The series that this came from, "Wonders of the Solar System", was really great -- recommended, as was another series by the same folks, same narrator, "Wonders of the Universe". In the "..Universe" series they get into pretty cool stuff like, "What determines the direction of time?"
. The physicist-narrator -- Dr. Brian Cox -- does a great job and really conveys an enthusiasm for the "wonder" of the natural world . I watched it several years ago...not sure if you can find it online for streaming, but there are DVDs to order.
The demonstration is really just a
conceptual example -- the method described won't give accurate results to estimate energy flux from the Sun to the Earth
in general. For one thing, the water in the bucket needs to be stirred while the measurement is going on -- thermometer in stagnant water won't do it. And the color/reflectivity of the bucket (shiny silver vs white or black) affects the rate of heat absorption, too.
If I was limited to equipment commonly-available while camping and I wanted to know how much energy from the sun was currently striking my spot on the Earth...I'd use a black solar-shower bag containing a small measured amount of water at equilibrium with the ambient air temperature. Measure the water temperature. Lay the bag flat in the sun (NOT on hot sand). Squish/jostle the bag a bit while it's absorbing the solar energy to try to equilibrate the water with the bag surface. After a few minutes, stick a thermometer in the bag port and measure the water temperature again. (I'd probably measure the temperature at regular intervals a few times)
Specific heat capacity of water is, by definition, 1 BTU/lb/°F so use that conveniently-simple number along with the water-weight, bag-area, temperature change and time interval to estimate the solar energy flux.