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Lake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesLake TemperaturesMohammed Darvesh
Outline
We are given fortnightly data on the surfacetemperature of lakes in the Lake District from1947-2013.
The lakes of interest are Esthwaite, Blelham andWindermere (North and South).
Our aim is to detect any trends, abnormalities andcorrelations.
The research will be useful for enhancements intowater quality and improving understanding of thelakes ecosystems.
Introduction
To begin our analysis, we will look at Esthwaite beforeapplying our methods to the rest of the lakes.
We will look at the extreme values and then analysethe effects of NAO (North Atlantic Oscillation) andrainfall on the lake temperatures.
Finishing with forecasting and comparisons with otherlakes.
Exploring the data
Esthwaite Blelham North-W South-WMin 0.25 0.24 1.38 1.17
Mean 10.73 10.78 10.65 10.84Max 24.84 24.09 23.42 23.81
Strong seasonal pattern.
Statistically significant temporal trend with gradientof 0.0007.
This means that there has been an approximately0.05°C increase in temperature over the period.
Surprisingly, March 1947 is the coldest recordedtemperature.
The data are non-stationary. Hence methods suchas differencing will need to be used whenimplementing time series models.
Minimum Temperatures
We can observe that there has been a trend inincreasing minimum temperatures over the 67-yearperiod.
We also found that maximum temperatures havenot changed significantly over the period.
When looking at the months the minimumtemperatures occurred, we can see March had moreoccurrences than December. Whilst February hadthe most.
Effects of NAO
NAO, formally known as North Atlantic Oscillation,is the difference of atmospheric pressure at sealevel.
We find that that the correlation with the wholedata is very small, whereas comparing by season,the data are much more correlated.
Effects of Rainfall
The data shows that the largest correlationcoefficient, -0.654, occurs at 121 days of rainfallaccumulation.
The data shows that there is more rainfall in thewinter.
There is also a hint that suggests rainfall isincreasing over time.
Forecasting
Using time series analysis, we created the optimalforecast for Esthwaite water temperature.
This was done by looking at different processes likeAutoregressive (AR) and Moving Averages (MA),including combinations of the two with/withoutdifferencing or seasonal differencing (ARMA,ARIMA and SARIMA).
The forecast we decided on was the SARIMA withseasonal differencing of 26, seasonal moving averageof 2, AR (2) and MA (1).
Table of optimal models:
AR I MA SAR SI SMA SBlelham 1 0 0 1 0 0 26
Windermere N 2 0 0 1 0 0 26Windermere S 1 0 0 1 0 0 26
All models have a seasonal difference correspondingto a years’ data.
Models for Windermere North and South aredifferent.
Applying to other lakes
We found that the lakes are strongly correlated witheach other, as expected.We compare the other lakes with NAO during thewinter from seasonal averages across December,January, February and March.
Conclusion
We have found a suitable time series model toforecast lake temperatures for Esthwaite.
We have also discovered relationships between NAOand rainfall with respect to temperature.
Furthermore, we are seeing a rise in minimumtemperatures and a small increase of overalltemperatures over time- giving evidence to theoriesof global warming.
Further Work
Producing a better time series model of the lakes.Since data are collected fortnightly, some years havean extra observation, and this may affect the model.
Put together a model that incorporates rainfallaccumulation and NAO.
Check whether rising minimum temperatures isoccurring in other lakes in the Lake District andelsewhere in the UK.
