Chapter 545 Radar first shows its power (Part 1)
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At this moment.
Look at the face that appears next to you.
Without any precautions.
Ye Duzheng barely reached into his pocket and took out the natal wooden sign his mother gave him back then and threw it towards the other party - it was said that the thing was made of peach wood and could ward off evil spirits.
Of course.
Before taking out the wooden sign, Ye Duzheng reacted first.
The guy who appeared in front of him was not a mummy, but someone who had become famous in the base recently.
An acquaintance, Han Li.
See this situation.
While Ye Du was secretly relieved, he also covered up the initial panic in his heart with a slow speaking speed, and said:
"Comrade Han Li, who I thought it was, turns out to be you."
to be honest.
Ye Duzheng actually had a very good impression of Xu Yun.
After all, if it weren't for the weather Doppler radar he brought out, the weather center would probably never have a chance to prove itself again.
If that's true
It is foreseeable that the entire meteorological center will lose fighting spirit for a long time.
Also from an industry perspective.
The help of meteorological Doppler radar to meteorology as a whole is also obvious.
The emergence of this kind of equipment is likely to open up a new avenue for the meteorological field that has always been unable to see the future - the kind in which China occupies the leading position.
Therefore, whether it was based on his job or personal feelings, Ye Duzheng had a very good impression of Xu Yun, and even felt a little grateful.
So after being shocked.
Ye Duzheng did not show any dissatisfaction, but smiled and asked Xu Yun:
"Comrade Han Li, why are you here? By the way, have you had dinner?"
At this time, more than seven or eight hours had passed since the first batch of data was released. The sky had already changed from day to night, and in a few hours it would be almost twelve o'clock.
Not long ago, dinner was delivered to the base.
"Well, I just drank some porridge."
Xu Yun tilted his head towards a certain direction outside the tent. At this time, he could vaguely see several sideline team members busy distributing dinner.
However, tonight's "standard meal" is not of high standard. Most of them are steamed potatoes and vegetable leaf soup with elm leaves.
The cornstarch grinds the teeth, and the elm leaves become bitter.
Xu Yun's ability to drink polished rice porridge was mainly related to his status as a patient, who needed to be nursed back to health during the recovery period.
Then Xu Yun turned his attention to Ye Duzheng's calculation paper and looked at it carefully:
"Huh? Director Ye, is this a variation of Stokes' equations?"
Ye Duzheng was slightly startled and seemed a little surprised that Xu Yun could recognize the contents of the equation.
However, he soon remembered Xu Yun's identity and nodded lightly:
"Yes, it is the N-S equations with a little change based on vorticity."
According to Lao Guo’s previous introduction.
Xu Yun is a graduate of the Department of Mathematics of Cambridge University, so it is normal for him to recognize the N-S equations. After all, this equation is a major problem in the field of mathematics.
Or put it another way.
Considering Xu Yun's ability to come up with the theory of meteorological Doppler radar, it is strange that he cannot recognize the N-S equations.
Xu Yunze turned around and looked at the crackling scene full of abacus sounds, and casually asked Ye Duzheng:
"Director Ye, how is your progress now?"
"Progress?"
Ye Duzheng raised his eyes and looked at Xu Yun for a second, shook his head, and pulled a wry smile from the corner of his mouth:
"Where is the progress? Comrade Han Li, what you see now is all - I don't even know how to deduce it later."
Ye Duzheng said.
His fingers also held the front half of the ballpoint pen to make a small lever, and slapped the end of the pen on the math paper twice. It was obvious that he was a little annoyed.
The calculation of weather data was not a secret, so Ye Duzheng didn't want to hide anything.
After all, everyone has a desire to talk.
Then Ye Duzheng sighed and shook his head, ready to change his mind honestly - since the variation he was considering was not feasible, he could only calculate according to the plan given by Mr. Zhu.
Even
There are probably some problems with that idea.
And just as Ye Duzheng was writing, Xu Yun's weak voice suddenly came to his ears:
"Director Ye, I have an idea. Do you think it is feasible to add a Bernoulli function after this variant?"
Ye Duzheng's pen tip, which had already written a few letters, suddenly stopped.
After a while.
Ye Duzheng raised his head in surprise and looked at Xu Yun with an expression as if he was seeing a mummy:
"Comrade Han Li, what do you say (fourth tone↓)?"
Under emotion.
Ye Duzheng even had an accent from his hometown of Jinmen.
And opposite him.
Looking at Ye Duzheng with wide-eyed eyes, Xu Yun was actually a little surprised in his heart - he thought that the concept of localized distributed vorticity was relatively complete now.
But soon, he reacted quickly.
Too.
The key figure in the convection-diffusion equation is Suhas Patankar, and judging by his age, he is only in his early twenties.
Although Xu Yun can't remember exactly when he proposed the SIMPLE improvement algorithm, Suhas Patankar is not a genius who became famous at a young age.
He wanted SIMPLE to improve the algorithm, but proposed that it would be more than ten years later anyway.
Not an exaggeration.
These days, the research on the Navier-Stokes equations in the entire mathematics and physics circles is still in a very primitive state.
Even the SIMPLE algorithm, the original version of the semi-implicit method for solving pressure coupling equations, would not be proposed until 1972.
Think of this.
Xu Yun decided to help Ye Duzheng in a small way - although he had no plans in this regard before.
But he was naturally happy to do something that could allow Rabbit to catch up with or even overtake the first echelon.
It doesn’t cost any money anyway, just give it a try.
Then Xu Yun paused, quickly organized some thoughts in his mind, and said to Ye Duzheng:
"Director Ye, what I mean is to add a Bernoulli function after this variation, and then take a curl. Do you think it is feasible?"
"This is what I heard from a senior student when I was at Cambridge University. The scenario they deduced at that time happened to be the same variant"
Swish——
As a result, Xu Yun didn't finish his words.
Ye Duzheng lowered his head and wrote a function on the paper:
C=p/ρ+u/2.
This function comes from the equation (u/2)=(u)u+u×ω, which is the Bernoulli function.
Then Ye Duzheng took the curl according to Xu Yun's statement and got a new formula:
ω/t=×[u×ω]+vω.
Although this formula looks like emojis, it seems to be (￣▽￣)~*(￣▽￣)/(ω)[]~(￣▽￣)~* again.
For Ye Duzheng.
The moment he saw it, his heart skipped a beat!
This is
The evolution equation of ω!
At the same time, because ×(u×ω)=(ω)u(u)ω, this evolution equation can also be rewritten in the form of convective derivative:
Dω/Dt=(ω)u+vω.
Write here.
Ye Duzheng paused again, turned to look at Xu Yun, and asked impatiently:
"Comrade Han Li, what's next? What's the next idea?"
At this moment.
Ye Duzheng seemed to have returned to the days when he was studying in Chicago.
At that time, he was following a mystery novel serialized in the Chicago Daily News. Every time he finished reading a chapter, he couldn't wait to update it like crazy.
If it weren’t for the fear of losing the valuable qualification to study abroad.
Ye Duzheng even considered whether to tie the author to a small black room to update - he must update 50,000 words a day, otherwise he will not be able to eat that day!
And opposite him.
Xu Yun signaled Qiao Caihong to move his wheelchair closer to Ye Duzheng.
Then he took the paper and pen from Ye Duzheng and explained while writing:
"Director Ye, if you want to continue deriving this equation, you must first understand the physical meaning of this variant."
"Let's introduce another angular momentum equation here for comparison. The physical meaning should be obvious, right?"
Ye Duzheng looked at it carefully for half a minute, and then quickly said:
"Oh, I see."
"What is described on the right is due to the elongation of the fluid element, the change in the moment of inertia of the body element, and the viscous moment acting on the body element, right?"
Xu Yun nodded.
The physical meaning of this variant can almost be regarded as the entry-level concept of vorticity in later generations.
That is, the vorticity of a fluid mass may change due to its elongation, causing a change in the moment of inertia, or accelerating or decelerating due to viscous stress.
Immediately afterwards.
Xu Yun wrote another Peclet number.
That is, Pe=ud/α, and then change the circle on top, and bring it back to the original form.
See here.
An unexpected nasal sound suddenly came from Ye Duzheng's nose, and his brows suddenly raised.
He discovered a problem that he had never realized before:
Look at the variations.
Vorticity in a two-dimensional flow is convection and can be diffused like heat, so the analogy to the Peclet number is
Re=u/v.
This means that vorticity, like heat, cannot be created or destroyed inside a two-dimensional flow.
And it can move from one place to another by convection currents.
But on the other hand.
∫ωdV is conserved for all localized vorticity groups.
That is to say
The vortices convect through the velocity field and propagate through diffusion, but the total vorticity within each vortex remains constant.
In other words.
The boundary is where the vorticity comes from!
This is a concept that Ye Duzheng has never thought of, which means that many of his previous ideas were wrong, and he did underestimate the depth of the border.
But it also means
A new model possible!
To be precise, it should be.
The first truly working new model in meteorology!
To know.
Although the Norwegian school has made great contributions to numerical weather prediction, even now, the entire meteorological industry still does not have a real model.
In fact.
develop according to normal history.
Meteorology would not develop its first climate model until 1971 by Rasoul.
And the model built by Rasul predicts not local weather, but a climate model related to global warming.
And now.
A new road appeared in front of Ye Duzheng.
A new road that no one has ever traveled before.
Looking at Ye Duzheng who looked shocked, Xu Yun looked very calm.
The concepts he mentioned were not based on his personal abilities, but came from the relatively complete knowledge system of later generations. They are nothing to be proud of.
After all, it is different from the current period.
Although the N-S equation is still in the cracking stage in later generations, the general form of analytical solution is still far away - because it is stuck on the nonlinear advection term.
But on the other hand.
It still has analytical solutions in various extreme situations, such as irrotational and inviscid situations.
As long as sufficient computing resources are invested in DNS, future generations can even solve complex fluid flows.
These are the results that Xu Yun had already established before his time travel, so that people like Xu Yun who are not in the meteorological field can easily use them for interpretation.
Of course.
Due to professional barriers, Xu Yun's understanding of vorticity is almost finished here.
As for the more advanced concepts of equivalent potential temperature, pseudo-equivalent potential temperature, latent heat, sensible heat, and radiation.
There is no problem if you want Xu Yun to explain their meaning, but any further derivation would be pure wishful thinking.
But it doesn't matter.
At this point, Ye Duzheng has obviously entered the state of 'enlightenment'.
Judging from the ability of the main founder of modern Chinese meteorology, he can probably handle the rest of the process by himself even without Xu Yun's help.
Not to mention that there is Tao Shiyan, a top expert in weather dynamics, beside him.
So it's quick.
Ye Duzheng began to deduce the next steps on his own.
"The governing equation of temperature is DT/Dt=αT"
"Then the equation of the temperature field is naturally DT/Dt=T/t+uT/x=αT"
"It can be obtained based on hydrostatic equilibrium and temperature lapse rate."
"Brother Shiyan, what do you think about changing the turning point pressure to a piecewise function?"
"Just what I wanted."
More than twenty minutes later.
Ye Duzheng wrote another calculation on the paper:
D/Dt(ω/2)=ωiωjSijv(×ω)+v[ω×(×ω)].
And when I saw this calculation.
Xu Yun's expression under the bandage also relaxed.
Huh.
His mission is finally accomplished.
The smart classmates must have noticed it too.
That’s right!
The formula Ye Duzheng wrote at this time is exactly the vorticity quasi-energy equation.
It comes from the scalar product of the convection derivative above and ω, and is the vorticity for a localized distribution.
The rightmost divergence term usually integrates to zero and is not needed as much as the brain.
The remaining two terms on the right correspond to the vorticity pseudo energy generated by the elongation of the vortex line, and the vortex pseudo energy lost due to viscous force.
From this formula, we can intuitively see that eddy quasi-energy is like mechanical energy and can be dissipated by friction.
This formula will be mentioned repeatedly when discussing turbulence in later generations, and it can be regarded as an iconic formula.
More importantly.
As everyone knows.
Atmospheric diffusion belongs to turbulent diffusion, and there are currently three widely used theories:
Gradient transport theory,
Statistical theory of turbulence,
Similarity theory.
This formula is the important core of the statistical theory of turbulence. On this basis, a model called WRF was born in later generations.
That's right.
WRF.
This is the most common model for meteorological numerical simulation forecasting in later generations. Many civilian scientists also use this thing to run numerical values at home.
Of course.
Folk science in the field of meteorology is far more intelligent than folk science in the fields of physics and mathematics. There is a clear difference between the two.
Civil science in the field of meteorology is not so much ‘civil science’.
Rather, it is more like those astronomy enthusiasts who drive with astronomical telescopes to see the stars, and rarely make too many outrageous remarks.
At least I won’t always say that I have invented a perpetual motion machine, and then when I look at the drawing, it looks like a Tai Chi diagram
What civilians in the meteorological field like most is to quietly run the local weather model at home, and then look at the sky to see if their results are accurate. Overall, it is quite Buddhist.
all in all.
WRF will be a very important model even in 2023, let alone this period.
Even
What appears at this time is only a prototype.
Later, Ye Duzheng extended the formula to the fields of isobaric surfaces and isopycnal surfaces, and performed calculations related to circulation.
During this period, the girl Qiao Caihong also came forward and watched with interest for two minutes. When she returned to Xu Yun, her expression changed like this:
@v@
An hour later.
Ye Duzheng and Tao Shiyan worked together to derive the complete vorticity field and fit a special mathematical model.
From Xu Yun's perspective.
This model is still quite different from the WRF of later generations - after all, there is no computing power of later generations these days, but the core logic is still similar.
To put it simply, the cylindrical tangent space and horizontal mapping are first used to construct a local space and map its neighbors to construct an isometric mapping.
Then the conditional local convolution kernel is redesigned to meet the convolution characteristics adapted to local conditions. Adjacent convolution kernels with similar adjacent local features and different geographical characteristics share three conditions.
As for the mathematical mechanism of the model, it is Fourier transform. Ye Duzheng constructed the mixing operation as a continuous global convolution, which can be effectively realized through FFT in the Fourier domain, and the spatial mixing complexity is reduced to a minimum.
The model even takes into account accumulated liquid and frozen water and total rainfall particles as a diagnostic variable, bringing the number of data sets to 20. (Inspiration comes from this paper arxiv.org/abs/2101.01000)
It can be said that.
In today's world where computer models have not yet come out, this model can be said to be the pinnacle of what is humanly possible.
Also, I don’t know if it was Xu Yun’s illusion.
He always felt that Ye Duzheng's model seemed to vaguely touch on the Fourier neural operator.
Of course.
It's just a feeling.
After all, he is indeed not very good at this aspect, so he cannot make a specific conclusion for a while.
It might be an illusion, or it might be true.
It would be fine if it was just a misjudgment.
But if this is true.
So in the current timeline of this dungeon, the fun will be great in the future.
After all, this thing has long gone beyond the scope of fluid mechanics and involves AI.
Then more than ten minutes passed.
Tao Shiyan summarized the data of each group in front of the stage, and Ye Duzheng introduced his model ideas to everyone.
Considering that everyone has different understanding abilities, Ye Duzheng mainly focused on calculations.
That is to say, they focus on telling everyone how to calculate, and the specific principles are ignored for the first time - because what they need now are direct calculation models and tools, and they do not need to know how the tools are derived.
Fifteen minutes later.
Each group started
Final calculation.
soon.
Crackling——
The sound of abacus and the sound of a few hand-cranked computers were heard in the tent again.
That's right, a hand-cranked computer.
This thing can be regarded as a standard old antique equipment, which is almost extinct in later generations, and has very strong characteristics of the times.
How to say it
In terms of contemporary nature, it is somewhat similar to the DVD and PHS of later generations, and is a product of a specific period.
Hand-cranked calculators were invented in 1878. Most of them used a pinwheel structure and could generally only perform four arithmetic operations: square numbers, cubic numbers, square root, and cube root.
If you need to input trigonometric functions and logarithms, you need to look up the table.
The hand-crank computers used in China today are all of the "Feiyu" brand, one of the few domestically produced mechanical devices that are better than imported ones during this period.
The first batch of 500 "Feiyu" brand handheld computers was produced, most of which were given to the Second Machinery Department and the Fifth Institute, and some were given to the 156 project that year.
The Fifth Academy used this hand-operated computer to calculate a trajectory from the missile's takeoff point to shutdown, which took almost two months - this is a missile that does not have the ability to change orbit.
In addition, the "Flying Fish" brand hand-cranked computer is much more sophisticated than the one imported from Germany and looks as petite as a girl.
Therefore, it was also given a nickname by the Second Machinery Department that a certain author sounded unhappy about:
Fish girl.
all in all.
At this point, Xu Yun has nothing to do with him - if we talk about written arithmetic and mental arithmetic ability, he is probably not as good as many seniors of this era.
So he waited alone for the results, while Qiao Caihong and several sideline team members helped drive away the mosquitoes.
Half an hour passed.
Lao Guo, who stayed for a while in the morning and then went to continue the research project, got off work and hurried to the scene with Cai Shaohui from the research group.
I don’t know if it was Xu Yun’s illusion.
He always felt that Lao Guo coughed much more frequently than before
An hour later.
A final report was handed over to Ye Duzheng.
However, Ye Duzheng did not rush to Lao Guo to report. Instead, he and Tao Shiyan randomly inspected several links for verification.
After verification.
Ye Duzheng just came to Lao Guo quickly with the report.
"Guo Gong, Cheng Gong."
Ye Duzheng first said hello to Lao Guo, then glanced at Cheng Kaijia, who had been staying at the scene next to Lao Guo, and said with a serious expression:
"Fortunately, a new batch of weather forecast results have been released."
"This result has been rechecked by Comrade Tao Shiyan and I, and there are no mathematical errors or omissions."
Lao Guo's expression remained unchanged, but his left hand holding the briefcase still exerted a little more strength.
It can be seen that his heart is not peaceful:
"Director Ye, what have the higher-ups deduced?"
Ye Duzheng took a deep breath after hearing this, opened the manuscript in his hand, and introduced:
"Gong Guo, Gong Cheng, first of all I want to emphasize one thing."
"That is, our meteorological data collection started 12 hours ago, but due to efficiency issues, the results were not released until just now."
"That is to say, the result we derived actually includes the weather forecast for the past twelve hours."
Lao Guo nodded when he heard this.
This sentence is not difficult to understand.
According to their prior arrangements.
The weather Doppler radar collects data every 20 minutes. The data is filtered and transmitted to the Capital Computer Institute. The computer then processes it into a parameter field and sends it back to the base, where Ye Duzheng and the others conduct further calculations.
This process was repeated over and over again, and the process lasted for more than ten hours, almost half a day.
Although due to computational efficiency issues, these data cannot produce results instantly or in a short time.
But this situation does not affect the objective existence of the weather forecast results of the past ten hours - it is just that they have lost their timeliness.
But from a reference point of view.
The weather conditions in the past 12 hours can actually verify the derivation results to a certain extent.
It's like someone sent a letter predicting the situation in the next six months, but due to various reasons, a year has passed since it was delivered to the recipient.
Although this letter has lost the meaning of conveying information, it can verify whether the writer's judgment and vision of the current situation are correct.
Think of this.
Lao Guo couldn't help but glance at Ye Duzheng, thought for a moment, and asked him:
"Director Ye, what are the prediction results of the past 12 hours in the report?"
Ye Duzheng turned the document over to him, revealing the contents on it, and introduced:
"Guo Gong, look."
"According to the forecast results, there was less Doppler feedback from rainfall particles in the past 12 hours, so there will be no rainfall on the entire Jinyintan grassland."
"However, the efficiency of vertical dust emission is high, the long straight vector of aerosol shows a regional distribution, and the vertical discriminant variable is very obvious."
"So based on data fitting, we judge that there may be a northwest wind with small intensity of sand and dust between 11:00 and 13:00 noon."
After listening to Ye Duzheng's introduction quietly, Lao Guo immediately looked at Zhou Cai and asked him:
"Assistant Zhou, what is the actual situation in the grassland today?"
As the assistant to the factory director of the base, Zhou Cai's weather conditions on that day are data that he must follow up and summarize every day.
In the current period when digital communication has not yet appeared, he got the overall weather conditions even earlier than Ye Duzheng and Tao Shiyan.
Hearing Lao Guo's question.
Zhou Cai immediately took out a small book, flipped through a few pages, and said quickly:
"There is indeed no rainfall record on the grassland in the past twelve hours. To be precise, there is no rainfall record in the entire Haiyan County. However, there was a light rain in Huangyuan County nearby, which lasted for about 40 minutes."
"As for sand and dust. Oh, there is indeed a sand and dust record, which was reported by comrades from the Animal Husbandry and Sideline Team."
"The starting point of the dust was near the Sixth Branch Factory. The time was around 1:30 in the afternoon, and the direction was indeed northwest wind."
Hear this.
The atmosphere at the scene suddenly became a little subtle.
It didn’t rain, but dust appeared again
Forecast for the first 12 hours
It's actually accurate?
After a while.
Cheng Kaijia, who had been silent all this time, spoke, his face still maintaining a very controlled calmness:
"The information is correct, but some comrades, I think this situation has a certain degree of chance. At least these results alone cannot explain too much."
"First of all, it's very common here in the grassland to not rain for half a day. Secondly, if I remember correctly, the dust appearing on Jinyintan Beach this season should basically be northwest wind."
"So in order to determine whether the deduction results are accurate, I think a new round of evaluation needs to be continued."
Hear this.
Several people present nodded in agreement.
Students who have studied geography should all know this.
In summer.
The southwest monsoon reaches the Bay of Bengal and then encounters the Tibetan Plateau as it advances northward, dividing into east and west branches:
One wind turned eastward along the Himalayas and blew westward.
The other branch flows along the direction of the mountains to southwest my country, intensifying the water vapor channel effect, increasing precipitation on the edge of the plateau, and further intensifying drought in the interior of the plateau due to the rain shadow effect.
So in the West Sea.
The northwest wind accounts for more than 80% in winter and summer, and the southeast wind occurs occasionally.
So just relying on the description of no rain for half a day and a small amount of northwest dust really doesn't prove much.
To prove that the derivation results are accurate enough, a larger test must be passed.
Think of this.
Lao Guo looked at Ye Duzheng again and asked him:
"Director Ye, how does the derivation result predict the next weather? - For example, is there any prediction of rainfall?"
"It's raining"
When Ye Duzheng heard this, a subtle expression appeared on his face:
"Of course there is, and the time is very close to now."
Lao Guo was shocked and asked:
"Oh? When?"
Wow——
Ye Duzheng turned over another page of the report, looked at the results above and said to Lao Guo:
"Three hours later, that is, between 11pm and 1am, there should be a fight lasting half an hour"
"Thunderstorm."
Note:
Yesterday, in order to change my body clock, I woke up very late at night and coded all night, so I updated it in the early morning.
I have said before that this situation is very common when updates are released. The quantity will not be small, but the time may not be fixed, so please don’t rush me. If there is no update that day, I will ask for leave in advance. (End of chapter)