tue, 13-sep-2016, 18:31

Introduction

Update: An update that includes 2016—2020 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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