USGS - science for a changing world

Calculating Moving Averages and Historical Flow Quantiles

Laura DeCicco

This post will show simple way to calculate moving averages, calculate historical-flow quantiles, and plot that information. The goal is to reproduce the graph at this link: PA Graph. The motivation for this post was inspired by a USGS colleague that that is considering creating these type of plots in R. We thought this plot provided an especially fun challenge - maybe you will, too!

First we get the data using the dataRetrieval package. The siteNumber and parameterCd could be adjusted for other sites or measured parameters. In this example, we are getting discharge (parameter code 00060) at a site in PA.

It may be important to note that this script is a bit lazy in handling leap days.

Get data using dataRetrieval

library(dataRetrieval)

#Retrieve daily Q
siteNumber<-c("01538000")
parameterCd <- "00060" #Discharge
dailyQ <- readNWISdv(siteNumber, parameterCd) 
dailyQ <- renameNWISColumns(dailyQ)
stationInfo <- readNWISsite(siteNumber)

Calculate moving average

Next, we calculate a 30-day moving average on all of the flow data:

library(dplyr)

#Check for missing days, if so, add NA rows:
if(as.numeric(diff(range(dailyQ$Date))) != (nrow(dailyQ)+1)){
  fullDates <- seq(from=min(dailyQ$Date),
                   to = max(dailyQ$Date), by="1 day")
  fullDates <- data.frame(Date = fullDates, 
                          agency_cd = dailyQ$agency_cd[1],
                          site_no = dailyQ$site_no[1],
                          stringsAsFactors = FALSE)
  dailyQ <- full_join(dailyQ, fullDates,
                      by=c("Date","agency_cd","site_no")) %>%
    arrange(Date)
}

ma <- function(x,n=30){stats::filter(x,rep(1/n,n), sides=1)}

dailyQ <- dailyQ %>%
  mutate(rollMean = as.numeric(ma(Flow)),
         day.of.year = as.numeric(strftime(Date, 
                                           format = "%j")))

Calculate historical percentiles

We can use the quantile function to calculate historical percentile flows. Then use the loess function for smoothing. The argument smooth.span defines how much smoothing should be applied. To get a smooth transistion at the start of the graph, we can add include an earlier year which is not plotted at the end.

summaryQ <- dailyQ %>%
  group_by(day.of.year) %>%
  summarize(p75 = quantile(rollMean, probs = .75, na.rm = TRUE),
            p25 = quantile(rollMean, probs = .25, na.rm = TRUE),
            p10 = quantile(rollMean, probs = 0.1, na.rm = TRUE),
            p05 = quantile(rollMean, probs = 0.05, na.rm = TRUE),
            p00 = quantile(rollMean, probs = 0, na.rm = TRUE)) 

current.year <- as.numeric(strftime(Sys.Date(), format = "%Y"))

summary.0 <- summaryQ %>%
  mutate(Date = as.Date(day.of.year - 1, 
                        origin = paste0(current.year-2,"-01-01")),
         day.of.year = day.of.year - 365)
summary.1 <- summaryQ %>%
  mutate(Date = as.Date(day.of.year - 1, 
                        origin = paste0(current.year-1,"-01-01")))
summary.2 <- summaryQ %>%
  mutate(Date = as.Date(day.of.year - 1, 
                        origin = paste0(current.year,"-01-01")),
         day.of.year = day.of.year + 365)

summaryQ <- bind_rows(summary.0, summary.1, summary.2) 

smooth.span <- 0.3

summaryQ$sm.75 <- predict(loess(p75~day.of.year, data = summaryQ, span = smooth.span))
summaryQ$sm.25 <- predict(loess(p25~day.of.year, data = summaryQ, span = smooth.span))
summaryQ$sm.10 <- predict(loess(p10~day.of.year, data = summaryQ, span = smooth.span))
summaryQ$sm.05 <- predict(loess(p05~day.of.year, data = summaryQ, span = smooth.span))
summaryQ$sm.00 <- predict(loess(p00~day.of.year, data = summaryQ, span = smooth.span))

summaryQ <- select(summaryQ, Date, day.of.year,
                   sm.75, sm.25, sm.10, sm.05, sm.00) %>%
  filter(Date >= as.Date(paste0(current.year-1,"-01-01")))

latest.years <- dailyQ %>%
  filter(Date >= as.Date(paste0(current.year-1,"-01-01"))) %>%
  mutate(day.of.year = 1:nrow(.))

Plot using base R

Many of the graphical requirements defined by the USGS are difficult to achieve in ggplot2. Base R plotting can be used to obtain these types of graphs:

title.text <- paste0(stationInfo$station_nm,"\n",
        "Provisional Data - Subject to change\n",
        "Record Start = ", min(dailyQ$Date),
        "  Number of years = ",
        as.integer(as.numeric(difftime(time1 = max(dailyQ$Date), 
        time2 = min(dailyQ$Date),
        units = "weeks"))/52.25),
        "\nDate of plot = ",Sys.Date(),
        "  Drainage Area = ",stationInfo$drain_area_va, "mi^2")

mid.month.days <- c(15, 45, 74, 105, 135, 166, 196, 227, 258, 288, 319, 349)
month.letters <- c("J","F","M","A","M","J","J","A","S","O","N","D")
start.month.days <- c(1, 32, 61, 92, 121, 152, 182, 214, 245, 274, 305, 335)
label.text <- c("Normal","Drought Watch","Drought Warning","Drought Emergency")

summary.year1 <- data.frame(summaryQ[2:366,])
summary.year2 <- data.frame(summaryQ[367:733,])

plot(latest.years$day.of.year, latest.years$rollMean, 
     ylim = c(1, 1000), xlim = c(1, 733),
     log="y", axes=FALSE, type="n", xaxs="i",yaxs="i",
     ylab = "30-day moving ave",
     xlab = "")
title(title.text, cex.main = 0.75)
polygon(c(summary.year1$day.of.year,rev(summary.year1$day.of.year)),
        c(summary.year1$sm.75, rev(summary.year1$sm.25)), 
        col = "darkgreen", border = FALSE)
polygon(c(summary.year2$day.of.year,rev(summary.year2$day.of.year)),
        c(summary.year2$sm.75, rev(summary.year2$sm.25)), 
        col = "darkgreen", border = FALSE)
polygon(c(summary.year1$day.of.year,rev(summary.year1$day.of.year)),
        c(summary.year1$sm.25, rev(summary.year1$sm.10)), 
        col = "yellow", border = FALSE)
polygon(c(summary.year2$day.of.year,rev(summary.year2$day.of.year)),
        c(summary.year2$sm.25, rev(summary.year2$sm.10)), 
        col = "yellow", border = FALSE)
polygon(c(summary.year1$day.of.year,rev(summary.year1$day.of.year)),
        c(summary.year1$sm.10, rev(summary.year1$sm.05)), 
        col = "orange", border = FALSE)
polygon(c(summary.year2$day.of.year,rev(summary.year2$day.of.year)),
        c(summary.year2$sm.10, rev(summary.year2$sm.05)), 
        col = "orange", border = FALSE)
polygon(c(summary.year1$day.of.year,rev(summary.year1$day.of.year)),
        c(summary.year1$sm.05, rev(summary.year1$sm.00)), 
        col = "red", border = FALSE)
polygon(c(summary.year2$day.of.year,rev(summary.year2$day.of.year)),
        c(summary.year2$sm.05, rev(summary.year2$sm.00)), 
        col = "red", border = FALSE)
lines(latest.years$day.of.year, latest.years$rollMean, 
      lwd=2, col = "black")
abline(v = 366)
axis(2, las=1, at=c(1,100, 1000), tck = -0.02)
axis(2, at = c(seq(1,90, by = 10)), labels = NA, tck = -0.01)
axis(2, at = c(seq(100,1000, by = 100)), labels = NA, tck = -0.01)
axis(1, at =  c(mid.month.days,365+mid.month.days), 
     labels = rep(month.letters,2), 
     tick = FALSE, line = -0.5, cex.axis = 0.75)
axis(1, at = c(start.month.days, 365+start.month.days),
     labels = NA, tck = -0.02)
axis(1, at = c(182,547), labels = c(current.year-1,current.year), 
     line = .5, tick = FALSE)
legend("bottom", label.text, horiz = TRUE,
       fill = c("darkgreen","yellow","orange","red"),
       inset = c(0, 0), xpd = TRUE, bty = "n", cex = 0.75)
box()

TODO

Plot using ggplot2

Finally, we can also try to create the graph using the ggplot2 package. The following script shows a simple way to re-create the graph in ggplot2 with no effort on imitating desired style:

library(ggplot2)

simple.plot <- ggplot(data = summaryQ, aes(x = day.of.year)) +
  geom_ribbon(aes(ymin = sm.25, ymax = sm.75, fill = "Normal")) +
  geom_ribbon(aes(ymin = sm.10, ymax = sm.25, fill = "Drought Watch")) +
  geom_ribbon(aes(ymin = sm.05, ymax = sm.10, fill = "Drought Warning")) +
  geom_ribbon(aes(ymin = sm.00, ymax = sm.05, fill = "Drought Emergency")) +
  scale_y_log10(limits = c(1,1000)) +
  geom_line(data = latest.years, aes(x=day.of.year, y=rollMean, color = "30-Day Mean"),size=2) +
  geom_vline(xintercept = 365) 

simple.plot

30-day moving average daily flow plot, no effort on style

Next, we can play with various options to do a better job to imitate the style:

styled.plot <- simple.plot+
  scale_x_continuous(breaks = c(mid.month.days,365+mid.month.days),
                   labels = rep(month.letters,2),
                   expand = c(0, 0),
                   limits = c(0,730)) +
  annotation_logticks(sides="l") +
  expand_limits(x=0) +
  annotate(geom = "text", 
           x = c(182,547), 
           y = 1, 
           label = c(current.year-1,current.year), size = 4) +
  theme_bw() + 
  theme(axis.ticks.x=element_blank(),
        panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank()) +
  labs(list(title=title.text,
            y = "30-day moving ave", x="")) +
  scale_fill_manual(name="",breaks = label.text,
                    values = c("red","orange","yellow","darkgreen")) +
  scale_color_manual(name = "", values = "black") +
   theme(legend.position="bottom")

styled.plot

30-day moving average daily flow plot

Questions

Please direct any questions or comments on dataRetrieval to: https://github.com/USGS-R/dataRetrieval/issues