8
Model output statistics MOS
3 Model output statistics MOS
With regard to standard weather elements, MOS reduces about 50% of the error variance of Direct
Model Output predictions for particular predictands (weather elements) (KNÜPFFER, 1999). Subsequent
verification has shown that this ratio has been unchanged in the past 10 years: numerical models have
improved, MOS methods have improved as well, and the relative difference between the RMSE values
of DMO and MOS has remained more or less unchanged. Other successful MOS applications are
nowcast applications such as lightning, radar, and cellMOS, and their integration into the automated
WarnMOS forecasting systems of DWD (HOFFMANN, 2008) and in aviation weather forecasting systems
(e. g. Auto-TAF, {KNÜPFFER, 1997}), predictions of wind speeds, pollutant concentrations (particulate
matter, ground-level ozone) water levels of rivers, among many others. Generally speaking, MOS
applications always are promising in predictions of parameters depending essentially on the weather,
and for which long-term observation series are available. The success of MOS is generally attributable
to intelligent coupling between the predictions of numerical weather prediction models and observation
data. In MSWR-MOS, this has been achieved particularly by linearising the frequently non-linear
relationships between predictors and predictand via analytical and empirical transformations. An
interesting question concerning surge predictions was whether, in view of the existence of a high-
performance 2D model (as DMO) whose prediction quality only in the first 15 forecasting hours has
been surpassed by the oceanographers of the forecasting service, it would be possible to achieve
comparable quality improvements using MOS. After completion of the development phase and
6 1 /2-month operational use, this question can be answered as follows: the development results suggest
the possibility of a 60% reduction of the error variance RV(MOS,DMO) which is defined as follows:
RV(MOS,DMO) = 100% ■ (MSE dmo -MSE mos )/MSE dmo (1)
Operationally about 40% RV has been achieved so far. Even in the hypothetical case that further
improvement is not feasible, the project may be considered a full success because 10% RV generally
is considered a noticeable improvement. The following rule of thumb illustrates the effect of RV: 1 % RV
corresponds to one hour additional predictability at unchanged prediction quality. A method improving
another method’s forecast by 24% RV thus generates predictions for T+dt+24 hours whose RMSE is
comparable to that of the T+dt hours predicted before.
3.1 Most important groups of predictors
MOS equations are developed for hourly output and for prediction periods of up to T+33 hours, i.e.
typically for the next 5 to 6 times of tidal high and low water. In the North Sea, which is dominated by
semidiurnal tides, the average time between two tidal high waters is 12.42 hours. Duration of rise and
fall normally is not equal: tidal rivers have a reduced duration of rise, with duration of fall reduced
accordingly. Depending on the number of hours between the time of MOS prediction output and the
times of high or low water, suitable coefficients for the 5 to 6 matching times are taken from 33 available
equations. The predictor „wind surge“ at the required gauge stations is determined automatically at the
times of high and low water, i. e. it is not available continuously (MÜLLER-NAVARRA, 2009b).The most
important groups of predictors (in about the sequence of their linear correlation to the predictand) are:
1. Latest surge observation at Borkum, best correlated (about 0.97) only for T+1 and T+2 because
a particular surge event occurs 2-3 hours earlier at Borkum than at Cuxhaven.
2. DMO surge forecast (2Dv4), with meteorological input from GME/COSMO-EU of DWD. Correlation
decreasing from 0.94 to 0.88 between T+1 and T+33 h.
3. Persistence of last observation: (auto-) correlation of the predictand decreasing rapidly from 0.81 to
0.3 between T+1 and T+33 h.
