<p>Depends quite a bit upon the geographic scale between the two places.  But in general there will tend to be some interdependence, even for locations large distances apart, as the large-scale upper atmosphere is controlled by a <a href="https://www.weather.gov/jetstream/basic" rel="nofollow noreferrer">wave pattern</a>:</p>
<p><a href="https://i.sstatic.net/gtLkT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gtLkT.png" alt="enter image description here" /></a></p>
<p>This flow pattern <a href="https://www.weather.gov/jetstream/longshort" rel="nofollow noreferrer">continues around the globe</a>.  In addition, the fact that the temperature of the Pacific Ocean <a href="https://www.climate.gov/news-features/featured-images/global-impacts-el-ni%C3%B1o-and-la-ni%C3%B1a" rel="nofollow noreferrer">has impacts on weather almost worldwide</a> shows just significant interconnection can be:</p>
<p><a href="https://i.sstatic.net/NBI1n.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NBI1n.png" alt="enter image description here" /></a></p>
<p>The most independent phenomena will tend to be mesoscale (local) phenomena like seabreeze thunderstorms and lake effect snow... though even they tend to have some fair reliance upon wind direction and pressure regime, which are involved with the larger pattern.  The amount of dependence between two reasonably distant locations though will often be quite small.</p>
<p>On the other hand, it's quite common to have a few days where rain thousands of miles apart is not just slightly correlated, but directly the consequence of the same feature, such as this front from January 2013 that Wikipedia <a href="https://en.wikipedia.org/wiki/Squall_line#/media/File:Eastern_US_squall_line_30_January_2013_radar_mosaic.png" rel="nofollow noreferrer">had saved</a>:</p>
<p><a href="https://i.sstatic.net/dL6k5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dL6k5.png" alt="enter image description here" /></a></p>
<p>So fundamentally there is some, at least small, interconnection between precipitation events at any two locations globally.  But if you can choose locations with consideration of geographic (distance/surroundings) and meteorological factors (seasons), you can likely get results that are empirically basically independent, as the large-scale pattern connection between them is such a minor contributing factor compared to other influences.  <strong>In other words, there is a dependent relationship part between the precipitation at any two locations and an independent part.  Statistically the dependence is often very (very) small for many location choices, but is greater for nearer locations and in certain seasons/weather events.</strong></p>
<p>If you are, for example, designing a school science fair experiment, you would likely struggle if you wanted to see <a href="https://www.cleveland.com/weather/blog/2018/02/meet_20_other_weather-predicti.html" rel="nofollow noreferrer">which animal specie is best at predicting the weather</a> (spoiler: none!) by looking at snowfall totals, because there's quite a lot of dependence between the weather at the sites listed since they are mostly in the same region and their winter/spring climate is heavily tied to the large-scale upper atmospheric pattern and storm system tracks, so that would likely swamp out any &quot;contribution&quot; from the animal (in addition, geographical differences, such as terrain and relationship to bodies of water, would be another huge uncontrolled independent factor).  On the other hand, if you were wanting to compare the influence of industrial pollution on the number of rainfall days, and carefully chose, for example, distant tropical coastal sites (perhaps a site in SE Asia versus one in the Caribbean) with similar weather influences/patterns, and looked at large datasets... you might be able to fairly inspect the magnitude of such influence for the chosen regime type.</p>
<p>I often found meteorological phenomena to be challenging to design simple science fair projects around, as there are so many different interconnected variables, and it is hard to control most and leave one independent.  That's why many meteorological studies are often focused more on <a href="https://en.wikipedia.org/wiki/Multivariate_statistics" rel="nofollow noreferrer">multivariate analysis</a> of large datasets and effects like <a href="https://en.wikipedia.org/wiki/Urban_heat_island" rel="nofollow noreferrer">urban heat island</a> took quite a bit of careful analysis to recognize.  It's not impossible, but to find two locations that are for all intents and purposes seeing independent weather events, while still not being controlled by other factors like their climate regimes/topography, can be quite challenging.</p>
<p><strong>But while fundamentally no precipitation events are ever absolutely perfectly independent, with the right distance and location considerations their interdependence can be so negligible so as to consider the precipitation independent phenomena.  I would consult a meteorologist to analyze how independent two such sites may be.</strong></p>

CC BY-SA 4.0
2022-02-08T16:08:14.850Z
Maybe I didn't go into it enough, but even comparing like Kansas City to Charlotte would see connection issues... they'd have more of a negative correlation in precipitation, as they're typically in opposites of the [trough/wave pattern](https://www.weather.gov/jetstream/basic) (I may go back and eventually edit this into the answer)
JeopardyTempest
CC BY-SA 4.0
2022-02-08T16:38:30.483Z
Thank you very much for your brilliant answer. I was considering two cities in the middle of Europe; thus, the interdependence there is negligible, right?
Anna-Kat
CC BY-SA 4.0
2022-02-08T18:20:12.567Z
:-) That's a tough one, in winter particularly, and even spring and fall quite a bit, I'd think there's a heavy interdependence in such areas, when fronts/larger storm systems come through.  The midlatitudes unfortunately are a tough area as they have a lot of impact by large systems.  It may help to have a better idea of the question and data scale you're trying to look at to better gauge just how challenging the interdependence would be.
JeopardyTempest
CC BY-SA 4.0
2022-02-08T18:29:53.100Z
Thanks. I have dates - days, and corresponding values of precipitation. The Pearson correlation parameter is 0.15.
Anna-Kat
CC BY-SA 4.0
2022-02-08T18:58:48.590Z
The 0.15 sounds reasonable, and actually suggests to me that there's probably some connection between them.  If you have a large enough data set, 0.15 may prove there is correlation (and thus the lack of complete independence)... I believe you use a statistic calculation to actually test the correlation coefficient to see if it is fairly conclusive proof that a connection exists.  Basically you'd go to [this site](https://www.socscistatistics.com/pvalues/pearsondistribution.aspx) and put in your Pearson and the number of days you have, and see if it says the result is significant.
JeopardyTempest
CC BY-SA 4.0
2022-02-08T19:02:46.577Z
Either way, I'm pretty confident that a 0.15 correlation coefficient won't allow you to definitely conclude they aren't connected. Though the connection is indeed somewhat limited in degree. The value suggests there is indeed a connection (which would match the thinking I gave in the writeup) (in addition, I didn't emphasize before that precipitation at sites will almost always be heavily connected to the date [especially outside the tropics], so there will always be indirect connection between any 2 site's values because both are season dependent, even aside from direct meteorological link)
JeopardyTempest
CC BY-SA 4.0
2022-02-08T19:05:23.810Z
Thanks, I have 14610 days: The P-Value is < .00001. The result is significant at p < .05.
Anna-Kat
CC BY-SA 4.0
2022-02-08T19:07:27.143Z
Indeed, p < .05 (and actually even < .01 in your case) shows that statistically we can very reasonably conclude that there is a connection of some kind between those two locations, they are not independent.  If you are taking a statistics class (which it's sounding like you are!), you'll want to word that carefully to be properly scientific with your ideas, but generally you have enough evidence to indicate there is some connection (again, not a giant connection, but some connection, **they are not fundamentally completely independent phenomena**)
JeopardyTempest
CC BY-SA 4.0
2022-02-08T19:11:53.510Z
Thank you very much
Anna-Kat
CC BY-SA 4.0
2022-02-08T16:02:10.147Z
2022-04-04T22:39:37.857Z
2022-04-04T22:39:37.857Z
JeopardyTempest
<p>Is it possible to consider the occurrences of precipitation in two different places to be independent phenomena?</p>

CC BY-SA 4.0
2022-02-08T15:23:03.543Z
Welcome to ESSE. I think your question can not be answered unless you provide more detail/context. If you consider the precipitation statistically you could for example argue that uncorrelated rain occurrences at the two places are indeed independent. However, if you are trying to argue using physics you are going to have a hard time.
Joscha Fregin
CC BY-SA 4.0
2022-02-08T15:42:19.577Z
Thank you very much
Anna-Kat
CC BY-SA 4.0
2022-04-05T07:05:14.333Z
If they occur on different planets, yes ;-)
gerrit
<meteorology>
Precipitation in two places as independent phenomena
Anna-Kat
# Precipitation in two places as independent phenomena

(Asked by: username_0 on 2022-02-08)

Is it possible to consider the occurrences of precipitation in two different places to be independent phenomena?

**Tags:** meteorology

> **Comments:**
> **username_1**: Welcome to ESSE. I think your question can not be answered unless you provide more detail/context. If you consider the precipitation statistically you could for example argue that uncorrelated rain occurrences at the two places are indeed independent. However, if you are trying to argue using physics you are going to have a hard time.  
> **username_0**: Thank you very much  
> **username_2**: If they occur on different planets, yes ;-)  

---

## 1 answers

### Answer by username_3 on 2022-02-08. Score: 6 | Accepted answer

Depends quite a bit upon the geographic scale between the two places. But in general there will tend to be some interdependence, even for locations large distances apart, as the large-scale upper atmosphere is controlled by a [wave pattern](https://www.weather.gov/jetstream/basic):

[![enter image description here](https://i.sstatic.net/gtLkT.png)](https://i.sstatic.net/gtLkT.png)

This flow pattern [continues around the globe](https://www.weather.gov/jetstream/longshort). In addition, the fact that the temperature of the Pacific Ocean [has impacts on weather almost worldwide](https://www.climate.gov/news-features/featured-images/global-impacts-el-ni%C3%B1o-and-la-ni%C3%B1a) shows just significant interconnection can be:

[![enter image description here](https://i.sstatic.net/NBI1n.png)](https://i.sstatic.net/NBI1n.png)

The most independent phenomena will tend to be mesoscale (local) phenomena like seabreeze thunderstorms and lake effect snow... though even they tend to have some fair reliance upon wind direction and pressure regime, which are involved with the larger pattern. The amount of dependence between two reasonably distant locations though will often be quite small.

On the other hand, it's quite common to have a few days where rain thousands of miles apart is not just slightly correlated, but directly the consequence of the same feature, such as this front from January 2013 that Wikipedia [had saved](https://en.wikipedia.org/wiki/Squall_line#/media/File:Eastern_US_squall_line_30_January_2013_radar_mosaic.png):

[![enter image description here](https://i.sstatic.net/dL6k5.png)](https://i.sstatic.net/dL6k5.png)

So fundamentally there is some, at least small, interconnection between precipitation events at any two locations globally. But if you can choose locations with consideration of geographic (distance/surroundings) and meteorological factors (seasons), you can likely get results that are empirically basically independent, as the large-scale pattern connection between them is such a minor contributing factor compared to other influences. **In other words, there is a dependent relationship part between the precipitation at any two locations and an independent part. Statistically the dependence is often very (very) small for many location choices, but is greater for nearer locations and in certain seasons/weather events.**

If you are, for example, designing a school science fair experiment, you would likely struggle if you wanted to see [which animal specie is best at predicting the weather](https://www.cleveland.com/weather/blog/2018/02/meet_20_other_weather-predicti.html) (spoiler: none!) by looking at snowfall totals, because there's quite a lot of dependence between the weather at the sites listed since they are mostly in the same region and their winter/spring climate is heavily tied to the large-scale upper atmospheric pattern and storm system tracks, so that would likely swamp out any "contribution" from the animal (in addition, geographical differences, such as terrain and relationship to bodies of water, would be another huge uncontrolled independent factor). On the other hand, if you were wanting to compare the influence of industrial pollution on the number of rainfall days, and carefully chose, for example, distant tropical coastal sites (perhaps a site in SE Asia versus one in the Caribbean) with similar weather influences/patterns, and looked at large datasets... you might be able to fairly inspect the magnitude of such influence for the chosen regime type.

I often found meteorological phenomena to be challenging to design simple science fair projects around, as there are so many different interconnected variables, and it is hard to control most and leave one independent. That's why many meteorological studies are often focused more on [multivariate analysis](https://en.wikipedia.org/wiki/Multivariate_statistics) of large datasets and effects like [urban heat island](https://en.wikipedia.org/wiki/Urban_heat_island) took quite a bit of careful analysis to recognize. It's not impossible, but to find two locations that are for all intents and purposes seeing independent weather events, while still not being controlled by other factors like their climate regimes/topography, can be quite challenging.

**But while fundamentally no precipitation events are ever absolutely perfectly independent, with the right distance and location considerations their interdependence can be so negligible so as to consider the precipitation independent phenomena. I would consult a meteorologist to analyze how independent two such sites may be.**

> **Comments:**
> **username_3**: Maybe I didn't go into it enough, but even comparing like Kansas City to Charlotte would see connection issues... they'd have more of a negative correlation in precipitation, as they're typically in opposites of the [trough/wave pattern](https://www.weather.gov/jetstream/basic) (I may go back and eventually edit this into the answer)  
> **username_0**: Thank you very much for your brilliant answer. I was considering two cities in the middle of Europe; thus, the interdependence there is negligible, right?  
> **username_3**: :-) That's a tough one, in winter particularly, and even spring and fall quite a bit, I'd think there's a heavy interdependence in such areas, when fronts/larger storm systems come through.  The midlatitudes unfortunately are a tough area as they have a lot of impact by large systems.  It may help to have a better idea of the question and data scale you're trying to look at to better gauge just how challenging the interdependence would be.  
> **username_0**: Thanks. I have dates - days, and corresponding values of precipitation. The Pearson correlation parameter is 0.15.  
> **username_3**: The 0.15 sounds reasonable, and actually suggests to me that there's probably some connection between them.  If you have a large enough data set, 0.15 may prove there is correlation (and thus the lack of complete independence)... I believe you use a statistic calculation to actually test the correlation coefficient to see if it is fairly conclusive proof that a connection exists.  Basically you'd go to [this site](https://www.socscistatistics.com/pvalues/pearsondistribution.aspx) and put in your Pearson and the number of days you have, and see if it says the result is significant.  
> **username_3**: Either way, I'm pretty confident that a 0.15 correlation coefficient won't allow you to definitely conclude they aren't connected. Though the connection is indeed somewhat limited in degree. The value suggests there is indeed a connection (which would match the thinking I gave in the writeup) (in addition, I didn't emphasize before that precipitation at sites will almost always be heavily connected to the date [especially outside the tropics], so there will always be indirect connection between any 2 site's values because both are season dependent, even aside from direct meteorological link)  
> **username_0**: Thanks, I have 14610 days: The P-Value is < .00001. The result is significant at p < .05.  
> **username_3**: Indeed, p < .05 (and actually even < .01 in your case) shows that statistically we can very reasonably conclude that there is a connection of some kind between those two locations, they are not independent.  If you are taking a statistics class (which it's sounding like you are!), you'll want to word that carefully to be properly scientific with your ideas, but generally you have enough evidence to indicate there is some connection (again, not a giant connection, but some connection, **they are not fundamentally completely independent phenomena**)  
> **username_0**: Thank you very much  

---

