Posts tagged with meteorology

(I had to look up MLLW—it means mean lower low water. As in there’s a lower high tide, a higher low tide, a lower low tide, and a higher high tide.) Normal tide cycle from Wikipedia:

9449880 Friday Harbor, WA water level/meterological data plot


climate estimates for 2000 years

climate estimates for 2000 years

(Source: Wikipedia)



You can see the “edge” of a cloud from far away so it should be obvious what ∂cloud means. But up close (from an airplane) you can see there is no edge. The mist fades gradually into blue sky.

Here’s another job for schwartz functions: to define a “fuzzy boundary”  that looks sharp from far away but blurred up close. In other words, to map each Cartesian 3-point to a fuzzy inclusion % in the set {this cloud}.


Jan Koenderink, in his masterpiece Solid Shape, notes that a typical European cumulus cloud has density 𝓞(100 droplets) per cm³ (times 16 in inch⁻³). Droplets are 3–30 μicrons in diameter. (3–30 hair widths across) Typical clouds have a density of .4g/m³ or 674 pounds of water per cubic football field of cloud.

To lift directly from page 508:

What is actually meant by “density” here? Clearly the answer depends on the inner scale or resolution.

At a resolution of 1 μm the density is either that of liquid water or that of air, depending critically on the position within the cloud. At a resolution of ten miles the density is near zero because the sample in the window is diluted.

Both results are essentially useless. The right scale is about a meter, with maybe an order of magnitude play on both sides.

Rather than having just one sharp boundary, ∂cloud is a sequence of level surfaces that enclose a given density at a given resolution. To avoid having to choose an arbitrary resolution parameter, we can define the fuzzy inclusion with a schwartz function. We get a definite beginning and end (compact support) without going too into particulars (like rate of the % dropoff) and this is true at any sensible resolution.


We can’t say exactly where the boundary is, but we can point to a spot in the sky that’s not cloud and we can point to a spot in the sky that is cloud.

Predict the weather for the coming week by looking at the whole continent. If the jetstream is above you, you’ll get warm Mexican air. If the jetstream is below you, you’ll get cool Canadian air.

(Works if you live in the midwest. Of the US.)

Current National

Current Visible Satellite

Current Infrared Satellite

Current Temperatures

Current Northeast Temperatures

Current Wind Chill

Current Heat Index

Current Dewpoints

Monday Jet Stream

Tuesday Jet Stream

Wednesday Jet Stream

Thursday Jet Stream

Friday Jet Stream

Saturday Jet Stream

Sunday Jet Stream

Today’s Lows

Today’s Highs

My dad made this.

(Source: )