## 1 Introduction
This commonality is the reduction of what is in the final analysis, a three- dimensional (3-D) spatial phenomena being projected down to a zero-dimensional (0-D) spatial value for the terminus location to evaluate the distance the glacier has advanced/retreated along its path of motion. This dimensionality reduction provides a level of efficiency in the analysis of the glacier motion and is a useful model simplification when it is appropriate. A comparison of standard methods including the center-line, bow, rectilinear-box, curvilinear-box, and extrapolated is provided by [PERSON] et al. 2014. Each of the above-mentioned methodologies is subject to its own advantages and weaknesses and the use of any one of the methods involves considerations of glacial geometry along with the aim of the study being undertaken [10]. Other work applies a more general approach to terminus estimation which relies heavily on optical imagery. An advantage of which is to avoid specific geometric dependencies of a particular glacier. The method exploits the properties of the multiband attributes of satellite imagery and the flexibility of Nonparametric Regression [7]. Taking advantage of the return times of the LANDSAT satellite platform, this method uses selected spectral bands of the images to identify which regions of the spectrum produce the largest intensity changes along the path of the glacier. This intensity change is indicative of the transition from soil, vegetation, and debris of the mountain landscape to the ice of the glacier. These intensity changes are collected through time as this process is repeated on a series of images. On each image a glacier path is manually drawn, this path is simply a hand drawn curve. Then along the length of this path the intensity of each pixel is collected. Using the derivatives and the inflection points of the collected intensity values to identify the terminal points of the glacier, the method can capture the glacier movement against a ground truth, based on direct measurements. A major drawback to this method is its dependency on an investigator drawing the path of the glacier manually. As was mentioned previously this would make the method problematic in large scale glacier networks, or global glacier studies. It would also prevent, in its current state, an automated implementation given the dependency on a human drawn path to derive the intensity profile. It is with the final goal of limiting or eliminating manual input that this papers current methodology was developed. In addition to increasing ease  
Figure 2: **(Left panel)** Illustrative Terminal point identification methods. Top: (left) Center-Line method; (middle) Bow method (right) Rectilinear Box method. Bottom: (left) Curvilinear Box method; (right) Extrapolated Center-Line method. (**Right panel**) Illustrative Terminal point tracking method. of automation, robust and flexible models for estimating glacier variations in response to global and local climate factors is developed by either detection of the glacier terminal point or quantification of the glacier area. The objectives of this research are to implement a generic method for quantifying glacier area and locating its terminus and model their variations in response to climate factors using both parametric and nonparametric supervised techniques. The geometry of individual glaciers has been estimated using remote sensing techniques to include various semi-automated image analysis techniques such as supervised classification, edge detection, and region segmentation in an attempt to develop a pipeline for quantification of glacier changes that could be potentially applicable to a large set of glaciers around the globe.