Why don't cloud shadows over the sea have a visible penumbra?

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goran d
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I have seen shadows of clouds over the sea. What could be the explanation? Let me explain why there needs to be an explanation:
Radius of sun: ~600000km
Distance to sun: ~150000000km
(assumed) distance to cloud: 2km
This means that there should be a 16 metre edge around the shadow where the shadow goes smoothly from dark to light. But there wasn't such an edge, at least not an easily visible one.
 
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Keep in mind that the sun is a sphere, so you are getting almost no light from the left edge of it or the right. You can probably halve your estimate to 8m because of that.
 
What will be the brightness in the penumbra with respect to the umbra and the bright area outside the penumbra?
 
goran d said:
...at least not an easily visible one.
So what did you see? A sharp shadow boundary edge like from a building? How far away was the shadow, and at what angle where you looking at it? Where the clouds really 2km above, or maybe just 500m?
 
rumborak said:
Keep in mind that the sun is a sphere, so you are getting almost no light from the left edge of it or the right. You can probably halve your estimate to 8m because of that.
This isn't how it works. Every point on the surface emits light in all directions, so the brightness is pretty uniform to the edges. You can see this in eclipse photos.
 
russ_watters said:
This isn't how it works. Every point on the surface emits light in all directions, so the brightness is pretty uniform to the edges. You can see this in eclipse photos.

I think you misunderstood my point. I wasn't saying that the emitted light has some kind of directionality to it (I agree with you, it doesn't), but instead that if you section the "sun disk" into vertical slices, the slices towards the edge of the sun are shorter and thus contribute less to the overall shadow effect. Because of that, the penumbra will *look* thinner.
 
goran d said:
I have seen shadows of clouds over the sea. What could be the explanation? Let me explain why there needs to be an explanation:
Radius of sun: ~600000km
Distance to sun: ~150000000km
(assumed) distance to cloud: 2km
This means that there should be a 16 metre edge around the shadow where the shadow goes smoothly from dark to light. But there wasn't such an edge, at least not an easily visible one.
Are you sure you don't see a transition zone? From what distance are you viewing the shadow?
 
goran d said:
why there needs to be an explanation:
A totally opaque cloud?