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Please see other posts for more coverage of the sometimes remarkable correlations between the Pacific Decadal Oscillation and New Mexico streamflow hydrographs. This is a small animation for the time series of these features over the first half of the 1990s.
In a previous set of posts I barely explored the stochastic landscapes of two of these time series shown, the PDO and the Otowi gage along the Rio Grande. This animation is simply another means to graphically assess some of the same information. I will add more animations like this over time.
Some Ph.D. work in progress is adapted here to the stochastic landscape strip representations that are being pioneered at this site as well.
As with some stochastic landscape strips, the time in years is captured by the column index and the position in months is captured by the row index. The color of the resulting pixel color is the exemplary value of the hydraulic or other energy parameter for that region of interest.
The resulting ‘landscapes’ for many explorations, exhibit unique signature patterns that have apparent added value in ergodic forecasting techniques. In this example I am hoping it will help in a diagnostic exercise regarding other research.
The stochastic response surfaces of seasonal time varying data can often result in results that are both visually interesting and useful. In some ways these graphics are reminiscent of wavelet approaches.
Here are representations of the stochastic landscape of the Pacific Decadal Oscillation (PDO) and the Otowi Gage records in North Central New Mexico over the 20th Century plus change. For each time series, the years are represented by columns and each row represents a separate month. The rows start from (end of) December at the bottom and go to (end of) November at the top row.
The apparent ergodic properties of the two time series allow an exploration of related ‘stationary waves’. Consider a metaphor of water flowing over a rocky stream bed. In this example, the Otowi gage record is the ‘water’ and the PDO record is the ‘rocky stream bed’. Some caveats include fall and winter Otowi stream flows, which are depressed across the time series, likely due to watershed storage and freezing conditions and not necessarily due to lack of precipitation.
The next image captures the relative proportions of monthly flows for each year of record.
The next image shows the same coverage for absolute flows. In this image, a viewer can see the actual magnitudes of flow for every month of every year.
In our open approach (with a propietary core) to streamflow forecasting, we employ the best available stochastic practices and data sets.