Data assimilation for weather forecasting: Are we optimizing the appropriate initial conditions?

Weather forecasting being an initial value problem, we generally seek to minimize the error on the initial state of the model in hopes of reducing errors at future forecast times. However, if our primary goal were to reduce forecast errors, would we minimize initial condition errors differently? Forecast errors are determined by two terms: the initial condition error, and the error growth during the forecast. The first term dominates the errors for short forecast times, but as forecast time increases, the second term becomes increasingly important. Thus, we wondered if there is a way to also lower forecast error growth by minimizing initial conditions errors differently.In that context, we considered whether other possible strategies such as minimizing errors on tendencies and minimizing errors on larger more predictable scales could lead to better forecasts. We chose to answer these questions by analyzing four months of ensemble forecasts from the Canadian Global Ensemble Prediction System. Each member was successively taken to be the truth, and different forms of initial condition “errors” (in values, in tendencies, at large scales) of other members were computed and compared with forecast errors as a function of forecast time.We found that for short-range forecasts, forecast errors are better correlated with errors on initial state variables, whereas for long-range forecasts, forecast errors are better correlated with a combination of errors on the initial state variables and their tendencies. Furthermore, we found that lowering initial tendencies errors by 10% leads to better forecast improvement than lowering initial state variable errors by 10% for all forecast times. Lastly, focusing strictly on initial condition errors at larger scales did not provide better forecasts. These results suggest that having data assimilation systems also minimize errors on initial tendencies could yield better forecasts

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