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We present results of validating the algorithms used to estimate sea surface solar radiation at 400-700 nm, photosynthetically available radiation (PAR), from satellite ocean color data and an appropriate validation procedure when data are collected using a moving ship. The validation was performed using field measurements of PAR during a transit cruise from the Baltic to the White Sea during the summer of 2014. The PAR was measured at 10-minute intervals using a deck radiometer throughout the daylight hours. The satellite estimate of daily surface PAR with an acceptable error, on the scale of 1 day-102 km, is shown.
© 2016 Optical Society of America
1. Introduction
Quantitative assessment of solar radiation at a 400-700 nm (so-called photosynthetically available radiation [PAR]) on the sea surface is required for solving several important problems, such as light utilization in marine primary production, underwater visibility, surveillance, television, filming and photography, and the influence of volume absorption of solar radiation on the ocean’s heat balance. However, systematic in situ measurements of PAR are carried out only at discrete points, and they do not provide for the possibility of assessing the spatial variability of PAR and its acting factors. The only way to achieve this is through the use of satellite data, which are regularly held for many years and cover large areas simultaneously.
At present, PAR is available as a standard satellite product [1], but it certainly requires a comprehensive validation by direct in situ measurements. Results of such comparisons between satellite and in situ PAR values, measured at a stationary site in the North Atlantic, are presented in [2] as daily, weekly, and monthly uncertainties averaged between 2005 to 2010. In our work, we focused on mesoscale variability and considered the practically important case of using moving ships, including ferry boats and other ships of opportunity, for taking in situ measurements. The comparison was performed for satellite PAR derived by both a standard NASA algorithm and the SIORAS algorithm [3]. The most appropriate method of comparison is discussed.
2. Data and processing methods
2.1. Field data
The in situ measurements were taken by a deck radiometer [4] throughout the daylight hours at 10-minute intervals during a scientific cruise of the RV Professor Shtokman from the Baltic to the White Seas from the end of July to the beginning of August 2014. The instrument was built up on the basis of a four-channel radiometer produced by Biospherical Instruments Inc. and measured the surface irradiance at four spectral channels (443, 490, 555, and 625 nm) with a bandwidth of 10 nm FWHM; dynamic range of irradiance within each of the spectral band was 1x10−2 ÷ 30 W⋅m−2; angular response of cosine collector ± 2% from 0° to 65°; ± 10% from 65° to 85° [5]. The radiometer was located in a non-shaded position at height of 6 m from the sea surface; a special stabilizer prevented the ship’s pitching from influencing the measured values of irradiance.
The surface spectral irradiance Es(λ) from 400 to 700 nm was calculated by a specially developed algorithm [4]; the model of the atmosphere included six absorbing and/or scattering layers: ozone, oxygen, water vapor, Rayleigh, aerosol, and cloud. A simplified formula for calculating the surface irradiance has the form
where F0(λ) is the mean extraterrestrial solar irradiance corrected for earth-sun distance and orbital eccentricity (W m−2 nm−1), θ is the sun zenith angle; Tr(λ) represents the diffuse transmittance after Rayleigh scattering (calculated in a single-scattering approximation); Toz(λ), Tw(λ), and Tox(λ) - the transmittances after ozone, water vapor, and oxygen absorption, respectively; α1(θ) and α2(θ) - the unknown parameters of the transmittance of cloud and aerosol layers, respectively, depending on the sun zenith angle θ. The algorithm uses the known formulas and parameters to calculate Tr(λ), Toz(λ), Tw(λ), and Tox(λ) [6]; α1(θ) and α2(θ) are determined by the least squares method from measured spectral values of Es(λ) at the above four spectral channels. The model was validated by comparison of the spectral values of Es(λ) calculated with the model and continuously measured by the floating spectroradiometer [7]; the standard error of calculation Es(λ) is equal to 2.5% [4].The value of the instantaneous surface iPAR is calculated by integrating the values of Es(λ) in the spectral range of 400-700 nm:
To calculate the daily dPAR (Einstein m−2 day−1) from instantaneous in situ measurements, it is necessary to know how the parameters α1 and α2 in Eq. (1) vary depending on the sun zenith angle. Different algorithms for cloudless and cloudy atmospheres must be used: in the former, α1 = 1 and α2(θ) = α2(θ*) cosθ*/cosθ, where θ* is the sun zenith angle at the time of measurement; in the latter, α2(θ) = 0 and α1(θ) = α1(θ*) (1 + 2 cosθ)/(1 + 2 cosθ*). A more detailed description can be found in the literature [3]. The atmosphere was considered to be cloudy when iPAR < 0.75⋅iPARclear, where iPARclear was the value for a clear atmosphere without cloud or aerosol layers (α1 = 1 and α2 = 0).
2.2. Satellite data
We used Level 1A data from the satellite scanner MODIS-Aqua with a spatial resolution of 1 km, which was available at the NASA website [1]. Unlike the scanner SeaWiFS, which had visible channels that were not saturated above the clouds, data from 3 channels, 469, 555, and 645 nm, were available in cloudy periods from the MODIS-Aqua.
For convenience, computations of dPAR Level 2 values (Einstein m−2 d−1) using both algorithms (NASA [1] and SIORAS [3]) were performed using Level 1A data by employing SeaDAS software [8]. Comparisons between our calculated values of NASA dPAR and the standard NASA dPAR Level 2 product [1] agreed within 1% in nearly all cases. Such a difference is probably due to use of different versions of SeaDAS and it is insignificant. In both algorithms, the input values for calculation of the daily dPAR were the instantaneous radiance measurements from the MODIS-Aqua. Atmospheric conditions were then assumed stable throughout the day, and the estimates for different times of day were weighted using the cosine of the sun zenith angle. But the algorithms have also some significant differences.
The NASA algorithm is based on the plane-parallel theory and assumes that the effects of clouds and clear atmosphere can be decoupled [1,2]. The atmosphere is modeled as a clear sky atmosphere above a cloud layer, and surface PAR is expressed as the product of a clear-sky component and cloud transmittance. Knowledge of pixel composition is not required, and the need for cloud screening and assumptions about sub-pixel cloudiness is eliminated. The aerosol properties are specified from climatology.
The SIORAS algorithm uses different algorithms for clear sky and for a cloudy case; the presence or absence of clouds is determined using the cloud flag [1]; each pixel is accepted as homogeneous. Both cases were described in details [9,10].
The surface spectral irradiance for clear sky is calculated by using a model [6]. All required input parameters (such as ozone content, aerosol properties) are taken from MODIS data products provided by SeaDAS after atmospheric correction [1,8].
The cloudy case is modeled as a plane-parallel medium with Rayleigh atmosphere above and under a cloud layer. Its reflectance and transmittance are expressed in terms of the cloud parameter X by using the simple analytical formulas for non-absorbing optically thick scattering layer [11]. The value of X for each cloud pixel is derived from the cloud radiance which is determined from the satellite measured values of the top-of-atmosphere radiance. By using the found value of X, the downwelling irradiance at the lower boundary of the cloud layer Ecl is calculated, and then the sea surface irradiance Es is computed as the product of Ecl and the diffuse transmittance of the Rayleigh layer under cloud.
The numerical computations by DISORT code have shown that the errors in the sea surface irradiance are less than 15% even in a case of low Sun (θ = 60°) (cloud optical thickness 5-10, the viewing zenith angle less than 45°).
It is appropriate to mention the ability of the SIORAS algorithm to calculate from satellite data not only the value of PAR incident on the sea surface, but other components of the PAR budget, including the water-leaving radiation and underwater irradiance at various depths in the near-surface layer [3,12].
2.3. Comparison of in situ and satellite data
As the input data for comparison, we had instantaneous iPAR values from in situ daylight measurements and from 1 to 2 satellite images for a given day. The SIORAS algorithm provided spatial distribution of the iPAR in both cloudless and cloudy pixels, but the NASA algorithm could do so only in cloudless pixels [1]. As a satellite product for practical use, both algorithms computed daily dPAR.
Direct comparison of the satellite and in situ instantaneous values of surface iPAR under partly cloudy conditions is meaningless because the values are physically different: ship data are measured at a point, whereas satellite data relate to an area measuring about 1 km2. When comparing the satellite and in situ values at the time of satellite observation, we should bear in mind that the in situ values are more sensitive to variations in cloud cover and the results of comparison strongly depend on whether the sensor is illuminated by direct sunlight or is in the shadow created by clouds.
Figure 1(a) shows an example, taken on August 2, 2014, of the time dependences of iPAR during daylight hours, calculated in two different ways, in comparison with the data from direct in situ measurements. In one case (curve 1), the values of iPAR during the day were calculated from satellite data using the SIORAS algorithm, and in the other (curve 2), with the instantaneous in situ value of iPAR, measured at the time of satellite overflight (10:00 GMT). In both cases, stable atmospheric conditions were assumed, and only the changes in sun zenith angle during the day were taken into account.
Fig. 1 Comparison of the time dependences of PAR during August 2, 2014, calculated in different ways, with the in situ measured iPAR dependence (red curve). The vertical dash-dot line shows the time of the satellite overflight. (A) iPAR (W m−2) during the day, calculated using the value at the time of satellite overflight, assuming stable atmospheric conditions (changes in the sun zenith angle are taken into account): yellow-green curve 1, from satellite data (SIORAS algorithm); violet curve 2, from in situ measured iPAR. (B) Changes in the daily dPAR along the ship route at the times corresponding to in situ measurements: blue curve 3, NASA algorithm; green curve 4, SIORAS algorithm (right axis, Einstein m−2 d−1). The in situ measured iPAR dependence (left axis, W m−2) is given for comparison (coincidence of the iPAR and dPAR curves is accomplished by a choice of scales for the vertical axes).
As seen in Fig. 1(a), iPAR values calculated from in situ measurements during the day (red curve) are strongly varied, primarily as a result of changes in cloud cover. Measurement at the time of satellite overflight was performed when the light collector was shaded by clouds, and the calculated value of iPAR was less than that from satellite data.
Naturally, the above difference results to a discrepancy of the daily dPAR: calculation from curve 2 gave 12.5 Einstein m−2 d−1, whereas from curve 1, it was 15.3 Einstein m−2 d−1; from the in situ measured iPAR (red curve), it was 15.7 Einstein m−2 d−1.
When comparing these results, the fact that in situ measurements were carried out from a moving ship should be taken into account; therefore, the value for daily dPAR did not refer to the point of satellite overflight. It was a value averaged over the daily path travelled by the ship. For comparison in such a case, it is more correct to use the spatial dependence of satellite dPAR along the ship path during daylight hours, replacing the coordinates of a given point with the time t when the ship passed this point and weighting the dPAR values by the cosine of the sun zenith angle cos[θ(t)].
Figure 1(b) shows the time dependencies of daily dPAR, calculated by the above method with NASA and SIORAS algorithms. For comparison, the in situ measured iPAR dependence is also presented. One can see good agreement between the dPAR values derived by the two algorithms, and the correlation of the obtained changes in PAR over time and along the ship route was tolerable.
We believe that the best way for validating the satellite algorithm using in situ data collected with a moving ship is by comparing the calculated daily dPAR averaged over the ship’s path with that obtained using the in situ measurements. Such an approach is justified by the assumption of ergodicity, very reasonable for the mesoscale variability of the cloud system. The comparison for August 2, 2014 showed a very good agreement between the daily dPAR values: 15.7 Einstein m−2 d−1 from the in situ measurements and 16.4 and 15.5 Einstein m−2 d−1 from satellite values using NASA and SIORAS algorithms, respectively.
3. Results and discussion
In total, 11 MODIS-Aqua satellite images over the North Sea and the Norwegian and Barents Seas were obtained during the cruise of the RV Professor Schtokman from July 29 to August 4, 2014; ten were used for validation of satellite PAR algorithms using data collected in situ (there were no continuous in situ measurements taken on July 30, 2014).
An example, taken July 30, 2014, of daily dPAR distributions, calculated from MODIS-Aqua data at the boundary between the North and Norwegian Seas using NASA and SIORAS algorithms, is shown in Fig. 2.
Fig. 2 Comparison of the spatial distributions of the daily dPAR calculated from MODIS-Aqua data July 30, 2014 by NASA (left) and SIORAS (right) algorithms.
For the most part, two satellite algorithms gave almost the same estimates of dPAR. Some differences were observed, but mainly for cloud-free pixels (high values of dPAR). Most likely, this was a result of the NASA algorithm using model parameters for the cloudless atmosphere while the SIORAS algorithm used parameters measured by the satellite sensor.
Results of the comparison between dPAR values are shown in Table 1. For satellite data, the weighted average values <dPAR> are presented. The relative errors of satellite estimates of dPAR ranged between 5% and 73% when using the NASA algorithm and between 1% and 51% using the SIORAS algorithm; mean relative errors were 32% and 17%, respectively.
Table 1. Values of dPAR (Einstein m−2 d−1) computed from continuous field measurements during the day and from satellite data using NASA and SIORAS algorithms with averaging over the daily RV route. Satellite data are presented as weighted average values <dPAR>; the percentage of cloud pixels and relative errors (%).
Table 1 shows a significant increase of difference between the ship and satellite estimates of the daily dPAR at different satellite overflights: by the SIORAS algorithm, 01.08.2014 – from 15% at 10:55 to 49% at 12:35, 03.08.2014 – from 7% at 09:05 to 51% at 10:45. As seen in Table 1, the above satellite images differ in the percentage of cloud pixels (ratio of the numbers of cloud pixels to total pixels along the daily path travelled by the ship): 01.08.2014 – 100% at 10:55, 93% at 12:35; 03.08.2014 – 75% at 09:05, 65% at 10:45.
Figure 3 shows a comparison between the satellite images at different points in time on August 1, 2014. Increasing the number of cloudless pixels 01.08.2014 at 12:35 compared to 10:55 is well seen at the beginning of the ship route, in the middle (that is most important due to the cosine of the sun zenith angle cos[θ(t)] as the weighting factor) and at the end.
Fig. 3 Comparison of the spatial distributions of the daily dPAR derived by the SIORAS algorithm from MODIS-Aqua satellite images for August 1, 2014 taken at 10:55 (left) and 12:35 (right). The white line shows the ship route, and the markers designate the position of the ship at the times when data-taking began and ended (04:04 and 16:02) and when satellite overflights occurred (10:55 and 12:35).
The comparison between probability density functions for the values of iPAR along the ship track from the satellite images and from the in situ measurements during this day showed that the assumption of ergodicity was not fulfilled for the image at 12:35; it was greatly disturbed by high values for PAR. We compared the contributions in the daily dPAR arising from the values of iPAR less and higher than 150 W m−2 calculated from ship and satellite data by using the SIORAS algorithm (with an account of cos(θ)]. The difference between the ship and satellite data at 12:35 was 12.5% for the iPAR values less than 150 W m−2 and 6.8 times more for the higher values of iPAR.
In Table 2, the statistical estimates of the results of validation of the daily dPAR are given for the SIORAS and NASA algorithms and for different methods of comparison with the in situ values. As seen, the lowest value for RMS Diff was obtained when comparing daily dPAR derived from the satellite image using the SIORAS algorithm, averaged over the daily path of the ship (column #3) with the daily dPAR from in situ measurements, averaged over daylight hours. This value is even lower than when calculated from 1582 points [2].
Table 2. Statistical estimates of the results of validation of the daily dPAR (Einstein m−2 d−1) using the NASA and SIORAS algorithms under different conditions of comparison with the in situ values.
The bias value of 3.5 for this case is about twice higher than in the rightmost column which was 1.85 [2]. The observed bias errors may be attributed to the diurnal variability of cloudiness; the same conclusion was found by others [2]. The appropriate correction can be made if the data on the diurnal variability of cloudiness for a considered region is available. In particular, the problem can be solved by using information about cloudiness from radiometers continuously working on board of geostationary satellites (where it is accessible).
4. Conclusion
Validation of the algorithms for estimating sea surface solar radiation at 400-700 nm from satellite ocean color data has shown that satellite estimates of surface daily dPAR with an acceptable error are possible on a scale of 1 day-102 km (the spatial scale corresponds to the daily distance travelled by a ship). An appropriate procedure for the validation when a moving ship is used has been offered; it is applicable when ferry boats and other ships of opportunity are used for taking measurements. The main reason for errors in satellite estimates of the daily dPAR is the diurnal variability of cloudiness; the necessary corrections can be made if the appropriate information on this variability is available.
Acknowledgments
This study was carried out using grant No. 14-17-00800 of the Russian Research Foundation at the P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences.
The authors thank two anonymous reviewers for very helpful comments.
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