Fig. 1.
The necessary ingredients: a climatology cumulative probability distribution function (grey), a probabilistic forecast (blue) and a verification (red). The projection of the circle and square onto the probability space, τf and τy , are called the forecast and verification crossing-points, respectively.
Fig. 2.
Getting familiar with the error function. (a) S as a function of τf for three different values of τy : 0.1 (dashed line), 0.3 (dotted line) and 0.5 (solid line). (b) S as a function of τy for three different values of τf : 0.1 (dashed line), 0.3 (dotted line) and 0.5 (solid line).
Fig. 3.
Comparing two scores in ‘probability space’ using a toy-model while varying the forecast bias (a) and the multiplicative spread factor σ (b). Normalised expected value of the score S (solid line) is compared with normalised expected value of a naive score in probability space computed as (dotted line).
Fig. 4.
(a) Two metre temperature crossing-point forecast derived from ENS at day 5, (b) crossing-point observation on 1 June 2020 and (c) corresponding score S.
Fig. 5.
Same as Figure 1 but based on a real data set: 2 m temperature ENS forecasts at day 5 valid at three different stations illustrating: (a) the single intersection condition, (b) a case of multiple (2) intersections and (c) a case with zero intersections. The climatology is site-specific, based on a 30-year observation records covering the period 1980–2009.
Fig. 6.
Distribution of intersection points between each pair of forecast and climate probability distributions. Results for (a) 2 m temperature, and (b) daily precipitation at day 2, 5, and 10, in July 2018, at station level over Europe.
Fig. 7.
Score sensitivity to ensemble size and climatology definition: score as a function of the number of ensemble members M (SM ) relative to the score when M = 50 (S 50) for different climate definitions. Results for scores computed with the diagonal score are shown in black, results based on Eq. (3) in grey, for 2 m temperature (a) and daily precipitation (b).