I wanted to see a formula for ice growth on lake...this melted my brain...

[Sundancefisher]

http://www.britannica.com/EBchecked/topic/328152/lake-ice/65643/Ice-growth


Ice growth
Rates of growth

Once an initial layer of ice has formed at the lake surface, further growth proceeds in proportion to the rate at which energy is transferred from the bottom surface of the ice layer to the air above. Because at standard atmospheric pressure the boundary between water and ice is at 0° C, the bottom surface is always at the freezing point. If there is no significant flow of heat to the ice from the water below, as is usually the case, all the heat loss through the ice cover will result in ice growth at the bottom. Heat loss through the ice takes place by conduction; designated ϕ in the figureHeat flow through an ice cover (see text). [Credits : Encyclopædia Britannica, Inc.], it is proportional to the thermal conductivity of the ice (ki) and to the temperature difference between the bottom and the top surface of the ice (Tm - Ts), and it is inversely proportional to the thickness of the ice (h). Heat loss to the air above (also designated ϕ) occurs by a variety of processes, including radiation and convection, but it may be characterized approximately by a bulk transfer coefficient (Hia) times the difference between the surface temperature of the ice and the air temperature (Ts - Ta). (In practice, the top surface of an ice layer is not at the air temperature but somewhere between the air temperature and the freezing point. The exact figures are rarely available, but fortunately the top surface temperature, Ts, is not needed for analysis.)

Assuming that the heat flow through the ice equals the heat flow from the surface of the ice to the air above, the following formula for the thickening of ice may be fashioned:

In this formula h is the thickness of the ice, Ta is the air temperature, Tm is the freezing point, k is the thermal conductivity of ice (2.24 watts per metre kelvin), ρi is the density of ice (916 kilograms per cubic metre), L is the latent heat of fusion (3.34 × 105 joules per kilogram), and t is the time since initial ice formation. The exact value of the bulk transfer coefficient (Hia) depends on the various components of the energy budget, but it usually falls between 10 and 30 watts per square metre kelvin. Higher values are associated with windy conditions and lower values with still air conditions, but, with other information unavailable, a value of 20 watts per square metre kelvin fits data on ice growth quite well. The formula is particularly useful in predicting growth when the ice cover is thin. The first growth rate of the ice cover is proportional to the time since formation; as the ice thickens, however, the top surface temperature more closely approaches the air temperature, and growth proceeds proportional to the square root of time.

If there is a snow layer on top of the ice, it will offer a resistance to the flow of heat from the bottom of the ice surface to the air above. In this case, the incremental thickening rate (that is, the incremental thickening [dh] in an incremental time period [dt]) may be predicted by the following formula:

where hi is now the ice thickness with thermal conductivity ki, and hs is the snow thickness with thermal conductivity ks. The thermal conductivity of snow depends on its density. It is greater at higher densities, ranging from about 0.1 to 0.5 watt per metre kelvin at densities of 200 to 500 kilograms per cubic metre, respectively.

[Redfrog]

:huh:

I did not know that.

[WayneChristie]

Hmmm, thanks for the headache :lol:

[Walleyes]

So what its saying is,, if its cold water freezes and ice forms from the bottom.. Hmm I have known that for my entire life and I didn't even need a P.H.D. chemistry to know it...

[altaberg]

it does make sense. It's somewhat similar to processes that happen in a snow pack which are important for avalanche predictions.

I'll try to clarify a bit.

Growth of ice depends on the transfer of energy (or "heat"). The bottom of an ice layer is always at the melting point of ice (around 0C or thereabouts, only pure water at sea level actually freezes at exactly 0C). If the top of the ice is colder you have a temperature gradient and energy will flow, in other words the water is being cooled by the transfer of heat out of it to the cold air above and this causes the ice to grow at the bottom of the ice layer.

The more the temperature gradient between the bottom of the ice and the top, the more heat will be transferred and the faster the ice will grow. Obviously, the colder at the top the bigger the temperature gradient and also the thicker the ice the less the temperature gradient.

Example, if you have -10C at the surface and the ice is 1m thick, assuming it really is 0C at the bottom of the ice layer you have a temperature gradient of 10degreeC/meter. If the ice is 2m thick you have less of a temperature gradient, teh gradient is less steep 5deg/m, if it's only 50cm thick you have twice the temperature gradient or 20deg/m. In a simple case the thickness of the ice and the temperature difference is all that matters because conductivity, density etc are constant.

(I don't think for very accurate scientific measurements the latter would actually be true across a wide temperature range. I'm pretty sure glaciologists have more complex formula because density and conductivity of ice are temperature and pressure dependent at least at extremes of both. Thankfully, this formula seems to be reasonably accurate while assuming they are constant.)

The above holds probably reasonably well on a cloudy, windless day without snow on the ice. Snow on the ice will insulate differently from ice and wind will increase heat transfer. Things probably become much more complex.

Bottom line, bottom of a ice layer is around 0C, if the top is colder ice will grow at the bottom. The thinner the ice and the bigger the temperature difference the faster the ice will grow. Snow on top will insulate more and ice will grow slower, wind on top will increase heat transfer and the ice will grow faster.

Tryng to quantify any natural process is rarely very simple, especially if trying to be very accurate.

[Redfrog]

Right that clears that up.

Now can you tell me if light is the absence of dark or is dark the absence of light?:huh:

[WayneChristie]

what that says to me is with the relatively warmer temperatures the last weeks, the warmer water temp and the cold high wind speeds this weekend, is the ice is going to get thick fast, and thats a good thing to me :D Tired of waiting for the hardwater season!!!!

[altaberg]

Right that clears that up.

Now can you tell me if light is the absence of dark or is dark the absence of light?:huh:

that's easy: dark is the absence of light, look at the universe, the night sky.

[Paul C]

Water freezes at 0 degrees and turns to liquid at the 0 degrees. This is latent which is even harder on the brain.:lol::wave::lol:

[Penner]

Right so your saying I should put 3 ice cubes in my drink instead of 2? :confused:

[rocky97]

interesting but to much to bother figuring out, there is ice when there is ice

[Reeves1]

Right so your saying I should put 3 ice cubes in my drink instead of 2? :confused:

:lol::lol::lol:

[pecker]

So what its saying is,, if its cold water freezes and ice forms from the bottom.. Hmm I have known that for my entire life and I didn't even need a P.H.D. chemistry to know it...

ice continues to form from the bottom - because its already ice on the top.:lol: :wave:

[Sundancefisher]

it does make sense. It's somewhat similar to processes that happen in a snow pack which are important for avalanche predictions.

I'll try to clarify a bit.

Growth of ice depends on the transfer of energy (or "heat"). The bottom of an ice layer is always at the melting point of ice (around 0C or thereabouts, only pure water at sea level actually freezes at exactly 0C). If the top of the ice is colder you have a temperature gradient and energy will flow, in other words the water is being cooled by the transfer of heat out of it to the cold air above and this causes the ice to grow at the bottom of the ice layer.

The more the temperature gradient between the bottom of the ice and the top, the more heat will be transferred and the faster the ice will grow. Obviously, the colder at the top the bigger the temperature gradient and also the thicker the ice the less the temperature gradient.

Example, if you have -10C at the surface and the ice is 1m thick, assuming it really is 0C at the bottom of the ice layer you have a temperature gradient of 10degreeC/meter. If the ice is 2m thick you have less of a temperature gradient, teh gradient is less steep 5deg/m, if it's only 50cm thick you have twice the temperature gradient or 20deg/m. In a simple case the thickness of the ice and the temperature difference is all that matters because conductivity, density etc are constant.

(I don't think for very accurate scientific measurements the latter would actually be true across a wide temperature range. I'm pretty sure glaciologists have more complex formula because density and conductivity of ice are temperature and pressure dependent at least at extremes of both. Thankfully, this formula seems to be reasonably accurate while assuming they are constant.)

The above holds probably reasonably well on a cloudy, windless day without snow on the ice. Snow on the ice will insulate differently from ice and wind will increase heat transfer. Things probably become much more complex.

Bottom line, bottom of a ice layer is around 0C, if the top is colder ice will grow at the bottom. The thinner the ice and the bigger the temperature difference the faster the ice will grow. Snow on top will insulate more and ice will grow slower, wind on top will increase heat transfer and the ice will grow faster.

Tryng to quantify any natural process is rarely very simple, especially if trying to be very accurate.


argggg....brain.....re.....melting....

[Sundancefisher]

what that says to me is with the relatively warmer temperatures the last weeks, the warmer water temp and the cold high wind speeds this weekend, is the ice is going to get thick fast, and thats a good thing to me :D Tired of waiting for the hardwater season!!!!

Yes...I am hoping. I will measure the ice thickness tomorrow

[pecker]

Yes...I am hoping. I will measure the ice thickness tomorrow

bring on the hardwater-PLEEASE.:cry::wave:

[DustDee]

It's too bad that the formulas didn't come through on your post, that's the interesting part. I think I remember doing some triple integrals in calculus class (computer engineering degree) that described the transfer of heat through a solid. They are pretty cool. Then we wrote a program to visually show the heat movement. Maybe I should write a program to show the heat transfer through ice!! I could show the ice growth over time! We could make it real fun and simulate a natural spring and observe how it effects the ice formation.

And by the time I was finished all that, the real ice outside will have formed sufficiently for me to go fishing!!! You know you're itchin' to get out fishin' when you start doing the math to calculate how much ice should theoretically be on your favorite lake!

[Walleyes]

ice continues to form from the bottom - because its already ice on the top.:lol: :wave:


:lol: :lol: thats a pretty cool way of looking at it...

P.S. Hey pecker quick question for yah... How many people on a football field,,, sorry man just couldn't resist...

[pecker]

:lol: :lol: thats a pretty cool way of looking at it...

P.S. Hey pecker quick question for yah... How many people on a football field,,, sorry man just couldn't resist...

OUCH- I'm going to go out and get me a 13 pack of pilsner.:( :cry:

[Sundancefisher]

looks like there is 10 -12 inches of ice on Lake Sundance now.

Hopefully they will open the lake up for perch fishing soon.

[WayneChristie]

looks like there is 10 -12 inches of ice on Lake Sundance now.

Hopefully they will open the lake up for perch fishing soon.

if you have a perch gathering I would love to come in for it. I used that 10 second method of cleaning mine today. took me a lot longer, but a sharp knife in my hands and doing anything quick just isnt going to happen :lol:

[Oilberta]

OUCH- I'm going to go out and get me a 13 pack of pilsner.:( :cry:

Isn't that called a Roughrider's dozen? ;)

[jpietrzak1979]

Wha?

[pottymouth]

Right that clears that up.

Now can you tell me if light is the absence of dark or is dark the absence of light?:huh:

That's easy dark is faster than the speed of light, cause light is always trying to catch up!!!!:lol:

[Oilberta]

13 is a Roughriders dozen! Thats how many guys they had on the field to lose the Grey cup!

[rxxxm22]

looks like there is 10 -12 inches of ice on Lake Sundance now.

Hopefully they will open the lake up for perch fishing soon.

kids are getting antzy about those perch ......ive got em all reved up .....new rods new ice hut .......they just can;t wait lol

Grampa and the Gkids

[mooseknuckle]

http://www.britannica.com/EBchecked/topic/328152/lake-ice/65643/Ice-growth


Ice growth
Rates of growth

Once an initial layer of ice has formed at the lake surface, further growth proceeds in proportion to the rate at which energy is transferred from the bottom surface of the ice layer to the air above. Because at standard atmospheric pressure the boundary between water and ice is at 0° C, the bottom surface is always at the freezing point. If there is no significant flow of heat to the ice from the water below, as is usually the case, all the heat loss through the ice cover will result in ice growth at the bottom. Heat loss through the ice takes place by conduction; designated ϕ in the figureHeat flow through an ice cover (see text). [Credits : Encyclopædia Britannica, Inc.], it is proportional to the thermal conductivity of the ice (ki) and to the temperature difference between the bottom and the top surface of the ice (Tm - Ts), and it is inversely proportional to the thickness of the ice (h). Heat loss to the air above (also designated ϕ) occurs by a variety of processes, including radiation and convection, but it may be characterized approximately by a bulk transfer coefficient (Hia) times the difference between the surface temperature of the ice and the air temperature (Ts - Ta). (In practice, the top surface of an ice layer is not at the air temperature but somewhere between the air temperature and the freezing point. The exact figures are rarely available, but fortunately the top surface temperature, Ts, is not needed for analysis.)

Assuming that the heat flow through the ice equals the heat flow from the surface of the ice to the air above, the following formula for the thickening of ice may be fashioned:

In this formula h is the thickness of the ice, Ta is the air temperature, Tm is the freezing point, k is the thermal conductivity of ice (2.24 watts per metre kelvin), ρi is the density of ice (916 kilograms per cubic metre), L is the latent heat of fusion (3.34 × 105 joules per kilogram), and t is the time since initial ice formation. The exact value of the bulk transfer coefficient (Hia) depends on the various components of the energy budget, but it usually falls between 10 and 30 watts per square metre kelvin. Higher values are associated with windy conditions and lower values with still air conditions, but, with other information unavailable, a value of 20 watts per square metre kelvin fits data on ice growth quite well. The formula is particularly useful in predicting growth when the ice cover is thin. The first growth rate of the ice cover is proportional to the time since formation; as the ice thickens, however, the top surface temperature more closely approaches the air temperature, and growth proceeds proportional to the square root of time.

If there is a snow layer on top of the ice, it will offer a resistance to the flow of heat from the bottom of the ice surface to the air above. In this case, the incremental thickening rate (that is, the incremental thickening [dh] in an incremental time period [dt]) may be predicted by the following formula:

where hi is now the ice thickness with thermal conductivity ki, and hs is the snow thickness with thermal conductivity ks. The thermal conductivity of snow depends on its density. It is greater at higher densities, ranging from about 0.1 to 0.5 watt per metre kelvin at densities of 200 to 500 kilograms per cubic metre, respectively.

Well Duhhhh. I could have told ya that. Wow and I thought I had time on my hands:lol:

[Sundancefisher]

kids are getting antzy about those perch ......ive got em all reved up .....new rods new ice hut .......they just can;t wait lol

Grampa and the Gkids

Hopefully the whole lake will freeze well. We should hopefully be fishing by the 19th or 26 of December.

[Badback]

Yes...I am hoping. I will measure the ice thickness tomorrow


I phoned my great great uncle who is from the old counrty and asked him how he figured it was safe to go on the ice and this was his reply...."I sent mutder out on zee ice and if she fell true, I'd wait 1 more weke."

[Sundancefisher]

I phoned my great great uncle who is from the old counrty and asked him how he figured it was safe to go on the ice and this was his reply...."I sent mutder out on zee ice and if she fell true, I'd wait 1 more weke."


Maybe the ice will be safe this weekend...cold but safe!

[Geezle]

OUCH- I'm going to go out and get me a 13 pack of pilsner.:( :cry:

Wait...you're a fellow SK boy? You poor bugger :(

[hal53]

Holy Cow!!!!!...I think I just figured out where my trucks went for the last 3 yrs.!!!!,I thought it was 1.0-5.0 watts per kelvin meter, not 0.1-0.5 and I had the densities at 200 grams-500 grams ...not kilo grams....will have to read my notes better..:lol::lol:...seriously be safe...one cold snap does not make ice safe...Good Luck to the hard water guys!!!