sat, 28-sep-2019, 18:46

Introduction

At the 57th running of the Equinox Marathon last weekend Aaron Fletcher broke Stan Justice’s 1985 course record, one of the oldest running records in Alaska sports. On the Equinox Marathon Facebook page Stan and Matias Saari were discussing whether more favorable weather might have meant an even faster record-breaking effort. Stan writes:

Where is a statistician when you need one. Would be interesting to compare times of all 2018 runners with their 2019 times.

I’m not a statistician, but let’s take a look.

Results

We’ve got Equinox Marathon finish time data going back to 1997, so we’ll compare the finish times for all runners who competed in consecutive years, subtracting their current year finish times (in hours) from the previous year. By this metric, negative values indicate individuals who ran faster in the current year than the previous. For example, I completed the race in 4:40:05 in 2018, and finished in 4:33:42 this year. My “hours_delta” for 2019 is -0.106 hours, or 6 minutes, 23 seconds faster.

Here’s the distribution of this statistic for 2019:

//media.swingleydev.com/img/blog/2019/09/twenty_nineteen_histogram.svgz

There are several people who were dramatically faster (on the left side of the graph), but the overall picture shows that times in 2019 were slower than 2018. The dark cyan line is the median value, which is at 0.18 hours or 10 minutes, 35 seconds slower. There were 53 runners that ran the race faster in 2019 than 2018 (including me), and 115 who were slower. That’s a pretty dramatic difference.

Here’s that relationship for all the years where we have data:

//media.swingleydev.com/img/blog/2019/09/slower_faster.svgz

The orange bars are runners who ran that year’s Equinox faster than the previous year and the dark cyan bars are those who were slower. 2019 is dramatically different than most other years for how much slower most people ran. 2013 is another particularly slow year. Fast years include 2007, 2009, and last year.

Here’s another way to look at the data. It shows the median number of minutes runners ran Equinox faster (negative numbers) or slower (positive) in consecutive years.

//media.swingleydev.com/img/blog/2019/09/median_diff_one_year.svgz

You can see that finish times were dramatically slower in 2019, and much faster in 2018. Since this comparison is using paired comparisons between years, at least part of the reason 2019 seemed like such a slow race is that 2018 was a fast one.

Two-year lag

Let’s see what happens if we use a two-year lag to calculate the differences. Instead of comparing the current year’s results with the previous year for individual runners that raced in both years, we’ll compare the current year with two years prior. For example runners that ran the race this year and in 2017.

Here’s what the distribution looks like comparing 2019 and 2017 results from the same runner.

//media.swingleydev.com/img/blog/2019/09/two_year_histogram.svgz

It’s a similar pattern, with the median values at 0.18 hours, indicating that runners were almost 10 minutes slower in 2019 when compared against their 2017 times. This strengthens the evidence that 2019 was a particularly difficult year to run the race.

Median difference by year for all years of the two-year lag data:

//media.swingleydev.com/img/blog/2019/09/two_year_diffs.svgz

Remember that the dark cyan bars are years with slower finish times and orange are faster. 2019 still comes out as an outlier, along with 2013. 2007 is the clear winner for fast times.

All pairwise race results

If we can do one and two year lags, how about combining all the pairwise race results? At some point the comparison is no longer a good one because of the large time interval between races, so we will restrict the comparisons to six or fewer years between results. We’ll also remove the earliest years from the results because those years are likely biased by having fewer long lag results.

Here’s the same plot showing difference times in minutes for all pairwise race results, six years and fewer.

//media.swingleydev.com/img/blog/2019/09/all_through_six_median_diff_minutes.svgz

You can see that there’s a pretty strong bias toward slower times, which is likely due to people aging and their times getting slower. The conditions were good enough in 2007 that this aging effect was offset and people running in that race tended to do it faster than their earlier performances despite being older. Even so, 2019 still stands out as one of the most difficult races.

Here’s the aging effect:

##
## Call:
## lm(formula = hours_delta ~ years_delta, data = all_through_six)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -6.3242 -0.3639 -0.0415  0.3115  6.4441
##
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)
## (Intercept) -0.03390    0.01934  -1.752              0.0797 .
## years_delta  0.05152    0.00558   9.234 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8845 on 8664 degrees of freedom
## Multiple R-squared:  0.009745,   Adjusted R-squared:  0.00963
## F-statistic: 85.26 on 1 and 8664 DF,  p-value: < 0.00000000000000022

There’s a very significant positive relationship between the difference in years and the difference in marathon times for those runners (years_delta in the coefficient results above). The longer the gap between races, the slower a runner is by just over 3 minutes each year. Notice, however, that the noise in the data is so great that this model, no matter how significant the coefficients, explains almost none of the variation in the difference in marathon times (dismally small R-squared values).

Weather

The conditions in this year’s race were particularly harsh with a fairly constant 40 °F temperature and light rain falling at valley level; and below freezing temperatures, high winds, and snow falling up on Ester Dome. The trail was muddy, soft, and slippery in places, especially the single track and the on the unpaved section of Henderson Road. Compare this with last year when the weather was gorgeous: dry, sunny, and temperatures ranging from 39—60 °F.

We took a look at the differences in weather between years to see if there is a relationship between weather differences and finish time differences, but none of the models we tried were any good at predicting differences in finish times, probably because of the huge variation in finish times that had nothing to do with the weather. There are too many other factors contributing to an individual’s performance from one year to the next to be able to pull out just the effects of weather on the results.

Conclusion

2019 was a very slow year when we compared runners who completed Equinox in 2019 and earlier years. In fact, there’s some evidence that it’s the slowest year of all the years considered here (1997—2019). We could find no statistical evidence to show that weather was the cause of this, but anyone who was out there on race day this year knows it played a part in their finish times. I ran the race this year and last and managed to improve on my time despite the conditions, but I don’t think there’s any question that I would have improved my time even more had it been warm and sunny instead of cold, windy, and wet. Congratulations to all the competitors in this year’s race. It was a fun, but challenging year for Equinox.

tags: running  R  Equinox Marathon 
wed, 18-sep-2019, 13:14

Introduction

A couple years ago I wrote a post about past Equinox Marathon weather. Since that post Andrea and I have run the relay twice, and I ran the full marathon. This post updates the statistics and plots to include two more years of the race.

Methods

Methods and data are the same as in my previous post, except the daily data has been updated to include 2018. The R code is available at the end of the previous post.

Results

Race day weather

Temperatures at the airport on race day ranged from 19.9 °F in 1972 to 35.1 °F in 1969, but the average range is between 34.3 and 53.2 °F. Using our model of Ester Dome temperatures, we get an average range of 29.7 and 47.4 °F and an overall min / max of 16.1 / 61.3 °F. Generally speaking, it will be below freezing on Ester Dome, but possibly before most of the runners get up there.

Precipitation (rain, sleet or snow) has fallen on 16 out of 56 race days, or 29% of the time, and measurable snowfall has been recorded on four of those sixteen. The highest amount fell in 2014 with 0.36 inches of liquid precipitation (no snow was recorded and the temperatures were between 45 and 51 °F so it was almost certainly all rain, even on Ester Dome). More than a quarter of an inch of precipitation fell in three of the sixteen years when it rained or snowed (1990, 1993, and 2014), but most rainfall totals are much smaller.

Measurable snow fell at the airport in four years, or seven percent of the time: 4.1 inches in 1993, 2.1 inches in 1985, 1.2 inches in 1996, and 0.4 inches in 1992. But that’s at the airport station. Five of the 12 years where measurable precipitation fell at the airport and no snow fell, had possible minimum temperatures on Ester Dome that were below freezing. It’s likely that some of the precipitation recorded at the airport in those years was coming down as snow up on Ester Dome. If so, that means snow may have fallen on nine race days, bringing the percentage up to sixteen percent.

Wind data from the airport has only been recorded since 1984, but from those years the average wind speed at the airport on race day is 4.8 miles per hour. The highest 2-minute wind speed during Equinox race day was 21 miles per hour in 2003. Unfortunately, no wind data is available for Ester Dome, but it’s likely to be higher than what is recorded at the airport.

Weather from the week prior

It’s also useful to look at the weather from the week before the race, since excessive pre-race rain or snow can make conditions on race day very different, even if the race day weather is pleasant. The year I ran the full marathon (2013), it snowed the week before and much of the trail in the woods before the water stop near Henderson and all of the out and back were covered in snow.

The most dramatic example of this was 1992 where 23 inches (!) of snow fell at the airport in the week prior to the race, with much higher totals up on the summit of Ester Dome. Measurable snow has been recorded at the airport in the week prior to six races, but all the weekly totals are under an inch except for the snow year of 1992.

Precipitation has fallen in 44 of 56 pre-race weeks (79% of the time). Three years have had more than an inch of precipitation prior to the race: 1.49 inches in 2015, 1.26 inches in 1992 (most of which fell as snow), and 1.05 inches in 2007. On average, just over two tenths of an inch of precipitation falls in the week before the race.

Summary

The following stacked plots shows the weather for all 56 runnings of the Equinox marathon. The top panel shows the range of temperatures on race day from the airport station (wide bars) and estimated on Ester Dome (thin lines below bars). The shaded area at the bottom shows where temperatures are below freezing.

The middle panel shows race day liquid precipitation (rain, melted snow). Bars marked with an asterisk indicate years where snow was also recorded at the airport, but remember that five of the other years with liquid precipitation probably experienced snow on Ester Dome (1977, 1986, 1991, 1994, and 2016) because the temperatures were likely to be below freezing at elevation.

The bottom panel shows precipitation totals from the week prior to the race. Bars marked with an asterisk indicate weeks where snow was also recorded at the airport.

Equinox Marathon Weather

Here’s a table with most of the data from the analysis. A CSV with this data can be downloaded from all_wx.csv

Date min t max t ED min t ED max t awnd prcp snow p prcp p snow
1963-09-21 32.0 54.0 27.5 48.2   0.00 0.0 0.01 0.0
1964-09-19 34.0 57.9 29.4 51.8   0.00 0.0 0.03 0.0
1965-09-25 37.9 60.1 33.1 53.9   0.00 0.0 0.80 0.0
1966-09-24 36.0 62.1 31.3 55.8   0.00 0.0 0.01 0.0
1967-09-23 35.1 57.9 30.4 51.8   0.00 0.0 0.00 0.0
1968-09-21 23.0 44.1 19.1 38.9   0.00 0.0 0.04 0.0
1969-09-20 35.1 68.0 30.4 61.3   0.00 0.0 0.00 0.0
1970-09-19 24.1 39.9 20.1 34.9   0.00 0.0 0.42 0.0
1971-09-18 35.1 55.9 30.4 50.0   0.00 0.0 0.14 0.0
1972-09-23 19.9 42.1 16.1 37.0   0.00 0.0 0.01 0.2
1973-09-22 30.0 44.1 25.6 38.9   0.00 0.0 0.05 0.0
1974-09-21 48.0 60.1 42.5 53.9   0.08 0.0 0.00 0.0
1975-09-20 37.9 55.9 33.1 50.0   0.02 0.0 0.02 0.0
1976-09-18 34.0 59.0 29.4 52.9   0.00 0.0 0.54 0.0
1977-09-24 36.0 48.9 31.3 43.4   0.06 0.0 0.20 0.0
1978-09-23 30.0 42.1 25.6 37.0   0.00 0.0 0.10 0.3
1979-09-22 35.1 62.1 30.4 55.8   0.00 0.0 0.17 0.0
1980-09-20 30.9 43.0 26.5 37.8   0.00 0.0 0.35 0.0
1981-09-19 37.0 43.0 32.2 37.8   0.15 0.0 0.04 0.0
1982-09-18 42.1 61.0 37.0 54.8   0.02 0.0 0.22 0.0
1983-09-17 39.9 46.9 34.9 41.5   0.00 0.0 0.05 0.0
1984-09-22 28.9 60.1 24.6 53.9 5.8 0.00 0.0 0.08 0.0
1985-09-21 30.9 42.1 26.5 37.0 6.5 0.14 2.1 0.57 0.0
1986-09-20 36.0 52.0 31.3 46.3 8.3 0.07 0.0 0.21 0.0
1987-09-19 37.9 61.0 33.1 54.8 6.3 0.00 0.0 0.00 0.0
1988-09-24 37.0 45.0 32.2 39.7 4.0 0.00 0.0 0.11 0.0
1989-09-23 36.0 61.0 31.3 54.8 8.5 0.00 0.0 0.07 0.5
1990-09-22 37.9 50.0 33.1 44.4 7.8 0.26 0.0 0.00 0.0
1991-09-21 36.0 57.0 31.3 51.0 4.5 0.04 0.0 0.03 0.0
1992-09-19 24.1 33.1 20.1 28.5 6.7 0.01 0.4 1.26 23.0
1993-09-18 28.0 37.0 23.8 32.2 4.9 0.29 4.1 0.37 0.3
1994-09-24 27.0 51.1 22.8 45.5 6.0 0.02 0.0 0.08 0.0
1995-09-23 43.0 66.9 37.8 60.3 4.0 0.00 0.0 0.00 0.0
1996-09-21 28.9 37.9 24.6 33.1 6.9 0.06 1.2 0.26 0.0
1997-09-20 27.0 55.0 22.8 49.1 3.8 0.00 0.0 0.03 0.0
1998-09-19 42.1 60.1 37.0 53.9 4.9 0.00 0.0 0.37 0.0
1999-09-18 39.0 64.9 34.1 58.4 3.8 0.00 0.0 0.26 0.0
2000-09-16 28.9 50.0 24.6 44.4 5.6 0.00 0.0 0.30 0.0
2001-09-22 33.1 57.0 28.5 51.0 1.6 0.00 0.0 0.00 0.0
2002-09-21 33.1 48.9 28.5 43.4 3.8 0.00 0.0 0.03 0.0
2003-09-20 26.1 46.0 22.0 40.7 9.6 0.00 0.0 0.00 0.0
2004-09-18 26.1 48.0 22.0 42.5 4.3 0.00 0.0 0.25 0.0
2005-09-17 37.0 63.0 32.2 56.6 0.9 0.00 0.0 0.09 0.0
2006-09-16 46.0 64.0 40.7 57.6 4.3 0.00 0.0 0.00 0.0
2007-09-22 25.0 45.0 20.9 39.7 4.7 0.00 0.0 1.05 0.0
2008-09-20 34.0 51.1 29.4 45.5 4.5 0.00 0.0 0.08 0.0
2009-09-19 39.0 50.0 34.1 44.4 5.8 0.00 0.0 0.25 0.0
2010-09-18 35.1 64.9 30.4 58.4 2.5 0.00 0.0 0.00 0.0
2011-09-17 39.9 57.9 34.9 51.8 1.3 0.00 0.0 0.44 0.0
2012-09-22 46.9 66.9 41.5 60.3 6.0 0.00 0.0 0.33 0.0
2013-09-21 24.3 44.1 20.3 38.9 5.1 0.00 0.0 0.13 0.6
2014-09-20 45.0 51.1 39.7 45.5 1.6 0.36 0.0 0.00 0.0
2015-09-19 37.9 44.1 33.1 38.9 2.9 0.01 0.0 1.49 0.0
2016-09-17 34.0 57.9 29.4 51.8 2.2 0.01 0.0 0.61 0.0
2017-09-16 33.1 66.0 28.5 59.5 3.1 0.00 0.0 0.02 0.0
2018-09-15 44.1 60.1 38.9 53.9 3.8 0.00 0.0 0.00 0.0
thu, 13-sep-2018, 17:40

Introduction

A couple years ago I wrote a post about past Equinox Marathon weather. Since that post Andrea and I have run the relay twice, and I plan on running the full marathon in a couple days. This post updates the statistics and plots to include two more years of the race.

Methods

Methods and data are the same as in my previous post, except the daily data has been updated to include 2016 and 2017. The R code is available at the end of the previous post.

Results

Race day weather

Temperatures at the airport on race day ranged from 19.9 °F in 1972 to 35.1 °F in 1969, but the average range is between 34.1 and 53.1 °F. Using our model of Ester Dome temperatures, we get an average range of 29.5 and 47.3 °F and an overall min / max of 16.1 / 61.3 °F. Generally speaking, it will be below freezing on Ester Dome, but possibly before most of the runners get up there.

Precipitation (rain, sleet or snow) has fallen on 16 out of 55 race days, or 29% of the time, and measurable snowfall has been recorded on four of those sixteen. The highest amount fell in 2014 with 0.36 inches of liquid precipitation (no snow was recorded and the temperatures were between 45 and 51 °F so it was almost certainly all rain, even on Ester Dome). More than a quarter of an inch of precipitation fell in three of the sixteen years when it rained or snowed (1990, 1993, and 2014), but most rainfall totals are much smaller.

Measurable snow fell at the airport in four years, or seven percent of the time: 4.1 inches in 1993, 2.1 inches in 1985, 1.2 inches in 1996, and 0.4 inches in 1992. But that’s at the airport station. Five of the 12 years where measurable precipitation fell at the airport and no snow fell, had possible minimum temperatures on Ester Dome that were below freezing. It’s likely that some of the precipitation recorded at the airport in those years was coming down as snow up on Ester Dome. If so, that means snow may have fallen on nine race days, bringing the percentage up to sixteen percent.

Wind data from the airport has only been recorded since 1984, but from those years the average wind speed at the airport on race day is 4.8 miles per hour. The highest 2-minute wind speed during Equinox race day was 21 miles per hour in 2003. Unfortunately, no wind data is available for Ester Dome, but it’s likely to be higher than what is recorded at the airport.

Weather from the week prior

It’s also useful to look at the weather from the week before the race, since excessive pre-race rain or snow can make conditions on race day very different, even if the race day weather is pleasant. The year I ran the full marathon (2013), it snowed the week before and much of the trail in the woods before the water stop near Henderson and all of the out and back were covered in snow.

The most dramatic example of this was 1992 where 23 inches (!) of snow fell at the airport in the week prior to the race, with much higher totals up on the summit of Ester Dome. Measurable snow has been recorded at the airport in the week prior to six races, but all the weekly totals are under an inch except for the snow year of 1992.

Precipitation has fallen in 44 of 55 pre-race weeks (80% of the time). Three years have had more than an inch of precipitation prior to the race: 1.49 inches in 2015, 1.26 inches in 1992 (most of which fell as snow), and 1.05 inches in 2007. On average, just over two tenths of an inch of precipitation falls in the week before the race.

Summary

The following stacked plots shows the weather for all 55 runnings of the Equinox marathon. The top panel shows the range of temperatures on race day from the airport station (wide bars) and estimated on Ester Dome (thin lines below bars). The shaded area at the bottom shows where temperatures are below freezing.

The middle panel shows race day liquid precipitation (rain, melted snow). Bars marked with an asterisk indicate years where snow was also recorded at the airport, but remember that five of the other years with liquid precipitation probably experienced snow on Ester Dome (1977, 1986, 1991, 1994, and 2016) because the temperatures were likely to be below freezing at elevation.

The bottom panel shows precipitation totals from the week prior to the race. Bars marked with an asterisk indicate weeks where snow was also recorded at the airport.

Equinox Marathon Weather

Here’s a table with most of the data from the analysis. A CSV with this data can be downloaded from all_wx.csv

Date min t max t ED min t ED max t awnd prcp snow p prcp p snow
1963-09-21 32.0 54.0 27.5 48.2   0.00 0.0 0.01 0.0
1964-09-19 34.0 57.9 29.4 51.8   0.00 0.0 0.03 0.0
1965-09-25 37.9 60.1 33.1 53.9   0.00 0.0 0.80 0.0
1966-09-24 36.0 62.1 31.3 55.8   0.00 0.0 0.01 0.0
1967-09-23 35.1 57.9 30.4 51.8   0.00 0.0 0.00 0.0
1968-09-21 23.0 44.1 19.1 38.9   0.00 0.0 0.04 0.0
1969-09-20 35.1 68.0 30.4 61.3   0.00 0.0 0.00 0.0
1970-09-19 24.1 39.9 20.1 34.9   0.00 0.0 0.42 0.0
1971-09-18 35.1 55.9 30.4 50.0   0.00 0.0 0.14 0.0
1972-09-23 19.9 42.1 16.1 37.0   0.00 0.0 0.01 0.2
1973-09-22 30.0 44.1 25.6 38.9   0.00 0.0 0.05 0.0
1974-09-21 48.0 60.1 42.5 53.9   0.08 0.0 0.00 0.0
1975-09-20 37.9 55.9 33.1 50.0   0.02 0.0 0.02 0.0
1976-09-18 34.0 59.0 29.4 52.9   0.00 0.0 0.54 0.0
1977-09-24 36.0 48.9 31.3 43.4   0.06 0.0 0.20 0.0
1978-09-23 30.0 42.1 25.6 37.0   0.00 0.0 0.10 0.3
1979-09-22 35.1 62.1 30.4 55.8   0.00 0.0 0.17 0.0
1980-09-20 30.9 43.0 26.5 37.8   0.00 0.0 0.35 0.0
1981-09-19 37.0 43.0 32.2 37.8   0.15 0.0 0.04 0.0
1982-09-18 42.1 61.0 37.0 54.8   0.02 0.0 0.22 0.0
1983-09-17 39.9 46.9 34.9 41.5   0.00 0.0 0.05 0.0
1984-09-22 28.9 60.1 24.6 53.9 5.8 0.00 0.0 0.08 0.0
1985-09-21 30.9 42.1 26.5 37.0 6.5 0.14 2.1 0.57 0.0
1986-09-20 36.0 52.0 31.3 46.3 8.3 0.07 0.0 0.21 0.0
1987-09-19 37.9 61.0 33.1 54.8 6.3 0.00 0.0 0.00 0.0
1988-09-24 37.0 45.0 32.2 39.7 4.0 0.00 0.0 0.11 0.0
1989-09-23 36.0 61.0 31.3 54.8 8.5 0.00 0.0 0.07 0.5
1990-09-22 37.9 50.0 33.1 44.4 7.8 0.26 0.0 0.00 0.0
1991-09-21 36.0 57.0 31.3 51.0 4.5 0.04 0.0 0.03 0.0
1992-09-19 24.1 33.1 20.1 28.5 6.7 0.01 0.4 1.26 23.0
1993-09-18 28.0 37.0 23.8 32.2 4.9 0.29 4.1 0.37 0.3
1994-09-24 27.0 51.1 22.8 45.5 6.0 0.02 0.0 0.08 0.0
1995-09-23 43.0 66.9 37.8 60.3 4.0 0.00 0.0 0.00 0.0
1996-09-21 28.9 37.9 24.6 33.1 6.9 0.06 1.2 0.26 0.0
1997-09-20 27.0 55.0 22.8 49.1 3.8 0.00 0.0 0.03 0.0
1998-09-19 42.1 60.1 37.0 53.9 4.9 0.00 0.0 0.37 0.0
1999-09-18 39.0 64.9 34.1 58.4 3.8 0.00 0.0 0.26 0.0
2000-09-16 28.9 50.0 24.6 44.4 5.6 0.00 0.0 0.30 0.0
2001-09-22 33.1 57.0 28.5 51.0 1.6 0.00 0.0 0.00 0.0
2002-09-21 33.1 48.9 28.5 43.4 3.8 0.00 0.0 0.03 0.0
2003-09-20 26.1 46.0 22.0 40.7 9.6 0.00 0.0 0.00 0.0
2004-09-18 26.1 48.0 22.0 42.5 4.3 0.00 0.0 0.25 0.0
2005-09-17 37.0 63.0 32.2 56.6 0.9 0.00 0.0 0.09 0.0
2006-09-16 46.0 64.0 40.7 57.6 4.3 0.00 0.0 0.00 0.0
2007-09-22 25.0 45.0 20.9 39.7 4.7 0.00 0.0 1.05 0.0
2008-09-20 34.0 51.1 29.4 45.5 4.5 0.00 0.0 0.08 0.0
2009-09-19 39.0 50.0 34.1 44.4 5.8 0.00 0.0 0.25 0.0
2010-09-18 35.1 64.9 30.4 58.4 2.5 0.00 0.0 0.00 0.0
2011-09-17 39.9 57.9 34.9 51.8 1.3 0.00 0.0 0.44 0.0
2012-09-22 46.9 66.9 41.5 60.3 6.0 0.00 0.0 0.33 0.0
2013-09-21 24.3 44.1 20.3 38.9 5.1 0.00 0.0 0.13 0.6
2014-09-20 45.0 51.1 39.7 45.5 1.6 0.36 0.0 0.00 0.0
2015-09-19 37.9 44.1 33.1 38.9 2.9 0.01 0.0 1.49 0.0
2016-09-17 34.0 57.9 29.4 51.8 2.2 0.01 0.0 0.61 0.0
2017-09-16 33.1 66.0 28.5 59.5 3.1 0.00 0.0 0.02 0.0
sun, 09-sep-2018, 10:54

Introduction

In previous posts (Fairbanks Race Predictor, Equinox from Santa Claus, Equinox from Gold Discovery) I’ve looked at predicting Equinox Marathon results based on results from earlier races. In all those cases I’ve looked at single race comparisons: how results from Gold Discovery can predict Marathon times, for example. In this post I’ll look at all the Usibelli Series races I completed this year to see how they can inform my expectations for next Saturday’s Equinox Marathon.

Methods

I’ve been collecting the results from all Usibelli Series races since 2010. Using that data, grouped by the name of the person racing and year, find all runners that completed the same set of Usibelli Series races that I finished in 2018, as well as their Equinox Marathon finish pace. Between 2010 and 2017 there are 160 records that match.

The data looks like this. crr is that person’s Chena River Run pace in minutes, msr is Midnight Sun Run pace for the same person and year, rotv is the pace from Run of the Valkyries, gdr is the Gold Discovery Run, and em is Equniox Marathon pace for that same person and year.

crr msr rotv gdr em
8.1559 8.8817 8.1833 10.2848 11.8683
8.7210 9.1387 9.2120 11.0152 13.6796
8.7946 9.0640 9.0077 11.3565 13.1755
9.4409 10.6091 9.6250 11.2080 13.1719
7.3581 7.1836 7.1310 8.0001 9.6565
7.4731 7.5349 7.4700 8.2465 9.8359
... ... ... ... ...

I will use two methods for using these records to predict Equinox Marathon times, multivariate linear regression and Random Forest.

The R code for the analysis appears at the end of this post.

Results

Linear regression

We start with linear regression, which isn’t entirely appropriate for this analysis because the independent variables (pre-Equinox race pace times) aren’t really independent of one another. A person who runs a 6 minute pace in the Chena River Run is likely to also be someone who runs Gold Discovery faster than the average runner. This relationship, in fact, is the basis for this analysis.

I started with a model that includes all the races I completed in 2018, but pace time for the Midnight Sun Run wasn’t statistically significant so I removed it from the final model, which included Chena River Run, Run of the Valkyries, and Gold Discovery.

This model is significant, as are all the coefficients except the intercept, and the model explains nearly 80% of the variation in the data:

##
## Call:
## lm(formula = em ~ crr + gdr + rotv, data = input_pivot)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -3.8837 -0.6534 -0.2265  0.3549  5.8273
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   0.6217     0.5692   1.092 0.276420
## crr          -0.3723     0.1346  -2.765 0.006380 **
## gdr           0.8422     0.1169   7.206 2.32e-11 ***
## rotv          0.7607     0.2119   3.591 0.000442 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.278 on 156 degrees of freedom
## Multiple R-squared:  0.786,  Adjusted R-squared:  0.7819
## F-statistic:   191 on 3 and 156 DF,  p-value: < 2.2e-16

Using this model and my 2018 results, my overall pace and finish times for Equinox are predicted to be 10:45 and 4:41:50. The 95% confidence intervals for these predictions are 10:30–11:01 and 4:35:11–4:48:28.

Random Forest

Random Forest is another regression method but it doesn’t require independent variables be independent of one another. Here are the results of building 5,000 random trees from the data:

##
## Call:
##  randomForest(formula = em ~ ., data = input_pivot, ntree = 5000)
##                Type of random forest: regression
##                      Number of trees: 5000
## No. of variables tried at each split: 1
##
##           Mean of squared residuals: 1.87325
##                     % Var explained: 74.82

##      IncNodePurity
## crr       260.8279
## gdr       321.3691
## msr       268.0936
## rotv      295.4250

This model, which includes all race results explains just under 74% of the variation in the data. And you can see from the importance result that Gold Discovery results factor more heavily in the result than earlier races in the season like Chena River Run and the Midnight Sun Run.

Using this model, my predicted pace is 10:13 and my finish time is 4:27:46. The 95% confidence intervals are 9:23–11:40 and 4:05:58–5:05:34. You’ll notice that the confidence intervals are wider than with linear regression, probably because there are fewer assumptions with Random Forest and less power.

Conclusion

My number one goal for this year’s Equinox Marathon is simply to finish without injuring myself, something I wasn’t able to do the last time I ran the whole race in 2013. I finished in 4:49:28 with an overall pace of 11:02, but the race or my training for it resulted in a torn hip labrum.

If I’m able to finish uninjured, I’d like to beat my time from 2013. These results suggest I should have no problem acheiving my second goal and perhaps knowing how much faster these predictions are from my 2013 times, I can race conservatively and still get a personal best time.

Appendix - R code

library(tidyverse)
library(RPostgres)
library(lubridate)
library(glue)
library(randomForest)
library(knitr)

races <- dbConnect(Postgres(),
                   host = "localhost",
                   dbname = "races")

all_races <- races %>%
    tbl("all_races")

usibelli_races <- tibble(race = c("Chena River Run",
                                  "Midnight Sun Run",
                                  "Jim Loftus Mile",
                                  "Run of the Valkyries",
                                  "Gold Discovery Run",
                                  "Santa Claus Half Marathon",
                                  "Golden Heart Trail Run",
                                  "Equinox Marathon"))

css_2018 <- all_races %>%
    inner_join(usibelli_races, copy = TRUE) %>%
    filter(year == 2018,
           name == "Christopher Swingley") %>%
    collect()

candidate_races <- css_2018 %>%
    select(race) %>%
    bind_rows(tibble(race = c("Equinox Marathon")))

input_data <- all_races %>%
    inner_join(candidate_races, copy = TRUE) %>%
    filter(!is.na(gender), !is.na(birth_year)) %>%
    collect()

input_pivot <- input_data %>%
    group_by(race, name, year) %>%
    mutate(n = n()) %>%
    filter(n == 1) %>%
    ungroup() %>%
    select(name, year, race, pace_min) %>%
    spread(race, pace_min) %>%
    rename(crr = `Chena River Run`,
           msr = `Midnight Sun Run`,
           rotv = `Run of the Valkyries`,
           gdr = `Gold Discovery Run`,
           em = `Equinox Marathon`) %>%
    filter(!is.na(crr), !is.na(msr), !is.na(rotv),
           !is.na(gdr), !is.na(em)) %>%
    select(-c(name, year))

kable(input_pivot %>% head)

css_2018_pivot <- css_2018 %>%
    select(name, year, race, pace_min) %>%
    spread(race, pace_min) %>%
    rename(crr = `Chena River Run`,
           msr = `Midnight Sun Run`,
           rotv = `Run of the Valkyries`,
           gdr = `Gold Discovery Run`) %>%
    select(-c(name, year))

pace <- function(minutes) {
    mm = floor(minutes)
    seconds = (minutes - mm) * 60

    glue('{mm}:{sprintf("%02.0f", seconds)}')
}

finish_time <- function(minutes) {
    hh = floor(minutes / 60.0)
    min = minutes - (hh * 60)
    mm = floor(min)
    seconds = (min - mm) * 60

    glue('{hh}:{sprintf("%02d", mm)}:{sprintf("%02.0f", seconds)}')
}

lm_model <- lm(em ~ crr + gdr + rotv,
               data = input_pivot)

summary(lm_model)

prediction <- predict(lm_model, css_2018_pivot,
                      interval = "confidence", level = 0.95)

prediction

rf <- randomForest(em ~ .,
                   data = input_pivot,
                   ntree = 5000)
rf
importance(rf)

rfp_all <- predict(rf, css_2018_pivot, predict.all = TRUE)

rfp_all$aggregate

rf_ci <- quantile(rfp_all$individual, c(0.025, 0.975))

rf_ci
tue, 13-sep-2016, 18:31

Introduction

Update: An update that includes 2016 and 2017 data is here.

Andrea and I are running the Equinox Marathon relay this Saturday with Norwegian dog musher Halvor Hoveid. He’s running the first leg, I’m running the second, and Andrea finishes the race. I ran the second leg as a training run a couple weeks ago and feel good about my physical conditioning, but the weather is always a concern this late in the fall, especially up on top of Ester Dome, where it can be dramatically different than the valley floor where the race starts and ends.

Andrea ran the full marathon in 2009—2012 and the relay in 2008 and 2013—2015. I ran the full marathon in 2013. There was snow on the trail when I ran it, making the out and back section slippery and treacherous, and the cold temperatures at the start meant my feet were frozen until I got off of the single-track, nine or ten miles into the course. In other years, rain turned the powerline section to sloppy mud, or cold temperatures and freezing rain up on the Dome made it unpleasant for runners and supporters.

In this post we will examine the available weather data, looking at the range of conditions we could experience this weekend. The current forecast from the National Weather Service is calling for mostly cloudy skies with highs in the 50s. Low temperatures the night before are predicted to be in the 40s, with rain in the forecast between now and then.

Methods

There is no long term climate data for Ester Dome, but there are several valley-level stations with data going back to the start of the race in 1963. The best data comes from the Fairbanks Airport station and includes daily temperature, precipitation, and snowfall for all years, and wind speed and direction since 1984. I also looked at the data from the College Observatory station (FAOA2) behind the GI on campus and the University Experimental Farm, also on campus, but neither of these stations have a complete record. The daily data is part of the Global Historical Climatology Network - Daily dataset.

I also have hourly data from 2008—2013 for both the Fairbanks Airport and a station located on Ester Dome that is no longer operational. We’ll use this to get a sense of what the possible temperatures on Ester Dome might have been based on the Fairbanks Airport data. Hourly data comes from the Meterological Assimilation Data Ingest System (MADIS).

The R code used for this post appears at the bottom, and all the data used is available from here.

Results

Ester Dome temperatures

Since there isn’t a long-running weather station on Ester Dome (at least not one that’s publicly available), we’ll use the September data from an hourly Ester Dome station that was operational until 2014. If we join the Fairbanks Airport station data with this data wherever the observations are within 30 minutes of each other, we can see the relationship between Ester Dome temperature and temperature at the Fairbanks Airport.

Here’s what that relationship looks like, including a linear regression line between the two. The shaded area in the lower left corner shows the region where the temperatures on Ester Dome are below freezing.

Ester Dome and Fairbanks Airport temperatures

And the regression:

##
## Call:
## lm(formula = ester_dome_temp_f ~ pafa_temp_f, data = pafa_fbsa)
##
## Residuals:
##    Min     1Q Median     3Q    Max
## -9.649 -3.618 -1.224  2.486 22.138
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.69737    0.77993  -3.458 0.000572 ***
## pafa_temp_f  0.94268    0.01696  55.567  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.048 on 803 degrees of freedom
## Multiple R-squared:  0.7936, Adjusted R-squared:  0.7934
## F-statistic:  3088 on 1 and 803 DF,  p-value: < 2.2e-16

The regression model is highly significant, as are both coefficients, and the relationship explains almost 80% of the variation in the data. According to the model, in the month of September, Ester Dome average temperature is almost three degrees colder than at the airport. And whenever temperature at the airport drops below 37 degrees, it’s probably below freezing on the Dome.

Race day weather

Temperatures at the airport on race day ranged from 19.9 °F in 1972 to 68 °F in 1969, and the range of average temperatures is 34.2 and 53 °F. Using our model of Ester Dome temperatures, we get an average range of 29.5 and 47 °F and an overall min / max of 16.1 / 61.4 °F. Generally speaking, in most years it will be below freezing on Ester Dome, but possibly before most of the runners get up there.

Precipitation (rain, sleet, or snow) has fallen on 15 out of 53 race days, or 28% of the time, and measurable snowfall has been recorded on four of those fifteen. The highest amount fell in 2014 with 0.36 inches of liquid precipitation (no snow was recorded and the temperatures were between 45 and 51 °F so it was almost certainly all rain, even on Ester Dome). More than a quarter of an inch of precipitation fell in three of the fifteen years (1990, 1992, and 2014), but most rainfall totals are much smaller.

Measurable snow fell at the airport in four years, or seven percent of the time: 4.1 inches in 1993, 2.1 inches in 1985, 1.2 inches in 1996 and 0.4 inches in 1992. But that’s at the airport station. Four of the 15 years where measurable precipitation fell at the airport, but no snow fell, had possible minimum temperatures on Ester Dome that were below freezing. It’s likely that some of the precipitation recorded at the airport in those years was coming down as snow up on Ester Dome. If so, that means snow may have fallen on eight race days, bringing the percentage up to fifteen percent.

Wind data from the airport has only been recorded since 1984, but from those years the average wind speed at the airport on race day is 4.9 miles per hour. Peak 2-minute winds during Equinox race day was 21 miles per hour in 2003. Unfortunately, no wind data is available for Ester Dome, but it’s likely to be higher than what is recorded at the airport. We do have wind speed data from the hourly Ester Dome station from 2008 through 2013, but the linear relationship between Ester Dome winds and winds at the Fairbanks airport only explain about a quarter of the variation in the data, and a look at the plot doesn’t give me much confidence in the relationship shown (see below).

Ester Dome and Fairbanks Airport wind speeds

Weather from the week prior

It’s also useful to look at the weather from the week before the race, since excessive pre-race rain or snow can make conditions on race day very different, even if the race day weather is pleasant. The year I ran the full marathon (2013), it had snowed the week before and much of the trail in the woods before the water stop near Henderson and all of the out and back were covered in snow.

The most dramatic example of this was 1992 where 23 inches of snow fell at the airport in the week prior to the race, with much higher totals up on the summit of Ester Dome. Measurable snow has been recorded at the airport in the week prior to six races, but all the weekly totals are under an inch except for the snow year of 1992.

Precipitation has fallen in 42 of 53 pre-race weeks (79% of the time). Three years have had more than an inch of precipitation prior to the race: 1.49 inches in 2015, 1.26 inches in 1992 (which fell as snow), and 1.05 inches in 2007. On average, just over two tenths of an inch of precipitation falls in the week before the race.

Summary

The following stacked plots shows the weather for all 53 runnings of the Equinox marathon. The top panel shows the range of temperatures on race day from the airport station (wide bars) and estimated on Ester Dome (thin lines below bars). The shaded area at the bottom shows where temperatures are below freezing. Dashed orange horizonal lines represent the average high and low temperature at the airport on race day; solid orange horizonal lines indicate estimated average high and low temperature on Ester Dome.

The middle panel shows race day liquid precipitation (rain, melted snow). Bars marked with an asterisk indicate years where snow was also recorded at the airport, but remember that four of the other years with liquid precipitation probably experienced snow on Ester Dome (1977, 1986, 1991, and 1994) because the temperatures were likely to be below freezing at elevation.

The bottom panel shows precipitation totals from the week prior to the race. Bars marked with an asterisk indicate weeks where snow was also recorded at the airport.

Equinox Marathon Weather

Here’s a table with most of the data from the analysis. Record values for each variable are in bold.

  Fairbanks Airport Station Ester Dome (estimated)
  Race Day Previous Week Race Day
Date min t max t wind prcp snow prcp snow min t max t
1963‑09‑21 32.0 54.0   0.00 0.0 0.01 0.0 27.5 48.2
1964‑09‑19 34.0 57.9   0.00 0.0 0.03 0.0 29.4 51.9
1965‑09‑25 37.9 60.1   0.00 0.0 0.80 0.0 33.0 54.0
1966‑09‑24 36.0 62.1   0.00 0.0 0.01 0.0 31.2 55.8
1967‑09‑23 35.1 57.9   0.00 0.0 0.00 0.0 30.4 51.9
1968‑09‑21 23.0 44.1   0.00 0.0 0.04 0.0 19.0 38.9
1969‑09‑20 35.1 68.0   0.00 0.0 0.00 0.0 30.4 61.4
1970‑09‑19 24.1 39.9   0.00 0.0 0.42 0.0 20.0 34.9
1971‑09‑18 35.1 55.9   0.00 0.0 0.14 0.0 30.4 50.0
1972‑09‑23 19.9 42.1   0.00 0.0 0.01 0.2 16.1 38.0
1973‑09‑22 30.0 44.1   0.00 0.0 0.05 0.0 25.6 38.9
1974‑09‑21 48.0 60.1   0.08 0.0 0.00 0.0 42.6 54.0
1975‑09‑20 37.9 55.9   0.02 0.0 0.02 0.0 33.0 50.0
1976‑09‑18 34.0 59.0   0.00 0.0 0.54 0.0 29.4 52.9
1977‑09‑24 36.0 48.9   0.06 0.0 0.20 0.0 31.2 43.4
1978‑09‑23 30.0 42.1   0.00 0.0 0.10 0.3 25.6 37.0
1979‑09‑22 35.1 62.1   0.00 0.0 0.17 0.0 30.4 55.8
1980‑09‑20 30.9 43.0   0.00 0.0 0.35 0.0 26.4 37.8
1981‑09‑19 37.0 43.0   0.15 0.0 0.04 0.0 32.2 37.8
1982‑09‑18 42.1 61.0   0.02 0.0 0.22 0.0 37.0 54.8
1983‑09‑17 39.9 46.9   0.00 0.0 0.05 0.0 34.9 41.5
1984‑09‑22 28.9 60.1 5.8 0.00 0.0 0.08 0.0 24.5 54.0
1985‑09‑21 30.9 42.1 6.5 0.14 2.1 0.57 0.0 26.4 37.0
1986‑09‑20 36.0 52.0 8.3 0.07 0.0 0.21 0.0 31.2 46.3
1987‑09‑19 37.9 61.0 6.3 0.00 0.0 0.00 0.0 33.0 54.8
1988‑09‑24 37.0 45.0 4.0 0.00 0.0 0.11 0.0 32.2 39.7
1989‑09‑23 36.0 61.0 8.5 0.00 0.0 0.07 0.5 31.2 54.8
1990‑09‑22 37.9 50.0 7.8 0.26 0.0 0.00 0.0 33.0 44.4
1991‑09‑21 36.0 57.0 4.5 0.04 0.0 0.03 0.0 31.2 51.0
1992‑09‑19 24.1 33.1 6.7 0.01 0.4 1.26 23.0 20.0 28.5
1993‑09‑18 28.0 37.0 4.9 0.29 4.1 0.37 0.3 23.7 32.2
1994‑09‑24 27.0 51.1 6.0 0.02 0.0 0.08 0.0 22.8 45.5
1995‑09‑23 43.0 66.9 4.0 0.00 0.0 0.00 0.0 37.8 60.4
1996‑09‑21 28.9 37.9 6.9 0.06 1.2 0.26 0.0 24.5 33.0
1997‑09‑20 27.0 55.0 3.8 0.00 0.0 0.03 0.0 22.8 49.2
1998‑09‑19 42.1 60.1 4.9 0.00 0.0 0.37 0.0 37.0 54.0
1999‑09‑18 39.0 64.9 3.8 0.00 0.0 0.26 0.0 34.1 58.5
2000‑09‑16 28.9 50.0 5.6 0.00 0.0 0.30 0.0 24.5 44.4
2001‑09‑22 33.1 57.0 1.6 0.00 0.0 0.00 0.0 28.5 51.0
2002‑09‑21 33.1 48.9 3.8 0.00 0.0 0.03 0.0 28.5 43.4
2003‑09‑20 26.1 46.0 9.6 0.00 0.0 0.00 0.0 21.9 40.7
2004‑09‑18 26.1 48.0 4.3 0.00 0.0 0.25 0.0 21.9 42.6
2005‑09‑17 37.0 63.0 0.9 0.00 0.0 0.09 0.0 32.2 56.7
2006‑09‑16 46.0 64.0 4.3 0.00 0.0 0.00 0.0 40.7 57.6
2007‑09‑22 25.0 45.0 4.7 0.00 0.0 1.05 0.0 20.9 39.7
2008‑09‑20 34.0 51.1 4.5 0.00 0.0 0.08 0.0 29.4 45.5
2009‑09‑19 39.0 50.0 5.8 0.00 0.0 0.25 0.0 34.1 44.4
2010‑09‑18 35.1 64.9 2.5 0.00 0.0 0.00 0.0 30.4 58.5
2011‑09‑17 39.9 57.9 1.3 0.00 0.0 0.44 0.0 34.9 51.9
2012‑09‑22 46.9 66.9 6.0 0.00 0.0 0.33 0.0 41.5 60.4
2013‑09‑21 24.3 44.1 5.1 0.00 0.0 0.13 0.6 20.2 38.9
2014‑09‑20 45.0 51.1 1.6 0.36 0.0 0.00 0.0 39.7 45.5
2015‑09‑19 37.9 44.1 2.9 0.01 0.0 1.49 0.0 33.0 38.9

Postscript

The weather for the 2016 race was just about perfect with temperatures ranging from 34 to 58 °F and no precipitation during the race. The airport did record 0.01 inches for the day, but this fell in the evening, after the race had finished.

Appendix: R code

 library(dplyr)
 library(readr)
 library(lubridate)
 library(ggplot2)
 library(scales)
 library(grid)
 library(gtable)

 race_dates <- read_fwf("equinox_marathon_dates.rst", skip=5, n_max=54,
                        fwf_positions(c(4, 6), c(9, 19), c("number", "race_date")))

 noaa <- src_postgres(host="localhost", dbname="noaa")
 # pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
 #                               WHERE station_name = 'UNIVERSITY EXP STN'"))
 # pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
 #                               WHERE station_name = 'COLLEGE OBSY'"))
 pivot <- tbl(noaa, build_sql("SELECT * FROM ghcnd_pivot
                               WHERE station_name = 'FAIRBANKS INTL AP'"))

 race_day_wx <- pivot %>%
     inner_join(race_dates, by=c("dte"="race_date"), copy=TRUE) %>%
     collect() %>%
     mutate(tmin_f=round((tmin_c*9/5.0)+32, 1), tmax_f=round((tmax_c*9/5.0)+32, 1),
            prcp_in=round(prcp_mm/25.4, 2),
            snow_in=round(snow_mm/25.4, 1), snwd_in=round(snow_mm/25.4, 1),
            awnd_mph=round(awnd_mps*2.2369, 1),
            wsf2_mph=round(wsf2_mps*2.2369), 1) %>%
     select(number, race_date, tmin_f, tmax_f, prcp_in, snow_in,
            snwd_in, awnd_mph, wsf2_mph)

 week_before_race_day_wx <- pivot %>%
     mutate(year=date_part("year", dte)) %>%
     inner_join(race_dates %>%
                    mutate(year=year(race_date)),
                copy=TRUE) %>%
     collect() %>%
     mutate(tmin_f=round((tmin_c*9/5.0)+32, 1), tmax_f=round((tmax_c*9/5.0)+32, 1),
            prcp_in=round(prcp_mm/25.4, 2),
            snow_in=round(snow_mm/25.4, 1), snwd_in=round(snow_mm/25.4, 1),
            awnd_mph=round(awnd_mps*2.2369, 1), wsf2_mph=round(wsf2_mps*2.2369, 1)) %>%
     select(number, year, race_date, dte, prcp_in, snow_in) %>%
     mutate(week_before=race_date-days(7)) %>%
     filter(dte<race_date, dte>=week_before) %>%
     group_by(number, year, race_date) %>%
     summarize(pweek_prcp_in=sum(prcp_in),
               pweek_snow_in=sum(snow_in))

 all_wx <- race_day_wx %>%
     inner_join(week_before_race_day_wx) %>%
     mutate(tavg_f=(tmin_f+tmax_f)/2.0,
            snow_label=ifelse(snow_in>0, '*', NA),
            pweek_snow_label=ifelse(pweek_snow_in>0, '*', NA)) %>%
     select(number, year, race_date, tmin_f, tmax_f, tavg_f,
            prcp_in, snow_in, snwd_in, awnd_mph, wsf2_mph,
            pweek_prcp_in, pweek_snow_in,
            snow_label, pweek_snow_label);

 write_csv(all_wx, "all_wx.csv")

 madis <- src_postgres(host="localhost", dbname="madis")

 pafa_fbsa <- tbl(madis,
                  build_sql("
   WITH pafa AS (
     SELECT dt_local, temp_f, wspd_mph
     FROM observations
     WHERE station_id = 'PAFA' AND date_part('month', dt_local) = 9),
   fbsa AS (
     SELECT dt_local, temp_f, wspd_mph
     FROM observations
     WHERE station_id = 'FBSA2' AND date_part('month', dt_local) = 9)
   SELECT pafa.dt_local, pafa.temp_f AS pafa_temp_f, pafa.wspd_mph as pafa_wspd_mph,
     fbsa.temp_f AS ester_dome_temp_f, fbsa.wspd_mph as ester_dome_wspd_mph
   FROM pafa
     INNER JOIN fbsa ON
       pafa.dt_local BETWEEN fbsa.dt_local - interval '15 minutes'
         AND fbsa.dt_local + interval '15 minutes'")) %>% collect()

 write_csv(pafa_fbsa, "pafa_fbsa.csv")

 ester_dome_temps <- lm(data=pafa_fbsa,
                        ester_dome_temp_f ~ pafa_temp_f)

 summary(ester_dome_temps)
 # Model and coefficients are significant, r2 = 0.794
 # intercept = -2.69737, slope = 0.94268

 all_wx_with_ed <- all_wx %>%
   mutate(ed_min_temp_f=round(ester_dome_temps$coefficients[1]+
                              tmin_f*ester_dome_temps$coefficients[2], 1),
          ed_max_temp_f=round(ester_dome_temps$coefficients[1]+
                              tmax_f*ester_dome_temps$coefficients[2], 1))

 make_gt <- function(outside, instruments, chamber, width, heights) {
     gt1 <- ggplot_gtable(ggplot_build(outside))
     gt2 <- ggplot_gtable(ggplot_build(instruments))
     gt3 <- ggplot_gtable(ggplot_build(chamber))
     max_width <- unit.pmax(gt1$widths[2:3], gt2$widths[2:3], gt3$widths[2:3])
     gt1$widths[2:3] <- max_width
     gt2$widths[2:3] <- max_width
     gt3$widths[2:3] <- max_width
     gt <- gtable(widths = unit(c(width), "in"), heights = unit(heights, "in"))
     gt <- gtable_add_grob(gt, gt1, 1, 1)
     gt <- gtable_add_grob(gt, gt2, 2, 1)
     gt <- gtable_add_grob(gt, gt3, 3, 1)

     gt
 }

temps <- ggplot(data=all_wx_with_ed, aes(x=year, ymin=tmin_f, ymax=tmax_f, y=tavg_f)) +
   # geom_abline(intercept=32, slope=0, color="blue", alpha=0.25) +
   geom_rect(data=all_wx_with_ed %>% head(n=1),
            aes(xmin=-Inf, xmax=Inf, ymin=-Inf, ymax=32),
            fill="darkcyan", alpha=0.25) +
   geom_abline(aes(slope=0,
                  intercept=mean(all_wx_with_ed$tmin_f)),
               color="darkorange", alpha=0.50, linetype=2) +
   geom_abline(aes(slope=0,
                  intercept=mean(all_wx_with_ed$tmax_f)),
               color="darkorange", alpha=0.50, linetype=2) +
   geom_abline(aes(slope=0,
                  intercept=mean(all_wx_with_ed$ed_min_temp_f)),
               color="darkorange", alpha=0.50, linetype=1) +
   geom_abline(aes(slope=0,
                  intercept=mean(all_wx_with_ed$ed_max_temp_f)),
               color="darkorange", alpha=0.50, linetype=1) +
   geom_linerange(aes(ymin=ed_min_temp_f, ymax=ed_max_temp_f)) +
   # geom_smooth(method="lm", se=FALSE) +
   geom_linerange(size=3, color="grey30") +
   scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015, 2)) +
   scale_y_continuous(name="Temperature (deg F)", breaks=pretty_breaks(n=10)) +
   theme_bw() +
   theme(plot.margin=unit(c(1, 1, 0, 0.5), 'lines')) +  # t, r, b, l
   theme(axis.text.x=element_blank(), axis.title.x=element_blank(),
         axis.ticks.x=element_blank(), panel.grid.minor.x=element_blank()) +
   ggtitle("Weather during and in the week prior to the Equinox Marathon
            Fairbanks Airport Station")

 prcp <- ggplot(data=all_wx, aes(x=year, y=prcp_in)) +
     geom_bar(stat="identity") +
     geom_text(aes(y=prcp_in+0.025, label=snow_label)) +
     scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015)) +
     scale_y_continuous(name="Precipitation (inches)", breaks=pretty_breaks(n=5)) +
     theme_bw() +
     theme(plot.margin=unit(c(0, 1, 0, 0.5), 'lines')) +  # t, r, b, l
     theme(axis.text.x=element_blank(), axis.title.x=element_blank(),
           axis.ticks.x=element_blank(), panel.grid.minor.x=element_blank())

 pweek_prcp <- ggplot(data=all_wx, aes(x=year, y=pweek_prcp_in)) +
     geom_bar(stat="identity") +
     geom_text(aes(y=pweek_prcp_in+0.1, label=pweek_snow_label)) +
     scale_x_continuous(name="", limits=c(1963, 2015), breaks=seq(1963, 2015)) +
     scale_y_continuous(name="Pre-week precip (inches)", breaks=pretty_breaks(n=5)) +
     theme_bw() +
     theme(plot.margin=unit(c(0, 1, 0.5, 0.5), 'lines'),
           axis.text.x=element_text(angle=45, hjust=1, vjust=1),
           panel.grid.minor.x=element_blank())

 rescale <- 0.75
 full_plot <- make_gt(temps, prcp, pweek_prcp,
                      16*rescale,
                      c(7.5*rescale, 2.5*rescale, 3.0*rescale))
 pdf("equinox_weather_grid.pdf", height=13*rescale, width=16*rescale)
 grid.newpage()
 grid.draw(full_plot)
 dev.off()

 fai_ed_temps <- ggplot(data=pafa_fbsa, aes(x=pafa_temp_f, y=ester_dome_temp_f)) +
   geom_rect(data=pafa_fbsa %>% head(n=1),
               aes(xmin=-Inf, ymin=-Inf, xmax=(32+2.69737)/0.94268, ymax=32),
               color="black", fill="darkcyan", alpha=0.25) +
   geom_point(position=position_jitter()) +
   geom_smooth(method="lm", se=FALSE) +
   scale_x_continuous(name="Fairbanks Airport Temperature (degrees F)") +
   scale_y_continuous(name="Ester Dome Temperature (degrees F)") +
   theme_bw() +
   ggtitle("Relationship between Fairbanks Airport and Ester Dome Temperatures
           September, 2008-2013")

 pdf("pafa_fbsa_sept_temps.pdf", height=10.5, width=10.5)
 print(fai_ed_temps)
 dev.off()

 fai_ed_wspds <- ggplot(data=pafa_fbsa, aes(x=pafa_wspd_mph, y=ester_dome_wspd_mph)) +
   geom_point(position=position_jitter()) +
   geom_smooth(method="lm", se=FALSE) +
   scale_x_continuous(name="Fairbanks Airport Wind Speed (MPH)") +
   scale_y_continuous(name="Ester Dome Wind (MPH)") +
   theme_bw() +
   ggtitle("Relationship between Fairbanks Airport and Ester Dome Wind Speeds
           September, 2008-2013")

 pdf("pafa_fbsa_sept_wspds.pdf", height=10.5, width=10.5)
 print(fai_ed_wspds)
 dev.off()

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