xs_calcs.R

library(tidyverse)

prep_xs <- function(data, sta, elev, delta_x=0.1) {
  data %>%
    arrange({{sta}}) %>%
    mutate(sta = {{sta}}) %>%
    complete(sta = seq(from = min({{sta}}), to = max({{sta}}), by = delta_x)) %>%
    mutate(gse = zoo::na.approx({{elev}}, x = sta)) %>% 
    select(c(sta, gse))
}

calc_xs <- function(data, water_elev) {
  data %>% 
    arrange(sta) %>%
    mutate(wse = case_when(water_elev > gse ~ water_elev),
           delta_x = abs(lag(sta, 1) - sta),
           delta_z = abs(lag(gse, 1) - gse),
           depth = wse - gse, 
           hyp_length = sqrt(delta_x^2 + delta_z^2)
    ) %>%
    filter(!is.na(wse)) %>% 
    summarize(thalweg_elevation = min(gse),
              water_surface_elevation = water_elev,
              max_depth = water_surface_elevation - thalweg_elevation,
              cross_sectional_area = sum(delta_x * depth),
              wetted_perimeter = sum(hyp_length),
    ) %>% 
    as.list() %>% 
    list_flatten()
}

plot_xs <- function(data, water_elev) {
  data %>% 
    arrange(sta) %>%
    mutate(wse = case_when(water_elev > gse ~ water_elev)) %>%
    ggplot(aes(x = sta)) + 
    geom_line(aes(y = gse)) + 
    geom_line(aes(y = wse))
}

solve_xs <- function(data, discharge, slope, mannings_n, delta_y=0.1) {
  depth_vs_wse <- seq(from=min(data$gse)+delta_y, to=max(data$gse), by=delta_y) %>% 
    as_tibble() %>%
    mutate(result = map(value, function(x){calc_xs(data = data, water_elev = x)})) %>% 
    unnest_wider(col = result) %>%
    drop_na()
  wse_vs_discharge <- depth_vs_wse %>% 
    mutate(discharge_cfs = 1.486 * cross_sectional_area * (cross_sectional_area / wetted_perimeter)^(2/3) * slope^(1/2) * mannings_n^(-1)) %>%
    bind_rows(tribble(~selected_water_level, ~discharge_cfs, TRUE, discharge)) %>%
    arrange(discharge_cfs) 
  wse_vs_discharge %>%
    mutate(output_wse = zoo::na.approx(water_surface_elevation)) %>%
    filter(selected_water_level) %>% 
    pull(output_wse)
}