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Board » General Discussion » SOL maps Datum & Interpolations.

Posted by
JB


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2013-03-07 08:54:34
2015-04-16 16:47:25 - SOL maps Datum & Interpolations.
Viva all,

Two questions for the STC:

1 - What is the SOL maps Datum?
2 - What is/are the algorithm/s used for (TWS; TWD) interpolation?

Thank you STC.
Sail Fair.
Posted by
A2


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2015-04-16 17:20:59 - Re: SOL maps Datum & Interpolations.
SOL uses data from GSHHG (Global Self-consistent, Hierarchical, High-resolution Geography Database)

http://en.wikipedia.org/wiki/GSHHG

Data for each resolution is formatted to tiles which are visible in the game. The tiles are compressed files with XML-formatted polygons (list of lat/lon coordinates) of the shorelines of islands and continents.
None so blind
Posted by
kroppyer


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2015-04-16 18:22:58 - Re: SOL maps Datum & Interpolations.
sol uses h and i resolutions of GSHHG, and c and l resolutions are used in the client only for when you are zoomed out and don't need to see all details.

Interpolation:
this is what I found by measuring and fitting:
u/v interpolation (not TWS/TWD)
over space: linear
over time: I found this a close match (but not exact):
previous+(next-previous)*(0.5+0.5*cos(t/(2pi)))
with 0<=t<=1, previous the value for t=0 and next the value for t=1.

jakob said @ 2010-12-03 16:17:40:
Hi

So, about the interpolation of weather in time and space :-) Maybe some out there is longing for a short one-liner as explanation but I am afraid there is a little more to it… Here is in short the steps we take to get an "observation" (as we call it) at an arbitrary time (called t) and location based on forecasts.

1) Find the two forecast time steps (here called t1 and t2) surrounding the time t.
2) In space we simply use linear interpolation (in the 2 dimensions lat/long) of the forecast-data in the 4 closest forecast-nodes in the grib-file. Since the forecast has separate fields, one for northerly wind and one for easily wind we need to treat these entities separately, in our case by using complex notation. We also need to do this for both frames t1 and t2 from step 1 which thus gives us a set of two complex-valued space-interpolated wind speeds, one at t1 and one at t2.
3) Now we need to interpolate in time as smoothly as we can. We chose to do this using simple shape functions ensuring continuous wind speed and actually in our case continuous time derivatives.

Now, there are naturally many ways of doing this. One draw-back of this kind of interpolation is that we loose energy. Imagine the situation with constant wind speed but rotating wind direction so that at t1 the wind is due easily and at t2 it is due westly. In our interpolation we would (falsely) get that the wind speed at the time (t1+t2)/2 would be zero.

Also note that we do not always use the GFS model from NOAA. In particular around Sweden we have more detailed forecasts.

Hope this helped a little.

Regards
Jakob


(end quote)
Posted by
JB


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2015-04-17 11:04:45 - Re: SOL maps Datum & Interpolations.
Viva “A2”, Huib and Jakob,

Thank you for your quick and detailed replies.
Following now more comments.
Sail Fair.
Posted by
JB


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2015-04-17 11:05:14 - Re: SOL maps Datum & Interpolations.
Viva Huib

From what I understood the Wind vector field is divided in two vector components along orthogonal directions: North -South (“u” Wind vector component) and East - West (“v” Wind vector component) - see also included file.

Confirm pls if your approximation formula for interpolation over time (between time “t0” and time “t1”, with t1 > t0) is:

u1 = u1 + ( u1 - u0 ) x ( 1/2 + cos ( t/2PI )/2 ).
v1 = v1 + ( v1 - v0 ) x ( 1/2 + cos ( t/2PI )/2 ).

Did you managed to find a sigma (STD) for your (time, distance) interpolation results?

Thank you Huib.
Sail Fair.
Posted by
JB


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2015-04-17 11:06:14 - Re: SOL maps Datum & Interpolations.
Viva Jakob,

Very interesting this subject, to say the least.
I’m one of the SOLers being puzzled for a long time, first, with the process for the SOL Wind interpolation process. “How it’s done?”
Secondly, the ruthless lack of consistency between routing software results and GRIB data in the low wind range, i.e., aprox. 0 < TWS < 6,00 - 8,00 Kts, independently of the GRIB given TWA, normally obtaining over rated BS.

For the last issue I strongly believe that that are two main causes for this discrepancies:

1 - Different Wind interpolation processes (routing software vs. SOL one);
2 - Time step calculation used on routing,

IMHO the second factor is the preponderant one.
If we think that, for instance, the minimum step calculation for qTVlm is 5 minutes, and if we have an 8º/minute induced Wind veering, difficulty you reach a 5 minute distance in the routing software with the calculated BS, not to say TWA. The implications are obvious.
But now, it’s time for understanding the first factor: Wind interpolations.

So, for the”distance” interpolation SOL uses bi-linear interpolation.
For the “time” one you mentioned “simple shape functions”, Can you pls detail more what are those “shape functions (linear, polynomial, 3D mesh, …)?

Thank you Jakob.


--- Last Edited by JB at 2015-04-17 11:09:16 ---
Sail Fair.
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Posted by
kroppyer


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2015-04-17 22:47:27 - Re: SOL maps Datum & Interpolations.
I quoted Jakob from a post from 2010, I don't expect him to elaborate on that soon.

The formulas show you understood what I meant. Use t=t'/(t1-t0)-t0 to "normalise" t to [0,1]. I have no real sigma, but from what I remember it's around 2% at t=0.25/t=0.75, it's exact at t=0,0.5,1
It's weird to use a cos for this purpose, it's relatively heavy to calculate and far to precise for something that doesn't need geometry. Sol probably uses some 3rd to 5th order polynomial approximation that is faster to calculate, but slightly different from cos().

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