Abstract

The following is a document-style version of a presentation I gave at work a couple weeks ago. It's a little less useful for a general audience because you don't have access to the same database I have, but I figured it might be useful for someone who is looking at using dplyr or in manipulating the GHCND data from NCDC.

Introduction

Today we’re going to briefly take a look at the GHCND climate database and a couple new R packages (dplyr and tidyr) that make data import and manipulation a lot easier than using the standard library.

For further reading, consult the vignettes for dplyr and tidyr, and download the cheat sheet:

• http://cran.r-project.org/web/packages/dplyr/vignettes/introduction.html
• http://cran.r-project.org/web/packages/dplyr/vignettes/databases.html
• http://cran.r-project.org/web/packages/tidyr/vignettes/tidy-data.html
• http://www.rstudio.com/wp-content/uploads/2015/02/data-wrangling-cheatsheet.pdf

GHCND database

The GHCND database contains daily observation data from locations around the world. The README linked above describes the data set and the way the data is formatted. I have written scripts that process the station data and the yearly download files and insert it into a PostgreSQL database (noaa).

The script for inserting a yearly file (downloaded from http://www1.ncdc.noaa.gov/pub/data/ghcn/daily/by_year/) is here: ghcn-daily-by_year_process.py

“Tidy” data

Without going into too much detail on the subject (read Hadley Wickham’s paper) for more information, but the basic idea is that it is much easier to analyze data when it is in a particular, “tidy”, form. A Tidy dataset has a single table for each type of real world object or type of data, and each table has one column per variable measured and one row per observation.

For example, here’s a tidy table representing daily weather observations with station × date as rows and the various variables as columns.

Getting raw data into this format is what we’ll look at today.

R libraries & data import

First, let’s load the libraries we’ll need:

library(dplyr)      # data import
library(tidyr)      # column / row manipulation
library(knitr)      # tabular export
library(ggplot2)    # plotting
library(scales)     # “pretty” scaling
library(lubridate)  # date / time manipulations

dplyr and tidyr are the data import and manipulation libraries we will use, knitr is used to produce tabular data in report-quality forms, ggplot2 and scales are plotting libraries, and lubridate is a library that makes date and time manipulation easier.

Also note the warnings about how several R functions have been “masked” when we imported dplyr. This just means we'll be getting the dplyr versions instead of those we might be used to. In cases where we need both, you can preface the function with it's package: base::filter would us the normal filter function instead of the one from dplyr.

Next, connect to the database and the three tables we will need:

noaa_db <- src_postgres(host="mason",
                        dbname="noaa")
ghcnd_obs <- tbl(noaa_db, "ghcnd_obs")
ghcnd_vars <- tbl(noaa_db, "ghcnd_variables")

The first statement connects us to the database and the next two create table links to the observation table and the variables table.

Here’s what those two tables look like:

glimpse(ghcnd_obs)

## Observations: 29404870
## Variables:
## $ station_id  (chr) "USW00027502", "USW00027502", "USW00027502", "USW0...
## $ dte         (date) 2011-05-01, 2011-05-01, 2011-05-01, 2011-05-01, 2...
## $ variable    (chr) "AWND", "FMTM", "PRCP", "SNOW", "SNWD", "TMAX", "T...
## $ raw_value   (dbl) 32, 631, 0, 0, 229, -100, -156, 90, 90, 54, 67, 1,...
## $ meas_flag   (chr) "", "", "T", "T", "", "", "", "", "", "", "", "", ...
## $ qual_flag   (chr) "", "", "", "", "", "", "", "", "", "", "", "", ""...
## $ source_flag (chr) "X", "X", "X", "X", "X", "X", "X", "X", "X", "X", ...
## $ time_of_obs (int) NA, NA, 0, NA, NA, 0, 0, NA, NA, NA, NA, NA, NA, N...

glimpse(ghcnd_vars)

## Observations: 82
## Variables:
## $ variable       (chr) "AWND", "EVAP", "MDEV", "MDPR", "MNPN", "MXPN",...
## $ description    (chr) "Average daily wind speed (tenths of meters per...
## $ raw_multiplier (dbl) 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0....

Each row in the observation table rows contain the station_id, date, a variable code, the raw value for that variable, and a series of flags indicating data quality, source, and special measurements such as the “trace” value used for precipitation under the minimum measurable value.

Each row in the variables table contains a variable code, description and the multiplier used to convert the raw value from the observation table into an actual value.

This is an example of completely “normalized” data, and it’s stored this way because not all weather stations record all possible variables, and rather than having a single row for each station × date with a whole bunch of empty columns for those variables not measured, each row contains the station × data × variable data.

We are also missing information about the stations, so let’s load that data:

fai_stations <-
    tbl(noaa_db, "ghcnd_stations") %>%
    filter(station_name %in% c("FAIRBANKS INTL AP",
                               "UNIVERSITY EXP STN",
                               "COLLEGE OBSY"))
glimpse(fai_stations)

## Observations: 3
## Variables:
## $ station_id   (chr) "USC00502107", "USW00026411", "USC00509641"
## $ station_name (chr) "COLLEGE OBSY", "FAIRBANKS INTL AP", "UNIVERSITY ...
## $ latitude     (dbl) 64.86030, 64.80389, 64.85690
## $ longitude    (dbl) -147.8484, -147.8761, -147.8610
## $ elevation    (dbl) 181.9656, 131.6736, 144.7800
## $ coverage     (dbl) 0.96, 1.00, 0.98
## $ start_date   (date) 1948-05-16, 1904-09-04, 1904-09-01
## $ end_date     (date) 2015-04-03, 2015-04-02, 2015-03-13
## $ variables    (chr) "TMIN TOBS WT11 SNWD SNOW WT04 WT14 TMAX WT05 DAP...
## $ the_geom     (chr) "0101000020E6100000A5BDC117267B62C0EC2FBB270F3750...

The first part is the same as before, loading the ghcnd_stations table, but we are filtering that data down to just the Fairbanks area stations with long term records. To do this, we use the pipe operator %>% which takes the data from the left side and passes it to the function on the right side, the filter function in this case.

filter requires one or more conditional statements with variable names on the left side and the condition on the right. Multiple conditions can be separated by commas if you want all the conditions to be required (AND) or separated by a logic operator (& for AND, | for OR). For example: filter(latitude > 70, longitude < -140).

When used on database tables, filter can also use conditionals that are built into the database which are passed directly as part of a WHERE clause. In our code above, we’re using the %in% operator here to select the stations from a list.

Now we have the station_ids we need to get just the data we want from the observation table and combine it with the other tables.

Combining data

Here’s how we do it:

fai_raw <-
    ghcnd_obs %>%
    inner_join(fai_stations, by="station_id") %>%
    inner_join(ghcnd_vars, by="variable") %>%
    mutate(value=raw_value*raw_multiplier) %>%
    filter(qual_flag=='') %>%
    select(station_name, dte, variable, value) %>%
    collect()
glimpse(fai_raw)

In order, here’s what we’re doing:

• Assign the result to fai_raw
• Join the observation table with the filtered station data, using station_id as the variable to combine against. Because this is an “inner” join, we only get results where station_id matches in both the observation and the filtered station data. At this point we only have observation data from our long-term Fairbanks stations.
• Join the variable table with the Fairbanks area observation data, using variable to link the tables.
• Add a new variable called value which is calculated by multiplying raw_value (coming from the observation table) by raw_multiplier (coming from the variable table).
• Remove rows where the quality flag is not an empty space.
• Select only the station name, date, variable and actual value columns from the data. Before we did this, each row would contain every column from all three tables, and most of that information is not necessary.
• Finally, we “collect” the results. dplyr doesn’t actually perform the full SQL until it absolutely has to. Instead it’s retrieving a small subset so that we can test our operations quickly. When we are happy with the results, we use collect() to grab the full data.

De-normalize it

The data is still in a format that makes it difficult to analyze, with each row in the result containing a single station × date × variable observation. A tidy version of this data requires each variable be a column in the table, each row being a single date at each station.

To “pivot” the data, we use the spread function, and we'll also calculate a new variable and reduce the number of columns in the result.

fai_pivot <-
    fai_raw %>%
    spread(variable, value) %>%
    mutate(TAVG=(TMIN+TMAX)/2.0) %>%
    select(station_name, dte, TAVG, TMIN, TMAX, TOBS, PRCP, SNOW, SNWD,
           WSF1, WDF1, WSF2, WDF2, WSF5, WDF5, WSFG, WDFG, TSUN)
head(fai_pivot)

## Source: local data frame [6 x 18]
##
##   station_name        dte  TAVG TMIN TMAX TOBS PRCP SNOW SNWD WSF1 WDF1
## 1 COLLEGE OBSY 1948-05-16 11.70  5.6 17.8 16.1   NA   NA   NA   NA   NA
## 2 COLLEGE OBSY 1948-05-17 15.55 12.2 18.9 17.8   NA   NA   NA   NA   NA
## 3 COLLEGE OBSY 1948-05-18 14.40  9.4 19.4 16.1   NA   NA   NA   NA   NA
## 4 COLLEGE OBSY 1948-05-19 14.15  9.4 18.9 12.2   NA   NA   NA   NA   NA
## 5 COLLEGE OBSY 1948-05-20 10.25  6.1 14.4 14.4   NA   NA   NA   NA   NA
## 6 COLLEGE OBSY 1948-05-21  9.75  1.7 17.8 17.8   NA   NA   NA   NA   NA
## Variables not shown: WSF2 (dbl), WDF2 (dbl), WSF5 (dbl), WDF5 (dbl), WSFG
##   (dbl), WDFG (dbl), TSUN (dbl)

spread takes two parameters, the variable we want to spread across the columns, and the variable we want to use as the data value for each row × column intersection.

Examples

Now that we've got the data in a format we can work with, let's look at a few examples.

fai_winter_year_minimum <-
    fai_pivot %>%
        mutate(winter_year=year(dte - days(92))) %>%
        filter(winter_year < 2014) %>%
        group_by(station_name, winter_year) %>%
        select(station_name, winter_year, TMIN) %>%
        summarize(tmin=min(TMIN*9/5+32, na.rm=TRUE), n=n()) %>%
        filter(n>350) %>%
        select(station_name, winter_year, tmin) %>%
        spread(station_name, tmin)

last_twenty <-
    fai_winter_year_minimum %>%
        filter(winter_year > 1993)

last_twenty

## Source: local data frame [20 x 4]
##
##    winter_year COLLEGE OBSY FAIRBANKS INTL AP UNIVERSITY EXP STN
## 1         1994       -43.96            -47.92             -47.92
## 2         1995       -45.04            -45.04             -47.92
## 3         1996       -50.98            -50.98             -54.04
## 4         1997       -43.96            -47.92             -47.92
## 5         1998       -52.06            -54.94             -54.04
## 6         1999       -50.08            -52.96             -50.98
## 7         2000       -27.94            -36.04             -27.04
## 8         2001       -40.00            -43.06             -36.04
## 9         2002       -34.96            -38.92             -34.06
## 10        2003       -45.94            -45.94                 NA
## 11        2004           NA            -47.02             -49.00
## 12        2005       -47.92            -50.98             -49.00
## 13        2006           NA            -43.96             -41.98
## 14        2007       -38.92            -47.92             -45.94
## 15        2008       -47.02            -47.02             -49.00
## 16        2009       -32.98            -41.08             -41.08
## 17        2010       -36.94            -43.96             -38.02
## 18        2011       -47.92            -50.98             -52.06
## 19        2012       -43.96            -47.92             -45.04
## 20        2013       -36.94            -40.90                 NA

sink("last_twenty.rst")
print(kable(last_twenty, format="rst"))
sink()

q <-
    fai_winter_year_minimum %>%
        gather(station_name, tmin, -winter_year) %>%
        arrange(winter_year) %>%
        ggplot(aes(x=winter_year, y=tmin, colour=station_name)) +
            geom_point(size=1.5, position=position_jitter(w=0.5,h=0.0)) +
            geom_smooth(method="lm", se=FALSE) +
            scale_x_continuous(name="Winter Year", breaks=pretty_breaks(n=20)) +
            scale_y_continuous(name="Minimum temperature (degrees F)", breaks=pretty_breaks(n=10)) +
            scale_color_manual(name="Station",
                               labels=c("College Observatory",
                                        "Fairbanks Airport",
                                        "University Exp. Station"),
                               values=c("darkorange", "blue", "darkcyan")) +
            theme_bw() +
            # theme(legend.position = c(0.150, 0.850)) +
            theme(axis.text.x = element_text(angle=45, hjust=1))

print(q)

fai_winter_year_minimum %>%
    gather(station_name, tmin, -winter_year)

## Source: local data frame [321 x 3]
##
##    winter_year station_name tmin
## 1         1905 COLLEGE OBSY   NA
## 2         1907 COLLEGE OBSY   NA
## 3         1908 COLLEGE OBSY   NA
## 4         1909 COLLEGE OBSY   NA
## 5         1910 COLLEGE OBSY   NA
## 6         1911 COLLEGE OBSY   NA
## 7         1912 COLLEGE OBSY   NA
## 8         1913 COLLEGE OBSY   NA
## 9         1915 COLLEGE OBSY   NA
## 10        1916 COLLEGE OBSY   NA
## ..         ...          ...  ...

ggplot(aes(x=winter_year, y=tmin, colour=station_name)) +

geom_point(size=1.5, position=position_jitter(w=0.5,h=0.0)) +
geom_smooth(method="lm", se=FALSE) +

scale_x_continuous(name="Winter Year", breaks=pretty_breaks(n=20)) +
scale_y_continuous(name="Minimum temperature (degrees F)",
                    breaks=pretty_breaks(n=10)) +
scale_color_manual(name="Station",
                    labels=c("College Observatory", "Fairbanks Airport",
                            "University Exp. Station"),
                    values=c("darkorange", "blue", "darkcyan")) +

theme_bw() +
theme(axis.text.x = element_text(angle=45, hjust=1))

summary(lm(data=fai_winter_year_minimum, `COLLEGE OBSY` ~ winter_year))

##
## Call:
## lm(formula = `COLLEGE OBSY` ~ winter_year, data = fai_winter_year_minimum)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -19.0748  -5.8204   0.1907   3.8042  17.1599
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -275.01062  105.20884  -2.614   0.0114 *
## winter_year    0.11635    0.05311   2.191   0.0325 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.599 on 58 degrees of freedom
##   (47 observations deleted due to missingness)
## Multiple R-squared:  0.07643,    Adjusted R-squared:  0.06051
## F-statistic:   4.8 on 1 and 58 DF,  p-value: 0.03249

summary(lm(data=fai_winter_year_minimum, `FAIRBANKS INTL AP` ~ winter_year))

##
## Call:
## lm(formula = `FAIRBANKS INTL AP` ~ winter_year, data = fai_winter_year_minimum)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -15.529  -4.605  -1.025   4.007  19.764
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -171.19553   43.55177  -3.931 0.000153 ***
## winter_year    0.06250    0.02221   2.813 0.005861 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.037 on 104 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.07073,    Adjusted R-squared:  0.06179
## F-statistic: 7.916 on 1 and 104 DF,  p-value: 0.005861

summary(lm(data=fai_winter_year_minimum, `UNIVERSITY EXP STN` ~ winter_year))

##
## Call:
## lm(formula = `UNIVERSITY EXP STN` ~ winter_year, data = fai_winter_year_minimum)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -15.579  -5.818  -1.283   6.029  19.977
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -158.41837   51.03809  -3.104  0.00248 **
## winter_year    0.05638    0.02605   2.164  0.03283 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.119 on 100 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.04474,    Adjusted R-squared:  0.03519
## F-statistic: 4.684 on 1 and 100 DF,  p-value: 0.03283

RMarkdown

This presentation was produced with the RMarkdown package. Allows you to mix text and R code, which is then run through R to produce documents in Word, PDF, HTML, and presentation formats.

• Cheat sheet
• Reference guide

Introduction

Last week I gave a presentation at work about the National Climate Data Center’s GHCND climate database and methods to import and manipulate the data using the dplyr and tidyr R packages (a report-style version of it is here). Along the way, I used this function to calculate the average daily temperature from the minimum and maximum daily temperatures:

mutate(TAVG=(TMIN+TMAX)/2.0))

One of the people in the audience asked why the Weather Service would calculate average daily temperature this way, rather than by averaging the continuous or hourly temperatures at each station. The answer is that many, perhaps most, of the official stations in the GHCND data set are COOP stations which only report minimum and maximum temperature, and the original instrument provided to COOP observers was likely a mercury minimum / maximum thermometer. Now that these instruments are digital, they could conceivably calculate average temperature internally, and observers could report minimum, maximum and average as calculated from the device. But that’s not how it’s done.

In this analysis, I look at the difference between calculating average daily temperature using the mean of all daily temperature observations, and using the average of the minimum and maximum reported temperature each day. I’ll use five years of data collected at our house using our Arduino-based weather station.

Methods

Our weather station records temperature every few seconds, averages this data every five minutes and stores these five minute observations in a database. For our analysis, I’ll group the data by day and calculate the average daily temperature using the mean of all the five minute observations, and using the average of the minimum and maximum daily temperature. I’ll use R to perform the analysis.

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

dw1454 <- src_postgres(dbname="goldstream_creek_wx",
                       user="readonly")

raw_data <- tbl(dw1454, build_sql("SELECT * FROM arduino_west"))

daily_average <-
    raw_data %>%
    filter(obs_dt>'2009-12-31 23:59:59') %>%
    mutate(date=date(obs_dt)) %>%
    select(date, wtemp) %>%
    group_by(date) %>%
    summarize(mm_avg=(min(wtemp)+max(wtemp))/2.0,
              h_avg=mean(wtemp), n=n()) %>%
    filter(n==24*60/5) %>%   # 5 minute obs
    collect()

write_csv(daily_average, "daily_average.csv")
save(daily_average, file="daily_average.rdata", compress=TRUE)

anomaly <-
    daily_average %>%
    mutate(month=month(date),
           anomaly=mm_avg-h_avg) %>%
    ungroup() %>%
    arrange(date)

Results

This is what the results look like:

summary(anomaly$anomaly)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
## -6.8600 -1.5110 -0.1711 -0.1341  1.0740  9.3570

The average anomaly is very close to zero (-0.13), and I suspect it would be even closer to zero as more data is included. Half the data is between -1.5 and 1.1 degrees and the full range is -6.86 to +9.36°F.

Plots

Let’s take a look at some plots of the anomalies.

# All anomalies
q <- ggplot(data=anomaly,
            aes(x=date, ymin=0, ymax=anomaly, colour=anomaly<0)) +
    geom_linerange(alpha=0.5) +
    theme_bw() +
    scale_colour_manual(values=c("red", "blue"), guide=FALSE) +
    scale_x_date(name="") +
    scale_y_continuous(name="Difference between min/max and hourly aggregation")

print(q)

mean_anomaly <- mean(anomaly$anomaly)

# seasonal pattern of anomaly
q <- ggplot(data=anomaly,
            aes(x=as.factor(month), y=anomaly)) +
    geom_hline(data=NULL, aes(yintercept=mean_anomaly), colour="darkorange") +
    geom_boxplot() +
    scale_x_discrete(name="",
                     labels=c("Jan", "Feb", "Mar", "Apr",
                              "May", "Jun", "Jul", "Aug",
                              "Sep", "Oct", "Nov", "Dec")) +
    scale_y_continuous(name="Difference between min/max and hourly aggregation") +
    theme_bw()

print(q)

# distribution of anomalies
q <- ggplot(data=anomaly,
            aes(x=abs(anomaly))) +
    stat_ecdf() +
    scale_x_discrete(name="Absolute value of anomaly (+/- degrees F)",
                     breaks=0:11,
                     labels=0:11,
                     expand=c(0, 0)) +
    scale_y_continuous(name="Cumulative frequency",
                       labels=percent,
                       breaks=pretty_breaks(n=10),
                       limits=c(0,1)) +
    annotate("rect", xmin=-1, xmax=1, ymin=0, ymax=0.4, alpha=0.1, fill="darkcyan") +
    annotate("rect", xmin=-1, xmax=2, ymin=0, ymax=0.67, alpha=0.1, fill="darkcyan") +
    annotate("rect", xmin=-1, xmax=3, ymin=0, ymax=0.85, alpha=0.1, fill="darkcyan") +
    annotate("rect", xmin=-1, xmax=4, ymin=0, ymax=0.94, alpha=0.1, fill="darkcyan") +
    annotate("rect", xmin=-1, xmax=5, ymin=0, ymax=0.975, alpha=0.1, fill="darkcyan") +
    theme_bw()

print(q)

Conclusion

We looked at more than five years of data from our weather station in the Goldstream Valley, comparing daily average temperature calculated from the mean of all five minute temperature observations and those calculated using the average minimum and maximum daily temperature, which is the method the National Weather Service uses for it’s daily data. The results show that the difference between these methods average to zero, which means that on an annual (or greater) basis, there doesn't appear to be any bias in the method.

Two thirds of all daily average temperatures are within two degrees of the actual daily average, and with a few exceptions, the error is always below five degrees.

There is some evidence that there’s a seasonal pattern to the error, however, with April and May daily averages particularly low. If those seasonal patterns are real, this would indicate an important bias in this method of calculating average daily temperature.

Exercise

2013 was the year I decided to, and did, run the Equinox Marathon, so I spent a lot of time running this year and a lot less time bicycling. Since the race, I’ve been having hip problems that have kept me from skiing or running much at all. The roads aren’t cleared well enough to bicycle on them in the winter so I got a fat bike to commute on the trails I’d normally ski.

Here are my totals in tabular form:

I spent just about the same amount of time running, bicycling and skiing this year, and much less time hiking around on the trails than in the past. Because of all the running, and my hip injury, I didn’t manage to commute to work with non-motorized transport quite as much this year (55% of work days instead of 63% in 2012), but the exercise totals are all higher.

One new addition this year is a heart rate monitor, which allows me to much more accurately estimate energy consumption than formulas based on the type of activity, speed, and time. Riding my fat bike, it’s pretty clear that this form of travel is so much less efficient than a road bike with smooth tires that it can barely be called “bicycling,” at least in terms of how much energy it takes to travel over a certain distance.

Here’s the equations from Keytel LR, Goedecke JH, Noakes TD, Hiiloskorpi H, Laukkanen R, van der Merwe L, Lambert EV. 2005. Prediction of energy expenditure from heart rate monitoring during submaximal exercise. J Sports Sci. 23(3):289-97.

where

• hr = Heart rate (in beats/minute)
• w = Weight (in pounds)
• a = Age (in years)
• t = Exercise duration time (in hours)

And a SQL function that implements the version for men (to use it, you’d replace the nnn and yyyy-mm-dd with the appropriate values for you):

--- Kcalories burned based on average heart rate and number
--- of hours at that rate.
CREATE OR REPLACE FUNCTION kcal_from_hr(hr numeric, hours numeric)
RETURNS numeric
LANGUAGE plpgsql
AS $$
DECLARE
    weight_lb numeric := nnn;
    resting_hr numeric := nn;
    birthday date := 'yyyy-mm-dd';
    resting_kcal numeric;
    exercise_kcal numeric;
BEGIN
    resting_kcal := ((-55.0969+(0.6309*(resting_hr))+
                    (0.0901*weight_lb)+
                    (0.2017*(extract(epoch from now()-birthday)/
                    (365.242*24*60*60))))/4.184)*60*hours;
    exercise_kcal := ((-55.0969+(0.6309*(hr))+
                     (0.0901*weight_lb)+
                     (0.2017*(extract(epoch from now()-birthday)/
                     (365.242*24*60*60))))/4.184)*60*hours;
    RETURN exercise_kcal - resting_kcal;
END;
$$;

Here’s a graphical comparison of my exercise data over the past four years:

It was a pretty remarkable year, although the drop in exercise this fall is disappointing.

Another way to visualize the 2013 data is in the form of a heatmap, where each block represents a day on the calendar, and the color is how many calories I burned on that day. During the summer you can see my long runs on the weekends showing up in red. Equinox was on September 21st, the last deep red day of the year.

Weather

2013 was quite remarkable for the number of days where the daily temperature was dramatically different from the 30-year average. The heatmap below shows each day in 2013, and the color indicates how many standard deviations that day’s temperature was from the 30-year average. To put the numbers in perspective, approximately 95.5% of all observations will fall within two standard deviations from the mean, and 99.7% will be within three standard deviations. So the very dark red or dark blue squares on the plot below indicate temperature anomalies that happen less than 1% of the time. Of course, in a full year, you’d expect to see a few of these remarkable differences, but 2013 had a lot of remarkable differences.

2013 saw 45 days where the temperature was more than 2 standard deviations from the mean (19 that were colder than normal and 26 that were warmer), something that should only happen 16 days out of a normal year [ 365.25(1 − 0.9545) ]. There were four days ouside of 3 standard deviations from the mean anomaly. Normally there’d only be a single day [ 365.25(1 − 0.9973) ] with such a remarkably cold or warm temperature.

April and most of May were remarkably cold, resulting in many people skiing long past what is normal in Fairbanks. On May first, Fairbanks still had 17 inches of snow on the ground. Late May, almost all of June and the month of October were abnormally warm, including what may be the warmest week on record in Alaska from June 23rd to the 29th. Although it wasn’t exceptional, you can see the brief cold snap preceding and including the Equinox Marathon on September 21st this year. The result was bitter cold temperatures on race day (my hands and feet didn’t get warm until I was climbing Ester Dome Road an hour into the race), as well as an inch or two of snow on most of the trail sections of the course above 1,000 feet.

Most memorable was the ice and wind storm on November 13th and 14th that dumped several inches of snow and instantly freezing rain, followed by record high winds that knocked power out for 14,000 residents of the area, and then a drop in temperatures to colder than ‒20°F. My office didn’t get power restored for four days.

Dog Barn

The dog barn was the big summer project. It’s a seven by eleven foot building with large dog boxes inside that we keep warm. When the temperatures are too cold for the dogs to stay outside, we put them into their boxes in the dog barn and turn the heat up to 40°F. I have a real-time visualization of the conditions inside and outside the barn, and because the whole thing is run with a small Linux computer and Arduino board, I’m able to collect a lot of data about how the barn is performing.

One such analysis will be to see how much heat the dogs produce when they are in the barn. To estimate that, we need a baseline of how much heat we’re adding at various temperatures in order to keep it at temperature. I haven’t collected enough cold temperature data to really see what the relationship looks like, but here’s the pattern so far.

The graph shows the relationship between the temperature differential between the outside and inside of the barn plotted against the percentage of time the heater is on in order to maintain that differential, for all 12-hour periods where the dogs weren’t in the barn and there’s less than four missing observations. I’ve also run a linear and quadratic regression in order to predict how much heat will be required at various temperature differentials.

The two r² values shows how much of the variation in heating is explained by the temperature differential for the linear and the quadratic regressions. I know that this isn’t a linear relationship, but that model still fits the data better than the quadratic model does. It may be that it’s some other form of non-linear relationship that’s not well expressed by a second order polynomial.

Once we can predict how much heat it should take to keep the barn warm at a particular temperature differential, we can see how much less heat we’re using when the dogs are in the barn. One complication is that the dogs produce enough moisture when they are in the barn that we need to ventilate it when they are in there. So in addition to the additive heating from the dogs themselves, there will be increased heat losses because we have to keep it better ventilated.

It’ll be an interesting data set.

Power

Power consumption is a concern now that we’ve set up the dog barn and are keeping it heated with an electric heater. It’s an oil-filled radiator-style heater, and uses around 1,100 Watts when it’s on.

This table shows our overall usage by year for the period we have data.

Our overall energy use continues to go down, which is a little surprising to me, actually, since we eliminated most of the devices known to use a lot electricity (incandescent light bulbs, halogen floodlights) years ago. Despite that, and bringing the dog barn on line in late November, we used less electricity in 2013 than in the prior three years.

Here’s the pattern by month, and year.

The spike in usage in November is a bit concerning, since it’s the highest overall monthly consumption for the past four years. Hopefully this was primarily due to the heavy use of the heater during the final phases of the dog barn construction. December wasn’t a particularly cold month relative to years past, but it’s good to see that our consumption was actually quite low even with the barn heater being on the entire month.

That wraps it up. Have a happy and productive 2014!