Re: what is the total net charge of the earth's surface?

I found viewgraphs for a lecture titled Lightning, Nature's Fireworks on the University of Alberta's website. This answers your question, plus many more related ones.

The solid Earth has a negative charge of about a half million coulombs. The atmosphere has a roughly equal and opposite charge, so that the Earth as a whole is roughly neutral. The charge difference produces a "fair weather electric field" in the lower atmosphere averaging about 6 volts per meter -- however, this field varies strongly with altitude, and is nearly 100 volts per meter at ground level. The total voltage difference between the ground charge and the atmosphere's charge (which exists roughly 30-50 km up) is about 300,000 volts. A simple calculation shows that the total energy stored in the fair weather electric field is 150 billion joules.

Since air isn't a perfect insulator, electrons leak from ground to air constantly, trying to reduce the charge difference to zero. This current amounts to 2000 amps. (Easy exercise for the reader: what's the resistance of the atmosphere?) Another simple calculation shows that the electrical power dissipated is 600 megawatts. This is the output of a large electrical power plant. While it's theoretically possible to harness this power for use by people, the fact that it's spread throughout the entire globe (to the tune of about a watt per square kilometer) makes it impossible in practice.

Since charge is constantly leaking between ground and air, there must be an "electrical generator" somewhere which is pumping electrons from air to ground, against the electric field. Thunderstorms are the generators. The movement of air and charged cloud particles within them separates electrical charges vertically; lightning then transfers the extra electrons at the base of the cloud to the ground. Positive charge at the top of the cloud leaks into the upper atmosphere. This recharges the fair weather electric field.