Demonstrating that 100 days of weather can be used to predict reasonable weather in 3 days

100 days of weather.R

# --- Packages -----------------------------------------------------------------
library(ggplot2) # Plots
library(magrittr) # Pipes
library(dplyr) # Split-Apply-Combine
library(tidyr) # Reshape data
library(stringr) # String manipulation
library(lubridate) # Dates and times
library(readr) # Read in csv/tsv/fwf data
library(readxl) # Read in excel data
# ------------------------------------------------------------------------------

# Load data: Weather around Minneapolis from 3/1/2016 - 6/11/2016
weather_data <- read_csv("../Downloads/756608.csv", na = "-9999") %>%
  mutate(DATE = ymd(DATE),
         ddate = decimal_date(DATE)) %>%
  mutate(predict.data = DATE <= ymd("2016-06-01")) %>%
  select(which(colSums(!is.na(.)) > 0)) %>%
  select(DATE, ddate, predict.data, STATION, ELEVATION, LONGITUDE, LATITUDE, PRCP, TMAX, TMIN, TOBS)

# Summarize - average all stations in the area
weather_summary <- weather_data %>%
  select(-starts_with("STATION")) %>%
  group_by(DATE, ddate, predict.data) %>%
  summarize_each(funs(mean(., na.rm = T)))
# Result: 103 observations of 9 variables

# Plot temperature data
qplot(x = DATE, y = TMAX, data = weather_summary) + ylab("Max Temperature")
qplot(x = DATE, y = TMIN, data = weather_summary) + ylab("Min Temperature")

# Create sinusoidal functions and verify they are appropriately periodic:
qplot(x = ddate, y = sin(ddate*2*pi), data = weather_summary)
qplot(x = ddate, y = cos(ddate*2*pi), data = weather_summary)
qplot(x = ddate, y = sin(ddate*pi), data = weather_summary)
qplot(x = ddate, y = cos(ddate*pi), data = weather_summary)

# Temperature model
max_temp_model <- lm(TMAX ~ sin(ddate*2*pi) + cos(ddate*2*pi) + sin(ddate*pi) + cos(ddate*pi), data = filter(weather_data, predict.data))

# Predict for summary data
weather_summary$TMAX.pred <- predict(max_temp_model, newdata = weather_summary)

qplot(x = DATE, y = TMAX, color = predict.data, data = weather_summary) + ylab("Max Temperature") + 
  geom_smooth(aes(x = DATE, y = TMAX.pred), inherit.aes = F) + 
  scale_color_manual("Data\nused\nto fit\nmodel", values = c("grey40", "black")) + xlab("Date") + 
  ggtitle("Maximum Temperatures: Minneapolis")

# Temperature model
min_temp_model <- lm(TMIN ~ sin(ddate*2*pi) + cos(ddate*2*pi) + sin(ddate*pi) + cos(ddate*pi), data = filter(weather_data, predict.data))

# Predict for summary data
weather_summary$TMIN.pred <- predict(min_temp_model, newdata = weather_summary)

qplot(x = DATE, y = TMIN, color = predict.data, data = weather_summary) + ylab("Min Temperature") + 
  geom_smooth(aes(x = DATE, y = TMIN.pred), inherit.aes = F) + 
  scale_color_manual("Data\nused\nto fit\nmodel", values = c("grey40", "black")) + xlab("Date") + 
  ggtitle("Minimum Temperatures: Minneapolis")