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Wait there are tiny cities here. Isn't it the case that as geographies get smaller, the count of them gets higher, and you'll always get on square inch of the

Wait there are tiny cities here. Isn't it the case that as geographies get smaller, the count of them gets higher, and you'll always get on square inch of the US that's breaking the time-of-year temperature record right this second! I'm all for data, but the statistics here seem selected to drive towards the conclusion "global warming is a huge problem". Climate change is so real that we don't need to resort to this sort of trickery -- it harms rather than hurts the message.

jedberg 4y ago
No, that shouldn't be the case. Unless the planet is warming, we shouldn't constantly be setting new highs. I'm not sure what the trickery is here.
- aidenn0 4y ago
  It's not the case because temperatures are correlated; If <random suburb of $BIG_CITY> sets a high, it's likely that $BIG_CITY will as well. However, we should be somewhat regularly setting new highs just because we have on the order of just 200 years of data (so just 200 data points for each daily high); if the planet were not warming, and the high for any given day will be normally distributed around some average for that day, then as time marches on the odds of getting an extreme outlier increases. Some cities on some days will have a high that is very improbable, while others will not have gotten "lucky" yet.
- handmodel 4y ago
  The planet clearly is warming but I also agree this method is useless by itself. For Los Angeles (my city) the data goes back 145 days a year. If temperature has not been increasing (and therefore each individual day follows an identical distribution) that would still mean that 1/145 days we'd see a record high in Los Angeles - so about two highs a year. Highs in Los Angeles are obviously going to be correlated to highs in San Diego - but not exactly because of cloud cover and stuff so its reasonable to think that even if we were in a boring unchanging climate we'd still see hundreds if not thousands of records set every day across the country.
  - jedberg 4y ago
    I think your math is wrong. You wouldn't see two record highs every year with a normal distribution. The record high for each day would be set once, and would be an extreme outlier. Think about something like IQ. If you grab a group of people you wouldn't expect to find a genius every time, or even most of the time. Most of the time you'd expect to find someone near 100. Unless IQs had been steadily rising. With a normal distribution you wouldn't expect even one record to be set every year. The expected case would be zero records in a year.
    - handmodel 4y ago
      Perhaps you are misunderstanding the records it is describing. A record in that data is defined as a particular high in a particular city on a particular day. The data goes back 145 years in Los Angeles. So if it is the hottest May 24th ever that would be a record. If everyday followed an identical and uncorrelated distribution then we would expect that 1/145 days would be record. In your IQ example imagine if you had a school with 365 separate classrooms with 144 students in each one. A new 145th student then enters each classroom. The chance that the new student is the one with the highest IQ is 1/145. So in the universe of the 365 classrooms you'd expect 2 new IQ records to be set.
      - jedberg 4y ago
        I fully understand what they record is. Let me ask this, why in your school with 365 classrooms would you expect 2 new IQ records to be set with 145 new students. With a normal distribution, you'd expect all of those new students to be within one standard deviation of 100. > The chance that the new student is the one with the highest IQ is 1/145 Why do you think this is the case?
        handmodel 4y ago
        The student who enters the classroom has an IQ that follows the same distribution of intelligence of any of the other students. Therefore, one student out of the 145 must have the highest intelligence and the chances that it is student #4, #30, #100, or #145 is the same. Here is some python code you can run. You can change around the distribution however you want and you'd get the same exact results. The chance that a particular record is the highest in a set of IID variables is not dependent on the distribution itself. from numpy import random RecordsSet=0 TotalSimulations=365000 for i in range(0,TotalSimulations): ClassRoomSample = random.normal(100, 15, 144) RecordIQ = max(ClassRoomSample) NewStudentIQ = random.normal(100, 15, 1) if NewStudentIQ>RecordIQ: RecordsSet=RecordsSet+1 print(100*float(1)/145) print(100*float(RecordsSet)/TotalSimulations) A record is set 1 out of every 145 days/classes. Which means in a year/school of 365 days/classes you'd expect a bit more than 2 records on average.

jedberg 4y ago

No, that shouldn't be the case. Unless the planet is warming, we shouldn't constantly be setting new highs. I'm not sure what the trickery is here.

aidenn0 4y ago
It's not the case because temperatures are correlated; If <random suburb of $BIG_CITY> sets a high, it's likely that $BIG_CITY will as well. However, we should be somewhat regularly setting new highs just because we have on the order of just 200 years of data (so just 200 data points for each daily high); if the planet were not warming, and the high for any given day will be normally distributed around some average for that day, then as time marches on the odds of getting an extreme outlier increases. Some cities on some days will have a high that is very improbable, while others will not have gotten "lucky" yet.
handmodel 4y ago
The planet clearly is warming but I also agree this method is useless by itself. For Los Angeles (my city) the data goes back 145 days a year. If temperature has not been increasing (and therefore each individual day follows an identical distribution) that would still mean that 1/145 days we'd see a record high in Los Angeles - so about two highs a year. Highs in Los Angeles are obviously going to be correlated to highs in San Diego - but not exactly because of cloud cover and stuff so its reasonable to think that even if we were in a boring unchanging climate we'd still see hundreds if not thousands of records set every day across the country.
- jedberg 4y ago
  I think your math is wrong. You wouldn't see two record highs every year with a normal distribution. The record high for each day would be set once, and would be an extreme outlier. Think about something like IQ. If you grab a group of people you wouldn't expect to find a genius every time, or even most of the time. Most of the time you'd expect to find someone near 100. Unless IQs had been steadily rising. With a normal distribution you wouldn't expect even one record to be set every year. The expected case would be zero records in a year.
  - handmodel 4y ago
    Perhaps you are misunderstanding the records it is describing. A record in that data is defined as a particular high in a particular city on a particular day. The data goes back 145 years in Los Angeles. So if it is the hottest May 24th ever that would be a record. If everyday followed an identical and uncorrelated distribution then we would expect that 1/145 days would be record. In your IQ example imagine if you had a school with 365 separate classrooms with 144 students in each one. A new 145th student then enters each classroom. The chance that the new student is the one with the highest IQ is 1/145. So in the universe of the 365 classrooms you'd expect 2 new IQ records to be set.
    - jedberg 4y ago
      I fully understand what they record is. Let me ask this, why in your school with 365 classrooms would you expect 2 new IQ records to be set with 145 new students. With a normal distribution, you'd expect all of those new students to be within one standard deviation of 100. > The chance that the new student is the one with the highest IQ is 1/145 Why do you think this is the case?
      - handmodel 4y ago
        The student who enters the classroom has an IQ that follows the same distribution of intelligence of any of the other students. Therefore, one student out of the 145 must have the highest intelligence and the chances that it is student #4, #30, #100, or #145 is the same. Here is some python code you can run. You can change around the distribution however you want and you'd get the same exact results. The chance that a particular record is the highest in a set of IID variables is not dependent on the distribution itself. from numpy import random RecordsSet=0 TotalSimulations=365000 for i in range(0,TotalSimulations): ClassRoomSample = random.normal(100, 15, 144) RecordIQ = max(ClassRoomSample) NewStudentIQ = random.normal(100, 15, 1) if NewStudentIQ>RecordIQ: RecordsSet=RecordsSet+1 print(100*float(1)/145) print(100*float(RecordsSet)/TotalSimulations) A record is set 1 out of every 145 days/classes. Which means in a year/school of 365 days/classes you'd expect a bit more than 2 records on average.