In the last blog post, I went into specifics on how I have measured the rifts. Here, I will talk about how I have observed the Amery Ice Shelf to be changing over time.

As a refresher, below is an image of the Amery Ice Shelf that was made by overlaying on Python an image from 2010 and another from 2018. The yellow portions of it indicate the parts of the Amery Ice Shelf that have been changing over time.

Figure 1: changes in the Amery Ice Shelf from 2010 to 2018

__Overall Trends__

As is shown in figure 2.1, the rift is getting wider over time, and the midpoint of the width is shifting to the northeast. As is shown in figure 2.2, the rift is getting longer over time, and the endpoint of the length is generally shifting northwest. However, the rift appeared to lengthen significantly within the winter 2012 season, which

Figures 2.1 and 2.2: Changes in rift width and length, respectively, over time

Figure 3 shows four crucial rift measurements plotted over time. As can be seen, I have included various best-fit lines and curves in these graphs. The process of obtaining these best fits is explained in the following section.

Figures 3.1-3.4: Plots of variables of interest over time

__Regressions__

After plotting all these points, I tried to examine overall trends and patterns in the graphs. To do so, I fitted on each graph a linear, exponential, logarithmic, and power function through Excel, and I recorded their accompanying correlation coefficients. The following values were obtained, with the highest correlation coefficient in each data set bolded and italicized.

Widths | Width Midpoint Shifts | Lengths | Length Endpoint Shifts | |

Linear trend | 0.9464 | 0.9986 |
0.9661 |
0.9767 |

Logarithmic trend | 0.5155 | 0.7759 | 0.8219 | 0.596 |

Exponential trend | 0.9593 |
0.8006 | 0.7142 | 0.9087 |

Power trend | 0.6329 | 0.9978 | 0.9608 | 0.8091 |

As can be seen from the above table, most of the best-fit lines are linear. As such, the data and graphs suggest that the rates of change in rift length, length endpoint position, and width midpoint position have been roughly the same since at least 2001. The rift width is the measurement that’s rate of position change has most likely not remained constant since 2001. It is also evident that the width midpoint shifts and lengths over time could also be modeled well with the power function, as their correlation coefficients differ by less than 0.01. Nevertheless, the only data set I chose to model non-linearly was the widths over time.

In the equations below, note that “x” represents the number of days since 1/1/2001, and “y” represents the corresponding data set of interest in meters. Also note that these equations might change, as I might revise them to include data from the Landsat satellite and/or other sources.

Data set | Best-fit equation |

Widths | y = 1.1992168110015 e^{0.000252156397473x} |

Width midpoint shifts | y = 0.003531107969x – 0.064263624599 |

Lengths | y = 0.004887396812x + 0.795232275191 |

Length endpoint shifts | y = 0.002879858183x + 1.332537375363 |

__Other Observations__

Another thing I noticed through eyeballing the graphs of rift length and length endpoint is that while the overall 2-decade trend is most likely linear, there might be other trends embedded within the overall trends. For each of these graphs, I split the data points up into three time intervals: 2001-2007; 2007-2013 (first half of 2013); and 2013-2019 (second half of 2013). With each of these, I then repeated the process of testing out regression equations and finding the one with the highest correlation coefficient.

Figures 4.1 and 4.2: Plots of length measurements split up into three intervals

Below are the correlation coefficients I obtained for the rift lengths in each time interval:

Lengths: 2001-2007 | Lengths: 2008-2013 | Lengths: 2013-2019 | |

Linear trend | 0.9472 | 0.8772 | 0.924 |

Logarithmic trend | 0.5377 | 0.8307 | 0.9145 |

Exponential trend | 0.9735 |
0.9048 |
0.9356 |

Power trend | 0.6701 | 0.8705 | 0.9311 |

Endpoints: 2001-2007 | Endpoints: 2008-2013 | Endpoints: 2013-2019 | |

Linear trend | 0.9668 |
0.8309 | 0.9339 |

Logarithmic trend | 0.7552 | 0.8017 | 0.9171 |

Exponential trend | 0.8838 | 0.8529 |
0.9537 |

Power trend | 0.9592 | 0.8313 | 0.9434 |

When split up into these three time chunks, it appears that the data can best be modeled with exponential, rather than linear, equations. Thus, while most overall two-decadal trends are likely linear, there could exist other trends embedded within the overall trend.

Similar to the previous best-fit equations table, note that “x” represents the number of days since 1/1/2001, and “y” represents the corresponding data set of interest in meters. Also note that these equations might change, as I may, in the future, revise them to include data from the Landsat satellite, and/or adding in data from other sources.

Data set | Best-fit equation |

Lengths: 2001-2007 | y = 2.531246757670 e^{0.000760775188x} |

Lengths: 2008-2013 | y = 4.613242316488 e^{0.000362826084x} |

Lengths: 2013-2019 | y = 11.017525959676 e^{0.000169141280x} |

Midpoints: 2001-2007 | y = 0.004481479544x – 0.603884594986 |

Midpoints: 2008-2013 | y = 5.795148826366 e^{0.000199377559x} |

Midpoints: 2013-2019 | y = 4.481513328281 e^{0.000234047062x} |

__Seasonal Trends__

While there are overall decadal trends that can be observed, there are also possible seasonal fluctuations that influence the rate of rift propagation. I had hypothesized that the rift propagates quicker in the summer and slower in the winter, due to how surrounding temperatures fluctuate within a year.

To explore seasonality, I calculated the rates of rift widening; rift midpoint position change; rift lengthening; and rift length endpoint position change between each spring and fall season that had seasonal data available.

I then performed an ANOVA test to determine whether or not a statistically significant difference between rates existed. However, because my F-critical value was always significantly lower than my F-statistic, I failed to find any statistically significant seasonal variability.

Figure 5: An example of ANOVA, with data of rift midpoint shift rates

Due to the limited sets of images and lack of statistically significant tests, seasonal variability is not something that I will continue investigating in this research project.

In the future, I might further investigate the dynamics of the AIS rift propagation by examining more satellite images and/or compiling others’ data sets. In the rest of my blog posts, however, I will move on from exploring the HOW to exploring the WHY behind this rift propagation.

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