No offense but you're missing the point:
LOSS + GAIN = EQUILBRIUM
Now remove gain without changing loss:
LOSS + ... = LOSS
Which results in temperature drop and, ultimately, freezing.
I've studied that kind of stuff and your evaporation thing is really protracted. I mean cooling by evaporation is a well known fact but it doesn't apply here. Actually the "clear sky effect" (whatever one wants to call it) also apply without water and usually result in condensation on object initially dry (and don't tell me that condensation is triggered by evaporation).
Oh I understand the point but I think we are talking about different things because you came into the conversation at a different time and I suspect you didn't read all the posts between TLM and myself. There are two examples and story lines going on here. The first is whether you feel colder under clear sky versus cloudy sky conditions. The second was introduced by TLM when he indicated that he has seen water freeze during a clear sky nights even when the air temperature has never dropped below zero.
Lets be clear that both cases are non-equilibrium thermodynamics. Our bodies, unless we are dead, are usually maintained at a higher temperature than air due to our metabolism. If this isn't the case, we most certainly do not feel cold. For the freezing lake story, the air is warmer than the body.
The first story is one where I conceded to TLM. Ultimately, we agreed that you feel colder on the clear sky night and we also agreed that this was likely a result of net heat gain through IR. Initially my beef was that he indicated it was because you lose more IR on a clear night compared to a cloudy one. When we reconciled that the IR emissions by our bodies are the same regardless of conditions and since temperature is a function of gain plus loss, then in the cloudy condition the warmer feeling must be due to IR gain. The gain was provided by the scattering of IR emissions.
Evaporative cooling from our skin can also play a role here if the cloudy night has high humidity and the clear night has very low. This is why using a vapour barrier with your sleeping bag in the winter helps increase its warmth. Initially you sweat and raise the humidity within the vapour barrier to 100%. When you have 100% humidity in the interior of your bag your sweat no longer evaporates and therefore evaporative cooling no longer occurs. In this example, you feel warmer in the sleeping bag because you reduced a heat loss mechanism.
Now let jump back to the example of the puddle of water freezing when the air temperatures remain above zero degrees Celsius. Again, we clearly have a non-equilibrium phenomena (equilibrium occurs when net gain of heat is matched by net loss of heat). At some point during the night, the water which presumably was at a higher temperature than zero, had to lose heat such that its temperature (at least at the surface of the water) had to drop to zero degrees to initiate freezing. So, we went from temperature greater than zero to temperature of zero. The air temperature has stayed above zero all the time. So we have to establish that the water has lost heat. It may still be a net change, but clearly the loss is greater than the gain. So we have to focus on the loss thing and we have to ask, why is the loss greater than the gain?
The next variable in this scenario is that the water only freezes during the clear sky night and it doesn't freeze during the cloudy night. Now if the water starts off at the same temperature in the clear/cloudy scenario, and we have already laboriously established in past posts that the IR mechanism of radiation loss by the water will be the same regardless of cloudy/clear conditions, then we are put into a logical decision tree forced by the physical reality that water only freezes when its temperature reaches zero degrees Celsius. Here is where the example deviates from the human case discussed earlier. We cannot explain the freezing of water under clear conditions as due to a 'lack of heat gain' which we invoked as a reason why it feels warmer to us on a cloudy night. The reason why we cannot invoke this explanation is that it would force us to suggest that the freezing point of water is above zero degree Celsius. If the loss by IR is the same on clear/cloudy nights but the gain of IR is higher on cloudy nights then yes this could potentially contribute to a higher water temperature on cloudy night. However, on a clear night the water temperature would not drop below zero degrees because the air is above this value and gain of heat from air though convection should counter the loss of heat from water by the IR. I suspect in this case that convection heat transfer at the air/water interface is a far more rapid kinetic process than IR gain and heat and this is why asked if TLM would be willing to model the process using a non-steady state state model. I would provide the complimentary non-steady state model to describe the rate of evaporative cooling. We would both agree to specific conditions on which to parameterize the model that would include variables such as wind speed, air humidity, water/air temperatures and the water surface area and volume, pathlength for boundary layers etc....Model speak stuff.
Thus, we have to invoke an alternative cooling mechanism that can work in parallel with loss of IR and is consistent with the clear/cloudy critiera; that this alternative heat loss mechanism results in higher heat loss on a clear night compared to a cloudy night. My suggestion is that the cloudy night is likely to have higher humidity compared to the clear night. The higher humidity reduces the evaporation rate from the water surface. Thus the net loss of heat is reduced on the cloudy night. On the clear night, you have the same amount of IR losses, but also have lower humidity which increases the evaporative rate. Thus heat losses are greater on the clear night.
Regarding condensation. I don't see how this factors into the example. I should clarify that in my example above I am talking about relative humidity and not absolute humidity and perhaps this is where we are running into differences. Absolute humidity is the amount of water vapour contained within a volume of air. Relative humidity is the ratio of the absolute humidity divided by the saturation water solubility in air at a specified temperature. Relative humidity is the appropriate thermodynamic criteria because it specifies the potential for vaporization/condensation processes to occur. So when I talk about 100% humidity in air, net vaporization approaches 0 and evaporative cooling is minimized. When relative humidity approaches 0%, evaporative cooling is maximized.
When you are talking about absolute humidity, it is true that under conditions of 100% humidity and high temperatures in the day, that you will have condensation occurring with a drop in temperature. This is because the water holding capacity of air drops with temperature and the excess water must condense out. However, this condensation will not change the relative humidity. At the cooler temperature, the air will still be at 100% relative humidity, it will just have a lower absolute humidity. So on our cloudy night, sure some of the water may have condensed out but the relative humidity stays what it was during the day. On the clear night, relative humidity was probably close to zero in both the day and night so no change has occurred here anyway.
What you might be trying to indicate is that the lower saturating air capacity of air during the night will place a cap on how much evaporative cooling can take place. This is true and it is one reason we have to have a condition of very low relative humidity at night for the evaporative cooling process to explain the phenomenon of water freezing at air temperatures above zero. In other words we can't be at 70 or 80% humidity and still explain the freezing phenomena. Is this consistent with the example set forth by TLM? My understanding is yes I was under the impression that the observation for the example occurred in the desert where both absolute and relative humidty are generally low to zero. So, we can also establish a testable hypothesis: you won't get puddles of water freezing above zero degrees Celcius in wet temperate areas. Again, one could readily develop a model here to make more specific hypotheses about the windspeed and relative humidity values under which such a prediction would hold and would not hold. That would be a fun science study but probably not so novel as to warrant serious consideration for publication. Who knows though, I don't read read that kind of literature.
I should qualify that for a living, I am a scientist and I regularly publish models that describe pollutant transfer in abiotic and biotic media. Most of my models are based on diffusive flux processes which have close analogies to heat transfer. I'm also fascinated by non-equilibrium, non-steady state transfer processes and determining the kinetic bottlenecks that maintain such conditions. This is why I chose to participate so vigorously in this topic area, I find it very interesting and fun.
