Time Series Analysis

Ryan E. Emanuel, Joshua S. Rice, and Jasmine N. Gregory. North Carolina State University (ryan_emanuel@ncsu.edu)

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Introduction

Time series data are common in hydrologic sciences and other fields. Time series data are observations that are ordered chronologically. In contrast, other forms of data may be independently ordered (e.g., a collection of biometric measurements from individuals in a population). The purpose of this unit is to introduce students to some of the basic characteristics of time series and to commonly-applied analyses. Steps within the unit focus on hydrologic data (e.g., streamflow, precipitation) as well as climate signals (El Nino - Southern Oscillation). Examples are drawn from North Carolina (Neuse River) and Arizona (Colorado River). These activities were developed with support from NSF Award Number EAR 1558675.

Intended Audience

Advanced undergraduates, or graduate students who are just beginning to work with environmental time series data.

Conceptual Learning Outcomes

1) Students gain an understanding of autocorrelation
2) Students gain an understanding of stationary and nonstationary behavior
3) Students gain basic understanding of periodic behavior

Practical Learning Outcomes

1) Use open source tools to conduct basic characterization and analysis of hydrologic time series
2) Use open source tools to visualize information about time series including autocorrelation functions and power spectra

Student Time Required

Each step should take 1-2 hours, depending on comfort level with modifying small amounts of Python code (e.g., file paths) and depth of response expected for discussion questions embedded within each step's iPython Notebook. Time estimate assumes students have already installed an interactive python environment (iPython or jupyter) with the Numpy, SciPy, matplotlib, and pandas libraries (all of which should be included in the open source Anaconda distribution of Python).

Supporting Reference Documents and Files

1) Background reading materials (we leave appropriate readings to be determined by individual users and instructors)
2) Example data to be used in each step
3) Example code for each step

Instructions

Instructions are embedded within the iPython notebook provided with each step. Sample hydrologic data are provided; however, the instructions and code sections can be used with any dataset. (Use the example data as a formatting template.)

Steps within this lesson

Assessment

While no formal assessment is provided, questions are incorporated into each step along with detailed instructions. Output plots and questions are intended to be used to develop a graded version of this unit (e.g., figures and discussion questions for formal laboratory reports).