Is it possible to find the temperature at the center of a lake if you know the temperature of the water on the shore line and other factors?
Is it possible to find the temperature at the center of a lake if you know the temperature of the wa
I’m going to venture a “no” here … if I understand your question then just knowing the temperature at one point in a lake won’t tell you very much about the temperature someplace else in the lake.
You’d need to know a lot of “other factors”.
I live on Lake Michigan. The surface temperatures alone are highly variable all over the lake, with frequent ranges of over 30 degrees Fahrenheit. Here’s a surface temperature map showing just that.
And given that the bottom of the lake varies from less than 100 feet deep to over 900 feet in different places, you’d be hard pressed to figure out what’s going on at the bottom at any one spot without measurements.
Here’s a nice little graphic about Water Temperature in a large lake, which helps illustrate a few variables.
The OP isn’t clear on “center”. Does it mean the top surface in the middle or halfway down in the middle?
The keyword is uniformity". For a very small body of water on a calm day, yadda-yadda-yadda, you might be able to make a guesstimate for the temp near the surface in the middle.
But vertical differences in temperature are widely variable based on each body of water, time of year, etc. Some lakes go thru biannual turnovers. No way can you make semi-reasonable assumptions and get anything meaningful.
Corrected link, sorry:
Right after you take all of your measurements, I throw a chunk of sodium into the middle of the lake. Poof, now the center is a lot hotter than you would have calculated it to be.
Or, if you think that’s cheating, suppose that there’s cloud cover over most of the lake, with just one clear sunny spot right in the middle.
That seems like that’s be a bit of, what they call in the industry, a “dick move”. 
Do you often follow around measurement takers with a jar of sodium?
Be careful; **Chronos **threw a black hole at the last guy dissing. The last thing we all heard was a very red-shifted Aiiiiiyyyyyyyyy! as he spiraled in. 
In more seriousness, this is what’s called a “boundary value problem”: In many cases, if you know relevant information for the boundary of a region, you can determine the value for all points within the region. But you don’t have enough information, here. In principle, I think that if you had the temperature at all points on the shore for all time, that’d be enough to get the temperature everywhere else for all time, but in practice, even if you had all that information, I suspect that you’d be killed by measurement noise.
Dude, you don’t even know. Seriously, it’s like step three on the measurement taker’s checklist now: Check for Chronos and his frickin’ sodium first.
Except Chronos already gave the counter-example to that, with sun shining on the center of the pond but not the shore. Now if you knew the temperature along the shore and all of the bottom and top of the pond for sufficiently far back, then you’d in theory be able to know the temperature of the center.
In the real world, for any particular pond, if you knew roughly the size and shape of the pond, the flows in and out, and the typical yearly climate, and had some shoreline+center temperature data to calibrate with, you could build a model that, with the shoreline temp, the weather for the last week or two, and time of year, you could make a pretty good prediction of the temperature at the center of the lake.
A good hydrologist could even make a decent guess without the calibration data, just knowing size, location, flows in and out, etc. But both the guess and the model aren’t guaranteed, and have limited precision in any case.
However … we do know the temperature at the very deepest parts of the oceans is 4ºC … that’s the temperature water is at it’s highest density …
ETA: In natural settings I should qualify … ice will take on a crystal structure that’s denser, but at about 250 atms of pressure
That’s why you need the data for all time: The extra heat from the sun shining in the middle (or even from my sodium bomb) will eventually diffuse out to the edge and be detected, and with precise enough data you could in principle deduce the details of the heat source.
the lake i am referring to is a small lake with the deepest point around 14 feet and only around 80 acres in area.
the lake i am referring to is a small lake with the deepest point around 14 feet and only around 80 acres in area.
I guess it depends on how deep and large the lake is, but I can’t see that info in the thread anywhere.
What other factors, specifically?
never mind - misread the post. update coming.
You need to have more than just the shoreline temperature for all time. In a lake that size, the greatest heat flux is going to be at the water surface - this is a combination of latent heat flux (evaporation) and sensible heat flux (heat conduction between the air and the water). You also have longwave radiative heat fluxes and shortwave solar radiation, which are attenuated at different rates in the water column. At the lake bed, you have heat conduction between the water and the bed material, and you may or may not have a stratified lake body - if it’s stratified, you have a warm layer on top and a cool layer on below it, and you have to then figure out the distribution of heat within the lake. To model this mathematically, you have to start with an initial temperature distribution in both the horizontal and vertical dimensions, known lakebed temperatures for all time, and at least air temperature, relative humidity, wind speed, and shortwave solar radiation for all times you’re concerned with.
Or you could get a boat and a thermometer. It’s both more practical and more fun.
And don’t forget water physically moving into/out of groundwater. So you also really need to know groundwater flow in the area. (and surface flows, too of course).
This boils down to one of the “other factors” being the temperature at the center of the lake … then with shore temperature and this “other factor”, we can tell exactly what the temperature is at the center.