Kd and Remote Sensing Reflectance

Kd and Remote Sensing Reflectance

Tim Wynne

Using Remote Sensing Reflectance as a proxy for Chlorophyll-a Concentration using in situ Data and Data from a Hydrolight Simulation.


Remote Sensing Reflectance (RRS) was calculated using data obtained from a Hyperspectral Tethered Radiometer Spectral Radiometer (HTSRB), and from modeling data from an ac9 with Hydrolight. The RRS values that were obtained from the two different methods were then compared, and resulted with curves of approximately the same shape, but with the HTSRB data having a factor of two higher than the Hydrolight RRS curve. The RRS was then used to calculate the chlorophyll-a concentration, using the SeaWiFS/OC4v4 and SeaWiFS/OC2v4 algorithms. The derived chlorophyll concentration compared favorably with the chlorophyll concentration that was measured with a profiling fluorometer. The Lu sensor on the HTSRB measures the upwelling radiance 63 cm below the surface. This was corrected for and the resultant RRS curves and chlorophyll values showed little change.


The ocean optics class went on a cruise on Friday, 9 July 2004 aboard the R/V Ira C. Among other data the class collected data from a Hyperspectral Tethered Radiometer Spectral Radiometer (HTSRB), an ac9, and a bb2f from the mouth of the Damariscotta River Estuary (ME, USA). The HTSRB is a hyperspectral instrument from Satlantic ( The instrument floats at the surface and collects upwelling radiance (Lu) and downwelling irradiance (Ed). The ac9 is a profiling multispectral instrument from WETLabs ( The ac9 collects absorption (a) and attenuation (c) data from nine wavelengths ranging between 412 and 715 nanometers (nm). The bb2f is a profiling instrument that collects backscatter (bb) information, but also contains a fluorometer.


Calculating RRS with a HTSRB

The first method that was evaluated uses data obtained from a HTSRB to calculate RRS. Thirteen different deployments of the HTSRB were examined. Ed was graphed for each deployment with respect to wavelength (figure 1). For ease of analysis the mean was then calculated and graphed in figure 2. Likewise Lu was graphed and then the mean was calculated (figure 3).

RRS is defined in equation 1.

RRS = Lw/Ed(1)

Where Lw is the upwelling water leaving radiance (W m-2 sr-1 nm -1) and Ed as previously stated is the downwelling plane irradiance (W m-2 nm -1). After the division the resultant units for RRS are 1/sr.

The instrumentation available did not measure Lw, but Lu, so Lw must be calculated for.

Lw was calculated using equation 2 (Kirk, 1994).

Lw = Lu * (t/n2)(2)

Where t is the Fresnel Transmittance, which is a constant of 0.98 and n is the index of refraction of seawater (1.33). We can now rewrite equation one.

RRS = (0.55*Lu)/Ed(3)

The calculated RRS is graphed in figure 4.

Correction for the Lu measured at 63 cm

The HTSRB measures Lu from a sensor that is 63 cm deep in the water column. This is not the same as Lu at the surface, and therefore a correction is needed in order to get a more accurate representation of the value. Equation 4 illustrates the new Lu that should be calculated.

Lu(at_surface) = Lu(at_0.63 meters) * e^(Klu*0.63)(4)

Where Klu is defined at the attenuation of water leaving radiance.

In order to solve for this must be Klu calculated. It is assumed that Klu = Kd, where Kd (attenuation coefficient) is defined by equation 5.

Kd = (a^2 + G*a*b)^1/2(5)

Where G is a constant equal to 0.256 (Kirk, 1994).

The absorption (a) and scatter (b) values were derived from a depth integrated ac9 cast.

But first the ac9 data were corrected for salinity, temperature, and scattering, using a spectrally varying correction. Scatter was calculated by equation 6. The results of a,b,and c are graphed in figure 5

b = c – a(6)

The ac9 data was integrated over depth (the cast went to 30 meters), so that only one value per wavelength is calculated. Before the absorption could be used to derive Kd the absorption of water was added onto the data, using coefficients from Pope and Fry (1997).

With an accurate representation of Kd available (figure 6) it now becomes possible to solve for the water leaving radiance (Lu) at the surface using equation 4. Lu at the surface is in figure 7.

Using a Hydrolight Simulation

The second method of calculating RRS utilized the acquired ac9 data and was modeled using Sequoia Scientifics’ Hydrolight software. Hydrolight is designed to model the light field at a user defined place and time and under user defined conditions. Essentially the user defines the inherent optical properties (IOPs) and a few ancillary inputs, and Hydrolight outputs the apparent optical properties (AOPs). Hydrolight calculated the sun angle for the input latitude (43 degrees N), longitude (69 degrees W), and time (15:00 GMT). The software also prompts the user for cloud cover, which was entered at 90% for a very overcast day. The corrected attenuation and absorption values were entered into the Hydrolight software. The output values of Lu and Lw from the Hydrolight simulation were graphed with respect to wavelength and shown in figure 8. The RRS from the Hydrolight run is graphed in figure 9.

RRS values from the Hydrolight simulation and RRS values calculated using Lu values at 63 cm, and at the surface are show in figures 10 and 11, respectively.

Calculating Chlorophyll with OC2 and OC4

The SeaWiFS OC2v4 algorithm modified for cubic polynomials was used to calculate the chlorophyll from the remote sensing reflectance1 see equation 7.

Chl-a (ug/l) = 10.0^(a(0) + a(1)*R + a(2)*R^2 + a(3)*R^3) +a(4)(7)

Where R = log(RRS490/RRS555), a(0)=0.319, a(1)=-2.336, a(2)=0.879, a(3)=-0.135, and a(4)=-0.071.

For comparison the SeaWiFS OC4v4 algorithm was also used in order to calculate the chlorophyll-a concentration from RRS, see equation 8.

Chl-a (ug/l) = 10.0^(a(0)+ a(1)*R + a(2)*R^2 + a(3)*R^3 + a(4)*R^4)(8)

Where R = log((Rrs443>Rrs490>Rrs510)/Rrs555), a(0)=0.366, a(1)=-3.067, a(2)=1.930, a(3)=0.649, a(4)=-1.532


There were three different methods used to derive at RRS values, and two different algorithms were used to derive chlorophyll-a concentration. The values are found in table 1. The corrected HTSRB values refer to Lu being measured at the surface, while the uncorrected HTSRB values refer to Lu being measured at 0.63 meters.

Method / Chlorophyll-a (ug/l)
HSTRB corrected OC2 algorithm / 2.4377
HTSRB uncorrected OC2 algorithm / 2.4487
HTSRB corrected OC4 algorithm / 3.4757
HTSRB uncorrected OC4 algorithm / 3.51
Hydrolight OC2 algorithm / 1.8786
Hydrolight OC4 algorithm / 2.0212
Fluorometer / 2.48

Assuming that the fluorometer on the bb2f was accurate, the results derived from the OC2 algorithm are in near perfect agreement.


Ocean color satellite platforms have used RRS to calculate chlorophyll-a concentrations for years. The Coastal Zone Color Scanner (CZCS), SeaWiFS, and MODIS sensors all calculate chlorophyll-a concentrations using different ratios of RRS. The estimated chlorophyll from satellites must be verified by in situ measurements, such as the measurements described here. There was no available satellite imagery, to compare to the calculated chlorophyll value for the sampled day, as the local conditions were masked under heavy cloud cover.

The agreement between the fluorometer and the OC2 algorithms were freakishly close to one another. Attached to this paper is my code for review. The OC4 algorithm produced

results in the same ball park, but higher relative to the fluorometer. Once again the Hydrolight simulation produced results in the same ball park, but lower than the fluorometer.

It does not appear that correcting Lu from 0.63 meter to the surface made any noticeable difference in calculating the chlorophyll-a concentration. There was a loss of data from going from the 200 channel HTSRB to the 9 channel ac9.

I have dealt with ocean color satellite data for over two years, and have never done any validation. This was a truly enlightening exercise and I appreciate all of the people that helped me along the way.


Kirk, J.T.O. Light and Photosynthesis in Aquatic Ecosystems. Second edition. 1994. Cambridge University Press.

Pope, R. and E. Fry (1997). Absorption spectrum (380-700 nm) of pure water. Integrating cavity measurements. Applied Optics 36(33): 8710-8723.