expAnalysis.Rmd

---
title: "algorithmic avalanche forecasting"
author: "Charles Katerba"
date: "2022-10-03"
output: html_document
---

```{r setup, include=T}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(caret)
```

## Weather exploration and imputation

We begin by looking at the weather data from the Whitefish range during the 19-20 season to develop a strategy for all seasons and all ranges. 

```{r}
weather <- read_csv("./weatherData/whitefish_19-20weather.csv") 
```

**weather** data was collected from the [FAC website](https://looper.avalanche.state.co.us/fac/) and reports conditions at 6A (or as close as possible)

- `date`: the date

- `station`: station name, probably not relevant. 

- `Elev`: station elevation in feet

- `Temp`: current temp, F

- `MxTp`: 24 hour max temp

- `MnTp`: 24 hour min temp

- `DewP`: dew point

- `RH`: relative humidity

- `Spd`: current wind speed, mph   

- `Dir`: wind direction in degrees      

- `Gst`: wind gusts, mph      

- `Pcp1`: 1-hour melted precipitation in

- `Pcp24`: 24-hour melted precipitation, in    

- `PcpAc`: precipitation accumulation since midnight, in

- `Sno24`: 24 hour snowfall, in

- `SWE24`: 24 hour SWE, in  

- `SnoHt`: snow height, in   

- `SWE`: snow water equivalent, in. 

The various stations measure different things, so this data set has a bunch of NA values. We need to figure out which variables are important and how to appropriately impute missing values when appropriate. 

```{r}
weather <- weather %>%
  mutate(dateNum = row_number() - 1)
corTable <- cor(weather[3:18], use = "pairwise.complete.obs")

# look at first 4 rows of each station to see common patters
small <- weather %>%
  group_by(Station) %>%
  filter( row_number() %in% 1:4) %>%
  view() %>%
  ungroup()
```

**Issues/Remedies** Different stations have different weather monitoring strengths and deficiencies.  

1. Biggest issue don't all record precip and those that do record it in different ways!

2. Dont all record temp/wind data, but those that do do it in different ways. Less of an issue and more consistent measurement. 

3. Merge 2 Polebridge records? 


```{r}
# First work on Max/Min Temp; try basic MLR on temp and elevetion.
# makes sense but Temp at 6A is a good predictor of min temp. Elevation helps too but not as much as you'd expect. 
minTemp1 <- lm(MnTp ~ Temp, data = weather)
minTemp2 <- lm(MnTp ~ Temp  + Elev, data = weather)
anova(minTemp1, minTemp2)

maxTemp1 <- lm(MxTp ~ Temp, data = weather)
maxTemp2 <- lm(MxTp ~ Temp + Elev, data = weather)
anova(maxTemp1, maxTemp2)

library(mgcv)


```

### Max/min temperature

Generate prediction intervals for min and max temp, then look at plots to decide if we should simply use point estimate or something else. 

alt idea: make model using temps from other elevations/stations on a given day to predict max/min missing temps 

```{r}
df <- weather %>% select(Temp, Elev)
minHat <- predict(minTemp2, df, interval = "prediction", level = .95) 
colnames(minHat) <- c("minFit","minLwr","minUpr")

minHat <- df %>%
  bind_cols(date = weather$date,
            MnTp = weather$MnTp) %>%
  bind_cols(minHat) %>%
  pivot_longer(cols = 5:7, 
               names_to = "minEst", 
               values_to = "minTemp")

maxHat <- predict(maxTemp2, df, interval = "prediction", level = .95)
colnames(maxHat) <- c("maxFit","maxLwr","maxUpr")

maxHat <- df %>%
  bind_cols(date = weather$date,
            MxTp = weather$MxTp) %>%
  bind_cols(maxHat) %>%
  pivot_longer(cols = 5:7, 
               names_to = "maxEst", 
               values_to = "maxTemp")
```

The plot below makes our point estimates for `MnTp` seem pretty good.  For simplicity, we'll get started with just the point estimate. 

```{r}
ggplot(minHat, aes(x = Temp, y = MnTp)) + 
  geom_point() + 
  geom_point(aes(x = Temp, y = minTemp, color = minEst))

```

No surprise, max temp is much more involved. For simplicity, we'll simply impute with the point estimate.

```{r}
p1 <- ggplot(maxHat, aes(x = date, y = MxTp, color = Elev)) + 
  geom_point() + 
  geom_smooth()
p2 <- ggplot(maxHat, aes(x = Temp, y = MxTp)) + 
  geom_point() + 
  geom_point(aes(x = Temp, y = maxTemp, color = maxEst))

p1
```

#### Conclusion

Max/min temp are reasonably well-modeled as linear in `Temp + Elev`; we'll impute with this model just to get things going.


### Dew point and RH

Temp and DewPoint are highly correlated

```{r}
cor(weather$Temp, weather$DewP, use = "pairwise.complete.obs")
qplot(Temp, DewP, data = weather)
dewPoint <- lm()
```

relative humdidty is ... not

```{r}
qplot(Temp, RH, data = weather)

```