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During an ice age, would it be possible for a great lake to be frozen while a relatively nearby river was still running? To help illustrate my point:

Would it be possible for Lake Michigan (or parts of it) to be frozen up to ten meters deep? All the while the Missouri River was still running around Kansas City? Or would all surrounding bodies of water necessarily be frozen solid?

Are such varying temperatures and conditions feasible in any way? What should be taken into account?

Edit 1: Rephrased.

Edit 2: While the question's technically answered, further insight is much appreciated.

Edit 3: Clarification.

Sure, and it did. While there was no Lake Michigan during the Last Glacial Maximum, the Laurentide Ice Sheet was up to a 1500 meters or more thick around the Chicago area, while it never reached as far south as Kansas City, which means rivers would be running during the summer. A sufficiently large river could run al year (albeit frozen over).

I think I can realistically say that the Glacial Ice was, in fact far far deeper that a handful of meters. Most estimates range from the mile-thick to only a couple of thousand meters. In most cases, it is considered that the Missouri river's current location is a direct result of the glaciers depositing earth, rocks, etc at the terminal edge. Prior to the Ice Ages, it is thought that there simply were no 'great lakes', they were scraped from the earth by ice over long periods of time.

It sort of depends. Rivers rarely (if ever) have a single source for their headwaters. Rivers are a collection of hundreds of smaller tributaries.

Sealing a single source, even a major one in ice would certainly reduce the flow of water downstream, but unless you remove the majority it will still flow to some degree.

So the real question I think we need to ask is, what all is frozen? Once you define that I think you will be able to answer it yourself.

A few things to consider:

• Is the glacial area spreading or retreating?
  
  
  • If it is expanding you can expect the flow of the river to continue to dwindle
  
  
  • If it is retreating (end of the ice age) you'd likely see larger flows.
  
  
  • If its just sort of stable the edges of the glaciers will melt, providing a regular flow, probably heavier in the summer months and lower in the winter months...possibly turning off completely in the winter.