A couple days ago I got an email from a Galoot who was hoping to come north to see the aurora and wondered if March was a good time to come to Fairbanks. I know that March and September are two of my favorite months, but wanted to check to see if my perception of how sunny it is in March was because it really is sunny in March or if it’s because March is the month when winter begins to turn to spring in Fairbanks and it just seems brighter and sunnier, with longer days and white snow on the ground.
I found three sources of data for “cloudiness.” I’ve been parsing the Fairbanks Airport daily climate summary since 2002, and it has a value in it called Average Sky Cover which ranges from 0.0 (completely clear) to 1.0 (completely cloudy). I’ll call this data “pafa.”
The second source is the Global Historical Climatology - Daily for the Fairbanks Airport station. There’s a variable in there named ACMH, which is described as Cloudiness, midnight to midnight (percentage). For the Airport station, this value appears in the database from 1965 through 1997. One reassuring thing about this parameter is that it specifically says it’s from midnight to midnight, so it would include cloudiness when it was dark outside (and the aurora would be visible if it was present). This data set is named “ghcnd.”
The final source is modelled data from the North American Regional Reanalysis. This data set includes TCDC, or total cloud cover (percentage), and is available in three-hour increments over a grid covering North America. I chose the nearest grid point to the Fairbanks Airport and retrieved the daily mean of total cloud cover for the period of the database I have downloaded (1979—2012). In the plots that follow, this is named “narr.”
After reading the data and merging the three data sets together, I generate monthly means of cloud cover (scaled to percentages from 0 to 100) in each of the data sets, in R:
library(plyr) cloud_cover <- merge(pafa, ghcnd, by = 'date', all = TRUE) cloud_cover <- merge(cloud_cover, narr, by = 'date', all = TRUE) cloud_cover$month <- month(cloud_cover$date) by_month_mean <- ddply( subset(cloud_cover, select = c('month', 'pafa', 'ghcnd', 'narr')), .(month), summarise, pafa = mean(pafa, na.rm = TRUE), ghcnd = mean(ghcnd, na.rm = TRUE), narr = mean(narr, na.rm = TRUE)) by_month_mean$mon <- factor(by_month_mean$month, labels = c('jan', 'feb', 'mar', 'apr', 'may', 'jun', 'jul', 'aug', 'sep', 'oct', 'nov', 'dec'))
In order to plot it, I generate text labels for the year range of each data set and melt the data so it can be faceted:
library(lubridate) library(reshape2) text_labels <- rbind( data.frame(variable = 'pafa', str = paste(min(year(pafa$date)), '-', max(year(pafa$date)))), data.frame(variable = 'ghcnd', str = paste(min(year(ghcnd$date)), '-', max(year(ghcnd$date)))), data.frame(variable = 'narr', str = paste(min(year(narr$date)), '-', max(year(narr$date))))) mean_melted <- melt(by_month_mean, id.vars = 'mon', measure.vars = c('pafa', 'ghcnd', 'narr'))
Finally, the plotting:
library(ggplot2) q <- ggplot(data = mean_melted, aes(x = mon, y = value)) q + theme_bw() + geom_bar(stat = 'identity', colour = "darkred", fill = "darkorange") + facet_wrap(~ variable, ncol = 1) + scale_x_discrete(name = "Month") + scale_y_continuous(name = "Mean cloud cover") + ggtitle('Cloud cover data for Fairbanks Airport Station') + geom_text(data = text_labels, aes(x = 'feb', y = 70, label = str), size = 4) + geom_text(aes(label = round(value, digits = 1)), vjust = 1.5, size = 3)
The good news for the guy coming to see the northern lights is that March is indeed the least cloudy month in Fairbanks, and all three data sources show similar patterns, although the NARR dataset has September and October as the cloudiest months, and anyone who has lived in Fairbanks knows that August is the rainiest (and probably cloudiest) month. PAFA and GHCND have a late summer pattern that seems more like what I recall.
Another way to slice the data is to get the average number of days in a month with less than 20% cloud cover; a measure of the clearest days. This is a pretty easy calculation:
by_month_less_than_20 <- ddply( subset(cloud_cover, select = c('month', 'pafa', 'ghcnd', 'narr')), .(month), summarise, pafa = sum(pafa < 20, na.rm = TRUE) / sum(!is.na(pafa)) * 100, ghcnd = sum(ghcnd < 20, na.rm = TRUE) / sum(!is.na(ghcnd)) * 100, narr = sum(narr < 20, na.rm = TRUE) / sum(!is.na(narr)) * 100);
And the results:
We see the same pattern as in the mean cloudiness plot. March is the month with the greatest number of days with less that 20% cloud cover. Depending on the data set, between 17 and 24 percent of March days are quite clear. In contrast, the summer months rarely see days with no cloud cover. In June and July, the days are long and convection often builds large clouds in the late afternoon, and by August, the rain has started. Just like in the previous plot, NARR has September as the month with the fewest clear days, which doesn’t match my experience.
Over the past couple days in Fairbanks, there has been a strong flow of warm, moist air from the Pacific which culminated in a record (for January 14th) 0.22 inches of precipitation, most of which fell as rain. Nasty. Similar events happened in 2011 and in November 2010, which everyone will remember for the inch or more of ice that glazed the roads for the rest of the winter that year.
The question people always ask after a series of events like this is whether this is a new weather pattern (let’s hope not!) and whether it may be the result of global climate change (which I probably can’t answer).
To look at this, I examined the historical record for Fairbanks, searching for dates that met the following criteria:
- At least six inches of snow on the ground
- During the winter months (October through February)
- Daily high temperature above freezing
- Precipitation falling as rain
The last criteria isn’t part of the historical record, but we can guess the amount of rain by comparing the amount of snow (measured each day on a snow board that is cleared after measurement) with the amount of liquid precipitation gathered in a tube and melted, if necessary. In my experience, the ratio of snow to liquid precipitation is almost always less than 10 to 1 (meaning that 10 inches of snow melts down to less than an inch of liquid), so I’m looking for dates where the precipitation amount is greater than 10 times the snowfall for that date. I’m also estimating the amount of rain by subtracting (snow × 10) from the precipitation total.
Here’s the query:
SELECT dte, tmin_f, tmax_f, prcp_in, snow_in, rain_in, row_number() OVER (ORDER BY rain_in desc) AS rank FROM ( SELECT to_char(dte, 'YYYY-MM') AS dte, round(avg(tmin_f), 1) AS tmin_f, round(avg(tmax_f), 1) AS tmax_f, sum(prcp_in) AS prcp_in, sum(snow_in) AS snow_in, sum(rain_in) AS rain_in FROM ( SELECT dte, tmin_f, tmax_f, prcp_in, snow_in, snwd_in, round(prcp_in - (snow_in / 10.0), 2) AS rain_in FROM get_ghcnd('Fairbanks Intl Ap') WHERE extract(month from dte) IN (10, 11, 12, 1, 2) AND snwd_in > 6 AND tmax_f > 32 AND prcp_in * 10 > snow_in ORDER BY dte ) AS foo GROUP BY to_char(dte, 'YYYY-MM') ) AS bar ORDER BY dte;
And the results, ordered by the year and month of the event. None of the winter rain events stretched across a month boundary, so it was convenient to aggregate them this way (although 1937 is problematic as I mention below).
|Date||Min Temp (°F)||Max Temp (°F)||Precip (in)||Snow (in)||“Rain” (in)||Rank|
The 2010 event was had the third highest rainfall in the historical record; yesterday’s rain was the tenth highest. The January 1937 event is actually two events, one on the 10th and 11th and one on the 20th and 21st. If we split them up into two events, the 2010 rainfall amount is the second largest amount and the two January 1937 rainfalls come in third and tied for fifth, with November 1935 holding the record.
Grouping the events into decades, we get the following:
Here’s a visualization of the same data:
I don’t think there’s evidence that what we’ve seen in the last few years is exceptional in the historical record, but it does seem like the frequency of winter rainfall does come in cycles, with a peak in the 30s and 40s, and something of a decline in the 80s and 90s. That we’ve already had three events in this decade, in just over two years, seems like a bad sign to me. I wonder if there are larger scale climatological phenomena that could help to explain the pattern shown here?
Thinking a little more about my previous post on the cold winter we’ve been experiencing for the past three months, it would be easier to understand the analysis if I reported average temperature for the period, rather than a cumulative value. I also realized that if there were missing days in any of the record, that this would skew the results against those years with missing data. So here’s a better query and the results through December 23rd:
SELECT year, round(cum_f / n, 2) AS avg_tempf, rank() OVER (ORDER BY cum_f / n) AS rank FROM ( SELECT year, CASE WHEN year = 2012 THEN round(sum(tavg_f), 2) - 261.5 ELSE round(sum(tavg_f), 2) END AS cum_f, CASE WHEN year = 2012 THEN count(*) + 7 ELSE count(*) END AS n FROM ( SELECT extract(year from dte) AS year, extract(doy from dte) AS doy, (tmin_f + tmax_f) / 2.0 AS tavg_f FROM get_ghcnd('Fairbanks Intl Ap') ORDER BY year, doy ) AS foo WHERE doy between extract(doy from '2011-10-01'::date) AND extract(doy from '2012-12-23'::date) GROUP BY year ORDER BY year ) AS bar ORDER BY rank;
|Rank||Year||Average temp (°F)||Minimum temp (°F)||Maximum temp (°F)|
We’ve moved to third place on the list, with an average temperature over the period of less than zero Fahrenheit.
Here’s the same analysis for November and December (through the 23rd):
|Rank||Year||Average temp (°F)||Minimum temp (°F)||Maximum temp (°F)|
The Weather Service is forecasting some warmer weather starting today, so it’s likely we’ll begin to drop down the list, but it will be interesting to see where we wind up at the end of December.
Regardless, it’s been an exceptionally cold October, November and December in Fairbanks. We’re all just hanging on, hoping our houses, vehicles and other equipment continues to function until we get some warmer weather.
It seems like it’s been cold for almost the entire winter this year, with the exception of the few days last week when we got more than 16 inches of snow. Unfortunately, it’s been hard to enjoy it, with daily high temperatures typically well below -20°F.
Let’s see how this winter ranks among the early-season Fairbanks winters going back to 1904. To get an estimate of how cold the winter is, I’m adding together all the daily average temperatures (in degrees Celsius) for each day from October 1st through yesterday. Lower values for this sum indicate colder winters.
Here’s the SQL query. The CASE WHEN stuff is to include the recent data that isn’t in the database I was querying.
SELECT year, CASE WHEN year = 2012 THEN cum_deg - 112 ELSE cum_deg END AS cum_deg, rank() OVER ( ORDER BY CASE WHEN year = 2012 THEN cum_deg - 112 ELSE cum_deg END ) AS rank FROM ( SELECT year, round(sum(tavg_c) AS cum_deg FROM ( SELECT extract(year from dte) AS year, extract(doy from dte) AS doy, tavg_c FROM ghcnd_obs WHERE station_id = 'USW00026411' ORDER BY year, doy ) AS foo WHERE doy between extract(doy from '2011-10-01'::date) and extract(doy from '2012-12-19'::date) GROUP BY year ORDER BY year ) AS bar ORDER by rank;
And the results: this has been the fifth coldest early-season winter since 1904.
|O/N/D rank||year||O/N/D cumulative °C||N/D rank|
In addition to the ranks for October through today (O/N/D rank in the table), the last column (N/D rank) shows the same calculation without October temperatures. It’s always a good idea to examine how well a relationship holds up when the interval is manipulated in order to see if the results are an artifact of the choice of period. In this case, the rankings change, but not dramatically.
Tonight we may cross -50°F for the first time this year at our house, but even without the very cold temperatures predicted (but not record cold) through the weekend, the start of the 2012/2013 winter has been exceptionally chilly.
It’s now December 1st and the last time we got new snow was on November 11th. In my last post I looked at the lengths of snow-free periods in the available weather data for Fairbanks, now at 20 days. That’s a long time, but what I’m interested in looking at today is whether the monthly pattern of snowfall in Fairbanks is changing.
The Alaska Dog Musher’s Association holds a series of weekly sprint races starting at the beginning of December. For the past several years—and this year—there hasn’t been enough snow to hold the earliest of the races because it takes a certain depth of snowpack to allow a snow hook to hold a team back should the driver need to stop. I’m curious to know if scheduling a bunch of races in December and early January is wishful thinking, or if we used to get a lot of snow earlier in the season than we do now. In other words, has the pattern of snowfall in Fairbanks changed?
One way to get at this is to look at the earliest data in the “winter year” (which I’m defining as starting on September 1st, since we do sometimes get significant snowfall in September) when 12 inches of snow has fallen. Here’s what that relationship looks like:
And the results from a linear regression:
Call: lm(formula = winter_doy ~ winter_year, data = first_foot) Residuals: Min 1Q Median 3Q Max -60.676 -25.149 -0.596 20.984 77.152 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -498.5005 462.7571 -1.077 0.286 winter_year 0.3067 0.2336 1.313 0.194 Residual standard error: 33.81 on 60 degrees of freedom Multiple R-squared: 0.02793, Adjusted R-squared: 0.01173 F-statistic: 1.724 on 1 and 60 DF, p-value: 0.1942
According to these results the date of the first foot of snow is getting later in the year, but it’s not significant, so we can’t say with any authority that the pattern we see isn’t just random. Worse, this analysis could be confounded by what appears to be a decline in the total yearly snowfall in Fairbanks:
This relationship (less snow every year) has even less statistical significance. If we combine the two analyses, however, there is a significant relationship:
Call: lm(formula = winter_year ~ winter_doy * snow, data = yearly_data) Residuals: Min 1Q Median 3Q Max -35.15 -11.78 0.49 14.15 32.13 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.947e+03 2.082e+01 93.520 <2e-16 *** winter_doy 4.297e-01 1.869e-01 2.299 0.0251 * snow 5.248e-01 2.877e-01 1.824 0.0733 . winter_doy:snow -7.022e-03 3.184e-03 -2.206 0.0314 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 17.95 on 58 degrees of freedom Multiple R-squared: 0.1078, Adjusted R-squared: 0.06163 F-statistic: 2.336 on 3 and 58 DF, p-value: 0.08317
Here we’re “predicting” winter year based on the yearly snowfall, the first date where a foot of snow had fallen, and the interaction between the two. Despite the near-significance of the model and the parameters, it doesn’t do a very good job of explaining the data (almost 90% of the variation is unexplained by this model).
One problem with boiling the data down into a single (or two) values for each year is that we’re reducing the amount of data being analyzed, lowering our power to detect a significant relationship between the pattern of snowfall and year. Here’s what the overall pattern for all years looks like:
And the individual plots for each year in the record:
Because “winter month” isn’t a continuous variable, we can’t use normal linear regression to evaluate the relationship between year and monthly snowfall. Instead we’ll use multinominal logistic regression to investigate the relationship between which month is the snowiest, and year:
library(nnet) model <- multinom(data = snowiest_month, winter_month ~ winter_year) summary(model) Call: multinom(formula = winter_month ~ winter_year, data = snowiest_month) Coefficients: (Intercept) winter_year 3 30.66572 -0.015149192 4 62.88013 -0.031771508 5 38.97096 -0.019623059 6 13.66039 -0.006941225 7 -68.88398 0.034023510 8 -79.64274 0.039217108 Std. Errors: (Intercept) winter_year 3 9.992962e-08 0.0001979617 4 1.158940e-07 0.0002289479 5 1.120780e-07 0.0002218092 6 1.170249e-07 0.0002320081 7 1.668613e-07 0.0003326432 8 1.955969e-07 0.0003901701 Residual Deviance: 221.5413 AIC: 245.5413
I’m not exactly sure how to interpret the results, but typically you’re looking to see if the intercepts and coefficients are significantly different from zero. If you look at the difference in magnitude between the coefficients and the standard errors, it appears they are significantly different from zero, which would imply they are statistically significant.
In order to examine what they have to say, we’ll calculate the probability curves for whether each month will wind up as the snowiest month, and plot the results by year.
fit_snowiest <- data.frame(winter_year = 1949:2012) probs <- cbind(fit_snowiest, predict(model, newdata = fit_snowiest, "probs")) probs.melted <- melt(probs, id.vars = 'winter_year') names(probs.melted) <- c('winter_year', 'winter_month', 'probability') probs.melted$month <- factor(probs.melted$winter_month) levels(probs.melted$month) <- \ list('oct' = 2, 'nov' = 3, 'dec' = 4, 'jan' = 5, 'feb' = 6, 'mar' = 7, 'apr' = 8) q <- ggplot(data = probs.melted, aes(x = winter_year, y = probability, colour = month)) q + theme_bw() + geom_line(size = 1) + scale_y_continuous(name = "Model probability") \ + scale_x_continuous(name = 'Winter year', breaks = seq(1945, 2015, 5)) \ + ggtitle('Snowiest month probabilities by year from logistic regression model,\n Fairbanks Airport station') \ + scale_colour_manual(values = \ c("violet", "blue", "cyan", "green", "#FFCC00", "orange", "red"))
Here’s how you interpret this graph. Each line shows how likely it is that a month will be the snowiest month (November is always the snowiest month because it always has the highest probabilities). The order of the lines for any year indicates the monthly order of snowiness (in 1950, November, December and January were predicted to be the snowiest months, in that order), and months with a negative slope are getting less snowy overall (November, December, January).
November is the snowiest month for all years, but it’s declining, as is snow in December and January. October, February, March and April are increasing. From these results, it appears that we’re getting more snow at the very beginning (October) and at the end of the winter, and less in the middle of the winter.