Kevin correctly alludes to the root zone temperature.
Root system of most tropical plants in my greenhouse is very poorly tolerate long-term cooling below 15 Celsius.
I really like your idea to use the ravine, but I would not put plants directly into the soil.
Your greenhouse air warms the ground not deeper than 10-20 cm. This will not be enough. Moreover, it is likely to be too wet.
You can construct your greenhouse floor on screw piles. The stream would flow freely under the floor.
Floor area over the flow can be transparent (tempered glass or steel mesh).
I haven't had the time yet to get out there and estimate flow rates. But I'm thinking, perhaps the simple solution would instead just be to build it, have everything there in pots for several months, then dig and measure the temperature where the roots would be. Whever it's warm enough, things could go straight into the ground. Where it's not, they'd have to remain in pots, or perhaps raised beds. Do you think that would be a reasonable approach?
I do however disagree about the statement, "Your greenhouse air warms the ground not deeper than 10-20 cm. ". One cannot make a blanket statement like that, it depends entirely on geometry. The broader a structure's footprint and especially the deeper it is submerged, the deeper and broader the warm area surrounding it is (the ground acts as insulation). Here's an example (not, mind you, of a greenhouse!) of how heat flow patterns work out in the real world:
The graph is mistitled, the object in that case is 10 feet underground (not 100), as is pointed out in the study and in the 10' label, but anyway... the point is, there's no single rule that "heat only moves X centimeters", it's entirely contingent on your geometry, and if something is below ground level, the hot zone goes *much* further due to the distance that heat has to flow to reach the surface. Soil ranges from an R value of 1 m*K/W (wet, compact) to 4 (dry, loose). That's an order of magnitude less than regular insulation, but when you're talking several meters distance for heat to flow, it really adds up.. And you can greatly extend it by insulating the area near the surface at the edges of your structure with conventional insulation if so desired.
I have no concerns about regular heat flow. The real question I have is, as others pointed out, whether water influx would counter this. Water influx through insulating soil is like an air leak through insulating panels. How fast heat would be lost by water leaking in, honestly, I don't know, because I don't know how fast it leaks in through the soil (I'm not particularly concerned about the creek, it should flow in and then out without an appreciable change in temperature - it moves too fast to fully warm). All I know is that there's some areas which remain persistently damp, and there's a couple little trickly side streams that drip in in places (drops at a time). I don't even know if those seeps are year-round persistent - the creek is, but the seeps normally get buried under a super-deep snow bank (ravine in a windy area = snow collector), so I can't see them.
Hmm, I suppose another option would be to trench geothermal water pipes through the soil instead of using geothermal radiators - heating the soil rather than the air directly. It'd be more cost / work, though.
Northern wall covered with mirrors will greatly increase the illumination.
Not in a valley in Iceland. I may do it anyway, mind you, but the sun works differently here, it goes around you more like a slightly tilted horizontal circle. In the summer, the sun rises and sets behind Sandfell in the north - it does maybe 300 degrees arc around you at the solstice (rises in the NNE, then goes to E to S to W to NNW where it sets again). In the winter, it's entirely behind Esja to the south for over two months - no direct light at all. It's not that the valley is unusally deep, it's just that the sun is so dang low in the sky in the winter.. There's no direct light in the immediate southern portion of the sky for maybe a third to half a year - primary sun in my location comes from west and southeast, primarily the former, due to the sun's low angle and my location in this particular valley.
Compare:
http://www.timeanddate.com/astronomy/usa/miamihttp://www.timeanddate.com/astronomy/iceland/reykjavikFor the summer solstice, picture those arcs slid up by about 4 degrees from where they are now. For the winter solstice, picture them down by about 42 degrees.
As a general rule for Iceland, also, a higher percent of the sun's energy is indirect light. In the middle of winter, even for locations without mountains on your southern horizon almost all light is indirect, you only get direct sunlight for maybe a couple hours a week. The sun takes such a low arc it's so easy for clouds or ground-based objects to obstruct it, it only peaks a couple degrees over the horizon. But there's always a surprising amount of "dim". And in the summer, even when the sun is hidden behind something to the north, it's still more than bright enough to keep doing everyday activities outside all night. You even get multiple sunrises / sunsets on a single day sometimes, depending on your location - the sun moves at such a shallow angle that when it passes behind, say, a mountain range, it can set and then rise beyond each peak it passes through
Basically, the way it works out for everyone with a greenhouse here is that in the summer, there's a crazy amount of natural light available for growth, but in winter, it's a "suppliment just to keep them alive" sort of thing. Thankfully, I currently grow entirely on electric lighting, so I should be able to manage that. Most people here use HPS but I'm mostly LED.