Freezing water: in layers or all at once? (First question here on physics, hope it is OK)
Since it is getting cold here in Berlin, Germany and temperatures are falling below the freezing point, we want to make a little ice rink in our back yard (for regular shoes, we just want to slide over the water).

My question is: should I

*

*do it layer by layer: fill the plastic with just a bit of water, wait it for it to get frozen, and fill a bit more, wait for the next freezing and keep on filling and waiting in small amounts until the level is heigh enough?

Or should I


*all in once: fill the plastic with enough water and wait (no intermediate steps).

Or perhaps another way?
My goal is to have a solid layer of ice (about 1-2cm - 1/2 inch), not just the top being frozen.
The water from the tap is rather warm, currently about 14°C, probably a bit cooler when I take more than just a (10 liters) bucket.

Edit a day later: I can now report back. Thank you for all the answers. I have filled the plastic with layers of water, waited for it to freeze and then filled another layer and so on.
@Andrew I was thinking about doing the experiment a second area with the other method, but I don't have the same conditions twice so I could not compare each method.
It is hard for me to accept the "right" answer. The "puddle" is frozen, it is a few degrees below 0°C.
Next time I do it, I try without the plastic at the bottom. There are some air bubbles below the plastic and that breaks the ice when sliding. When the (solid) ground is cold enough, the water will freeze anyway.

Edit (2)
The plastic bottom was crap. The ice brake (way too thin) and was not slippery at all. So the next attempt is to remove the plastic and get the ice on the stone floor, layer by layer. (I assume it is getting off-topic now).

 A: The surface of the water evaporated due to partial pressure. As this transformation from a liquid to a gas state costs energy (the so called latent energy), the remaining water becomes "cold" (decreases its temperature). Thus the more water evaporates per time unit the more ice you obtain. Thus the question is, do you get more gas molecules if the water is in its solid form or in its liquid form.
I'm pretty sure that the vapour pressure is larger in the liquid state as in the solid state. Thus, less water evaporates, once a thin surface of ice is formed which covers the rest of the liquid. Therefore, you should build the ice layer by layer.
Arguments, why I believe that the dominant contribution comes from the latent heat:

*

*The heat capacity of the air is smaller than the heat capacity of the ground. Hence, on cold days (or nights) the air is probably colder than the ground.

*The heat flow is linear in the temperature difference (gradient),
$$
\textrm{heat flux} = \mu \cdot \Delta T
$$
To freeze the water heat needs to flow from the water to its surrounding (ground and air). The wind constantly replaces the "heated" air above the water by "cold" air. Thus, the temperature gradient is larger between water and air than between water and ground.

*The "sheet" shown in the above picture is probably a rather good thermal isolator. In addition, there will be a tiny layer of air between the ground and the "sheet". Hence, the coefficient $\mu$ determining the heat transfer between ground and water is probably small.

A: For a centimeter or so, I wouldn't try to complicate it.  Given cold enough temperatures, that depth can freeze solid in a single night.  Also, trying to control the layers thinner than that would be difficult.
If you needed it much thicker, then the layered approach would help.  The problem with putting all the water down at once is that basically all of the heat loss is through the upper surface.  Once ice forms on the top, it insulates the remaining water and the heat loss slows.  By forming the ice in layers, you keep the liquid water as exposed as possible and maximize the heat transfer.  If you are diligent about watching when the freezing is complete and put on the next batch of water, it will reduce the total time to freeze.
A: For fastest freezing make sure the rink is shaded during the day, and exposed to the sky at night.
Optionally you can add environmental snow or ice to the fill water to reduce the amount of cooling (and the amount of tap water) needed
allwing you to build thickness more rapidly.
Ice tends to insulate the water below it a bit, so work in layers you'll soon get a feel for how quickly it freezes.
A: Water in a fluid phase has density of $1.00~\text{g/cm}^3$, while in a solid form (ice) - $0.92~\text{g/cm}^3$. So while freezing water expands in volume (and thus drops in density), it becomes lighter. That's why we see pieces of ice floating in a river. Due to same water anomalous property, deep lake bottoms may never get completely frozen, because liquid water heat going-up may never reach lake surface and may dissipate in the lower layers of ice. Thanks to that, fish may enjoy living in a winter seasons.
Thus, if your pool is deep enough it may never get frozen fully, or at least will do it slowly if you fill it in one go. A Better tactic is - freezing the ice layer by layer. So that you'll have total control over how thick the ice is. In addition to that, the heat amount contained in a thin layer of fluid water will be lower compared to the case of a fully filled volume, so this heat will escape to surface faster. My advice - fill thin layer of water in the bottom, wait until it freezes to ice. Then fill another layer of water on top of it and repeat the process until whole pit will be complete ice.
