Global Sea Ice EDA and Analysis
Jack Rabe
4/28/2022
Modeling temporal trends in global and hemispheric sea ice change
Since it appears we have a declining trend in sea ice by year, let’s make some simple linear models to estimate annual trends in sea ice and predict when sea ice will disappear. Model summaries, residual vs fitted plots, and fitted model plots are all in order from global to northern hemisphere to southern hemisphere.
##
## Call:
## lm(formula = mean_ice_extent ~ Year, data = global_ice_year.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0262 -0.3830 -0.0058 0.3960 1.2481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 121.21108 12.45421 9.73 0.0000000000032 ***
## Year -0.04912 0.00623 -7.89 0.0000000009479 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.507 on 41 degrees of freedom
## Multiple R-squared: 0.603, Adjusted R-squared: 0.593
## F-statistic: 62.2 on 1 and 41 DF, p-value: 0.000000000948##
## Call:
## lm(formula = mean_ice_extent ~ Year, data = nohem_ice_year.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5010 -0.1687 0.0225 0.1707 0.3300
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 119.55461 5.33322 22.4 <0.0000000000000002 ***
## Year -0.05409 0.00267 -20.3 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.217 on 41 degrees of freedom
## Multiple R-squared: 0.909, Adjusted R-squared: 0.907
## F-statistic: 411 on 1 and 41 DF, p-value: <0.0000000000000002##
## Call:
## lm(formula = mean_ice_extent ~ Year, data = sohem_ice_year.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9825 -0.2006 0.0013 0.1675 1.0565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.67151 10.20383 0.16 0.87
## Year 0.00496 0.00510 0.97 0.34
##
## Residual standard error: 0.415 on 41 degrees of freedom
## Multiple R-squared: 0.0226, Adjusted R-squared: -0.00127
## F-statistic: 0.947 on 1 and 41 DF, p-value: 0.336
When will sea ice disappear from the earth globally and in each hemisphere?
Based on these simple linear models, if mean annual sea ice trends continued at the same rate as they have since 1979, we would predict that average sea ice extent will reach 0 in the northern hemisphere by the year 2210, and it will reach 0 globally and, thus, in the southern hemisphere, by the year 2468.
Let’s calculate the duration of sea ice expansion and and recession for each year
Now make plots showing trends in days if increasing and decreasing ice
Now make make plots looking at sea ice anomaly data
It looks like global anomalies in sea ice are mostly driven by the northern hemisphere sea ice as opposed to the southern hemisphere. Let’s run some simple linear models to check it out. Summaries, resid vs. fitted, and best fit model plots shown as southern hemisphere first, then northern hemisphere.
##
## Call:
## lm(formula = global_anomaly ~ sohem_anomaly, data = total_ice.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.692 -0.546 0.113 0.594 1.571
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2739 0.0348 -7.87 0.000000000000021 ***
## sohem_anomaly 0.8863 0.0625 14.19 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.791 on 514 degrees of freedom
## Multiple R-squared: 0.281, Adjusted R-squared: 0.28
## F-statistic: 201 on 1 and 514 DF, p-value: <0.0000000000000002
##
## Call:
## lm(formula = global_anomaly ~ nohem_anomaly, data = total_ice.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1877 -0.3161 -0.0229 0.3070 1.8240
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0205 0.0259 -0.79 0.43
## nohem_anomaly 0.9434 0.0309 30.49 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.557 on 514 degrees of freedom
## Multiple R-squared: 0.644, Adjusted R-squared: 0.643
## F-statistic: 930 on 1 and 514 DF, p-value: <0.0000000000000002
As expected from an earlier visual assessment of anomaly data, the model with northern hemisphere anomaly explains 64.3% of variation in global anomaly data, relative to only 28% explained by the southern hemisphere anomalies. Also, based on the residuals vs. fitted plot for the southern hemishpere anomaly, it might be better to explore some nonlinear options for model fitting and to satisfy model assumptions (equal variance and normality in the residuals). But for the sake of this project, we’ll keep it simple
Modeling relationship between sea ice change and sea level rise
Let’s look at modeling the effect of global sea ice on global sea level
##
## Call:
## lm(formula = mean_sea_level ~ global_ice + poly(global_ice, 2),
## data = sea_levelandice.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.263 -0.762 -0.203 0.531 2.495
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.868 5.545 2.86 0.0075 **
## global_ice -0.454 0.285 -1.59 0.1212
## poly(global_ice, 2)1 NA NA NA NA
## poly(global_ice, 2)2 1.672 1.040 1.61 0.1181
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.04 on 31 degrees of freedom
## Multiple R-squared: 0.142, Adjusted R-squared: 0.0864
## F-statistic: 2.56 on 2 and 31 DF, p-value: 0.0934##
## Call:
## lm(formula = mean_sea_level ~ global_ice_change + poly(global_ice_change,
## 2), data = sea_levelandice.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.859 -0.656 -0.208 0.559 2.352
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.037 0.170 41.31 <0.0000000000000002 ***
## global_ice_change 0.116 0.210 0.55 0.5839
## poly(global_ice_change, 2)1 NA NA NA NA
## poly(global_ice_change, 2)2 2.866 0.993 2.89 0.0071 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.993 on 31 degrees of freedom
## Multiple R-squared: 0.218, Adjusted R-squared: 0.167
## F-statistic: 4.32 on 2 and 31 DF, p-value: 0.0222
Suprisingly, aside from a significant quadratic effect of change in sea ice extent on global sea level change, we don’t see and significant effects of sea ice extent on global sea level change, something I did not expect. What might work better in the future is to instead calculate the mean rate of change from year to year (difference in mean global temperature) instead of this running total. Doing so may show different trends.
Monthly sea ice and temperature
Let’s construct some linear models comparing global temperature change with global sea level.
##
## Call:
## lm(formula = global_ice ~ Mean, data = ice_temp_gis.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.227 -2.568 0.848 2.146 4.510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.383 0.287 85.01 < 0.0000000000000002 ***
## Mean -2.571 0.546 -4.71 0.0000033 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.75 on 452 degrees of freedom
## Multiple R-squared: 0.0468, Adjusted R-squared: 0.0447
## F-statistic: 22.2 on 1 and 452 DF, p-value: 0.00000327##
## Call:
## lm(formula = global_anomaly ~ Mean, data = ice_temp_gis.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8921 -0.3729 0.0605 0.4468 1.6615
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6942 0.0694 10.0 <0.0000000000000002 ***
## Mean -1.6366 0.1319 -12.4 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.666 on 452 degrees of freedom
## Multiple R-squared: 0.254, Adjusted R-squared: 0.252
## F-statistic: 154 on 1 and 452 DF, p-value: <0.0000000000000002
From the Q-Q plot, we can see that the residuals do not meet the assumption of being normally distributed in the model comparing temperature with sea ice extent. This suggests we should try alternative models, likely nonlinear, but for the sake of this project, we will not. However, we do see in the case of sea ice anomalies, a much stronger linear trend between global temperature and global sea ice anomalies, indication that increasing temperature is causing more significant (greater magnitude) monthly declines in sea ice extent.
Spatial plots of sea ice
No linear models developed for this stage, just spatial plots