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While these rules are designed for 5th edition, they could be ported to another system with some small adjustments. These are the rules I am using for The Lazarus Expedition

Technically, a desert is a place that receives very little rainfall. In theory, a desert could have any range of temperature, humidity, or water availability. You could have a massively wide crater with sides that form tremendous mountain ranges that cause clouds to drop their rain on the outside or at the peaks, and the water could run down into the crater into the flat land with a lot of clay in the soil turning the whole area into an eternal swamp. The very same mountains that prevent the rain from coming into the area would trap evaporating water from the marsh, creating a hot, humid, damp zone that receives little to no rain.

But let's not be technical. In this article when we are talking about a desert, we're talking about a place that is very hot, with lots of direct sunlight, little to no shade, and little to no available water. We mean a "classic desert". We're talking about something akin to the The Serengeti, The Mojave, The Arabian, or the Gobi.

So let's get started! When traveling through a desert you need the same things you do everywhere else, only the environmental extremes make things more important: Food, Water, Clothing, Shelter. Of these, food is the most obvious and least changed, so we're going to skip it.

Water
Water is the most critical resource when traveling through a desert. Evaporation is the mode of cooling for humans, humanoids, and our mounts. Humans and horses cool through sweat on the skin. Dogs use evaporative cooling of their breath, mouths, and nose. Cats will lick moisture onto their skin which will evaporate off. We of course also need water for bodily functions, so as we run out we slow down and eventually die.

How much water do our characters traveling through a desert need?
This is a deep rabbit hole. What is "need", what is "effective", what qualifies "minimum threshold"... looking for truth here is messy and doesn't make the game more fun. So let's keep game mechanics simple.

Traveling characters normally need a waterskin. We don't usually track how much water they come across, how often they refill it, or any of those details, so I like to assume that a character can get through a day one 1 waterskin if they need to. In a desert, a character will need more water, and so for simplicity sake I like to run with, "You consume twice as much water in a desert." That means a character needs 2 waterskins per day. If you want to have more inhospitable deserts, maybe yours require 3 per day, or even 4 per day.

However much water you need, what we really care about is what happens when you run out. The survival rule of thumb is 3 minutes without air, 3 days without water, 3 weeks without food. In a desert, the water will go faster, so we're looking for a system that would imply death by dehydration in ~1.5 days -> 1 - 2 days on average. And since it's D&D, we should have some dice rolls involved, and we should say characters with a higher skill or score in a relevant ability should do better. With these ideas in mind, I like to use Constitution Saving Throws that give Exhaustion Levels. The better your Con Save, the fewer exhaustion levels you take.

Constitution Saving Throws
DC | Exhaustion Levels
<5 | 6 levels / Death
05 |  5 levels
10 |  4 levels
15 |  3 levels
20 |  2 levels
25 |  1 level
30 |  0 levels

The math here is pretty straight forward. A normal person with 10 or 11 con and no proficiency in this save will be likely to roll between a 5 and a 15, taking 3-5 exhaustion levels each day without water which is lethal in 2 days. It's possible for them to roll poorly (4/20 -> 20%) and die the first day. It's possible they roll well and survive 2 days. They cannot survive 3 days, even if they're all natural 20s.

To survive for more than 3 days without water, you'd need at least 1 25, and a few 20s, which is pretty tough. A 5th level fighter with 16 Con has +6 on their save, and would need a 19+, and two 14s+, which is pretty unlikely.

Once a character hits 3 levels of exhaustion, they take disadvantage on their saving throws, so surviving past 2 days is going to be difficult no matter how good your stats are.

5 Exahustion levels means speed is 0, which could be a death sentence if you're traveling alone. With friends, maybe they can drag you, or use a Tensor's Floating Disk to help you out.

What about rationing water?
Let's say our characters have 1 water skin left each, or they want to split their two water skins over the next two days. How do we handle this? We don't want to create a situation whereby the players are at an advantage to dehydrate themselves on their journey, but we do need a mechanics for this middle ground. A con save at advantage for every day of half water might do the trick.

For the party who only has 1 skin / character and is desperate, this is a fine answer that isn't exploitable. For the party who has water but is trying to stretch it, they're going to end up making a lot more saves. Let's do some math for this group below.

Situation: The party has 1 day of water they're trying to stretch for 2 days. Or characters have +2 - +5 on their con saves. On a normal roll, they'll score between an 8 and a 13 on their d20, for a total save range of 10-18. On an advantage roll, they'll roll between 11 and 16, for a total save range of 13-21.

Option A: Drink it on the first day and suffer dehydration on the 2nd. The characters each make 1 save like normal at the end of the 2nd day. They have 3-4 exhaustion levels at this point.

Option B: Drink half on the first day, and half on the 2nd day. At the end of the first day, the party makes a Con save at advantage, and probably gets 2-3 exhaustion levels. At the end of the 2nd day, the party makes a 2nd Con save. If they only have 2 exhaustion levels, it's at advantage. If they have 3, it's at flat. They'll gain 2-4 levels of Exhaustion here, ending up with 4-7 levels of exhaustion and possible death.

So rationing water in the long run is only going to hurt you, which is as it should be.

Note: In our last session of The Lazarus Expedition, I used the rule of, "you have half the water, to the saves are cut in half". This was an off the cuff ruling I made but I instantly regretted. Such a rule would make it sensible to ration your water day after day, and I really dislike that. If you want your party to be able to survive on half water rations for a long time, then this might work. It will certainly prolong their survivability since making a 15 and suffering no ill effects isn't difficult, especially with a few points in con. This would certainly be a more Heroic ruling.

Clothing
Exposure to the elements is a real danger, but most of the time our characters are probably dressed appropriately for their environment. We should make sure we either assume our characters have the right clothes for this environment, or go out of our way to tell them they need to buy clothes for it. We should never let our players walk into a desert and then hit them with a, "Well you never said you dressed for the weather appropriately". If for some reason a character insists on wearing inappropriate clothes, here are some easy consequences

Not enough clothing: You get sunburned, take an exhaustion level for each day of travel like this. You have very fair skin? Maybe it's extreme sunburn, everything is blistering and hurts, and you take 2 exhaustion levels. If a sand storm hits and your skin is bare, or worse, bare and burned, you're going to have a bad time. 1d4 damage for each hour of the storm, or 1d6 damage if your sunburned, or 1d8 damage if you're extremely sunburned and your skin is being shredded under the pelting sands.

Too much clothing: Your inner layers that are touching your skin aren't evaporating well, they're just soaking the outer layers. You'll need to poor extra water on yourself. You need twice as much water to live like this.

Wearing armor: Your sweat won't even cool you down since it can't evaporate except at the edges of the armor, which are insignificant compared with your surface area. You are overheating right away. You take an exhaustion level every after 3-5 hours (lets just call it 4), and then again every 2 hours after that. Walking around in the desert in armor is a sure way to die. If you expect a battle is soon upon you, maybe you can put it on for a short fight and take it off again.

A good solution is to have the party "rotate armor" as they overheat. This way we don't have to track who has what on, or for how long, we just know that when one person starts to overheat, someone else puts on their armor, etc. etc. If at least 3 people are in the rotate, each person will have 2x their armor on time to cool off and this solution can be handwaved. We roll a die to see who has their armor on at any given moment.

With 2 characters switching armor in a party of 2, I'd just handwave it as well. With 2 characters switching armor for min/maxing in a party of 3 or 4 who can wear armor... it's nice when everybody shares the load, and each character will also want more time without it on than with it, so perhaps push the group rotation. 

Shelter
Shelter is important for a few reasons. It gives shade at the worst of the day, it keeps you warm at night (somewhat), and it gives you cover from sandstorms that might blind, choke, or hurt you.

I like to play that traveling without shelter in these conditions inhibits any form of short or long rest - you simply can't recover exposed to the elements like that. Burying yourself in the sand or dust might save you from a storm, but you're going to struggle to breath, and surely can't rest well, let alone sleep.

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So there you have it. Those are the desert travel rules, and why I think you should use these sets, and some options for modifying them as you see fit. I do love the higher simulationist side of things and strive to find ways to bring that into 5th edition. If you wanted to make special rules for desert people who are more adept at traveling in the desert, I'd start by saying they need less water per day, and then maybe give them a special bonus on their con saves when they do run out of water. Something like a +5 for this one type of save only. This flat mod here means they'd take 1 level of exhaustion less than an ordinary person. 

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