Water Absorption and Heating from Sunlight

[chem geek]

I created a rough spreadsheet (here) to calculate the amount of heating of pool water from sunlight. The absorption spectrum of water is shown in this post and the spectrum of sunlight at the surface of the Earth is described here (with averages computed in a spreadsheet here). The amount of absorption after traveling various depths is as follows:

1 inch -- 24%
1 foot -- 39%
3 feet -- 48%
6 feet -- 54%
12 feet -- 61%
16 feet -- 63.7%
17 feet -- 64.4%

You can see that about 1/4 of sunlight is absorbed within the first inch of water and about 40% in the first foot, but this is mostly infrared radiation so you don't see it (about half of solar energy at the Earth's surface is infrared and half is visible light plus some UV). Nevertheless, it explains why the surface of the water can be so much warmer than deeper water unless the circulation is very good. The sunlight that is absorbed after the first foot is more in the red (and some green) which is part of the reason why pool water has a cyan-blue color.

If I use 85% reflection (15% absorption) for white plaster (see this link which gives 91% but that's bright new plaster), then this implies an absorption in the shallow end with 3 feet of water (with reflection and double path length) of 1-(1-0.54)*0.85 = 61% while the deep end of 6 feet is 1-(1-0.61)*0.85 = 67% absorption. So around 64% of sunlight energy gets absorbed by a white plaster pool to heat it. If a pool had a darker bottom, then even more would be absorbed. [EDIT] Note that actual absorption will be higher due to diffuse reflection which will generally increase path lengths (so closer to 64% absorption in water which with 85% reflection would be 69%) and add additional absorptive reflections (two 85% reflections with my original calculation would get to 69% and combining the longer path length effect would get to 74%). Some assume overall absorption to be around 80%.[END-EDIT]

During the peak of summer with the sun nearly directly overhead at solar noon, the amount of power is around 1000 Watts per square meter which is 860,421 calories per hour per square meter. If the average depth is 4.5 feet, that's 1.37 meters so the rate of heating of 1.37 cubic meters or 1370 liters is 66% * 860,421 / (1370 * 1000 ml/l) = 0.41ºC per hour or a heating of pool water by the sun at the rate of 0.75ºF per hour. Of course, the pool can get cooled by evaporation (more in dry climates) and if the air is cool and there is wind then one doesn't usually see this amount of temperature rise. Use of a clear (or light clear blue) solar cover will cut down evaporation, shield from wind, and maximize heating even during the day.

Black mat unglazed plastic solar panels are around 80% efficient (i.e. they transfer 80% of the sun's energy into heating pool water) with no temperature difference between the air and water or with a small difference and minimal wind. If one had solar panels with the same amount of area as the pool surface, then this would be produce a temperature increase of around 0.9ºF per hour at peak solar noon. A cloudy/overcast (but not really dark) day has roughly 1/3rd the solar power of a sunny day -- on the order of 300 Watts per square meter though this varies a lot on the thickness of the clouds. Since the clouds are water vapor, they absorb more of the infrared which means the pool surface heating effect on a cloudy/overcast day will be negligible though overall heating will still occur at a around 0.2ºF per hour.

There are some websites that claim that evacuated tube solar panels are more efficient, but on clear sunny days they are not. I'll write more about various solar panel types (unglazed black plastic, glazed flat panel, evacuated tube) in another thread (here).

Richard

 

[amjohn]

We live in a "high sun" area, and can see as much as 5 degrees fluctuation in a day on the pool, particularly this time of the year with lows in the 50s and breezy at night and highs in the 80s during the day.
I look forward to more info about solar panels. It will start our season earlier and make it last longer, and not have to wait all day for the water to warm up on its own after a cool night. I am using a clear solar blanket already, which we can definitely see that it is keeping the temp up at night (it would really fall at night if we did not have it).
We are looking at design possibilities now to install this winter for next year. We have lots of ground area, full sun, and are both structural engineers, so we could build ours from scratch if we can figure out how, or will use one of the kits. Trying to figure out the difference among the kits is tough- they all claim marvelous things, but do not give much hard info. Thanks for your attention to detail.

 

[Boudreaux]

I live in the the DFW area and have been thinking about a solar cover for our pool we recently built. My current high water temperature for today is 81. Does any in my area have any experience with the number of degrees a solar cover will raise the temperature?

 

[amjohn]

My water is 85 degrees today (according to my not so accurate thermometer. It might be more like 83, but still not bad). We just got out of the pool a few minutes ago- it was a little coolish in the north wind, but really refreshing. I am about 40 miles east of you, and our temps have been about 5-8 degrees cooler than what the news reports for DFW airport. The water never got below 80 degrees this last week, even with several nights in a row of low 50's with only daytime highs of 70's. The lowest was Thursday, when it was cloudy all day here, so we did not get much sun. I am amazed by how much the pool temp fluctuates between night and day. Even with the solar cover, it will be about 5 degrees difference between morning and afternoon. The big advantage has been much less heat loss at night- we have had two nights that it has been around 50 degrees air temp, yet we are still swimable with the warm (85 degree) air temps today. Several of my friends with AGP are down in the mid to lower 70s in water temp without a solar cover.
We have a clear one- I just bought that type by accident, but it seems to gain the most warmth from day time sun, and still limit the night time heat loss. I leave it on all the time- only take it off to swim and clean the pool. It also helps to keep dirt, leaves, pollen controlled and I have less evaporation in the dry breezy weather we are having right now.
An in ground pool would probably have different results in temp- less fluctuation I would think.
I cannot wait until we get a solar heater- with as much sun as we get here it should be really pleasant in the evening- would have been great to be out in warm water on these full harvest moon nights.

 

[chem geek]

Your experience is pretty typical of what I've read from others. We have an opaque electric safety cover and it seems to be about half as insulating as a typical bubble-type cover. Our pool ends up around 88-90ºF at the end of the day, but loses 3ºF at night when the low is around 55ºF and 4ºF when the low is around 50ºF. Basically, your pool water temperature will stabilize when the heat gained during the day equals the heat lost at night and you'll bounce between two temps with the low sometime in the morning and the high sometime in the late afternoon to early evening.

It's easy to calculate the heat loss due to evaporation. Though the rate of evaporation varies a lot (see this link) a not atypical high evaporation rate of 1/4" per day is a volume of water over a square meter of surface area of 0.00635 cubic meters or 6350 ml. The heat of evaporation is 2428 J/g (at 30ºC or 86ºF) or about 2428 J/ml. So that's 2428*6350 = 15,417,800 Joules or 4.3 kWh loss per day per square meter. Given that over that same square meter during peak noontime sun is 1 kW, this means that high evaporation counteracts about 4.3 hours of peak noontime sun. So, 1/4" of evaporation will lower a 4.5 foot average pool depth temp by 4.9ºF. This link will tell you the solar insolation (solar energy at the surface of the Earth) per area of flat horizontal surface. In a place like Arizona, the peak in July is around 7.8 kWh/m²/d (5.3ºF temp rise in white plaster pool) while in New York in June it's around 5.7 kWh/m²/d (3.9ºF temp rise in white plaster pool). So even with evaporation there may be a net gain during the day, but there is significant loss at night from convection in addition to evaporation. Evaporation is greatest when the humidity is low and is lowest when the humidity is high. However, it is also a function of temperature with the net result being that the evaporation rate is roughly the same during the day and at night since the higher relative humidity at night is offset by the lower temperature (i.e. the partial vapor pressure is roughly the same in both cases).

Studies described here indicate that heat loss is 56% by evaporation, 26% by radiation, and 18% by convection.

A pool cover, of any type, will virtually eliminate evaporation. If the pool cover is relatively transparent to infrared and most visible light, then the sun will significantly heat the pool during the day. Ideally, it should be relatively opaque to UV so that chlorine loss is minimized. If the pool cover is relatively well-insulating, such as a bubble-type, then it will also cut down on heat loss from convection at night (as well as during windy cool days). An opaque electric safety cover (such as what I have) may be convenient, but it is not as energy efficient as a clear bubble cover as it loses more heat at night and does not allow the sun to heat the pool during the day.

Richard

 

[mas985]

Thanks for doing the research on this Richard. This is very useful information. Given that I have an 8.5' deep end, I would be interested in the absorption for a round trip of 17'.

I am not clear on your calculation for absorption. I would have thought that at the 3' shallow end the absorption would be the 6' absorption, 54% times 92% reflection or ~50% and the deep end would be the 12' absorption, 61% * 92% or 56%. Or did I not read your post correctly?

Anyway, if I assume that the 60% number is correct and I use the July 21st data from this site, a 550 sq-ft pool surface, 21000 gallons, I get about a 4.8 degree temp rise for the pool. Normally I get about 3-4 degrees in temp rise without solar but I have seen 5 degree days.

Doing a similar calc for my solar, I get about a 5 degree rise per day for a total of 9.8 degrees which is pretty close to the maximum that I have ever seen (~10 degrees). Normally, I can get about an 8 degree rise on most days which would be about 20% lost during the day which isn't too bad. But without a cover, overnight I loose about 6 degrees which is close to 75% of the gain.

 

[gtm]

I am not clear on your calculation for absorption. I would have thought that at the 3' shallow end the absorption would be the 6' absorption, 54% times 92% reflection or ~50% and the deep end would be the 12' absorption, 61% * 92% or 56%. Or did I not read your post correctly?

The 58% number Richard gives for the 3' end is 54% from the 6' total water path plus 4% that is absorbed by the plaster at the bottom. You get that 4% number as 8% of what reaches the bottom. What reaches the bottom is 52% (i.e. what is NOT absorbed on the 3' downward path), so you take 8% of 52%, which is roughly 4%.

I hope jumping in here is not ill-mannered, but since you were nice enough to answer my plumbing question, I thought I'd try to return the favor. But if I've gotten it wrong, or done wrong, I will submit to whatever form of flogging you and Richard deem most appropriate.

Cheers, Gary

 

[mas985]

That makes sense although I would argue that not all of the heat absorbed by the plaster is returned to the water either. But probably most is returned to the water so that is a good approximation.

[EDIT] Actually, I think this is how Richard got to the answer. Assuming a full plane reflection at the bottom of the pool, the total transmission through the pool water of 6' depth (12' round trip) would be:

(1 - 0.61) * 0.92 = 0.36 or 64% absorption.

for the three foot depth it would be:

(1 - 0.54) * 0.92 = 0.42 or 58% absorption

 

[chem geek]

Mark,

You got it right. Because water absorbs different wavelengths at different rates you have to do the calculation wavelength by wavelength (in small ranges) and then sum to get a net result. My spreadsheet does that and gives the 1 inch to 12 feet numbers I listed in the first post. The assumption for the white plaster was that the 92% reflectance was broad spectrum and equal across all wavelengths (or in practical terms, for those wavelengths that make it to the pool bottom so mostly visible and not much infrared). That means that the reflectance is a factor that affects all wavelength calculations equally so can be factored out and applied to the non-reflectance sum.

Gary's method is very interesting, but let's see if it gives the same result. The 3' path absorption is 47.79% while the 6' path absorption is 54.08%. So comparing the two methods we have:

1 - (1 - 0.5408)*0.92 = 57.75%

54.08% + (1 - 0.4779)*(1 - 0.92) = 58.26%

The reason for the difference is the fact that the first term doesn't take into account what happens from the reflection so is too high for what occurs on the return path. Let's take an extreme example with no wavelength dependence. Let's say that absorption in the water is 50% for every 3 feet and that there is 50% reflectance of the bottom surface. After 3 feet we are at 50% left, then we reflect 50% so 50%*50%=25% left, then we lose another 50% on the return 3 feet so that's 50%*25%=12.5%. We could alternatively look at what happens after 6 feet without reflection which is 50%*50%=25% left and then apply the reflection of 50% to get 50%*25%=12.5% which is the same correct number.

However, using Gary's method would have us add the absorption over 6 feet with no reflection, which is 100%-25%=75% to the (correct) amount absorbed upon reflection which is 50%*50%=25%, but the sum of these is 100% which is too high. The problem is that the 75% number is the product of two losses, each 50%, but the second loss is not really 50% because reflection has reduced what is getting returned and you can't just add what was absorbed on reflection to figure that out. The first 3 feet loses 50% and then with no reflection, the return 3 feet loses 25% through absorption while with reflection what is actually lost is 12.5% or half as much. The amount lost in reflection is 25% so the sum is 50+25+12.5=87.5%. So the true loss from the first 3 feet and the second 3 feet is 62.5%, not the 75% that a non-reflected path would give.

Richard

 

[gtm]

Richard,

You're absolutely right. I somehow lost out the decrease in the transmission after the reflection at the bottom of the pool, which is where the additional factor of 0.92 comes from. I guess I need to find the smiley faced thingie that shows egg on the face.

In my own defense, I thought that showing the absorption in each of the 3 paths (downward, plaster, upward) might be be illuminating, but obviously I was careless with the upward leg. Sorry to waste your time finding my mistake.

Probably should've just kept quiet. Julie says that's generally my best option.

Gary

 

[chem geek]

Gary,

Not a problem at all -- don't worry about it. If you look back through my posts, you'll find many where I make a mistake. Most of the time, I reread the posts and catch the mistake and correct it (using [EDIT] [END-EDIT] if some time has past), but none of us is perfect (my wife will certainly attest to that) and I'm sure I've got some mistakes still out there. One of the main reasons I post technical details (in The Deep End) is so that others can review what I've done and catch mistakes I may have made. For the longest time, I was using ppm HOCl directly not realizing that all chlorine measurements were done as ppm Cl₂ equivalent.

Richard

 

[gtm]

Richard,

Thank you. I was raised in Charleston, SC, where you can be forgiven for major felonies, but never for bad manners. You would do very well there. Meaning that your response was very, very gracious. I wish the reviewers for my other papers were so kind.

I don't understand all the chemsitry, but am okay with some of the physics, which is why I chimed in (badly!) on this one. I've read just about everything with your name on it (here and on the other forum). Understood about half. The bottom line, though, is that I want the baseball jersey with your name on the back.

If the baseball jersey reference seems odd, let me explain that I'm in St. Pete (Florida), the Rays are about to win the AL East, and the 9-year old and I watch the games on TV in our Evan Longoria jerseys. Can't afford the "live" seats.

Thanks again, Gary

P.S. Do you use Matlab at all for your calculations? I might be able to help with some of the programs, but I'm hopeless with spreadsheets.

 

[chem geek]

I've used Matlab at work in the past but I don't use it anymore (I have a Mac and they stopped Mac support a while ago). I've been using spreadsheets for most of the pool water chemistry/physics stuff. I'm keeping around Microsoft Excel 2004 since Microsoft dropped support for macros in Excel 2008 for Mac (though will be putting it back in since so many people screamed about that). I like the spreadsheets since they are portable and most everyone has Excel so can use it (not that many use my spreadsheets, but it's better than a proprietary program for someone else to review the calculations).

 

[gtm]

I understand. The Mathworks also eliminated support for SGI systems awhile back, which hurt some of my colleagues here. Fortunately they still support the Linux systems that comprise my entire lab, but who knows what the future holds.

I guess it doesn't really matter if we can exchange actual code. If you'd like a reality check on a calculation and think I might be able to help, then please let me know. I'd be happy to help. I'd have to do an awful lot of calculating to pay back what I've already learned here.

Cheers, Gary

 

[nedleigh]

Here’s a question for you: what’s the most efficient way to add some BTU to my pool using sunshine/solar? I’m talking about a down and and dirty, flat-out cheap and easy method that I can use temporarily, until I can afford to install the solar panels. I have three scenarios in mind and was wondering what the consensus opinion would be on which would be the best.

1) Lay black plastic sheeting on top of the pool cover. We have an Aquamatic opaque automatic pool cover (light green in color, so not much solar gain there), that cuts down on evaporation, and prevents some heat loss at night, though obviously not as much as an insulated solar cover. My thinking is that the black plastic will absorb way more solar energy and will transmit it to the pool water through the pool cover, since the water is way more conductive than air.

2) Lay black plastic sheeting on the bottom of the pool and open the cover during the day. The pool plaster is Tahoe Blue, which reads as sort of medium gray and is darker than the pool cover. Combined with the solar absorption that occurs directly into the water, as mentioned at the top of this thread, I’m thinking that this method is probably more effective. I read the post about evaporative heat loss, which would obviously cut down on the total heat gain, but if I’m reading it correctly, the solar heat gain is generally more than the evaporative heat loss. I have a feeling that trying to spread out the plastic neatly on the floor of the pool may be a big pain, but that’s just a guess at the moment……

3) Lay 4” black ABS pipe on the floor of the pool – seems 10’ or 12’ lengths in groups of three or so could be a manageable grouping. One advantage of laying it on the south facing slope of the pool floor would be that it might create some thermo siphoning. A downside would be the cost to achieve a significant size would start to add up pretty quickly….

Since the devil is always in the details, let me give you some information to fill out the picture:
- 18’ x 38’ IG gunite & plaster, 3’6” at both ends, sloping down to 5’6” in the middle (works out to approx. 21,000 gals after subtracting for beach steps);
- current water temp is around 76 and would like to get up to 82 – 84 range;
- air temp is currently ranging from lo of 65 to hi around 78, location is Kauai, Hawaii;
- weather has been a bit spotty, with a fair amount of cloudy days and some good sunny days, wind has been calm to breezy – the big rain last week knocked the water temp down to 73 for a few days;
- currently getting approx. 25 – 30% shaded by palm trees during mid-day;

I had the plumber stub out the piping over to where the future solar panels will go onto the roof of the house, but that will have to wait a little while until the budget recovers. You guys are way ahead of me with the math skills, but I’m just wondering if you have a quick opinion as to whether any of these schemes are worth bothering with?

Ned

 

[chem geek]

Option #1 is definitely NOT the way to go. Though the black plastic will absorb much of the sun's energy (perhaps 80-90%, but probably not much more than that), if it were to efficiently transfer that to the pool water then by definition it will be conductive to heat and that allows heat to escape from the pool just as easily. There is no such thing as a diode (one-way transfer) for heat -- if a material conducts heat in one direction, it conducts it equally well in the other; when one insulates, one does so in both directions (at least for thermal conductivity). The main advantage of option #1 is eliminating heat loss from evaporation.

Option #2 is also not the way to go (at least not by itself), though is better than option #1 unless it is windy with air cooler than the water. Having the black at the bottom of the pool would raise the absoprtion of sunlight from around 60% to perhaps the 90% range. The absorbed heat would mostly get transferred to the water, especially if there is circulation (say from a floor drain that was kept uncovered). However, without a cover on top, there would be heat loss from evaporation, conduction/convection, especially if there is wind and the air is dry and/or cool.

I don't understand option #3 very well in terms of how it's any better than option #2 unless there isn't much circulation of water at the pool bottom and you're hoping to have heated water rise upward through the pipe.

The bottom line is that none of these options is good. If you want to do something that is relatively inexpensive, get yourself a clear solar pool cover that has reasonable insulating properties but lets sunlight through (it can be opaque to UV, but should let most visible and infrared light through, if possible). It can be a less expensive cover if you aren't going to be keeping it since in that case it doesn't have to last as long. If you wanted to do option #2 along with this, then that would add to the efficiency. Sunlight would pass through the cover and be absorbed by the water and by the black mat. Heat would be retained in the pool. This is the best you can do for the pool's surface area.

Richard

 

[nedleigh]

Hi Richard –

Very interesting observations! Your theory about option #1 (black plastic on cover) raises some intriguing questions. Given that there is no such thing as a heat ‘diode’ (if only there were!), that seems to suggest that the black plastic would somehow make the pool cover material MORE conductive to heat loss than it already is (?!?), presumably through radiation and or convection, since the evaporation is limited by the cover itself. I get the theory, but I’m having trouble wrapping my brain around the real world implication….

I wonder what would happen if the black plastic was on in the day time and taken off at night? Under that scenario, wouldn’t you get an overall solar boost (presumably without the evaporative loss factor)? My other thought is that since heat rises, the upper layer of water in contact with the cover would be warmer and therefore less receptive to more heat being added? (that concept is more than a little fuzzy, given my pitiful understanding of physics and thermodynamics) We’re currently running the pump for about 8 hrs during the daytime, so there is some circulation and mixing of the heat layers.

Option #2 (black plastic on bottom) seems like it would be an overall wash in terms of solar gain – the added absorption rate would be neutralized by the evaporative loss factor. I think your concept of the clear insulating cover with black on the pool bottom is probably the best in terms of efficiency, but it’s also the maximum amount of hassle (since I’d have to wrestle with the thermal cover whenever anyone wanted to swim)

Option #3 (black ABS tubes on the bottom) is effectively the same as #2, but I was trying to think of solutions that would be easy to put in and out and be somewhat aesthetically acceptable to my wife. The thermo siphoning (if it happened at all) was just something that I noticed in another post. I don’t think that it would add anything in terms of efficiency.

I think you’re right that none of these hare brained ideas offer much benefit, so it’s probably better to just wait for the solar panels….. Thanks for the reply!

Ned

 

[chem geek]

Ned,

No, the black plastic does not make it more conductive. Not being a "diode" just means that whatever insulating or conductive properties it has operate in both directions -- transferring hotter temperatures from the sun absorbing side to the water or transferring warmer water temperatures to the cooler air when the sun isn't shining (such as at night). In other words, to be efficient at transferring heat during the day implies that it will be inefficient in trying to stop heat loss (from conduction) at night. The cover would virtually eliminate evaporation so does have that benefit, but it doesn't need to be black in order to do that. The problem with a black top is that any warming of the water is at the surface so unless you've got really good circulation near that surface you don't have very efficient heat transfer, and hotter water tends to rise anyway (as you point out) so it would be better to do more heating from the bottom of the pool.

Having the black cover on during the day would be OK, but you'd have to put on a very insulating cover at night to keep the heat in the pool. Sounds like a real pain when all you really need is a clear well insulating cover. That way, the sunlight passes through, gets absorbed in the water, and then that heat is trapped by the cover. Essentially, the cover acts like a greenhouse, letting light wavelengths through, but not letting heat escape (at least not quickly).

You are probably going to want a solar cover anyway if you want to maximize your heating, even after you get your solar system. So getting a clear bubble-type well-insulating cover would make sense. It essentially turns your entire pool into a reasonable solar collector -- even if you have white plaster, it's at 60% efficiency (ignoring the loss through the cover which I don't know). In my own pool, I have an opaque electric safety cover which is for convenience, but having the cover on at night cuts the heat loss in half so helps us keep the temperature hotter with the solar. With a bubble-type cover, the heat loss would be cut in half again (about 1/4th the loss without a cover). It all depends on how hot you want to get your pool, but if you want it really warm and have nights that are quite a bit cooler than your water (say, more than 20F degrees), then you're really going to want a pool cover, at least at night.

Richard

 

[JohnT]

I'll throw in my 2 cents here. My son did a science fair project this summer on pool covers. Several kind members here sent him samples of various types of covers for testing. I believe our experiment was flawed in that the test vessels weren't large enough and weren't in the ground, and the buckets didn't have circulation, which might be an issue, but I think we got some useful information. We are going to try again next summer with an improved setup.

What the experiments seemed to show was that any type of cover being on all day is better than no cover. We had to simulate a black/silver cover, as we didn't have a sample of that, but it was a rare day that the control (uncovered bucket) saw a larger heat gain on a sunny day than the test buckets.

We took overnight pool temperatures as a "control-control" to try to see if what we were seeing had real world usefulness, and we saw that windy nights resulted in better heat retention in our inground pool with the cover on than we saw in the buckets.

My gut feeling is that even though some covers reduce the warming from the sun, they also reduce the heat loss to the air if wind is present by a good chunk as well. This may result in less heat energy entering the pool, but it results in a larger net gain.

We took temperature readings every 5 minutes, and it was very interesting to see the effects of a front moving in on the temperature of the control bucket. Very shortly after the clouds (and usually wind) rolled in, the uncovered bucket began cooling far more quickly than any of the covered buckets.

We'll see if an improved experiment produces more concrete results.