Geomagnetic Flux and Global Warming?

A paper just out in Science uses old sailing records to show that strength of the Earth's magnetic field was relatively constant from the 1500s to around the 1840s, at which time it entered into a decline that has continued up to the present day. I came across an interesting theory suggesting that this decline is responsible for global warming, which seems to have begun around the same time. Hmmm...does the Earth's magnetic field really shield it's surface from Solar radiation?