pre-writing opinions: Reddit's markdown support sucks ass, no LaTeX and no mermaid support, fuck u/spez

Disclaimer: [UPDATED 16/05]

These values are adjusted only assuming that BITS would keep their tradition for keeping numbers steady and change the rigor of the exams to stabilize the inflation
LONG READ. These are predicted and the opinions and results may vary for every individual, gaali mat bakna, mai thoda weak ho rakha hu abhi. Although I am pretty confident about what I found, but still, DO NOT BLINDLY BELIEVE EVERYTHING YOU SEE , you are only allowed to take notes of what could happen.

Table of Contents

1. 5 Year score v/s cutoff v/s no. of applicants v/s seats available comparison
2. Projected scores required for 2024
3. Fee details broken down w/ projected costs of living, hostels and mess charges and miscellaneous
4. Should you join it?
5. Toughness of the courses offered
6. What courses to take <-- needs personal introspection
7. My remarks and need for amateur developers.

5 Years' scores detailed review

BITSAT has always seen large number of candidates giving their exams. I used 3 different regression methods for finding the projected number of candidates scoring 88% and above in BITSAT.
Here's the catch, BITSAT was of 450 marks before 2021, but I noticed a linear relation whatsoever for which some blogs claim was due to the ease of solving paper which was higher as of then.[1]
Projected number of candidates scoring >= 316 marks
Don't worry about how I plotted the graph, for the ease of viewing I used a calculative exaggeration method, while all the calculations being done on the raw data only.
Here, all the regressions have too much difference between them which throws off the ease of just averaging the three. Instead I used what is called the R-squared value to find an accurate follow-up projection for the number of candidates.
The R-squared value for the three are as follows:

R-squared values: Linear Regression: 0.8401621913740709 Polynomial Regression: 0.9161966003792115 Exponential Regression: 0.922505755755209 Projected next outcome using damped Exponential Regression: 15916.26589649187 

Cutoff Prediction

Now, the best part, cutoff prediction. Here, you need to know one more thing that all the campuses have a record of increasing the number of seats for their programs every year which has somehow worked a little to adjust to the 'population inflation' and has kept the numbers steady.
AAAAAANNNND, here comes the issue, while looking at the seat matrices for BITS, the seats in all branches has remained the same since 2017 (increase in seats for CSE). (2018 for Goa campus).
ALTHOUGH, due to the addition of the new Mathematics and Computing course, it can have significant impact on the No. of seats v/s Cutoff debate
Seeing with the lowest marks required for joining B.Pharm at three campuses of BITS:
Cutoff v/s Candidates remained consistent till 2020
[2][3][4][5]
NOTE: some of you jhaatus will be paranoid about how the cutoff decreased with much higher candidates. It's due to increase in the number of seats due to the new MnC branch
NOTE 2: I am speculating about the predicted number of candidates, since, the popularity has seemingly exponentially increased due to youtuber bhaiyya didis.
Notice that I used a simple polynomial regression here due to having much simpler values for predicting the consecutive iterations.

Why I couldn't correctly predict for CSE

See, the choices of students during counselling is really complicated and after reviewing some previous year details and cutoff scores, I couldn't have a perfect idea about how the relationship is maintained. That's why I will need someone else with more free time to help me polish my code for predictions.
Anyways, here's the predicted cutoff for some branches using exponential regression:

Branch	Pilani Campus	Goa Campus	Hyderabad Campus
CSE	~356	~312	~299
MnC*	~310-ish	~290-ish	~280-ish
ECE	~300**	~279**	~272**
EEE	~278	~261	~258

INACCURACIES IN DATA BEGINS

Branch	Pilani Campus	Goa Campus	Hyderabad Campus
EIE	~268	~251	~250
Mech	~252	~236	~228
Chemical Engg	~230**	~215**	~215**
Manufacturing	~220**	----	----
B.Pharm.	~172**	----	~153

ACCURACY ASSUMED BELOW 60% FOR THE FOLLOWING DATA

Branch MSc. Courses	Pilani Campus	Goa Campus	Hyderabad Campus
Economics	~264	~247	~240
Mathematics	~240****	~229****	~220****
Physics	~237****	~225****	~219****
Chemistry	~216****	~210****	~210****
Biological Science	~217****	~212****	~210****

* no regression, only compared ratios with the cutoffs of IIT Roorkee (JoSSA 2023)
** accuracy assumed to be <60% due to highly bland iterations
**** too much discrepant previous years' data present + regressions often not aligning with what was predicted for other B.E. Branches (accuracy<~40%), need volunteers for enhancing accuracy.

Broken Down Fee details and Costs of Living

With inflation and the enduring lust for money, the hostel charges are continuously being increased since a few years, here's the detailed breakdown for what I have observed.

Academic Year	Semester fees (per sem) B.E only	Hostel + mess + elec (per sem) + advance	Summer term fee (whole)	costs of living (projected and adjusted for inflation)
2019-20	1,78,000	22,900 + 15,000	62,300	~10,000 (covid)
2020-21	1,99,000	24,150 + 15,000	69,900	~27,000 (covid)
2021-22	2,18,500	25,550 + 15,000	78,000	<~50,000 (post-covid inflation)
2022-23	2,31,500	27,100 + 15,000	83,700	<~50,000
2023-24 (CURRENT)	2,51,000*	28,800 + 15,000*	87,900*	<~55,000

* The fees are as per the archive since their webpage went down -> 2023-24 fee structure
The projected 4 year B.E. course price you have to pay would not exceed ~INR 27,55,000 /-
I am too lazy for finding projected for other courses.

Should you join it?

as a disclaimer, I am in no position to judge as I have lost hopes getting into BITS this year, since I have wasted a lot of money and seeing our house put of collateral for securing my admission into VIT I am in no way entitled to ask more money for second attempt from parents, but I can give you suggestions from what I've researched when I used to daydream about getting into BITS.
Overall Culture: when it comes to projects and teams, the students get highly competent, and after finding a good partner, you could go for numerous competitions like the Mars Rover Challenge (personal favourite), which needs skills from almost all branches inclusive of chemical and materials department. Which in turn also leads to better communicative skills and a top tier social life.
Imagine your parents get to see you with bunch of smart ass people just discussing about different stuff ranging from algorithms to spatial modelling of biological molecules, they will feel on top of the world.
Student life: I will not talk about the zero attendance policy nor about the strictness inside campus. Here, you NEED to have a control over yourself, drug peddling is quite common although no one talks about it, even at VIT Vellore, kids find a way to get that mind numbing puff. You will have an urge to just try it for once to find what is it for real, but DON'T. I guess I don't need to elaborate more.
Second, remember:

Darshane Punyam, Sparshane Paapam 

Look at all the chics, maybe even flirt with them under limits, but don't indulge in bad stuff since you already know how horny you really are.
Now, for a better part BITS hosts numerous fests varying from cultural to tech clubs, some of the highlighted as follows:

Type of Event	Pilani	Goa	Hyderabad
Cultural Annual	Oasis	Waves	Fervour, PEARLS(?)
MUNs	BITSMUN	BITSMUN	BITSMUN
Tech Annual	APOGEE	Quark	ATMOS
Sports	BITS Open Sports Meet (BOSM)	Spree	Arena
Entrepreneurial	-----	Coalescence	Launchpad
Social Service	-----	-----	IGNITE

Click on the campus names for detailed info about all the events.

Toughness @ BITS

doesn't need much of a warning, it's tough. Although, the first year may go on a cakewalk for smarties, same stuff for everyone to learn, you might have problems with the engineering physics and drawing classes** so be prepared. Maintaining 9+ GPA is really hard, you have work your arse off more than what you are doing right now.
Getting scholarships is on the tougher side too, you can manage to get 10% off by little work, but getting those sweet 80% waivers can be tough, you have to ace your quizzes and assignments.
By the 3rd year, you will start getting tensed about internships, their interviews, your GPA and finally your courses. You have to be ready and try to complete all the side courses (if any) by the end of the third year so you can focus more on placements the next year (only for low pointers).
That's all of what I've learnt and understood from the students, there are easier aspects too but only if you are actually smart and can do more work in much less of a timeframe.

What course should I take?

You need to introspect yourself before asking this question, many people say to follow your interest but it's not always practical.
You see, I have a friend who wants to become a physicist, and yet he isn't able to solve measly problems in physics which might need more brainpower, and even shitting himself on questions of nuclear physics when he wants to do research in that specific field. Not only about questions, he doesn't even properly know about how the Hadron Collider works, just spurts out some random Fission and Fusion chickenshit when asked about.
OK, you should totally give your interests a higher ground during the counselling but ask yourself if you are actually ready for what you have to learn for the next four years, probably even your whole life. Since, it's BITS you'll be able to adapt yourself, but always take caution before every choice you're going to fill in during choice filling. Don't embarrass yourself afterwards.
Here are few courses your might be interested in anyways:

Interests	Skills	Course recommendation
Computers, Maths, Hardware (JOB BIASED)	Little bit of OOP, good statistical knowledge, knows how shit works	Computer Science, Mathematics and Computing, Electronics and Communication, Electrical and Electronics
Physics, Building stuff, Likes to experiment (JOBS OR RESEARCH)	Classical physics, mechanics, civil engineering stuff	Mechanical, Electronics and Instrumentation, MSc Physics, Civil
chemistry	chemistry	chemistry
Maths, economics, next harshad mehta	Maths (a little bit advanced is good), statistics, Economical and current affairs	MSc Economics, MSc Mathematics
Biology, chemistry	Biology, chemistry, (teeny weeny bit of Physics)	B.Pharm, MSc Chemistry

My rants, remarks and opinions

Some iterations are showing values too good to be true, don't blindly trust them, always take a safe score of +15 the values given in tables.
Need volunteers to research and scrape more previous years' data for much more accuracy. BITSians are welcome
Honestly, this was a ride and an escape for me to relieve a little bit of stress about how I was fcked this year. Denied EWS certificate, filed for an appeal, and no progress. Gave JEE as an OPEN candidate. Somehow got 10k rank in VITEEE, got cat 3 CSE, dad told me to leave no opportunities, now have to pay 4 lakhs tuition fee per annum, dad's income is 4 lakhs per annum. Took an educational loan from Indian Bank (13% interest + our house on collateral).
Called VIT, told me they will give a full refund if withdrawn before 11th September, but have to pay a cut of interest for the loan taken (did not specify how much). I am pretty sure they will be asking easily at 2-3 lakhs, unprepared for BITS after Nanu's death on 22nd April, (my VITEEE was on 24th), went with my mom to Kerala and back the next day and then again back to Kerala with dad and my 24 year old brother who has cerebral palsy. spent about 50k on the flight tickets alone. Wouldn't get BITS in the first attempt, afraid to register for 2nd.
Can't even commit suicide thinking about my brother, entitled school topper yesterday after results, teachers saying that I am not getting of what I am capable upto, really disappointed about me joining VIT instead of IITs (for god's sake).
Cousin sister told me to join her in Germany, (I've learnt german from her) but the living costs so high and the amount of stress my parents would have to take for this year has concerned me enough already. No one asks for this but please dm me, tell me your stories, it's nice to have someone around to talk shit.
Enough of rants, best of lucks to everyone
FOR AMATEUR DEVELOPERS OR INTERESTED IN DEVELOPING/RESEARCH
Since, this June and July are going to be an empty and un-exciting month for most of you, I need some amateur developers who can help me in building a college recommendation portal, which will help ease out the stresses students have to take while counselling and choice filling, I mean if not interested in joining some random dude and working your arse off, just take it as a recommendation for your next project :)
[1] Find the blog here for detailed scores from 2012
[2] BITSAT 2020 Cutoff scores
[3] BITSAT 2021 Cutoff Scores
[4] BITSAT 2022 Cutoff scores
[5] BITSAT 2023 Cutoff scores
This was a high effort post btw :) Thank you to the readers who read the whole thing

Please help

It looks like we touched upon KP11, a G6 storm (if such a thing existed). Serious solarmax spaceweather
“The geomagnetic Hpo index is a Kp-like index with a time resolution of half an hour, called Hp30, and one hour, called Hp60. besides that, the Hpo index is not capped at 9 like Kp, but is an open ended index that describes the strongest geomagnetic storms more nuanced than the three-hourly Kp, which is limited to the maximum value of 9. Next to the Hpo we also provide the linear apo index (ap30 and ap60). The Hpo index was developed in the H2020 project SWAMI and is described in Yamazaki et al (2022).
Abstract The geomagnetic activity index Kp is widely used but is restricted by low time resolution (3-hourly) and an upper limit. To address this, new geomagnetic activity indices, Hpo, are introduced. Similar to Kp, Hpo expresses the level of planetary geomagnetic activity in units of thirds (0o, 0+, 1−, 1o, 1+, 2−, …) based on the magnitude of geomagnetic disturbances observed at subauroral observatories. Hpo has a higher time resolution than Kp. 30-min (Hp30) and 60-min (Hp60) indices are produced. The frequency distribution of Hpo is designed to be similar to that of Kp so that Hpo may be used as a higher time-resolution alternative to Kp. Unlike Kp, which is capped at 9o, Hpo is an open-ended index and thus can characterize severe geomagnetic storms more accurately. Hp30, Hp60 and corresponding linearly scaled ap30 and ap60 are available, in near real time, at the GFZ website (https://www.gfz-potsdam.de/en/hpo-index).
Key Points New Kp-like planetary geomagnetic activity indices, Hpo, are presented
Hourly (Hp60) and half-hourly (Hp30) indices are available from GFZ website
Hpo indices are open-ended without the upper limit at 9o
Plain Language Summary The geomagnetic activity index Kp is a measure of planetary geomagnetic activity, expressed in units of thirds (0o, 0+, 1−, 1o, 1+, 2−, …9o). Kp is widely used in the space physics community, as it is known to be a good proxy of the solar-wind energy input into the magnetosphere-ionosphere-thermosphere system. Kp has two important limitations. One is the temporal resolution. Kp is a three-hourly index, so that temporal features within 3 hr are not resolved. The other is the upper limit of the index. Kp does not exceed a maximum value of 9o, so that under extremely disturbed conditions, geomagnetic activity is not accurately represented. We introduce a group of new geomagnetic activity indices Hpo that overcomes these limitations. Hpo is designed to represent planetary geomagnetic activity in a similar way as Kp but with higher temporal resolution and without the upper limit at 9o. This paper describes the production of 30-min (Hp30) and 60-min (Hp60) indices, and demonstrates their properties in comparison with Kp. Hpo indices since 1995, including near-real-time values, are distributed through the GFZ website (https://www.gfz-potsdam.de/en/hpo-index).
1 Introduction Variations in the solar wind cause changes in electric currents that flow in the magnetosphere and ionosphere. The associated changes in the magnetic field can be observed using magnetometers on the ground. There exist various types of geomagnetic indices to monitor the intensity of geomagnetic disturbance associated with solar wind variations (Mayaud, 1980). The Kp index is one of the most widely used indices of geomagnetic activity. The derivation, application and historical background of Kp are detailed in Matzka, Stolle, et al. (2021), and thus are described here only briefly.
Kp is derived from K indices (Bartels et al., 1939) evaluated at 13 subauroral observatories from both northern and southern hemispheres. A K index expresses geomagnetic activity on a scale of 0–9 at each observatory for a given 3-hourly interval of the UT day (00–03, 03–06, …, 21–24 UT). It is based on the range of geomagnetic disturbance over the 3-hourly interval, which may contain geomagnetic pulsations (McPherron, 2005; Saito, 1969), bays associated with substorms (McPherron, 1970; Lyons, 1996), sudden storm commencements and sudden impulses (Araki, 1994), geomagnetic storm main phase (Gonzalez et al., 1994) and solar-flare and eclipse effects (Yamazaki & Maute, 2017). K is designed to have a similar frequency distribution regardless of observatory, and thus it does not depend on latitude. K indices are converted to standardized Ks indices, which take into account the influence of seasonal and UT biases. Kp is the average of the 13 Ks indices expressed in units of thirds (0o, 0+, 1−, 1o, 1+, 2−, …, 9o), thus it represents planetary, rather than local, geomagnetic activity. The complete time series of the definitive Kp index since 1932 and nowcast indices for the most recent hours are available from the Kp website at Deutsches GeoForschungsZentrum GFZ (https://www.gfz-potsdam.de/en/kp-index/) with a digital object identifier (DOI; Matzka, Bronkalla, et al., 2021). Real-time Kp forecasts (Shprits et al., 2019) based on solar wind data are also available from the GFZ website (https://spaceweather.gfz-potsdam.de/products-data/forecasts/kp-index-forecast).
The Kp index has a wide range of applications in space physics studies. For example, Kp can be used to select undisturbed data from the measurements obtained from the magnetosphere, ionosphere or thermosphere to determine their climatological base states (e.g., Drob et al., 2015; Fejer et al., 2008). Kp is also often used for modeling the geospace response to solar wind variations. Just to give a few examples, Kp is used to drive the 3-D Versatile Electron Radiation Belt model (Subbotin et al., 2011), the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X; Liu et al., 2018) and the Naval Research Laboratory Mass Spectrometer Incoherent Scatter radar empirical atmospheric model (Emmert et al., 2021), among many other models of the magnetosphere, ionosphere and thermosphere. Thomsen (2004) argued that what makes Kp so useful is its sensitivity to the latitudinal distance from the Kp stations to the equatorial edge of auroral currents, which is tightly linked to the strength of magnetospheric convection.
Kp has two important limitations. One is the temporal resolution. Kp cannot resolve temporal features within 3 hr. For example, the onset of geomagnetic disturbance determined by Kp could be off from the actual onset by up to 3 hr. This could be an issue when Kp is used to drive a geospace model, because the state of the magnetosphere, ionosphere and thermosphere can change significantly within the 3-hr interval. As a compromise, some models use interpolated Kp values as input data, for example, thermospheric density models (Vallado & Finkleman, 2014), WACCM-X (Liu et al., 2018). The other limitation of Kp is its upper limit at 9o. Kp is not able to quantify geomagnetic activity after it reaches 9o. Extreme geomagnetic storms involving Kp = 9o are not necessarily equally strong in terms of geomagnetic disturbance. Extrapolated values of Kp above 9o are sometimes used for a better representation of geomagnetic activity during severe geomagnetic storms (e.g., Shprits et al., 2011).
The objective of this paper is to introduce a new group of Kp-like geomagnetic indices. The indices are collectively called Hpo, where “H” stands for half-hourly or hourly, “p” for planetary, and “o” for open-ended. Hpo has been conceived and developed under the EU Horizon 2020 project, Space Weather Atmosphere Model and Indices (SWAMI; Jackson et al., 2020). Hpo is designed to represent planetary geomagnetic activity in a similar manner as Kp but with higher time resolution and without an upper limit, to overcome the limitations of Kp described above. The derivation of 30-min (Hp30) and 60-min (Hp60) indices is outlined in Section 2, and their basic properties are described in Section 7.
2 Derivation of Hpo Hpo indices are derived using 1-min magnetic data from the same 13 subauroral observatories as Kp (see Section 2.2 of Matzka, Stolle, et al., 2021). Time series of Hpo starts from the year 1995, because 1-min digital data are not available from all the observatories before 1995. The procedure for deriving Hpo is similar to that for nowcast Kp described in Matzka, Stolle, et al. (2021), involving the steps described below.
2.1 Evaluation and Removal of Quiet Curve
Records of the geomagnetic field from a ground station contain regular quiet daily variation and geomagnetic disturbance (Chapman & Bartels, 1940). The estimation of the quiet curve for Hpo is based on the Finnish Meteorological Institute method (Sucksdorff et al., 1991), which uses 1-min data from the previous day, present day, and subsequent day. The quiet curve is obtained for the northward X and eastward Y components of the geomagnetic field, and subtracted from the corresponding data, which leaves geomagnetic disturbance.
2.2 Evaluation of the Magnitude of Geomagnetic Disturbance
The magnitude of geomagnetic disturbance is evaluated for every 30-min interval for Hp30 and 60-min interval for Hp60. For a given time interval, the range of geomagnetic disturbance (i.e., maximum minus minimum value) is compared with the maximum absolute value of geomagnetic disturbance, and the larger value of the two is adopted as the magnitude of geomagnetic disturbance. This contrasts with the derivation procedure for Kp, which always uses the range of geomagnetic disturbance. We found that this modification of the procedure improves the compatibility between Hpo and Kp. The magnitude of geomagnetic disturbance is obtained for the X and Y components, and the larger value is used in the next step.
2.3 Evaluation of H30 and H60 Indices
H30 and H60 indices are analogous to K indices for Kp, and are collectively called H herein. For the evaluation of K, an observatory-specific table is used for converting the magnitude of geomagnetic disturbance (in nT) to an integer K value (0–9). An example of the conversion table for the Niemegk observatory can be found in Table 1. New tables have been created for each observatory that convert the magnitude of geomagnetic disturbance to an H value (0–9). This was done, for each observatory, by generating a conversion table for H in such a manner that the frequency distribution of H is as similar as possible to the frequency distribution of K. The construction of the conversion tables for H is based on the geomagnetic data during 1995–2017, which were all the available data when the construction of Hpo was initiated. The conversion table for H30 and H60 for Niemegk is presented in Table 1. Furthermore, extended conversion tables are produced in order to allow H to go beyond 9. In the extended conversion tables, the maximum value of H is unlimited. The lower limit for H = 10 is given by the lower limit of H = 9 multiplied by a factor of 1.35. The lower limit of H = 11 is given by the lower limit of H = 10 multiplied by a factor of 1.30, and the lower limit of H = 12 is given by the lower limit of H = 11 multiplied by a factor of 1.20. For values of H greater than 12, the multiplication factor will be always 1.20, so that H can be defined no matter how large the magnitude of geomagnetic disturbance is. These multiplication factors were determined on a trial-and-error basis so that the behavior of the final Hpo index above 9o will be compatible with those of other open-ended indices (see Section 7).
Table 1. Lower Limits of H30, H60, and K for the Niemegk Observatory Index 0 1 2 3 4 5 6 7 8 9 H30 (nT) 0 2.16 4.46 8.89 17.9 33.9 65.7 119 190 267 H60 (nT) 0 2.97 6.11 12.1 24.3 44.7 82.7 144 218 337 K (nT) 0 5.00 10.0 20.0 40.0 70.0 120 200 330 500 2.4 Evaluation of Hp30 and Hp60 Indices
H indices are converted to standardized Hs indices using the same method for converting K to Ks. The conversion tables can be found in the Supporting Information of Matzka, Stolle, et al. (2021). The conversion of H to Hs minimizes the influence of seasonal and UT biases. Finally, the average of the 13 Hs indices is converted into Hpo values in units of thirds (0, 1/3, 2/3, 1, 4/3, 5/3, 2, …) in analog fashion as with the nowcast Kp (see Section 3.3 of Matzka, Stolle, et al., 2021) and expressed as (0o, 0+, 1−, 1o, 1+, 2−, …) following the convention for Kp. The Hpo value is derived using the H indices evaluated with the conversion tables capped at 9 (like the one shown in Table 1). If this initial Hpo value is 9o, all the H indices are re-evaluated using the extended conversion tables, in which H can go beyond 9, to re-calculate Hpo. This ensures that Hpo and Kp behave similarly up to 9− (and differently only at 9o and above).
Like Kp, Hpo indices are a quasi-logarithmic, rather than linear, measure of geomagnetic activity, and thus are not suitable for basic arithmetic operations such as addition and multiplication. To avoid this issue, linearly scaled ap30 and ap60 indices (collectively called apo) are produced for Hp30 and Hp60, respectively, by using the table that is used for producing ap from Kp (Matzka, Stolle, et al., 2021) but extending its higher end in a similar manner as the extension of H tables above 9. The relationship between Hpo and apo is illustrated in Figure 1a. Like ap, values of apo correspond to half the magnitude of geomagnetic disturbance at Niemegk.
Details are in the caption following the image Figure 1 Open in figure viewer PowerPoint (a) The relationship between Hpo and apo. (b–j) Frequency distributions of the occurrence of Kp, Hp60, and Hp30 values for different years. (k) Monthly mean values of ap, ap60, and ap30 during 1995–2020. The total sunspot number is also indicated.
Hp30 and Hp60, along with their corresponding ap30 and ap60, are archived since 1995 and available, in near real time, from the GFZ website (https://www.gfz-potsdam.de/en/hpo-index) with DOI (https://doi.org/10.5880/Hpo.0002) under the CC BY 4.0 license (Matzka et al., 2022, for data publication).
3 Some Properties of Hpo The frequency distributions of the occurrence of Hp30, Hp60, and Kp values are compared in Figures 1b–1j for every 3-year interval from 1995 to 2021. The distribution pattern of Kp is different in different solar cycle phases. For instance, during the solar minimum years 2007–2009 (Figure 1f) and 2019–2021 (Figure 1j), the occurrence rate of low Kp values (e.g., Kp ≤ 1o) is appreciably higher than during the solar maximum years 2001–2003 (Figure 1d) and 2013–2015 (Figure 1h). Hp30 and Hp60 reproduce different distribution patterns of Kp well, even for the later years not used in the construction of the conversion tables defining the H indices. The agreement of Hp30 and Hp60 with Kp during 2018–2021 (Figure 1j) suggests that the conversion tables for H indices are valid beyond the period 1995–2017.
The linearly scaled ap30 and ap60 indices are suitable for assessing average geomagnetic activity over a certain period. Monthly mean values of ap30 and ap60 are plotted in Figure 1k. They are in good agreement with monthly mean ap, showing 11-year solar-cycle variation. The sunspot number is also displayed in Figure 1k for comparison. Geomagnetic activity is known to be highest during the declining phase of solar cycle due to the effects of recurrent high speed solar wind streams (Lockwood et al., 1999).
In Figure 2, Hp30 (top), Hp60 (middle), and Kp (bottom) are compared with other geospace indices. The left panels show comparisons with Newell's coupling function (Newell et al., 2007), which is a measure of the energy input from the solar wind into the magnetosphere. The coupling function was derived using OMNI 5-min solar wind data (King & Papitashvili, 2005). Panels in the middle and right columns show comparisons with AE and PC indices, respectively. The AE index is a measure of auroral electrojet activity based on geomagnetic field measurements in the auroral region. The PC index represents geomagnetic activity in the polar region (Troshichev et al., 1988). Following Stauning (2007), the average of the PC indices from the northern (PCN) and southern (PCS) hemispheres were calculated using non-negative values. For comparisons with Hpo and Kp indices, 5-min solar wind data and 1-min AE and PC indices were averaged over every 30-min intervals. Hp60 and Kp are assumed to remain the same within their temporal windows. The solar wind data were shifted by 20 min to account for the delay due to energy transfer from the bow shock to the ionosphere (Manoj et al., 2008).
Details are in the caption following the image Figure 2 Open in figure viewer PowerPoint Dependence of (a–c) Hp30, (d–f) Hp60, and (g–i) Kp on (a, d, g) Newell's solar-wind coupling function, (b, e, h) AE index, and (c, f, i) PC index. For the PC index, the average of the northern (PCN) and southern (PCS) indices is used, considering only their positive values. In each panel, black dots indicate the average of the solar-wind coupling function, AE or PC index at each Hpo or Kp value (0o, 0+, 1−, …, 9−), with error bars representing the standard deviation and the green curve representing the best-fitting third-order polynomial function for Hpo or Kp below 9o. The gray dots in panels (a–f) are individual data points for Hpo ≥9o, and the yellow dot is their average value.
The solar-wind coupling function, AE and PC indices averaged at each value of Hpo and Kp from 0o to 9− are indicated in Figure 2 by black dots, with error bars representing the standard deviation. Curves in green show the best-fitting third-degree polynomial function for Hpo and Kp below 9o. The fitted curves for Hp30, Hp60, and Kp are similar to each other. The results suggest that for Hpo <9o, the dependence of Hp30 and Hp60 on the solar-wind coupling function, AE and PC indices is consistent with that of Kp. For Hpo ≥9o, the number of data points is rather small, and thus the average solar-wind coupling function, AE and PC indices were not calculated for each Hpo value. Instead, a single average value was derived using all the data corresponding to Hpo ≥9o (gray dots), which is indicated by the yellow dot in each panel of Figures 2a–2f. It is seen that the average value falls near the polynomial curve derived from the data for Hpo <9o. The results suggest that Hp30 and Hp60 can represent geomagnetic activity for Hpo ≥9o in the manner expected from their behavior for Hpo <9o.
The behavior of Hpo at its high end is further illustrated in Figure 3 based on five geomagnetic storm events. The selected geomagnetic storms are those in November 2003, March 2001, October 2003, November 2004, and July 2002, which are the five most intense geomagnetic storms during the period considered in this study (1995–2021) according to the minimum value of the Dst index. The left panels show time series of Hp30, Hp60, and Kp, as well as the Dst index, over a 7-day interval, in which the third day corresponds to the storm main phase. The temporal evolution of Kp is generally well captured by Hp30 and Hp60. Variations within 3 hr are seen in Hp30 and Hp60, which are not resolved by Kp. The maximum values of Hp30, Hp60, Kp, and the minimum value of Dst are (9−, 9−, 9−, and −422) for the November 2003 event, (10o, 10−, 9−, and −387) for the March 2001 event, (12−, 12−, 9o, and −383) for the October 2003 event, (11−, 9−, 9−, and −374) for the November 2004 event and (11o, 11o, 9o, and −300) for the July 2002 event. Thus, according to Hpo, the October 2003 event is the strongest among the five. Hpo ≥9o is seen mainly during the storm main phase, when the Dst index rapidly decreases. The right panels compare the 3-hourly mean of Hp30 (calculated from ap30) and Kp. The correlation is rather good; the correlation coefficient r is greater than 0.98 in all cases. Similarly good correlation is found for the comparison between 3-hourly mean of Hp60 and Kp (not shown here). These results suggest that Hpo can represent geomagnetic activity in a similar way as Kp even during the strongest geomagnetic storms.
Details are in the caption following the image Figure 3 Open in figure viewer PowerPoint (a, c, e, g, i) Time series of Kp, Hp60, Hp30, and Dst over a 7-day interval during strong geomagnetic storm events. Zero in the horizontal axis corresponds to 00 UT of the day with the storm main phase. (b, d, f, h, j) Comparison of Kp and three-hourly average of Hp30 during the strong geomagnetic storm events. The 3-hourly average of Hp30 is derived from the corresponding values of ap30. The correlation coefficient r is also indicated.
To provide some insight into variations of Hp30 and Hp60 within 3 hr, Figure 4 depicts the response of ap30, ap60, and ap to isolated substorms. The substorm onset list based on the technique described by Newell and Gjerloev (2011a) was obtained from the SuperMAG website (https://supermag.jhuapl.edu/). We selected isolated substorm events where there is no other substorm onset in the preceding 6 hr and following 12 hr. A total of 1947 isolated substorm events have been identified during 1995–2018. Figure 4a shows the variation of the AE index averaged over those substorm events. The average AE index peaks approximately 1 hr after the onset, and decays gradually to go back to the pre-onset level in 3–4 hr. The average ap30 and ap60 indices (Figures 4b and 4c) show the increase and decrease of geomagnetic activity that occur within 3 hr around the substorm onset. ap (Figure 4d) is not able to fully resolve such a short-term variation due to its low time resolution. The results suggest that variation of Hpo within 3 hr can contain physically meaningful information, which is not resolved by Kp.
Details are in the caption following the image Figure 4 Open in figure viewer PowerPoint Superposed epoch analysis of (a) AE, (b) ap30, (c) ap60, and (d) Kp over 1947 isolated substorm events identified during 1995–2018 based on the method of Newell and Gjerloev (2011a). Error bars represent the standard error of the mean. Zero in the horizontal axis corresponds to the substorm onset.
4 Summary and Outlook We have described a group of new open-ended geomagnetic activity indices Hpo. Hourly (Hp60) and half-hourly (Hp30) indices, along with their linearly scaled counterparts (ap30 and ap60), are available in near real time from the GFZ website (https://www.gfz-potsdam.de/en/hpo-index) with DOI (Matzka et al., 2022). Important properties of Hpo that are revealed by our initial analysis can be summarized as follows: The frequency distributions of the occurrence of Hp30 and Hp60 values are consistent with that of Kp at different phases of the solar cycle (Figures 1a–1i).
Month-to-month variations of Hp30 and Hp60 are consistent with that of Kp (Figure 1k).
The relationships between Hpo indices and Newell's solar wind coupling function, AE and PC indices are similar to those between Kp and these three quantities.
Hp30 and Hp60 can capture temporal variation of Kp during strong geomagnetic storm events (Figure 3).
Hp30 and Hp60 can reproduce short-term variation of geomagnetic activity within 3 hr associated with substorms (Figure 4).
These results demonstrate that Hpo can be used as a higher time-resolution alternative to Kp. Indeed, there are already a few studies that utilized Hpo for its advantage over Kp. Yamazaki et al. (2021) used Hp30 to select quiet-time measurements of the geomagnetic field from Swarm satellites. The orbital period of a Swarm satellite is approximately 90 min, thus using Hp30, geomagnetic activity can be evaluated for every one third of the orbit, while there is only one Kp value for every two orbits. The high-cadence output of Hpo enables a more accurate selection of quiet-time data than the three-hourly Kp index. Bruinsma and Boniface (2021) used Hp60 to drive a recent version of the Drag Temperature Model, DTM-2020, which is a semi-empirical model of the Earth's thermosphere, developed for orbit determination and prediction of spacecraft and debris. They showed that the use of Hpo leads to the improvement of the model compared with the predecessor model DTM-2013 (Bruinsma, 2015) that is driven by Kp. Similarly, Hpo may be used for improving other geospace models driven by Kp. Recalibration and validation are recommended when Hpo is used as an input for existing models that are parameterized with Kp.

Suppose I have a zernike wavefront generated from some random modes.
phase
Inorder to reconstruct the wavefront, i calculated its slopes values by performing tip/tilt fit at each sub aperture.
sy(tilt y)
sx (tilt x)
Then i perform polynomial fit by mutiplying the slopes with some polynomial matrix. I should be getting same original wavefront but the amplitude is incorrect.
reconstructed wavefront
What could I be possibly doing wrong here?
l = 14
n_l = 20
n = l*n_l
plt.rcParams['image.cmap'] = 'jet'
"""
#OSA index
0 = piston
1 = tilt y
2 = tilt x
"""
def zernike(n_l, case):
x = np.linspace(-1 + 1/n_l, 1 - 1/n_l, n_l)
y = x
X,Y = np.meshgrid(x,y)
rho = np.sqrt(X**2+Y**2)
circle = np.where(rho > 1)
theta = np.arctan2(Y, X)
Z_piston = np.ones((n_l, n_l))
Z_piston[circle] = 0
rho[circle] = 0
Z_tilty = 2*rho*np.sin(theta)
Z_tiltx = 2*rho*np.cos(theta)
Z_oblastig = np.sqrt(6)*(rho**2)*np.sin(2*theta)
Z_verastig = np.sqrt(6)*(rho**2)*np.cos(2*theta)
Z_defocus = np.sqrt(3)*(2*rho**2 - 1)
#Zernike matrix for the tip tilt fit
if(case == "fit"):
Z_fit = np.stack((Z_piston.flatten(), Z_tiltx.flatten(), Z_tilty.flatten()))
Z_fit = Z_fit.T
return Z_fit
else:
Z = np.stack((Z_piston, Z_tilty,Z_tiltx,Z_oblastig, Z_verastig))
zCoeffs = np.random.uniform(-1, 1, len(Z))
np.random.seed(0)
wavefront =[zCoeffs[i] * Z[i] for i in range(len(zCoeffs))]
phase = np.zeros((n,n))
for w in wavefront:
phase += w
return phase
Z_fit = zernike(n_l, case = 'fit') #zernike matrix for tip tilt fit
phase = zernike(l*n_l, case = 'wavefront') #a zernike wavefront with some random modes
Phi = []
Phi_ori = []
coeffs = []
Z_cop = []
sx = np.zeros((l,l))
sy = np.zeros((l,l))
for i in range(l):
for j in range(l):
"""
fit the zernike phase for each sub aperture and get sx and sy values
.......step 2
"""
phi = phase[j*n_l:(j*n_l)+n_l,i*n_l:(i*n_l)+n_l]
Phi_ori.append(phi)
idx = np.argwhere(phi.flatten() == 0.0)
z_cop = Z_fit.copy()
Phi_cop = np.delete(phi, idx)
z_cop = np.delete(z_cop, idx, axis=0)
Phi.append(Phi_cop)
Z_cop.append(z_cop) #zernike matrix
c1 = np.dot(np.linalg.pinv(z_cop), Phi_cop)
# c1 = np.dot(np.linalg.pinv(Z_fit), phi.flatten())
sx[i,j] = c1[2]
sy[i,j] = c1[1]
plt.figure()
plt.imshow(phase, origin = 'lower')
plt.colorbar()
plt.figure()
plt.imshow(sx, origin = 'lower')
plt.colorbar()
plt.figure()
plt.imshow(sy, origin = 'lower')
plt.colorbar()
now for reconstruction, i am using a code from my supervisor who took reference from a company developing wfs.
function [w, dw] = polymonom(D, x, y)% D is the degree of the polynomial, x and y the coordinates% returns wavefront w and slope dw M=(D+1)*(D+2)/2; rows=size(x, 1); cols=M; w=zeros(rows, cols); dw=zeros(2*rows, cols); for h=1:rows for i=0:D for j=0:i m=i*(i+1)/2+j+1; w(h, m)=x(h)^j * y(h)^(i-j); dw(h, m)=j*x(h)^(j-1) * y(h)^(i-j); dw(h+rows, m)=x(h)^j * (i-j)*y(h)^(i-j-1); end end end end
[wpol, dwpol] = polymonom(D, x, y); s2a=pinv(dwpol); s = [sx sy]; srand = reshape(s,1,[]); a=s2a*s'; % srand are the slopes you want to plot as wf wf=wpol*a; wf=wf-mean(wf); I have used the shape meshgrid for both the cases but I don't know if my slope values are correct. Or if there is anything missing with the scaling? If someone could help me with the math to understand it, I would appreciate it.
Thank you.
Polyfit math:
https://preview.redd.it/yf9na68r1wyc1.jpg?width=1080&format=pjpg&auto=webp&s=db33088fd96b274d69228dbeec744a46ed9d727b