Statistical Analysis of Massive Data Streams Proceedings of a Workshop (2004) / Chapter Skim
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Pages 43-51
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From page 43... ...
It isn't really the real system, but the data set that underlies the massive data stream ~ am going to talk about today is the surface winds over the global ocean. These all have begun to explode in volume and precision since about 1991 when, within the Earth-observing era of satellite data sets, the first global wind data set began with the European Space Agency mission, ERS-l and 2.
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From page 44... ...
Well, what do ~ mean by physically sensible surface winds? One property of the surface wind field that has emerged from the scatterometer data set, an average property that we can hang our hat on as physicists and use statistical techniques to drive and time our interpolations is the spectral properties in wave number space.
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From page 45... ...
You can see that the scatterometer detects the very sharp spatial features of the front, and the high-amplitude wind stress curl that occurs there when it crosses. The blending procedure, because it is a spatial model, can't keep track of the propagation of this system.
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From page 46... ...
This is another polar low signal in the Labrador Sea. This sets up a Bayesian hierarchical mode} that we use to retrieve a uniform surface wind field with estimates of uncertainty at each and point, from the scatterometer data.
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From page 47... ...
We do what are called calibration validation studies. Calibration validation studies will inform the likelihood distribution to excellent precision and allow the satellite data -- the volume of it - to actually speak to the posterior very clearly.
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From page 48... ...
When we overlay the original satellite data it shows, in fact, they misplaced the low-pressure center. So, their region of ocean deep convection triggering would have been in the wrong place and, in fact, the intensity was considerably weaker than it is in the posterior mean distribution from the Bayesian hierarchical model.
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From page 49... ...
So, here is the leap to probablistic ocean stream function, and these operators are modeled directly after their finite-difference counterparts in the deterministic world. We have the linear operators on the previous time level, the non-linear operator, surface wind stress, boundary process, and we have added a mode} misfit term.
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From page 50... ...
Then, we idealized the surface forcing of a polar low, and sampled it as thought we had a scatterometer, and sampled the ocean as though we had an altimeter, corrupted those data with proper measurement noise, fed those to our data stages in the Bayesian hierarchical models. So, these are days one, three, five and seven of the simulated data.
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From page 51... ...
Now, in fact, there is a whole probability distribution that needs to be exploited that comes from these satellite data. Bayesian hierarchical models are amenable and readily adaptable to multiplatform data.
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