Rivers on Mars
Article written by Jim Secosky. Jim is a retired science teacher who has used the Hubble Space Telescope, the Mars Global Surveyor, and HiRISE.
There is much evidence that water once flowed in river valleys on Mars. Images of curved and branched channels have been seen in images from Mars spacecraft dating back to the early seventies with the Mariner 9 orbiter.       These river valleys are called Vallis (plural Valles), the Latin word for valley.
Researchers have grouped Martian river valleys into two groups. One type, called outflow channels, carried as much as or more water any on Earth and maybe at any time in Earth’s history. Rushing water formed large streamlined islands. Vast quantities of water seem to have just burst out of the ground.     The water originated in areas of collapsed terrain where the ground ended up formed into mesas and large blocks. This collapsed terrain has been called chaos. The water is thought to have flowed to lower elevations and created an ocean to the north that may have been one third the area of Mars.  Some researches postulated that floods erupted from the ground many times.  Since Mars is very cold, ice would have quickly formed on the top and allowed the water to move along for some time. Scientists generally agree that Mars has a thick shell of ice under the surface. Perhaps in the past there was a vast interconnected layer of water under it. If an asteroid, fault, or volcanic eruption caused the ice to break, water could pour out.   
Another type of channel exists mostly in the old, southern highlands. They were discovered by Mariner 9 in 1971. Sometimes called valley networks, these channels closely resemble streams in drainage basins on the Earth. The channels are branched (dendritic). However, branches are typically shorter on Mars than on the Earth.  Also, most channels do not exhibit a high branching density. But, in some places the stream branches are, in fact, as dense as some on Earth. Many look as if they were made with precipitation. Further support for abundant water flow, came from a research team that developed a computer program to look for valleys made by streams found that the stream networks were much longer than previous thought (2.3 times longer) and that they were much denser. Valleys were especially dense in northern Terra Cimmeria and the Margaritifer Terra. There results suggest that precipitation may have caused them.  
Warrego Valles system as seen by the Thermal Emission Imaging System on the Mars Odyssey spacecraft
Channels displaying curves, wide meanders, oxbow lakes, and wide meanders are similar to those on Earth. Many channels end in low areas such as craters. At times, deltas form where the stream enters a crater; they look like a stream entering a lake. Some small streams are found on valley floors. Stream channels on valley floors imply more than one episode of flow. 
Even though some channels go for relative short distances, some may run for hundreds or thousands of kilometers. One long system of lakes and rivers may reach from the far south to the far north.    In a study released in 2018, researchers found 34 palelakes and associated channels in the northeastern Hellas Basin. Because some were close to the Hadriacus volcano, some channels may have been created by hydrothermal systems; thereby allowing ice to melt. A number look as if they were formed from precipitation, others from groundwater.  
Was Mars too cold for running water?
It seems that these valley networks happened in the past when Mars was much warmer and wetter. But, climate models all say that Mars was always too cold to have much liquid water. The sun is too far away. It likely did not give off as much light energy in the past.   Another factor that could still have made the climate warmer is that the atmosphere may have been much thicker in the past and could have contained greenhouse gases like carbon dioxide. However, if this were the case, carbon dioxide would have ended up in large deposits of carbonate rocks such as limestone. Despite looking with instruments designed to detect carbonates, scientists have found very little.  They do exist in tiny areas, have been found in meteorites that came from Mars, and have been found by landers, but there just does not seem to be enough to say that Mars once had a thick carbon dioxide atmosphere.      Some researchers have proposed that other greenhouse gases may have been involved.  So we are left with what appears to be certain proof that Mars had great amounts of liquid water—somehow channels were made. On the other hand, we do not know how the climate could have ever supported very much liquid water. Nevertheless, scientists have suggested many ways for channels to be created. We must keep in mind that the planet does not have to that warmed to 32 degrees F for running water to exist because water on Mars would likely contain dissolved minerals that would lower its freezing point. Also, water may have collected in vast aquifers under the ground and released at different times by things such as heating from magma moving underground or by impacts of asteroids. After large impacts, the nearby area might be warm enough, long enough for water to erode channels.        It has even been suggested that the weather after a big impact may be changed enough to generate rainfall.   Some researchers think that streams may have existed under thick ice sheets.       As of today, we just do not have a definite answer.
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- Head, J., et al. 2023. GEOLOGICAL AND CLIMATE HISTORY OF MARS: IDENTIFICATION OF POTENTIAL WARM AND
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- Water on Mars - James Secosky - 2021 Mars Society Virtual Convention -- Tells where water was and where ice is today on Mars (34 minutes)
- https://mail.google.com/mail/u/0/?tab=wm&pli=1#inbox/FMfcgzGrbHtSWzJjdRzftxgXCrbxXNnK Water on Mars - A Literature Review" by Mohammad Nazari-Sharabian