Summary
For complete details and codes, see the display-friendly pdf below
There has been ongoing data collected concerning climate change, we are here to evaluate the seriousness and velocity of those changes.
Data related to drought, heavy rain and sea level has been analysed and predictions were given for the near future.
Predicting sea level is important because it helps us understand and prepare for the impacts of climate change on coastal communities and infrastructure. Rising sea levels can cause coastal flooding, erosion, saltwater intrusion into freshwater aquifers, and other environmental and economic consequences. Accurate sea level predictions allow governments, businesses, and communities to plan and adapt to these impacts, reducing the risk of harm to people and property.
Model Reasoning
For time series like climate data, it is highly unlikely we can use simple models such as linear regression
But we also would not want to rely on complex models such as neural networks
We want to enable a level of interpretation that is helpful to draw a conclusion on climate change, which is why our focus would be Autoregressive and Moving Average models.
Random walk with drift or Deterministic trend?
A random walk has infinite variance, while a deterministic trend has finite variance. It can be incredibly useful to know the nature of a series.
A time series that is increasing may either be a Random walk with drift or Deterministic trend.
The Dicky-Fuller test will help us find out. For more details see the pdf below.
For example, discovering a weather pattern is a deterministic trend may help the government plan the future with more certainty.
Normalization
The official method of normalization is described but formula is not given
There maybe a 10% inconsistency from the (X-E)/S formula but this is negligible
For example, Sea level has an average of -7024.94 and standard deviation of 39.0834
Findings
| Climate Data | Concluding Description | Applied Models |
|---|---|---|
| Consecutive Dry Days | Has periods of high and low volatility, but in general it is stationary | Series: MA(10) Residuals: ARCH(5) |
| Maximum 5-Day Rainfall | A random walk with a small drift component | ARIMA(0, 1, 1) |
| Sea Level | Deterministic trend since year 2000 | Series: Deterministic Trend Residuals: ARMA(1, 7) |
Surprisingly, we didn’t find much systematic trends on drought and heavy rainfall. But we did find that sea level has been increasing at 0.035906 * 4 * 39.0834 = 5.5367052 milimeters per year.
Since 1993, however, average sea level has risen at a rate of 0.12 to 0.14 (about 3.302 milimeters) inches per year
Our result is much higher than what is mentioned by United States Environmental Protection Agency. This difference would eventually come down to the solidarity of data, the choice of data, and timeframe of analysis.
I do, however, believe in my own analysis and this could be an indication of how variable different research’s sea level analysis could be.
Nevertheless, this gives us confidence that the sea level changes are not far from the 4 milimeters range in a meta-review sense.
Seletected Visualizations
Here you can see the rainfall data, forecasted in a way that has expanding variance along time. This is the characteristics of a random walk.
Here you can see the stationary part of the sea level (made up of trend and stationary component), it is expected to stay within a fairly stable range as forecasted below.
In my own opinion, ARIMA-type forecasts are most useful in perceiving general direction and it is useful to look at the upper and lower bounds, but it might not be useful for accurate forecasts. SARIMA, in contrary, are more useful in predictions, if indeed the data is seasonal.
Detailed Document
The complete details and codes are provided below