

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Case Studies for SeaWiFS Calibration and Validation, Part 3

Table 5. Immersion coefficients measured experimentally for the MER-1032 (S/N 8301).

Wavelength 22 July 1994 26 July 1994 Immersion Coefficient

[nm] 131.6 cm 123.5 cm 131.6 cm 117.2 cm μ σ Range

411.3 1.4532 1.4508 1.4458 1.4427 1.4481 0.0041 0.0105

442.0 1.4216 1.4214 1.4165 1.4156 1.4188 0.0027 0.0060

489.9 1.3999 1.4017 1.3987 1.3961 1.3991 0.0020 0.0056

509.1 1.3859 1.3877 1.3845 1.3819 1.3850 0.0021 0.0058

555.4 1.3664 1.3658 1.3664 1.3595 1.3645 0.0029 0.0069

529.1 1.3788 1.3783 1.3773 1.3735 1.3770 0.0021 0.0053

633.0 1.3108 1.3271 1.3103 1.3204 1.3172 0.0070 0.0168

670.9 1.3237 1.3113 1.3249 1.3068 1.3167 0.0078 0.0181

Table 6. Immersion coefficients measured experimentally for the MER-2040 (S/N 8724).

Wavelength 22 July 1994 26 July 1994 Immersion Coefficient

[nm] 121.6 cm 107.2 cm 121.6 cm 107.2 cm μ σ Range

453.2 1.4086 1.4077 1.4116 1.4117 1.4099 0.0018 0.0040

440.3 1.4144 1.4143 1.4186 1.4187 1.4165 0.0021 0.0044

486.7 1.3942 1.3931 1.3987 1.3980 1.3960 0.0024 0.0056

516.9 1.3783 1.3825 1.3828 1.3870 1.3827 0.0031 0.0087

530.2 1.3724 1.3762 1.3770 1.3807 1.3766 0.0029 0.0083

565.1 1.3560 1.3554 1.3604 1.3602 1.3580 0.0023 0.0050

664.0 1.3175 1.3167 1.3218 1.3213 1.3193 0.0022 0.0050

Table 7. Immersion coefficients measured experimentally for the MER-2040 (S/N 8725).

Wavelength 2 September 1994 Immersion Coefficient

[nm] 125.4 cm 111.0 cm μ σ Range

408.6 1.3150 1.3177 1.3164 0.0014 0.0028

438.9 1.3451 1.3380 1.3415 0.0035 0.0071

484.9 1.3449 1.3394 1.3421 0.0028 0.0056

617.6 1.3366 1.3398 1.3382 0.0016 0.0032

564.0 1.3223 1.3206 1.3215 0.0008 0.0016

662.6 1.3011 1.2997 1.3004 0.0007 0.0014

Table 8. Immersion coefficients measured experimentally for the MER-2040 (S/N 8738).

Wavelength 24 June 1994 29 June 1994 Immersion Coefficient

[nm] 120.7 cm 106.2 cm μ σ Range

340.0 1.4281 1.4170 1.4225 0.0055 0.0111

380.0 1.4127 1.4033 1.4080 0.0047 0.0094

412.0 1.3996 1.3917 1.3956 0.0039 0.0079

443.0 1.3870 1.3804 1.3837 0.0033 0.0066

395.0 1.4053 1.3977 1.4015 0.0038 0.0076

665.0 1.3126 1.3078 1.3102 0.0024 0.0047

455.0 1.3835 1.3772 1.3803 0.0032 0.0064

490.0 1.3714 1.3652 1.3683 0.0031 0.0062

510.0 1.3638 1.3580 1.3609 0.0029 0.0058

532.0 1.3570 1.3467 1.3518 0.0052 0.0103

555.0 1.3486 1.3380 1.3433 0.0053 0.0106

570.0 1.3447 1.3325 1.3386 0.0061 0.0122

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 1. Immersion coefficients (Fi) for several MER-series radiometers. The symbol designations appear in the

figure.

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Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 2. Immersion coefficients from replicate immersion tests on the MER-1012f (S/N 8107) Ed channels. The

legend in the figure provides experiment dates and lamp-to-collector distances. The solid line is the least-squares

regression fit to the mean coefficients.

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 3. Immersion coefficients from replicate immersion tests on the MER-1015 (S/N 8205) Ed channels. The

legend in the figure provides experiment dates and lamp-to-collector distances.

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Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 4. Immersion coefficients from replicate immersion tests on the MER-1032 (S/N 8301) Ed channels. The

legend in the figure provides experiment dates and lamp-to-collector distances. The solid line is the least-squares

regression fit to the mean coefficients.

10
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 5. Immersion coefficients from replicate immersion tests on the MER-1032 (S/N 8301) Eu channels. The

legend in the figure provides experiment dates and lamp-to-collector distances. The solid line is the least-squares

regression fit to the mean coefficients.

11
Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 6. Immersion coefficients from replicate immersion tests on the MER-2040 (S/N 8724) Ed channels. The

legend in the figure provides experiment dates and lamp-to-collector distances. The solid line is the least-squares

regression fit to the mean coefficients.

12
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 7. Immersion coefficients from replicate immersion tests on the MER-2040 (S/N 8725) Ed channels. The

legend in the figure provides experiment dates and lamp-to-collector distances. The solid line is the least-squares

regression fit to the mean coefficients.

13
Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 8. Immersion coefficients from replicate immersion tests on the MER-2040 (S/N 8738) Ed channels. The

legend in the figure provides experimental dates and lamp-to-collector distances. The solid line is the leastsquares regression fit to the mean coefficients

14
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Table 9. Linear regression fits to immersion coefficients, as expressed in (1), for irradiance collectors on several

MER underwater radiometers manufactured by BSI. In addition, the squared correlation coefficient, R2, and

the residual standard deviation, sxy, are listed.

MER Number of Measurement Regression Coefficient

Model S/N Channels Type a bR2 sxy

1012 8107 7 Ed 1.4745 2.6759 0.900 0.010

1032 8301 11 Ed 1.5833 4.0050 0.980 0.005

1032 8301 8 Eu 1.6496 5.1186 0.980 0.007

2040 8724 7 Ed 1.6084 4.3755 0.998 0.002

2040 8725 6 Ed 1.3826 1.0907 0.355 0.015

2040 8738† 12 Ed 1.5405 3.5163 0.998 0.002

† MER-2040 S/N 8738 is equipped with a Teflon diffuser. All other instruments tested have Plexiglas diffusers.

Table 10. Statistics of variability between immersion coefficients for different irradiance collectors at selected

wavelengths.

Wavelength Number of Immersion Coefficient

±2 nm Collectors μ σ Range

406 3 1.3791 0.0346 0.0668

410 7 1.3966 0.0520 0.1513

442 8 1.3920 0.0377 0.1244

489 8 1.3744 0.0387 0.1157

555 3 1.3562 0.0113 0.0212

664 3 1.3194 0.0191 0.0382

670 5 1.3424 0.0419 0.0998

explained by experimental uncertainty in the characterization procedure. The observed scatter far exceeds the

allowable uncertainty implied by the radiometric calibration goals (that is, 1% uncertainty) of the SeaWiFS Calibration and Validation Program. It is essential, therefore,

to experimentally characterize immersion factors for every

profiling irradiance sensor to be used as part of SeaWiFS

validation.

15
Case Studies for SeaWiFS Calibration and Validation, Part 3

Chapter 2

The Effect of Oxygen Absorption on

Band-7 Radiance

Robert S. Fraser

NASA Goddard Space Flight Center

Greenbelt, Maryland

Abstract

Atmospheric oxygen absorbs about 13% of the available sunlight reflected from the Earth in band 7 of the

SeaWiFS instrument, which has a bandwidth spanning 745–785 nm. If a correction is made for the average

amount of absorption, then the measured radiance would vary by ±0.004 for a two standard deviation (2σ)

variability in the amount of oxygen in a vertical column. For comparison, the instrumental noise is about

one-half, or 0.002, of this variation. A correction based on the regional changes in absorption, as a function of

season, would not significantly reduce the statistical variation in absorption, but a correction based on surface

pressure would be accurate.

2.1 INTRODUCTION

Atmospheric oxygen absorbs approximately 13% of the

radiant energy in SeaWiFS band 7, which has a width

spanning 745–785 nm. Since the total amount of oxygen is

proportional to the surface pressure, the amount of oxygen

varies directly with the variation in surface pressure. The

standard deviation (1σ) of the surface pressure over the

entire ocean is only about 1%. It is expected, therefore,

that oxygen will cause a variability, equivalent to 2σ, in the

radiance in band 7, i.e., about 0.02 × 0.13 =0.0026. This

variability is about 1.5 times the instrument radiance noise

(Hooker et al. 1992). The detailed analysis presented here

supports this conclusion.

2.2 THEORY

The radiance (Lt), measured at a satellite, can be expressed as

Lt = Latm + Lsfc, (2)

where Latm is the radiance of light reflected from the atmosphere, and Lsfc is the radiance of light leaving an ocean

surface and passing through the atmosphere. Although

Latm receives contributions from light scattered throughout the atmosphere, a slightly more conservative approach

to estimating the effect of oxygen absorption is to assume

that the scattering occurs in a thin layer near the surface,

and that the absorbing oxygen lies entirely above the surface layer.

In this simulation, sunlight is considered to reflect from

both the sea surface and a concentrated layer of air just

above the sea surface. The combined reflectance (for the

sea surface and the layer of air) is equal to ρ. Light would

be absorbed along a two-way path through the entire atmosphere. Then the total radiance measured by the SeaWiFS instrument (in orbit) would be

Lt =



ρ(λ)f(λ)T(λ)S(λ)dλ, (3)

where f is the instrument spectral response function, S is

the solar spectral irradiance, T is the two-way transmission

through the volume of oxygen

T(λ, θ, θ0) = e−m(θ,θ0)τox(λ) (4)

where τox is the oxygen absorption optical thickness, and

m represents the air mass:

m = 1

cos θ0

+

1

cos θ

. (5)

In (5), θ0 is the solar zenith angle, and θ is the zenith

angle of the line-of-sight in a plane-parallel atmosphere.

In (4), the oxygen absorption optical thickness, τox(λ), is

defined as

τox(λ) = k(λ)N, (6)

where k is the molecular absorption cross-section area, and

N is the total number of oxygen molecules per unit area

in a vertical column of the atmosphere.

16
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 9. Oxygen absorption band (A-band), the integrand of (13), for an air mass m = 2. The curve is adapted

from data given by Wu (1985).

Two models, one with oxygen and another without oxygen, will be examined and compared with regard to the radiance SeaWiFS will measure in orbit. In the model without absorbing oxygen, L0 represents the radiance. The

number of absorbing molecules above the reflecting layer,

N, is then equal to 0, the optical thickness τ=0, the transmission T=1, and from (3) the radiance is

L0 = ρ S(λ1)



f(λ)dλ

= ρ S(λ1)B.

(7)

In this expression, the reflectance, ρ, can be considered

constant without loss of generality, and S(765) has a value

of 122.5 mW cm−2 μm−1 when λ1 is equal to 765 nm. The

width of band 7, B, is approximately 40.5 nm, as defined by

the integrated SeaWiFS spectral response function, f(λ),

supplied by Barnes (1994). The wavelength λ1 = 765 nm

is selected so that (3) and (7) are equal.

If oxygen absorption is accounted for, the radiance, L,

of light transmitted through the absorbing oxygen along a

two-way path is, from (3) and (4),

L =



ρ(λ)f(λ)e−m(θ,θ0)τ(λ)

S(λ)dλ. (8)

With T = 1 in (3), the absorbed radiation is then found

as the difference between (3) and (8):

∆L = L0 − L, (9)

=



ρ(λ)f(λ)



1 − e−m(θ,θ0)τ(λ)



S(λ)dλ, (10)

= ρf(λ2)S(λ2)



1 − e−m(θ,θ0)τ(λ)



dλ, (11)

= ρf(λ2)S(λ2)W, (12)

W =



1 − e−m(θ,θ0)τ(λ)



dλ, (13)

with the following values in effect: λ2 = 764 nm, f



λ2



=

0.94, and S



λ2

 = 124 mW cm−2 μm−1. Note that λ2

is a wavelength within the absorbing band (758 < λ2 <

771 nm) and not within the total band (735–800 nm). The

integral in (13) represents an equivalent bandwidth, W, of

complete absorption and depends on the amount of oxygen.

The integrand of (13) is given in Fig. 9. The absorption

band is restricted to a width of 13 nm (758 <λ< 771 nm).

17
Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 10. The equivalent width, W, of the oxygen A-band for sunlight reflected from surfaces at increasing

pressure levels in the atmosphere. Curves are given for air masses 2 and 3. This figure is adapted from

computations made by Curran (pers. comm.).

Table 11. Equivalent width, W, of oxygen A-band

for sunlight passing to the surface (1,013 mb) and

reflected into space. The data presented are taken

from Fig. 10. The symbol p represents surface pressure.

Air W ∆W /∆p Fractional

Mass [nm] [nm/mb] Absorption W/B

2 4.6 0.0031 0.11

3 5.2 0.0035 0.13

The change in W with respect to the total surface pressure of all atmospheric gases (N2, O2, etc.) is shown in

Fig. 10. Table 11 gives W for band 7, calculated for sunlight reaching sea level and then reflected to space. The

change in W with respect to pressure appears in the third

column, and the fraction of energy absorbed in band 7,

from (15), appears in the last column.

The relative loss of radiance caused by oxygen absorption is found by dividing (12) by (7):

∆L

L0

= ρf(λ2)S(λ2)W

ρS(λ1)B

= β W

B ,

(14)

where for air mass m = 2,

β = f(λ2)S(λ2)

S(λ1)

= 0.94 × 124

122.5

= 0.95.

(15)

The relative amount of absorbed energy taken out of

the band is approximately that given by letting β = 1 in

(14):

∆L

L0

= W

B . (16)

The relative loss in radiance equals the ratio of the equivalent width W of the oxygen band, to band 7 width B.

The change in the equivalent bandwidth caused by a

change in the amount of oxygen can be calculated from

(14):

∆L

L0

= ∆W

B

= ∆W

∆p

∆p

B ,

(17)

18
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

where p is the total sea level pressure of all atmospheric

gases, i.e., surface pressure.

Statistical data on the atmospheric surface pressure are

not available with high spatial and temporal resolution.

The median value of pressure over the oceans is 1,012.5 mb,

and the extreme monthly values are 969 and 1,043 mb(McClain et al. 1994). The extremes and reference pressure

(pref) data are given in Table 12. The deviations of −44

and +30 mbare the changes of the monthly extreme pressures from 1,013 mb(United States Navy 1978). The maximum presssure variations occur in the middle latitudes

during the winter. The deviations of −30 and +34 mb, appearing in the last column of the second row, are based on

the maximum data given by Cantor and Cole (1985); the

deviations are computed as the local average (± 2σ) minus

the worldwide average. For example, the All ocean deviations=1,015 ± 32 − 1,013 = −30, +34 mb. The tropical

deviation for a 2σ variability in pressure (−6, +2 mb) is

much weaker. Because extreme low-pressure cyclones are

associated with strong winds, rain, and overcast clouds,

satellite observations of the surface would not be possible

under such conditions.

Table 12. Sea level pressure data for oxygen absorption estimation. The deviation column values

(pdev) are the differences between the minimum and

maximum surface pressures compared to 1,013 mb.

Statistical pref pdev

Basis [mb] [mb]

All-ocean average† 1,015 −30, +34

Monthly extreme low 969 −44

Monthly extreme high 1,043 +30

Tropics† 1,011 −6, +2

† Cantor and Cole (1985); all others from McClain et

al. (1994).

Absorption changes caused by extreme variations in

oxygen absorption are given in Table 13 for air masses 3

and 4. The minimum (−44 mb) and maximum (+34 mb)

pressure changes are taken from Table 12. The changes in

equivalent bandwidth (∆W/∆p) are taken from Table 11

for air mass 3 and extrapolated for air mass 4. The magnitude of the variations is 0.003–0.004, which can be compared with the instrumental noise, 0.002, estimated from

the signal-to-noise ratio (SNR) for band 7 (Hooker et al.

1992). As seen from Table 12, the small pressure variations in the tropics would have a small effect on absorption

changes in band 7.

Table 13. Absorption changes for band 7.

Air ∆W/∆p pdev W Absorption

Mass [nm/mb] [mb] Change

3 0.0035 −44 −0.15 −0.004

3 0.0035 +34 +0.12 +0.003

4 0.0041 −44 −0.18 −0.004

4 0.0041 +34 +0.14 −0.003

2.3 CONCLUSION

The simplest correction for oxygen absorption is based

on a constant amount of atmospheric oxygen in a vertical

direction. In this case, oxygen absorbs about 13% of the

radiant energy available for remote sensing by SeaWiFS

band 7. The absorption depends on the length of the path

through the atmosphere: from the sun [i.e., total solar irradiance at the top of the atmosphere (TOA)] to the surface,

and back to SeaWiFS. Even if the amount of oxygen in a

vertical direction is assumed to be constant, oxygen corrections have to be adjusted for the geometry. Statistical data

are not available for making a precise estimate of the variation in absorption caused by the change in the amount of

oxygen that occurs when the atmospheric pressure varies

from an average value of 1,013 mb. For a 2σ variation in

the amount of oxygen, however, the variable absorption in

band 7 is not more than twice the instrumental noise.

The operational procedure for making an atmospheric

correction for molecular scattering will use the surface pressure in the correction algorithm. This pressure data can

also be utilized to make a correction for oxygen absorption.

In this case, the statistical variations discussed here would

not occur.

In the above discussions, the vertical gradient of atmospheric optical properties has been neglected, but Ding

and Gordon (1994) have shown that the vertical profile

must be included for the derivation of the water-leaving

radiance to be sufficiently accurate. Corrections based on

a single reference profile are adequate except for the following three cases: large amounts of stratospheric aerosol,

such as occurred after the volcanic eruptions of El Chich ́on

and Mount Pinatubo; thin cirrus clouds; and aeolian dust,

such as that from the Sahara or Gobi Deserts.

19
Case Studies for SeaWiFS Calibration and Validation, Part 3

Chapter 3

Second SeaWiFS Preflight Solar Radiation-Based

Calibration Experiment

Stuart F. Biggar

Kurtis J. Thome

Philip N. Slater

Remote Sensing Group, Optical Sciences Center

Universityof Arizona, Tucson, Arizona

Alan W. Holmes

Santa Barbara Research Center

Goleta, California

Robert A. Barnes

ManTech, Inc.

Wallops Island, Virginia

Abstract

This paper describes the second solar radiation-based calibration of SeaWiFS. The experiment was done on 1

November 1993 in the rock garden at SBRC. The results of the calibration are presented, along with a comparison

to the SIS calibration done at SBRC. The estimated uncertainty of the SIS calibration is 2.8%, compared to

the 4% estimated uncertainty for the solar-based calibration. There is also an uncertainty in the value of the

exoatmospheric solar irradiance used to make this comparison, which is probably on the order of 1%. In addition,

the integrated out-of-band blocking for SeaWiFS is in the 1–3% range, which can introduce significant differences

between the lamp- and solar-based calibrations. This agreement is better than anticipated, and better than the

agreement achieved in March 1993 from the first experiment. The better agreement is probably due to a sphere

recalibration between the two experiments.

3.1 INTRODUCTION

The basic concept for a solar radiation-based calibration of a satellite sensor is to attempt to simulate the solar

irradiance incident on the diffuser in space while doing

the experiment on the ground. A thorough discussion of

the concept was presented in April 1993 at the Society of

Photo-optical Instrumentation Engineers (SPIE) meeting

in Orlando, Florida (Biggar et al. 1993). This presentation

included results from the first calibration performed on

SeaWiFS. After this calibration, a stray light, or transient

response, problem was discovered in SeaWiFS. The sensor

was subsequently modified to reduce the response to outof-field radiation, such as that caused by clouds, within 10

pixels of the SeaWiFS instantaneous field-of-view (IFOV).

After the modifications, the sensor was recalibrated in the

laboratory using the 100 cm SIS at SBRC. Another solar

radiation-based calibration was scheduled for late October

1993, to coincide with a look at the full moon on 29 October. Cloud and visibility conditions, caused in part from

haze and smoke from fires in the Southern California area,

prevented the calibration from taking place on 29–31 October. On 1 November, sky conditions were good enough

for calibration purposes. The sensor was taken outside at

about 1115 Pacific Standard Time (PST), and measurements were taken at about 1215, 1255, and 1400 PST. The

instrument was covered immediately after the last data set

was collected.

3.2 EXPERIMENTAL METHOD

The transmittance along the path to the sun was measured with a solar radiometer possessing 10 bands covering the spectral range of about 370–1,040 nm. Table 14

shows representative radiometer data for the nine bands

that were not affected by water vapor absorption. The

sky conditions on 1 November 1993 were not sufficiently

favorable to allow a Langley plot determination of the optical depth; therefore, instantaneous measurements of the

transmittance were made by using previous calibrations

20
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Table 14. Solar radiometer optical depth measurements.

Band Wavelength Optical

Number [nm] Depth σ

1 368.9 1.0109 0.0061

2 399.1 0.8279 0.0070

3 440.0 0.6623 0.0061

4 518.6 0.4633 0.0050

5 608.5 0.3499 0.0045

6 669.0 0.2756 0.0039

7 779.7 0.2008 0.0033

8 869.8 0.1643 0.0028

10 1,027.2 0.1284 0.0020

Table 15. SeaWiFS measurements on 1 November 1993 at 1400 PST. Pixel 312 (the center pixel) and

pixel 0 (zero offset) were used for the determinations of the total and diffuse only signals.

Band Shaded Shaded Unshaded Unshaded Diffuse/ ∆ Unshaded

Number (zero offset) (312) (zero offset) (312) Global vs. Shaded

1 20 60 20 254 0.17094 194

2 17 58 17 294 0.14801 236

3 20 52 20 282 0.12261 229

4 20 55 20 332 0.11218 277

5 22 60 22 421 0.09520 361

6 24 60 24 508 0.07438 448

7 24 55 24 508 0.06405 453

8 21 58 21 591 0.06491 533

of the instrument zero-airmass intercept. Measurements

by the same solar radiometer were also made, after the

calibration described here, during subsequent satellite calibration campaigns at White Sands National Monument in

New Mexico. For the intercepts done before and after the

solar radiation-based calibration, the standard deviation

(σ) is about 1% of the intercept value. It is expected that

the error in the transmittance measurement when using

these intercepts will be less than approximately 3% at the

measurement wavelengths.

The optical depths and the barometric pressure are

used to separate the optical depth components due to Rayleigh scattering, aerosol scattering and absorption, and absorption due to ozone (Biggar et al. 1990). The procedure employed here assumes a Junge power law distribution for aerosol particle size. The results on 1 November

give a Junge parameter of 3.50–3.43, and a derived columnar ozone amount of 0.246–0.260 cm-atm† for the three

measurement times. Using the Junge parameter, ozone

† The centimeter-atmosphere (cm-atm) is a measure of trace

gas columnar amount. It can be envisioned as if the entire

trace gas content within a 1 cm2 column of the Earth’s atmosphere was accumulated at the base of this column under

standard temperature and pressure conditions. The cm-atm

would give the length of this volume of gas in centimeters.

amount, and the barometric pressure, the optical depth

components can be computed for each of the SeaWiFS

bands. MODTRAN was used to compute the effects of gaseous

absorption for each band. The only band that exhibits any

significant absorption is band 7, and the oxygen slant path

transmittance for this band is computed to be 0.927.

The transmittance measurements described above were

performed when the sensor was actually taking data from

the illuminated solar diffuser. Measurements of the diffuser

were made with the diffuser illuminated by the sun and the

sky (unshaded), and by only the sky (direct beam blocked,

or shaded). Data from pixel 312, the center pixel from the

diffuser, along with that from pixel 0 (the zero offset) were

used to determine the total and diffuse only signals. The

choice of pixel 312 is not critical, as the variation across

the diffuser is no more than one digital count (DC) for any

band.

3.3 RESULTS

The measurements from the diffuser are presented in

Table 15. These data are from the 1400 PST measurement sequence. The data in the table include the zero offset for each band for both the shaded and unshaded measurements, the actual measurements, and two computed

21
Case Studies for SeaWiFS Calibration and Validation, Part 3

Table 16. Transmittance and predicted DCs in orbit.

Band Vertical Slant Predicted

Number Path Path TOA DCs

1 0.4651 0.2860 677.5

2 0.5274 0.3512 671.1

3 0.6004 0.4342 526.8

4 0.6238 0.4622 598.7

5 0.6654 0.5136 702.2

6 0.7575 0.6349 705.1

7 0.7507 0.6565 689.7

8 0.8437 0.7573 703.5

Table 17. Sphere calibration computations.

Band Integrated Calibration BRDF† Spectral Offset Predicted

Number Irradiance (E) Correction DCs

1 170.827 0.00704 0.02682 0.963 20 695.8

2 188.992 0.00810 0.02786 0.983 17 678.3

3 193.383 0.01045 0.02751 0.980 20 539.5

4 189.022 0.00923 0.02806 0.998 20 595.8

5 187.431 0.00744 0.02755 0.991 22 722.4

6 151.546 0.00629 0.02800 1.011 24 691.3

7 121.715 0.00512 0.02854 0.995 24 705.9

8 98.168 0.00422 0.03011 1.011 20 712.8

† Bidirectional Reflectance Distribution Function

quantities—the ratio of the diffuse signal to the global

(or total) signal, and the difference between unshaded and

shaded measurements. This difference is the direct solar

beam signal without the diffuse sky contribution.

A forward-scatter correction must be made to account

for the small amount of forward-scattered diffuse light that

is blocked by the disk. This corrected measurement of the

direct solar beam is then further corrected for the transmittance in order to compute an expected solar diffuser

measurement at TOA, i.e., in orbit. The forward-scatter

correction is wavelength dependent, but in all cases it is

very small, i.e., less than 1 DC. This correction is subtracted from the difference in measurements.

The DCs for each SeaWiFS band are then divided by

the slant path transmittance, which has been computed

for each band. This transmittance is computed with Beer’s

Law, using the optical depth components in each band, and

further multiplied by the oxygen transmittance in band

7. The transmittance values computed for each band are

given in Table 16. These values correspond to a time of

14:00:30 and an effective airmass of 1.6354. The uncertainty in airmass for a five-minute period around this time

is 0.0079, which corresponds to an uncertainty in transmittance of less than 0.5%.

The predicted DCs have some associated uncertainties, which can be difficult to quantify. The major source

of uncertainty is the transmittance measurement. Other

sources of uncertainty are interpolation from the radiometer wavelengths to the SeaWiFS wavelengths, the forwardscatter correction, the oxygen transmittance computation

for band 7, and atmospheric variability. The transmittance measurement uncertainty is probably less than 3%,

as this uncertainty is dependent on the radiometer calibration. The interpolation uncertainty can be estimated by

using the calculated optical-depth components to compute

the expected transmittance, which was also measured in

the solar radiometer bands. The largest difference is for

band 4 of the radiometer, and it corresponds to an error

in transmittance of about 0.9%. The second error term in

Equation 3 of Biggar et al. (1993), representing the airmass uncertainty, is less than 0.2% for all bands. The atmospheric variability can be estimated by comparing the

standard deviation of the transmittance measurements to

the average. The variability in transmittance in the radiometer bands was about 1%. The average transmittance

was used so that this variability should not cause a significant uncertainty. A total uncertainty on the order of 4% is

expected, with the radiometer calibration being the dominant term. The solar radiometer gives a much more repeatable measurement, so it would be better if the sky conditions were stable enough for a Langley plot determination

of the transmittance. Conditions in Santa Barbara were

not good enough, however, for such a determination.

22
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 11. Measured atmospheric transmittances during the two solar calibration experiments. The transmittances are given at the wavelengths of the Arizona solar radiometer.

Fig. 12. Comparison of the laboratory- and solar-based calibrations of SeaWiFS. The laboratory measurements

were made by SBRC with a 100 cm SIS. For the 1 November 1993 solar calibration, the two techniques agreed

to better than 3%.

23
Case Studies for SeaWiFS Calibration and Validation, Part 3

3.4 DISCUSSION

As a check on the results, and in an effort to relate

these results to the International System of Units (SI†),

these results were compared to the calibration of the SeaWiFS system with the SBRC 100 cm SIS. The SIS results

were taken from the SeaWiFS Calibration and Acceptance

Data Package, which is described in Barnes et al. (1994).

Exoatmospheric solar irradiance data, based on Neckel and

Labs (1984), were used; these data were integrated over

the SeaWiFS band and then divided by the radiance-toDC calibration. This value was then multiplied by the

diffuser BRDF and divided by the correction for spectral

shape. The zero signal offset was then added to give the

predicted TOA DC value. The results are summarized in

Table 17. The results in Table 17 can be easily compared

to those in Table 16. The summary of this comparison is

shown in Table 18.

For all bands, the differences between the solar-based

and sphere-based methods are less than 3%. The estimated uncertainty of the SIS calibration is 2.8%, compared

to the 4% estimated uncertainty for the solar-based calibration. There is also an uncertainty in the value of the

exoatmospheric solar irradiance used to make this comparison, which is probably on the order of 1%. In addition,

the integrated out-of-band blocking for SeaWiFS is in the

1–3% range, which can introduce significant differences between the lamp- and solar-based calibrations.

This agreement is better than anticipated, and better

than the agreement achieved in March 1993 for the first

† The SI acronym is derived from the original French title,

Syst ́eme International d’ Unit ́es.

experiment. The better agreement is probably due to a

sphere recalibration between the two experiments.

It is also instructive to compare the SeaWiFS band

transmittances from the two dates (Fig. 11). The atmosphere was clearer in March compared to late October, when smoke from fires in the Los Angeles area affected conditions in Santa Barbara. The measurements

in March were also at a lower solar zenith angle than in

November. Both of these factors could possibly make the

November data more uncertain; however, the results still

compare well with laboratory measurements. This favorable comparison leads to the conclusion that the transmittance measurements are fairly accurate even though a

Langley plot was not possible. Figure 12 shows the percentage difference between the calibration methods for the

two dates.

Table 18. Comparison between solar radiationbased and laboratory (SIS based) calibrations.

Band Solar SIS Difference

Number Based Based [%]

1 677.5 695.8 2.6

2 671.1 678.3 1.1

3 526.8 539.5 2.3

4 598.7 595.8 −0.5

5 702.2 722.4 2.8

6 705.1 691.3 −2.0

7 689.7 705.9 2.3

8 703.5 712.8 1.3

24
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Chapter 4

In Situ Evaluation of a Ship’s Shadow

Christian T. Weir

David A. Siegel

David W. Menzies

Universityof California at Santa Barbara

Santa Barbara, California

Anthony F. Michaels

Bermuda Biological Station for Research

FerryReach, St. George’s, Bermuda

Abstract

In situ measurements of optical properties made from a ship can be biased by the ship’s shadow. In an effort to

evaluate the ship shadow perturbation created by the R/V Weatherbird II, profiles of downwelling irradiance,

Ed(z, λ); upwelling radiance, Lu(z, λ); as well as derived AOPs were obtained at four distances—1 m, 3 m, 6 m,

and 20 m or more—off the ship’s stern. Two statistical analyses of these data are explored here. The first

analysis uses data from pairs of simultaneously-obtained light profiles, one profile obtained at a distance greater

than 20 m from the stern of the ship, and the other taken either 1 or 6 m off the stern. The second analysis

compares the derived AOPs for each profiling distance from the ship, using data obtained throughout the length

of the experiment. Significant differences are rare in comparisons of profiles obtained at least 3 m off the ship’s

stern. At 1 m off the stern, however, significant discrepancies are intermittently observed. This work illustrates

that the inherent sources of noise in determining radiative fluxes and AOPs in the upper ocean are generally

greater than the effects incurred by the ship’s own shadow under optimal conditions.

4.1 INTRODUCTION

Accurate measurements of AOPs are required to develop a detailed understanding of the processes regulating bio-optical property distributions and their relationship to remotely sensed signals. Instrumentation designed

to measure properties of the underwater radiation field,

when deployed at relatively close proximity to a ship, may

encounter perturbations caused by the ship’s shadow (e.g.,

Poole 1936, Strickland 1958, Gordon 1985, Voss et al. 1986,

Waters et al. 1990, and Helliwell et al. 1990). This source

of error is of obvious importance and must be accurately

assessed. Poole (1936) estimated that the ship shadow error under diffuse skylight is about 10% at a depth of 5 m

when the radiometer is deployed approximately 2 m off the

stern, and also noted that this source of error decreases in

significance with increasing depth. The Monte Carlo simulations performed by Gordon (1985) indicate that the error

Editors’ Note: This chapter originally appeared as an article

in Ocean Optics XII, published by SPIE (Weir et al. 1994),

and is being included in this volume with the permission of the

authors and SPIE. Minor editorial changes have been made to

reflect the style of The SeaWiFS Technical Report Series.

in downwelling irradiance rarely exceeds 2% as long as skies

are clear and the sun is within 45◦ of the stern. At low solar elevations, however, these errors can increase to about

10%. Gordon (1985) also shows that the errors are reduced

as the instrument is moved horizontally away from the

ship, although errors during diffuse light conditions may

remain as high as 30%. Voss et al. (1986) conducted an experiment with an extendable sea-going crane that showed

values of upwelling radiance, Lu(z, λ), decrease by 10–20%

unless the instrument is deployed more than 5 m from the

ship.

Ship shadow perturbations are likely to be the greatest

near the sea surface. This factor is critical for the development of ocean color algorithms, as maximum accuracy

must be sought for the determination of calculated parameters such as the remote sensing reflectance, Rrs(λ).

Several studies have attempted to completely avoid the

ship’s shadow by floating optical instrumentation a considerable distance from a ship (Gordon and Clark 1980, Clark

1981, and Waters et al. 1990). These deployment strategies are difficult to conduct operationally, particularly in

rough seas. Such strategies also place severe limits on the

25
Case Studies for SeaWiFS Calibration and Validation, Part 3

amount of data that can be collected, restrict linkages to

other oceanographic observations, and limit time-scale resolution, e.g., Dickey and Siegel (1993).

In order to completely avoid the ship’s shadow when

measurements of downwelling irradiance, Ed(z, λ), are being made, Mueller and Austin (1992 and 1995) suggest that

the deployment of optical instrumentation should be at a

distance, ξd. Mueller and Austin (1992 and 1995) define

ξd using

ξd = sin(48.4◦)

Kd(λ) , (18)

where Kd(λ) represents the vertical attenuation coefficient

for downwelling irradiance. Typical values for Kd(λ) off

Bermuda range from 0.02–0.08 m−1 (Siegel et al. 1994),

which result in recommended deployment distances of 9–

40 m from a ship’s stern. Similarly, recommendations for

deployment distances for Eu(z, λ) and Lu(z, λ) (ξu and ξL,

respectively) are given by Mueller and Austin (1992 and

1995) as

ξu = 3

Ku(λ)

, (19)

and

ξL = 1.5

KL(λ)

, (20)

where Ku(λ) and KL(λ) are the vertical attenuation coefficients for upwelled irradiance and radiance, respectively.

Values of Ku(λ) and KL(λ) are roughly equal to values

of Kd(λ). Typical values of ξu and ξL are usually greater

than 30 m, which is nearly the length of the ship used in

this study. The distances recommended by (18)–(20) are

based only on geometric relations, and are independent of

ship size, sky conditions, sea state, deployment method,

and the orientation of the ship with respect to the solar

beam.

In this study, the effects of ship shadows upon data collected from the R/V Weatherbird II—length 35.05 m, beam

8.53 m, and draft 2.60 m—are examined. The Weatherbird

II is used by the Bermuda Bio-Optics Project (BBOP) to

make routine spectroradiometer casts in conjunction with

the Joint Global Ocean Flux Study (JGOFS) Bermuda Atlantic Time-Series Study (BATS). Spectroradiometer profiles were made using an extendable boom to deploy the

BBOP package, which allowed profiles to be made up to

6 m off the stern of the Weatherbird II. These data are

compared with data collected using the optical free-falling

instrument (OFFI) described by Waters et al. (1990). The

OFFI data provide a control which can be used to search

statistically for the effects of the ship’s shadow. The measurements used were made under optimal conditions (i.e.,

clear skies, stern-to-ship solar orientation, near-constant

illumination, etc.), and thus, provide the basis for evaluating the role of the ship shadows in developing ocean color

remote sensing algorithms using the BBOP data set.

4.2 EXPERIMENTAL METHODS

The observations presented here were made from the

Weatherbird II off Bermuda on 7 July and 9–10 July 1992.

Two underwater spectroradiometers—the BBOP and the

OFFI—were lowered simultaneously from the Weatherbird

II to about 50 m (Fig. 13). The BBOP package consisted

of a BSI MER-2040 underwater spectroradiometer, interfaced with a SeaTech transmissometer, chlorophyll fluorometer, and SeaBird conductivity, temperature, and pressure sensors (Siegel et al. 1994). The OFFI is a modified

BSI MER-2020 underwater unit with a case outfitted with

buoyant fins to provide stability and control in its descent

rate (Waters et al. 1990).

The BBOP was lowered at three distances off the stern

(1, 3, and 6 m) using the extendable boom. The OFFI was

fished out, i.e., deployed astern of the ship, at least 20 m

before descent. Profiles were made simultaneously so that

instantaneous fluxes from the two instruments could be

compared. Both instruments were deployed with the sun

off the stern so that the ship’s shadow trailed away and

behind, which is part of the normal BBOP sampling procedure. Both instruments sampled Ed(z, λ) and Lu(z, λ)

in spectral wavebands centered at 410, 441, 488, 520, and

565 nm.

Using laboratory facilities at the University of California at Santa Barbara (UCSB), radiometric calibrations

were performed on both instruments two weeks prior to,

and two months after, this cruise. The same calibration

lamp (UCSB lamp F-303) was used for both calibrations.

The calibration coefficients for the BBOP instrument varied by less than 0.5% for irradiance, and less than 3% for

radiance, between both calibration dates. The OFFI calibration coefficients differed by 1–4% for both the irradiance

and radiance channels. Calibration coefficients, which were

obtained from the precruise determinations, were used for

the analysis presented here.

The two individual bio-optical data sets were processed

using the BBOP data processing system (Sorensen et al.

1994). The BBOP data processing system is used to:

1) Eliminate radiation values that are below a specified threshold;

2) Identify time segments where cloud perturbations are minimal;

3) Smooth specified channels of data and remove

spikes, although not for Ed(z, λ) or Lu(z, λ); and

4) Bin the data into 1 m vertical depth bins.

The derived AOPs, such as Kd(z, λ) and the remote sensing reflectance Rrs(z, λ), are also calculated. In addition,

the downwelling irradiance and upwelling radiance spectra

just beneath the sea surface, Ed(0−, λ) and Lu(0−, λ), are

determined by fitting profile data from the upper 20 m to

the Beer-Lambert relation. Sorensen et al. (1994) gives a

complete description of the BBOP data processing system

and data handling procedures used by BBOP.

26
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 13. Diagram of the BBOP ship shadow evaluation experimental design.

4.3 RESULTS

Two distinct statistical analyses are performed to evaluate the effects of the shadow cast by the R/V Weatherbird

II. The first analysis compares the statistical differences

between simultaneously sampled BBOP and OFFI data as

the BBOP radiometer is deployed at various distances off

the ship’s stern. Differences between the two data sets are

interpreted here to indicate the effects of the ship shadow,

after accounting for a constant calibration error and the

occurrence of random errors, i.e., noise. This analysis will

be referred to as the simultaneous comparison. The second analysis, referred to as the multi-distance comparison,

uses data obtained throughout the experiment to compare

mean derived AOP values at each of the four distances (1,

3, 6, and greater than 20 m). The object of this comparison is to address whether any significant differences can

be found among the AOP determinations.

4.3.1 Simultaneous Comparison

The simultaneous comparison evaluates the statistical

difference between the fluxes and AOPs measured by the

BBOP profiler at two distances off the ship’s stern, and

identical parameters determined using the OFFI profiler.

The BBOP casts with ξ = 1 m are referred to as the B1

casts, and the BBOP casts with ξ = 6 m are denoted as

B6. A total of 15 paired OFFI-BBOP casts, 7 B6 and 8

B1 casts, are used in this analysis. In the following discussion, the OFFI casts are designated O20. Data from the

two instruments are estimated to be collected simultaneously to within 5 sec. The statistical differences between

OFFI (O20) and BBOP (B1 or B6) measurements of downwelling irradiance, upwelling radiance, and derived AOPs

are compared. A positive difference means that the BBOP

measurements underestimate the O20 values, which may

indicate a ship shadow influence. The error bars shown

correspond to 90% confidence intervals (c.i.) for the mean

estimates throughout the analysis.

For the experimental measurement of downwelling irradiance at 441 nm, there are no statistically significant

differences (at the 90% confidence level) between the O20

casts and either the B1 or the B6 casts (Fig. 14, top).

However, the B1 mean differences are consistently positive, suggesting that the B1 casts may be affected by the

ship’s shadow, although not in a statistically significant

manner. The B1 − O20 difference increases as the sea surface is approached, which also suggests the signature of a

ship shadow. The vertical profile of the B6 − O20 differences does not give any indication of a ship shadow influence. The other matching wavelengths (410, 488, 520,

and 565 nm) for Ed(z, λ) gave similar results, which are

not shown here. The differences between the B1 and O20

upwelled radiance data at 441 nm, Lu(z, 441), are significantly different from zero and show a ship shadow pattern

with depth, as the mean difference increases significantly

towards the sea surface (Fig. 14, bottom). This divergence

of the measurements is particularly apparent over the top

20 m, and the differences become smaller with increasing

27
Case Studies for SeaWiFS Calibration and Validation, Part 3

depth. The B6 − O20 mean difference for Lu(z, 441) shows

no statistically significant pattern with depth. This observed reduction in ship shadow effects with distance from

the ship is consistent with previous studies.

In terms of the derived AOPs Kd(z, λ) and Rrs(z, λ),

no significant differences are found between either the B1

or B6 BBOP casts and the O20 data (Fig. 15). In particular, there are no consistent variations in these differences with depth that may be simply attributed to a ship

shadow. This is true even for the mean Rrs(z, λ) differences (Fig. 15, bottom) where the O20−B1 Lu(z, λ) observations showed some deviations attributed to ship shadow.

This lack of a signature in Rrs(z, λ) may be due to the fact

that both the O20 − B1 Lu(z, λ) and Ed(z, λ) determinations are affected by the ship shadow. The decrease in both

Lu(z, λ) and Ed(z, λ) due to the ship shadow, may actually

cancel the effects of the shadow on values of Rrs(z, λ).

Accurate measurement of both the upwelling and downwelling light streams just beneath the sea surface is critical

to the development of algorithms for estimating bio-optical

properties from satellite sensors. The differences between

the O20 and B1 or B6 estimates of Ed(0−, λ) and Lu(0−, λ),

for both the B1 and B6 distances off the stern, are shown

in Fig. 16. The mean Ed(0−, λ) differences show no significant differences from zero, or between the two deployment

distances (Fig. 16, top). Significant divergence from zero

is found, however, for the mean Lu(0−, λ) differences for

all wavelengths except 565 nm.

Significant differences are also found for some of the

wavelengths in the B6 − O20 comparison, although it is

unclear how large of a calibration difference remains between the two instruments. In particular, the size of the

disparity in the mean differences between the two BBOP

deployment distances increases as λ is decreased. These

spectral observations are consistent with numerical results

that indicate that the ship shadow effects scale as c(λ) ξ,

where c(λ) is the beam attenuation coefficient and ξ is the

distance from the ship (Gordon 1985). The value of c(λ)

at 565 nm is likely to be larger than its value at 441 nm.

These results further show that the influence of the ship’s

shadow will be more critical for the upwelling light stream

rather than for downwelling light, as is expected. These

results can be compared to Mueller and Austin (1992 and

1995).

4.3.2 Multi-Distance Comparison

The second analysis compares the mean values of derived AOPs using data obtained for each of the four distances (1, 3, 6, and greater than 20 m) throughout the experiment. All available casts are used for this analysis and

the AOP determinations are classified by their distance

from the stern of the Weatherbird II. The variations in Kd

and Rrs at 441 nm with depth and deployment distance are

shown in Fig. 17. Only rarely are there statistically significant differences (i.e., non-overlapping error bars), for the

four deployment distances, though trends with distance are

apparent. Similar results, not shown here, are found with

the other wavelengths sampled by the BBOP.

Spectral differences in the remote sensing reflectance

just beneath the sea surface, Rrs(0−, λ), can be used to surmise the spectral structure of the ship’s shadow (Fig. 18).

Again, no significant differences are found for any of the

wavelengths. This analysis again suggests that the effects

of the ship shadow on the upwelled light field may be effectively canceled out when normalized by the downwelling

irradiance.

4.4 DISCUSSION

In order to correctly interpret the present results, it

must be recognized that the observed mean differences

are a composite of one or more signals: the actual ship

shadow perturbation, a constant calibration difference between the OFFI and BBOP, and random errors due to the

poor sampling of short time-scale noise (i.e., wave glint,

small clouds, ship roll, and other effects). The influence

of random noise can be reduced by averaging over many

individual casts; however, the sample size for the simultaneous comparison is relatively small (N = 7 or 8). Comparisons between the pre- and post-cruise calibrations indicate the occurrence of only small calibration differences.

The mean difference observed is, therefore, primarily composed of the ship shadow perturbation as modulated by

an incompletely sampled random noise field. Elucidation

of the ship shadow perturbation above this random noise

element is the present goal.

The results of the simultaneous comparison show that

there are no significant differences between the comparison

of O20 Ed(z, λ) values and either B6 or B1 irradiance determinations (Fig. 14, top). This result is consistent with

the irradiance direct beam cone remaining off the stern

(Gordon 1985 and Voss et al. 1986). The determination

of upwelled radiance, however, clearly shows the effects of

the ship shadow for the B1 comparison, but not for the B6

comparison (Fig. 14, bottom). A significant difference is

also observed between the B1 and B6 mean Lu(0−, λ) differences (Fig. 16, bottom). At all wavelengths, B1 mean

differences were consistently larger than those calculated

from B6 data, with the O20 value being predictably and

significantly greater than its simultaneous BBOP measurement. These results clearly show that BBOP data must

be taken more than 1 m off the stern of the Weatherbird

II, but does not have to be taken beyond 6 m, in order to

avoid the ship’s shadow perturbation.

The results of the multidistance comparison provide additional information for fine tuning of the distance criteria

for the Weatherbird II. The derived AOP profiles showed

little variability among the four different deployment distances. The multidistance comparisons support the notion

that the effects of the ship’s shadow may be effectively

masked by random errors associated with the many sources

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Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 14. Mean differences (with 90% c.i.) of simultaneous determinations of downwelling irradiance at

441 nm, shown in the top panel, and upwelling radiance at 441 nm, shown in the bottom panel. The

differences are between O20 casts and B1 (o; 1 m off the stern) or B6 (×; 6 m off the stern) BBOP casts.

29
Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 15. Mean differences (with 90% c.i.) of simultaneous determinations of the diffuse attenuation

coefficient for downwelling irradiance, Kd(z, 441), shown in the top panel, and the remotely sensed

reflectance, Rrs(z, 441), shown in the bottom panel. The differences are between O20 casts and B1 (o;

1 m off the stern) or B6 (×; 6 m off the stern) BBOP casts.

30
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 16. Mean differences (with 90% c.i.) of simultaneous determinations of the downwelling irradiance

spectrum just beneath the sea surface, Ed(0−, λ), shown in the top panel, and the upwelling radiance

spectrum just beneath the sea surface, Lu(0−, λ), shown in the bottom panel. The differences are between

O20 casts and B1 (o; 1 m off the stern) or B6 (×; 6 m off the stern) BBOP casts.

31
Case Studies for SeaWiFS Calibration and Validation, Part 3

Fig. 17. Mean (with 90% c.i.) determinations of the diffuse attenuation coefficient for downwelling

irradiance, Kd(z, 441), shown in the top panel, and the remotely sensed reflectance, Rrs(z, 441), shown

in the bottom panel, as a function of depth for four different deployment distances (1, 3, 6, and > 20 m).

32
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 18. Spectral structure of the remote sensing reflectance just beneath the sea surface, Rrs(0−, λ),

evaluated at four different deployment distances (1, 3, 6, and greater than 20 m).

of geophysical and sampling noise. Voss et al. (1986) found

very little differences (less than 6%) in values of Kd(z, λ)

and Rrs(z, λ) profiles taken at 0 and 9 m from the ship.

The differences were 0–3% and 1–6%, respectively, in the

upper 20 m. Below 20 m, moreover, they found that the

effects of the ship shadow have altogether disappeared, as

is shown in this study.

In conclusion, little variability in downwelling irradiance is observed for any of the deployment distances off

the Weatherbird II. Significant variations are found, however, for upwelling radiance when the deployment distance

is less than 3 m. These findings suggest that the ship’s

shadow exerts its greatest influence in the upper 20 m, with

the largest perturbation at the sea surface. Measurements

of optical properties from the Weatherbird II during clear

skies with the stern pointed into the sun can be made as

long as the deployment distance off the stern is 3 m or

greater. It is stressed that this analysis holds only for

deployments made off the stern of the R/V Weatherbird

II under clear sky conditions. The effects of variable sea

state, sun glint, diffuse sky, and different hull shapes and

sizes have not been evaluated, and additional experiments

are necessary.

Acknowledgments

This work was supported by the National Science Foundation

(OCE 91-16372 and OCE 90-16990), NASA (NAGW-3145),

and the SeaWiFS Project Office. Computational support from

Digital Equipment Corporation’s flagship research project, Sequoia 2000, is also gratefully acknowledged.

33
Case Studies for SeaWiFS Calibration and Validation, Part 3

Chapter 5

SeaWiFS Global Fields: What’s In a Day?

Guillermo Podesta

Rosenstiel School for Marine and Atmospheric Sciences

Universityof Miami

Miami, Florida

Abstract

This chapter defines the procedure to be employed to delineate data corresponding to one day of SeaWiFS

operation. The definition is required for data analysis with minimal temporal aliasing in the same region of

observation. The definition also allows proper assignment of data into daily fields which will be used for the

generation of weekly and monthly average products.

5.1 INTRODUCTION

The basic products to be generated by the SeaWiFS

Project are global daily fields of geophysical quantities,

such as phytoplankton pigment concentration. The daily

fields will be the basis of subsequent temporal compositing

into weekly and monthly products. One basic question,

however, is: what constitutes a day’s worth of data? This

question is the subject of this chapter.

The need for a consistent definition of a data day is

only truly relevant to the production or analysis of global

data fields. If one is dealing with a limited area (although

in this case, limited means anything less than global, and

can encompass entire ocean basins), one takes advantage

of the fact that satellite sensors usually sample a region

at approximately the same time, or times, every day. In

this way, data separated by approximately 24-hour periods

can be assigned to different data days. Analyses of the

resulting daily data fields will introduce a minimal amount

of temporal aliasing, as the difference in sampling times

will be on the order of a couple hours over an approximate

repeat cycle of a few days.

In contrast, when daily global satellite data fields are

to be constructed, a consistent definition of a data day

needs to be adopted. This definition should be easy to implement in practice and should minimize temporal aliasing

and discontinuities in the resulting products. In the following sections, some of the various alternatives will be

explored.

5.2 TEMPORAL DEFINITION

The most obvious definition of a data day is a 24-hour

period. For instance, a daily field would encompass all

the data collected between 00:00:00 Coordinated Universal Time (UTC) (or any other arbitrary start of the day)

and 23:59:59 UTC. This definition is simple, intuitive, and

extremely easy to implement. Its negative aspects, however, will become apparent when one considers the orbital

characteristics of the SeaStar spacecraft on which SeaWiFS

will be flown.

To illustrate the problem, a plot of nadir tracks is presented for the SeaStar spacecraft (Fig. 19). To simplify

the visualization, only the descending tracks are displayed,

i.e., the spacecraft is flying from north to south. The SeaStar descending tracks correspond to daytime data, which

is the only data archived for SeaWiFS other than special

calibration measurements. The nadir tracks were generated using the program SeaTrack, made available by the

SeaWiFS Project. A dummy set of orbital elements for the

SeaStar spacecraft [in North American Air Defense (NORAD) Command two-line format] was also obtained from

the Project.

For comparison with subsequent cases, the choice is to

begin the hypothetical 24-hour data day on 2 April 1994

at 00:00:00 UTC, when the nadir track intersects the 180◦

meridian (marked Beg on Fig. 19). The descending orbit

immediately after the beginning of the data day is labeled

N. Subsequent descending tracks pass to the west, and are

offset by a distance of about 25◦ of longitude at the equator. The swaths viewed by SeaWiFS in consecutive orbits

have an increasingly larger overlap with latitude. This

means that areas at high latitudes (greater than about

50◦) may be sampled twice or more during a data day.

When an area is sampled in two consecutive descending

orbits, measurements will be separated by about an hour

and a half. Unless one is concerned with features having

34
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

0 ̊ 60 ̊E 120 ̊E 180 ̊E 120 ̊W 60 ̊W

60 ̊S

30 ̊S

0 ̊

30 ̊N

60 ̊N

Beg

N+2

N+1

N

N+14

N+13

Fig. 19. Descending SeaStar tracks for a 24-hour data day beginning on 2 April 1994 00:00:00 UTC.

The data day begins at the point labeled Beg. The day ends during an ascending orbit (not shown). The

first orbit after the beginning of the data day is labeled N, and subsequent orbits are labeled N+1...N+14.

very small scales, or with calculation of rates, it is probably safe to assume that the ocean fields will not change

significantly between consecutive passes; thus, temporal

aliasing should be negligible. At the same time, at low

and intermediate latitudes (approximately between 50◦ S

and 50◦ N), the swaths do not overlap, and there will be

gaps in the daily coverage (Hooker and Esaias 1993).

The SeaStar polar platform, which will carry SeaWiFS,

is planned to have an orbital period of approximately 99

minutes. The actual period will depend on the spacecraft

altitude, and therefore, may vary with time as the altitude

of the satellite changes. Given an orbital period of about

99 minutes, the number of revolutions that the SeaStar

spacecraft will complete in a 24-hour period is approximately 14.55. The last descending orbit of the 24-hour

data day is labeled N+14. It is apparent from Fig. 19 that

the 24-hour day leaves a large gap in coverage north of the

beginning of the day, between orbits N+1 and N+14.

A second problem inherent in the temporal definition

of a data day is the existence of areas on the global fields

with large temporal discontinuities in sampling times, even

though these areas may be spatially contiguous. For instance, consider descending track N+14 in Fig. 19, the last

track of the data day. To the north of that track, i.e., over

the Arctic Ocean north of Alaska, data are contributed by

track N+1 and, possibly N+2, although this orbit appears

to be too far north. These two tracks, however, were sampled near the beginning of the data day, more than 20 hours

before track N+14. The daily fields will then contain, in

addition to a wide gap, large temporal discontinuities between data swaths from tracks N+14 and N+1. If there is

overlap between the two swaths, data collected far apart

in time may be averaged, once again introducing potential

aliasing. Similar problems occur in the area south of track

N (south of New Zealand), which is sampled by tracks N+14

and N+13 much later in the day.

The large gaps in coverage, as well as potential aliasing

and temporal discontinuity effects associated with the 24-

hour definition, are further complicated by the fact that

the locations where gaps occur change in time. Figure 20

shows the locations, along the SeaStar nadir tracks, of the

boundaries between 24-hour data days for a 10-day period beginning on 2 April 1994. The dot labeled 1 corresponds to the beginning of the period on 2 April 1994

at 00:00:00 UTC. The dot labeled 2 indicates the beginning of the second 24-hour data day, and so forth. The

dot marked 11 corresponds to the end of the period on 12

April 1994 at 00:00:00 UTC. The shift in the location of

the daily boundaries is a direct result of the difference between the 24-hour data day and the longer time it would

take the spacecraft to complete a number of revolutions

which would ensure global coverage.

5.3 SPATIAL DEFINITION

Because of the problems associated with a temporal

data day definition, the implications of adopting a spatial

definition have been explored. In this case, the boundary between data days is not defined by time, but by a

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Case Studies for SeaWiFS Calibration and Validation, Part 3

0 ̊ 60 ̊E 120 ̊E 180 ̊E 120 ̊W 60 ̊W

60 ̊S

30 ̊S

0 ̊

30 ̊N

60 ̊N

1

2

3

5

7

9

11

4

6

8

10

Fig. 20. Locations of the boundaries of 24-hour data days for a 10-day period beginning on 2 April

1994 00:00:00 UTC, at the dot labeled 1.

fixed geographic reference. A similar criterion is commonly

used for designating orbit numbers in several spacecraft—

the orbit number usually is incremented upon crossing the

equator. For initial investigations, the 180◦ meridian was

selected as the boundary between data days.

Figure 21 shows SeaStar nadir tracks for a spatiallydefined data day. Because the nadir tracks cross the reference line seven or eight times during a day, one of the

crossings must be selected to be the beginning of a data

day. An operational definition for the selection of the crossing, which initiates the data day, is presented in Fig. 21.

For this discussion, the day is defined to begin on 2 April

1994 at 00:00:00 UTC, when the spacecraft crosses the 180◦

meridian flying from north to south. Notice that this is the

same time at which the 24-hour data day shown on Fig. 19

started, but it is entirely fortuitous that the 180◦ crossing

took place at 00:00:00. The first descending track of the

day is labeled N.

In this case, the end of the data day is defined as the

moment when the nadir track crosses the 180◦ meridian

during revolution N+15. This happens, for the example

given, approximately on 3 April 1994 at 00:30:00 UTC.

The observation most readily apparent is that a spatial

definition will result in a data day that does not necessarily correspond to a 24-hour day; in this case, the data day

is approximately 24 hours and 30 minutes long.

Note that Fig. 21 is approximate for two reasons. First,

sometimes one less revolution is required to ensure almost

complete global coverage, that is, the last orbit of the day

would be N+14. The data day would be about 23 hours and

22 minutes long in this case. Second, the spatial definition

is applied on a pixel-by-pixel basis, that is, pixels along the

same scan line on a given orbit can be assigned to different

days, depending on whether they are on one side or the

other of the 180◦ meridian.

Figure 22 illustrates the pixel-by-pixel assignment of

data to a given day. The figure shows a schematic description of the sampling pattern of the SeaWiFS instrument as

it flies over the 180◦ meridian. Because there is not yet a

scanner model for SeaWiFS, nadir tracks and scan lines are

shown for the Advanced Very High Resolution Radiometer

(AVHRR), which has slightly wider scans than SeaWiFS.

The figure shows about 20 minutes of nadir track, i.e.,

±10 minutes from the 180◦ meridian crossing. The scan

lines shown on Fig. 22 are separated by one minute. Pixels

along a given scan line that are located east of 180◦ are

assigned to day K (K is an arbitrary designation for a given

day). If pixels along the same scan line are west of 180◦,

those pixels are assigned to the following day (K+1). It

is apparent from Fig. 22 that even before the nadir track

crosses the 180◦ meridian, pixels are already being assigned

to day K+1. Conversely, after the nadir track has crossed

the reference meridian, pixels east of the meridian are still

being allocated to day K. It is this allocation mechanism

that makes it difficult to precisely define the duration of a

data day.

5.3.1 Beginning of the Data Day

How is the spatial definition of a data day implemented

in routine processing of global satellite data fields? The

first step is to define a meridian, which will serve as the

36
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

0 ̊ 60 ̊E 120 ̊E 180 ̊E 120 ̊W 60 ̊W

60 ̊S

30 ̊S

0 ̊

30 ̊N

60 ̊N

Beg

End

N+2

N+1

N

N+15

Fig. 21. SeaStar descending orbits for a spatially-defined data day beginning on 2 April 1994 00:00:00

UTC. At this time, the nadir track crosses the 180◦ meridian. The day ends when the nadir track crosses

the 180◦ meridian (square labeled End) on 3 April 1994 00:30:00 UTC.

120 ̊E 180 ̊E 120 ̊W

30 ̊S

0 ̊

30 ̊N

60 ̊N

Day K+1 Day K

Fig. 22. AVHRR nadir track and scan lines for a 20 minute period centered about the 180◦ meridian

crossing. Pixels to the east of the 180◦ meridian (marked in a thicker line) get assigned to a given data

day K, whereas the pixels to the west of the meridian correspond to data day K+1.

37
Case Studies for SeaWiFS Calibration and Validation, Part 3

reference for the spatial definition. The 180◦ meridian used

in the previous examples is a good choice, as it minimizes

differences between actual dates and the dates assigned

to the data days. As the spatial data days are not 24

hours long, a suitable naming convention will have to be

established.

A second step in defining a data day is to decide which

of the descending crossings of the reference meridian will

mark the beginning of each data day. As mentioned above,

there are either seven or eight descending crossings of the

reference meridian in a day. This pattern is illustrated in

Fig. 23, which shows the latitude of descending crossings

of the 180◦ meridian as a function of time for the SeaStar

spacecraft, beginning on 2 April 1992 at 00:00:00 UTC. A

period of about 10 days duration, ending on 12 April 1994

at 00:37:00 UTC, is shown in the figure. Most of the crossings (shown as dots) take place at high latitudes, and one

or two crossings per day occur at tropical-to-intermediate

latitudes.

For a given day, any of the crossings of the 180◦ meridian shown on Fig. 23 can be potentially selected as the

one marking the beginning of a data day for descending

orbits. For operational purposes, the following definition

is proposed: A data day for descending orbits is defined

to begin at the descending crossing of the 180◦ meridian

that is closest to the equator. Crossings that satisfy this

definition are shown as large squares in Fig. 23. Such a

definition will be the easiest to implement because there is

always only one crossing in a day that fulfills the condition.

Consecutive crossings may, however, in certain instances

have very similar absolute latitudes of intersection, one in

the Southern Hemisphere, and the other in the Northern

Hemisphere.

The alternating solid and dashed lines in Fig. 23 indicate consecutive data days. Initially, the latitude of

data day initiation seems to follow a regular progression to

the south, alternating between the Northern and Southern

Hemispheres. Note, however, that the progression is interrupted near the end of the period illustrated. In this case,

the next to last crossing would continue the progression,

but the following crossing (the last square in the sequence)

is actually closer to the equator. Following the proposed

definition, the data day is extended until the next crossing,

which is located in the Northern Hemisphere, i.e., the data

day is slightly longer—one more revolution in this case.

The southward progression of the crossings subsequently

resumes.

Table 19 lists the start times of descending data days

for a 15-day period beginning on 2 April 1994, as well

as the latitude where the crossing of the 180◦ meridian

occurs. It must be stressed that, because of the pixelby-pixel allocation described above, parts of the field will

include data collected both before and after the times listed

in Table 19. In addition, as stated above, an appropriate

naming convention will have to be worked out for the data

days. For instance, the data day considered as April 4

actually begins on 3 April 23:52 UTC and ends on 5 April

00:23 UTC.

Table 19. The beginning times of 15 data days for

descending orbits of the SeaStar spacecraft. The

latitude of the 180◦ meridian crossing is also shown.

Date Beginning Time Latitude of

[April 1994] [UTC] 180◦ Crossing

2 00:00:00 −16.1

3 00:30:00 35.7

3 23:52:00 −22.9

5 00:23:00 27.4

5 23:46:00 −31.8

7 00:17:00 18.0

7 23:39:00 −39.5

9 00:11:00 7.8

9 23:32:00 −46.0

11 00:05:00 − 2.7

12 00:37:00 42.9

12 23:59:00 −13.0

13 23:52:00 −22.9

15 00:24:00 27.4

15 23:46:00 −31.7

5.3.2 Advantages of the Spatial Definition

In the previous sections, a spatial definition was proposed for a data day, together with an objective definition

for the temporal beginning and end of such a data day.

So far, however, the advantages or disadvantages of the

proposed definitions have not been discussed.

Problems associated with the temporal definition of the

data day were:

1) The potential presence of gaps,

2) Aliasing and large temporal discontinuities, and

3) The changing locations of the 24-hour data day

boundaries.

The spatial definition avoids temporal changes in the location of boundaries, as the boundary is fixed, e.g., the 180◦

meridian. Furthermore, the spatial definition, to some

extent, reduces gaps in the coverage. The presence of

large temporal discontinuities among adjacent areas is still

present, however.

The large temporal discontinuities identified on Fig. 19,

north of Alaska and south of New Zealand, are still present

in Fig. 21. It is clear that the large temporal discontinuities occur in two places near the meridian that define the

separation between data days. The first place is the area

south of the first track of the data day and west of the

reference line. The second area with discontinuities occurs

north of the last track of the data day, east of the reference

line. As a result of the large temporal discontinuities that

occur between adjacent swaths when the swaths overlap

at higher latitudes, data that were sampled far apart in

time will once again be averaged. Elsewhere on the global

38
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Fig. 23. Latitude of crossing of the 180◦ meridian for SeaStar descending orbits. The data shown are

for a period approximately 10 days long, beginning on 2 April 1994 00:00:00 UTC and ending on 12

April 1994 00:37:00 UTC. Crossings are indicated by small dots. Large squares indicate crossings that

begin data days. The alternating solid and dashed lines indicate consecutive data days.

fields, any given track is surrounded by tracks sampled one

orbital period (about 99 minutes) earlier or later.

The presence of temporal discontinuities, or the averaging of data collected at very different times, may not be

too important for some applications, although users should

certainly be made aware of the occurrence of these events.

In other situations, however, such temporal discontinuities

may cause significant problems. Examples of such applications may be the estimation of the translation speed of

certain features, or the computation of fluxes.

In order to limit the large meridional temporal discontinuities near the data day boundary, the short track segments north and south of the first and last tracks of the

data day could simply be eliminated (e.g., parts of N+1,

N+2, N+3, N+13, and N+14). This approach is illustrated

in Fig. 24, which shows descending tracks between 2 April

1994 00:00:00 UTC and 3 April 1994 00:30:00 UTC, i.e.,

the data day shown on Fig. 21. The map is now centered

at 0◦, rather than at 180◦, as in Fig. 21. Note that the

nadir tracks, for which segments were eliminated, seem to

end a bit before or after the 180◦ line. This break occurs

because positions were predicted at one-minute increments

by the orbital model used.

The elimination of segments may result in areas not being sampled, e.g., upper left and lower right corners of the

map. These gaps might possibly be filled by the swath of

the first and last tracks of the data day (tracks N and N+15

in the south and north, respectively). The size of the gaps

is, however, a function of the latitude of the reference line

crossing which defines the beginning of the data day. As

shown in Fig. 23, this latitude changes with time, moving

north and south approximately between 50◦ N and 50◦ S.

When the crossing is farther north, the gap to the south of

the first track will be larger. Conversely, when the crossing is further south, the gap north of the last track will get

larger.

It is proposed that one additional swath be added at

each end of the data day in order to replace the eliminated segments. Plots of nadir tracks for days in which

the crossings are farthest north or south (not shown here)

have shown that one additional swath is enough to fill each

of the gaps, and a second swath would not make a significant contribution. The added swaths would be temporally

continuous with the first and last tracks of each data day,

thus eliminating the problems of temporal discontinuities.

An operational scheme would involve the following steps:

1. The times corresponding to the beginning and

end of a spatially-defined data day are found

following the definition suggested above. These

times will be referred to as the beginning and

end of the data day.

2. Data east of the 180◦ meridian, collected up to

12 hours after the beginning of the data day,

39
Case Studies for SeaWiFS Calibration and Validation, Part 3

180 ̊W 120 ̊W 60 ̊W 0 ̊ 60 ̊E 120 ̊E 180 ̊E

60 ̊S

30 ̊S

0 ̊

30 ̊N

60 ̊N

Beg

N+2

N+1

N

End

N+15

N+14

Fig. 24. SeaStar descending orbits for a spatially-defined data day beginning on 2 April 1994 00:00:00

UTC. Segments that introduce large north-south temporal discontinuities (see text) are excluded.

will be excluded. Data west of the 180◦ meridian, sampled up to 12 hours before the end of the

data day, will be similarly excluded. The net result of these actions is similar to the elimination

of segments shown in Fig. 24.

3. To ensure full coverage, data collected up to 99

minutes before the beginning of the data day,

and covering the area west of the 180◦ meridian,

will be added to the beginning of the data day.

This addition fills the gap to the south of the

first track of the day. Data collected up to 99

minutes after the end of the data day, sampling

the area east of 180◦, are also added. These data

fill the gap north of the last track of the data day.

The end result is illustrated in Fig. 25.

Figure 25 shows the descending orbits for the data day

beginning approximately on 2 April 1994 00:00:00 UTC.

The gaps shown in Fig. 24 have been filled by the addition of two short segments, indicated by arrows and dotted

lines, on Fig. 25. Note that these segments have been sampled before (N-1) and after (N+16)—the times estimated

for the beginning and end of this data day (see Table 19).

However, because the added segments are close in time to

orbits N and N+15, the large temporal discontinuities have

been eliminated. The segments excluded from this data

day are the first portion of tracks N+1, N+2, and N+3 east

of 180◦, and the last portion of tracks N+13 and N+14 west

of 180◦.

5.3.3 An Alternative Explanation

To facilitate comprehension of the methodology, a simple analogy may be helpful. Envision a continuous strip

chart on which the continents are drawn. Above the chart

recorder there is a clock showing UTC time and date. As

the chart moves from left to right, a pen draws descending

tracks one at a time. The speed of the chart movement is

appropriate to ensure that the nadir track’s latitude and

longitude, corresponding to any given UTC time, are correct, i.e., the nadir tracks should look similar to those on

Figs. 24 and 25.

Suppose the chart is positioned so that the pen is just

crossing the 180◦ meridian, near the equator, on 2 April

1994. The clock time should be about 00:00:00 UTC. The

chart recorder is then allowed to run for almost 24 hours,

until a track crosses the 180◦ meridian again at about

36◦ N. The time should be about 00:30:00 UTC on 3 April

1994. If the chart is cut along the two 180◦ meridians

drawn (left and right), the tracks on the chart should look

exactly like Fig. 24. As in Fig. 24, there will be some gaps

in the coverage. On the right side of the chart, there is

a gap south of the first track (N) of the day. This gap

should have been filled by the last portion of tracks N+13

and N+14, which have been drawn to the left of the 180◦

meridian on the left side of the chart. These lines, however, were eliminated when the chart was cut along the left

180◦ line. Similarly, the gap north of the last track of the

day should have been filled by the initial portions of tracks

40
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

180 ̊W 120 ̊W 60 ̊W 0 ̊ 60 ̊E 120 ̊E 180 ̊E

60 ̊S

30 ̊S

0 ̊

30 ̊N

60 ̊N

N

N+15

N+16

N-1

Fig. 25. The data day beginning on 2 April 1994 00:00:00 UTC, showing the addition of two segments

(indicated by arrows and dotted lines) in order to minimize temporal discontinuities. The first track

sampled after the estimated beginning time of the day (Beg) is track N. The added segment south of

this track corresponds to the previous orbit (N-1). The last track before the estimated end time of the

data day (End) is track N+15. The added segment to the north corresponds to the next orbit (N+16).

N+1, N+2 and N+3. These segments were drawn east of the

180◦ meridian on the right side of the plot. As the 180◦ line

was cut along on the right, however, these segments were

excluded. It is apparent that the chart recorder analogy

reproduces the action of eliminating tracks which cause

large temporal discontinuities, as the end result looks exactly like Fig. 24. The gaps can be filled in the global fields

using the same chart recorder analogy.

Now envision the case in which the chart recorder does

not start at 00:00:00 UTC on 2 April 1994, but rather, the

chart is moved backwards and is started about 99 minutes earlier. If the recorder starts then, an additional

track (N-1) will be drawn before the nadir track of orbit N

crosses the 180◦ meridian at 00:00:00 UTC, which defines

the temporal beginning of the data day. The southern portion of track N-1 will fall west of the 180◦ meridian, filling

the gap previously existing in the south. Then the recorder

is allowed to run up to 99 minutes past the time originally

defined as the end of the day (3 April 1994, 00:30:00 UTC),

and again, an additional track will be drawn. If the last

track of the day is N+15, the northern portion of track

N+16 will fill the northern gap. Once the recorder has

been allowed to run for the estimated duration of the data

day, plus the additional 99 minutes on either end, a pair

of scissors is used to cut the chart along both 180◦ meridians. By doing this, the spatial pixel-by-pixel assignment

of data is applied to a given data day. The end result

should look exactly like Fig. 25. Finally, envision running

the recorder for long periods and repeatedly cutting the

long chart along the 180◦ meridians. Each of the maps

would correspond to one data day.

When discussing an elimination of orbital segments that

would result in large temporal discontinuities, the presentation could have given the impression that data in these

segments would be unused, and therefore wasted. If the

analogy presented above is followed, however, it is easy to

see that the data will not be deleted, but rather the data

will be assigned to the previous, or the following, data

days. For instance, the northern portions of tracks N+1,

N+2, and N+3 (not labeled) in Fig. 24 would be plotted to

the east of the right 180◦ meridian on the chart. When

the chart is cut, these portions get assigned to the previous data day, which begins on 1 April 1994 UTC. In the

same way, the southernmost portions of tracks N+13 and

N+14 are plotted to the west of the left 180◦ meridian;

thus, being assigned to the next data day after the chart

is cut along the meridian. The end result of the scheme

proposed is a daily global field where all parts of a field

are temporally separated from adjacent areas by, at most,

one orbital period.

41
Case Studies for SeaWiFS Calibration and Validation, Part 3

5.4 OTHER ISSUES

An aspect that has not been discussed so far is that at

both the extreme north and extreme south of the fields,

data from several tracks might be averaged within a data

day. At high latitudes, the spacecraft is flying in nearly an

east-west direction and, thus, the scan lines have a northsouth orientation. For instance, there are five or six passes

a day at high latitudes (Fig. 23) near the 180◦ meridian.

Some of these passes are excluded at high latitudes, as described above. In other high latitude regions, however, the

fields will contain the average of several passes. This overlap should not have too many consequences on SeaWiFS

products, as the areas affected will be mostly on land in

the Southern Hemisphere and under permanent ice cover

in the Northern Hemisphere. Furthermore, in these regions

the sensor may encounter limitations in available sunlight,

which may preclude sampling.

One final issue requiring discussion is that the spatial

scheme proposed above will result in temporal discontinuities in areas that straddle the reference line. Suppose that

a study is made of an area of the North Pacific Ocean, encompassed between 150◦ W and 150◦ E, and straddling the

180◦ line. If this study obtains a global field for a given

data day, it must be realized that the portion of the study

area west of 180◦ has been sampled much earlier than the

portion to the east. Again, this may not be relevant for

some research, but it could be in some cases. A solution

would be to place the reference line elsewhere, e.g., along

0◦, but there will always be some location where areas on

either side of the line will be sampled far apart in time.

Alternatively, a user might obtain product fields for two

consecutive data days and paste the appropriate portions.

In the Pacific example presented above, the eastern part

of the study area would be extracted from data day K and

the western part from day K+1.

To study the daily data of a region that includes 180◦

longitude, two consecutive daily products should be joined

at the seam. This procedure will produce data that are

continuous across the 180◦ meridian. These daily scenes

can then be averaged over time using a time binning algorithm to construct weekly or longer period composites of an

area straddling the 180◦ meridian. This method would produce the most accurate long-term composites. One could,

however, use the standard global products by joining areas

east and west of 180◦ from the same weekly, monthly, or

annual product. The latter method will result in a slight

temporal discontinuity across the 180◦ meridian, since the

earliest data contributing to the composite west of 180◦ is

not matched by continuous data east of 180◦. Similarly,

data east of 180◦ is not matched by data west of 180◦ on

the final day of the composite.

42
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

Glossary

A-band Absorption Band

AOP Apparent Optical Properties

AVHRR Advanced Very High Resolution Radiometer

BATS Bermuda Atlantic Time-Series Study

BBOP Bermuda Bio-Optics Project

BRDF Bidirectional Reflectance Distribution Function

BSI Biospherical Instruments, Inc.

CHORS Center for Hydro-Optics and Remote Sensing

c.i. confidence interval

CVT Calibration and Validation Team

CZCS Coastal Zone Color Scanner

DC Digital Count

EOSDIS Earth Observing System Data Information System

FEL Not an acronym; designates a type of irradiance

lamp.

GSFC Goddard Space Flight Center

IFOV Instantaneous Field-of-View

JGOFS Joint Global Ocean FluxStudy

MER Marine Environmental Radiometer

NASA National Aeronautics and Space Administration

NIST National Institute of Standards and Technology

NORAD North American Air Defense (Command)

OFFI Optical Free-Falling Instrument

PST Pacific Standard Time

R/V Research Vessel

SBRC Santa Barbara Research Center

SDSU San Diego State University

SeaWiFS Sea-viewing Wide Field-of-view Sensor

SI International System of Units (Syst ́eme International d’ Unit ́es)

SIS Spherical Integrating Source

S/N Serial Number

SNR Signal-to-Noise Ratio

SPIE Society of Photo-Optical Instrumentation Engineers

TOA Top of the Atmosphere

UCSB University of California at Santa Barbara

UTC Coordinated Universal Time

Symbols

a Regression coefficient.

b Regression coefficient.

B Band 7 width.

B1 BBOP casts 1 m from the ship’s stern.

B6 BBOP casts 6 m from the ship’s stern.

c(λ) Spectral beam attenuation coefficient.

Ed Incident downwelling irradiance.

Ed(z, λ) Downwelled spectral irradiance.

Eu Incident upwelling irradiance.

Eu(z, λ) Upwelled spectral irradiance.

f(λ) Instrument spectral response function.

Fi Immersion coefficient.

k Molecular absorption cross-section area.

Kd(z, λ) Vertical attenuation coefficient for downwelling irradiance.

KL(z, λ) Vertical attenuation coefficient for upwelled radiance.

Ku(z, λ) Vertical attenuation coefficient for upwelled irradiance.

L Radiance of light transmitted through absorbing oxygen.

Lt Radiance measured at a satellite, i.e., orbiting sensor.

L0 Model radiance without absorbing oxygen.

Latm Radiance of light reflected from the atmosphere.

Lsfc Radiance of light leaving an ocean surface and passing through the atmosphere.

Lu(z, λ) Upwelled spectral radiance.

m Air mass.

N Total number of oxygen molecules per unit area in

a vertical column of the atmosphere.

O20 OFFI casts 20 m from the ship’s stern.

p Surface pressure.

pdev Pressure deviation between the minimum and maximum surface pressures compared to 1,013 mb.

pref Reference pressure.

R2 The square of the linear correlation coefficient.

Rrs(z, λ) Remote sensing reflectance.

S(λ) Solar spectral irradiance.

sxy Residual standard deviation.

T(λ) Two-way transmission through oxygen in the model

layer.

T(λ, θ, θ0) Two-way transmission through oxygen in the model

layer in terms of zenith angle (θ), and solar angle

(θ0).

W Equivalent bandwidth.

∆L The difference between L and L0.

∆p The difference in atmospheric pressure.

θ Zenith angle of the line-of-sight in a plane-parallel

atmosphere.

θ0 Solar zenith angle.

λ Wavelength.

ρ Reflectance.

σ Standard deviation.

τox(λ) Optical thickness due to oxygen absorption.

ξ Actual deployment distance.

ξd Calculated deployment distance for downwelling irradiance measurements.

ξu Calculated deployment distance for upwelling irradiance measurements.

ξL Calculated deployment distance for upwelling radiance measurements.

χ Proportionality constant.

43
Case Studies for SeaWiFS Calibration and Validation, Part 3

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3,300 and 12,500  ̊A. Solar Phys., 90, 205–258.

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O’Brien, 1994: Seasonal variability of light availability and

its utilization in the Sargasso Sea. J. Geophys. Res., (submitted).

Sorensen, J.C., M. O’Brien, D. Konoff, and D.A. Siegel, 1994:

The BBOP data processing system. Ocean Optics XII, J.S.

Jaffe, Ed., SPIE, 2,258, 539–546.

Strickland, J.D.H., 1958: Solar radiation penetrating the ocean:

A review of requirements, data, and methods of measurement, with particular reference to photosynthetic productivity. J. Fish. Res. Bd. Canada, 15, 453–493.

Voss, K.J., J.W. Nolten, and G.D. Edwards, 1986: Ship shadow

effects on apparent optical properties. Ocean Optics VIII,

P.N. Slater, Ed., SPIE, 637, 186–190.

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South Atlantic Ocean, Vol. 4, NAVAIR 50-1C-531, US Government Printing Office, Washington, DC, 325 pp.

Waters, K.J., R.C. Smith, and M.R. Lewis, 1990: Avoiding

ship induced light-field perturbation in the determination

of oceanic optical properties. Oceanogr., 3, 18–21.

Weir, C.T., D.A. Siegel, D.W. Menzies, and A.F. Michaels,

1994: In situ evaluation of a ship’s shadow. Ocean Optics

XII, J.S. Jaffe, Ed., SPIE, 2,258, 815–821.

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Appl. Meteorol., 24, 540–546.

44
Mueller, Fraser, Biggar, Thome, Slater, Holmes, Barnes, Weir, Siegel, Menzies, Michaels, and Podesta

The SeaWiFS Technical Report Series

Vol. 1

Hooker, S.B., W.E. Esaias, G.C. Feldman, W.W. Gregg, and

C.R. McClain, 1992: An Overview of SeaWiFS and Ocean

Color. NASA Tech. Memo. 104566, Vol. 1, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 24 pp., plus color plates.

Vol. 2

Gregg, W.W., 1992: Analysis of Orbit Selection for SeaWiFS:

Ascending vs. Descending Node. NASA Tech. Memo.

104566, Vol. 2, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 16 pp.

Vol. 3

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., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 41 pp.

Vol. 4

McClain, C.R., E. Yeh, and G. Fu, 1992: An Analysis of GAC

Sampling Algorithms: A Case Study. NASA Tech. Memo.

104566, Vol. 4, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 22 pp., plus color plates.

Vol. 5

Mueller, J.L., and R.W. Austin, 1992: Ocean Optics Protocols

for SeaWiFS Validation. NASA Tech. Memo. 104566, Vol.

5, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 43 pp.

Vol. 6

Firestone, E.R., and S.B. Hooker, 1992: SeaWiFS Technical

Report Series Summary Index: Volumes 1–5. NASA Tech.

Memo. 104566, Vol. 6, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 9 pp.

Vol. 7

Darzi, M., 1992: Cloud Screening for Polar Orbiting Visible

and IR Satellite Sensors. NASA Tech. Memo. 104566, Vol.

7, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 7 pp.

Vol. 8

Hooker, S.B., W.E. Esaias, and L.A. Rexrode, 1993: Proceedings of the First SeaWiFS Science Team Meeting. NASA

Tech. Memo. 104566, Vol. 8, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 61 pp.

Vol. 9

Gregg, W.W., F.C. Chen, A.L. Mezaache, J.D. Chen, J.A.

Whiting, 1993: The Simulated SeaWiFS Data Set, Version 1. NASA Tech. Memo. 104566, Vol. 9, S.B. Hooker,

E.R. Firestone, and A.W. Indest, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 17 pp.

Vol. 10

Woodward, R.H., R.A. Barnes, C.R. McClain, W.E. Esaias,

W.L. Barnes, and A.T. Mecherikunnel, 1993: Modeling

of the SeaWiFS Solar and Lunar Observations. NASA

Tech. Memo. 104566, Vol. 10, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 26 pp.

Vol. 11

Patt, F.S., C.M. Hoisington, W.W. Gregg, and P.L. Coronado,

1993: Analysis of Selected Orbit Propagation Models for

the SeaWiFS Mission. NASA Tech. Memo. 104566, Vol.

11, S.B. Hooker, E.R. Firestone, and A.W. Indest, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 16 pp.

Vol. 12

Firestone, E.R., and S.B. Hooker, 1993: SeaWiFS Technical Report Series Summary Index: Volumes 1–11. NASA Tech.

Memo. 104566, Vol. 12, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 28 pp.

Vol. 13

McClain, C.R., K.R. Arrigo, J. Comiso, R. Fraser, M. Darzi,

J.K. Firestone, B. Schieber, E-n. Yeh, and C.W. Sullivan, 1994: Case Studies for SeaWiFS Calibration and Validation, Part 1. NASA Tech. Memo. 104566, Vol. 13,

S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 52 pp., plus

color plates.

Vol. 14

Mueller, J.L., 1993: The First SeaWiFS Intercalibration RoundRobin Experiment, SIRREX-1, July 1992. NASA Tech.

Memo. 104566, Vol. 14, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 60 pp.

Vol. 15

Gregg, W.W., F.S. Patt, and R.H. Woodward, 1994: The Simulated SeaWiFS Data Set, Version 2. NASA Tech. Memo.

104566, Vol. 15, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 42 pp., plus color plates.

Vol. 16

Mueller, J.L., B.C. Johnson, C.L. Cromer, J.W. Cooper, J.T.

McLean, S.B. Hooker, and T.L. Westphal, 1994: The Second SeaWiFS Intercalibration Round-Robin Experiment,

SIRREX-2, June 1993. NASA Tech. Memo. 104566, Vol.

16, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 121 pp.

Vol. 17

Abbott, M.R., O.B. Brown, H.R. Gordon, K.L. Carder, R.E.

Evans, F.E. Muller-Karger, and W.E. Esaias, 1994: Ocean

Color in the 21st Century: A Strategy for a 20 -Year Time

Series. NASA Tech. Memo. 104566, Vol. 17, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 20 pp.

Vol. 18

Firestone, E.R., and S.B. Hooker, 1994: SeaWiFS Technical Report Series Summary Index: Volumes 1–17. NASA Tech.

Memo. 104566, Vol. 18, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 47 pp.

45
Case Studies for SeaWiFS Calibration and Validation, Part 3

Vol. 19

McClain, C.R., R.S. Fraser, J.T. McLean, M. Darzi, J.K. Firestone, F.S. Patt, B.D. Schieber, R.H. Woodward, E-n. Yeh,

S. Mattoo, S.F. Biggar, P.N. Slater, K.J. Thome, A.W.

Holmes, R.A. Barnes, and K.J. Voss, 1994: Case Studies

for SeaWiFS Calibration and Validation, Part 2. NASA

Tech. Memo. 104566, Vol. 19, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 73 pp.

Vol. 20

Hooker, S.B., C.R. McClain, J.K. Firestone, T.L. Westphal,

E-n. Yeh, and Y. Ge, 1994: The SeaWiFS Bio-Optical

Archive and Storage System (SeaBASS), Part 1. NASA

Tech. Memo. 104566, Vol. 20, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 40 pp.

Vol. 21

Acker, J.G., 1994: The Heritage of SeaWiFS: A Retrospective on the CZCS NIMBUS Experiment Team (NET) Program. NASA Tech. Memo. 104566, Vol. 21, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 43 pp.

Vol. 22

Barnes, R.A., W.L. Barnes, W.E. Esaias, and C.R. McClain,

1994: Prelaunch Acceptance Report for the SeaWiFS Radiometer. NASA Tech. Memo. 104566, Vol. 22, S.B. Hooker, E.R. Firestone, and J.G. Acker, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 32 pp.

Vol. 23

Barnes, R.A., A.W. Holmes, W.L. Barnes, W.E. Esaias, C.R.

McClain, and T. Svitek, 1994: SeaWiFS Prelaunch Radiometric Calibration and Spectral Characterization. NASA

Tech. Memo. 104566, Vol. 23, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 55 pp.

Vol. 24

Firestone, E.R., and S.B. Hooker, 1995: SeaWiFS Technical Report Series Summary Index: Volumes 1–23. NASA Tech.

Memo. 104566, Vol. 24, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, (in press).

Vol. 25

Mueller, J.L., and R.W. Austin, 1995: Ocean Optics Protocols

for SeaWiFS Validation, Revision 1. NASA Tech. Memo.

104566, Vol. 25, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 67 pp.

Vol. 26

Siegel, D.A., M.C. O’Brien, J.C. Sorensen, D.A. Konnoff, E.A.

Brody, J.L. Mueller, C.O. Davis, W.J. Rhea, and S.B.

Hooker, 1995: Results of the SeaWiFS Data Analysis

Round-Robin (DARR), July 1994. NASA Tech. Memo.

104566, Vol. 26, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 58 pp.

Vol. 27

Mueller, J.L., R.S. Fraser, S.F. Biggar, K.J. Thome, P.N. Slater,

A.W. Holmes, R.A. Barnes, C.T. Weir, D.A. Siegel, D.W.

Menzies, A.F. Michaels, and G. Podesta 1995: Case Studies for SeaWiFS Calibration and Validation, Part 3. NASA

Tech. Memo. 104566, Vol. 27, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 46 pp.

46
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13. ABSTRACT (Maximum 200 words)

This document provides brief reports, or case studies, on a number of investigations sponsored by the Calibration and

Validation Team (CVT) within the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project. Chapter 1 describes a

comparison of the irradiance immersion coefficients determined for several different marine environmental radiometers

(MERs). Chapter 2 presents an analysis of how light absorption by atmospheric oxygen will influence the radiance measurements in band 7 of the SeaWiFS instrument. Chapter 3 gives the results of the second ground-based solar calibration of the

instrument, which was undertaken after the sensor was modified to reduce the effects of internal stray light. (The first groundbased solar calibration of SeaWiFS is described in Volume 19 in the SeaWiFS Technical Report Series.) Chapter 4 evaluates

the effects of ship shadow on subsurface irradiance and radiance measurements deployed from the deck of the R/V

Weatherbird II in the Atlantic Ocean near Bermuda. Chapter 5 illustrates the various ways in which a single data day of

SeaWiFS observations can be defined, and why the spatial definition is superior to the temporal definition for operational

usage.

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SeaWiFS, Oceanography, Immersion Coefficients, MER, Band 7 Radiance, 46

Solar Radiation, Ship Shadow, Data Day, Global Fields, Case Studies

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 SeaWiFS Technical Report Series

Volume 27–Case Studies for SeaWiFS Calibration and Validation, Part 3 Code 970.2

 May 1995 Technical Memorandum

6. AUTHOR(S) James L. Mueller, Robert S. Fraser, Stuart F. Biggar, Kurtis J. Thome,

 Philip N. Slater, Alan W. Holmes, Robert A. Barnes, Christian T. Weir,

 David A. Siegel, David W. Menzies, Anthony F. Michaels, and Guillermo Podesta

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

 Technical Editor: James G. Acker

 James L. Mueller: San Diego State University, San Diego, California; Stuart F. Biggar, Kurtis J. Thome, and Philip N.

Slater: Univrsity of Arizona, Tucson, Arizona; Alan W. Holmes: Santa Barbara Research Center, Santa Barbara, California; Robert A. Barnes: ManTech

Environmental Technology, Inc., Wallops Island, Virginia; Christian T. Weir, David A. Siegel, and David W. Menzies: University of California at Santa

Barbara, Santa Barbara, California; Anthony F. Michaels: Bermuda Biological Station for Research, Ferry Reach, Bermuda; Guillermo Podesta: University of

Miami, Miami, Florida; and Elaine R. Firestone: General Sciences Corporation, Laurel, Maryland