This will expand the event designator after you type space to end it. So you type “!” “$” “space” and the designated argument expands in-place.

Look under the section “Surprise”. This gives a construction that produces a new function g, whose transform is itself, that is a simple modification of any function ”f” that you supply.

In essence, the class of “functions that transform into themselves” is surprisingly broad and non-specific for those of us who key in on that fact about the Gaussian.

OP is considering power laws in the frequency domain.

You are considering power laws in the heavy tail of a distribution.

Different things! But there are confounders that make discussion seem similar:

- questions about moments and convergence (OP: do we have finite energy in the Fourier domain; your comment: do the tails of the distribution fall off fast enough to have finite moments of order 1 or 2)

- questions about averaging (OP: in the time domain; your comment: as an expectation obtained by integrating a distribution, or as a closure property of the stable class of distributions)

I'll try to remember the setup. The CMP axioms imply that, in a shift-invariant system X(t) (which is a different class than "stationary" -- not necessarily implying existence of second moments), if the mean of X(t) exists finite, then a long-term average of X(t) must converge.

However, you can observe time-invariant physical systems (such as a noisy resistor in a static environment) with spectra that obey the 1/f law down to very low frequencies (i.e., over very long time baselines) -- the time average does not converge. My advisor had a stack of magnetic tapes on his bookshelf with such samples.

These systems would seem to be disobeying the axioms of CMP, thereby motivating searches for alternative formulations that are more general.

Turns out this property is not unusual. There are many such pairs - there’s a reasonably well-known journal paper with a construction technique.

If the pixels really are 20x20km, located at 1AU, I get 500k photons (within that bandpass) per pixel per frame at 740 Hz, not counting optical losses.

Space solar instruments like HMI on SDO (https://science.nasa.gov/mission/sdo/) have one or more pre-filters in front of the instrument to block some light far from the passband and keep heating under control. I’m not sure if DKIST has such filters.

I’m less informed about simulations in this era - perhaps some simplified MHD simulations had been more quantitative in linking equations of state to the emergence of these features - but I believe they were not realistic enough to provide definite constraints on the scale of the structures.

It was clear that these features had to do with energy transport and some of the mechanisms were hypothesized. But the spatial scale of the gross energy transfer in these convective cells was not known, either through simulations or observation.

Remote sensing of the Sun is different from anything else, because you have so many photons. The idea of binning it down so fine (20x20km, 740Hz, a single nm of spectrum around a band center) is unheard of for any other target.

It's been believed for decades that these small-scale (~100km and below) turbulent features are critical to understanding how energy dissipates in the Sun. And thus, how sunspots and flares form.

The subject has been very qualitative but is yielding on both observational and simulation fronts. I worked adjacent to this area from the 1990s-2010s, and it had been true that MHD numerical simulations of significant volumes of the Sun (but at a scale fine enough to resolve these features) were not possible. That has obviously changed!

Additionally, it had been that the best solar observatories could not quite resolve these features. In the late 1990s some of the best images came from a couple of observatories in the Canary Islands (e.g., the 1-meter Swedish telescope -- https://svs.gsfc.nasa.gov/4715/). The spatial resolution was perhaps in the ~100km range.

Of course, these are absolutely mind-boggling images. You're looking at a slice of the solar photosphere that has a temperature such that it activates a spectral line around 400nm. By isolating that wavelength, we can see what's happening at that temperature, and thus, sample a slice of the photosphere.

So, that had been the state of affairs. Now DKIST (4m aperture), with the particular instrument highlighted in OP, appears to be at a spatial resolution ~5x finer than the above imagery -- see Fig. 1c in the Nature paper (https://www.nature.com/articles/s41586-026-10871-3). It appears also (https://dkist.virtualsolar.org/vanNoortfastcam/) to be observing at 740Hz (!) for speckle reconstructions at ~1Hz.

At this scale, vortices of the flow are well-resolved -- where before you just resolved the convective cells but not the turbulent features around them. It's these turbulent features that are transporting energy.

To contextualize with respect to a HN perennial topic: DKIST (commissioned 2021) is funded by NSF, from the same pile of money that once funded Arecibo (up to 2020).

Vidiots: https://vidiotsfoundation.org/history-mission/

Video Journeys: https://conorholt.medium.com/video-store-interview-video-jou... (Keanu Reeves, Laurence Fishburne)

Video Active: Down the street, they kept a stock popular with visual artists although reviews concentrate on other content (https://www.yelp.com/biz/video-active-los-angeles)

Video Archives: https://www.bbc.com/articles/c4g40ndzpe0o (Tarantino)

Some phrases have stuck with me, like “mandatory defaults“, “they told their users to see figure 1 a long time ago” and the flippant “sometimes we blow it though”.

- frequent revisit, so can track even sub-monthly changes

- the L-band radar is at a wavelength (24cm) that penetrates vegetation canopy, removing a confounder from the measurement

- excellent spatial resolution that is relevant to urban scenes

The data volume is exceptionally high and required a lot of engineering effort. All radars are demanding, but this one was a new high-water mark.

(https://www.earthdata.nasa.gov/news/now-that-nisar-launched-...)

Note in particular the last one, which is a classic. Roads, buildings, and all underground infrastructure is affected. As well as anyone else who uses that groundwater, as well as future users - because come groundwater reservoirs do not recover, the compaction is permanent.

Elbridge Colby is also Catholic, and some of his religious beliefs factor into his policy preferences. Groton, Harvard BA, Yale Law, hard-to-get service medals.

I’m not saying I like the guy, but his knowledge and background should not be underestimated as some nearby are doing.

Jewish/socialist physicists:atomic weapons::”foreign“ AI scientists:automated targeting

I’m not looking forward to the loss of innocence of computer science that is parallel to that of physics from 1945 onward, but here we are.

Comments URL: https://news.ycombinator.com/item?id=46969657

Points: 3

# Comments: 0

It turns out that yes, better forecasts is a large part of what motivated the launch of this instrument.

High-spectral-resolution IR spectra at GEO allow estimation of vertically-resolved temperature and water vapor (over large spatial areas, at high temporal cadence), which are then assimilated. Forecasts and nowcasts thus improve.

These "spectra-to-get-temperature-and-water" measurements were pioneered by other instruments in LEO (e.g., NASA's AIRS, https://airs.jpl.nasa.gov/mission/overview/), but LEO does not provide enough coverage to help forecasts.

To understand the benefits of GEO IR spectra, we do "OSSE's" (Observing System Simulation Experiments) to quantify how much improvement you get. You take a "Nature Run", make simulated observations (existing and proposed), and see if there is an improvement. (Since the Nature Run, which you made, provided ground truth, you can judge if there really was an improvement.)

Thankfully, many people have already done this. See: https://www.ssec.wisc.edu/geo-ir-sounder/osse/

In particular, looking at the figure there from Li et al., compare panels:

* (d) -- (Nature Run) - (existing data) ("CNTRL")

* (e) -- (Nature Run) - (existing data + GEO IR)

which both show differences between the Nature Run (NR) and the forecast.

The RMSE improvement (on a CONUS storm) is given as RMS of 0.55 (existing) versus 0.43 (with GEO IR), in degrees Kelvin. So that's 0.12 Kelvin or 0.22 Fahrenheit. Also, and probably more interestingly, the spatial pattern changes.

There are a lot of OSSE's reported on that page for these sounders. NASA is also conducting OSSE studies for a more ambitious multi-spacecraft observing system (https://science.nasa.gov/earth-science/decadal-surveys/decad...).

Studies like this (i.e., OSSEs like the ones above) are one of the main ways we decide how to build the next instruments -- what provides the most benefits vs. cost, which system parameters to push to improve and which are good enough.