Interactive Tools for Global Sustainability and Earth Systems: Sea Level Change and Temperature

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1 Interactive Tools for Global Sustainability and Earth Systems: Sea Level Change and Temperature Linda Hinnov Department of Earth and Planetary Sciences Johns Hopkins University Baltimore, Maryland USA Karthikeyan Natesan Ramamurthy, Huan Song, Mahesh Banavar SenSIP Center, School of ECEE, Arizona State University Tempe, AZ {knatesan, Huan.Song, Louis Spanias College of Natural Resources University of California, Berkeley Berkeley, CA 9474 Abstract Understanding global change is important for creating a sustainable environment, and is a key interest of the Earth systems science community. Here we present an educational tutorial that explores the relationship between sea level and global temperature using modern-day records and time-series analysis and the Java-DSP Earth Systems Edition (J-DSP/ESE) application. The objectives of the tutorial are to apply pre-processing steps based on signal type, perform spectral analysis and identify significant frequencies, perform coherency and cross-phase analysis between two records, and arrive at an informed understanding about the relationship between sea level and global temperature change. Preliminary student assessment indicates that students were comfortable using J- DSP/ESE, and quickly understood the signal processing concepts. The analysis reveals correlation between sea level variations and global temperature at inter-annual timescales related to the El Niño climatological phenomenon. In sum, the tutorial improved students understanding of basic factors that influence global sustainability and habitability. Keywords Earth signals, Java-DSP, multidisciplinary education, global sustainability, time series analysis. I. INTRODUCTION Global change science investigates the physical, chemical and biological processes that regulate the Earth s surface systems. A fundamental objective of the science is to understand the effects of anthropogenic activities on Earth systems. Primary among these are the consequences of elevated Earth surface temperatures on the global sea level. With rising Earth surface temperatures, the oceans are expected to experience thermal expansion and mass contributions from an ablating cryosphere. Quantifying the relationship between sea level and global warming is fundamental to forecasting future changes. The Intergovernmental Panel on Climate Change (IPCC) [1] reported that over the latter half of the 2 th century ocean temperatures and sea level increased, both with significant interannual variability. Over the 2 th century there was an average sea level rise of mm/year, with evidence for acceleration to mm/year from [2]. This rise is attributed to thermal expansion of the oceans and mass contributions from melting glaciers, the latter becoming the dominant source for sea level rise late in the century. Thus far, the polar ice sheets have not been considered by the IPCC to be major contributors to recent sea level rise. Projecting forward with these estimates, sea levels will rise another.18 to.31 meters by the end of the 21 st century. However, the acceleration of global warming would mean that the rise could be greater, a.26 to.59 m rise by 21 for business as usual, and could even exceed 1 meter if polar ice sheets start to melt faster [3]. The new book, Rising Sea Levels: Past, Present, Future [4] explains the implications of sea level rise on modern society. The problem arises from the increased incidence of higher high tides and storm surges riding atop an elevated sea level. Thus, if sea level rises only.5 m, many of the world s largest cities, which are preferentially situated along coastlines, will be affected; a 5 m rise could affect ~67 million people, and a 1 m rise as many as 871 million. This is a significant change in society s habitable zone that needs to be anticipated by governments around the world, and ideally ameliorated through concerted reduction of anthropogenic activities and emissions contributing to global warming and climate change. The tutorial presented here examines the global warming - sea level link through multivariate time /13/$ IEEE

2 series analysis of the global temperature and sea level records. While both global temperature and sea level have been increasing, it is not possible to ascribe causation based simply on linear trends. Numerical modeling is needed to demonstrate how added energy from global warming melts an ice sheet or thermally expands an ocean. Time-series analysis, such as that carried out in this tutorial, provides other, key empirical constraints. The global temperature and sea level records have strong inter-annual variations, which will allow the identification of lead and lags between the records, from which a determination of forcing and response time may be inferred. II. CRITICAL SIGNALS OF GLOBAL CHANGE 2.1 The Global Temperature Record The global temperature record consists of monthly-mean temperature data that are averaged over 5ºx5º (longitude, latitude) grids from more than 3 stations. The data are preprocessed to remove the seasonal cycle and biases from stations at different elevations, and presented as a temperature anomaly record. Today there are now independent versions of the global temperature record; much of the contributing station data is the same, but the processing techniques and decisions are different [5,6]. The HadCrut3 temperature anomaly record [7] is used in this study (top curve in Fig. 1). 2.2 The Global Sea Level Record Global sea level records are constructed from tidal gauge measurements and satellite altimetry [8,9]. Tidal gauges have been in operation since the early 18 s; sea level measurements from satellite altimetry have been available since The combined TOPEX-Jason 1 and 2 satellite altimeter record [9] with seasonal components removed is used in this study (middle curve in Fig. 1). T-anomaly ºC SOI Hadcrut3 TOPEX-Jason -15 SOI Year Fig. 1. Critical global change signals, Top: the Hadcrut3 global temperature record, sampled at Δt=.833 years [7]. Center: the TOPEX-Jason satellite altimeter measurements of global sea level sampled at Δt=.272 years [9], low-pass Gaussfiltered over f=[,4 cycles/year]. Bottom: the Southern Oscillation Index (SOI), sampled at Δt=.833 years [1]. 2.3 The El Niño-Southern Oscillation The El Niño/Southern Oscillation is a coupled ocean-atmosphere system in the tropical Pacific that generates interannual climate variability at the global scale, related to the Southern Oscillation and the sea level (cm) atmospheric pressure difference between Tahiti and Darwin [1]. The variability carries over to both global temperature and sea level change [5,9] (compare the different curves in Fig. 1), but the phasing of the variations among the three processes is unknown, and is to be determined in this tutorial. III. GLOBAL CHANGE ANALYSIS WITH J-DSP/ESE 3.1 The J-DSP/ESE standalone application Java-Digital Signal Processing (J-DSP) is a webbased, platform-independent, visual programming environment that enables users to perform signal processing calculations and simulations. J-DSP was built from the ground up in Java to provide free and universal access to an array of signal processing functions that can be used for research and education. Signal manipulation functions appear in J-DSP as "blocks" that are brought into the simulation environment by a drag-n-drop process. Signal and data flow is established by linking the blocks. Original J-DSP functionality targeted engineering algorithms for signal processing, imaging, controls, timefrequency analysis and communications applications, and is currently used as an online Java-applet for undergraduate education [11]. A standalone version, J-DSP/Earth Systems Edition (J-DSP/ESE), was developed with functions for input/output, interpolation, re-sampling, windowing, filter design, univariate and multivariate spectrum estimation, and time-frequency analysis, customized for the analysis of Earth signals. A full description of J-DSP/ESE appears in Ramamurthy et al. [12]; the application workspace is displayed in Figure 2. The application is free and available for download at ( ). Here J-DSP/ESE is used to perform univariate and multivariate time series analysis on the critical global change signals presented above. 3.2 Artificial test case Figure 2 illustrates functions that are applied in this tutorial. Two test series of length 1 with a uniform sample rate of Δt=1 are defined (t =nδt, n=1,2,,1): data1(t) = sin(2πt/1)+n 1 (t) data2(t)= cos(2πt/1)+n 2 (t) Simple periodograms (parameters set to singleframe, rectangular) of these time series are very similar, with a spectral peak at f =.1. Time-wise, data2 could be considered to lead data1 by a quartercycle, i.e., phased by 9º, consistent with the sinecosine relationship. To examine this in the spectral domain single-frame coherency analysis is performed, with data1 input first ( top branch ), and indicates a peak at f =.1, where cross-phase registers -9º. Thus, in the J-DSP/ESE coherency function, negative crossphase indicates that data2 leads data1.

3 Fig. 2. Workspace of J-DSP/ESE showing periodogram and coherency analysis of two test series data1 and data Global change spectra A first important step in comparing these critical global change signals is to characterize their spectra. This is accomplished with periodogram analysis. Here, the simple (single-frame) periodogram is used to calculate univariate spectra of the three records. All three records share a common trait, namely, largemagnitude inter-annual variations (i.e., cycles longer than 1 year); visual inspection of Figure 1 suggests that many of the recorded variations are common among them. Thus, the frequency band f=[,1 cycles/year] is expected to have most of the power in these records, and is the focus of this exercise. The time interval is examined, which is a common interval for all three records. The sample rates of the records are different (Fig. 1), and so are resampled to uniform Δt=.2 years. Means and linear trends are subtracted. Each record is zeropadded to 8192 points prior to the periodogram estimation. Zero-padding is useful even essential when the record length is short (16.96 years here), and the frequencies of interest are low. The periodograms reveal multiple inter-annual frequencies in the three records (Fig. 3). Common among them are 1/(4 years); others may also reflect a common origin, e.g., 1/(3 years) and 1/(6 years) or 1/(7 years). The sea level spectrum has fewer higher frequency components, possibly indicating a filter response to forcing from temperature and/or the SOI. Multivariate methods must be applied to determine whether there are statistical relationships among the three records, as follows. 3.4 Coherency and cross phase spectra To examine the correlation among the three records presented above, eight-frame, un-tapered coherency and cross-phase spectra are calculated (Figs. 4-6). For f=[,1 cycles/year], coherency is elevated in all three analyses, indicating correlated inter-annual power yr 3.8 yr 7 yr 3. yr 12 yr 1 yr 6 yr 4 yr 4 yr 3 yr 2.3 yr 1.8 yr 1.7 yr Hadcrut3 TOPEX-Jason SOI cycles/year Fig. 3. Single-frame periodograms of the three records in Figure 1, for the time interval , and zero-padded to a 8192 point length (see text). Top: the Hadcrut3 global temperature record. Center: the TOPEX-Jason satellite altimeter measurements of global sea level. Bottom: the SOI index

4 Fig. 4. Eight-frame coherency (top) and cross-phase (bottom) spectra for global temperature v. SOI for The means and linear trends of the inputs have been estimated and removed. For f=[,1/year] cross-phase decreases slightly from 18º, i.e., SOI leads global temperature. Fig. 6. Eight-frame coherency (top) and cross-phase (bottom) spectra for temperature v. sea level for The means and linear trends of the inputs have been estimated and removed. For f=[,1/year] cross-phase is positive, i.e., sea level leads global temperature. The cross-phase spectra indicate that SOI and global temperature are out of phase, with the slightly decreasing phase indicating SOI leading temperature. SOI and global sea level are anti-phase-locked, and global sea level leads temperature. Additional measurements are required to determine the statistical significance of the coherency and cross phase. For example, is the measured global sea level lead over global temperature a significant result, or are the measurement uncertainties too large to rule out a zerophase relationship? If it is determined that the lead is significant, then the more complicated question of why can be examined with confidence. III. TUTORIAL OBJECTIVES AND ASSESSMENT The objectives of this tutorial are as follows: 1. Introduce concepts of time series, frequency, spectrum, and correlation. 2. Introduce common preprocessing steps and their benefits. 3. Perform periodogram analysis and identify significant frequencies. 4. Perform coherency and cross-phase analysis between two signals. 5. Analyze the relationship between El Niño, global temperature and sea level. Fig. 5. Eight-frame coherency (top) and cross-phase (bottom) spectra for sea level v. SOI for The means and linear trends of the inputs have been estimated and removed. For f=[,1/year] cross-phase is 18º, i.e., SOI and sea level are out of phase. The overall objective is to increase student awareness of the response of the oceanic response to global warming, through hands-on manipulation of state-of-the-art global change data. The analyzed data reveal a dynamic and interactive Earth surface system that is rapidly evolving, and that poses profound

5 TABLE I. ASU WORKSHOP CONCEPTUAL ASSESSMENT QUESTIONS WITH THE CORRECT ANSWERS No. Question Type Answer 1. Consumption of energy by humans from a million years has Multiple-choice 1 fold increased: 2. The primary energy source in the USA is : Multiple-choice Fossil fuels 3. The average human sitting burns: Multiple-choice 1 watts 4. Interannual variations of atmospheric carbon dioxide are Multiple-choice Periodicities in the 3-5 year range characterized by: 5. Long term trend in the global temperature is: Multiple-choice Increasing but slowing in the past decade 6. Global temperature variations have the following relationship Multiple-choice Carbon dioxide lags temperature with carbon dioxide variations 7. Global sea level variations have the following relationship Multiple-choice Sea level lags temperature with global temperature variations 8. At a frequency of 1 cycle/year, if the cross phase is 9 Multiple-choice 3 months degrees, what is the lag between the two signals (Global temperature and carbon dioxide)? 9. Over the past 3 years, what change has happened in the Multiple-choice The lag period has increased phase relationship between the global temperature and carbon dioxide variations? 1. The phase relationship between the sea level and global temperature variations point to the possible following cause(s): Multiple-choice De-glaciation TABLE II. ASU WORKSHOP SUBJECTIVE ASSESSMENT QUESTIONS No. Question 1. I understand the concept the use of coherency and cross-phase more clearly after performing the exercises. 2. The user interface of J-DSP/ESE is intuitive and easy to use. 3. I will be able to perform analysis of similar Earth systems datasets comfortably using the J-DSP/ESE version. 4. How much time did you need to become comfortable in using the J-DSP/ESE version? challenges to global sustainability and habitability. We administered this tutorial at a workshop at Arizona State University in January 212 to an audience of 14 electrical engineering graduate students with a background in signal processing, but not in Earth science. Prior to the tutorial, the students were introduced to key concepts behind 2 th century climate change. A pre-quiz conceptual assessment with seven questions was administered before the start of the workshop. At the end of the workshop, the participants answered a post-quiz conceptual questionnaire that consisted of the same seven prequiz questions plus three questions, and a subjective assessment questionnaire. The ten questions along with their correct answers are given in Table I. The questions in the subjective questionnaire are given in Table II. For each of the first three questions in the assessment questionnaire, the participants were asked to choose from the following responds: (a) Strongly agree, (b) Agree, (c) Neutral, (d) Disagree, and (e) Strongly disagree. For question 4, the possible four responds were (a) Less than 5 minutes, (b) Less than 1 minutes, (c) Less than 3 minutes and (d) More than 3 minutes. The correction rates to the assessments and first three questions in the subjective questionnaire are summarized in Figure 7. The average performance in the assessments improved from 4% to 69%, as evaluated from the pre- and post-quiz results, which points to a successful use of the tutorials and J- DSP/ESE in interdisciplinary education. Furthermore, from the subjective assessment results, 85% of the participants agreed that J-DSP/ESE was easy to use and they were comfortable in understanding the concepts. Over 85% of the participants answered that they became comfortable using J-DSP/ESE in less than 1 minutes. From these assessment results, this tutorial along with the software, provided valuable information about global change to the non-specialist audience. IV. CONCLUSIONS This tutorial explores the relationship between critical global change signals related to global warming and sea level change. Students were asked to evaluate the frequency content of three records, global temperature, global sea level, and Southern Oscillation (SOI), and to assess correlations between the records. The strongest correlation was between global temperature and sea level change, that included frequencies associated with SOI variations. Sea level was shown to lead temperature variations. These results demonstrate couplings between major Earth surface processes that directly impact global sustainability and habitability of the Earth s coastal zones.

6 Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., Miller, H.L. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp [3] Overpeck, J.T., Weiss, J.M., 29: Projections of future sea level becoming more dire. Proceedings of the National Academy of Sciences, 16, pp [4] Gornitz, V., 213: Rising Seas: Past, Present, Future. Columbia University Press, New York, 36 pp. Fig. 7. Summary of the results in the technical assessment and first three questions of the subjective assessment. This tutorial introduces students to basic concepts in global change and time series analysis. The new standalone application J-DSP/ESE was used to carry out sophisticated but simple exercises to elucidate the strong link between global temperature and sea level change. The plan is to build on this approach with alternative data, and to develop ways to statistically assess the measured dynamical interactions. ACKNOWLEDGMENTS This work was funded by NSF CCLI (TUES) grant awards and REFERENCES [1] IPCC, 27: Climate Change 27: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., Miller, H.L. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 996 pp. [2] Bindoff, N.L., Willebrand, J., Artale, V., Cazenave, A., Gregory, J., Gulev, S., Hanawa, K., Le Quéré, C., Levitus, S., Nojiri, Y., Shum, C.K., Talley, L.D., Unnikrishnan, A., 27: Observations: Oceanic Climate Change and Sea Level. In: Climate Change 27: The Physical Science Basis. Contribution of [5] Hansen, J., Ruedy, R., Sato, M., Lo, K., 21: Global surface temperature change. Reviews of Geophysics, 48, RG44, doi:1.129/21rg345. [6] Rohde R., Muller R.A., Jacobsen R., Muller E., Perlmutter S., et al., 213: A New Estimate of the Average Earth Surface Land Temperature Spanning 1753 to 211. Geoinformatics and Geostatistics: An Overview 1:1, doi:1.4172/gigs.111. [7] Brohan, P., Kennedy, J.J., Harris, I., Tett, S.F.B., Jones, P.D., 26: Uncertainty estimates in regional and global observed temperature changes: a new dataset from 185. Journal of Geophysical Research, v. 111, D1216, doi:1.129/25jd6548. [8] Church, J.A., White, N.J., 211: Sea-level rise from the late 19 th to the early 2 th century. Surveys of Geophysics, 32, pp [9] Nerem, R. S., Chambers, D., Choe, C., Mitchum, G. T., 21: Estimating mean sea level change from the TOPEX and Jason altimeter missions. Marine Geodesy, 33, pp [1] The Southern Oscillation Index; accessed July 14, 212: [11] Spanias, A. and Atti, V., 25: Interactive online undergraduate laboratories using J-DSP. IEEE Transactions on Education, 48, pp [12] Ramamurthy, K.N., Hinnov, L.A. and Spanias, A.S., in review: Teaching Earth signals analysis using the Java-DSP/Earth Systems Edition: Modern and Past Climate Change. Journal of Geoscience Education.