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In this study, the probabilistic forecasts of exceeding the reflectivity threshold L= 19 dBZ

based on Rad-TRAM and COSMO-DE-EPS are combined. The basis for the additive combi- nation of the probabilities is the knowledge of the development of their forecast quality with lead time. In the last two chapters, this development was evaluated with the Brier score, the CSRR, and the area under the ROC curve in three case studies (Fig. 3.8, Fig. 3.16, Fig. 3.24) and for the entire period (Fig. 4.9).

Figure 5.1: Development of CSRR with lead time for Rad-TRAM and calibrated COSMO- DE-EPS forecasts from 8 to 16 August 2007.

The development of forecast skill as evaluated with the CSRR is chosen to be the basis for the derivation of the weighting functions for the additive combination (Fig. 5.1). As discussed in detail in Chapter 4.3, the skill of Rad-TRAM forecasts decreases steadily over all lead times in all scores. The CSRR is found to be more reliable than the Brier score as it does not depend on the observed frequency of the event and has smaller standard devi- ations. The mean performance of COSMO-DE-EPS forecasts is significantly worse, but as Rad-TRAM’s skill as well decreases to low values, after about six hours a first cross-over point can be identified. The differences between the skill of the different approaches applied on the ensemble output are small.

The weighting functions are derived similar to Kilambi and Zawadzki (2005) as their ap- proach was simple and straight forward. They defined their weighting functions according to the performance of the respective method i at the time of the forecastt with the critical success index (CSI)

weight= 1 1−CSI2.5

i,t

−1. (5.1)

In their study, i denoted four different forecast types. Two were based on extrapolation (MAPLE and OMAPLE) and two on NWP models (GEM and WRF).

In this study, the weighting functions are defined based on the mean performance of Rad- TRAM with CSRR. The weight for Rad-TRAM wr is defined depending on lead time τ

as

wr(τ) = 2.11−

1

1−CSRR(τ)2.8 (5.2)

and normalised to one at the first lead time. Due to the model set up for COSMO-DE-EPS forecasts, a real lead time dependent evaluation of forecast skill was not possible. Therefore, the weighting function of the model forecasts has to be defined differently. Since the combined quantity is probability of precipitation, the weights of both methods should sum to one. The weight for all COSMO-DE-EPS based forecasts wc is calculated on basis of Rad-TRAM’s

weighting function

wc(τ) = 1−wr(τ). (5.3)

Figure 5.2: Weighting functions for the combination of probabilities based on radar extrap- olation with Rad-TRAMwr and probabilities derived from COSMO-DE-EPS wc.

The skill of the three methods applied on the COSMO-DE-EPS output to derive probabilis- tic forecasts does not vary significantly or systematically. Hence, one common weighting

function is defined for all model forecasts. The resulting weighting functions are displayed in Fig. 5.2.

The weight for the extrapolation based probabilities wr decreases steadily from one. As

long lead times of Rad-TRAM might show some skill as well and the differences between Rad-TRAM’s and COSMO-DE-EPS’s forecast skill then are small, wr does not fall to zero

but reaches a minimum at 0.38. The cross-over point is after 5.75 hours in agreement to the findings in Fig. 4.9. This means, after this time more weight is given to the model derived probabilities. Note, the maximum weight for COSMO-DE-EPS is 0.62.

The weighting functions are multiplied to the respective probabilistic forecasts from Rad- TRAM, PLL, and COSMO-DE-EPS, PEP S, to combine the two probabilities at each time

step in the respective eight hour interval (Fig. 3.1) to a combined probabilityPblendaccording

to

Pblend,i =wr(τ)∗PLL(τ) +wc(τ)∗PEP S,i (5.4)

withibeing the 22 respective COSMO-DE-EPS forecasts. All forecasts derived from COSMO- DE-EPS are treated with the same weightwcas differences between the methods turned out

to be small in the evaluation.

Figures 5.3 and 5.4 reveal examples of the combination at two different lead times. These are chosen such, that at one lead time the maximum weight is at the nowcaster and on the other it is at the model forecast. As well the components for the combination as the resulting combined probabilities are shown. For the sake of clarity, only the fraction method of the 22 model forecasts is displayed. Of course, the blending procedure results in 22 different forecasts based on the combination of Rad-TRAM with the 22 different forecasts derived from COSMO-DE-EPS output.

Figure 5.3 shows probabilistic forecasts for 12 August 2007, 23:15 UTC with lead time of τ = 1.25 h. As explained in sec. 3.2, during this phase of the day, precipitation ahead of a cold front was in the evaluation domain (Fig. 3.11). At the lead time τ = 1.25 h, the Rad-TRAM forecast (Fig. 5.3, top left) is multiplied by a larger weightwr than the COSMO-

DE-EPS forecast (fraction method, Fig. 5.3, top right). Therefore, the combined probability field (Fig. 5.3, bottom) reflects the high probabilities from the Rad-TRAM forecast. Nev- ertheless, the influence of the forecast with the fraction method is visible in additional low probabilities.

Figure 5.4 displays forecasts valid at the same time, but with a lead time τ = 7.25 h. The model forecast is the same as in Fig. 5.3 as only one model run per day is available. At this lead time, the weight for the model wc is larger than for Rad-TRAM. Therefore, the

blended probability field (Fig. 5.4, bottom) is dominated by the fraction method forecast. The probabilities of both components are low, and therefore, the combined probability is low as well.

Comparing Fig. 5.3, bottom and 5.4, bottom, the decreasing influence of the nowcaster can be seen clearly. Only with the information from the blended probability field, it is not pos- sible to deduce which forecast source leads to which pattern in the blended probability field. This illustrates that the blended forecasts deliver a seamless combination of the Rad-TRAM

Components from Rad-TRAM and calibrated COSMO-DE-EPS

Blended forecast

Figure 5.3: Blended probabilities for 12 August, 23:15 UTC (bottom) with components from Rad-TRAM and the calibrated COSMO-DE-EPS fraction method (top) forτ = 1.25 h. Ob- servations used to initialise the Rad-TRAM forecasts are shown in colour in the background. and COSMO-DE-EPS based probabilistic forecasts.

Components from Rad-TRAM and calibrated COSMO-DE-EPS

Blended forecast

Figure 5.4: Blended probabilities for 12 August, 23:15 UTC (bottom) with components from Rad-TRAM and the calibrated COSMO-DE-EPS fraction method (top) for τ = 7.25 h. Ob- servations used to initialise the Rad-TRAM forecasts are shown in colour in the background.