This post will serve to fill space.

Really, I feel like my mind has drawn a blank in the last semester. So sad 😦 (I’ve been thinking about some stuff, but nothing too deep.)

Anyway, I don’t feel like studying, I do feel kinda stressed though, and I feel a bit sick. So what else is there to do but blog post and *hope* your mind will start generating bloggable stuff in the next 30 minutes of your life.

Only six people have responded to my poll question about spherical coordinate notation, which is too bad. One thing that has intrigued me lately is that appearance of the greek letters \phi and \theta naturally naturally lend to angulations.

First, let’s look at \theta. I hope all readers (lol) can see how the outline of theta resembles a sphere, and how the line/curve that cuts through the middle resembles a circle parallel to the x-y plane (use your imagination, at least!). This circle is a curve of constant radius r and constant polar angle, and spans the space of all possible azimuth angles in [0, 2\pi].

Now, let's look at \phi. Likewise, the "circular" thing is the sphere, and the line that cuts through the sphere resembles a line of constant azimuth angle, with the polar angle varying across the line.

That's why I personally think the physics notation [radius, azimuth angle, polar angle] \rightarrow [ r, \phi, \theta ] makes more sense, because \phi looks like a visual representation of a line with constant azimuth angle, while \theta looks like a visual representation of a great circle with constant polar angle. But I suppose the math notation [radius, azimuth angle, polar angle] \rightarrow [ r, \theta, \phi ] makes sense too, since the circle that cuts through \theta occupies the space of azimuth angles, while the line that cuts through \phi occupies the space of polar angles. To each his/her own.


Next short thought: modeling atmospheric parameters. We'll denote an arbitrary parameter P that depends on all three spatial variables: the horizontal position \vec{\rho} \equiv (x,y) and z. Note this does NOT include integrated quantities like CAPE or SRH whose integration effectively reduce one degree of freedom (in my examples, the z direction) when we attempt to look at the atmosphere. It does, however, include lesser-known parameters such as the positive buoyant energy which goes by the difference between the virtual temperature of a parcel and that of the environment. Or, of course, the wind velocity field.

The problem with what we have now is that we are given maps of either constant z (the weather maps on a standard pressure level such as H5, H7, H85, etc) or constant \vec{\rho} (skew-t or hodograph plots). And neither of these maps tell the complete, because we are always losing one dimension when we look at them. Not saying they aren't useful---because they are incredibly so, but I feel at least that one of the greatest challenges of an interpreter of these maps is to keep track of the bigger picture---one that includes both \vec{\rho} and z.

The obvious remedy is to create three-dimensional weather maps, but the computational power needed for such a maps might still be a long ways away. Until then, this is a challenge for weather forecasters. We can look at different soundings for different locations, but the most impressive (or nonimpressive) soundings will stand out, which may lead us to forget the spatial variance of the parameters in those soundings. Likewise, we can look at maps from standard pressure levels, but if we treat them independently rather than see how they link together from the tropopause to the surface, we will often miss something. It's a challenge, for sure, and my opinion is that for amateurs, this is one of the greatest obstacles to overcome.


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