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My case is this:

My protagonists live in an earthlike world where living in a city on 90kms approximately, protected by extremely big fences so the sandstorm won't hit them.

Anyway, they think the government is lying and that this planet is not really a desert, but they can not leave the fences to prove it.

Is there a scientific way to do it?

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  • $\begingroup$ Since you are asking about the actions of a character, this question is not about building a fictional world, and as such is off topic for this site. $\endgroup$ – sphennings Nov 17 '17 at 16:34
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    $\begingroup$ A city cannot exist in isolation like that. It would be common knowledge. $\endgroup$ – Raditz_35 Nov 17 '17 at 16:53
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    $\begingroup$ It's good practice to wait at least 24 hours before accepting an answer so that people from every time zone get a chance to weigh in. $\endgroup$ – sphennings Nov 17 '17 at 17:45
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    $\begingroup$ Where does food come from?.. $\endgroup$ – Mołot Nov 17 '17 at 18:27
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    $\begingroup$ @Mołot - simple - the great and glorious government - in its wisdom, generosity and capability - can feed the masses, even though the world is a desert! And don't let those traitors tell you otherwise. $\endgroup$ – colmde Nov 20 '17 at 12:39
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Analyse the air as it blows over and through the city. Is there a reasonable moisture content? Are there soil paricles? What type? Seeds and pollen would give them an idea of the local flora. Are they all desert plants or would you find some in wetter climes?

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  • $\begingroup$ i am gonna go with the local flora! is a great idea $\endgroup$ – caryarit ferrer Nov 17 '17 at 16:57
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    $\begingroup$ Is there a breathable concentration of oxygen in the atmosphere? If so, there are plants somewhere that produce it. $\endgroup$ – jamesqf Nov 17 '17 at 19:18
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    $\begingroup$ Nice answer. Granted, if your civilization's entire history is confined to one city, you may not know about other kinds of flora or to check these things. $\endgroup$ – Vincent Nov 19 '17 at 7:55
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Yes
Someone needs to buy or make a rain gauge and measure the rainfall that they receive in a year. If there is less than 25cm then they live in an arid area if they do not receive any rain at all then they know they live in a very arid region, both can be considered deserts. If there is more than 25cm of rain a year then they do not live in a desert. https://sciencing.com/rainfall-deserts-6632010.html .

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  • $\begingroup$ Which doesn't answer the OP's question of whether the world is a desert, not whether a particular area is $\endgroup$ – nzaman Nov 18 '17 at 5:08
  • $\begingroup$ @nzaman True it doesn't answer it exactly however it does give an indication. And it would seem that the correct answer didn't answer the questuon either. $\endgroup$ – Slarty Nov 18 '17 at 9:55
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It's not really difficult. The definition of a 'Desert' is any place that receives less than 10 inches of rainfall or precipitaion per year: From Merriam-Webster "1 a :arid land with usually sparse vegetation; especially :such land having a very warm climate and receiving less than 25 centimeters (10 inches) of sporadic rainfall annually b :an area of water apparently devoid of life

Simply measure ( suggest balloons to sample) the atmospheric humidity levels of air coming over the wall. If the air is extremely dry by comparison, you may have a desert on the other side. If the air returns elevated humidity, it is unlikely there is a 'wet desert' beyond the wall. Secondary to that- moist air such as is found in temperate areas is often unstable, while dry air is much more stable. Weather patterns that cross the wall would further indicate the exterior climates' state.

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You can't do it scientifically (read until the end) or everyone would know from the beginning. You cannot possibly keep this a secret if a high school experiment will disprove everything people think they know about the world. Also, if more advanced scientific equipment is needed, well, such a totalitarian government wouldn't fund it. I'm worried about the integrity of your world here, so let's save it.

So he needs to do what nobody else has done so far and was in the position to be lucky: be lucky and overhear/see/notice something is up. Some people have to know and people make mistakes. How this happens is story-based, but unless this is for a kids book getting that information from someone else is an easy way to keep your world intact. There must be food deliveries, I would start there.

So, you asked about "scientific" specifically, so here I go: Alcohol. The best way to get that information it is alcohol. A person under the influence of alcohol is more likely to tell you stuff. If you don't like that idea: a blow to the head, any other drug, lack of sleep - there are a lot of options here.

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Molot makes a good point: where does the food come from? There must be a sufficient source of water to grow enough food to feed the population of a 90 sq. km city. That and have enough left over to provide sanitation.

The only real way to prove to the general public that the world is not a desert is to actually go there in person. If your civilization has access to aircraft, it makes things a lot easier. Fly in a straight line in any direction, till you've used just under half your fuel, identify a place to set up a base camp, fly back, repeat for another direction. Once you're sure there is no water within a single flight, start bringing supplies over to establish your base camps, then use those as relay points for further exploration.
This, of course, assumes the government is not trying to stop you, as the amount of logistics required simply can't be kept secret.
If light is not available, or the whole thing needs to be secret, the only real option is Jack Judge's answer.

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