James Riley

85 minute read

Hi y’all, short one today.

Partially it’s about how days of sunlight change through the year, unless you’re on the equator. Partially it’s about how hard it is to make 3d plots in a 2d space.

I have SAD, which seems to flare up at the solstices and equinoxes, plus and minus a couple of weeks.

The solstices make sense - there’s either too much or too little sunshine. But the equinoxes? I think we’re dealing with the hours of sunshine per day changing too quickly. I think the equinoxes are the steepest parts of that curve?

I have 2 options:

  1. A lot of geometry involving a tilted oblate spheroid in an eliptic…. no…
  2. Find a library.

Enter Suncalc. The first thing to worry about is “what is the start of day?”, and “what is the end of day?”. There seem to be about 3 events that you could call the start of the day! For SAD purposes, let’s just say that we’re interested in the difference between sunrise and sunset.

leeds <- getSunlightTimes(date = as.Date("2018-09-21")+0:365,
                          lat = 53.8008,
                          lon = -1.5491,
                          keep = c("sunrise", "sunset")) %>%
  select(-lat,-lon) %>%
  mutate(date = as.Date(date)) %>%
  mutate(day_length = sunset-sunrise)


ggplot(leeds, aes(x=date,y=day_length)) + geom_line() + theme + labs(
  title = "Daylight in Leeds for 1 year",
  y="hours of daylight"
)

plotly::ggplotly()

Looks a bit like a sine wave to me, with the peaks and stuff in approximately the right places. Maybe worth giving it more than 1 year to see:

leeds <- getSunlightTimes(date = as.Date("2018-09-21")+0:3650,
                          lat = 53.8008,
                          lon = -1.5491,
                          keep = c("sunrise", "sunset")) %>%
  select(-lat,-lon) %>%
  mutate(date = as.Date(date)) %>%
  mutate(day_length = sunset-sunrise)


ggplot(leeds, aes(x=date,y=day_length)) + geom_line() + theme + labs(
  title="10 years of daylight, Leeds",
  y="hours of daylight"
)

plotly::ggplotly()

Eyeball method says it looks like a sine. I’m considering converting to audio to let my ears consider it as well.

More dimensions

This falls apart if I want a lot of latitudes. Then I have 2 free dimensions (date, latitude), and one dependent dimension (length of day).

3d plots are a pain. The obvious 3d render can look pretty, but doesn’t usually tell us much. In this case, I’m going to let the x axis be date (again), the y axis be latitude, and show the length of day in various ways through colour.

First I need my data. For simplicity, I’m fixing the longitude at 0.

world_times <- getSunlightTimes(
  data = expand.grid(date = as.Date("2018-09-21") + 0:365,
                     lat = seq(-90,90, by=1),
                     lon = 0),
   keep = c("sunrise", "sunset")
) %>%
  mutate(date = as.Date(date)) %>%
  mutate(day_length = sunset-sunrise) %>%
  mutate(day_length = as.numeric(day_length)/60)

The defaults in ggplot when supplying continuous data are kinda useful, but…


ggplot(world_times, aes(x=date, y=lat, fill=day_length)) + geom_raster() + 
  theme + labs(
    title = "Length of day around the world, over a year",
    y = "latitude",
    fill = "length of day (hours)"
  )

Yeah, I can’t read that well.

Interestingly, we’ve got grey zones, that are exactly where a given day does not have a sunrise or a sunset. So they’re the polar circles dealing with eternal day, or eternal night.

One option is to make the day lengths a categorical variable, and throw it at a rainbow. Everyone I talk to at first think this makes good plots, and I did, at first. Rather than going with the defaults, I’m going to round to the nearest hour.


world_times %>%
  mutate(day_length = round(day_length, 0) %>% as.factor()) %>%
  ggplot(aes(x=date, y=lat, fill=day_length)) + geom_raster() + 
  theme + labs(
    title = "Rainbow plot of day lengths",
    y="latitude",
    fill = "length of day (nearest hour)"
  ) 

We see the nice shapes in the data, but it fails on accesibility. Ggplot ships with 2 colourblind-friendly scales; 1 discrete and 1 continuous, so I’ll throw them at the rounded and unrounded data.

Also, Olga is going to kill me when she sees this ugly graph. :)

world_times %>%
  mutate(day_length = round(day_length, 0) %>% as.factor()) %>%
  ggplot(aes(x=date, y=lat, fill=day_length)) + geom_raster() + 
  theme + labs(
    title = "Colourblind-friendly rounded daylight",
    y="latitude",
    fill = "length of day (nearest hour)"
  ) + scale_fill_viridis_d()

world_times %>%
  ggplot(aes(x=date, y=lat, fill=day_length)) + geom_raster() + 
  theme + labs(
    title = "Colourblind-friendly unrounded daylight",
    y="latitude",
    fill = "length of day (nearest hour)"
  ) + scale_fill_viridis_c()

My favourite in this example involves thinking about what the data is representing. If 12 hours is “normal”, then we’re interested in “how unusal” each location is on a given day. There’s a scale for that.


world_times %>%
  ggplot(aes(x=date, y=lat, fill=day_length)) + geom_raster() + 
  theme + labs(
    title = "Comparison against 12-hour days",
    y="latitude",
    fill = "length of day"
  ) + scale_fill_gradient2(midpoint = 12)

Someone will complain if I don’t give you it as an actual 3d plot. (Well, the nearest approximation you can get on a 2d screen. 3d printing it or throwing it at 3d goggles is an exercise for the reader.) I consider this another example of how not to do it:


plotly::plot_ly(world_times%>% filter(lat %% 3 == 0), x=~date, y=~lat, z=~day_length, type='mesh3d')

If Olga didn’t murderise me for the first one, I’m definitely a gonner for this one.

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