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Time Series Analysis and ARIMA Forecasting Modeling of Antarctic Glacier Melting Rate (2022-US-EPO-1120)

This STEM paper studies the time series Antarctic glacier mass from April 2002 to March 2021. The objective of this paper is to forecast the Antarctic glacier mass level for 2021-2041. Among four STEM components: Science is geoscience of the glacier; Technology is using the GRACE-FO satellites to collect glacier ice sheet mass data; Engineering would focus on the COVID-19 factor on the glacier melting rate, and mathematics is mainly on time series ARIMA models. Both non-seasonal and seasonal ARIMA models were studied and compared. Both the 12-month seasonal pattern and long-term year-to-year trend were significantly observed. The glacier melting rate was 2% faster based on the seasonal ARIMA model. Smoothing models were also significantly identified in the seasonal ARIMA model to smooth out the random noise component to enhance the time series trend and the seasonal component to enhance the forecasting model. Forecasting glacier melting for 2021-2041 would be a challenging task to address both seasonal and trend components for a longer horizontal time from today. The prediction interval would become too wide to predict the future glacier melting rate, if more than 5 years away. The seasonal ARIMA model could provide a better fit than the non-seasonal ARIMA model. STEM methodology is a powerful and holistic way of conducting scientific research projects by modern GRACE-FO Technology in a practical engineering sense through a mathematical ARIMA forecasting analysis.

Hi, everyone.

I'm Mason.

T oday, I'll be presenting a study

on Antarctic glacier melting rate using time series platforms.

The motivation behind this project was that we wanted to investigate

the long- term effects of climate change,

and we targeted places most affected by global warming,

which are Antarctica and Greenland.

Previously, we tried using smoothing and decomposition techniques

to study and forecast the glacier melting rate.

But many of those models had quite important limitations.

For example, they were unable to consider the seasonal or trend pattern.

To improve the forecasting accuracy and precision,

we wanted to try other methods, such as the ARIMA model,

which is our main focus for today.

The objective of this presentation is to utilize time series platforms in JMP

to examine the glacier melting mass data from 2002 to 2021,

and to forecast the glacier melting rates for the next 20 years.

Why are we studying glacier melting rates

instead of, for example, atmospheric temperature?

Should we study the Greenland ice sheet or the Antarctic ice sheet?

We'll be studying the Antarctic data because the rate

a t which the Thwaites glacier in Antarctica is melting

has been rapidly increasing in the past years

in terms of the surface height.

The Thwaites glacier is significant

because it is the broadest glacier in the world

and already contributes to 4% of global sea level rises.

But what's more concerning is that recently, in 2021,

scientists found that there was more warm water

underneath the glacier than previously thought,

which could have even more dire consequences

in terms of further contributing to sea level rises.

We want to help forecast

the Antarctic glacier melting rate to inform the public

about the effects of global warming and bring more awareness

to the problem that climate change can cause.

We got our data from the NASA website, as shown on the right,

and we transformed the data into JMP, as you can see on the left side.

Now, the Antarctic mass is measured in giga metric tons,

and 1 metric ton is equal to 1,000 kilograms.

When you get metric ton, it's equal to 10¹² kilograms.

The GRACE-FO mission, which is where th is data was collected,

measures the mass variation.

It's not the total mass,

which is practically impossible to measure,

but the change in mass relative to April 2002,

when the GRACE mission started tracking glacier mass variation.

Previously, as I said,

we use the smoothing anti- composition models,

but these techniques either fail to consider

the nonlinear downward trend in glacial mass

since the glacier melting rate is increasing over the years,

or these models failed to consider the seasonal variations.

Warm months are going to have a faster melting rate.

We wanted to use the ARIMA model

because we hope to improve the trend so that it is nonlinear

and also incorporates the seasonal component at the same time.

We also hope that the ARIMA model

can help further narrow the prediction interval

so that our forecasts are more precise.

There's two types of ARIMA models.

There's nonseasonal and seasonal.

The nonseasonal ARIMA model

does not consider that there is a seasonal pattern,

while the seasonal ARIMA model emphasizes that there is a seasonal component

before the model is generated.

The nonseasonal ARIMA model,

it does implement decomposition and searches for a seasonal component,

but it has no knowledge of the seasonal lag period

which should be 12 months before it generates a model.

Now, glacier mass variation should have a seasonal pattern

because we expect glaciers to melt faster during the summer months

and accumulate during the winter months.

But from a previous preliminary time series analysis,

we do not see an obvious lag period of 12 months.

We aren't really sure what the optimal seasonal width is

because of growing weather inconsistencies as a result of global warming.

Without specifying what our seasonal lag is,

we can't use the seasonal ARIMA model.

It's also common practice to use the non seasonal ARIMA model

to verify that lag period, and then run the seasonal ARIMA model

once we know what the seasonal lag would be.

First, we'll run the non seasonal ARIMA model

to confirm the seasonal lag period is indeed 12 months.

Then, we'll implement the seasonal ARIMA model

based on the optimal seasonal lag

to better forecast the glacier melting rate

in the next 20 years.

If you look at the model results for (0, 1, 0)

which is the best nonseasonal model,

you can see that the slope is not significant.

The p-value is 0.18, and the parameter estimate is -10.42.

Every year, the glacier mass is forecasted to decrease at about 10 giga metric tons.

However, this model is not significant,

which may indicate that we need to use a seasonal model.

We see that 12 has the highest auto correlation

for lags greater than zero on this right graph.

The auto correlation plot further confirms

that we should be using a seasonal lag of 12.

After running the non seasonal ARIMA model,

we wanted to compare the (0, 1, 0) nonseasonal model

and the best seasonal model.

The nonseasonal ARIMA model is shown in dark pink

and the seasonal ARIMA model is shown in light pink.

The colors are a bit similar here.

But you can see

that the prediction interval for the seasonal model is much wider

than the nonseasonal model,

and the prediction interval from the seasonal model

reflect the seasonal pattern.

Interestingly, the overall trend for the seasonal model

is much steeper than the nonseasonal model,

which may indicate

that if we do not decompose the seasonal component,

then the seasonal pattern may end up being a random noise factor

which will dilute the signal

and make the slope less steep than it should be.

The prediction interval for the seasonal ARIMA model is larger,

most likely because it considers the seasonal variation,

which is another factor of uncertainty.

However, we do not want to see the seasonal pattern in the forecasts

since we want to predict the glacier mass variation for each month,

not just each year.

If you look at the ACF graphs on the bottom left,

the seasonal ARIMA model has a much smaller peak

at of seasonal lag of 12, which is right over here,

than the non seasonal ARIMA model, which is on the right.

It's hard to see because the graphs are overlapping,

but for the season al ARIMA model, the auto correlation is approximately zero

for residuals greater than zero

which shows that we chose a good lag period.

Also, from the table on the right, the MA2, 12 is significant,

which once again shows that 12 is a good choice

for the seasonal lag.

M A2, 12 would be the seasonal model at a seasonal lag of 12 months.

In conclusion, we applied nonseasonal and seasonal ARIMA models

to forecast the Antarctic glacier melting rate

in the next 20 years.

While the nonseasonal ARIMA model can predict

the general downward trajectory of glacier mass variation,

it fails to consider the seasonal pattern in the forecasts.

The seasonal ARIMA model can forecast the seasonal and trend behaviors,

but it's prediction interval is much larger.

The seasonal ARIMA model also has a slope that is 20% steeper

than the slope found from the non seasonal ARIMA model.

That's all I have for today.

Thanks for listening.

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