• absorption coefficient a(z,λ), measured as a function of depth z and wavelength λ.

• volume scattering function VSF(z,λ,ψ); ψ is the scattering angle, 0-180 degree.

What can be measured today:

Commercial instruments are available for in situ absorption measurements, and promising new instruments are under development.

No commercially produced instruments are currently available for in situ measurement of the VSF over the full range of scattering angles, but several unique instruments exist. Others are under development. Bench-top commercial instruments exist for measurements made on water samples. Given the current lack of readily available in situ VSF instruments, a reasonable proxy is to measure:

• the beam attenuation coefficient c(z,λ), measured as a function of depth and wavelength.

• the backscatter coefficient bb(z,λ), measured as a function of depth and wavelength.

Commercial instruments are available for in situ measurement of beam attenuation, although (as with many measurements) there are instrument design issues that require standardization (Boss et al., 2009). The same is true for measurement of the backscatter coefficient.

Measurement of c allows the scattering coefficient b to be obtained from b(z,λ) = c(z,λ) – a(z,λ). Knowing the scattering and backscatter coefficients allows the scattering phase function to be estimated from bb(z,λ)/b(z,λ), which can give acceptable inputs to the RTE (Mobley et al., 2002).

Boundary Conditions Needed to Solve the RTE

In principle the needed measurements are:

• the in-air, sea-level downwelling (sun and sky) radiance Ld (in air,θ,ϕ,λ) as a function of direction (polar angle q and azimuthal angle f) and wavelength.

• the sea surface wave spectrum.

• the bidirectional reflectance distribution function, BRDF(θ′,ϕ,′,θ,ϕ,λ), of the bottom, if not infinitely deep water, as a function of all incident (θ′,ϕ,′) and reflected (θ,ϕ) directions and wavelength.

What can be measured today:

Although these boundary conditions can be measured, they are almost never measured in the field because of instrument limitations. Therefore, it is reasonable to measure the following:

• the above-water, downwelling plane irradiance Ed(in air,λ) incident onto the sea surface, which can and should be partitioned into direct and diffuse contributions (Gordon, 1989).

• sun zenith angle (or compute from latitude, longitude, date, and time).

• sky and cloud conditions.

• wind speed.

Bottom irradiance reflectance Rb(l) = Eu(l)/Ed(l) can be used along with the assumption that the BRDF is Lambertian to obtain satisfactory predictions of water-leaving radiance for most remote sensing purposes (Mobley et al., 2003).

In-Water Outputs

Ideally, the following should be measured for comparison with RT model predictions:

• the full radiance underwater distribution L(z,θ,ϕ,λ) as a function of depth, direction, and wavelength.

• the irradiances, Ed(z,λ), Eu(z,λ), and Eo(z,λ), which give a consistency check by integrating the radiance to compare with the irradiances.

• the in-air upwelling radiance Lu(in air,θ,ϕ,λ).

What can be measured today:

There are no commercial instruments for in situ measurement of the full radiance distribution, although a few unique instruments do exist (Voss and Chapin, 2005). Commercial instruments are available for Ed and Eu, which are routinely measured. Commercial instruments are available for radiance measurements in a given direction, so radiance is usually measured only for selected directions (most commonly the upwelling direction, which can be used in estimating the remote sensing reflectance Rrs). An acceptable set of radiometric measurements is then:

• the upwelling (nadir-viewing), in-water radiance Lu(z,λ).

• the upwelling and downwelling in-water plane irradiances, Ed(z,λ) and Eu(z,λ).

• the above-water upwelling radiance in one direction, e.g., Lu(in air,q=40,f=135,λ). The recommended direction is at 40 deg off-nadir and at 135-degree relative to the sun, which minimizes the sun glint (Mobley, 1999).

• the in-air downwelling (sky) radiance in the reflection direction, e.g., Ld(in air,q=40,f=135,λ), plus a gray-card measurement for estimation of Ed and Rrs (the so-called Carder method of estimating Rrs; see Mobley, 1999).

• the downwelling in-air plane irradiance, Ed(in air, λ) for both direct and diffuse lighting.

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