How well can an ensemble predict the uncertainty in the location of winter storm precipitation?

Figures & data

Fig. 1. An example of a slightly misplaced forecast precipitation field.

Notes: The forecast field (left) is the 24-h forecast of the 1-h accumulated precipitation starting at 0000 UTC 1 June 2005 and the verifying analysis field (right) is the 1-h accumulated Stage II precipitation analysis. In the left panel, the grey shades indicate the contours of the verifying precipitation field.

Fig. 2. Illustration of the effect of the normalization factor K′/(K′ + 1) on the ratio of the estimates of the right- and left-hand sides of Equation (20(20) $$E\left[\frac{1}{K^{\prime }-1}\sum _{k=1}^{K^{\prime }}{\left(d{\mathit{X}}^k-\overline{d\mathit{X}}\right)}^2\right]\left(t_f\right)=E\left[\frac{K^{\prime }}{K^{\prime }+1}{\overline{d\mathit{X}}}^2\right]\left(t_f\right).$$(20) ).

Notes: The values shown are based on randomly generated samples of 10, 000 realizations of $\mathit{r}$, ${\mathit{r}}_a$, ${\mathit{r}}_f^k,k=1,\dots ,K^{\prime }$, assuming a Gaussian random distribution with mean $\overline{\mathit{r}}=\mathbf{0}$. Because of the sampling fluctuations, the simulation is repeated 10 times for each value of K′ and the results are shown by scatter-plots.

Fig. 3. The dependence of the prediction σ_loc and the estimate δ_loc on Σ_loc for a finite size search region.

Notes: The values shown are based on a randomly generated sample of 1000 realizations of $\mathit{r}$, ${\mathit{r}}_a$, ${\mathit{r}}_f^k,k=1,\dots ,100$, assuming a truncated Gaussian random distribution with mean $\overline{\mathit{r}}=\mathbf{0}$ in a one-dimensional search domain of size 2d. The values of Σ_loc on the x-axis are shown using the search radius d as unit, while the values of σ_loc and δ_loc on the y-axis are normalized by Σ_loc.

Fig. 4. Evolution of the average of K′ over all forecast cases for different values of a in the range from 0.6 to 0.9.

Fig. 5. Evolution of the percentage M′/M of the forecast cases for which K′ ≥ 2 for different values of a in the range from 0.6 to 0.9.

Fig. 6. Top: the values of $\overline{\mathit{dV}}$ for the individual ensemble forecasts (dark blue dots) and the evolution of the estimate of the meridional component of the location bias $E\left[{\mathit{b}}_{\mathit{loc}}\right]$ with the forecast lead time, bottom: the values of $\overline{\mathit{dU}}$ for the individual ensemble forecasts (dark blue dots) and the evolution of the estimate of the zonal component of the location bias $E\left[{\mathit{b}}_{\mathit{loc}}\right]$.

Fig. 7. The evolution of σ_loc (solid black), δ_loc (solid blue) and bias-corrected δ_loc (dashed blue) with the forecast lead time.

Fig. 8. Top: the values of ${\mu }_a-\overline{{\mu }_f}$ for the individual ensemble forecasts (dark blue dots) and the evolution of the estimate of the amplitude bias $E\left[b_{\mathit{amp}}\right]$ with the forecast lead time, bottom: the evolution of σ_amp (solid black), δ_amp (solid blue) and bias-corrected δ_amp (dashed blue) with the forecast lead time.