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A method for directly measuring water-leaving radiance using an above-water sensor with a domed cover painted flat black has been proposed. In order to confirm the validity of the result of this method, field experiments have been conducted in Katagami Bay. Radiances measured by this method are slightly less than those obtained from the vertical profile of the upwelling radiance in the sea. This can be attributed to self-shading due to the shape of the instrument used in this study. The advantages of the proposed method are that it does not require empirical processes and minimizes manual procedures after measurements.
©2006 Optical Society of America
1. Introduction
Water-leaving radiance (L w), which is defined as the upwelling radiance from the sea to the air is a fundamental parameter for ocean-color remote sensing, since its spectrum provides informations on the sea-surface layer, such as chlorophyll a concentration [1]. In fact, remote sensing reflectance (R rs) which normalized L w by the downwelling vector irradiance just above the sea surface, E d(0+), can be used to estimate the concentrations of water constituents. Ocean-color algorithms have been developed in order to estimate the exact value of the R rs in the atmospheric correction algorithm and/or to obtain accurate concentrations of water constituents from the R rs [2–8]. Therefore, the measurement of the actual value of L w is crucial for developing the algorithm as well as for its verification.
However, L w cannot be measured directly since the upwelling radiance above the sea surface comprises not only L w but also radiances of the sun and sky reflected from the sea surface (L sr), which does not include information on the sea. In order to determine L w by above-water measurement, L sr should be estimated first.
Cox and Munk were the first to attempt the statistical determination of the sea-surface reflection [9]. Carder and Steward [10] estimated L w from above-water measurements based on the assumption that L w at 750nm was equal to 0; on the other hand, Lee et al. [11] pointed out that this assumption was not applicable to turbid waters. A numerical solution for estimating the influence of L sr was attempted by Mobley [12]. He applied a ray tracing method based on the Monte Carlo technique to Hydrolight [13], and estimated the influence of L sr under several conditions such as the field of view (FOV) of the sensor, wind speeds, sun zenith angles and cloud conditions. It is difficult to validate this estimation method in an actual scenario. As an alternative method, Carder et al. attempted the above-water measurement of L w with reduced L sr by using a polarizer [14]. Similarly, Fougnie et al. [15] demonstrated that the sea-surface reflectance could be reduced by 2%-10% by using a vertical polarizer at 45° from the zenith, relative azimuth angles greater than 90°, and a low solar zenith angle. Although the measurement method can reduce L sr from the above-water radiance, the influence of L sr persists.
Because it is difficult to estimate L sr, a method that estimates L w from the upwelling radiance beneath the sea surface, L u(0-), by using the transmittance of the air/sea interface and the refractive index of the sea is used extensively [16–18]. L u(0-) is estimated by extrapolating the L u vertical distribution and the diffuse attenuation coefficient for L u (K LU). In order to determine K LU, a given layer near the surface must be selected from the L u vertical distribution. There are no quantitative methods for layer selection; therefore, empirical procedures are required for L w estimation.
A buoy that contains two sensors for L u at two given depths is also used for L w estimation, e.g., the Yamato bank optical moored buoy system (YBOM) [16, 17], and the marine optical buoy (MOBY) [19]. L w estimation using buoys is also based on the assumption that K LU near the surface is constant. However, K LU may vary depending on conditions such as a high concentration of phytoplankton in a thin layer below the sea surface. Additionally, self-shading, which is the production of a shadow by the measuring instrument, affects the quality of L w estimation [20, 21].
As described above, L w has thus far been estimated by indirect measurements whose basic principle is based on several assumptions, which in turn depend on the prevailing conditions. Moreover, empirical processes are required after indirect measurement, such as the estimation of L u(0-) or L sr.
This paper proposes a new method for measuring L w. In this method, it is not necessary to estimate L sr and assume that K LU is constant, i.e., the method can be used to measure L w directly. In order to verify whether the radiance estimated by the method is the L w, the radiance spectrum obtained by this method is compared with the L w spectra obtained from the vertical distribution of L u, which is representative of the standard method for measuring L w. In this study, the self-shading correction is not considered, since several models for the correction exist already [22, 23].
2. Measurement Method and Field Experiments
A schematic diagram of the proposed method for L w measurement is shown in Fig. 1. Based on the definition of L w, a radiance sensor is positioned above the sea surface to measure the upwelling radiance. In order to avoid the influence of L sr, a domed cover is attached to the radiance sensor with its edge on the sea surface. The inside of the cover requires low reflection since the radiance due to the scattering between the cover and the sea surface should be minimized. The measurement method can estimate L w without considering the influence of L sr and the assumption that K LU is constant near the surface. Hereafter, the proposed measurement method will be referred to as the domed-cover method.
In order to verify whether the ability of the domed-cover method to measure L w, field observations were conducted at 3 stations in the Katagami Bay (Fig. 2), which is a small bay located to the west of Kyushu in Japan. The observations were carried out in 2004 on June 30, July 29, August 11, August 26, and September 30. In order to minimize the influence of a shadow by the ship, all measurements were performed in the direction of the sun to the ship.
In this study, RAMSES-ARC (TriOS GmbH, Germany) is used as a radiance sensor for the measurements by the domed-cover method. RAMSES-ARC is a 256-channel silicon photodiode array, and it can detect in the range of 320-950 nm. Its FOV is 7° in air. A tilt sensor is additionally attached inside RAMSES-ARC. The dome is a hollow hemisphere, and is painted flat black on the inside in order to maintain a low reflection. The diameter of the dome is 15 cm.
L w was estimated from the vertical profile of the L u, which was measured using PRR-800 (Biospherical Instruments Inc., San Diego). PRR-800 can measure 14 bands with center wavelengths of 380, 412, 443, 465, 490, 510, 532, 555, 565, 589, 625, 665, 683 and 694 nm. The FOV is a 10° half angle in water. PRR-800 is a cylindrical in shape and its length and diameter are 55.9 cm and 10.2 cm, respectively. A stainless-steel lowering frame with a diameter of 18.4 cm was attached to PRR-800 for measuring the vertical profile of the L u.
As a reference, the vector irradiance of the sun and the sky, E d(0+), was measured from a ship. RAMSES-ACC and PRR-810 were used as vector irradiance sensors corresponding to RAMSES-ARC and PRR-800, respectively. Radiance and irradiance calibrations based on the NIST standards of spectral irradiance were performed for both the radiance and vector irradiance sensors.
3. Results
The radiance obtained by the domed-cover method and the L u vertical profile were observed in rapid succession at all stations in order to avoid any change in the radiance depending on sky conditions. Therefore, both measurements had a very small time lag. However, despite this short time lag, at some stations, the values of E d(0+) obtained by both measurements differed by more than 10%. These values were eliminated from the verification data. As a result, nine data was selected carefully among all 14 data.
In all observations, clear sky conditions and calm sea-surface conditions prevailed since there was little wind. Further, high chlorophyll a concentrations near the surface were not observed at any station. It is possible to estimate L u(0-) based on the assumption of constant K LU. However, as a condition for L u(0-) estimation, data with tilt angles greater 10° were eliminated from L u profile. On the other hand, in the proposed domed-cover method, the radiance was obtained on the basis of the nearest nadir angle.
The spectra of the radiance obtained by the domed-cover method and those of L w obtained using PRR-800 are shown in Fig. 3. As shown in this figure, the L w spectra exhibit a common peak wavelength of 565 nm. However, their shapes and magnitudes are different. On the other hand, the radiance spectrum obtained by the domed-cover method were similar to those of L w obtained using PRR-800.
The comparison between the L w obtained using PRR-800 and the radiance obtained by the domed-cover method based on PRR-800 wavelengths is shown in Fig. 4. As shown in this figure, the values of radiance and L w obtained by the proposed method and PRR-800, respectively, showed a one-to-one correspondence. The root mean square error of all values was 0.024. The linear regression line had a slope of 0.973 and an intercept of -0.003 (r 2 = 0.987); therefore, the radiance obtained by the domed-cover method was less than the L w obtained using PRR-800.
Fig. 4. Comparison of L w based on the wavelengths of PRR-800 bands. The solid line and the single dotted line represent the liner regression line and the one-to-one correspondance line, respectively.
4. Discussion
Because of the prevailing conditions during the observations, K LU near the surface could be assumed to be constant. Therefore, in this study, L w obtained using PRR-800 is accurate.
The radiance obtained by the domed-cover method can be considered as the L w. This is because, the radiance obtained by the domed-cover method and L w obtained using PRR-800 had similar values although the former was slightly less than the latter. For same reason, the accuracy of the L w obtained by the domed-cover method may be also considered to be comparable to that of L w obtained using PRR-800.
The influence of self-shading poses a problem in the measurement of L w by the domed-cover method. Self-shading also affects the measurement of L u, i.e., it is a problem for the method used widely to measure L w. Piskozub et al. [24] attempted to minimize the influence of self-shading by attaching an arm from the instrument body to the L u sensor. However, the influence of self-shading could not be eliminated entirely. The error due to self-shading was evaluated by using the backward Monte Carlo simulation [20–22] or analytical model [23]. Results of the simulation revealed that the error due to self-shading was affected by the absorption coefficient of the water, radius of the instrument and sun zenith angle.
In this study, measurements by the domed-cover method and PRR-800 are carried out almost simultaneously and at the same location. Therefore, the assumption that the absorption coefficients during both measurements are the same is valid. Since the vector irradiances on the ship are almost similar, the difference in the sun zenith angles during both measurements can be negligible. The radius of the domed cover in this study is greater than that of PRR-800 by 24 mm. The difference in the radius might be considered to influence the underestimation of the radiance by the domed-cover method.
Although the FOVs of RAMSES-ARC and PRR-800 are different, Zibordi and Ferrari [21] reported that the error due to the FOV did not exert a significant influence in comparison with the absorption coefficient, radius of the instrument, and sun zenith angle.
Self-shading error for the domed-cover method is estimated less than 20% for absorption coefficient less than 1.0 m-1 and sun zenith angle larger than 20° using the analytical model [23].
5. Conclusion
In this study, we have proposed a new method for the direct measurement of L w by using an above-water sensor with a domed cover. This method does not require the estimation of the sun and the sky reflections from the sea surface and the assumption of constant K LU. In comparison to L w obtained from the L u profile, L w obtained by the proposed method was slightly less due to the magnitude of self-shading. However, we emphasize that the domed-cover method does not required the estimation of L sr, K LU, and L u(0-). Therefore, the advantages of the proposed method over the existing method of L w measurement are that it does not require empirical processes and minimizes manual procedures after measurements.
Since L w estimated by indirect measurement was applied to ocean color remote sensing, the error due to the assumptions may be considered to lie within the allowable range. However, the assumption was not validated directly by field experiments. The development of a method for directly L w measurement, such as the domed-cover method, may play an important role in determining the applicable range of the assumptions and its accuracy.
The instrument used in this study was poorly balanced, since commercial products were used for the radiance sensor and the dome. Although no difficulties were encountered while carrying out measurements with this instrument in a calm sea conditions, the poorly balanced design of this instrument could pose some difficulties in rough sea conditions. The development of instruments with improved designs for the domed-cover method might enable the measurement of L w in rough sea conditions.
The dome is placed in the sea, while the sensor is located in air. Therefore, it can be expected that the degradation of the sensor sensitivity due to contact with living matter will be minimum. For long-term operation, the instrument can be designed as an optical mooring buoy.
Acknowledgments
This study was supported by a grant from the Collaboration of Regional Entities for the Advancement of Technological Excellence (CREATE) project in the Nagasaki Prefecture under the Japan Science and Technology Agency (JST) and from the ADEOS-II program of the Japan Aerospace Exploration Agency (JAXA). Dr. M. Kishino of Tokyo University of Marine Science and Technology and Dr. T. Oishi of Tokai University are acknowledged for their fruitful discussions.
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