Summer of Math Exposition

You motivate the problem well, the breakdown of the terms is pretty clear, and the graphics are very helpful.

I don’t really get an “aha” moment anywhere. The big insight is just “here’s a list of things that affect a radar measurement”. It’s useful information, but it doesn’t feel like exposition of a topic. I suspect the deep dive you mention would capture my interest better.

This was a very digestible breakdown. I appreciate the effort put into the algebra manipulations.

The “how to explain weather-channel radar maps” problem motivation is very relatable, and introduced with good pacing. The questions about radar “agreement” lack obvious motivation (they imply a baseline assumption that the same equipment positioned differently would produce different results when measuring the same entity, which certainly isn’t my default assumption). The animation style is cute and memorable. The explanation of $P_r$ (and $Z$) should probably precede the hypothesis that $P_r = Z$. In contrast, it was a good choice not to hold the introduction of the full equation for a comprehensive explanation of every variable, and instead to explain the wall of variables in the context of the overall power equation.

Interesting but insufficient reasoning prior to dropping big equations.

Really enjoyable, good job on the animations!

Nice animations.

• The animations are immaculate, I can tell a lot of effort was put into making them and it really pays off when you’re describing each term in the equation.
• As someone who’s not familiar with radar, I was a little confused at what the initial radar readout (around 2:00) looks like - is the x-axis distance? How can the radar tell how far away a reflection is coming from? Obviously this wasn’t the focus of the video, but I think a little more high-level overview would be helpful before getting into the equation.
• I was also a little confused about the units, since I didn’t understand what units $P_r$ was measured in

Interesting if you are in the field, but difficult to be hooked in the contrary. Suggestion : the topic very probably extends to other fileds, the could be mentionned.

I really love the visuals, the splitting up the formula to explain each part, and how it is complemented by some visual highlights every time!

I’m really impressed with this creation. Excellent hook and premise. Love to see 3D graphics; It looks like that’s a fairly new addition to your videomaking process, and we love to see folks picking up new skills for the competition! I was not expecting such a careful discussion of units at the end, but that really landed for me.

I have no serious complaints; the main thing holding my score back is that content-wise it wasn’t too ambitious. But, a few comments:

This is a rare submission where I think your stated target audience is actually more advanced than the audience the video actually hits, which is probably any high-school student who can remain calm when faced of a big multivariable fraction. Generally, that’s a good thing! (Maybe that’s because you had planned your audience target when the video was longer and more dense, and didn’t mentally update?)

Viewers with inclinations more mathematical than physical (like me, and a lot of SoME reviewers, let’s be honest) may have been hoping you would say a few words about why all those pi’s are hanging around. I’m assuming that the (4pi) is bracketed because that’s the surface area of a sphere, although I don’t see what the cube is about, and I’m surprised that shows up in the radar factor rather than the weather factor. The pi^5 is a complete mystery to me >_<

Very nice! But hard to follow when the weather radar equation pops up and one is not familiar with you prior radar videos.

Well-explained and inspires interest in future videos. The largest weakness was the motivation. It’s not necessarily obvious why different radars (and more particularly different distances) are a concern, so that would be better placed more up-front.

This video held my interest for its duration which is not the norm for most submissions. I feel like you put a lot of effort into explaining details, without putting much effort into explaining the big picture. Not having seen your other videos, I didn’t have a clear idea for what reflectivity was as a concept (the thing radar is supposed to measure), so diving into the details of the calculations didn’t have a lot of payoff for me. When you’re trying to reach a general audience, err on the side of big picture, or at least start with big picture before looking under the hood. Still, the visuals were great, your narration was wonderful, and the pacing was smooth.

I appreciate what this video set out to do and that it approaches it’s audience candidly and maturely: here’s the whole equation—let’s break it down! But I admittedly struggled to follow. Maybe I needed have more context to get much out of this, but overall I found it too technical and perhaps trying to cover too much in one go.

Great video! I learned a few things about weather radars! The reflectivity notion makes total sense to account for radar-storm distance, but it was interesting to see that this normalization has to do with many more things such as radar-specific attributes.

The animations were really really helpful here, especially to visualize volumes in 3D space. Keeping the video restricted to a specific equation was also good imo, as trying to explain everything that has to do with radars would’ve probably been too overwhelming to absorb.

One improvement in my opinion may be to explore “converging towards the equation”, as opposed to showing it to us and then breaking it down. That way I believe as audience we would feel like we “built the equation” through the explainer.

Thanks a lot for sharing your work, I hope you keep it going!

Please include subtitles! They are not too hard to do! :) I feel like the merch plug is placed at a bad moment and breaks the momentum for the video’s payoff. The dielectric constant is deferred to your next video, but I think doing so undercuts the payoff of this current video. The constant is central to why reflectivity works as a comparable quantity! I feel like deferring the explanation to another video is like spreading the bulk of the Aha moment between two videos. I was interested in where the (4pi)^3 and stuff came from but it was never explained!

Overall nice video tho well done

I think I saw one of your videos show up in my Youtube feed already, so the algorithm’s starting to learn! Cool nerdy stuff, I love it.

Excellent production design. Very nice audio and visuals.

I think the maths/informative content is lacking. I think trying to motivate the entirety of the Weather Radar Equation is too ambitious. I would have preferred first defining Z and then, for example, arguing why it is inversely proportional to lambda squared, and repeating this for a few of the other physical constants.

Interesting topic!

Not the first video I’ve reviewed this year that reminded me of a Radon Transform - taking a bunch of readings from different angles and inferring some kind of 3D picture within. Cool stuff.

Apologies if the score seems low, I did enjoy it, but I can be quite selfish about a video’s value to me (as a regular person who is not a part of the Meteorological community!) and you hinted that, to fully appreciate this video, I’d need to have watched previous (and even future) videos.

But I absolutely thought you did a great job - loved the animations!

I like the video topic since it addresses something that one often sees in everyday life. I enjoyed seeing the “Weather Radar Equation” and the explanation of all the different parts. I would have enjoyed some more detailed explanation how one goes from the measurements to the actual weather radar because it feels like only a single point of the weather radar was explained and how it is generated from one radar station. Are there usually several radar stations used to create the weather map and how are their measurements combined? Furthermore, while I understand that it is necessary in this day and age, I did not enjoy the ads for your merch or other videos, since they felt a bit out of place to me.

I would say it checks out all the fields the SoME video should essentially target. Even though I am not in this particular field, I was able to understand the topic with ease, with animations that supported the explanation so beautifully. Motivation checks out, because it was made clear in the beginning, and it showed up in explanations as well. Clarity is excellent, We know from start to end on what we expect, and we are given proper explanations about those expectations. Its very clear and understandable because it works on a real world application, and shows supporting visuals and uses layman language to make it easier to understand, even for someone who is generally not from this specific field like me. In terms of novelty, I loved the way it animated the concept, because the way you show the visuals is very very important. it can make or break the understanding of the viewer, and also how engaging the video can be. memorability for me is excellent, even after a few weeks I would be able to recall the concept, not ully but a significant chunk.

Overall, great job, I loved the video in all aspects.

This is just so poorly explained. It jumps from childishly simple to assuming we know a lot of physics and back again.

Nice video, really well made. I enjoyed it, but this is just not too much related to maths

Motivation: 7/9. It is clear why a calibrated measure of the power received by a radar system (such as reflectivity) would be useful, but not how well reflectivity in particular performs (you mentioned it was an ATTEMPT at calibration---are there any issues? How significant are they?)

Clarity: 3/9. It is clear what each factor in the weather radar equation means, but not why they are combined in that particular way. Why is the received power inversely proportional to the wavelength squared, and not the wavelength to some other power? Why are the dimensionless factors such as pi^5 and the dielectric constant included? Is there a more specific interpretation of Z you glossed over? I think including a derivation of the equation (even just a brief wall of text that relatively advanced students can pause and ponder) would greatly improve this video.

Novelty: 5/9. Radar measurements are an important topic that I have not seen anyone dive into before.

Memorability: 5/9. Good visuals. Mentioning drop size distribution and scattering regimes also makes me interested in exploring the subject further.

This video was good. Just good all around. Even though my interest in radar isn’t the most intense, it’s really easy to stick with it from beginning to end, soaking up all the information in a single go.