Regional forecasts such as what I am running rely on larger continental forecasts to provide initial conditions and lateral boundary conditions. The continental forecasts in turn rely on observation data and global forecasts. Global forecasts rely on observation data and don't have lateral boundaries. Equipment that provides observations, models that interpret observations, and forecasts all add their own errors and pass them down the line, sometimes canceling each other out, sometimes magnifying errors. I have to either trust the next step back from my forecast or try to do a better job. I have looked at the quantity of data and amount of processing that go into RUC and NAM forecasts. I would rather trust them than try to replicate them. They are quite impressive. I once talked to one of the guys who is responsible for the RUC forecasts. He was so concerned about doing his job well and it being useful to me, that he seemed rather apologetic that RUC happened to have significant biases for my particular location. I want conscientious people like that putting out a national product like RUC.

But I would still like to have an idea of how much error in my forecasts is coming in from RUC and NAM. I suppose it sounds like I am trying to blame someone else for errors in my results, but I honestly just want to work with reality as it is and have a better handle on where to focus efforts to improve forecasts. The Bias and Error Graphed Against Forecast Hour page shows that WRF can remove general bias, but if the larger forecasts don't get location, timing of movement, and intensity of the large pressure systems right, there is nothing in my regional size model that can create a different, better set of pressure gradients. I can add some additional local observations, but as discussed in the "A Couple Thoughts About Using Observation Nudging (fdda)" section on this page, Main Research Page, those local observations are only valid for a short amount of time, which tends to make them not very useful in a forecast.

So I tried two approaches to identify error that comes through WRF from RUC and NAM initialization data. In both I used the bias corrected values for wind speed. As in other places, I am removing the bias from the same data from which the bias was calculated. This represents the best possible adjust by removing bias. It ends up removing some of the non-bias, "random error" also to the extent that the data has a too few data points or that it represents data that is non typical of whatever data I would have/should have used to calculate the bias correction.

The first method to identify incoming error was to calculate the correlation coefficient between the bias adjusted RUC error and the bias adjusted WRF error. These values are represented by the data points having bow tie shapes. The lines use the same coloration scheme used throughout this section of the website. The second method uses hour glass symbols on its lines. It was calculated by subtracting the bias adjusted WRF error from the bias adjusted RUC error and averaging the absolute values of the results.  If the error were independent, the results would be about the same values as the errors. If the errors were perfectly correlated, the resulting values would be close to zero. Perfect negative correlation would make the resulting values be the sum of WRF and RUC error.

I performed the two methods on data graphed against the different horizontal axes shown on other pages and the results are below. In general, there is a positive correlation coefficient between 0.5 and 1.0 in most cases. And the resulting mean absolute difference between the two bias adjusted error sources resulted in a value somewhat lower than both of the contributing sources, indicating a shared error. Correlation and shared error do not prove cause and effect. Another possible explanation is that RUC and WRF both have the same weaknesses. This analysis does not provide a silver bullet for fixing problems or even for clearly identifying them. As seen on the Bias and Error Graphed Against Forecast Hour page, WRF was able to remove a lot of general RUC bias. Perhaps an improved WRF PBL scheme could remove even more error that is current identified as "random error" simply because it is a bias related to an unidentified or missing piece of the model.

The graphs of WRF data initialized with RUC data are given here. They are labeled but they are small here, so you will need to click on them to enlarge or open in another window.

The below graphs are the NAM equivalents to the above four graphs. Click to enlarge or open them in another window.