Anomaly Construction in Climate Data : Issues and Challenges

Transcription

1 Anomaly Construction in Climate Data : Issues and Challenges Jaya Kawale*, Snighansu Chatterjee, Arjun Kumar, Stefan Liess, Michael Steinbach and Vipin Kumar University of Minnesota

2 Overview What is Anomaly Construction? Different aspects of anomaly construction Different measures. Different base periods. Impact of choosing the anomaly - Case study of the Sahel dipole. A Generalized approach for Anomaly construction.

3 Motivation Earth Science data has a strong seasonality due to the revolution of the Earth around the Sun. As a result of seasonal patterns in the data other signals in the data like long term decadal oscillations and trends are suppressed. General approach: Create Anomaly by removing monthly mean values from the data. Monthly mean air temperature at Minneapolis for a 20 year period. Anomaly construction is a fundamental problem in climate science.

4 Related Work Climate scientists often use 30 years as a reference interval and compute anomalies w.r.t. it. Many important results and implications are based upon it. For e.g., climate indices are the time series that characterize the behavior of selected regions and are used to characterize factors impacting global climate change. Climate Prediction Centre uses a 30 year moving base to compute these indices. Less common practices involve using a low pass filter or using an EOF analysis. Tingley et al.*, show that using a short reference the variance of the records at that interval is reduced and is inflated elsewhere. *M. Tingley. A bayesian anova scheme for calculating climate anomalies, submitted

5 Different aspects of Anomaly construction Measure of anomaly construction. Mean: Remove the monthly mean value. Z-score: Remove the monthly z-score value. Median: Remove the monthly median value. Jackknife: Consider all points apart from this point itself to remove the monthly mean point. Different time periods of anomaly construction. What base to choose to remove the mean? E.g. climate scientists generally use a 30 year period to compute a base. Entire Time Period Part of the time period

6 Different aspects of Anomaly construction However the manner in which the anomaly is constructed and the base period which is chosen introduces a bias in the results and significantly impacts the discovered patterns. Our study aims to highlight the issues and present a simple approach to handle anomaly construction.

7 Dataset NCEP/NCAR Reanalysis data. Gridded dataset consisting of 2.5 degree grid. There are location in all. We have data from We examine different variables like pressure, precipitation

8 Comparing different measures of anomaly construction 3 measures to compare the different methods Mean based difference: Compare the difference in means for each pair of the measure. Correlation based difference: Compute the correlation of each point with other points and check if the correlation values are impacted by using the different measures. Monthly variance based difference: Compute the monthly variance of the anomaly time series for each pair of the measure. Monthly variance reflects the differences in monthly variances using the different measures. T-test to compare the 3 measures. For every location, compute the anomaly time series using the 3 measures for precipitation. Compute t-test at every region to examine the differences. Compute the number of locations that rejected the null hypothesis at 95% confidence interval.

9 Comparing different measures of anomaly construction Median based anomaly stands out when we compare the anomaly time series using Mean based difference. Number of locations that rejected the null hypothesis using the correlation based measure Z-score based anomaly stands out when we compare the anomaly time series using the correlation based difference and monthly variance based difference. Number of locations that rejected the null hypothesis using the a) Mean based difference and b) monthly variance based measure.

10 Comparing different measures of anomaly construction Results intuitively suggest that z-score measure will lead to differences in the results. To compare the mean and median measure, we examine the skewness in the data. Kurtosis falls within for half of the locations on the Earth. However some locations have a very high skew and a kurtosis value as high as 10. Hence mean might not be a good measure. However further investigation is still required on this.

11 Different time periods for anomaly construction If we fix a measure say mean, what base period to choose to compute the anomaly? 60 years of data, what years to pick to compute the mean. Climate scientists generally use a 30 year base. We study the impact of changing the base by examining up 3 base periods in the data First 20 years. All 60 years. Last 20 years.

12 Different time periods for anomaly construction We compare the divergence in the anomaly time series using the first 20 years and the last 20 years as the base as compared to the entire 62 years using KL divergence. White regions show regions of maximum divergence. Regions around Sahel show a very high divergence using a 20 year base period as compared to the entire 62 year time period.

13 Different time periods for anomaly construction Further, if we change the base period to different 20 year time periods starting from 1948, we see that the variance of the time series changes. Further, different regions show different time steps where the variance is minimum.

14 Case study of the Sahel dipole Dipole: Sahel region received very heavy rainfall until 1969 and then went into a period of drought. At the same time gulf of Guinea received very heavy rainfall.

15 Case study of the Sahel dipole Base = 1 st 20 years Base = last 20 years Correlation of a single point in Sahel with other points in the world. The Sahel dipole appears at different time periods using the two bases.

16 Case study of the Sahel dipole Map showing the correlation of a single point in Sahel with other points on the Earth. Using the first 20 years as the base, the Sahel dipole appears in However, if we use the last 20 years as the base the Sahel dipole does not appear in the same time period.

17 A Generalized approach for Anomaly Construction Goal: Find a weighted base that minimizes the variance across all the points on the globe. Algorithm: Choose a base T Assume weights do not change with year Compute a set of weights Compute the anomaly at each location by taking a weighted subtraction of the base. Pick up a base that minimizes the variance for all the time series across the globe using Monte Carlo simulations.

18 A Generalized approach for Anomaly Construction Experiments: We used the precipitation data from NCEP/NCAR spanning 62 years Results: Picture below shows the weight vector to which the algorithm converged to. The algorithm converged to a base period of 55 years starting from Sahel dipole appears with the new base.

19 Future Work Evaluate different objective functions for anomaly construction. Examine approaches that learn the weight vector. Examine other measures of anomaly construction.

20 Acknowledgements This work was supported by the NSF Expeditions grant on Understanding climate change using data driven approaches. Access to computing resources was provided by the Minnesota Supercomputing Institute.

21 Thanks