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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.