Glacier Flow Modeling in Elwha and Quinault Basins
This MATLAB codebase is dedicated to simulating the flowlines of Olympic mountain glaciers in the Elwha and Quinault basins. It aims to provide an insightful analysis of the behaviour and evolution of glaciers in these basins.

The geometry of the glacier in this model is built upon the approximations provided by Professor Alison Anders (UIUC, Feb '21), while the mass balance computations are conducted following the methodology introduced by Professor Gerard Roe (Feb '21).

1) Parameters
The following parameters form the foundation of the glacier model:

rho: This denotes the density of ice (kg/m^3), a critical factor for glacier physics.
g: This represents the acceleration due to gravity (m/s^2), vital for calculating the force acting on the glacier.
n: The exponent in Glen's flow law, which is used to describe how ice deforms under stress.
gamma: Standard lapse rate (K/m), indicating the rate at which atmospheric temperature decreases with an increase in altitude.
fd: Deformation parameter (Pa^-3 s^-1), which encapsulates how the glacier's shape changes over time.
fs: Sliding parameter (Pa^-3 s^-1 m^2), representing the basal sliding of glaciers, a crucial part of glacier dynamics.
x: Distance along the glacier (m), defining the glacier's geometry and spatial scope.
h0: Initial glacier height (m), which serves as the starting point for the model's evolution.
delx: Grid spacing along the glacier (m), setting the spatial resolution for the simulation.
ts: Starting time (yr) for the model, indicating the commencement of the simulation.
tf: Final time (yr) for the model, indicating when the simulation stops.
xb_dat, zb_dat, wb_dat: These are the distances (m), elevations (m), and widths (m) of the glacier respectively, which describe the shape and profile of the glacier.
theta_dat: Angle of glacier sides, further detailing the geometric structure.
mu: Melt factor (m/yr /degC of melt-season temperature), necessary for determining the ice melt based on temperature changes.
Ptop: Annual accumulation at the top of the basin (m/yr), which feeds into the mass balance of the glacier.
down_basin_drying: Fraction of basin top precipitation at the bottom of the basin, giving an insight into the basin's climate patterns.
P_0: Basin precipitation adjusted for glacial drying, which accounts for changes in precipitation due to glacier-related climatic factors.
Tz0: Sea-level temperature (degC), a base value for the atmospheric temperature profile.
glacial_drying: Original precipitation is scaled by this factor (GDF), showing how precipitation may be altered due to the presence of the glacier.

2) Input Files
The initial condition of the model is determined by the glacier profiles encapsulated in either the "Elwha_Basin_Input.mat" or "Quinault_Basin_Input.mat" files. These files contain multidimensional arrays or matrices representing various physical attributes of the glaciers, such as elevation, width, angle of sides, and more. These serve as the model's input parameters, establishing a 'snapshot' from which the model initiates its simulation.

It's essential to verify the existence and correct location of these input files before running the model. The MATLAB working directory should either contain these files or the code should include appropriate paths to their location.

3) Climate Parameters
The climate parameters play a vital role in this model. The glacier's temperature is calculated as a function of its surface height. This is based on the sea-level temperature (Tz0) and a standard lapse rate (gamma), which represents the temperature drop per unit increase in altitude.

The mass balance of the glacier, i.e., the difference between accumulation and ablation, is a key part of this model. Accumulation mainly refers to snowfall, represented by precipitation (P), and ablation refers primarily to melting, which is computed using the melt factor (mu) and temperature data.

4) Time Loop
The core of the computational component of this model is a time-stepping loop, simulating the glacier's evolution over a given time span. It initializes arrays for thickness, flux, and height of the glacier, with the height array starting from the initial glacier height (h0).

At each time step, the model first computes the climatic conditions, primarily the temperature and precipitation. Then, it calculates the mass balance for that time step. Subsequently, it updates the height and flux arrays accordingly, reflecting the changes in the glacier's structure over time.

This loop repeats until it reaches the final time (tf), at which point the model outputs the final glacier height (h) along with other glacier parameters.

How to Use the Code
Ensure MATLAB is Installed: This is a MATLAB-based model, hence you need MATLAB software installed on your machine.

Prepare the Input Files: Ensure the "Elwha_Basin_Input.mat" or "Quinault_Basin_Input.mat" files are available and correctly placed in the MATLAB working directory or provide the code with appropriate paths to these files.

Set Parameters: Before running the model, set or adjust the parameters in the code as needed. Parameters include rho, g, n, gamma, fd, fs, x, h0, delx, ts, tf, mu, Ptop, down_basin_drying, P_0, Tz0, glacial_drying, and data parameters (xb_dat, zb_dat, wb_dat, theta_dat). Update these values with the most accurate data available.

Run the Model: Execute the main script in the MATLAB command window. It's advisable to monitor the output and computational performance during the first few runs to ensure the model is working as expected.

Interpret the Outputs: Upon completion, the model will output the final glacier height (h) along with other glacier parameters. Analyze these in the context of your study or compare them with empirical data to validate the model's accuracy and performance.

5) Notable Papers
To better understand the scientific background and principles used in this code, we recommend the following papers:

Andreson et al., 2006: Provides key insights into glacier modeling, from which the basis of this code was derived.
Roe and O'Neal, 2011: Offers a comprehensive understanding of glacier mass balance, crucial for interpreting the results of the model.
Oerlemans, 1997: Presents in-depth knowledge of glacial climate parameters and their impact on glacier evolution.


*Always remember to double-check your parameters and inputs, and interpret your results carefully in light of existing scientific knowledge and empirical data. Happy modeling!