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Glacier Calving in Svalbard with fdmr

Tian Li, Amin Shn, Ruitang Yang, Wenxue Cao

Source: vignettes/calving_tutorial.Rmd
calving_tutorial.Rmd

Introduction

This tutorial will guide you through the process of performing a simple linear regression using the inlabru and fdmr packages in R.

Loading the INLA Package

Load the necessary packages as follows:

The Data

  • For this tutorial, we will use a dataset including envrionmental variables measured in Svalbard. Specifically we want to check the controlling climatic parameters for calving front variability (length change) of tidewater glaciers in Svalbard.
  • We use six tidewater glaciers to demonstrate this
  • Variables include surface runoff, surface mass balance, surface meltwater production, air temperature, sea surface temperature, subsurface ocean temperature

The location of the tidewater glaciers are shown below.

# Firstly retrieve the data
calving_data <- read.csv("4DM_Calving_NEW.csv")

# visualize the glacier location
glacierNames <- unique(calving_data[c("glacierName")])
lats <- unique(calving_data[c("latitude")])
lons <- unique(calving_data[c("longitude")])

glac1 <- list(longitude = lons[0, ], latitude = lats[0, ], label = glacierNames[0, ])
glac2 <- list(longitude = lons[1, ], latitude = lats[1, ], label = glacierNames[1, ])
glac3 <- list(longitude = lons[2, ], latitude = lats[2, ], label = glacierNames[2, ])
glac4 <- list(longitude = lons[3, ], latitude = lats[3, ], label = glacierNames[3, ])
glac5 <- list(longitude = lons[4, ], latitude = lats[4, ], label = glacierNames[4, ])

glac6 <- list(longitude = lons[5, ], latitude = lats[5, ], label = glacierNames[5, ])

points <- list(glac1, glac2, glac3, glac4, glac5, glac6)
markers <- dplyr::bind_rows(points)

fdmr::retrieve_tutorial_data(dataset = "hydro")
## 
## Tutorial data extracted to  /home/runner/fdmr/tutorial_data/hydro
norway_polygon_path <- fdmr::get_tutorial_datapath(dataset = "hydro", filename = "Kvilldal_Catch_Boundary.geojson")
norway_polygon <- sf::read_sf(norway_polygon_path) %>% sf::st_zm()
sfc <- sf::st_transform(norway_polygon, crs = "+proj=longlat +datum=WGS84")
fdmr::plot_map(polygon_data = sfc, markers = markers, polygon_fill_opacity = 0.5)

Simple Linear Regression Model

We will model Calving’s front change using three important factors namely: surface runoff (mmWE/day), 3m air temperature (°C), sea surface temperature (°C).

Model Specification

We specify the model using a formula and the inla function.

formula <- fc ~ 0 +
  f(id.loc0, model = "iid") +
  f(id.loc0, RU, model = "iid") +
  f(id.loc0, AT, model = "iid") +
  f(id.loc0, SST, model = "iid")

# Fitting INLA
inla_fit <- inla(formula, family = "gaussian", data = calving_data, control.predictor = list(compute = TRUE))

Results

We can now examine the results of our INLA model.

fdmr::summary(result)

fdmr::plot(result)

Diagnostics

Checking the diagnostics of the model fit is an important step. We can plot the residuals to check for any patterns that might suggest a poor fit.

fdmr::pred_vs_obs(result)

fdmr::pred_vs_obs_over_time(result)