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Calibration of ocean color scanners: how much error is acceptable in the near infrared?
Remote Sensing of Environment 82 (2002) 497 – 504 www.elsevier.com/locate/rse
Calibration of ocean color scanners: how much error is acceptable in the near infrared? Menghua Wang a,*, Howard R. Gordon b a
University of Maryland, Baltimore County, NASA Goddard Space Flight Center, Code 970.2, Greenbelt, MD 20771, USA b Department of Physics, University of Miami, Coral Gables, FL 33124, USA Received 1 May 2000; received in revised form 24 October 2001; accepted 28 May 2002
Abstract We simulate vicarious calibration (VC) of a Sea-viewing Wide Field-of-view Sensor (SeaWiFS)-like ocean color sensor relative to its longer near infrared (NIR) spectral band (865 nm) to understand the influence of calibration error at 865 nm, which is difficult to assess in orbit. We show that as long as the calibration error at 865 nm less than f10% in magnitude, the post-vicarious-calibration-corrected radiances are sufficiently accurate to retrieve useful water-leaving reflectances at moderate aerosol optical depths. This is completely independent of the initial calibration error in the shorter-wave bands, but assumes an atmospheric correction approach similar to that currently used with SeaWiFS. Retrievals are only slightly improved by reducing the magnitude of the error at 865 nm below f5%. The simulations immediately suggest that pre-launch calibration is necessary only to the extent required to set the sensitivity of the instrument in the desired range. Rather than trying to achieve a highly accurate pre-launch calibration, e.g., uncertainty <5%, we assert that resources would be better expended on improved radiometric stability (and its monitoring) and complete characterization of the instrument, e.g., polarization sensitivity, out-of-band response, etc. However, these assertions assume the existence of a permanent vicarious calibration facility, e.g., the Marine Optical Buoy (MOBY). D 2002 Elsevier Science Inc. All rights reserved.
1. Introduction Ocean color remote sensing places very stringent requirements on the sensor’s radiometric calibration, particularly in the blue. This is simply due to the fact that the desired water-leaving radiance comprises such a small part of the total radiance measured by the instrument. For example, in the blue (443 nm), the water-leaving radiance typically less that 10% of the total radiance: scattering from the atmosphere and the sea surface comprises the rest (Gordon, 1997). Thus, even if the effects of the atmosphere and the sea surface are perfectly removed, the relative error in the water-leaving radiance will be at least 10 times the relative error in the sensor calibration. If we want the waterleaving radiance with an uncertainty <10% in the blue, the uncertainty in the radiometric calibration of the sensor must be <1%. It is not possible to achieve such an
*
Corresponding author. Tel.: +1-301-286-6421; fax: +1-301-286-1775. E-mail address: [email protected] (M. Wang).
uncertainty in pre-launch calibration of an ocean color sensor at this time, and even if it were, the stress of launch would likely cause unknown changes in the sensor’s radiometric response. The key to a successful mission is therefore in-orbit calibration or ‘‘vicarious calibration’’ (Evans & Gordon, 1994; Gordon, 1987; Slater et al., 1987; Slater, Biggar, Thome, Gellman, & Spyak, 1996). The basic strategy is to account for (by direct measurement or by prediction based on surface measurements, radiative transfer, and scattering theory) all of the components of the topof-the-atmosphere (TOA) radiance reflected from the ocean – atmosphere system and to compare the result with the sensor-measured radiance. Any difference between the measured and predicted radiance is attributed to error in the calibration of the sensor, and a modification to the calibration equation (or coefficients) is effected to bring the measurements and predictions into confluence. Gordon and Zhang (1996) investigated the accuracy with which such predictions can be made based on the assessment of atmospheric properties through measurement of sky radiance and atmospheric optical depth. They concluded that
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the uncertainty in the prediction of the TOA radiance was limited by, and approximately equal to or some-what larger than, the radiometric uncertainty in the sky radiance measurements. Making such measurements with a 1% uncertainty in the blue is still a significant challenge. In a recent paper, Gordon (1998) provided a new strategy of the in-orbit calibration of ocean color sensors. In this scheme, it is assumed that the longest-wave spectral band in the near infrared (NIR) is perfectly calibrated, and then the shorter-wave bands are in effect calibrated with respect to this band. Simulations of this procedure (Gordon, 1998) show that, for a given absolute calibration error at the longest-wave band, the calibration error at the shorter-wave bands progressively decreases with decreasing wavelength, roughly in inverse proportion to the increase in Rayleigh scattering. This decrease in error owes to the fact that the Rayleigh scattering component, which increases in importance from the red to the blue, can be computed with little error. Thus, applying the Gordon (1998) strategy to a hypothetical sensor for which the actual calibration error in the NIR (865 nm) was 5% (but assumed to be zero in the vicarious calibration procedure), the 5% error in the NIR was reduced to a 0.3% error at 412 nm. This procedure meets the calibration uncertainty challenge described above. A similar procedure has been used to effect the vicarious calibration of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) (Eplee et al., 2001) using the Marine Optical Buoy (MOBY) (Clark et al., 1997). In addition, it was applied to vicarious inter-calibration of the German Modular Optoelectrionic Scanner (MOS) sensor on the Indian IRS-P3 satellite using SeaWiFS data as the correct values (Wang & Franz, 2000). It is important to reiterate that, in the Gordon (1998) procedure, the longest-wave spectral band in the NIR is assumed to be perfectly calibrated, and therefore, retains its post-launch calibration error. Vicarious calibration of this band must be effected through a direct computation of the TOA radiance based on surface measurements of sky radiance and optical depth as described by Gordon and Zhang (1996). However, as mentioned above, a significant reduction of the calibration error (e.g., below f5%) is unlikely due to uncertainty in the radiometric response of the sky radiometer. See Slater, Biggar, Plamer, and Thome (2001) for a through discussion of radiometer calibration uncertainties. In the Gordon (1998) simulations, reducing the assumed error in the longest NIR band by a factor of two (from 5% to 2.5%), yielded only a slight improvement in the retrieved water-leaving reflectance using the Gordon and Wang (1994) atmospheric correction algorithm. This leads to the following question: how important is the radiometric calibration accuracy of the longest-wavelength NIR spectral band in ocean color sensors if the other bands are ‘‘calibrated’’ in orbit assuming that the NIR band has no calibration error? Here, we provide simulations to answer this question. This has important consequences regarding
resource allocation within both pre-launch and post-launch calibration efforts. We begin by reviewing the Gordon (1998) strategy for vicarious calibration, then describe our simulation of the strategy, and finally show some results of simulations regarding the effect of calibration error at various levels on the retrieved water-leaving reflectance.
2. Vicarious calibration method 2.1. General radiative transfer The reflectance (q=pL/F0cosh0, where L is radiance, F0 is the extraterrestrial irradiance, and h0 is the solar zenith angle) of the ocean –atmosphere system at a wavelength k can be written as qt ðkÞ ¼ qAtm&Sfc ðkÞ þ tðkÞqw ðkÞ;
ð1Þ
where qAtm&Sfc(k) is the reflectance of the atmosphere and the sea surface, qw(k) is the reflectance associated with radiance backscattered out of the water, and t is the diffuse transmittance of the atmosphere along a path from the sea surface to the satellite-borne sensor. Here, we have assumed that the data are acquired under whitecap-free conditions and avoiding sun glint. Because the molecular scattering properties of the atmosphere are well known, it is convenient to follow Gordon and Wang (1994) and write the first term as qAtm&Sfc ðkÞ ¼ qr ðkÞ þ qA ðkÞ; where qr(k) is the reflectance of an aerosol-free atmosphere bounded by a Fresnel-reflecting ocean. The second term represents the component of the reflectance due to the aerosol in the presence of molecular scattering, i.e., the contribution from any photon that has scattered at least once from the aerosol. It is computed by utilizing an optical model for the aerosol, computing qAtm&Sfc(k) using a radiative transfer code for an atmosphere bounded by a Fresnel-reflecting ocean (that absorbs all photons that penetrate the ocean surface) with and without aerosols, and subtracting them. The aerosol optical properties are derived from a physical – chemical model (particle size distribution and refractive index) using Mie theory. The diffuse transmittance is computed following Yang and Gordon (1997) by assuming that the backscattered radiance just beneath the sea surface is uniform, i.e., observed just beneath the sea surface, the water body is a lambertian reflector. 2.2. Application to VC In the vicarious calibration (VC) scheme, the quantities on the right-hand-side of Eq. (1) are estimated and summed, and the sensor calibration is adjusted to yield a value of
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qt(k) that is in agreement with the sum. This is effected in the following manner. First, the quantity qr is computed with little error by employing the surface atmospheric pressure and wind speed measured at the vicarious calibration site. Next, the water-leaving reflectance qw is measured directly at the site (Clark et al., 1997). Finally, estimates of qA(k) and t are made by radiative transfer computations using an aerosol model, henceforth called the ‘‘VC aerosol model’’ or just the ‘‘VC model.’’ The VC aerosol model is composed of an aerosol size distribution and refractive index providing the aerosol spectral scattering phase function and spectral extinction coefficient through Mie theory. It is chosen to conform to surface measurements of the spectral variation of the aerosol optical thickness sa(k) at the time of overpass; however, this is not a guarantee that the correct model size distribution (and therefore the scattering phase function) will be used (Lienert, Porter, & Sharma, 2001). An improvement would be to use sky radiance measurements as an additional constraint on the VC aerosol model choice. (Although sky radiance measurements are generally not accurate enough to enable computation of qAtm&Sfc(k) for VC via Gordon and Zhang (1996), they could provide the aerosol phase function at scattering angles less than about 90j (Cattrall, 2001), and further constrain the VC model choice.) Since the procedure assumes no calibration error at 865 nm (where qw=0), given the VC aerosol model, the value of qA(k) at 865 nm fixes the value of sa(865). Similarly, the spectral variation of sa(k) and the phase function is also fixed by the VC model. This is the basic scheme described in Gordon (1998). It was used in the vicarious calibration of SeaWiFS with the Marine Optical Bouy (MOBY) data (Eplee et al., 2001). In the SeaWIFS calibration, the VC aerosol model used in the computation of qA(k) and t was a priori taken to be an average of the Shettle and Fenn (1979) maritime aerosol models at 50%, 70%, 90% and 99% relative humidity (referred to here as M50, M70, M90, and M99, respectively), i.e., not inferred from direct surface measurements.
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2.3. Specific simulations
Fig. 1. Physical and optical properties of the various Shettle and Fenn (1979) aerosol models used in this study: (a) model aerosol size (volume) distributions normalized to their maximum value; (b) spectral variation of the aerosol optical thickness; (c) aerosol phase functions P(H), where H is the scattering angle, at 865 nm.
We used radiative transfer to simulate VC of an ocean color sensor with the properties of SeaWiFS (Hooker, Esaias, Feldman, Gregg, & McClain, 1992) and a variety of calibration errors at 865 nm. We used the Shettle and Fenn (1979) oceanic aerosol model at 99% relative humidity (O99) to generate simulated TOA reflectances qt(k), i.e., we assumed that the actual aerosol present at the VC site was O99. This model was chosen because it is similar to the Porter and Clarke (1997) models for humid conditions at moderate wind speeds, and therefore should be realistic for a clean maritime aerosol. Fig. 1 provides the physical and optical properties of O99 and all the other aerosol models used in this study. As the goal is to compute qA(k) with as little uncertainty as possible, which would be difficult if the
aerosol concentration were high because of uncertainty in determining a VC aerosol model, we used sa(k)=0.05 at 865 nm. This would be characteristic of a clear maritime atmosphere, i.e., just where one would ideally try to effect a VC. We took the sun-sensor geometry so that the solar zenith angle (h0) was 20j, the sensor viewing angle with the nadir (hv) was 20j, and the relative azimuth between the sun and the sensor view (uv) was 90j. Such a geometry is typical of the MOBY calibration site off Hawaii (Clark et al., 1997). We took qw(k)=0 in the simulations, and used qw(k)=0 in the analysis, which in effect, means that in our simulations, we have assumed no measurement error in the water-leaving reflectance at the VC site. Thus, a perfectly
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Table 1 Pseudo calibration errors k (nm)
a(k) (%)
412 443 490 510 555 670 765
+5 +10 +5 +5 5 +5 10
calibrated sensor and a perfect atmospheric correction would retrieve qw(k)=0, in our simulations. See Gordon (1998) for an analysis of the influence of measurement error in qw. We added error to the simulated TOA ‘‘true’’ reflectances qtTrue(k), so that qMeasured ðkÞ ¼ ½1 þ aðkÞqTrue ðkÞ; t t
ð2Þ
where qtMeasured(k) is the reflectance that would be ‘‘measured’’ by a sensor with the incorrect calibration. The values of a(k) that we used are provided in Table 1; however, as we shall show later, the a(k) values for k<865 nm are irrelevant, i.e., the results of the VC procedure are completely independent of the pre-launch calibration (except that at 865 nm). The error at k=865 nm assumed several different values: the point being to assess the results as a function of a(865). To complete the VC procedure, we need to compute qA(k). As mentioned above, this computation requires only a model for the aerosol present at the calibration site. The chosen VC aerosol model (MOD) was used to derive a computed qA(k) in the following manner. First, the value of saMOD(865) required by the model to reproduce the ‘‘measured’’ value of qA(k) at 865 nm was computed (not necessarily 0.05 because both the VC aerosol model and the ‘‘measured’’ value of qA(k) at 865 nm may be incorrect). Then, from saMOD(865), the VC aerosol model was used to determine saMOD(k). Finally, qA(k) was computed for each of the visible bands using the VC aerosol model’s spectral scattering phase function and the estimated saMOD(k). Combined with qr(k), this provides the computed value of qt, which we refer to as qtComputed. Note that qtComputed will be specific to the chosen VC aerosol model and to the particular sun-viewing geometry at the VC site. Taking these computed qt’s to be the correct values, the sensor calibration is then adjusted by a factor KVC(k), to bring qtMeasured(k) and qtComputed into confluence. The ‘‘measured’’ reflectances at any site are then used to provide what we believe to be the correct reflectances there through qCorrected ðkÞ ¼ K VC ðkÞqMeasured ðkÞ t t ðkÞ; ¼ K VC ðkÞ½1 þ aðkÞqTrue t
ð3Þ
Fig. 2. Summary of the VC procedure and application to a target site. ‘‘AP’’ refers to the aerosol actually present at the VC site (O99), and ‘‘AM’’ refers to the VC aerosol model chosen on the basis of surface measurements (O99, M99, or M50). The target site aerosol is either M80 or T80.
where KVC(k)=qtComputed(k)/qtMeasured(k) at the VC site. qtCorrected(k) is then used in all the algorithms as the correct value of qtTrue(k). To reiterate, qtMeasured(k) is what the original sensor calibration provides and qtCorrected(k) is the revised reflectance after VC., i.e., qtCorrected(k)=qtComputed(k) at the VC site, and only at the VC site. The only errors in this procedure (assuming that qw(k) is error-free) are the choice of an incorrect VC aerosol model (which is always likely), and the assumption that there is no calibration error at 865 nm (a(865)=0).
Table 2a Residual error in sensor absolute calibration after VC using O99 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) 0.82 1.17 1.88 2.25 3.25 6.63 10.64 15.0
0.55 0.79 1.26 1.51 2.18 4.43 7.10 10.0
0.28 0.40 0.64 0.77 1.10 2.23 3.56 5.0
0.01 0.02 0.02 0.02 0.03 0.02 0.02 0.0
+0.26 +0.37 +0.60 +0.72 +1.05 +2.18 +3.52 +5.0
+0.53 +0.76 +1.22 +1.47 +2.22 +4.38 +7.06 +10.0
+0.80 +1.15 +1.85 +2.21 +3.20 +6.59 +10.16 +15.0
M. Wang, H.R. Gordon / Remote Sensing of Environment 82 (2002) 497–504 Table 2b Residual error in sensor absolute calibration after VC using M99 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) 0.56 0.85 1.46 1.79 2.71 6.04 10.23 15.0
0.25 0.40 0.76 0.96 1.54 3.73 6.61 10.0
+0.07 +0.04 0.06 0.13 0.36 1.42 2.99 5.0
+0.39 +0.49 +0.64 +0.70 +0.81 +0.89 +0.63 +0.0
+0.72 +0.94 +1.34 +1.53 +1.99 +3.21 +4.24 +5.0
+1.04 +1.39 +2.05 +2.36 +3.17 +5.52 +7.86 +10.0
It is useful to recast Eq. (3) in a different form. " # 1 qComputed ðkÞ t VC K ðkÞ ¼ ; 1 þ aðkÞ qTrue ðkÞ t
+1.36 +1.85 +2.75 +3.20 +4.35 +7.83 +11.48 +15.0
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and hv=46j (scan ‘‘edge’’), and uv=90j. Note that the scan-sun geometries used for the target sites are different from those at the VC site. The aerosol models used to generate the pseudo data for the target sites were the Shettle and Fenn (1979) Maritime model at 80% relative humidity (M80) and their Tropospheric model at 80% relative humidity (T80). These were the same models used by Gordon and Wang (1994) to test the SeaWiFS atmospheric correction algorithm. The physical and optical properties for these models are also shown in Fig. 1. In contrast to M80, which is nonabsorbing, T80 is weakly absorbing (single scattering
ð4Þ
VC
where the quantities in the ‘‘VC’’ subscripted brackets are at the VC site. Then combining Eqs. (3) and (4) shows that " # qComputed ðkÞ t Corrected qt ðkÞ ¼ qTrue ðkÞ: ð5Þ t qTrue ðkÞ t VC
The ‘‘VC’’ subscripted brackets in Eq. (5) depends only on the actual aerosol at the calibration site and its optical thickness at 865 nm, the assumed VC aerosol model, the sun-sensor geometry, and the calibration error at 865 nm. It is completely independent of the initial calibration error a(k) for k<865 nm. Thus, writing Eq. (3) as qCorrected ðkÞ ¼ ½1 þ aa ðkÞqTrue ðkÞ; t t
ð6Þ
where aa(k) is the absolute calibration error after VC, Eq. (5) shows that aa(k) depends only on the correctness of the VC aerosol model, the VC geometry, and on a(865), but not on a(k) for k<865 nm. A measure of the efficacy of the VC is the quality of the qw(k) retrievals operating on qtCorrected(k) with the Gordon and Wang (1994) atmospheric correction algorithm. We tested this by creating pseudo data containing the original sensor calibration error, specified by a(k), at a set of locations we call ‘‘target site(s).’’ The scan-sun geometries for the target sites were h0=40j, hv=1j (scan ‘‘center’’)
Table 2c Residual error in sensor absolute calibration after VC using M50 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) +0.19 +0.08 0.25 0.45 1.17 4.31 9.01 15.0
+0.66 +0.71 +0.68 +0.63 +0.29 1.68 5.16 10.0
+1.12 +1.34 +1.62 +1.71 +1.76 +0.96 1.31 5.0
+1.59 +1.97 +2.55 +2.79 +3.23 +3.60 +2.53 +0.0
+2.05 +2.59 +3.48 +3.88 +4.69 +6.23 +6.38 +5.0
+2.52 +3.22 +4.41 +4.96 +6.16 +8.87 +10.23 +10.0
+2.98 +3.85 +5.34 +6.04 +7.62 +11.51 +14.08 +15.0
Fig. 3. Error in the retrieved value of qw(443) at the center of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was (a) O99, (b) M99, and (c) M50. The aerosol present at the target site was M80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
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effect the VC. Note that the rather large errors (Table 1) placed in the pseudo data are significantly reduced particularly in the blue and blue-green regions even when incorrect VC aerosol models were chosen to effect the vicarious calibration, and even when there is significant calibration error at 865 nm. However, after VC, the error in the red and NIR may actually be larger when a(865) is large. 3.2. How effective was the VC?
Fig. 4. Error in the retrieved value of qw(443) at the edge of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was M99. The aerosol present at the target site was M80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
Recalling that the revised calibration factor KVC(k) depends on the assumed VC aerosol model, the true sa(865), and the VC geometry, it is important to know how the retrieved qw(k) at target retrieval sites are affected by the VC, particularly when the atmosphere is significantly different at the target site from that at the VC site. For this, we used the above VC exercises effecting a new calibration, and the Gordon and Wang (1994) algorithm to retrieve
albedo f0.975 and 0.952 at 412 and 865 nm, respectively). Therefore, T80 model used in the simulations is significantly different from the oceanic type aerosol model, which existed at the VC site (O99), while the M80 model is somewhat similar. A summary of the radiative transfer simulations carried out for the VC procedure and its application to a target site is provided in Fig. 2.
3. Results 3.1. Simulated residual calibration error after VC (aa) We simulated the above VC procedure assuming that the surface measurements yielded the correct aerosol model, i.e., O99 (Fig. 1). More realistically, we also simulated the procedure assuming that an incorrect aerosol model, M99 or M50, was chosen based on the surface measurements. We note that surface measurements of sa(k), with their significant error (F0.01 to F0.02, Kaufman, 1993) at low aerosol optical depths, would make it difficult to distinguish between O99 and M99 (Fig. 1b). In contrast, the choice of M50 would require a rather large error in sa(k) and would be somewhat unlikely were the actual aerosol O99. If sky radiance measurements were also made to estimate the aerosol phase function, it is very unlikely that the M50 model would be chosen (Fig. 1c); however, such measurements would likely not distinguish between O99 and M99. The VC exercise was carried out for a(865)=15% to +15% in steps of 5%. The residual error in the sensor’s absolute calibration [aa(k)] after VC for various values of the actual calibration error at 865 nm are given in Tables 2a, 2b and 2c for the three choices of aerosol model used to
Fig. 5. Error in the retrieved value of qw(443) at the (a) center and (b) edge of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was M99. The aerosol present at the target site was T80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
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qw(k) from post-VC calibrated qt(k) values (Fig. 2), i.e., from qtCorrected(k). As before, we took the actual value of qw(k) to be zero. The results at the scan center when M80 is the aerosol actually present at the target site are provided in Fig. 3, which gives the error in the retrieved qw(k) at k=443 nm (positive values mean qw(k) is too large). A marginally acceptable error in this quantity is usually taken to be F0.002, i.e., an error that can be plotted in the figure as it is scaled. Panels (a), (b), and (c) refer to using O99, M99, and M50 as the VC aerosol model assumed in the vicarious calibration procedure. Clearly, better results (i.e., lower error in qw(k)) are obtained the closer the VC aerosol model is to the actual aerosol at the VC site (O99). Note that, even when aa(k)=0, the retrieval error is not null because the Gordon and Wang (1994) algorithm is not perfect. Panel (c) shows that a large error in the VC aerosol model will lead to large error in the retrieved qw(k), especially if the target-site aerosol optical depth at 865 is significantly different from that at the VC site (0.05). These figures suggest that calibration errors at 865 nm ranging from 5% to +10% lead to acceptable results when the VC model is M99 or the correct O99. Fig. 4 shows the retrieval error at the scan edge when the VC aerosol model is M99 and the actual aerosol present at the target site is M80, and Fig. 5 shows the errors when the actual aerosol present is T80. When the VC aerosol model is chosen to be the more unrealistic M50, the T80 retrieval errors are all off the bottom of the graphs for the scaling in Figs. 3, 4 and 5. It should be noted that were O99 or M99 used as the aerosol present at the target retrieval site, rather than M80 or T80, the error in the reflectance would be significantly reduced compared to that shown in the figures. M80 and T80 provide what might be considered an upper limit to the error.
4. Concluding remarks We have carried out a fictive vicarious calibration, in the spirit of that suggested by Gordon (1998), of a SeaWiFSlike sensor using simulated data. We showed that when the water-leaving reflectance is precisely measured, but the atmospheric measurements have errors leading to a close, but incorrect, choice of the VC aerosol model to predict the contribution of the aerosol component, the residual error in the calibration in the blue is small (<3% at 412 nm) even for a F15% calibration error at 865 nm. In addition, using the VC-corrected TOA reflectances, the resulting error in the Gordon and Wang (1994) retrieved water-leaving reflectance at 443 nm is always less than F0.002, and often less than F0.001, as long as the calibration error at 865 nm is less than f10%. This holds for sa(865)V0.2, which is significantly larger than that typically measured in a maritime atmosphere (Kaufman, Smirnov, Holben, & Dubovik, 2001). These results are completely independent of the initial calibration error in spectral bands below 865 nm.
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This suggests that pre-launch calibration is necessary only to the extent required to set the sensitivity of the instrument in the correct range, i.e., to achieve approximately the correct saturation radiances for each band. Therefore, we believe that there is no reason to try to achieve highly accurate pre-launch calibration, e.g., uncertainty <5%. Resources would be better expended to assure the highly desired radiometric stability, better monitoring of the stability, characterizing the instrument, e.g., its polarization sensitivity, out-of-band response, etc. These conclusions assume the presence of a permanent VC facility such as MOBY (Clark et al., 1997), and an atmospheric correction algorithm similar to that now used with SeaWiFS. Although, as we have shown, the calibration of the 865 nm band is clearly important, i.e., the performance after VC is better if a(865) is 5% as opposed to 10%, it should be relatively simple to reduce its uncertainty to within F5% through VC along the lines suggested by Gordon and Zhang (1996). Note that, in general, it is desirable to have a(865) slightly positive as opposed to negative, as the latter will cause qt(865)qr(865) to be negative in very clear atmospheres, preventing the retrieval of any ocean properties. Finally, it should be noted that, to accurately derive atmosphere products, e.g., aerosol optical thickness, it is necessary to reduce a(865) to within f5%. Acknowledgements The authors are grateful for the support from the NASA Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) project under contract NAS5-00203 (M.W.), NASA/GSFC under contracts NAS5-31363 (EOS/MODIS) and NAS5-31734 (SeaWiFS) (H.R.G.). References Cattrall, C. (2001). Retrieval of the columnar aerosol phase function and single scattering albedo from sky radiance over the ocean: measurements of African dust. PhD Dissertation, University of South Florida, 75 pp. Clark, D.K., Gordon, H.R., Voss, K.J., Ge, Y., Broenkow, W., & Trees, C. (1997). Validation of atmospheric correction over the oceans. Journal of Geophysical Research, 102D, 17209 – 17217. Eplee, R.E. Jr., Robinson, W.D., Bailey, S.W., Clark, D.K., Werdell, P.J., Wang, M., Barnes, R.A., & McClain, C.R. (2001). The calibration of SeaWiFS: Part 2. Vicarious techniques. Applied Optics, 40, 6701 – 6718. Evans, R.H., & Gordon, H.R. (1994). CZCS ‘‘System calibration:’’ a retrospective examination. Journal of Geophysical Research, 99C, 7293 – 7307. Gordon, H.R. (1987). Calibration requirements and methodology for remote sensors viewing the oceans in the visible. Remote Sensing of Environment, 22, 103 – 126. Gordon, H.R. (1997). Atmospheric correction of ocean color imagery in the earth observing system era. Journal of Geophysical Research, 102D, 17081 – 17106. Gordon, H.R. (1998). In-orbit calibration strategy for ocean color sensors. Remote Sensing of Environment, 63, 265 – 278.
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Gordon, H.R., & Wang, M. (1994). Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm. Applied Optics, 33, 443 – 452. Gordon, H.R., & Zhang, T. (1996). How well can radiance reflected from the ocean – atmosphere system be predicted from measurements at the sea surface? Applied Optics, 35, 6527 – 6543. Hooker, S. B., Esaias, W. E., Feldman, G. C., Gregg, W. W., & McClain, C. R. (1992, July). An Overview of SeaWiFS and Ocean Color, SeaWiFS Technical Report Series: Vol. 1. In S. B. Hooker, & E. R. Firestone (Eds.), NASA Technical Memorandum 104566, Greenbelt, MD. Kaufman, Y.J. (1993). Aerosol optical thickness and atmospheric path radiance. Journal of Geophysical Research, 98D, 2677 – 2692. Kaufman, Y.J., Smirnov, A., Holben, B.N., & Dubovik, O. (2001). Baseline maritime aerosol: methodology to derive the optical thickness and scattering properties. Geophysical Research Letters, 28, 3251 – 3254. Lienert, B.R., Porter, J.N., & Sharma, S.K. (2001). Repetitive genetic inversion of optical extinction data. Applied Optics, 40, 3476 – 3482. Porter, J.N., & Clarke, A.D. (1997). Aerosol size distribution models based on in situ measurements. Journal of Geophysical Research, 102D, 6035 – 6045.
Shettle, E. P., & Fenn, R. W. (1979). Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, AFGL-TR-79-0214, Air Force Geophysics Laboratory, Hanscomb AFB, MA. Slater, P.N., Biggar, S.F., Holm, R.G., Jackson, R.D., Mao, Y., Moran, M.S., Palmer, J.M., & Yuan, B. (1987). Reflectance- and radiance-based methods for the in-flight absolute calibration of multispectral sensors. Remote Sensing of Environment, 22, 11 – 37. Slater, P.N., Biggar, S.F., Plamer, J.M., & Thome, K.J. (2001). Unified approach to absolute radiometric calibration in the solar-reflective range. Remote Sensing of Environment, 77, 293 – 303. Slater, P.N., Biggar, S.F., Thome, K.J., Gellman, D.I., & Spyak, P.R. (1996). Vicarious radiometric calibration of EOS sensors. Journal of Atmospheric Oceanic Technology, 13, 349 – 359. Wang, M., & Franz, B.A. (2000). Comparing the ocean color measurements between MOS and SeaWiFS: a vicarious intercalibration approach for MOS. IEEE Transactions on Geoscience and Remote Sensing, 38, 184 – 197. Yang, H., & Gordon, H.R. (1997). Remote sensing of ocean color: assessment of the water-leaving radiance bidirectional effects on the atmospheric diffuse transmittance. Applied Optics, 36, 7887 – 7897.
Calibration of ocean color scanners: how much error is acceptable in the near infrared? Menghua Wang a,*, Howard R. Gordon b a
University of Maryland, Baltimore County, NASA Goddard Space Flight Center, Code 970.2, Greenbelt, MD 20771, USA b Department of Physics, University of Miami, Coral Gables, FL 33124, USA Received 1 May 2000; received in revised form 24 October 2001; accepted 28 May 2002
Abstract We simulate vicarious calibration (VC) of a Sea-viewing Wide Field-of-view Sensor (SeaWiFS)-like ocean color sensor relative to its longer near infrared (NIR) spectral band (865 nm) to understand the influence of calibration error at 865 nm, which is difficult to assess in orbit. We show that as long as the calibration error at 865 nm less than f10% in magnitude, the post-vicarious-calibration-corrected radiances are sufficiently accurate to retrieve useful water-leaving reflectances at moderate aerosol optical depths. This is completely independent of the initial calibration error in the shorter-wave bands, but assumes an atmospheric correction approach similar to that currently used with SeaWiFS. Retrievals are only slightly improved by reducing the magnitude of the error at 865 nm below f5%. The simulations immediately suggest that pre-launch calibration is necessary only to the extent required to set the sensitivity of the instrument in the desired range. Rather than trying to achieve a highly accurate pre-launch calibration, e.g., uncertainty <5%, we assert that resources would be better expended on improved radiometric stability (and its monitoring) and complete characterization of the instrument, e.g., polarization sensitivity, out-of-band response, etc. However, these assertions assume the existence of a permanent vicarious calibration facility, e.g., the Marine Optical Buoy (MOBY). D 2002 Elsevier Science Inc. All rights reserved.
1. Introduction Ocean color remote sensing places very stringent requirements on the sensor’s radiometric calibration, particularly in the blue. This is simply due to the fact that the desired water-leaving radiance comprises such a small part of the total radiance measured by the instrument. For example, in the blue (443 nm), the water-leaving radiance typically less that 10% of the total radiance: scattering from the atmosphere and the sea surface comprises the rest (Gordon, 1997). Thus, even if the effects of the atmosphere and the sea surface are perfectly removed, the relative error in the water-leaving radiance will be at least 10 times the relative error in the sensor calibration. If we want the waterleaving radiance with an uncertainty <10% in the blue, the uncertainty in the radiometric calibration of the sensor must be <1%. It is not possible to achieve such an
*
Corresponding author. Tel.: +1-301-286-6421; fax: +1-301-286-1775. E-mail address: [email protected] (M. Wang).
uncertainty in pre-launch calibration of an ocean color sensor at this time, and even if it were, the stress of launch would likely cause unknown changes in the sensor’s radiometric response. The key to a successful mission is therefore in-orbit calibration or ‘‘vicarious calibration’’ (Evans & Gordon, 1994; Gordon, 1987; Slater et al., 1987; Slater, Biggar, Thome, Gellman, & Spyak, 1996). The basic strategy is to account for (by direct measurement or by prediction based on surface measurements, radiative transfer, and scattering theory) all of the components of the topof-the-atmosphere (TOA) radiance reflected from the ocean – atmosphere system and to compare the result with the sensor-measured radiance. Any difference between the measured and predicted radiance is attributed to error in the calibration of the sensor, and a modification to the calibration equation (or coefficients) is effected to bring the measurements and predictions into confluence. Gordon and Zhang (1996) investigated the accuracy with which such predictions can be made based on the assessment of atmospheric properties through measurement of sky radiance and atmospheric optical depth. They concluded that
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the uncertainty in the prediction of the TOA radiance was limited by, and approximately equal to or some-what larger than, the radiometric uncertainty in the sky radiance measurements. Making such measurements with a 1% uncertainty in the blue is still a significant challenge. In a recent paper, Gordon (1998) provided a new strategy of the in-orbit calibration of ocean color sensors. In this scheme, it is assumed that the longest-wave spectral band in the near infrared (NIR) is perfectly calibrated, and then the shorter-wave bands are in effect calibrated with respect to this band. Simulations of this procedure (Gordon, 1998) show that, for a given absolute calibration error at the longest-wave band, the calibration error at the shorter-wave bands progressively decreases with decreasing wavelength, roughly in inverse proportion to the increase in Rayleigh scattering. This decrease in error owes to the fact that the Rayleigh scattering component, which increases in importance from the red to the blue, can be computed with little error. Thus, applying the Gordon (1998) strategy to a hypothetical sensor for which the actual calibration error in the NIR (865 nm) was 5% (but assumed to be zero in the vicarious calibration procedure), the 5% error in the NIR was reduced to a 0.3% error at 412 nm. This procedure meets the calibration uncertainty challenge described above. A similar procedure has been used to effect the vicarious calibration of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) (Eplee et al., 2001) using the Marine Optical Buoy (MOBY) (Clark et al., 1997). In addition, it was applied to vicarious inter-calibration of the German Modular Optoelectrionic Scanner (MOS) sensor on the Indian IRS-P3 satellite using SeaWiFS data as the correct values (Wang & Franz, 2000). It is important to reiterate that, in the Gordon (1998) procedure, the longest-wave spectral band in the NIR is assumed to be perfectly calibrated, and therefore, retains its post-launch calibration error. Vicarious calibration of this band must be effected through a direct computation of the TOA radiance based on surface measurements of sky radiance and optical depth as described by Gordon and Zhang (1996). However, as mentioned above, a significant reduction of the calibration error (e.g., below f5%) is unlikely due to uncertainty in the radiometric response of the sky radiometer. See Slater, Biggar, Plamer, and Thome (2001) for a through discussion of radiometer calibration uncertainties. In the Gordon (1998) simulations, reducing the assumed error in the longest NIR band by a factor of two (from 5% to 2.5%), yielded only a slight improvement in the retrieved water-leaving reflectance using the Gordon and Wang (1994) atmospheric correction algorithm. This leads to the following question: how important is the radiometric calibration accuracy of the longest-wavelength NIR spectral band in ocean color sensors if the other bands are ‘‘calibrated’’ in orbit assuming that the NIR band has no calibration error? Here, we provide simulations to answer this question. This has important consequences regarding
resource allocation within both pre-launch and post-launch calibration efforts. We begin by reviewing the Gordon (1998) strategy for vicarious calibration, then describe our simulation of the strategy, and finally show some results of simulations regarding the effect of calibration error at various levels on the retrieved water-leaving reflectance.
2. Vicarious calibration method 2.1. General radiative transfer The reflectance (q=pL/F0cosh0, where L is radiance, F0 is the extraterrestrial irradiance, and h0 is the solar zenith angle) of the ocean –atmosphere system at a wavelength k can be written as qt ðkÞ ¼ qAtm&Sfc ðkÞ þ tðkÞqw ðkÞ;
ð1Þ
where qAtm&Sfc(k) is the reflectance of the atmosphere and the sea surface, qw(k) is the reflectance associated with radiance backscattered out of the water, and t is the diffuse transmittance of the atmosphere along a path from the sea surface to the satellite-borne sensor. Here, we have assumed that the data are acquired under whitecap-free conditions and avoiding sun glint. Because the molecular scattering properties of the atmosphere are well known, it is convenient to follow Gordon and Wang (1994) and write the first term as qAtm&Sfc ðkÞ ¼ qr ðkÞ þ qA ðkÞ; where qr(k) is the reflectance of an aerosol-free atmosphere bounded by a Fresnel-reflecting ocean. The second term represents the component of the reflectance due to the aerosol in the presence of molecular scattering, i.e., the contribution from any photon that has scattered at least once from the aerosol. It is computed by utilizing an optical model for the aerosol, computing qAtm&Sfc(k) using a radiative transfer code for an atmosphere bounded by a Fresnel-reflecting ocean (that absorbs all photons that penetrate the ocean surface) with and without aerosols, and subtracting them. The aerosol optical properties are derived from a physical – chemical model (particle size distribution and refractive index) using Mie theory. The diffuse transmittance is computed following Yang and Gordon (1997) by assuming that the backscattered radiance just beneath the sea surface is uniform, i.e., observed just beneath the sea surface, the water body is a lambertian reflector. 2.2. Application to VC In the vicarious calibration (VC) scheme, the quantities on the right-hand-side of Eq. (1) are estimated and summed, and the sensor calibration is adjusted to yield a value of
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qt(k) that is in agreement with the sum. This is effected in the following manner. First, the quantity qr is computed with little error by employing the surface atmospheric pressure and wind speed measured at the vicarious calibration site. Next, the water-leaving reflectance qw is measured directly at the site (Clark et al., 1997). Finally, estimates of qA(k) and t are made by radiative transfer computations using an aerosol model, henceforth called the ‘‘VC aerosol model’’ or just the ‘‘VC model.’’ The VC aerosol model is composed of an aerosol size distribution and refractive index providing the aerosol spectral scattering phase function and spectral extinction coefficient through Mie theory. It is chosen to conform to surface measurements of the spectral variation of the aerosol optical thickness sa(k) at the time of overpass; however, this is not a guarantee that the correct model size distribution (and therefore the scattering phase function) will be used (Lienert, Porter, & Sharma, 2001). An improvement would be to use sky radiance measurements as an additional constraint on the VC aerosol model choice. (Although sky radiance measurements are generally not accurate enough to enable computation of qAtm&Sfc(k) for VC via Gordon and Zhang (1996), they could provide the aerosol phase function at scattering angles less than about 90j (Cattrall, 2001), and further constrain the VC model choice.) Since the procedure assumes no calibration error at 865 nm (where qw=0), given the VC aerosol model, the value of qA(k) at 865 nm fixes the value of sa(865). Similarly, the spectral variation of sa(k) and the phase function is also fixed by the VC model. This is the basic scheme described in Gordon (1998). It was used in the vicarious calibration of SeaWiFS with the Marine Optical Bouy (MOBY) data (Eplee et al., 2001). In the SeaWIFS calibration, the VC aerosol model used in the computation of qA(k) and t was a priori taken to be an average of the Shettle and Fenn (1979) maritime aerosol models at 50%, 70%, 90% and 99% relative humidity (referred to here as M50, M70, M90, and M99, respectively), i.e., not inferred from direct surface measurements.
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2.3. Specific simulations
Fig. 1. Physical and optical properties of the various Shettle and Fenn (1979) aerosol models used in this study: (a) model aerosol size (volume) distributions normalized to their maximum value; (b) spectral variation of the aerosol optical thickness; (c) aerosol phase functions P(H), where H is the scattering angle, at 865 nm.
We used radiative transfer to simulate VC of an ocean color sensor with the properties of SeaWiFS (Hooker, Esaias, Feldman, Gregg, & McClain, 1992) and a variety of calibration errors at 865 nm. We used the Shettle and Fenn (1979) oceanic aerosol model at 99% relative humidity (O99) to generate simulated TOA reflectances qt(k), i.e., we assumed that the actual aerosol present at the VC site was O99. This model was chosen because it is similar to the Porter and Clarke (1997) models for humid conditions at moderate wind speeds, and therefore should be realistic for a clean maritime aerosol. Fig. 1 provides the physical and optical properties of O99 and all the other aerosol models used in this study. As the goal is to compute qA(k) with as little uncertainty as possible, which would be difficult if the
aerosol concentration were high because of uncertainty in determining a VC aerosol model, we used sa(k)=0.05 at 865 nm. This would be characteristic of a clear maritime atmosphere, i.e., just where one would ideally try to effect a VC. We took the sun-sensor geometry so that the solar zenith angle (h0) was 20j, the sensor viewing angle with the nadir (hv) was 20j, and the relative azimuth between the sun and the sensor view (uv) was 90j. Such a geometry is typical of the MOBY calibration site off Hawaii (Clark et al., 1997). We took qw(k)=0 in the simulations, and used qw(k)=0 in the analysis, which in effect, means that in our simulations, we have assumed no measurement error in the water-leaving reflectance at the VC site. Thus, a perfectly
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Table 1 Pseudo calibration errors k (nm)
a(k) (%)
412 443 490 510 555 670 765
+5 +10 +5 +5 5 +5 10
calibrated sensor and a perfect atmospheric correction would retrieve qw(k)=0, in our simulations. See Gordon (1998) for an analysis of the influence of measurement error in qw. We added error to the simulated TOA ‘‘true’’ reflectances qtTrue(k), so that qMeasured ðkÞ ¼ ½1 þ aðkÞqTrue ðkÞ; t t
ð2Þ
where qtMeasured(k) is the reflectance that would be ‘‘measured’’ by a sensor with the incorrect calibration. The values of a(k) that we used are provided in Table 1; however, as we shall show later, the a(k) values for k<865 nm are irrelevant, i.e., the results of the VC procedure are completely independent of the pre-launch calibration (except that at 865 nm). The error at k=865 nm assumed several different values: the point being to assess the results as a function of a(865). To complete the VC procedure, we need to compute qA(k). As mentioned above, this computation requires only a model for the aerosol present at the calibration site. The chosen VC aerosol model (MOD) was used to derive a computed qA(k) in the following manner. First, the value of saMOD(865) required by the model to reproduce the ‘‘measured’’ value of qA(k) at 865 nm was computed (not necessarily 0.05 because both the VC aerosol model and the ‘‘measured’’ value of qA(k) at 865 nm may be incorrect). Then, from saMOD(865), the VC aerosol model was used to determine saMOD(k). Finally, qA(k) was computed for each of the visible bands using the VC aerosol model’s spectral scattering phase function and the estimated saMOD(k). Combined with qr(k), this provides the computed value of qt, which we refer to as qtComputed. Note that qtComputed will be specific to the chosen VC aerosol model and to the particular sun-viewing geometry at the VC site. Taking these computed qt’s to be the correct values, the sensor calibration is then adjusted by a factor KVC(k), to bring qtMeasured(k) and qtComputed into confluence. The ‘‘measured’’ reflectances at any site are then used to provide what we believe to be the correct reflectances there through qCorrected ðkÞ ¼ K VC ðkÞqMeasured ðkÞ t t ðkÞ; ¼ K VC ðkÞ½1 þ aðkÞqTrue t
ð3Þ
Fig. 2. Summary of the VC procedure and application to a target site. ‘‘AP’’ refers to the aerosol actually present at the VC site (O99), and ‘‘AM’’ refers to the VC aerosol model chosen on the basis of surface measurements (O99, M99, or M50). The target site aerosol is either M80 or T80.
where KVC(k)=qtComputed(k)/qtMeasured(k) at the VC site. qtCorrected(k) is then used in all the algorithms as the correct value of qtTrue(k). To reiterate, qtMeasured(k) is what the original sensor calibration provides and qtCorrected(k) is the revised reflectance after VC., i.e., qtCorrected(k)=qtComputed(k) at the VC site, and only at the VC site. The only errors in this procedure (assuming that qw(k) is error-free) are the choice of an incorrect VC aerosol model (which is always likely), and the assumption that there is no calibration error at 865 nm (a(865)=0).
Table 2a Residual error in sensor absolute calibration after VC using O99 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) 0.82 1.17 1.88 2.25 3.25 6.63 10.64 15.0
0.55 0.79 1.26 1.51 2.18 4.43 7.10 10.0
0.28 0.40 0.64 0.77 1.10 2.23 3.56 5.0
0.01 0.02 0.02 0.02 0.03 0.02 0.02 0.0
+0.26 +0.37 +0.60 +0.72 +1.05 +2.18 +3.52 +5.0
+0.53 +0.76 +1.22 +1.47 +2.22 +4.38 +7.06 +10.0
+0.80 +1.15 +1.85 +2.21 +3.20 +6.59 +10.16 +15.0
M. Wang, H.R. Gordon / Remote Sensing of Environment 82 (2002) 497–504 Table 2b Residual error in sensor absolute calibration after VC using M99 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) 0.56 0.85 1.46 1.79 2.71 6.04 10.23 15.0
0.25 0.40 0.76 0.96 1.54 3.73 6.61 10.0
+0.07 +0.04 0.06 0.13 0.36 1.42 2.99 5.0
+0.39 +0.49 +0.64 +0.70 +0.81 +0.89 +0.63 +0.0
+0.72 +0.94 +1.34 +1.53 +1.99 +3.21 +4.24 +5.0
+1.04 +1.39 +2.05 +2.36 +3.17 +5.52 +7.86 +10.0
It is useful to recast Eq. (3) in a different form. " # 1 qComputed ðkÞ t VC K ðkÞ ¼ ; 1 þ aðkÞ qTrue ðkÞ t
+1.36 +1.85 +2.75 +3.20 +4.35 +7.83 +11.48 +15.0
501
and hv=46j (scan ‘‘edge’’), and uv=90j. Note that the scan-sun geometries used for the target sites are different from those at the VC site. The aerosol models used to generate the pseudo data for the target sites were the Shettle and Fenn (1979) Maritime model at 80% relative humidity (M80) and their Tropospheric model at 80% relative humidity (T80). These were the same models used by Gordon and Wang (1994) to test the SeaWiFS atmospheric correction algorithm. The physical and optical properties for these models are also shown in Fig. 1. In contrast to M80, which is nonabsorbing, T80 is weakly absorbing (single scattering
ð4Þ
VC
where the quantities in the ‘‘VC’’ subscripted brackets are at the VC site. Then combining Eqs. (3) and (4) shows that " # qComputed ðkÞ t Corrected qt ðkÞ ¼ qTrue ðkÞ: ð5Þ t qTrue ðkÞ t VC
The ‘‘VC’’ subscripted brackets in Eq. (5) depends only on the actual aerosol at the calibration site and its optical thickness at 865 nm, the assumed VC aerosol model, the sun-sensor geometry, and the calibration error at 865 nm. It is completely independent of the initial calibration error a(k) for k<865 nm. Thus, writing Eq. (3) as qCorrected ðkÞ ¼ ½1 þ aa ðkÞqTrue ðkÞ; t t
ð6Þ
where aa(k) is the absolute calibration error after VC, Eq. (5) shows that aa(k) depends only on the correctness of the VC aerosol model, the VC geometry, and on a(865), but not on a(k) for k<865 nm. A measure of the efficacy of the VC is the quality of the qw(k) retrievals operating on qtCorrected(k) with the Gordon and Wang (1994) atmospheric correction algorithm. We tested this by creating pseudo data containing the original sensor calibration error, specified by a(k), at a set of locations we call ‘‘target site(s).’’ The scan-sun geometries for the target sites were h0=40j, hv=1j (scan ‘‘center’’)
Table 2c Residual error in sensor absolute calibration after VC using M50 k (nm) 412 443 490 510 555 670 765 865
Residual error (aa) after VC (%) +0.19 +0.08 0.25 0.45 1.17 4.31 9.01 15.0
+0.66 +0.71 +0.68 +0.63 +0.29 1.68 5.16 10.0
+1.12 +1.34 +1.62 +1.71 +1.76 +0.96 1.31 5.0
+1.59 +1.97 +2.55 +2.79 +3.23 +3.60 +2.53 +0.0
+2.05 +2.59 +3.48 +3.88 +4.69 +6.23 +6.38 +5.0
+2.52 +3.22 +4.41 +4.96 +6.16 +8.87 +10.23 +10.0
+2.98 +3.85 +5.34 +6.04 +7.62 +11.51 +14.08 +15.0
Fig. 3. Error in the retrieved value of qw(443) at the center of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was (a) O99, (b) M99, and (c) M50. The aerosol present at the target site was M80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
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effect the VC. Note that the rather large errors (Table 1) placed in the pseudo data are significantly reduced particularly in the blue and blue-green regions even when incorrect VC aerosol models were chosen to effect the vicarious calibration, and even when there is significant calibration error at 865 nm. However, after VC, the error in the red and NIR may actually be larger when a(865) is large. 3.2. How effective was the VC?
Fig. 4. Error in the retrieved value of qw(443) at the edge of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was M99. The aerosol present at the target site was M80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
Recalling that the revised calibration factor KVC(k) depends on the assumed VC aerosol model, the true sa(865), and the VC geometry, it is important to know how the retrieved qw(k) at target retrieval sites are affected by the VC, particularly when the atmosphere is significantly different at the target site from that at the VC site. For this, we used the above VC exercises effecting a new calibration, and the Gordon and Wang (1994) algorithm to retrieve
albedo f0.975 and 0.952 at 412 and 865 nm, respectively). Therefore, T80 model used in the simulations is significantly different from the oceanic type aerosol model, which existed at the VC site (O99), while the M80 model is somewhat similar. A summary of the radiative transfer simulations carried out for the VC procedure and its application to a target site is provided in Fig. 2.
3. Results 3.1. Simulated residual calibration error after VC (aa) We simulated the above VC procedure assuming that the surface measurements yielded the correct aerosol model, i.e., O99 (Fig. 1). More realistically, we also simulated the procedure assuming that an incorrect aerosol model, M99 or M50, was chosen based on the surface measurements. We note that surface measurements of sa(k), with their significant error (F0.01 to F0.02, Kaufman, 1993) at low aerosol optical depths, would make it difficult to distinguish between O99 and M99 (Fig. 1b). In contrast, the choice of M50 would require a rather large error in sa(k) and would be somewhat unlikely were the actual aerosol O99. If sky radiance measurements were also made to estimate the aerosol phase function, it is very unlikely that the M50 model would be chosen (Fig. 1c); however, such measurements would likely not distinguish between O99 and M99. The VC exercise was carried out for a(865)=15% to +15% in steps of 5%. The residual error in the sensor’s absolute calibration [aa(k)] after VC for various values of the actual calibration error at 865 nm are given in Tables 2a, 2b and 2c for the three choices of aerosol model used to
Fig. 5. Error in the retrieved value of qw(443) at the (a) center and (b) edge of the sensor’s scan as a function of sa(865) at the target site after vicarious calibration. The aerosol present at the vicarious calibration site was O99 and the VC-aerosol model was M99. The aerosol present at the target site was T80. Arrows label certain points with the value of a(865). Large solid squares provide the algorithm error in the absence of all calibration error, i.e., for a perfectly calibrated sensor. Retrieval with no error is desired; however, any retrieval that can be plotted in the figure as scaled is considered marginally acceptable.
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qw(k) from post-VC calibrated qt(k) values (Fig. 2), i.e., from qtCorrected(k). As before, we took the actual value of qw(k) to be zero. The results at the scan center when M80 is the aerosol actually present at the target site are provided in Fig. 3, which gives the error in the retrieved qw(k) at k=443 nm (positive values mean qw(k) is too large). A marginally acceptable error in this quantity is usually taken to be F0.002, i.e., an error that can be plotted in the figure as it is scaled. Panels (a), (b), and (c) refer to using O99, M99, and M50 as the VC aerosol model assumed in the vicarious calibration procedure. Clearly, better results (i.e., lower error in qw(k)) are obtained the closer the VC aerosol model is to the actual aerosol at the VC site (O99). Note that, even when aa(k)=0, the retrieval error is not null because the Gordon and Wang (1994) algorithm is not perfect. Panel (c) shows that a large error in the VC aerosol model will lead to large error in the retrieved qw(k), especially if the target-site aerosol optical depth at 865 is significantly different from that at the VC site (0.05). These figures suggest that calibration errors at 865 nm ranging from 5% to +10% lead to acceptable results when the VC model is M99 or the correct O99. Fig. 4 shows the retrieval error at the scan edge when the VC aerosol model is M99 and the actual aerosol present at the target site is M80, and Fig. 5 shows the errors when the actual aerosol present is T80. When the VC aerosol model is chosen to be the more unrealistic M50, the T80 retrieval errors are all off the bottom of the graphs for the scaling in Figs. 3, 4 and 5. It should be noted that were O99 or M99 used as the aerosol present at the target retrieval site, rather than M80 or T80, the error in the reflectance would be significantly reduced compared to that shown in the figures. M80 and T80 provide what might be considered an upper limit to the error.
4. Concluding remarks We have carried out a fictive vicarious calibration, in the spirit of that suggested by Gordon (1998), of a SeaWiFSlike sensor using simulated data. We showed that when the water-leaving reflectance is precisely measured, but the atmospheric measurements have errors leading to a close, but incorrect, choice of the VC aerosol model to predict the contribution of the aerosol component, the residual error in the calibration in the blue is small (<3% at 412 nm) even for a F15% calibration error at 865 nm. In addition, using the VC-corrected TOA reflectances, the resulting error in the Gordon and Wang (1994) retrieved water-leaving reflectance at 443 nm is always less than F0.002, and often less than F0.001, as long as the calibration error at 865 nm is less than f10%. This holds for sa(865)V0.2, which is significantly larger than that typically measured in a maritime atmosphere (Kaufman, Smirnov, Holben, & Dubovik, 2001). These results are completely independent of the initial calibration error in spectral bands below 865 nm.
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This suggests that pre-launch calibration is necessary only to the extent required to set the sensitivity of the instrument in the correct range, i.e., to achieve approximately the correct saturation radiances for each band. Therefore, we believe that there is no reason to try to achieve highly accurate pre-launch calibration, e.g., uncertainty <5%. Resources would be better expended to assure the highly desired radiometric stability, better monitoring of the stability, characterizing the instrument, e.g., its polarization sensitivity, out-of-band response, etc. These conclusions assume the presence of a permanent VC facility such as MOBY (Clark et al., 1997), and an atmospheric correction algorithm similar to that now used with SeaWiFS. Although, as we have shown, the calibration of the 865 nm band is clearly important, i.e., the performance after VC is better if a(865) is 5% as opposed to 10%, it should be relatively simple to reduce its uncertainty to within F5% through VC along the lines suggested by Gordon and Zhang (1996). Note that, in general, it is desirable to have a(865) slightly positive as opposed to negative, as the latter will cause qt(865)qr(865) to be negative in very clear atmospheres, preventing the retrieval of any ocean properties. Finally, it should be noted that, to accurately derive atmosphere products, e.g., aerosol optical thickness, it is necessary to reduce a(865) to within f5%. Acknowledgements The authors are grateful for the support from the NASA Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) project under contract NAS5-00203 (M.W.), NASA/GSFC under contracts NAS5-31363 (EOS/MODIS) and NAS5-31734 (SeaWiFS) (H.R.G.). References Cattrall, C. (2001). Retrieval of the columnar aerosol phase function and single scattering albedo from sky radiance over the ocean: measurements of African dust. PhD Dissertation, University of South Florida, 75 pp. Clark, D.K., Gordon, H.R., Voss, K.J., Ge, Y., Broenkow, W., & Trees, C. (1997). Validation of atmospheric correction over the oceans. Journal of Geophysical Research, 102D, 17209 – 17217. Eplee, R.E. Jr., Robinson, W.D., Bailey, S.W., Clark, D.K., Werdell, P.J., Wang, M., Barnes, R.A., & McClain, C.R. (2001). The calibration of SeaWiFS: Part 2. Vicarious techniques. Applied Optics, 40, 6701 – 6718. Evans, R.H., & Gordon, H.R. (1994). CZCS ‘‘System calibration:’’ a retrospective examination. Journal of Geophysical Research, 99C, 7293 – 7307. Gordon, H.R. (1987). Calibration requirements and methodology for remote sensors viewing the oceans in the visible. Remote Sensing of Environment, 22, 103 – 126. Gordon, H.R. (1997). Atmospheric correction of ocean color imagery in the earth observing system era. Journal of Geophysical Research, 102D, 17081 – 17106. Gordon, H.R. (1998). In-orbit calibration strategy for ocean color sensors. Remote Sensing of Environment, 63, 265 – 278.
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