Episode #122 - What's the Weather in Space? w/ Jose Arnal

But I don't understand.

The Math and Physics Podcast. This is episode number 122. My name is Ray, and today I am joined by my dear friend Jose Arnal, a senior PhD student here at the University of Toronto Institute for Aerospace Studies. And he's currently studying space physics and data assimilation, where we're gonna talk about. Essentially what he does, how he does it and What is there to learn from it? So Jose, welcome to the show. How are you?

Doing introduce yourself. Yeah, thanks Ray for having me, first of all. And yeah, doing great. Really excited to be here to talk to you and uh spr explain some of what I do to the audience a little bit. All right, so you're a senior PhD student here. This is your fourth or fifth uh fourth year? I don't usually like to talk about it too much. Just kidding. I'm kidding. I started in 2018. I felt like it's taking me a little bit longer than I than I would have liked.

Uh started at the masters level but then transitioned to the direct entry PhD program. So I think this is technically my sixth year, I would say. So yeah, this so this is a lot of very different for the European students who uh a lot of times don't even really have direct entries. I don't think they do. So I think this is more the Western Hemisphere where a lot of people have uh

chance to essentially skip your masters and go into straight into your PhD. So that's what she did. That's correct. Yeah. Right. Now essentially my understanding and one thing I should also say is that he helps me in a lot of my research as well, because uh one aspect of his is also mine.

But let's talk about the one that isn't. Let's talk about space weather and space physicians. So, what got you into there? What kind of determined that you were gonna do a PhD in that and just take us through your journey? Yeah, so if I can be fully honest. I saw some of the plots or some of the figures. uh that you can produce when you're making predictions or simulations of space physics or space weather.

and it just looked really, really cool. You see all these colorful streams and and what we call coronal mass ejections, which I'm sure we'll we'll go into. And it just looked really cool. But kinda going broader than that Um I don't know w since when, but I've always had a fascination with both space physics or

maybe let's say space generally but also with fluids, right? Independently, not not necessarily together. But these are not usually areas that you would think are are tied, right? When we think of fluids, we might think of o the ocean or we might think of airplanes. stuff like that and I thought that was really interesting.

Um and when we think of space we usually think of of a v of a vacuum, right? But actually space physics or space weather more more um precisely is actually a good example of how fluids can actually appear in in space and the equations of fluid dynamics and and modeling them um is actually really really relevant in that Alright. I mean it sounds a little weird to somebody that usually is probably thinking that space is almost a vacuum.

So tell me some of the some of the big things about so when you say space weather. The first thing that I'm thinking about is what's the temperature up there? That's probably not what you're thinking about though. Or maybe it is. So what exactly do you aim to model? What exactly do you aim to do? What are like some of the challenges when you are trying to?

kinda dabble in space weather for space weather. Right, right. So I think temperature is actually one of the variables that we're interested in, but it's not n I would say the primary one. Let's say in the Earth, maybe that is one of the primary variables that we're interested in. But

We can think of the the sun as a hot ball of plasma. So you can okay, you can see that's a fluid probably. But this this ball of plasma the sun is is essentially emitting or it's um sort of plasmas are escaping from the sun and the this stream of charged particles comes towards the earth right and and and these uh particles can actually have quite an effect on on our technology and on our infrastructure.

But sticking more on on the science side, what we're doing is that um by essentially using big computers to model uh how th this plasma comes out towards the earth and using the equations of of fluid dynamics

We can quantify how, for example, the velocity field changes how we go from the sun to the earth. So we can ch we can model the temperature and uh really important Quantities to also model is the magnetic field because the magnetic field hash has quite a a large impact on the geomagnetic events that happen uh at the Earth. So when you say magnetic field, I'm assuming you're talking about the magnetic field of the sun and how that impacts

The Earth. Yeah, so we call this the interplanet planetary magnetic field. Um But yeah, it's essentially the magnetic field that's coming out from the sun and how that's actually interacting with the Earth's magnetic magnetic field. So th this is um I guess something I never actually even thought about. All right. Yeah, I guess the sun obviously also has a magnetic field. But in the Earth, when you usually think about the magnetic field lines, you know, like the line thing of Earth.

Like that doesn't span very wide, right? Like it's not very far. So are you saying like the Earth is within the sun's influence of magnetic field? Or are you just saying that the magnetic energy, quote unquote, is transported to the So I would say both. Um in the sense that Certainly the the m the sun's magnetic field is much more powerful, right? But when you're near the Earth

w what's gonna be important will be the earth's magnetic magnetic field. Right? But they actually influence each other quite heavily, more s more so the sun's influencing the the earth and the than vice versa. Um but it's actually because of the Earth's magnetic field that the that our our atmosphere is not blown away, right? If we didn't have um if the Earth didn't have a magnetic field, our whole mag uh atmosphere would be blown away by the solar wind. Right?

When you say the word solar wind What is winding? What like what exact no that was exactly is the wind? Are you talking about the magnetic? Are you talking about the plasma? You're talking about a combination? What exactly is the wind? Right. So what by w what we mean by wind here is You can think of it as as the ions and electrons, this matter that's in space and and it

uh movement through through space. So I'm talking about here it's velocity. But I guess I'm talking about everything. Also it's its magnetic field. One of the unusual or maybe unintuitive aspects of of plasma Or at least these types of plasmas, is that we can say that the magnetic field's actually frozen into the plasma. So the the magnetic field is transported with matter, if that makes sense. See I've thought of electrical energy being transported before. Right.

Like any type of analogy or any kind of understanding that could help with understanding how I mean I guess it's one and the same, right? I mean saying that is it's it's obviously one and the same. But usually again when you think of magnetic energy. You think it's more like in whatever's in the field that's mainly being affected.

Right. But now you're not only saying that it's in the field, but you're also saying it's transported. That's correct. Yeah. So is there is there any way that I could better understand the transportation of this magnetic field? Yeah, I think I think maybe I'm making it more complicated than it needs to be. Think of

Parallel magnetic field lines, okay. And then let's say there's this cloud of plasma in between the top and bottom of this image that we have. And let's say that we can somehow push we're blowing this this cloud away. You can think that the magnetic field lines will actually move with that cloud. So while they might start out um

Then the magnetic field lines will also be sort of pulled in that way. So at the top and bottom of this image, th they'll be straight and and parallel, but they'll be dragged along with this cloud of plasma. All right. So and this is obviously only because of the fact that the elect because the plasma is electrically charged and there's a relationship between that that's essentially transporting this whole thing. That's correct. Yeah.

So when we say that there's a high solar activity, first of all I think this is a phenomenal time to also talk about this because Um again I don't know how many people are in the Western hemisphere here, but we had a I mean I guess the CME is uh observed everywhere. It's just where you can see it best. But there are coronal mass ejections or CMEs as you uh pointed out in the beginning that occur quite often. Or maybe they don't. Maybe you can explain what those are, why they impact us and

Why are we so interested in them almost? Right, right. So I would say in this last year in 2024, we've seen a lot of gem magnetic activity mainly due to uh kernel mass ejections. And I think for the first time it's in a lot of people's uh mind where it wasn't before. So maybe some of the listeners uh would have seen the Aurora Borealis for the first time in in their life.

I actually haven't been lucky enough to see it yet, but I'm I'm looking forward uh to the day that I can see it. Um but these um I'm sure most people are familiar with the Northern Lights, right? Aurora Borealis. Um and this effect this phenomenon usually happens uh much closer to the poles, but it's coming back uh a lot m more south if you're in the in the north. Um and it's appearing let's say in Toronto where we're located, right? And this is due uh primarily because of coronal mass.

So what's happening is that uh at a high level The the sun has this eleven year cycle where it it will have more sunspots, let's say we we call that solar maximum and and less sunspot sunspots, right? And maybe we'll call that when the when it's quiet. Okay. So that's not called solar minimum? Use the words. Yeah, maybe maybe it should be maybe it is. Uh okay.

So what's happening right now is that we're right now uh at a solar maximum where there's many sunspots and uh actually the phenomena by which uh this occurs is not fully, fully, fully understood yet. Um but we're getting a whole host of kernel mass injections which you can think of these Clouds or these um eruptions of magnetic energy that are uh traveling in in space. Now when we're unlucky and the earth passes by the trajectory of one of these coronavirus.

Um the magnetic field of the earth is compressed quite significantly and this causes um through reconnection in the magnetic tail, which is again a quite a complicated process to go into. uh a host of charged particles will come streaming down towards the earth's poles. And we see this as um yeah as as Aurora Borealis for for example.

So the charged particles from okay, so you said specifically it's a burst of magnetic energy. Yeah. So is there also again, this is might seem like a dumb question here, but like There's also plasma in there. Like it's just a heap of everything. It's a whole heap of of of plasma that's coming towards us and it's actually coming towards with a big shock.

So it's moving super of supersonically or super alvanically towards us. Sorry, what was the word you just used? Yeah, so I use the word super alvenic and and that comes from um the the physicist who came up with uh what I call the MHD equations, which maybe I will go into later. Um these equations describe the the motion of plasmas. His name was Forget his first name, but his last name was Alvin. Okay, kinda history lesson here.

But to get to cut to the chase, we can think of usually we we think of normal fluid as being supersonic. Um let's say we have a fighter jet traveling through the atmosphere and it's going so supersonically, right? So that means that the the uh the fluid is moving faster than the speed of sound, right? But when it comes to plasmas, we can also have a supersonic flow, but we could also have a superalvenic flow where the plasma is actually moving faster than the alvenic.

And that is that's essentially related to Uh let me see how we can discuss this. In the okay, so the sound speed, let's think back to normal fluids. What is the sound speed in space though? How does that even make sense? Space is defined in the same way that the sound speed is defined in a normal non-conducting fluid. Yeah, but where's the compression? Uh you're still compressing mass.

So it in in in the atmosphere we're compressing a gas. In in space weather or in in space, we're compressing a plasma. Okay. And so that's there's still a sound speed associated with that compression. Now When it comes to the the normal sound speed that we're used to, we're usually it's defined in terms of uh without getting too technical, um And too we can think of it as a magnitude of

Okay. Yeah, yeah. Um it's directly related to the pressure. Exactly. So the alvenics sound speed, when you look at it in equation form, looks very similar to the way that we define defined the sound speed. But it's instead of being based on the um on the thermo thermodynamic pressure, it's actually based on the magnetic pressure. Okay. So it's like magnetic field line concentration almost? So you're saying on earth that a relation is kind of if you're going faster than

The sound than the air can compress. Now here you're saying faster than the magnetic field can compress. That's a good analogy. Yeah. All right. All right. All right. So we're essentially so okay, so we've understood that

These CMEs have an effect on Earth. Now, before talking about various types of effects, would you care to discuss maybe how these magnetic events actually occur on the sun? Yeah, I mean that's a Deep, deep question. Right briefly, because I mean so um I think I've mentioned this on the podcast before, but in my Grade eleven, I think this was. I did a co-op at my high school. I think I told you about this too, where I went to York University. And I modeled a sunspot.

Okay. And my whole quote unquote thesis in grade eleven, obviously, so not thesis, but my research topic was essentially calculating the differential rotation of the sun. Okay. Knowing that uh to the listeners out there. The sun is, as he said, a ball of plasma. It's not a solid ball. So each latitude, almost you can think about it, rotates at a different velocity.

Because essentially it's not one solid ball. It's just all layers of plasma. So my whole research was essentially to model those sunspots. Right. And while I understood that hey, this is cool I never really understood where those sunspots kind of came from. What caused them. I know if and correct me if I'm wrong, that it's essentially like um regions of low magnetic activity, which is why they appear black. Or I could be wrong there, but maybe explain.'Cause when you look at the sun

through a obviously a solar filter and you're trying to look for sunspots. They're essentially just black spots on the sun. Right. So maybe you could explain why they're black. Is it why they're occurring? Is there a Like essentially what's the theory behind magnetic uh uh uh sunspots and why these things occur. So you're definitely putting me in the spot here. Okay, my apologies. Um

Now let me caveat a saying I consider myself more of a fit of a sorry of an engineer rather than a physicist. I focused on modeling, um, like the the practicals, you know, how do we do these calculations well and and fast. So yeah I think you're pushing me a little bit beyond, but I'll try my best and if anyone can correct me I'll um I'll be happy uh to to make a correction. But I believe that actually the the sunspots are regions of high magnetic uh activity.

Um and maybe so I feel like we're the blind leading the blind here. If may one of us is wrong, uh we'll we'll find out after which one of us it is. Um but essentially you have these um regions of of very high magnetic activity where you have magnetic field lines that are actually in opposite directions. So in the same sunspot you might have Some magnetic field lines pointing out and then some magnetic field lines pointing in.

Okay. As opposed to As opposed to just one direction, or all in or all out. Okay, so you're so you're saying most of the sun is all in or all out, but magnetic field lines usually have some in, some out. Yeah, and in in in the sun, sun particularly these these magnetic field lines are opposed to And this is this is creating a lot of let's say magnetic tension.

Okay. Okay. Um and I'm I don't fully understand how the process actually works and I actually think this is still like a pretty active r area of research. Um but one thing's that happened is is that you get uh something called a solar flare, which is essentially a burst of uh radio energy. So you can actually detect these these um flares before you can even before the CMEs actually come out.

Okay. At some at at a certain point, and again I I don't fully understand how it occurs, instead of just getting this energy that's being concentrated, uh matter, plasma in particular, will actually uh burst out as well. And and and so this is why uh sunspots are very much related to coral mass ejecta. Okay. So solar flares are not CMEs. No. Right. Yeah. So solar flares are simply just radio energy.

Yeah, they're more related. More or less. More or less. But the f CMEs or coronal mass ejections are more matter. We're talking about matter actually tr being transported out. Yeah. Alright, all right. Okay. So Am I wrong in saying that the temperature of the sunspot is significantly lower than the rest?

Yeah, so you might have noticed I didn't comment on that. Yeah, okay, okay, okay. And again, I I feel terrible because I'm supposed to be an expert in this. No, no, no. Um but again I like to think of myself more of an engineer working on the day data simulation uh side of things, which we haven't gotten into yet. But I believe and man, I'm really putting myself out here, but I believe that it's actually higher time.

Yeah. We're we're gonna have to we'll definitely talk about this later. Um sorry to put you in the spot. But I think the best part about this conversation that we're having right now is Of senior PhD student still like questioning things about what he himself is researching. So if anything, this is not a thing at you. This is more like everybody does this. Like no matter what year of research you're in, even if you're like the most senior level of researcher you are or you have or you know.

There's still more to know. Of course. Always always more. And it's so refreshing that a senior level PhD student as yourself is still like, oh, I'm not actually sure. And again, we've had professors, we've had all sorts of people do that as well. So it's always really nice to see that. You know, high level researchers.

also very curious in like in their whole research essentially. Right. And asking and asking still like what is this? Why is this? Right. Okay. So we've spoken about CMEs and how they kind of come out of the sun.

My very basic understanding of their effect on the earth is that they affect satellites. Because that's I guess the only thing obvious in space. But what else does it affect? Does it affect the actual weather on Earth? Like the c I I guess weather might not be the climate is actually too broad. Is weather? Yeah. I think that's a great question. Um so all of the we can think of Us putting aside uh anthropogenic effects, which are obviously important.

M a lot of or most of the Earth's weather is driven by by solar activity. If the sun were to pop out out of existence, then obviously the Earth would cool immediately. Right now, in terms of how do you relate the activity of the sun, let's in the sense of chronologies and the like, to terrestrial weather.

That I'm not sure about and I think that's still a a per fairly uh active research area. Okay. Okay. Now I also just to you comment another comment. So you mentioned satellites. So certainly satellites um are Certainly affected by by space weather. In recent news, you might have seen, I think it was either last year or the year before, Elon Musk.

lost lost I think forty of his satellites, uh Starlink satellites, due to essentially an increased uh drag, uh atmospheric drag um in the upper atmosphere that led to a bunch of I believe uh satellites com coming down. Yeah. Um and and then another big one and and specifically for us Canadians for us to think about, um, because we're a high latitude country is actually that space weather can cause huge widespread blackouts. Okay. So what happens is that

uh these uh b do two basically you can get um electric currents on on the sun on the surf on the sur surface of the earth, and that induces um high potential differences across um electrical lines, electrical grid lines and I think what happens is that you overheat capacity

So you get a mass you can get massive, massive uh black For us can I mention us Canadians, one not so recent but uh significant or historic event was in March of nineteen eighty nine, where a large region of Quebec lost um lost its Essentially had a big blackout for for nine hours. That was due to uh a geomagnetic event.

So what can we do to prevent stuff like this? So we know so okay, first actually I had this conversation with my other lab partner recently, so maybe you can describe this to the uh the audience as well, which is How long does it take from seeing that hey, first of all, how do we see that a CME exists? I guess you already said that we see a bunch of plasma and I'm sure we have satellites that are looking at that constantly. So how long does it take?

For this to come to us, because I'm assuming it's not traveling at the speed of light. No. Right. So a fast CME would be let's say from eight hundred to a thousand kilometers per second. All right. Okay. So that means we actually have days. Uh between the the eruption from the sun to the earth, but that's not always necessarily easy to detect. Another sort of s safety point that we have is we have um

satellites at Lagrange point one. So for those who are unfamiliar, um there's a point between the Earth and the Sun where their gravitational pull essentially cancels out and means that we can park, as it were, a satellite there to just observe the s the solar wind.

So this gives us a advanced warning of uh space weather activity, but it's pretty close to the Earth. So it's actually not great. Um so I think this is one of the the reasons that that we are actually researching uh how do we predict Space weather better. Now what can we do about it? So we can't do anything about it in the sense that we can't change

space weather. Right. In the same sense that we can't change terrestrial weather. There's no way we that we can change space weather. But if we can m r uh model it well or predict it well, then we can mitigate it straight. Can we minimize its impact on Earth? Yes. So in the same sense that let's say you're planning a a big event

Um and you know that okay, there's gonna be crappy weather, there might be a storm. I'm talking about just normal terrestrial weather. Okay. You you might be able to better prepare for that. Okay. So in the same sense, we want to mitigate the risk of space weather uh by

being able to to predict it. So and again, this is maybe another field where I'm not super familiar with, but electrical power companies, if they have advanced warning of space weather events, can prepare their capacitors, for instance, so that they don't uh over

And the techniques by which they do that I'm not super well versed on. So CME you mentioned takes a couple days to essentially get here. Now for it's again again, all the hype of CMEs and stuff has really been in especially this year, because we saw two big ones.

So my question is this. Both times that I've I've uh again, this might not be again in one of your areas of expertise because it is a physics-based question, but again, have at it. Um number one. Why so why does it last for so long? If it just takes that long to come to us. When I let me rephrase that question. If let's say it takes three days to come to us, usually I hear things like, oh

The Aurora Borealis will be looking better tomorrow than it will today. Right. So how do we know how long it will last for? And I guess that's the first question. Let me just ask you that. How how how do how do we know how long this thing will last for Okay, you can think of this ball of magnetic energy coming towards the Earth in with a shock, essentially. So There's gonna be w when you say shock, maybe maybe re explain that because again, shock, so you mean like almost a magnetic

Mm. So what I mean by that is there's a uh almost not instantaneous, but a very rapid increase in the m in the let's say the magnitude of the magnetic field. Magnetic field. Right. And that um because we're talking the b because we're talking about in the scale the scales of of space. These are these don't occur d don't come and go very quickly. So there's gonna be an increased uh

An increase in the magnetic magnetic field magnitude, and that'll remain high for for some time. And now when you're talking about, oh, tomorrow it might be better. That's actually cost because uh for a lot of these events, we don't just get one CME that's coming towards us, but we actually get a whole host of CMEs, let's say five, that all merge um and and impact the earth and that's why they they can last for for quite a while.

Alright. Okay, so it's basically a bunch of them that occur usually I at I'm assuming at the same time. Yeah, well they have it not necessarily right at the same time, but in close success. Yeah. Now why is twenty twenty four so special? Why why are we getting so many this year? Is it is it a solar because I'm told it's not even a solar maximum unless I'm completely sure. So we're not s we're not right at solar maximum but we're close to it. We're close to it. Um

But you're right in that there mean there's been solar max months before. But it seems at least to me that that yeah, this is a little bit different in that that we're just having more and more of these events happening in our day to day life. Um I think it's might just be a matter of the yeah. Really? Uh all right. Like I I can't think of any reason as to why this um solar this year of solar activity is any is any different than than let's say eleven years ago. All right, all right. Yeah.

Let me ask you a question here. Once the CME gets released from the sun, Is it I'm assuming because it's okay. So is I'm assuming it's getting released from the sun spot. I don't even know if this is correct technical terminology here. Yeah, maybe from that region. It's coming from the solar surface. Essentially my question being that is it like a radially outward or is it like going in a specific direction?

Essentially saying that can there be a CME on the other side, like going on the other side of the solar system where we just miss it? Or is it like a radial right radially outward? No, it's more the first that you mentioned where you have You can think of as many eruptions that are actually happening At the same time or close to the same time. All right. And we might just be unlucky in that the earth will be passing through the the trajectory of that CME at that point in time. So it's not

It's not like the whole s the the sun is all blowing up at once, as it were, but it's just an eruption at a particular place in time. All right, all right. Okay. Okay. So um

I'm just trying to think because I've always been interested in understanding more about like solar activity and how it really relates to the earth. Can you maybe explain and this probably is very, very related. My understanding is that northern lights occur twenty four seven. Because there's always there's always activity and there's always the charged particles going towards the the poles. Right. I know you explained this briefly, but maybe you can take me on a journey one more time onto why

they get c I mean, I guess'cause the magnetic field is concentrated towards the pole. So it goes there. But what is the process or what is kind of the transport of like the charged particles from the sun? Going to the poles. Is it just because they're like just attracted to high magnetic field or is there a little more than that? Yeah, so it's it's quite complicated, but you're right in that.

they're happening the you know so the so the aurora is happening constantly but you were usually more talking about them when when they come closer south. Yeah. Right. Um but the process by which had this happens is that Um I explained that the both the sun and the earth ha ha have uh independently a magnetic magnetic field.

And the solar wind is essentially compressing the Earth's magnetic field. Okay, so what what this looks like if you can picture it is ahead of the of the Earth. And what I mean by ahead is in between the sun and the earth. So ahead of the earth. you have a compression, you have a magnetic field that moves closer to the Earth.

And then on the r on the back side or the rare side of the earth, you have something that's called a magnetotail, where you actually have uh you can think of it as a wake if you're familiar with that terminology. So you you have the essentially a wake of magnetic field lines that are that are

Concentrated at at the uh backside of the earth and these can extend quite uh a distance away. And then What happens is you get this thing called magnetic reconnection where It it appears that magnetic field lines are essentially combining and it and it's through this process process that you ha essentially have a host of charged particles that are Uh along these field lines are shooting from this reconnection event all the way to to the uh poles of the earth. Oh. Yeah. Wait Oh, okay.

And what what dictates that connection like why is that? So they're they're following they're literally following the magnetic field line. So because the magnetic field lines are joining at this reconnection event and they're Going all the way to the to the poles where the magnetic field lines emanate from. That's where they're concentrated at the poles. Oh interesting.

Now, is it right to say so obviously it is right to s I mean obviously it is right to say that they're more concentrated on the magnetic poles. Sorry, the magnetic poles and not the geographic poles. Right. No, what's the whole ordeal with actually this is not even really related to I was just thinking of Uh let's let me maybe not'cause I'cause I know'cause I know the geomagnetic sorry, not the geo um the magnetic north is technically the geographic south. Yes, it's kinda

But that has nothing to do with it. That's just like once every I believe like twelve thousand years or something, the earth just goes through whole process, right? Right. Nothing really to do with solar wind or anything. I don't believe so. You don't believe so? Right, right, right. Okay.

When you were describing CMEs, you ex uh you explained the process of solar flares. Yes. Now. You were mentioning one of the biggest things about um about predicting these CMEs are Well, I mean sorry, th the the biggest thing with CMEs is predicting them. The hardest thing is predicting them. Now you mentioned that usually solar flares occur quite a lot before and obviously solar flares are traveling at the speed of light.

So is there any kind of thought process with like, oh, maybe we can just measure solar flares that occur at certain times? That may cause a CME. Yeah, so there's definitely a connection or correlation between flares and CMEs. But it's not necessarily one-to-one. Right, right. Um, but it's certainly a part of the puzzle piece, or a part of the puzzle, I should say, yeah, to track um or or predict.

That's solar activity, right? So is it right to say that every CME will have a solar flare, but every solar flare won't cause a CME? That's a good question. Um I don't know that's a good question. I'm not sure. So we've discussed why I think I'm gonna kinda stop the physics question soon because I'm still very curious about so solar flares.

Can can you maybe talk a little bit more about them? Do you know why? Cause we describe kind of why we think so why is there like a sudden burst of the radio energy? So we said that there's a magnetic field line s possibly pointing in both directions near the sunspot.

What kind of causes that first trigger that makes the solar flare I guess I mean the pl I mean if is there's a lot of energy there's gonna be some kind of burst, like a some kind of pressure bubble uh bubble. But Maybe you can if you can talk about the trigger Man, I you're really putting me on the spot. That's all right. That's all right. Because I mean in general if if anybody listening can put it in the comments or yeah, that would be very lovely because I've I've always wondered

about solar events and just a little bit more yeah about how this works. Okay, so we've spoken about CMEs and Um essentially

Space physics. Now let me ask you a little question about what you do with them. Sure. Now my understanding is that well, I know that you model them. And you very briefly described MHD equations or the magnetohydrodynamic equations. Right. Maybe you can explain a little bit more about what is what those exactly are, why you are able to model it using those equations. Right. And can you use a better set?

Right, this is a great question. So let's dive in into the into the modeling, which hopefully I'll be able to have better answers for. Um but okay, where do we start? So As I mentioned, we're modeling the the plasma essentially as uh as a continuum. Okay, so that's already quite a strong assumption. Okay. Okay, so we're assuming that this is a continuum of matter. And that we're assuming that this essentially behaves as a gap.

Right. But not only is it a gas, we're assuming that it behaves as a perfectly electrically conducting uh gas. So we there we've baked in already quite a few assumptions. So one of them being that it's perfectly electrically conducting, that there's no resistance. Um and we're also assuming that uh that the flow is inviscid, meaning that it has no viscosity, okay? Or sorry, I I I should say um

Yeah, n uh no viscosity. So what I just described, those assumptions that I just gave you, if you start with essentially um, you know, Newton's second law, F equals M A. Through some fancy math, you can arrive arrive at something that we called uh magnetohydrodynamics or ideal magnetohydrodynamics, which you mentioned already, which is MHD. Right. So you can think of this as

Uh the Euler equations of gas dynamics and these equations describe an inviscid flow. Okay. Sorry, just quickly the Euler equations. Um the best way I like to describe it is literally the conservation. So when we think of conservation, it's basically conservation of mass, momentum, and energy. And if you just write them with a bunch of derivatives, make it look cool, you all all of a sudden get these partial differential equations, which are often called the Euler equations.

Now these equations are differentiated from more famous Navier Stokes equations, which we won't get into now, because of the fact that they're investigating. That's great. So you're essentially dealing with in in an inviscid set of just conservation equations. That's right. And then what do you do? Do you add a couple equations to that? Do you just take those? What what exactly you've done a good description, you can think of the Euler equations of gas dynamics.

Coupled together with Maxwell's equations of electrodynamics. Okay. All right. And now how can we actually arrive at these? You can essentially without getting too into the nitty gritty, you can essentially um add an acceleration term that's due to the Lorentz force. Because of this extra acceleration term, you're you're gonna get um some coupling in the momentum equation uh for for the magnetic.

pr uh you can think of as uh the magnetic momentum or the momentum associated with the magnetic field. You'll get an equation for the time evolution of of the magnetic field, and you'll also get um some components in the in the energy equation. All right. So you so you essentially just add a bunch of Maxwell

Stuff tool you're already. But I would say it's not ad hoc. It's it's done very carefully. All right. And this is actually why Alvin won uh a Nobel Prize, a Nobel Prize in Physics for for this work. Fantastic. Yeah. So when you say carefully Obviously don't go into the details, but any like standout laws or any standout things that must be followed, anything that oh, you must satisfy this. Right. You must satisfy that. So the way I like to think about it is

Uh sort of at a deeper level. So so we can think of Euler or MHD as uh a result. A more specific result, but the the broader uh sort of physics that's going on is we can think of Boltzmann's equation. Okay, so Boltzmann equation Boltzmann's equations describe the essentially a transport of a particle description. Right.

No acceleration terms and we t take integrals of of these equations, we can arrive at Euler's equations. And actually we can arrive at um at Navier Stokes' equations as well. But we won't go into that. Now if thinking back to Boltzmann's equation. If we add the fact that um what I called the the Lorentz force.

Right, we have this force that that's essentially due to the cross product between the magnetic field and the velocity field and this is described this is called uh The Lorentz force, if you break that in into the Boltzmann equation, you go through the same process of taking integrals and the like, you'll then arrive at um what we call the ideal image.

And again you have to make a few a assumptions and and do a few sort of tricks. Um but it's it's done pretty care pretty carefully. Now before we go into nitty gritty of MHD, because I have a couple of questions in how you model this.

What is a diff what are some different models that you can use? So first you said ideal. Right. So I'm assuming there is a non ideal. That's correct. And on top of that, just to ask you another question, are there any other models that might be used to model solar wind? That's a great question. So

Um yes, we can definitely relax these assumptions quite a bit. So we can say, okay, resistive MHD, right? And what does that imply? And this is now where we instead of having a uh fluid that's perfectly conducting, now there's actually resistance in the conduction of electricity. Right. Okay, that's one uh assumption we could relax. We could also relax the inviscid part, so we can say now we have viscosity, so now we're have let's say Navier Stokes equations with Maxwell's equation.

Okay. What is visc sorry, I know I'm like kinda tangent. What is viscosity in space? I guess it's the plasma itself that's viscous? Yeah, so so this is w like the Right. Because the the the viscosity of of plasma in space will be minimal. Right. Right. So it is actually quite a quite a good assumption. But you can think of maybe laboratory plasmas. Yeah. Um definitely. Yeah. Or fusion plasmas where where

Perhaps these effects are more important. So the resistive part, how how bad of an assumption is the perfectly electrical conductor? I would say s it is a not the greatest assumption. Alright. And this is really the surprising fact. Okay, so so as I mentioned, we're we're we're essentially model ideal MHD assumes

A continuum, right? So it's not very rarefied. But we know that space f it space plasmas are. And if you look at the now, I'm gonna get really technical here. If you look at the mean free path. between particles in space, they're in the order of one astronomical unit. That means they're in the order of this the distance from the sun to the earth. Yeah. So if you know anything about fluid flow, this tells you that this approximation is terrible.

And it shouldn't work at all. Quick, quick, quick description for mean free paths for those that might not mean free path is essentially the average distance that any two uh uh a particle will travel before hitting another particle. Correct. So you're essentially saying the average distance for one of these particles to hit another one.

by this assumption is that it's one astronomical unit. No, so this is this is actually what's not the assumption, but what's actually the same. This is what actually oh sorry, sorry, I misunderstood. So this is what actually is taking place is that the mean free pass for the average distance

for a plasma, is that correct? So a pl a a plasma particle is one astronomical unit before it hits like another plasma particle. All right. All right. So this should sort of point you to well, this shouldn't work, right? Um But again, kinda g diving deeper into the physics, there's this uh There's a

Oh man, I'm I'm I'm losing the words here. But there's there's an effect that essentially re is has a a reduction in the effect of m mean free path. Okay and by what by that I mean that there's I think it's actually a quantum effect that makes it so that it appears or the floor the plasma behaves as if it had a much smaller mean for you.

Okay. While I understand this, I don't really understand the context to the resistive part. Why is this advantageous or disadvantageous for assuming a perfectly electrical? Right. Why does the mean free path have to do with that? Yeah, so that's it's sorry, I guess that doesn't actually have much to do with with with with resistiveness. This is I guess I just wanted to jump into

Uh w of the elephant in the room. The elephant in the room of of ideal MHD is that it's it shouldn't work. It shouldn't work. But when we So there's some justification talking about this uh This effect of being free path, but when you actually compare the predictions of ideal MHD with observations, it actually matches up decently well. So it's not necessarily that the model is is built on good groundwork, as it were, but when you actually compare it with observations, it does quite well.

So when you say observations, obviously I'm assuming you're talking about solar observations. That's like only MH like uh uh space weather based obviously that works pretty well. Yeah. Now are there other equations but non MHD equations that you may be able to use to model

Yeah, so you can go simpler. So you can for example the the the very simplest you could go is Parker Solar Wind model, which is a base basically it's not even a a partial differential equation or ordinary differential equation, it's just an algebraic equation. Oh all right um that's That describes the solar wind is very, very, very, very simple. Okay, now can you go more complicated? Non-MHD base.

I don't know if it if it would be non MHD based, but you can get, for example, multi multi species MHD. Okay, so one of the assumptions that we make with ideal MHD is that Uh we're treating the electrons and ions as a single s as a single fluid, but you can actually start treating ions and electrons as that.

Is that yeah, multiple temperature? Yeah, that's correct. Oh, so you can have that. Um you can have multiple temperatures, right? So in the same in the same line um way of thinking, right? Instead of having a single temperature, you you now have multiple temperatures. Um A pretty also popular technique is is a simulation technique is called particle and cell. Right. Um where you're now

Essentially keeping closer track of of particles themselves rather than or s or things that behave like particles rather than this continuum approach. Yeah. Yeah. But I I guess beyond I think you would always be tied in some way to MHD, but it might not be ideal. So MHD is essentially how you model the solar wind. Now do you okay. How do you start the modeling process? Because I know for let I mean let me kind of give context to a question for most.

Equations or most uh model or simulations you would probably give a set of initial conditions somewhere. And it would kind of just take it from there. That's correct. But my understanding of MHD, or at least the way that you guys do your um your modeling of your solar wind, is that you use multiple models depending on where you are modeling.

That's right. Yeah. So maybe you want to go over a little bit about how and again, this is not just you what you do, this is what most people do in the field of modeling solar wind. So how exactly just like start to finish, obviously brief, how do you model it? What models do you use and where? Yeah, it's a good question. So what we do, um at Utaius is that we start at the so at the surface of the sun, we actually have something called a magnetogram.

You can think of these as images of the magnetic field, the radiomagnetic field on the surface of the earth. And these are taken by satellites. Right. And these are actual um this is actually observational data. This is not a model. This is mesh these are Okay. So this is our sort of our ground truth. So you need that to start starting. For for our modeling capabilities, yes, you need these. All right, all right. Okay. Makes sense. So what you do is you start with these.

And then in the lower corona, and now let me explain what that means, the corona is essentially the region that's in the atmosphere of the sun. So you can think of perhaps from the solar surface to, let's say, twenty solar radii.

Twenty solar radii. It's approximately That's pretty big'cause usually when we think of atmosphere we think like a hundred uh like a hundred kilometers away. You're saying twenty five solar radii away. So this is very far. Yes. This is very far. Okay. Well So what we do is from let's say the surface of the sun to two point five solar radii in this lower region of the corona, we're assuming

We're assuming a um a cr we're not two things. We're assuming one thing and we're assuming that the magnetic field is current free. Okay, that means that there's no current free. Yeah, there's no electrical current. Um and math and the way we do this really is b uh it's motivated. I mean it is motivated physically if you look at um yeah, you can sort of look at observations and and you can somehow justify th this assumption. Um but mathematically it actually makes

the equation's quite a bit simpler. Okay. So what we do is that um we take the divergence free property of the magnetic field. So this just means that the the magnetic field doesn't have any sources or sinks, right? It can never just be popping in or out of out of of a single point. Okay, so we take that condition.

we take the current free condition, which we can essentially summed up as the the the curl of the magnetic field is zero. So you have now divergence and curl are both zero and Um we have now magnetic field uh the magnetic field on the surface of the sun through the magnetogram.

And we can actually now um extrapolate the m the magnetic field from the the surface of the sun to any other uh radial distance that we But we obviously don't do this to any radial distance that we want because we know that this is something. Won't hold for the whole ratio. So we do this essentially up until uh two point five solar radii. What we do beyond that point is that we um essentially open up the magnetic field lines. So any magnetic field lines that are um cloth that are

Yeah, that are close beyond this point. By close I just mean that they originate from the sun and they terminate at the sun. So any magnetic fields that that are still that are closed beyond beyond this uh um this radius we opened them up, meaning that instead of Uh pointing towards now the point outwards or vice versa. All right. And then we do this from two point five solar radii all the way to twenty-five solar radii.

Okay. And is this like a specific model? Does the model have a name? These are all sort of uh built by physicists. um through maybe wan since the sixties. Maybe you want to talk about like is there a name for this model? Yeah, so the the the one in the in the soul in the lower corona is called the PF PFFS. for uh I won't be able to to uh PFFS. Okay, the PFFS model. And then from from two point five to twenty five is the S C S or the shot in current sheet model.

And it's named after the the physicist who who came up with it. Um And it's still relying on similar assumptions. Okay, so now we've gone from observations of the magnetic field at the solar surface now all the way to twenty five solar radius. Sorry, what I I don't know if I missed this very, very briefly, but can you just summarize the difference between the um like the two point five to twenty five and the like what uh the assumptions, just the assumptions. What are the assumption differences?

The assumptions are are the the same, okay, but in the SCS model, the the Sean or the second model, we can actually have current. Appearing. And this happens because we've opened we've we've opened minority feel lines. And then this essentially results in something that we call a a current sheet. All right. Okay. Okay.

Um f then from that point onwards, now we're now let's say we're at twenty five solar radii. Now uh what we do is that we m we use essentially statistical Uh correlations that where we correlate the magnetic field lines or the magnetic field to the rest of the plasma properties. So we have correlations for the for the velocity field, we have correlations for the density, as well as for the for the temperature.

Once we have all these properties, we have magnetic field line from from the two models that I just described, we have the rest of the plasma properties, then this is where MHD can now kick. So now we have the appropriate boundary conditions that we need for MHD and then from twenty-five solar radii now to one AU, let's say, or two twenty-five solar radii approximately, then we employ the MHD equations and and we model these.

All right. Yeah. So the MHD really kicks in at twenty five. That's correct. Yeah. And this is I'm assuming to Because you don't need to model MHD all the way through and through the more can you? Mainly well actually some people do model MHD all the way f from the solar surface to to you know one eight. But it really simplifies the modeling to to just focus on the magnetic field in this lower in this lower region. Okay, okay.

Gage when would somebody use the MHD through and through versus when would they not do that? Is there an advantage? Is it just computational advantages? So a big advantage is computationally. Um but I would say it's probably more self con not probably, but it is more self consistent to just have MHD the whole way through. Okay.

Okay. But then you need y there's a few things that you have to take care of. For example, um coronal heating in in in the corona that we don't have to take care of if if we just use the magnetic field. Yeah.

So there's just there's a few difficulties in the in the magnetic field line is Really the main driver of the of the dynamics in the in the solar wind. Yeah. Now this doesn't this seems like a Pretty hefty calculation. Doesn't seem like something you can do on a on a laptop. How exactly do you do these calculations? Yeah, that's a good question. So certainly we could not do these uh on a laptop. Uh so what we do is we make use of supercomputing facilities.

Um to put it simply, let's say we have a computational domain. Um l of c consisting of let's say ten million computational cells. We're gonna break them up. uh operating on these cells on a single CPU, we're gonna break them up and we're gonna make use of let's say a thousand CPUs to process them independently and then there's some communication that has to happen at the boundary.

of where you have two different CPUs operating on um two separate cells So what are some challenges when you um so what you essentially described is very important, I feel like for a lot of listeners, especially in today's day and age where like Artificial intelligence and machine learning are just taking super big advantage of parallelization, essentially. Right, right. So what you described is essentially HPC or high performance computing, essentially using parallelization to your advantage.

So what are some challenges that you noticed in actually modeling, in actually writing the code for this model and were and how did the parallelization kind of add into the challenges? Right. It's a good question. So Whenever we're programming, let's say a Python script or whatever, uh we're just We're not worrying about what each processor is doing. We just have a single process.

That that's mo that's doing everything, right? Now when you have let's say ten thousand processors that are processing your data, one of the trickiest challenges is to focus is the interface between two CPUs, right? Because now we need to start needing to go to the U.S. Let's say one CPU needs data that's stored in another another CPU's memory. So we need to start doing some communication. Okay. Right. Um we do this through something called MPI or message passing interface.

It can get it it can get a little bit tricky and we we just need to pay attention to how we're gonna do this this communication between CPUs in in a in an efficient manner. Because if you don't do it efficiently it it could actually be quite quite a big bottleneck. Just moving the data around so that each processor has what it needs.

I'm assuming at one point it almost becomes worse to use a certain number of CPUs simply because of how many messages are being passed. Or am I wrong? And you can just use and like the more CPUs the better. Or is there like a number Well, n you're right that there there is a uh overhead, let's say, in using m you know, in splitting up your job or your calculation into multiple CPUs.

In in practice, we don't usually r like run into that that that uh bottleneck in that anytime we throw more CPUs at it, we will get faster uh speed. But but But um in principle, let's say you just had one CPU per cell, then you're having to do massive amounts of communications. And in and in that case I am I would imagine that yeah, like the message passing itself would slow you down more than than splitting up the job.

Maybe something I can't explain because I guess I also dabble in something similar. Um don't really research on MHD particularly, but also just have to model my own set of equations. And the way that that works in parallel and obviously the same as yours is and this is I believe how most parallel code works, is it is it not multi block for like most parallel code that they usually essentially

Let's say you as as you said you have 10 million cells. Instead of putting one cell obviously on each processor, the b the best way to do this is essentially to have a certain number of quote unquote blocks. So let's say you have 10 million cells. Let's say you have 10 blocks. Again, not very ideal, but let's say you do. Now you have a million cells per block.

So now you just put a block on each processor. Right. You know? So that's that's kind of the way we do it. I'm obviously assuming that's the way you do it as well. That's correct. Yeah. And I think that's the way that most people using parallel code with Modeling simulations and meshes and whatnot would do something like a multi block mesh. I think mol multi block approaches are pretty popular.

Because I know that um it can definitely get tricky when you so like for example, let's say I have ten processors and I have ten blocks and I now say use all ten processors. That would probab I mean that would be more ideal than putting, for example, two blocks on each processor. Right. But now, let's say I ask for twenty processors and I only have ten blocks.

Right. So you can't y actually make use of Oh you can't even make use of it. Oh my good thought will be slower. Okay. So what you could do in that situation to speed up your your calculation is to Take the ten blocks, split them into twenty. And now you have twenty blocks and twenty processors. Oh okay. So just split the blocks. So you so you would have each block would have less cells per block. So essentially you would want to maximize or you you would want to ideally get

One block per processor. Is that correct? Yeah essentially that I mean that that would be the fastest. Calculation. And then you also have to think about how many cells you want to pack in that block. Right. Yeah. Now I'm assuming things get a little more complicated when they're a little like uneven numbers. Like if l let's say they're like twenty-two blocks and twenty-three sub processors. Absolutely. Yeah. Yeah. Now you've got one processor with two blocks.

How does how does a supercomputer or sorry, not a super how do you, the coder, handle something like that? Having multiple blocks in one processor is not a problem. Okay. But having odd number of blocks and and the like can actually make things a little bit complicated in the sense that Um in the logic of okay, how are we gonna split split these tasks? We're we're usually actually assuming even numbers and I think I believe our code only handles even number of uh of cells, for instance.

Okay, I actually did not know this. Yeah. All right. I mean I guess it makes sense because odd number would be I mean I would just say it doesn't have to be that way. We could have coded it otherwise, but it makes the logic a little bit

So I'm assuming the biggest difficulty as well with the computing is not only like the passing of the message. But also making sure that Because again, we code in C, so it's all very memory dependent. We also have to make sure that the memory is allocated correctly. Now not that I've actually da dived into the message passing interface myself too much.

But is there any like again for those C plus plus developers or any developers that are dealing with allocation of memory, how does that impact or how does the parallelization impact that? Yeah. So I think What you're what you're asking is how does parallelism um increase or or change your memory p footprint? Yeah, yeah, yeah, yeah, yeah. Essentially. Yeah. And how and how do you deal with that? How do you deal with memory everywhere and putting it all and

if we had a a serial program that didn't parallelize, then our memory footprint would actually be quite a bit uh smaller. And the reason for that is because we need to essentially allocate or to use a different word, we need to give space Um so that we can store information about our neighbors. Or by neighbors I mean the the information on different So if if we had a serial code, it's a good idea.

We wouldn't need that that memory location. But because we need to transfer messages, we actually need to dedicate a a little space of memory to put the information that belongs to our neighbor so that we can use it So uh certainly it will increase um the the memory footprint. So essentially each processor must have information about all the other processors? Or is it just like one processor that needs to have this information?

So wouldn't that be more efficient? So you need information about your neighbor. So let's say let's go back to what we were talking about blocks, right? Right. So Let's say we have two blocks belonging to um let's say we have four blocks, okay? And there's There's two processors. So I I know for the audience this can get a little bit com complicated when we talk about about a little bit um a lot of numbers. But let's say we have t four blocks, two processors.

That means that each processor has two blocks on it. Okay. So that means that the the blocks that are are at an interface, and I by interface I mean that one block belongs to one CPU and the other block belongs to this other CPU needs to have information about that other block. So that it it can essentially do calculations with its own information.

I think I kinda that was a bit confusing. I don't know if I if I really answered your question. No, I mean I I kinda I kinda get like you essentially have to save memory for just like having the fact that there are more than there's more than one block. So then that memory itself will be adding to the fact that

If you did it in serial, you wouldn't need that. So you would be saving that memory. Now is adding this memory d i is is there a point where it gets too much? Is there because I'm assuming like You know, how much memory would you really need to allocate? What if you're not? if your computer is low on memory, high on power or maybe high on power, low on or sorry, uh low on power, high on memory.

How would it how would it deal with that? Yeah, it's a good question. And this is very much related to your earlier question regarding um Do you do you always benefit from more paralysis? And like I said, the answer is no. Yeah. Because of th this overhead related to storing information about your your neighbors. True, true. Yeah.

So there's a lot of there's a lot of just communication that you have to do and you have to make sure it's done correctly. That's correct, yeah. Okay. Now before we get into the nitty-gritty of your thesis. I do want to just close up with if you have any or sorry not if but I'm sure you do any challenges with the modeling of your MHD code because I would assume that or I don't know, maybe you tell me I'm wrong.

I don't know how many How is spacewe I'm I'm assuming space weather is getting popular only very recently because of all our satellites and our technology. Or maybe he's been popular for many years. I don't know. I mean depends what you mean by many years, but um our supervisor, so Ray and I both are supervised by the same by the same guy, and he started his MHD work.

in the late I would say in the late nineties. So is that recent? I'm not sure, but but certainly people have been working on this for for a few decades now. Okay, so so space weather is not new for sure. It's just it's definitely not new. And modeling it is not new. Okay, okay.

So any new challenges that you've experienced while modeling MHD as opposed to okay, first of all maybe you can discuss some general challenges with just modeling. Let's not Maybe discuss HP C anymore, just modeling challenges and then any specific to MHD that you went through? Yeah, so I think. In the context of space weather, the biggest challenges are the appropriate uh

specification of the boundary conditions, which we talked about the the whole all the different models that go into it and how we specify the plasma properties at the at the inner boundary. Okay, so that's quite a big challenge and that's and there's still r uh There's still lots of effort that that's dedicated to all that. The second challenge I would say that's more on the solved side, I would say, is the Um how do you deal with the solenoidal or the f or the

divergence free property of the magnetic field. And again, I I did uh I've mentioned that a little bit, but the the MHD the magnetic field from Gauss's law we know cannot have any sources or sync. Okay, and that's expressed mathematically as as divergence free. Right. So how do we bake that in so that our code also be uh respects that property?

And in the early two thousands there was quite a bit of effort that was dedicated to to dealing with this difficulty that's particular to MHD and maybe you don't see in in other flu fluid descriptions. Um but I would say that's pretty much handled at this point. So I would say now we're in the sort of let's call it the third generation of MHD modeling where we've solved the m the magnetic divergence free property. We you have a good grasp of the boundary conditions, okay?

or the the m the data driven boundary conditions. And the the next frontier is really uncertainty, quantification, and data simulation. And this is where we want to not only just use our model, but we want to know, okay, well, how accurate is our is our model and we want to make use of all the observational data that that we have to better inform our model.

Okay. I think this is the perfect way to ask you because you mentioned observational data. Yeah. To talk about the actual nitty gritty of your thesis, which is data assimilation. And that's actually fun fact that's not recording anymore. That's a fun fact how I got to know him because I'm currently also studying data assimilation. For my thesis which is

I was have promised I'll make a video on that I have not done yet. But um and that's actually how I met Jose because he has dabbled in data simulation for quite a while. So maybe you can start with explaining why what is data assimilation, why does it connect to MHD and I'm assuming it's advantageous, which is why you're using it. Why is it advantageous? Yeah, it's a great question. So

You mentioned okay, what are some of the challenges that we deal with when we do MHD modeling? And I and I went through that. But let's say now we have the perfect model. Our model behaves exactly how we would like it to. Even if that were the case. It's very likely and in fact. It is i not only likely but it occurs that that our models don't actually match the observations thou that that we record after the fact. Yeah. Okay.

Different reasons for that, but one of the ones that we're trying to to address with data simulations is that there's actually a lot of uncertainty in the con in the input. That we give our models. So again, let's say you have a perfect model, but if you give it bad data or bad information, it'll

The equations might be correct, but you're not actually predicting what you want to predict. Right? Or you can think of more simply garbage in, garbage out. Right. Okay. Right. And this is a problem that's not just relevant to MHD, this is a problem that's relevant to any type of predictive science. Okay. Okay. So any kind of w when you say predictive science, I think when a lot I think what we've been saying is the word modeling a lot. Right. And I think

Maybe I don't know if this is the perfect time to transition to the word forecasting. That's a good question. Yeah. Because forecast I think makes a lot of sense to a lot of people that are thinking about what is the point of modern. When you say mod sorry, when you say modeling, what are you doing? Your most of the goal, I I shouldn't say all modeling, but most of the goal is to forecast or predict what Something will be. The best example of that.

Let's say I want to know the temperature tomorrow. Right. And this is actually kind of important too because data assimilation is used everywhere in weather prediction as well. How do we know our w the weather app is accurate? Because of data assimilation. So knowing the temperature tomorrow If let's say I wish to know it exactly.

No matter essentially how good my model would be, there's some information that I have to put about it today or to run the model. So my whole goal is essentially to predict the temperature tomorrow. Now what Jose is explaining is that data assimilation, I mean or actually not only data assimilation, but just the fact about all models, is that no matter what I predict, because I did not have exactly perfect information today, because you never will.

It won't be perfect. So let's say I predicted seventeen degrees tomorrow, let's say it's sixteen point three. It's good enough, but it's not perfect. Right. Right? So that is kind of where data simulation comes in. That's correct. And so we I think there's m sort of two main

Areas where this is really really relevant. One is and you already alluded to it, is atmospheric weather predictions. Okay. So there's actually this huge, very expansive network of observations in involving millions and millions of observations that are assimilated or integrated into weather prediction models every single day. So this is essenti essentially for those who are interested, we're solving these huge optimization problems every single day when we do weather.

And we say optimization problems. That's basically saying like you're trying again, we haven't really gotten to the nitty-gritty yet, but essentially you're saying you're trying to optimize. for the temperature or whatever you're trying to find. Right. Given the data. Exactly. Right, exactly. Yeah. Briefly, what is what is some of this data that's generally is it just like temperature data?

Is it it's wind data? I have no idea. It's a whole host it's a whole host. It's it's like you said, wind like velocity, wind is is a good one, temperature, pressure, there's weather balloons, there's physical stations that that are station that are fixed to the ground. There's a whole host there's uh satellites that are taking radar measurements of the earth. And and th all those measurements in combination with the modeling capabilities.

uh that weather prediction centers have is what makes weather forecast work today. If you didn't have the the the data and you only had the model, there's no way that we could make any meaningful predictions. Okay. And I think that's One of the differences between weather for c uh sort of terrestrial or atmospheric weather forecasting and space weather forecasting is that um Atmospheric weather forecasting is highly chaotic.

meaning that a very small change to the initial conditions will lead to a huge uh change in in the output. So you can think some people call this the butterfly effect. Right. Now this is also the case in space weather, but I but in my experience it Its effect is much less it's m much more reduced. So it's not as chaotic this effect. It's not as chaotic as as as as far as I've uh experienced. Yeah. So

Data simulation, right? You have a bunch of parameters and you have to optimize them. Explain what that means in especially in relation to MHD. How are you relating Or I guess maybe I can give a little um so essentially the way that best I've understood data simulation works is that you essentially have a parameter that you wish to optimize for. And I'm gonna continue with the temperature example with the weather tomorrow. Let's say I want to know the weather tomorrow.

Now to know that the weather tomorrow I probably have to know, let's say I need to know the pressure of profile today. Right. Right. Let's say I need to know that. Like essentially my model, my model to predict the weather tomorrow, to give me that result.

That simulation, it needs some input data. And let's say one of those input data is pressure, like a pressure profile. Now I put in a bogus pressure profile, it's obviously gonna give me a bogus temperature result. You said garbage in, garbage out. So my whole goal with data assimilation is essentially to take observation

Of the pr maybe the pressure profile, but maybe not the pressure profile. Right? That's the biggest advantage of data simulation that you don't actually need to know exactly what you are trying to optimize for. So for example, let's say Um I d this is I don't nothing about weather, so please do not like cite any of this. But let's say the density profile was d directly related to the pressure profile, which I'm sure it is. And let's say there was no way for us to measure this pressure.

So data assimilation, the advantage that it gives us is that we can take data and as long as it's related to whatever parameter we want to optimize for, which in this case is the pressure profile for today. We can take that data. The goal of this data assimilation algorithm then is essentially to take that data and optimize for this pressure of today, for this pressure profile today.

Now, most people think, oh, aren't you trying to optimize for the temperature? Yes, but the whole goal is the only way that I get that temperature is by perfecting the input. So one big thing about data assimilation that we will talk about or at least that we are using in our codes that makes the programming and the math a lot easier is we are essentially assuming a perfect mod.

We're essentially assuming that the model that we're using, that means if we give it a pressure profile today, it will give like the exact temperature that we expect. That's what we're assuming. Not that is a that that is not a right assumption whatsoever, but it signific I mean not whatsoever. It's definitely it's it's not a correct assumption, but it can be taken. It significantly reduces the mathematics required to do a lot of this.

But essentially the idea is we're assuming a perfect model. We're obviously assuming an imperfect data set. We're assuming imperfect predictions. So we have uncertainties everywhere else, except in the model. So the model essentially is assumed to be perfect. So we're taking this density profile, let's say, that I've recorded today, and the whole goal, as I mentioned again of the data assimilation program, is essentially to optimize for the pressure for today.

So once I feed all this density data into my program, it's gonna give me Some pressure profile. Now I feed this pressure profile back into my model to then predict the temperature for tomorrow. And now that is kind of how modern weather prediction is done. We take all this data to better predict.

factors that we can then put in our model to then predict what we actually want to predict. Yeah. Right. It's a that's a good description, right? And I think something you touched on is is also very key and that's this art of weighing the the data and the model. So we we have we don't we don't we don't we're not gonna take all the data points as if they're equally like likely or equally um good. We're gonna say okay we know

Some of our measurement tools, let's say um our radar, our satellites, are more accurate than some of the other ones. And we uh we want to account for that accuracy in in our measurement. And the same is true of our what we call the background uh input.

We might think okay, let's going with with um Rahan's example, we might think of well this part of the pressure profile we w we're not sure but but we're actually pretty pretty We we have some uh idea of what it looks like, but other parts of the pressure profile are maybe much more uh

noisy. We we don't really know what it looks like. So we want to bake in that information that parts of parts of our inputs are more accurate, we're more confident, and parts of our measurements are more as well, more more accurate or more confident. Right. And by You know, making or leveraging that information, we can actually get much better results as well. So what is so now that we've I think understood the goal of data assimilation.

What is your use with it? How do you use data assimilation with MHD? What are you trying to optimize for? Right. And um yeah, what are some challenges? Yeah, so Before I answer that directly, let's go back to to n weather prediction. All right. So the goal of of data simulation for weather prediction is really to um come up with improved estimates of the in of the uh initial condition.

Okay, so the initial conditions is is everything. Okay. Right. Now when it comes to MHD or or or space weather modeling.

The initial conditions, funnily enough, are actually uh almost irrelevant. Okay. What's really important for us is actually the boundary conditions. And there's a this makes it this makes the the the the the problem a little bit So what we want to do then is we want to make have these take these observations, like I for example, like I said from uh Lagrange Point one or perhaps other satellites.

and update or correct the boundary conditions that I that we talked about at this at twelve twenty five solar radii. Right. Right. Okay. So I guess in my example, the pressure profile example that I was giving is more related to the initial condition. That oh this particular model or as I said forecast

needs the pressure to start the modeling. Right. It starts with some pressure and then again, this is all completely bogus. I'm just making stuff up here. So don't actually this is not how weather prediction is done. This is just an explanation for the assimilation part. So let's say you take some pr uh uh pressure profile And then you simulate. So that is an initial condition. Now what you're explaining is essentially instead of predicting or essentially so are you optimizing for the state?

Essentially at the boundary or are you optimizing for different variables at the boundary? So I don't know what you mean exactly by that. Do you mean some parameters or So are you optimizing like a certain parameter at the boundary or the entire state variable at the boundary? So what I'm doing in my thesis is just looking at the whole uh state variable at the boundary. Right. Right. That's related to

Associated with with the sun. Right. Um, but there is also some work being done on perhaps some of the underlying parameters. How can we uh optimize or or update those underlying parameters. Yeah. Yeah, because currently in my research, uh again, not that I've got into this in the podcast yet, but I will. Um

I'm also doing boundary uh data assimilation. So even in my problem I have uh the whole deal of the boundary needs to be uh I don't know if assimilated is the right word, but optimized for. So in your case it's

If I'm not mistaken, the twenty five are not boundary. That's correct. Right. So what are you opti like, okay, I didn't truly understand still you said you're optimizing the state variable, but maybe explain a little bit more just to somebody who doesn't really understand what that means. Yeah. And

What observations are you using? Yeah, it's a good question. So let's say let's make this very simple. Let's say we have two circles. One at a radius of twenty-five, and another one at a radius of two twenty five. Okay. So the inner circle is analogous to the surface of the sun, and the bigger circle is analogous to the location of the earth in in space relative to the sun.

So what we want to know is what is the density, the plasma density, what is the plasma pressure, what is the magnetic field, and what is the velocity field at this inner circuit. Once we know that Then again assuming that our model is perfect, which we know it's not true, but once we know that information, then we can predict what the the solar wind will look like at the at the larger circle or at the the surface of the earth. In in terms of observations.

We're mainly using observational data from a satellite called A. Um which measures like um all plasma properties at Lagrange point. And it's at the Lagrange point one. No, but where does it measure these properties? At Lagrange point one? At Lagrange point one. Yeah. All right. All right. So essentially you're using data

close to the earth to optimize for parameters close to the sun. Yes, that's exactly right. That's the advantage of data simulation. That you don't especially with again me we might get into this with the method that you're using for data simulation.

which is your your variational data assimilation. Right. And if I'm not mistaken in other methods You're not you're not able to do that, right? Like you can't optimize for a parameter that you're not measuring.

Am I wrong? So let's maybe we should just dive into this. Okay, sure. So let's let's let's break up data simulation into two main families. One we call uh variational. We also sometimes call it adjoint-based, but let's just call it variational for now. Um, and the second one we call it sequential data. Right. In the in the variational approach we it's named after uh the calculus of variations.

So we're essentially and this is the language that Ray and I have been using, we're treating this data simulation problem as one very big optimization problem where we want to optimize for the in inner boundary conditions or or whatever. We we've gone into that quite a bit. With the second approach, with the sequential approach, we take more of of a statistical

kind of uh framework where we say, okay, given these observations and given this model and g given these uncertainties, what is the most likely state? Um Of course, uh given given the data. Okay. And actually we're we're we're also asking that question in the variational approach, but we're just doing so in in a slightly different way. Now the difference is that because we can Um in the variational approach. We can

um track how does this point that's not at the surface relate to the surface of the of of let's say the of the sun or that's not quite at the sun, right? Um with a sequential approach. You could also ask this question, okay, but it would be a lot more complicated to essentially have this information travel back in in space and time.

So I'm not giving uh a a good explanation because it's it's it's a little bit challenging. So maybe maybe I'll give an an an analogy. Okay. So let's say our data simulation problem is very simple. All we're doing is we're throwing a ball in the air. Okay. And we have a single snapshot of that ball. Okay. Okay. And we want to predict where it lands.

So with a variational approach, what we're gonna do is we're gonna pose an optimization problem for let's say the initial velocity of the ball. Okay. And we're going to look at um essentially all the trajectories that this ball could have taken.

and and and figure out what's the most likely one by by by doing this this uh optimization problem. In the sequential approach, what we're doing is okay, given this snapshot right now and given my that my model tells me the the the position of the ball at this at the same time when when the observation was taken.

We're gonna now update our model so that it better matches the observations and then continue from there from there. Right. So just again to nail down on the difference, the variation approach is really just optimizing for the initial condition. Or let's say boundary conditions. Well the sequential approach is issues. changing your state at the point of o of where when the observation was taken. Is that

The way you explain it, it seems like sequential is far more is far more accurate not accurate is the wrong word, but far more useful because you can predict it at every state. Am I wrong in making that assumption? Or what are the advantages and disadvantages of each method? Yeah, so I would say that it's not always clear which method will win out and you c kinda have to do the the the the difficult work of of really quantifying the the merits of each four year problem.

Turns out that we we've done this a little bit for space weather and and it seems to show that the variational approach will be much better. Okay, now both methods are using the same amount of information. Okay, so let's say we have ten snapshots of this ball. We're gonna use all 10 snapshots to now reconstruct what the initial velocity of the ball was when it was thrown. With a sequential approach.

At each time that the observation is taken, we're gonna update the state. So, but at the end of that simulation or that forecast, Both the sequential approach and the variational approach used all ten observations to to update its information. Okay. Yeah. Okay. So that's All right.

Is it a so is it a computational advantage? I still don't truly understand. So I I get it that it's problem dependent and you see advantages in both. But is there just like a specific type of problem where you just can't use one method over the or like you just cannot use one.

I would say there's not a problem where you cannot use one. I think there's pro there's problems where it's a lot easier to use one or the other. Um and I think for the types of problems that we're doing where we're really just interested in boundary data, the variational approach. Is easier in that sense. Because we, with the sequential approach, you would essentially need a way to track information from the observation location to the boundary.

And with with a variational approach, we actually get this type of information uh transport through something called the adjoint equations, which I don't really wanna get into because it's it's quite it's quite uh complicated. Um but it's related to the corres c characteristics of our PDEs. Okay, that was actually a nice I think I think I really like that last line where you explained um Where like how the observation is transporting to um our boundary or whatever, our thing of choice.

Now let's say I wanted to know the state in the middle. I'm assuming variational is is useless. So what do you mean by the state in the middle? That was not a very good question. Let's say I wish to optimize. Let's say I have an unsteady problem. In this case, this is referring to a time-evolving system. Let's say I wanted to know the the state at every point in time. And I wanted to optimize for that state at every point in time. Right.

I'm assuming the variational would not be very good there. No, so the variational I would disagree. The variational approach is Is doing that actually. Maybe like let's go a little bit deeper then. So the way that we construct this we've talked a lot a bit about constructing an optimization problem, right? So what we're doing is that let's say we have let's let's stick to our ball analogy. So let's say we have ten snapshots of the ball.

Now we're gonna construct this function that's gonna tell us how good or bad our model is. And all we can think of is very simple. All we're doing is we're gonna just take the difference between our model and the observation and square it. Okay? And this this this um function is is updated with time. So if we have ten observations We're going to update update this function ten times. Right. Okay. So now what we're doing is um we want to minimize this essentially this misfit function.

By choosing the best parameters so that our model best matches the data. Now you're uh let me explain briefly because the misfit function was a good use of a word there. I really like that word. Never it never heard a misfit function used before, but I really like that.

Because essentially what the square is doing, for those of you that um I'm sure have seen like an L one norm or an L two or I guess an L two norm error, is essentially I don't know if this is the right term, but it kind of grabs the error of Your state versus what you already have. So let's say you're seeing the difference between the system and the observation. And you square it, that's essentially an analogy for trying to get the error estimate for how off.

either one of them are. Yes. And what you're now saying is essentially we wish to minimize that. Exactly. Right. So in the best case scenario, let's say we pick the most optimal the most optimal um parameters, then our model would perfectly match the observations. Now we won't actually see this in practice because observations have noise. So there's always gonna be a a misfit, but we like to minimize that misfit as as b as best as possible.

So now kind of getting it back into MHD and observations, what are so you said you mainly use ACE for solar Sorry, was it not surface uh observations? It was more like So Ace is measuring the properties? Yeah, L at its own location at L one. Any other observations that you can also add in there and maybe take advantage of? Because I'm I mean, I think

Somewhere in this podcast we mentioned that there are many, many, many, many satellites. So unfortunately there's not many, many, many satellites. Unfortunately there's only a few. Oh few. All right. So I think you were talking about many, many when you were talking about the weather, terrestrial weather. Sorry, not space weather. Sorry, my apologies. No, no, that's

So you got a few satellites. Yeah, so I I think Ace is one of the the the primary ones that we want certainly look at. And two other s satellites are the stereo satellites, and actually one of them It's not in in operation anymore. But these are stereo A and B and these are located um you can not they're they are at a sort of an L one distance, but they have a a a different um

sort of angle, angular distance. So one would be like ahead of the earth in terms of the angle and the other one would be f further than the earth in terms of the angle. All right. So how do you account for that difference when you assimilate? Yeah, so thinking back to our misfit function, our misfit function just cares about the difference between the model and the data. And it's gr gonna grab the model data at the right location so that it matches with the location of the satellite.

Yeah. Has there ever been a situation, because you said there were few satellites where satellites don't agree with each other, and there's like a little bit Yeah right? So how do you deal with that in data assimilation? So so I would say there's sort of two Sort of parts to this answer. One would be okay, well, there might be a bias in the measurements, right? And certainly we don't want that because

Bias is really hard to to account for. Then there could also then there's also um random noise, right? So when we compare two satellites, two measurements of anything, it doesn't have to be space related. Right. When we compare two measurements of anything. almost certainly there's gonna be noise that's gonna cause these observations to to be to be different. So accounting for that noise and weighing which one you prefer more is kind of what we talked about where we want to give more

weight to the ups to the measurements that are more accurate. Right. Right. Um And then the the second part of that would be that, well, these measurements might be be taking place at different points in space and time, right? So they ness don't they n they don't necessarily actually need to agree perfectly.

Right. Okay, we can actually account for this difference with our model. Okay. Right. Right. Because okay, that makes sense. Um Talking about data assimilation, the first thing that got me kind of excited about it was.

That I can convince an employer that it's basically machine learning. No, obviously I'm kidding. But I mean it basically is on a very low level. I guess question number one can be. Is there a difference? I mean, I'm not that you know you're a machine learning expert, obviously not. Um, but like what kind of description can does this or similarities does this have with machine learning and

If not, or just to add to that question uh entirely, can machine learning be used for data assimilation for optimizing these parameters? Yeah, these are great questions. So I would say there's actually quite a sizable uh

uh similarity between machine learning approaches and data simil like more traditional data simulation. Right. So because machine learning is such a wide term, I'm gonna just focus on neural networks for for this answer. Okay. Okay. And I think that's what I have the most familiarity with. Sure. So

If you were to take uh a neural network, or let's say let's say w you were to take my my MHD model, throw away the MHD, throw away the physics and replace it with a neural network, and you use the same misfit function and you try to Train or usually the language they use is train, but let's say you would try to optimize the parameters of your neural network so that it matches the data well. Now we call this machine. Right. So now let's let's remove the neural network, throw in physics.

We're still training in the sense that we're finding these optimal parameters. To best fit the data. So we can think of data simulation as a as a much more phys physics uh informed or physics heavy form of machine learning, if if that makes sense. No, it does. All right. So Simply because of the addition of physics is what makes you

the data assimilation kind of stand out from machine learning? Yeah, like for ex so What they use in neural networks and again I'm not a machine learning expert but I've read a little bit about it, and the one of the main algorithms they use for training their neural networks is b something called backpropagation.

where they're essentially taking differences between their um their output and their prediction and the and the data, and then they're tracking how that information is related to the input. That's basically an easier version of what we call the adjoint method. Okay, so the adjoint method that we use to calculate uh sensitivities or gra or our model gradient.

is uh is essentially just a chain rule, but applied to our to our to our physics. Whereas in the neural network approach is is the chain rule uh applied to the neural network parameters themselves. So to answer that second question, how does um machine learning or auto artificial intelligence can it help doing now I know you mentioned that replace this with a neural network, it it's machine learning.

Has anybody tried that? Is there is there because I know I mean is there I mean that's a guess that's a that's a separate question, but is there any um Forgetting the word for it, but like any push towards trying machine learning algorithms or artificial intelligence algorithms. with MHD.

Yeah, I think I think right now there's a big push in the scientific community at large to try to use um machine learning approaches for all types of science questions. And I and I and I welcome that. I think I think there's room for it and it could certainly help us quite a bit. Um in t I I'm not sure if I'm answering your question fully, but in terms of sort of plausible areas that that I I I could see this helping a lot with, um I would say

One that I'm thinking of is do using Bayesian optimization, which some people would would sort of put in the camp of machine learning to replace the the quasi Newton optimization that we use. So What we do in in sort of what I've done in my thesis is is just use sort of um pre-canned optimization packages that that are essentially just rely on Newton's method. But you can actually replace these optimization techniques with

More machine learning focused techniques that that essentially build a surrogate. But so you're essentially talking about replacing the technique.

To do the data assimilation with machine learning. I'm saying scrap that entirely. What do you just like has there been any push towards just using data? I mean, just using machine learning, towards like MHD or just using artificial intelligence. Or are the model backed approaches?

Um because it's it's a challenging problem. I think you could maybe someone could do some research on starting just from like let's say solar flare data or just observations of the sun and going all the directly to okay, what are the conditions at Earth?

And I think that's actually been tried, but I would be a little bit skeptical of those techniques. All right. All right. Maybe as as like a Uh closer, I could might maybe ask you, what is your opinion in general about artificial intelligence in what we like to call CFD codes or computational fluid dynamics, which is kind of the field in which we're both dabbling in.

What do you think about artificial intelligence and machine learning kind of coming in there? Is it do you not like the f the lack of physics-based modeling or are are there advantages maybe computational? Yeah, so from the work that I've seen, so I would just base my answer on okay, what does the what does the science tell us tell us? Okay, what what do the experiments show? And people have shown that if you throw away the cost for training Then using machine learning approaches came.

significantly uh accelerate C F D but the training is the problem. Now the training is the problem, but that's not always necessarily th that doesn't mean that we should throw away this this technique, right? So there are certain circumstances Where your problem looks very similar. Like let's say you need to solve the same problem many times with slightly different variations.

Maybe this is an avenue where where machine learning can really help you out, right? Because you might ha it might be expensive to train the model at first, but then when you just need to reuse it for slightly different variations. Then the the then it'll be per be very performant. Right, right. Right. So I would just like to highlight that

From my experience or from the work that I've seen, machine learning is very I would think of it as very, very, very good at interpolating. Yeah. It's completely trash at extravagant. So If you need to extrapolate, you need to use real physics. If you need to interpolate, I think machine learning could be a good avenue. So my next question that I think now you just answered with that was gonna be

Oh, we have so much data for terrestrial weather, why don't we use artificial intelligence models for that? But now you just said that it's not very good for extrapolating. In fact it it actually has been done. Because I would just think with terrestrial weather there's just So much information

that it's just got to perform at least somewhat good. So there's I saw some recent papers this summer about exactly that. So essentially replacing numerical weather prediction with machine learning. Okay. And they've got some very Uh encouraging results and I encourage yeah to to look further. And is that mainly just because of the amount of data available? I think that's part of it. I think part of it is that I think the argument that they make is that we've seen the earth

weather enough times that we can now start interpolating rather than extrapolating. Yeah, that's okay. Uh that's a good idea. And so for us it's a bit scary because they're t there maybe these uh technologies will will will take our our or will render our techniques useless. I don't think so, but it's it's exciting and it is difficult.

Artificial intelligence, the new leaf, you know? Um yeah, I've been definitely thinking about it in C F D for a while and like how it can impact any of us really in our jobs. Yeah. But as you very well said, um At least any time in the near future, I don't really seeing it taking up physics based models, especially for physics based modeling. Yeah. You know? Yeah. So I definitely see a little bit of there. But I can also see in a lot of just numerical methods in general where

Physics the physics of it may not be that important where artificial intelligence could definitely shine. Not that I know specific examples of this, but just from a little friends of mine that are not necessarily doing highly physics-based modeling. Maybe artificial intelligence could help them maybe here or there. You know, especially one of the biggest challenges that we hear with CFD engineers is or not challenges, but like I guess annoyances like mesh adaptation and stuff like that, right?

So maybe a like a lower level task could be a given off to a machine learning algorithm and then the actual physics based c calculations you can just do yourself. Yeah. Yeah. So there's a lot of avenues for the future.

Um hopefully we'll keep our jobs. But uh I'm very excited. Maybe just to close up, do you wanna maybe talk about any um future aspirations for what you maybe wanna do with this current PhD. Any do maybe you wanna continue in MHD, maybe you don't. Anything that you see that the MHD field, particularly space weather Is going to do in the future, anything coming up? Right. So I think in general, the the way that I would like to steer my career is to stick with this.

Let's take real observations and let's take advanced modeling techniques and let's marry them. Right. So I wanna stick with that and if I can, that'd be great. I think I would like my sort of goal or I or or the direction I'd like to take is to become a a faculty. uh at a Canadian university. As we all know that's quite a quite a big goal, so we'll see how it goes.

Um but yeah, if if I could if I were to sell, you know, be selling my research program or advertising my research program to to a h faculty hiring uh committee, I would frame it in the sense of both observational data and numerical modelling used for predictive science. So where do you see the future of space weather? Right. So sorry, I forgot to answer that. No, no worries. No worries.

Yeah, I think I think right now because we're in a s in near a solar maximum, there's gonna be more funding and and more research conducted. I I I fear that in the n somewhat near future, let's say five years from now, we're gonna be approaching more of a solar minimum. So there might be less funding um in in modeling capabilities. Saying that, um, I think every single day or every single year we rely more and more and more on the infrastructures that can be affected by space weather phenomena.

Uh right, like we we use GPS systems more and more. We like we rely on electricity more and more, not just in first world countries but in in in other countries as well. Um so I think if we sort of think at a wider scale, I think uh predicting space weather will become more and more relevant. Um, as time goes on. Right. Well, thank you so much for coming on. Any uh last remarks you might want to make to the lovely audience that we have? Any uh Final quote.

Perhaps in the in the spirit of one of the things that came up, we talked about, you know, senior PhD students asking questions and still ha not having the answer. I would just encourage uh the listeners to to maintain a spirit of of curiosity and and to uh to study hard and then learn a lot of math. Oh, that's a lovely way to finish it. All right. Uh Definitely agree with the curiosity part and the math part, I guess.

Not enjoyable for everyone. I did. I hope everyone does as well. I think through this podcast we've communicated that we love math. But uh it's kind of important for every scientist, at least in our field. But uh yeah, it was lovely having you on. I think uh we've all learnt a lot about d I mean, I've learnt a lot about my own topic today, I think. So that's been lovely. And space weather I think is

one of those niches that a lot of people reading it would kind of be like, Oh my, that sounds cool and then would kinda get into it. So I'm glad we had you talk about that as well. Thank you for coming on and uh Take care, everyone. Have a lovely day. This has been the Math and Physics Podcast, episode number one twenty-two. My name is Ray, and we'll see you soon. Peace.