The Satan Is In The Particulars, Even Under Zero

By: Ivo Pasmans 

An anniversary is arising within the household and I had determined to create a digital picture collage. Within the course of I used to be scanning a youth picture and observed that the scan appeared a lot less refined than the unique. The decision of my scanner, the variety of pixels per sq. inchsince every pixel can report solely one color, particulars smaller than a pixel get misplaced in the digitization course of. Now I doubt that the jubilees will actually care that their collage after all, it is the thought that counts. The story might be completely different for a program manager of a million-dollar earth-observation satellite tv for pc challenge.  

Determine 1: (A) unique satellite tv for pc picture of sea ice. (B) Similar picture however after 99.7% discount in decision (supply: NOAA/NASA). 

Identical to my analogue youth picture, a picture of sea-ice cowl taken from area (Determine 1A) incorporates a whole lot of particulars. Clearly seen are cracks, often known as leads, dividing the ice into main ice floats. At increased zoom ranges, smaller leads might be seen to emanate from the main leads, which in flip give rise to even smaller leads separating smaller floats, and so on. This so-called fractal construction is partially misplaced on the present era of sea-ice pc fashions. These fashions use a grid with grid cells and, just like the pixels in my digitized youth picture, sea-ice portions resembling ice thickness, velocity or the water/ice-coverage ratio are assumed to be fixed over the cells (Determine 1B). Particularly, which means if we wish to use satellite tv for pc observations to appropriate errors within the mannequin output in a course of known as knowledge assimilation (DA), we should common out all of the subcell particulars within the observations that the mannequin can’t resolve. Subsequently, many options within the observations are misplaced.

Determine 2: schematic instance of how mannequin output is constructed in DG fashions. In every of the 2 proven grid cells (separated by the black vertical traces), the mannequin output is the sum of a 0th order polynomial (purple), 1st order polynomial (inexperienced) and a pair ofnd order polynomial (blue). 

The intention of my analysis is to discover a strategy to utilise these observations with out shedding particulars within the DA course of for sea-ice fashions. At present, a brand new sea-ice mannequin is being developed as half the Scale-Conscious Sea Ice Venture (SASIP). On this mannequin, sea-ice portions in every grid cell are represented by a mixture of polynomials (Determine 2) as an alternative of as fixed values. The upper the polynomial order, the extra `wiggly` the polynomials turn into and the higher small-scale particulars might be reproduced by the mannequin. Furthermore, the contribution of every polynomial to the mannequin answer doesn’t should be the identical throughout all the mannequin area, a property that makes it doable to characterize bodily fields that change very a lot over the area. We have an interest to utilize the brand new mannequin’s skill to characterize subcell particulars within the DA course of and see if we are able to scale back the post-DA error in these new fashions by decreasing the quantity of averaging utilized to the satellite tv for pc observations.  

As an preliminary take a look at, we have now arrange a mannequin with out equations. There are not any sea-ice dynamics on this mannequin, however it has the benefit that we are able to create a man-made area mimicking, for instance, ice velocity with particulars on the scales we wish and the order of polynomials we need. For the aim of this experiment, we put aside one of many synthetic fields as our DA goal, create synthetic observations from this one and see if DA can reconstruct the ‘goal’ from these observations. The result of this experiment has confirmed our assumptions: when utilizing higher-order polynomials, the DA turns into higher in reconstructing the ‘goal’ as we scale back the width over which we common the observations. And it’s not simply the DA estimate of the `goal` that’s improved, but additionally the estimate of the slope of the `goal`. That is very promising: Forces within the ice scale with the slope of the speed. We can’t instantly observe these forces, however we are able to observe velocities. So, with assistance from higher-order polynomials we would be capable to use the velocities to detect any errors within the in sea-ice forces.  

Excessive-resolution sea-ice observations positively look higher than their low-res counterparts, however to have the ability to use all particulars current within the observations DA needs to be tweaked. Our preliminary outcomes recommend that it’s doable to include scale dependency within the design of the DA scheme thus making it scale conscious. We discovered that this permits us to reap the benefits of spatially dense observations and helps the DA scheme to take care of the wide selection of scales current within the mannequin errors.