During the Ocean Optics 2004 class, I vaguely remember Curt Mobley mentioning the method of holding a Spectralon panel ("a reference plaque ... having a known BDRF") in front of a radiance sensor in order to measure Ed(0+).

Here's a nice little paper I stumbled across from 2004 that describes how to do it and how to lower variability, esp. on cloudy days where:

        ...shadow effects induced by the cockpit of the boat, by the person or system holding the radiance sensor, and by the radiance sensor itself can dramatically modify the measured Ldspec signal. Errors up to 100% can easily be committed when a Spectralon plaque is used on the deck of a boat under a covered sky.

By careful placement of the radiance sensor and the plaque, they achieve an accuracy of better than +/- 15%. 

David Doxaran, Nagur C. Cherukuru, Samantha J. Lavender, and Gerald F. Moore
Use of a Spectralon panel to measure the downwelling irradiance signal: case studies and recommendations.
Applied Optics, Vol. 43, No. 32,10 November 2004