Descriptive Statistics on Time Series

Reporting on statistical values that are derived from a time series is often a key deliverable of a monitoring organization. It is often also desirable to calculate statistically derived values of a time series quickly.  To this end, the AQUARIUS Workstation provides the Descriptive Statistics toolbox.  The Descriptive Statistics toolbox allows users to calculate a table of derived statistical summary values and to have these values form a new time series.  The Descriptive Statistics toolbox eliminates the complexity of performing descriptive statistical calculations using mathematics languages (e.g. R or MATLAB) or other generic software such as Excel.

Flood and Drought Frequency Analysis

A key deliverable of many agencies responsible for collecting and managing river flow records is the statistical analysis of these records for information about extreme events such as values for various return periods (e.g. 100 year flood or 10 year expected 7 day average low flow).

The analysis of river flow records for the return frequency of both high flows (floods) and low flows (droughts) is accomplished in the AQUARIUS Workstation Hydrologic Statistics toolbox.  The Hydrologic Statistics toolbox is an interactive environmental that allows the user to visualize the empirical distribution of flood or drought events.  The toolbox allows users to apply statistical tests on the data population.

The distribution models that are common for flood and drought frequency modeling are built into the software (e.g. Log-Normal, Log-Pearson, Gumbel, Weibull, etc…) and can be fit to the observed data populations using either linear moments or maximum likelihood estimators.

Extending the System with Scripting

The AQUARIUS Workstation and AQUARIUS Server System provide great functionality, and use a rich set of internal code libraries to ensure accuracy of data computations.  These same interfaces are available to users who want to extend the system with their own code.  AQUARIUS supports extensions written in either C# or VB.NET scripting languages in conjunction with the AQUARIUS Optimized Package (AOP) Library.  The AOP Library has a rich set of methods and functions which can be drawn on to perform the basics like ensuring time stamps are aggregated and regularly spaced, calculating daily averages respecting interpolation rules, etc...  This frees the end user to program a better flood forecast model or better optimize their modeling ensemble.  Without the need to learn proprietary scripting languages AQUARIUS puts the power back in the end user’s hands.