# Is it possible to find the temperature at the center of a lake if you know the temperature of the wa **URL:** \ **Category:** Factual Questions\ **Created:** [October 18, 2016, 12:23pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937 "2016-10-18T12:23:30Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![joeytk7](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@joeytk7](https://boards.straightdope.com/u/joeytk7)\ **Post date:** [October 18, 2016, 12:23pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/1 "2016-10-18T12:23:30Z")
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? ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [October 18, 2016, 12:32pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/2 "2016-10-18T12:32:39Z")
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. ---
**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\ **Post date:** [October 18, 2016, 1:11pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/3 "2016-10-18T13:11:55Z")
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](http://www.coastwatch.msu.edu/michigan/m3.html) 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](http://www.miseagrant.umich.edu/lessons/files/2013/05/13-407-Water-Temperature-Illustration.jpg) in a large lake, which helps illustrate a few variables. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [October 18, 2016, 4:23pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/4 "2016-10-18T16:23:46Z")
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. ---
**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\ **Post date:** [October 18, 2016, 4:40pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/5 "2016-10-18T16:40:12Z")
Corrected link, sorry: [Water Temperature](http://www.miseagrant.umich.edu/lessons/files/2013/05/13-407-Water-Temperature-Illustration.jpg) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 18, 2016, 11:20pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/6 "2016-10-18T23:20:29Z")
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. ---
**Author:** ![snfaulkner](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/snfaulkner/32/433_2.png) [@snfaulkner](https://boards.straightdope.com/u/snfaulkner)\ **Post date:** [October 18, 2016, 11:39pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/7 "2016-10-18T23:39:13Z")
> [@Chronos](#): > > 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. 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? ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [October 19, 2016, 1:12am UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/8 "2016-10-19T01:12:53Z")
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. 🙂 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 19, 2016, 12:57pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/9 "2016-10-19T12:57:44Z")
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. ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [October 19, 2016, 1:50pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/10 "2016-10-19T13:50:32Z")
> [@snfaulkner](#): > > 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? 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. > [@Chronos](#): > > 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 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. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [October 19, 2016, 2:26pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/11 "2016-10-19T14:26:40Z")
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 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 19, 2016, 6:44pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/12 "2016-10-19T18:44:34Z")
> [@](#): > > Except Chronos already gave the counter-example to that, with sun shining on the center of the pond but not the shore. 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. ---
**Author:** ![joeytk7](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@joeytk7](https://boards.straightdope.com/u/joeytk7)\ **Post date:** [October 24, 2016, 1:47pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/13 "2016-10-24T13:47:30Z")
the lake i am referring to is a small lake with the deepest point around 14 feet and only around 80 acres in area. ---
**Author:** ![joeytk7](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@joeytk7](https://boards.straightdope.com/u/joeytk7)\ **Post date:** [October 24, 2016, 1:51pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/14 "2016-10-24T13:51:20Z")
> [@Qadgop\_the\_Mercotan](#): > > 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](http://www.coastwatch.msu.edu/michigan/m3.html) 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](http://www.miseagrant.umich.edu/lessons/files/2013/05/13-407-Water-Temperature-Illustration.jpg) in a large lake, which helps illustrate a few variables. the lake i am referring to is a small lake with the deepest point around 14 feet and only around 80 acres in area. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [October 24, 2016, 2:07pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/15 "2016-10-24T14:07:05Z")
I guess it depends on how deep and large the lake is, but I can’t see that info in the thread anywhere. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [October 24, 2016, 2:11pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/16 "2016-10-24T14:11:52Z")
> [@joeytk7](#): > > 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? What other factors, specifically? ---
**Author:** ![Enginerd](https://avatars.discourse-cdn.com/v4/letter/e/bcef8e/32.png) [@Enginerd](https://boards.straightdope.com/u/Enginerd)\ **Post date:** [October 24, 2016, 7:20pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/17 "2016-10-24T19:20:05Z")
> [@Chronos](#): > > 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. never mind - misread the post. update coming. ---
**Author:** ![Enginerd](https://avatars.discourse-cdn.com/v4/letter/e/bcef8e/32.png) [@Enginerd](https://boards.straightdope.com/u/Enginerd)\ **Post date:** [October 24, 2016, 7:29pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/18 "2016-10-24T19:29:02Z")
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. ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [October 25, 2016, 3:24pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/19 "2016-10-25T15:24:23Z")
> [@Enginerd](#): > > At the lake bed, you have heat conduction between the water and the bed material 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). ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [October 25, 2016, 5:04pm UTC](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937/20 "2016-10-25T17:04:02Z")
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. [Next page](https://boards.straightdope.com/t/is-it-possible-to-find-the-temperature-at-the-center-of-a-lake-if-you-know-the-temperature-of-the-wa/768937.md?page=2)