The convergence of the above- and in-water methods presented and discussed in the former sections was evaluated through the comparison of SeaPRISM and WiSPER data collected at the AAOT site. Specifically LSP
W (λ) and LW SW (λ), or LSPW N(λ) and
LW S
W N(λ), where the superscripts SP and WS indicate SeaPRISM and WiSPER data,
were compared at the specific center-wavelengths 413, 440, 501, 555 and 674 nm for SeaPRISM, and at 412, 443, 501 (synthetically obtained by interpolating data between 490 and 510 nm), 555 nm and 665 nm for WiSPER. The data analysis was restricted to measurement sequences (hereafter referred to as match-ups) starting within±5 min from each other and with sun azimuthφ0 ranging between 125 and 245 degrees. The latter constraint minimizes the tower superstructure perturbations. To ensure a direct comparison with SeaPRISM data, no correction for bottom effects was applied toLu(0−, λ) values computed from WiSPER data (for the cases considered in
the assessment, the corrections for the bottom effects estimated according to Zibordi et al. (2002b) would have been negligible at 412 and 665 nm, and increasing between 443 and 555 nm with average values ranging from -0.1 to -1.0%, respectively).
The data comparison was made using the relative percent difference ψj,n and its
absolute value|ψj,n|, applied to determine systematic biases and typical uncertainties,
respectively. In the formulation of the relative percent differences, WiSPER data are considered the reference values, so ψj,n is
ψj,n = 100A(j)n−B(j)n
A(j)n
(6.3.1) where A and B indicate either water-leaving radiances LSP
W (λ) and LW SW (λ), respec-
tively, or normalized water-leaving radiances LSP
Chapter 6 Measurement Protocols
is the match-up number covering the range 1 to M, with M being the total num- ber of match-ups; and j is the channel index (i.e., j=1–5 for the SeaPRISM center wavelengths 413, 440, 501, 555 and 674 nm).
The data analysis was carried out for the available match-ups on a channel-by- channel basis (i.e., for each single center wavelength) and across channels (through spectrally averaged values). Outliers were excluded to prevent biased estimates. The average relative percent differences were computed by removing single ψj,n values
exceeding the average plus or minus two times the standard deviation, σ, of the total number N (i.e. N =KM) of the ψj,n values (referred to as 2σ filtering), through
ψ = 1 K K X j=1 1 Mj Mj X n=1 ψj,n (6.3.2)
with K number of channels (i.e., K = 1 for single channel analysis and K = 5 for overall spectrally averaged values) and Mj 6M, match-ups for the jth channel satis-
fying the 2σ filtering condition. Similarly, the average absolute percent differences, |ψ|, were computed according to Eq. 6.3.2 using the |ψj,n| values.
The data analysis was applied to measurements from CoASTS campaigns con- ducted between June 2002 and May 2003, and included data collected during differ- ent atmospheric and marine conditions with Case-2 water occurrence of 40% (Zibordi et al., 2004c). The results for the LSP
W (λ) versus LW SW (λ) comparison are shown in
Fig. 6.3 through a scatter plot and the distribution of relative percent differences
ψi,j. The comparison of water-leaving radiances, instead of the normalized water-
leaving radiances alone, is justified by the clear-sky conditions and the short time difference between the collection interval of SeaPRISM and WiSPER data retained for the analysis (less than 5 minutes).
Chapter 6 Measurement Protocols
Figure 6.3: The comparison of LSP
W (λ) and LW SW (λ) determinations showing: the
scatter plot of the data (left panel), where a0 and b0 are the intercept and the slope, respectively, of the model II (major axis) linear regression; and the normalized fre- quency distribution of theψj,n values (right panel), whereσ is the standard deviation
of the N values of ψj,n, and, |ψ| and ψ are the averages of the N0 values of |ψj,n| and
of ψj,n satisfying the 2σ filtering conditions (after Zibordi et al. (2004a)).
Specifically, the comparison of the water-leaving radiances comprehensively pre- sented and discussed in Zibordi et al. (2004a) exhibits |ψ| varying from 5.9% at 413 nm to 3.1% at 555 nm, with spectrally averaged value of 4.5% in the 413-555 nm inter- val, and of 10.2% at 674 nm. The overall spectrally averaged values in the 413-674 nm interval exhibit |ψ|=5.5% and ψ=-1.2%. The presence of a systematic bias observed at 674 nm (ψ=-5.9%), is explained by the difference in the center-wavelengths of the two instruments (674 versus 665 nm). A bias observed at 440 nm (ψ =-3.7% ) is also attributed to a slight difference in the SeaPRISM and WiSPER center wavelengths in a spectral region characterized by high radiance gradients.
Chapter 6 Measurement Protocols
Figure 6.4: The same as in Fig. 6.3 but for LSP
W N(λ) andLW SW N(λ) (after Zibordi et al.
(2004a)).
The results from the comparison of normalized water-leaving radiance, LW N(λ),
are shown in Fig. 6.4 using the same presentation scheme applied in Fig. 6.3. The spectrally averaged |ψ| values for LW N(λ), when compared to those computed for
LW(λ), increase slightly from 5.5% to 6.2%. More significant variations are on av-
erage observed for the spectral |ψ| values (not presented). These results can be explained by the different methods applied in the determination of LSP
W N(λ) and
LW S
W N(λ). In the case of LSPW N(λ), the normalization relies on the computation of
the diffuse atmospheric transmittance t(λ), while in the case of LW S
W N(λ) it makes use
of the ES(λ)/Ed(0+, λ) ratio. The two methods should provide converging results
during clear-sky conditions, where the impact of clouds toEd(0+, λ) is negligible, and
ES(λ) Ed(0+, λ) ≈¡D2t(λ) cosθ 0 ¢−1 (6.3.3) The formulation given in Eq. 6.3.3, however, shows that uncertainties in the
Chapter 6 Measurement Protocols
absolute values of Ed(0+, λ) as well as in the value of the mean extraterrestrial solar
irradiance, ES(λ), or simply differences between the wavelengths under comparison
(for instance the difference in the 674 and 665 nm center wavelengths for SeaPRISM and WiSPER), can affect ES(λ)/Ed(0+, λ) and consequently LW N(λ).