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In the Martian, by Andy Weir, How did observation and deduction help Watney figure out he had entered a dust storm?

Observation and deduction helped Watney figure out he had entered the dust storm because he was able to observe how his power charge rates were changing.

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The Martian is a wonderful book that shows readers how science and the scientific method can be applied in the most harrowing of situations. The scientific method is all about answering questions and solving problems, and observation is a big part of that because it is through observation that data can be obtained and then conclusions can be deduced from that data.

The section of the book that this question is asking about can be found in chapters 22 and 23. Watney is on his way to Shiaparelli, but he is unable to know that a major dust storm is heading his way. The problem of the dust storm is explained quite well by Venkat.

“The edge of the storm isn’t a magic line. It’s just an area where the dust gets a little more dense... It’ll be really subtle; every day will be slightly darker than the last. Too subtle to notice.” Venkat sighed. “He’ll go hundreds of kilometers, wondering why his solar panel efficiency is going down, before he notices any visibility problems. And the storm is moving west as he moves east. He’ll be too deep in to get out.”

Venkat's information about solar panel efficiency is exactly what alerts Watney to the presence of the storm. He does notice that his batteries are not charging as quickly, and the wattage from the solar cells is less than normal. Watney figures it is due to aging equipment, but further observational data eventually convinces him otherwise. On an EVA, Watney arrives at the peak of a rim. He is hoping to better pinpoint his location; however, he can't see the other side of the crater. That direction is filled with dust, but behind him the air is clear. Watney now knows that he is in the dust storm.

His next challenges are to figure out how far into the dust storm he is and which direction the storm is moving. He does this by figuring out a method to measure his "percent power loss." Watney's plan is to set up three solar cells at 3 points equidistant from each other. He will then compare how many watts of power each cell collects in a single day. This observational data will allow him to deduce which way the storm is moving; therefore, he can better get out of the storm.