# 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()
```

## 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
```

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
```

## Questions

Please direct any questions or comments on `dataRetrieval`

to: https://github.com/USGS-R/dataRetrieval/issues