Over the past few months I and a colleague (Brian Wallace) have been working on a river flow forecasting paper. A draft version is available @ River Flow Paper.
The goal of our work was to beat the current forecast methods used by the Department of Water Resources for the April through July American River flow. The Department of Water Resources uses an aggregation of human judgement and linear regression equations for generating their forecasts. Given their methods they are surprisingly hard to beat!
We spent a few months trying different Machine Learning methods with little success. Many of the methods we tried resulted in forecasts that were significantly worse than the current forecasts, a few methods such as a properly trained neural network gave forecasts that were comparable to the current forecasts. Finally, I decided to use a Support Vector Machine (SVM) for producing forecasts, after testing a large combination of parameters the forecasts started being significantly better than the current ones.
The data we used for generating forecasts is available online @ https://github.com/bjwbell/California-Water-Runoff-Forecasting. The takeaway message is that we improved the forecast relative error from ~65% to ~48%. The below table shows the forecasts for the last 10 years.
| Year | Actual (AcreFt) | Predicted (AcreFt) | |Error| (AcreFt) |
| 2001 | 552,626 | 689,472 | 136,846 |
| 2002 | 973,817 | 1,028,681 | 54,864 |
| 2003 | 1,354,434 | 459,476 | 894,957 |
| 2004 | 632,159 | 713,440 | 81,281 |
| 2005 | 2,003,878 | 1,844,360 | 159,517 |
| 2006 | 2,622,387 | 2,315,193 | 307,193 |
| 2007 | 522,651 | 293,256 | 229,394 |
| 2008 | 674,287 | 800,080 | 125,793 |
| 2009 | 1,068,327 | 1,253,523 | 185,196 |
| 2010 | 1,486,780 | 1,023,649 | 463,130 |
| Mean | 1,189,135 | 1,042,113 | 263,817 |
| Root mean squared error | 355,856 | ||
| Relative absolute error | 48.65% | ||
| Root relative squared error | 54.14% | ||
The forecasts currently used by the Department of Water Resources produced relative errors of 63.82% and root relative squared errors of 69.15%. Using modern methods for SVM’s gave us an increase in relative accuracy of over 15%! This was a fantastic result and shows the large payoff in keeping up with the state of art for something as ordinary as river flow forecasting.
Math and More 