A scientist studying climate believes the the earth is growing warmerWhat should the scientist do to find out if this could be true?

See the recordings of temperature over the last 10 or 20 years. This could show an increasing temperature. Also, you could see how much of the ice has melted or the rise of sea level (not to be confused with tides). If the Earth is getting warmer, then more icecaps would melt, resulting in higher oceans and floods.

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Essentially right but it would need records over a lot more than a couple of decades to show any long-term change because the climate and weather wobble about all the time.