NASA Technical Memorandum 104566, Vol. 9

SeaWiFS Technical Report Series

Stanford B. Hooker, Elaine R. Firestone,

and A.W. Indest, Editors

Volume 9, The Simulated SeaWiFS Data Set,

Version 1

Watson W. Gregg, Frank C. Chen, Ahmed L. Mezaache,

Judy D. Chen, and Jeffrey A. Whiting

May 1993
NASA Technical Memorandum 104566, Vol. 9

SeaWiFS Technical Report Series

Stanford B. Hooker, Editor

NASA Goddard Space Flight Center

Greenbelt, Maryland

Elaine R. Firestone and A.W. Indest, Technical Editors

General Sciences Corporation

Laurel, Maryland

Volume 9, The Simulated SeaWiFS Data Set,

Version 1

Watson W. Gregg

NASA Goddard Space Flight Center

Greenbelt, Maryland

Frank C. Chen, Ahmed L. Mezaache,

Judy D. Chen, and Jeffrey A. Whiting

General Sciences Corporation

Laurel, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

1993
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

Abstract

Data system development activities for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) must begin well

before the scheduled 1994 launch. To assist in these activities, it is essential to develop a simulated SeaWiFS

data set as soon as possible. Realism is of paramount importance in this data set, including SeaWiFS spectral

bands, orbital and scanning characteristics, and known data structures. Development of the simulated data

set can assist in identification of problem areas that can be addressed and solved before the actual data are

received. This paper describes the creation of the first version of the simulated SeaWiFS data set. The data set

includes the spectral band, orbital, and scanning characteristics of the SeaWiFS sensor and SeaStar spacecraft.

The information is output in the data structure as it is stored onboard. Thus, it is a level-0 data set which

can be taken from start to finish through a prototype data system. The data set is complete and correct at the

time of printing, although the values in the telemetry fields are left blank. The structure of the telemetry fields,

however, is incorporated. Also, no account for clouds has been included. However, this version facilitates early

prototyping activities by the SeaWiFS data system, providing a realistic data set to assess performance.

1. INTRODUCTION

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS)

is an ocean color sensor scheduled for launch in 1994. A

follow-on to the highly successful Coastal Zone Color Scanner (CZCS) mission (1978–1986), SeaWiFS is intended to

provide improved estimates of chlorophyll concentrations

in the world’s oceans.

The SeaWiFS mission will provide an unprecedented

set of global ocean color data on a regular basis (every two

days in the absence of clouds, about a week otherwise).

The CZCS, a proof-of-concept mission, was able to produce

a single global image in its nearly eight year lifetime. The

volumes of data produced by an operational global ocean

color sensor pose challenges for a data processing system

that were not encountered by the CZCS system. Development and rigorous testing activities must begin well before

launch to avoid the sorts of delays in data processing and

distribution that plagued the CZCS mission.

To facilitate the development of the data system for

processing SeaWiFS data, it is essential to develop a simulated SeaWiFS data set as soon as possible. This data

set should incorporate the characteristics of the SeaWiFS

sensor, including spectral bands and orbital and scanning

characteristics, and should do so in a realistic manner to

allow proper preparation for actual data processing. While

many of the data characteristics, contents, and anomalies

may not be known until just before launch, development of

the simulated data set can assist in identification of problem areas that can be addressed and solved before a fuller

understanding of the data is achieved.

This paper describes the details of the creation of the

first version of the simulated SeaWiFS data set. The data

set includes the spectral band, orbital, and scanning characteristics of the SeaWiFS sensor and SeaStar spacecraft.

The information is output in the data structure as it is

stored onboard. Thus, it is a level-0 data set which can be

taken from start-to-finish through a prototype data system. The data set is complete and correct at the time of

printing, although, the values in the telemetry fields are

left blank (the structure of the telemetry fields is incorporated, however). Also, no account for clouds has been

included.

CZCS pigment data and a variety of radiative transfer

models were used to create realistic SeaWiFS total radiances. These total radiances were Earth-located using a

SeaWiFS orbital model to provide SeaWiFS-like viewing

and solar geometries.

2. BACKGROUND

The improvements of SeaWiFS over CZCS are largely

expected due to the existence of four new spectral bands:

one at 412 nm (to discern dissolved organic matter, or

Gelbstoff), one at 490 nm (to enable better estimates of

chlorophyll at high concentrations), and two in the nearinfrared at 765 and 865 nm (to improve the determination

of atmospheric aerosols). Thus, SeaWiFS contains eight

spectral bands compared to the four used in CZCS processing (CZCS actually contained six bands, but two were

not used). Table 1 shows a comparison of the SeaWiFS

spectral bands to the CZCS bands.

In addition to different spectral bands, SeaWiFS is also

in a different orbit than the CZCS and has different viewing

geometries. A comparison between SeaWiFS orbital and

sensor characteristics and those of the CZCS is summarized

in Table 2.

Due to limited onboard data recorder space, SeaWiFS

will be able to obtain global coverage only at reduced resolution (every fourth pixel along-track and along-scan).

These data are called Global Area Coverage (GAC) data.

High resolution data may be recorded in the remaining

data recorder area. There is estimated to be about 20

minutes per day of high resolution Local Area Coverage

1
The Simulated SeaWiFS Data Set, Version 1

(LAC) data. The effort here is to create both types of

data, in order to simulate a representative SeaWiFS data

set.

Table 1. SeaWiFS spectral bands and center

wavelengths, are shown with those of CZCS, for

comparison. Wavelengths (λ) are in nm.

SeaWiFS CZCS

Band No. λ Band No. λ

1 412 1 443

2 443 2 520

3 490 3 550

4 510 4 670

5 555 5 7501

6 670 6 13,5002

7 765

8 865

1. Intended for surface vegetation analyses only (Williams

et al. 1985).

2. Data suspect after 1979 (Williams et al. 1985).

3. METHODS

In order to maximize the usefulness and realism of the

simulated SeaWiFS data set, CZCS pigment data were

chosen as the data source. The method for simulating

SeaWiFS data involves creating both LAC and GAC data.

Details of the method are described in the following, but

a general overview here is helpful.

The basic equation of radiative transfer for ocean color

assumes separability of the radiance contributions from atmospheric and oceanic components:

Lt(λ) = Lr(λ) + T(λ)Lg(λ) + La(λ) + T(λ)LW (λ) (1)

where Lt is the total radiance at the sensor, Lr is the

Rayleigh radiance, Lg is the sun glint radiance, La is the

aerosol radiance, LW is the water-leaving radiance, and

T is the total transmittance (direct plus diffuse) from the

ocean through the atmosphere to the spacecraft. The variable of interest in the creation of simulated data is Lt,

which is what the sensor actually detects. To obtain realistic values of Lt, with ranges and means observed in

the real ocean, it is desirable to create it using representative values of the components. This process begins with

the generation of LW derived from CZCS pigment values,

and adding atmospheric contributions from simulated SeaWiFS viewing and solar geometries.

For both LAC and GAC data, real CZCS images of

pigments were selected. The pigment fields were used to

create normalized water-leaving radiances, LWN (λ), at the

eight SeaWiFS bands using a semi-analytic radiance model

modified for SeaWiFS (Gordon et al. 1988a). Then, simulated SeaWiFS orbits were propagated through these simulated radiance fields to produce actual SeaWiFS viewing geometries. An arbitrary day was chosen (the vernal

equinox) to produce solar geometry. Given these simulated

solar and viewing geometries, a realistic atmosphere was

added by including Rayleigh scattering, aerosol scattering

and absorption, water vapor absorption, oxygen absorption, and sun glint reflectance. Radiance contributions

of each were summed, and diffusely transmitted waterleaving radiance was added to produce simulated total radiance received by the sensor. Finally, data structures for

telemetry were inserted and science data were formatted

into 10-bit words to create level-0 data.

3.1 Normalized Water-Leaving Radiances

Creating normalized water-leaving radiances LWN is

the first step, because LWN is independent of viewing and

solar geometry. The method for creating LWN is taken

from Gordon et al. (1988a). According to this model,

LWN (λ) = (1 − ρn)(1 − ρN )F0(λ)R(0−, λ)

n2Q [1 − rR(0−, λ)] (2)

where ρn is the Fresnel reflectance of the sea surface for

normal incidence, ρN is a normalized mean value of surface

reflectance for direct and diffuse irradiance for a flat sea,

F0 is the extraterrestrial irradiance corrected for Earthsun distance, R(0−, λ) is the irradiance reflectance just

below the sea surface, n is the index of refraction, Q is

the irradiance-to-radiance ratio (equals π for totally diffuse radiance), and r is the water-air reflectance for totally

diffuse irradiance.

From Fresnel’s Law, ρn is known a priori (Jerlov 1976),

ρN is estimated from Gordon et al. (1988a) at 0.043, n is

taken to be 1.341 (Austin 1974), and r is taken to be 0.48

(Gordon et al. 1988a). The ratio R(λ)/Q is wavelength

dependent, and is taken from Gordon et al. (1988a) as:

R(λ)

Q = 0.110

bb(λ)

K(λ) (3)

where bb(λ) is the spectral backscattering coefficient, and

K(λ) is the spectral attenuation coefficient. K(λ) is determined from Baker and Smith (1982) as

K(λ) = KW (λ) + Kc(λ) + Kg(λ) (4)

where KW (λ) is the attenuation coefficient of pure seawater, Kc(λ) is that for phytoplankton, and Kg(λ) is that for

Gelbstoff, or yellow substances.

Use of this model for a SeaWiFS simulation requires

values for wavelength-dependent parameters be chosen for

SeaWiFS bands. Values for the mean extraterrestrial irradiance F0 were taken from Neckel and Labs (1984), and

spectrally weighted over all of the SeaWiFS bandwidths

assuming a full-width half-maximum (FWHM), Gaussian

spectral response (Table 3). The values were corrected for

Earth-sun distance following Gordon et al. (1983):

F0(λ) = F0(λ)



1+0.0167 cos

2π(D − 3)

365 2

(5)

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W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

Table 2. Orbit and sensor characteristics for the SeaWiFS and the CZCS, shown for comparison.

Characteristic CZCS SeaWiFS

Altitude (km) 955 705

Period (minutes) 104.0 98.9

Inclination 99.28◦ 98.25◦

Equator Crossing Time (local) Noon Noon

Node Type Ascending Descending

Scan Width 39.34◦ 58.3◦ (LAC); 45◦ (GAC)

Instantaneous Field of View (IFOV) 0.05◦ 0.09◦

Ground IFOV at Nadir (km) 0.825 1.12

Pixels Along Scan 1,968 1,285 (LAC); 248 (GAC)

Scan Period (seconds) 0.134 0.667 (LAC); 1.5 (GAC)

Scan Plane Tilt ±20◦ in 2◦ steps +20◦, 0◦, −20◦

Scan Ground Coverage (km) 1,566 2,802 (LAC); 1,502 (GAC)

Maximum Spacecraft Zenith Angle 46.8◦ 70.8◦ (LAC); 51.7◦ (GAC)

Digitization (bits) 8 10

where F0(λ) is the mean extraterrestrial irradiance and D

is the sequential day of the year.

Table 3. Values for mean extraterrestrial irradiance F0(λ) (mW cm−2 μm−1), kc(λ), k

c(λ), bW (λ)

(m−1), A(λ) (m−1), and B(λ) used in the creation

of the SeaWiFS simulated data set.

λ F0 kc k

c bW A B

410 171.92 0.208 1.077 0.0067 0.00313 0.20401

443 189.05 0.175 1.001 0.0048 0.00300 0.21770

490 193.60 0.121 0.963 0.0031 0.00284 0.23674

510 188.41 0.103 1.006 0.0026 0.00346 0.34070

555 185.90 0.076 1.144 0.0019 0.00330 0.35666

670 152.82 0.137 1.463 0.0008 0.00238 0.29579

765 123.27 0.040 1.732 0.0005 0.00221 0.32081

865 100.34 0.010 1.732 0.0003 0.00206 0.34400

The values for KW(λ) were taken from Baker and Smith

(1982), and again spectrally weighted FWHM assuming a

Gaussian response (Table 3). Kc(λ) was computed from

Baker and Smith (1982):

Kc(λ) = kc(λ)[chl. a] exp

−k

c(λ) log10

[chl. a]

Cref 2

+ 0.001[chl. a]

2

(6)

where [chl. a] is chlorophyll concentration, Cref is a reference chlorophyll value (0.5), and kc(λ) and k

c(λ) are spectral fit coefficients and were spectrally weighted over the

SeaWiFS bands (Table 3). For this simulation, Kg(λ) was

assumed to be zero.

The backscattering coefficient bb(λ) may be expressed

using components similar to the K(λ) formulation (4):

bb(λ)=0.5 bW (λ) + bbc(λ) (7)

where bW (λ) is the total scattering coefficient for pure seawater and bbc(λ) is the backscattering coefficient of phytoplankton. The coefficient 0.5 is the backscattering-to-total

scattering ratio for pure seawater. The backscattering coefficient for plankton, bbc(λ), was determined from an empirical relationship developed by Gordon et al. (1988a)

bbc(λ) = A(λ)[chl. a]

B(λ) (8)

where, the coefficients A(λ) and B(λ) were computed for

SeaWiFS bands as shown in Table 3. The only remaining unknown for the model, then, is [chl. a], which was

obtained from CZCS data.

3.2 Orbit Model

A simulated SeaWiFS orbit is required to obtain realistic viewing and solar geometries, which are then used to

produce the atmospheric contribution to the total radiance

detected by the sensor. The method used here is to propagate a SeaWiFS orbit over a field of CZCS pigment values,

use the values to compute LWN (λ) for SeaWiFS bands, and

use the simulated scan and tilt positions to determine the

location of the pigment value in Earth coordinates (geocentric latitude and longitude). Given this information,

the spacecraft and solar zenith and azimuth angles can be

calculated and then used to simulate the radiative properties of an atmosphere. This section describes the orbit

model employed, the equations to compute latitude and

longitude, and the viewing and solar geometries.

The orbital model used assumes a circular orbit. Thus,

the only parameters required to propagate a simulated orbit were inclination, altitude, and epoch (see Table 1 for

SeaWiFS inclination and altitude). The epoch was chosen

such that the first orbit crossed the equator on the descending node at the Greenwich Meridian at exactly noon

local time.

In such a simple orbit model, the location of successive sub-satellite points (the point on the Earth where the

projection of the satellite lies) is a simple function of the

3
The Simulated SeaWiFS Data Set, Version 1

previous sub-satellite point and the travel time between

the two points. From spherical trigonometry,

sin [Ψs(t − t0)] = cos δ sin [Ψs(t0)]

+ sin δ cos [Ψs(t0)] cos(i



) (9)

where Ψs is the sub-satellite latitude at times t0 and t−t0,

δ is the great circle distance from Ψs(t0) to Ψs(t−t0), and

i

 is inclination i − 90◦. The great circle distance is known

from

δ = 360

∆t

P (10)

where P is the nodal period. The longitude difference,

∆ωs, is calculated similarly:

∆ωs = cos−1



cos δ − sin [Ψs(t − t0)] sin [Ψs(t0)]

cos [Ψs(t − t0)] cos [Ψs(t0)] 

. (11)

The new longitude, ω, equals the old longitude ω0 minus the longitude difference ∆ω plus a correction for Earth

rotation

ω = ω0 − ∆ω + 0.004167 t (12)

where the coefficient 0.004167 is the rate of rotation (◦ s−1).

3.3 Navigation of Pixels

Given sub-satellite longitude and latitude, and the scan

and tilt angles, the Earth position of any given pixel is calculable. First, one must calculate the great circle distance

from the sub-satellite point to the pixel:

δ = θ − θ

s (13)

where θ is the spacecraft zenith angle, and θ

s is the scan

angle θs modified by tilt. Given θs, θ

s is computed by

a simple pitch rotation in the direction of the tilt. The

spacecraft zenith angle, θ, is computed directly from

θ = sin−1



Re + Hs

Re

sin θ

s



(14)

where Re is the mean Earth radius (6371.2 km) and Hs is

the spacecraft altitude (705 km).

The pixel latitude and longitude are determined from

spherical trigonometry. For the latitude:

Ψ = sin−1 [sin Ψs cos δ + cos Ψs sin δ cos η] (15)

where η is the bearing from the sub-satellite point to the

pixel along the direction of motion of the satellite (either

270◦ + i

 for the left-hand side of the scan facing north or

90◦ − i

 for the right-hand side facing south).

The longitude difference, ∆ω, from the sub-satellite

point to the pixel is determined by

∆ω = cos−1



cos δ − sin Ψs sin Ψ

cos Ψs cos Ψ 

. (16)

The pixel longitude is determined from ∆ω by either

adding to, or subtracting from, the sub-satellite longitude,

depending on which side of the scan the pixel is on; if it is

west of the sub-satellite point a subtraction is performed.

3.4 Viewing and Solar Geometries

Once the pixel has been navigated to Earth coordinates, computation of viewing geometry (spacecraft zenith

and azimuth angles) is straightforward. In fact, the spacecraft zenith angle θ has already been found (14). This

leaves the computation of the spacecraft azimuth angle,

which is defined as the angle from the pixel to the subsatellite point, measured counterclockwise from true north

(at the pixel)

Φ = sin Ψs − cos δ sin Ψ

sin δ cos Ψ (17)

where Φ is the spacecraft azimuth angle (the other terms

are defined above).

The determination of the solar geometry requires additional information to the pixel location. Specifically, this

additional information includes the solar declination latitude Ψd, equation of time Te [both obtained using standard methods, e.g., Iqbal (1983)], and the Greenwich Mean

Time (GMT). GMT is determined by

HGMT = tEC − ωe

15 + te (18)

where HGMT is GMT in hours, tEC is the equator crossing

time (in local time, i.e., noon) ωe is the equator crossing

longitude, and te is the time difference to or from the most

recent equator crossing to the present position (in hours).

Given this information, plus the pixel location, the solar zenith angle θ0 is computed from

cos θ0 = sin Ψ sin Ψd + cos Ψ cos Ψd cos Ω (19)

where Ω is the solar hour angle, computed from

Ω=(H − 12)15 + ω + Te. (20)

The solar azimuth angle Φ0 is computed by

Φ0 = cos−1



sin Ψd − sin Ψ cos θ0

cos Ψ sin θ0



(21)

The viewing geometries θ and Φ and solar geometries

θ0 and Φ0 are now known and attention may be focused

on the addition of an atmosphere.

3.5 Atmospheric Contributions

This section focuses on the computation of realistic atmospheric contributions to the total radiance, based on

representative atmospheric conditions and the simulated

4
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

SeaWiFS viewing and solar geometries. This means determining the Rayleigh scattering, ozone absorption, water vapor absorption, oxygen absorption, aerosol scattering and absorption, and sun glint contributions. As a first

step, absorption coefficients for the atmospheric gases must

be determined and spectrally weighted over the SeaWiFS

bands, as was done for the mean extraterrestrial irradiance.

Absorption coefficients for ozone, water vapor, and oxygen

(the spectral absorption characteristics of which all three

fall to some extent within some SeaWiFS bandwidths) are

shown in Table 4, along with the Rayleigh optical thickness

for the SeaWiFS bands.

Table 4. Spectrally weighted (FWHM) Rayleigh

optical thickness (τr), ozone absorption coefficient

(aoz), water vapor absorption coefficient (awv), and

oxygen absorption coefficient (aox). Wavelengths,

λ, are in nm. The units for the absorption coefficients are in cm−1; τr is dimensionless.

λ τr aoz awv aox

410 0.3191 0.0000 0.0000 0.0000

443 0.2364 0.0027 0.0000 0.0000

490 0.1562 0.0205 0.0000 0.0000

510 0.1326 0.0382 0.0000 0.0000

555 0.0938 0.0898 0.0000 0.0000

670 0.0437 0.0463 0.0006 0.0000

765 0.0255 0.0083 0.0000 6.9900

865 0.0155 0.0000 0.0008 0.0000

Following Gordon et al. (1983), the effects of the absorbing gases in the atmosphere were determined by assuming two trips of the extraterrestrial irradiance through

the atmosphere. This was accomplished by

F

0 = F0 Toz(θ0) Toz(θ) Twv(θ0) Twv(θ) Tox(θ0) Tox(θ) (22)

where wavelength dependence has been dropped and T

represents the transmittance of the gaseous component in

subscript. The θ0 and θ dependencies represent the two

paths through the atmosphere: θ0 is the path from the

sun to the Earth and θ is the path from the Earth to the

satellite. The path lengths for each path are computed for

water vapor and oxygen by (Kasten 1966):

M = 1

cos η + 0.15(93.885 − η)−1.253 (23)

where η is θ0 or θ.

The path length for ozone transmittance is slightly different due to the high altitude of ozone concentrations

(Paltridge and Platt 1976):

Moz = 1.0035

cos2 η + 0.007−0.5 . (24)

These formulations avoid the assumption of a flat Earth.

The next step is to compute the Rayleigh scattering

contribution Lr to the total radiance received at the satellite. Since multiple scattering Rayleigh tables are not yet

available for SeaWiFS bands, the tables for the CZCS

bands are used (Gordon et al. 1988b). There are two coincident bands for SeaWiFS and the CZCS (see Table 1):

one at 443 nm and the other at 670 nm. The CZCS multiple scattering Rayleigh tables are used for these two bands.

Values for non-coincident SeaWiFS bands are derived assuming a λ−4 principle. For bands 1–5 (412–555 nm), the

procedure is as follows. Let λ = 443 nm; then,

x = I(λ) λ4. (25)

Now, for λ = 412 and 555

I(λ) = xλ−4 (26)

from which the Rayleigh scattering is derived:

Lr(λ) = I(λ)F

0(λ) (27)

where I(λ) is the Rayleigh intensity taken from the CZCS

multiple scattering tables (Gordon et al. 1988b).

The procedure is similar for bands 6–8 (670–865 nm),

except 670 is substituted for λ in (25), and 670 and 865

replace 412 and 555 in (26). When this method is applied

to the CZCS bands at 520 and 550 nm, a maximum error

of 3.2% is obtained for θ0 = 60 and θ = 50. The error is

less at all smaller angles tested.

Next, the aerosol radiances, La, must be determined.

According to Gordon and Casta ̃no (1989) the aerosol radiance is determined by

La = ωa τa pa F

0 M

4π (28)

where ωa is the single scattering albedo of the aerosol, τa

is the optical thickness, and pa is a factor to account for

the probability of scattering to the spacecraft for three

different paths from the sun (Gordon and Casta ̃no 1989).

In (28) M has been substituted for Gordon and Casta ̃no’s

(1989) 1/ cos θ to allow calculations on a curved Earth.

The assumption is made that the aerosol obeys the

 ̊Angstr ̈om formulation

τa = βλ−α (29)

and the Gregg and Carder (1990) model may be used to

obtain β and α, as a function of wind speed. Wind speeds

were obtained from six years of data from the Fleet Numerical Oceanography Center (FNOC), made available from

the NASA Climate Data System (NCDS). The mean wind

speeds over these six years at 2.5 × 2.5◦ spatial resolution

were used.

5
The Simulated SeaWiFS Data Set, Version 1

The aerosol scattering albedo, ωa, was also computed

using Gregg and Carder (1990). The factor pa was computed from Gordon and Casta ̃no (1989)

pa = 1

4π



P(θ−)+[ρ(θ0) + ρ(θ)] P(θ+)

 (30)

where ρ(θ0) and ρ(θ) are the Fresnel reflectances for solar

and viewing geometries, respectively, and P is the aerosol

scattering phase function for the forward scattering angles

P(θ+), i.e., scattering toward the surface and reflected off

the ocean or reflected first and then scattered toward the

spacecraft, and backward angles P(θ−), i.e., backscattered

from the atmosphere.

P(θ±) is determined using a Henyey-Greenstein function for marine aerosols

P(θ±) = a(1 − g2

1)

(1 + g2

1 − 2g1 cos θ±)1.5

+ (1 − a)(1 − g2

2)

(1 + g2

2 − 2g2 cos θ±)1.5

(31)

where a = 0.983, g1 = 0.82, and g2 = −0.55 (Gordon and

Casta ̃no 1989). As defined in Gordon and Casta ̃no (1989):

cos θ± = ± cos θ0 cos θ − sin θ0 sin θ cos(Φ − Φ0). (32)

The next contribution to be accounted for is that of

sun glint radiance diffusely transmitted to the spacecraft

(T Lg). Sun glint at the surface for a given viewing and

solar geometry may be expressed by (Cox and Munk 1954):

Lg = ρn T0(λ, θ0) F0(λ) pw(θ, Φ, θ0, Φ0, W)

4 cos θ cos4 θN

(33)

where pw(θ, Φ, θ0, Φ0) is the probability of seeing sun glitter in the direction θ, Φ given the sun in position θ0,Φ0 as

a function of wind speed (W), and θN is the angle with respect to nadir of the sea surface slopes to produce a reflection angle to the spacecraft (Viollier et al. 1980). The term

T0(λ, θ0) represents the total downward transmittance of

irradiance as a function of θ0 and the absorbing gases in

the atmosphere. It may be expressed as the sum of the

direct and diffuse transmittances (again dropping wavelength dependence)

T0(θ0) = td(θ0) + ts(θ0) (34)

where the subscripts d and s represent direct and diffuse

components, respectively. The transmittance td is simply

the transmittance after absorption by the gaseous components of the atmosphere, scattering and absorption by

aerosols, and scattering by Rayleigh (dropping the angular

dependence):

td = tr taa toz twv tox. (35)

Some of the scattered Rayleigh and aerosol components

continues forward and contributes to the total irradiance

at the surface. These are expressed separately as:

ts = toz twv tox taa 

1 − t

0.95 r

2 + t

1.5

r Fa(1 − tas)



(36)

where taa is the aerosol transmittance after absorption

taa = e−(1−ωa)τaM (37)

and tas is analogously the transmittance after scattering

(Justus and Paris 1985)

tas = e(−ωaτaM)

. (38)

In (36)–(38), Fa is the forward scattering probability of

the aerosol, taken from Bird and Riordan (1986), ωa is the

single scattering albedo of the aerosol, and τa is the aerosol

optical thickness.

If Lg(λ) is the sun glint radiance at the surface, T Lg(λ)

is that received by the sensor, where T is the total transmittance from the Earth to the satellite. It is defined in

(34)–(38) with θ substituted for θ0.

Finally, the normalized water-leaving radiance LWN

must be converted into the water-leaving radiance measured at the satellite T LW . This is expressed by Gordon

(1990) as

T LW = LWN (1 − ρ) T0 cos θ0. (39)

The weighted direct plus diffuse reflectance, ρ, is computed

as:

ρ = ρnWd + ρNWs (40)

where Wd equals the direct irradiance divided by the total

irradiance at the surface, and Ws is the diffuse irradiance

divided by the total. These components are computed as a

function of the atmospheric constituents and solar zenith

angle using the model of Gregg and Carder (1990), as are

the direct and diffuse reflectances, which are functions of

the wind speed.

The simulated total radiance at the spacecraft, given

in (1) is calculated by summing (27), (28), (33), and (39).

3.6 Atmospheric Conditions

There are five attenuating sources in the atmosphere

that lie within SeaWiFS bands: Rayleigh scattering, ozone

absorption, water vapor absorption, oxygen absorption,

and aerosol scattering and absorption. Each was taken

for the simulated data set at mean values. Rayleigh scattering and oxygen absorption are functions of atmospheric

pressure for which a standard value of 1,013.25 mb was

used. Ozone absorption was taken to be 340 Dobson units

(DU) and absorption due to water vapor was assumed to

be 1.5 cm.

6
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

Aerosols may be calculated as a function of visibility,

a commonly reported meteorological parameter. Visibility

was set to 15 km for the simulation, which corresponds

to a mildly turbid atmosphere. Relative humidity (which

determines, in part, the size distribution of the aerosols)

was set at 80%. The 24-hour mean wind speed required for

the aerosol model used by Gregg and Carder (1990), was

estimated at 4.75 m s−1, the global mean from 6 years of

FNOC data, and the current wind speed, as noted before,

was determined as the mean over 2.5◦×2.5◦ grid cells from

the 6-year FNOC data set.

3.7 Ten-bit Words and Data Structures

The final step in developing a realistic SeaWiFS simulated data set is to convert the science data into 10-bit

words and to structure the data fields according to the

expected format for the downlink data. Not all of the

telemetry fields have been decided upon, but the purpose

here is to create as reasonable a data structure as possible

to allow data system testing. Further developments can be

incorporated as they are made.

Fig. 1 shows the preliminary stored data structures for

LAC and GAC data. Depicted are the structures for a

major frame of GAC and a major frame of LAC, each

consisting of 3 minor frames. A major frame of GAC thus

consists of 15 GAC scan lines, while a major frame of LAC

consists of 3 LAC scan lines. The number of bytes in each

minor frame is also denoted.

A single LAC scan line of SeaWiFS data contains 1,288

pixels, comprising 1,285 science pixels, a start synchronization pixel (also a 10-bit word) preceding the first pixel, a

stop synchronization pixel at the end of the scan line, followed by a time delay integration (TDI) pixel. A GAC

scan likewise contains 251 pixels, with 248 actual data pixels and three others in the same format as the LAC data.

This representation is included in the simulated data set.

SeaWiFS simulated total radiance data were packed

into 10-bit words according to

DC10(λ) = Lt(λ) − LNER(λ)

s(λ) , (41)

where DC10 is the digital counts at 10-bit digitization,

LNER(λ) is the noise equivalent radiance (NER), or the

minimum detectable radiance, and s is the slope for the

range 0–1,023, which is applicable for 10-bit digitization,

given by

s(λ) = Lsat(λ) − LNER(λ)

1,023 (42)

where Lsat(λ) is the saturation radiance for the sensor as a

function of wavelength. LNER(λ) and Lsat(λ) are shown in

Table 5. This provides a realistic data set corresponding

to the format stored on board the data recorder, and thus

may be considered a level-0 data set.

Table 5. LNER and saturation radiances (Lsat) for

SeaWiFS (units are mW cm−2 μm−1 sr−1).

Band λ [nm] LNER Lsat

1 412 0.0182 13.63

2 443 0.0125 13.25

3 490 0.0098 10.50

4 510 0.0088 9.08

5 555 0.0077 7.44

6 670 0.0056 4.20

7 765 0.0035 3.00

8 865 0.0023 2.13

4. APPLICATION OFCZCS DATA

The SeaWiFS GAC simulated data set was derived

from the global CZCS data set (Feldman et al. 1989). This

level-3 (remapped and gridded) data set was in dimensions

of 2,048 × 1,024 (0.176◦ longitude by 0.176◦ latitude), and

was cloud- and land-masked. The simulated SeaWiFS orbits passed through this CZCS pigment field in descending

node (from north to south) for approximately 6.8 orbits to

simulate a single data recorder dump of data. Start time

for the simulation was the first contact at Wallops Flight

Facility (WFF), the downlink station for SeaWiFS GAC

data. Succeeding start times, as well as all stop times, were

derived in previous simulations to maximize GAC coverage. The ultimate limit of the sensor was assumed to be 2

NER values, and the recorder was turned on whenever this

limit was reached, subject to land features and ice cover.

An 80% ice concentration was assumed as the limit for remote sensing purposes. Ice concentrations used were the

minimum of six years of International Satellite Cloud Climatology Project (ISCCP) data, made available by NCDS.

The start and stop times, in minutes travelled along the

orbital track from equator crossing at ascending node, are

given in Table 6.

The tilt was left at nadir pointing (0◦) for this simulation to test the response of the data system to excessive

sun glint. Normally, the sensor will be tilted aft when

approaching the solar declination latitude from the north,

and turned forward for the remainder of the descending

node track; however, this strategy has yet to be finalized.

For the GAC simulation, no attempt was made to include clouds, and land features were masked (set to zero)

as they occurred in the CZCS global data set.

The LAC simulation was initiated with the same global

CZCS pigment data, using the same orbit trajectories, as

will be the case for the real spacecraft. The sensor LAC

recorder was turned on for three separate occasions, comprising one 3-minute scene and two 2-minute scenes, for

a total of 7 minutes of LAC record time. This is about

the correct amount of time left on the recorder after GAC

data recording and some calibration activities. The start

and stop times for the LAC recorder, and the associated

simulated data set, are provided in Table 7. The difference

between LAC and GAC data is the amount of data in a

7
The Simulated SeaWiFS Data Set, Version 1

8
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

Table 6. Start and stop times (measured in minutes travelled along the orbit track from the equator crossing

on ascending node), total time, start and stop latitudes, and solar zenith angles for the orbital simulations for

the SeaWiFS simulated data set. The first contact with WFF is made on orbit 4 at 33.8743 min. and the second

contact is on orbit 11 at night. Thus, the simulated data begins at 33.8743 min. and ends at the stop time of

orbit number 10.

Day Orbit Times Latitude Solar Zenith

Number Start Stop Total Start Stop Start Stop

80 1 27.0571 71.3008 44.243 78.285 -76.530 81.396 79.507

80 2 26.9876 69.2139 42.226 78.460 -69.996 81.648 71.923

80 3 26.9043 69.9826 43.078 78.670 -72.499 81.954 74.716

80 4 26.9154 70.7818 43.866 78.642 -74.995 81.910 77.621

80 5 27.7986 70.5321 42.733 76.235 -74.230 78.701 76.713

80 6 26.8932 71.6449 44.751 78.698 -77.496 81.991 80.757

80 7 26.9099 71.6449 44.735 78.656 -77.496 81.931 80.757

80 8 26.8932 69.2139 42.320 78.698 -69.996 81.991 71.923

80 9 30.3202 68.4647 38.144 68.207 -67.492 69.537 69.200

80 10 28.7511 68.4647 39.713 73.336 -67.492 75.239 69.200

80 11 27.8374 68.4647 40.627 76.121 -67.492 78.560 69.200

80 12 26.8932 68.4647 41.571 78.698 -67.492 81.991 69.200

80 13 26.9876 69.2139 42.226 78.460 -69.996 81.648 71.923

80 14 27.0571 69.2139 42.156 78.282 -69.996 81.396 71.923

LAC scan (Table 1), which is 1,285 pixels, with no gaps

along-scan.

Table 7. Start and stop times (in minutes travelled along the orbit track from the equator crossing

on ascending node) orbit numbers, and corresponding latitudes for the LAC simulation.

Orbit Times Latitude

Number Start Stop Total Start Stop

4 54.6 57.6 3.0 -18.35 -29.13

6 64.3 66.3 2.0 -53.03 -60.06

6 68.6 70.6 2.0 -67.95 -74.44

5. RESULTS AND DISCUSSION

Imagery of the simulated SeaWiFS total radiances Lt(λ)

for all 8 bands is shown in Figure 2 for GAC data. The

start of the simulation was at the first visibility at WFF,

which can be noted by the truncated orbit at the eastern edge of the image. Recall that for this simulation the

sensor remained untilted, resulting in substantial sun glint

influence near the equator (which is the solar declination

for the vernal equinox, the time of the simulation). Tilting

the sensor aft of the velocity vector when approaching the

solar declination, and then forward when leaving would

decrease the sun glint contribution to the total radiance

substantially.

Note the decreases in Lt(λ) toward the poles, due to

a reduction in the flux of solar irradiance into the oceans,

and the increases in Lt(λ) at the scan edges, due to increased atmospheric contribution. The bands show progressively less total radiance from 412–865 nm. However,

band 7 (765 nm) is the lowest because of large oxygen absorption (see Table 4). This absorption reduces the amount

of saturation in the sun glint regions. Little evidence of

water-leaving radiances is evident in most of the images.

This is because the atmosphere dominates the total radiance over the oceans. Some evidence may be seen in

the image of band 2 (443 nm), where the contribution of

water-leaving radiance to the total is greatest under low

chlorophyll concentrations.

The LAC recording areas are also depicted in Figs. 2–4.

Note that they correspond with portions of the GAC orbits, but have a wider swath. Note also that the extra data

across-track have very large Lt(λ) values, due to increased

atmospheric contribution as a function of the greater LAC

spacecraft zenith angle at the edges.

This first version of the SeaWiFS simulated data set

contains realistic total radiances, in a representative data

record scenario: approximately 6.8 orbits of GAC data beginning at the first visibility of the downlink station at

WFF, and 8 minutes of LAC record time, interspersed in

the SeaWiFS orbits. Future improvements should incorporate representative values in the telemetry fields, accounting for clouds and land radiances. Also, a tilt strategy

to minimize sun glint should be included. However, this

version facilitates early prototyping activities by the SeaWiFS data system, providing a realistic data set to assess

performance.

6. DATA AVAILABILITY

Version 1 of the simulated SeaWiFS data set is available from the authors on 9-track tape at 6,250 bits per inch

(bpi). The tape is written using the VAX/VMS BACKUP

command, on the assumption that most users have access

9
The Simulated SeaWiFS Data Set, Version 1

Fig. 2. Simulated total radiances for GAC data for SeaWiFS bands 1–3.

10
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

Fig. 3. Simulated total radiances for GAC data for SeaWiFS bands 4–6.

11
The Simulated SeaWiFS Data Set, Version 1

Fig. 4. Simulated total radiances for GAC data for SeaWiFS bands 7-8, and LAC data for band 2.

12
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

to Digital Equipment Corporation (DEC) hardware. FORTRAN programs to read the data and strip out telemetry

fields and science data are provided in the Appendices.

Appendices

A. Description

B. Program RGAC.FOR

C. Program RLAC.FOR

D. Program EXPAND.FOR

E. Program B2W.FOR

Appendix A

Description

The SeaWiFS simulated data sets and programs to read

them are provided on a 6,250 bpi 9-track tape. The tape was

generated using the VMS (version 5.4–3) BACKUP command and

the following command sequence:

MOUNT/FOREIGN device

BACKUP/LOG device:simdat *.*/label=simdat/block=32256

DISMOUNT device

where device is the tape drive device name. (Note: 105 MBytes

of free disk space are required to read the tape in its entirety.)

When the tape is loaded onto disk, 6 files are put in the

current directory. GAC.DAT and LAC.DAT are the simulated data

sets for GAC and LAC data, respectively. Listings of the

source codes to read these data sets are provided in the following. This includes the main programs RGAC.FOR and RLAC.FOR

and the two supporting subroutines, EXPAND.FOR and B2W.FOR.

EXPAND.FOR is used toextract the minor frame data segments.

B2W.FOR is used tounpack a 5-byte field intofour 2-byte integers.

Appendix B

Program RGAC.FOR

program rgac

c

c Program to read and sort simulated SeaWiFS GAC data.

c by: Frank Chen, GSC.

c

implicit none

character c(13864)

integer*2 s1(12)

character s2(775)

integer*2 s3(10458)

character s4(2)

c

c Minor frame data structures

c

integer*2 FrameSync(6),SCID(2),TimeTag(4)

character SCSOH(775)

integer*2 InstTLM(44),CalTable(44),Spare(188)

integer*2 GAC(8,252,5)

integer*2 PAD1(2),AuxSync(100)

character PAD2(2)

c

c Science data array

c

integer*2 ilt(8,248)

c

c Total number of scan lines

c

integer*4 nscan

c

c Minor frame number(1,2,3)

c

c integer*4 MinorFrameNo,msec_of_day, spacecraft_id

integer*2 day_of_year

integer*4 i,j,k

c

c Orbit number, xlons, ylats, and gmt time(hr) for 5 GAC

c scan lines within one minor frame. These fields are

c temporary.

c

integer*4 iorb(5)

real*4 xlons(5),ylats(5),gmt(5)

c

c Map the above fields within SCSOH

c

equivalence (iorb(1),SCSOH(197)), (xlons(1),SCSOH(217))

equivalence (ylats(1),SCSOH(237)), (gmt(1),SCSOH(257))

c

c Map fields within minor frame to the three segments

c

equivalence (FrameSync(1),s1(1)), (SCID(1),s1(7))

equivalence (TimeTag(1),s1(9)), (SCSOH(1),s2(1))

equivalence (InstTLM(1),s3(1)), (CalTable(1),s3(45))

equivalence (Spare(1),s3(89)), (GAC(1,1,1),s3(277))

equivalence (PAD1(1),s3(10357)), (AuxSync(1),s3(10359))

equivalence (PAD2(1),s4(1))

c

100 format(i5,3f10.4)

200 format(8i5)

nscan = 0

c

open(4,file=’gac.dat’,status=’old’,form=’unformatted’)

20 continue

c

c Read in one minor frame

c

read(4,end=999)c

c

c Convert all 10-bit-word to 16-bit-word

c

call expand(c,s1,s2,s3,s4)

c

c Calculate s/c id, minor fram number, day of year,

c and msec of day

c

spacecraft_id = MOD(SCID(1)/8,16)

MinorFrameNo = MOD(SCID(1)/128,4)

day_of_year = TimeTag(1)/2

msec_of_day = TimeTag(2)*1024.0*1024.0 +

* TimeTag(3)*1024.0 + TimeTag(4)

do i=1,5

c

c GAC(k, 1,i),k=1,8 80 bits GAC GainTDI

c GAC(k, 2,i),k=1,8 80 bits GAC StartSync

c GAC(k, 3,i),k=1,8 80 bits GAC DarkRestore

c GAC(k,252,i),k=1,8 80 bits GAC StopSync

c

c Check if the GAC data are valid

c

if ((GAC(1,3,i).eq.0) .and. (GAC(2,3,i).eq.0) .and.

* (GAC(3,3,i).eq.0) .and. (GAC(4,3,i).eq.0) .and.

* (GAC(5,3,i).eq.0) .and. (GAC(6,3,i).eq.0) .and.

* (GAC(7,3,i).eq.0) .and. (GAC(8,3,i).eq.0)) then

write(6,*)’ no more valid data’

goto 999

end if

nscan = nscan + 1

do j=4,251

do k=1,8

ilt(k,j-3)=GAC(k,j,i)

end do

end do

end do

goto 20

999 continue

13
The Simulated SeaWiFS Data Set, Version 1

close(4)

write(6,*)’Total no. of scan lines =’,nscan

c

end

Appendix C

Program RLAC.FOR

program rlac

c

c Program to read and sort SeaWiFS simulated LAC data.

c by: Frank Chen, GSC.

c

implicit none

character c(13864)

integer*2 s1(12)

character s2(775)

integer*2 s3(10458)

character s4(2)

c

c Minor frame data structures

c

integer*2 FrameSync(6),SCID(2),TimeTag(4)

character SCSOH(775)

integer*2 InstTLM(44),LAC(8,1289)

integer*2 PAD1(2),AuxSync(100)

character PAD2(2)

c

c History SCSOH and OX25 in minorframe 2,3

c

character HistSOH(775),OX25(775)

c

c Ancilliary TLM and Calibration Table in minor

c frame 2,3

c

integer*2 AncTLM(44),CalTable(44)

c

c Science data array

c

integer*2 ilt(8,1285)

c

c Total number of scan lines

c

integer*4 nscan

c

c Minor frame number(1,2,3)

c

integer*4 MinorFrameNo,msec_of_day,spacecraft_id

integer*2 day_of_year

integer*4 i,j,k

c

c Orbit number,xlons,ylats, and gmt time(hr) for LAC

c scan line within one minor frame. These fields

c are temporary.

c

integer*4 iorb

real*4 xlons,ylats,gmt

c

c Map the above fields within SCSOH

c

equivalence (iorb,SCSOH(197)), (xlons,SCSOH(217))

equivalence (ylats, SCSOH(237)), (gmt,SCSOH(257))

c

c Map fields within minor frame to the three segments

c

equivalence (FrameSync(1),s1(1)), (SCID(1),s1(7))

equivalence (TimeTag(1),s1(9)), (SCSOH(1),s2(1))

equivalence (InstTLM(1),s3(1)), (LAC(1,1),s3(45))

equivalence (PAD1(1),s3(10357)), (AuxSync(1),s3(10359))

equivalence (PAD2(1),s4(1)), (HistSOH(1),SCSOH(1))

equivalence (OX25(1),SCSOH(1)), (AncTLM(1),InstTLM(1))

equivalence (CalTable(1),InstTLM(1))

c

100 format(i5,3f10.4)

200 format(8i5)

nscan = 0

c

open(4,file=’lac.dat’,status=’old’,form=’unformatted’)

20 continue

c

c Read in one minor frame

c

read(4,end=999)c

c

c Convert all 10-bit-word to 16-bit-word

c

call expand(c,s1,s2,s3,s4)

c

c Calculate s/c id, minor fram number, day of year,

c and msec of day

c

spacecraft_id = MOD(SCID(1)/8,16)

MinorFrameNo = MOD(SCID(1)/128,4)

day_of_year = TimeTag(1)/2

msec_of_day = TimeTag(2)*1024.0*1024.0 +

* TimeTag(3)*1024.0 + TimeTag(4)

c

c write(6,*)’day:’,day_of_year,’ scid:’,

c * spacecraft_id,

c * ’ frame:’,MinorFrameNo

c

c LAC(k, 1),k=1,8 80 bits LAC GainTDI

c LAC(k, 2),k=1,8 80 bits LAC StartSync

c LAC(k, 3),k=1,8 80 bits LAC DarkRestore

c LAC(k,1289),k=1,8 <80 bits LAC StopSync

c

nscan = nscan + 1

do j=4,1288

do k=1,8

ilt(k,j-3)=LAC(k,j)

end do

end do

goto 20

999 continue

close(4)

write(6,*)’Total no. of scan lines =’,nscan

end

Appendix D

Program EXPAND.FOR

c This subroutine converts the input buffer (c) into

c four minor frame segments: s1, s2, s3, and s4.

c S1 consists of 12 10-bit words containing the frame

c sync, the spacecraft id, and the time tag. S2

c is a the S/C SOH array. S3 is the remainder 10458

c 10-bit words without the last padding (1.5 bytes).

c S4 is the last padding.

c

subroutine expand(c,s1,s2,s3,s4)

implicit none

character c(13864)

integer*2 s1(12)

character s2(775)

integer*2 s3(10458)

character s4(2)

character b(5)

integer*2 w(4)

integer*4 i,j,k

c

c Process first I*2 segment

c

do i=0,11,4

k = i*5/4

do j=1,5

14
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

b(j) = c(k+j)

end do

call b2w(b,w)

do j=1,4

s1(i+j) = w(j)

end do

end do

c

c Process second C*1 segment

c

k = 12*5/4

do i=1,775

s2(i) = c(k+i)

end do

c

c Process third I*2 segment

c

do i=0,10455,4

k = (i+12)*5/4 + 775

do j=1,5

b(j) = c(k+j)

end do

call b2w(b,w)

do j=1,4

s3(i+j) = w(j)

end do

end do

k = 13860

do j=1,3

b(j) = c(k+j)

end do

b(4) = char(ichar(c(k+4)) .and. 240)

b(5) = char(0)

call b2w(b,w)

do j=1,3

s3(10456+j) = w(j)

end do

s4(1) = char(MOD(ichar(c(13863)),16)*16 +

* ichar(c(13864))/16)

s4(2) = char(MOD(ichar(c(13864)),16)*16)

return

end

Appendix E

Program B2W.FOR

c Convert packed 5 bytes character(b) into four

c two-byte-integer(w) each contains 10-bit information.

c MOD(n,2**m): modulus ’n’ by ’2**m’. extract lowest

c ’m’ bits from the number ’n’.

c n * (2**m): shift left the number ’n’ by ’m’ bits.

c n / (2**m): shift right the number ’n’ by ’m’ bits.

c

subroutine b2w(b,w)

implicit none

character b(5)

integer*2 w(4)

integer*4 c(5)

integer*4 i

integer*4 p0 /1/, p2 /4/, p4 /16/, p6 /64/,

integer*4 p8 /256/

c

do i=1,5

c(i) = ICHAR(b(i))

end do

w(1) = MOD(c(1),p8)*p2 + c(2)/p6

w(2) = MOD(c(2),p6)*p4 + c(3)/p4

w(3) = MOD(c(3),p4)*p6 + c(4)/p2

w(4) = MOD(c(4),p2)*p8 + c(5)/p0

return

end

Glossary

bpi bits per inch

CZCS Coastal Zone Color Scanner

DEC Digital Equipment Corporation

DU Dobson Units

FNOC Fleet Numerical Oceanography Center

FORTRAN Formula Translation (computer language)

FWHM Full-Width Half-Maximum

GAC Global Area Coverage

GMT Greenwich Mean Time

IFOV Instantaneous Field-of-View

ISCCP International Satellite Cloud Climatology Project

LAC Local Area Coverage

Level-0 Raw data.

Level-3 Gridded and averaged derived products.

MB Megabytes

MF Major Frame

mF Minor Frame

NCDS NASA Climate Data System

NER Noise Equivalent Radiance

OSC Orbital Sciences Corporation

SeaWiFS Sea-viewing Wide Field-of-view Sensor

S/C Spacecraft

SOH State of Health

TDI Time Delay Integration

TLM Telemetry

VAX Virtual Address Extension

VMS Virtual Memory System

WFF Wallops Flight Facility

Symbols

a A constant equal to 0.983.

aox Coefficient for oxygen absorption.

aoz Coefficient for ozone absorption.

awv Coefficient for water vapor absorption.

A(λ) Coefficient for calculating bb(λ).

bb(λ) Spectral backscattering coefficient.

bbc(λ) Spectral backscattering coefficient for phytoplankton.

bw(λ) Total scattering coefficient for pure seawater.

B(λ) Coefficient for calculating bb(λ).

Cref Reference chlorophyll value (0.5).

[chl. a] Chlorophyll concentration.

D Sequential day of the year.

DC10 Digital counts at 10-bit digitization.

F0(λ) Mean extraterrestrial irradiance.

F0 Extraterrestrial irradiance corrected for Earthsun distance.

F

0 Extraterrestrial irradiance corrected for the atmosphere.

Fa Forward scattering probability of the aerosol.

15
The Simulated SeaWiFS Data Set, Version 1

g1 A constant equal to 0.82.

g2 A constant equal to −0.55.

HGMT GMT in hours.

Hs Altitude of the spacecraft (for SeaStar 705 km).

i Inclination angle.

i

 Inclination angle minus 90◦.

I Rayleigh intensity.

kc(λ) Spectral fit coefficient weighted over the SeaWiFS bands.

k

c, (λ) Spectral fit coefficient weighted over the SeaWiFS bands.

K(λ) Spectral attenuation coefficient.

Kc(λ) Attenuation coefficients for phytoplankton.

KE(λ) Attenuation coefficient downwelled irradiance.

Kg(λ) Attenuation coefficients for Gelbstoff.

KL(z, λ) Attenuation coefficient upwelled radiance .

Kw(λ) Attenuation coefficients for pure seawater.

La(λ) Aerosol radiance.

Lg(λ) Sun glint radiance.

LNERλ) Noise equivalent radiance.

Lr(λ) Rayleigh radiance.

Lsat(λ) Saturation radiance for the sensor.

Lt(λ) Total radiance at the sensor.

Lu(z, λ) Upwelled spectral radiance.

LW (λ) Water-leaving radiance.

LWN (λ) Normalized water-leaving radiances leaving an

ocean of given optical properties assuming no

atmosphere and the sun directly overhead.

M Path length through the atmosphere.

Moz Path length for ozone transmittance.

n Index of refraction.

Q Irradiance-to-radiance ratio (equals π for totally

diffuse radiance).

pa A factor to account for the probability of scattering tothe spacecraft for three different paths

from the sun.

pw The probability of seeing sun glitter in the direction θ, Φ given the sun in position θ0, Φ0 as a

function of wind speed (W).

P Nodal period.

Pa Probability of scattering to the spacecraft.

P(θ+) Phase function for forward scattering.

P(θ−) Phase function for backward scattering.

r Water-air reflectance for totally diffuse irradiance.

R(0−, λ) Irradiance reflectance just below the sea surface.

Re Mean Earth radius (6371.2 km).

s(λ) Slope for the range 0–1,023.

t Time variable.

t0 Initial time.

taa Aerosol transmittance after absorption.

tas Aerosol transmittance after scattering.

td Direct component of transmittance after absorption by the gaseous components of the atmosphere, scattering and absorption by aerosols,

and scattering by Rayleigh.

te Time difference in hours between present position and most recent equator crossing.

tEC Equator crossing time.

toz Transmittance after absorption by ozone.

tr Transmittance after Rayleigh scattering.

ts Diffuse component of transmittance after absorption by the gaseous components of the atmosphere, scattering and absorption by aerosols,

and scattering by Rayleigh.

twv Transmittance after absorption by water vapor.

T(λ, θ) Total transmittance (direct plus diffuse) from

the ocean through the atmosphere to the spacecraft along the path determined by the spacecraft zenith angle θ.

T(λ, θ)LW (λ) The water-leaving radiance transmitted tothe

spacecraft.

T0(λ, θ0) Total downward transmittance of irradiance.

Te Equation of time.

Tox Transmittance of oxygen (O2).

Toz Transmittance of ozone (O3).

Ts(λ) Transmittance through the surface.

Twv Transmittance of water vapor (H2O).

W Wind speed.

Wd Direct irradiance divided by the total irradiance

at the surface.

Ws Diffuse irradiance divided by the total irradiance.

α The power constant in the  ̊Angstr ̈om formulation.

β A constant in the  ̊Angstr ̈om formulation.

δ Great circle distance from Ψs(t0) to Ψs(t − t0).

∆t Time difference.

∆ω The longitude difference from the sub-satellite

point to the pixel.

∆ωs Longitude difference.

η Bearing from the sub-satellite point to the pixel

along the direction of motion of the satellite.

λ Wavelength of light.

Ψ Pixel latitude.

Ψd Solar declination latitude.

Ψs(t) Sub-satellite latitude as a function of time.

Φ Spacecraft azimuth angle.

Φ0 Solar azimuth angle.

ρ Weighted direct plus diffuse reflectance.

ρ(θ) Fresnel reflectance for viewing geometry.

ρ(θ0) Fresnel reflectance for solar geometry.

ρn Sea surface reflectance for direct irradiance at

normal incidence for a flat sea.

ρN Reflectance for diffuse irradiance.

θ Spacecraft zenith angle.

θ0 Solar zenith angle.

θN The angle with respect tonadir that the sea surface slopes to produce a reflection angle to the

spacecraft.

θs Scan angle of sensor.

θ

s Scan angle of sensor adjusted for tilt.

16
W.W. Gregg, F.C. Chen, A.L. Mezacche, J.D. Chen, and J.A. Whiting

τa Aerosol optical thickness.

τr Rayleigh optical thickness.

τs(λ) Spectral solar atmospheric transmission.

ω Longitude variable.

ω0 Old longitude value.

ωa Single scattering albedo of the aerosol.

ωe Equator crossing longitude.

ωs Longitude variable.

Ω Solar hour angle.

References

Austin, R.W., 1974: The remote sensing of spectral radiance

from below the ocean surface, In: Optical Aspects of Oceanography, N.G. Jerlov and E. Steemann-Nielsen, Eds., Academic Press, 317–344.

Baker, K.S., and R.C. Smith, 1982: Bio-optical classification

and model of natural waters, 2. Limnol. and Oceanography,

27, 500–509.

Bird, R.E., and C. Riordan, 1986: Simple solar spectral model

for direct and diffuse irradiance on horizontal and tilted

planes at the Earth’s surface for cloudless atmospheres, J.

of Climate and Applied Meteorology, 25, 87–97.

Cox, C., and W. Munk, 1954: Measurement of the roughness

of the sea surface from photographs of the sun’s glitter, J.

Mar. Res., 44, 838–850.

Feldman, G.C., N. Kuring, C. Ng, W. Esaias, C.R. McClain,

J. Elrod, N. Maynard, D. Endres, R. Evans, J. Brown, S.

Walsh, M. Carle, G. Podesta, 1989. Ocean Color: Availability of the global data set, EOS, Transactions of the

American Geophysical Union, 70, 634–635, 640–641.

Gordon, H.R., 1990. Radiometric considerations for ocean color

remote sensors, Applied Optics, 29, 3,228–3,236.

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

W.W. Broenkow, 1983: Phytoplankton pigment concentrations in the Middle Atlantic Bight: Comparison of ship

determinations and CZCS estimates, Applied Optics, 22,

20–36.

, O.B. Brown, R.H. Evans, J.W. Brown, R.C. Smith, K.S.

Baker, and D.K. Clark, 1988a. A semianalytic radiance

model of ocean color, J. of Geophys. Res., 93, 10,909–

10,924.

, J.W. Brown, and R.H. Evans, 1988b: Exact Rayleigh

scattering calculations for use with the Nimbus-7 Coastal

Zone Color Scanner, Applied Optics, 27, 862–871.

, and D.J. Casta ̃no, 1989: Aerosol analysis with Coastal

Zone Color Scanner: A simple method for including multiple scattering effects, Applied Optics, 28, 1,320–1,326.

Gregg, W.W., and K.L. Carder, 1990: A simple spectral solar irradiance model for cloudless maritime atmospheres,

Limnol. and Oceanography, 35, 1,657–1,675.

Iqbal, M., 1983: An Introduction to Solar Radiation. Academic

Press, 390 pp.

Jerlov, N.G., 1976: Marine optics, Elsevier Scientific Publishing Co., New York, 231 pp.

Justus, C.G., and M.V. Paris, 1985: A model for solar spectral

irradiance and radiance at the bottom and top of a cloudless atmosphere, J. of Climate and Applied Meteorology,

24, 193–205.

Kasten, F., 1966: A new table and approximate formula for

relative optical air mass, Geophys. Biokimatol., B14, 206–

223.

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

3300 and 12500  ̊A. Solar Physics, 90, 205–258.

Paltridge, G.W., and C.M.R. Platt, 1976: Radiative processes

in meteorology and climatology, Developments in Atmospheric Science, Vol. 5. Elsevier Scientific Publishing Co.,

New York, 318 pp.

Viollier, M., D. Tanre, and P.Y. Deschamps, 1980: An algorithm for remote sensing of water color from space,Bound.-

Layer Meteorology, 18, 247–267.

Williams, S.P., E.F. Szajna, and W.A. Hovis, 1985: Nimbus 7

Coastal Zone Color Scanner (CZCS) Level 1 data product

users’ guide, NASA Technical Memorandum 86203, 49 pp.

17
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 SeaWiFS Technical Report Series

 Volume 9–The Simulated SeaWiFS Data Set, Version 1 Code 970.2

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 Oceanography, SeaWiFS, Data Set, Spectral Band, Orbital Characterisitics, 17

 Scanning Characteristics

Frank C. Chen, Ahmed L. Mezaache, Judy D. Chen, Jeffrey A. Whiting, Elaine R. Firestone, and A.W. Indest : General

Sciences Corporation, Laurel, Maryland.

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13. ABSTRACT (Maximum 200 words)

National Aeronautics and Space Administration

Washington, D.C. 20546–0001 TM–104566, Vol. 9

Laboratory for Hydrospheric Processes

Goddard Space Flight Center 93B00086

Greenbelt, Maryland 20771

6. AUTHOR(S)

 Watson W. Gregg, Frank C. Chen, Ahmed L. Mezaache, Judy D.Chen,

 and Jeffrey A. Whiting

 Series Editors: Stanford B. Hooker, Elaine R. Firestone, and A.W. Indest

Data system development activities for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) must begin well before the

scheduled 1994 launch. To assist in these activities, it is essential to develop a simulated SeaWiFS data set as soon as

possible. Realism is of paramount importance in this data set, including SeaWiFS spectral bands, orbital and scanning

characteristics, and known data structures. Development of the simulated data set can assist in identification of problem

areas that can be addressed and solved before the actual data are received. This paper describes the creation of the first

version of the simulated SeaWiFS data set. The data set includes the spectral band, orbital, and scanning characteristics of

the SeaWiFS sensor and SeaStar spacecraft. The information is output in the data structure as it is stored onboard. Thus, it

is a level-0 data set which can be taken from start to finish through a prototype data system. The data set is complete and

correct at the time of printing, although the values in the telemetry fields are left blank. The structure of the telemetry

fields, however, is incorporated. Also, no account for clouds has been included. However, this version facilitates early

prototyping activities by the SeaWiFS data system, providing a realistic data set to assess performance.