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EDIT 6/13/2020: Actual Jan average from same website was 50.3 °F, which is even above my one-sigma bound, so I failed badly. What did I miss now that we have hindsight?

On Nov 1, I looked at the Dallas monthly weather averages (pasted below) and tried to predict the average temperature for Jan 2020. It's hard to see any trend, so I would simply predict 46.2 +/- 3.5 °F.

What else should I have measured to predict this significantly better? I was thinking about looking at solar irradiance data (with sunspot solar cycles), sea currents, or sea temperatures...what data would improve my prediction by more than 1°F?

I'm hoping for an answer like, "Well, if you go to website X, their measurement of Y indicates that temperatures will likely deviate by Z" with perhaps some science showing that this is a good way to predict long-term weather.

Year  Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec   Total
-----------------------------------------------------------------------------------
2019  45.8  50.2  55.0  66.0  73.4  79.9  84.6  87.4  85.5  65.5       
2018  45.8  51.1  63.3  61.6  79.0  85.7  88.8  85.2  78.1  66.2  52.5  48.4  67.1
2017  51.2  60.6  65.7  69.3  75.4  82.5  86.6  84.4  80.6  69.6  62.4  49.7  69.8
2016  47.0  55.2  61.2  68.1  72.5  84.0  87.4  85.8  81.5  74.1  63.5  49.7  69.2
2015  44.5  45.7  56.1  65.8  70.9  82.1  87.1  87.3  82.7  71.2  58.7  53.7  67.2
2014  45.3  47.0  55.1  66.3  74.4  82.4  83.8  86.2  80.3  71.6  51.5  50.1  66.2
2013  49.1  52.0  56.4  63.0  72.3  82.6  84.5  87.1  82.4  68.2  53.5  43.1  66.2
2012  50.4  52.5  64.3  70.3  77.9  84.3  87.7  86.5  80.0  67.0  59.7  51.2  69.3
2011  42.8  49.5  61.3  70.8  72.8  86.8  91.4  93.4  80.0  68.2  57.9  47.6  68.5
2010  44.3  41.7  55.8  66.7  76.9  86.5  85.9  89.8  79.8  68.8  58.5  49.3  67.0
2009  48.1  55.8  58.9  64.8  73.3  83.8  86.6  85.3  76.2  62.7  59.5  42.7  66.5
2008  46.9  54.0  61.0  66.5  77.0  86.5  89.0  86.7  78.5  69.6  59.7  49.0  68.7
2007  42.3  49.4  63.9  62.4  74.6  81.4  83.8  87.8  81.6  72.1  61.3  49.8  67.5
2006  55.1  49.4  62.2  72.0  78.0  83.7  87.7  89.8  77.6  68.1  57.5  50.0  69.3
2005  49.5  52.6  56.7  65.5  73.5  83.6  85.1  86.8  83.7  68.8  60.8  48.1  67.9
2004  48.5  45.8  61.8  66.2  74.4  79.4  83.5  81.5  78.4  72.1  57.1  48.9  66.5
2003  43.7  45.6  56.2  66.9  75.5  79.0  86.3  86.7  74.5  68.7  59.4  49.6  66.0
2002  47.6  47.0  54.8  68.4  72.0  80.1  83.2  84.7  79.6  64.9  53.8  47.7  65.3
2001  42.7  50.2  51.8  67.8  74.2  80.3  86.7  84.9  74.7  65.0  59.7  49.5  65.6
2000  50.6  57.3  61.0  65.3  76.6  80.7  87.3  90.2  80.4  69.7  49.8  39.4  67.4
1999  48.6  55.5  56.4  67.9  73.8  82.1  86.1  90.2  79.0  69.2  62.9  51.5  68.6
1998  48.4  51.1  54.9  63.8  78.5  85.5  91.6  87.8  83.6  69.5  57.6  47.0  68.3
1997  44.0  49.5  58.3  60.4  70.1  78.8  84.9  83.1  80.2  67.2  52.1  45.6  64.5
1996  43.1  52.1  53.3  64.2  79.7  82.5  86.1  82.5  74.5  66.9  54.9  49.2  65.8
1995  48.1  52.5  56.9  64.2  73.2  79.9  85.5  85.5  76.6  67.8  54.8  47.4  66.0
1994  45.7  48.6  59.0  65.9  71.5  84.1  83.9  84.0  76.3  67.3  57.9  49.0  66.1
1993  45.1  49.0  56.1  63.3  71.9  81.7  87.3  87.5  78.2  63.8  51.6  49.5  65.4
1992  46.9  54.4  59.0  66.0  71.1  79.4  84.3  80.2  77.7  69.5  52.7  49.9  65.9
1991  42.8  53.7  59.8  67.4  75.4  81.0  85.0  82.5  75.2  68.1  51.7  50.3  66.1
1990  51.8  53.9  57.7  64.0  73.4  84.0  82.5  84.6  80.0  66.4  59.8  44.0  66.8
1989  50.0  42.2  56.7  66.4  74.3  77.9  82.8  82.3  74.7  69.0  58.2  39.0  64.5
1988  42.2  47.1  56.0  64.5  72.8  80.4  85.3  87.9  79.2  65.7  58.1  49.1  65.7
1987  44.5  50.8  53.9  65.0  75.1  79.6  83.4  86.5  77.1  66.5  55.7  47.3  65.5
1986  48.8  51.2  60.2  67.2  71.5  80.8  86.4  83.4  80.2  65.7  52.4  46.1  66.2
1985  37.8  45.0  60.8  67.2  74.0  80.2  84.4  87.6  77.7  67.6  56.3  42.3  65.1
1984  39.3  50.9  56.3  63.7  73.7  82.5  85.5  85.8  76.1  67.0  54.6  52.6  65.7
1983  43.4  48.5  54.5  60.6  69.5  77.3  83.6  84.9  77.1  67.8  57.3  34.8  63.3
1982  44.6  44.5  59.8  62.5  72.5  79.2  84.6  86.7  78.1  67.0  55.6  49.2  65.4
1981  44.6  48.9  55.7  69.2  70.5  80.3  85.9  83.4  76.2  66.1  57.5  47.3  65.5
1980  45.5  46.6  54.2  63.1  75.0  87.0  92.0  88.5  80.3  65.4  54.9  49.4  66.8
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  • $\begingroup$ I don't think it can be done with any useful confidence values. Weather is very chaotic, and small inputs could have drastic results. Daily temperature forecasts are often out by more than a degree F. $\endgroup$ – user824 Nov 12 '19 at 22:00
  • $\begingroup$ @bobuhito why not just use a climate model ? $\endgroup$ – gansub Nov 13 '19 at 0:50
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    $\begingroup$ I'm extremely skeptical that weather can be forecast with any usability at that range due to the uncertainties and errors that propagate and accumulate rapidly over time. Even the long-term climate outlook (i.e. generally warmer/colder, wetter/drier than average) is difficult and problematic. Anecdotally, I've tracked one of the major forecast corporations' very long-term predictions several times, and each time the quality rapidly degrades past ~10 days out, with cooling and warming trends becoming completely out of phase with reality - i.e., worse than just assuming the climatic average. $\endgroup$ – dplmmr Nov 14 '19 at 0:18
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    $\begingroup$ @gansub: Not really all that good beyond a week or so, really. It's those darned butterflies in the Amazon, you know :-) And a climate forecast won't tell you what the weather is going to be like. E.g. looking at El Nino will give you some idea about the climate in California next winter, but it's not much use in deciding whether to plan a skiing trip for President's Day weekend next year. $\endgroup$ – jamesqf Nov 14 '19 at 18:28
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    $\begingroup$ @jamesqf that was the point i was trying to make. Beyond two weeks nobody runs weather models. It is climate models such as cwrf to get likely trends. Yes you cant plan a ski trip that far out. $\endgroup$ – gansub Nov 15 '19 at 0:32