Verification of DMI wave forecasts 1st quarter of 2003

Transcription

1 DANISH METEOROLOGICAL INSTITUTE TECHNICAL REPORT - Verification of DMI wave forecasts st quarter of Jacob Woge Nielsen dmi.dk Copenhagen

2 ISSN -X ISSN - (trykt) (online)

3 Verification of DMI wave forecasts st quarter of Jacob Woge Nielsen The Danish Meteorological Institute, Copenhagen, Denmark forecast Scatter diagram h, all stations cc=. ervation Figure. Significant wave height: short range (-h) forecasts

4 Contents Introduction with Key Numbers DMI-WAM. Physical model Model set-up Weather model Wave data. Forecasts Observations Error measures Results. Significant wave height Extreme wave height Mean wave period Dominant wave period Mean wave direction Conclusion Appendix. Wave recorders Observed wave statistics Wave forecast statistics Significant wave height Mean wave period Dominant wave period References List of Tables List of Figures

5 Introduction with Key Numbers We analyse the quality of wave forecasts valid for the st quarter of, produced by DMI-WAM - DMI s operational set-up of the rd generation wave model WAM Cycle. Focus is on significant wave height. Other wave parameters (period, direction) are examined where the data material is adequate. No swell data is available. Standard error measures (bias, rms error,..) are calculated as a function of forecast range and of wave height. Special statistics are done for the highest waves. Grand averages are calculated as mean values over all stations, over all ranges, and for separate geographical regions. All model results are forecasts, without any analysed sea state. A forecast error may imply a wave model error, or errors in the wind forecast. Wave recorder data are retrieved via the GTS (Global Telecommunication System) from the National Data Buoy Center (UK). Additional data have kindly been provided by the Swedish Meteorological Institute, the National Center for Marine Research (Greece), the German Bundesamt für Seeschiffahrt in Hamburg, and the Danish Coastal Authority. DMI has produced short-range operational wave forecasts since. A pre-operational validation study was carried out in [], a combined wave-wind validation study in [], and a verification pilot study in []. Previous quarterly reports are [],[],[],[]. Outline: A Key Number Table is given below. Ch. describes the DMI wave model set-up, ch. lines out the data material, and in ch. we define the statistical error measures used to describe the forecast quality. Ch. presents and discusses the results. Ch. concludes the work. Comprehensive results for each station are found in the Appendix. References and lists of figures/tables are found at the end of the report. Key Numbers pertaining to the full model system are shown in Table below. Please refer to Ch. for a detailed explanation and discussion. Parameter H s T T p w bias cm.s.s o relative bias % % % rms error cm.s.s st.dev o scatter index... corr.coeff..... peak bias ;cm rel. peak bias ;% Table. Key numbers

6 DMI-WAM DMI runs an operational wave forecasting service DMI-WAM, using the rd generation wave model WAM Cycle forced by DMI s numerical weather prediction model HIRLAM.. Physical model WAM Cycle solves the spectral + ~c ~ rf = S in + S nl + S ds + S cu + S bf where F (f ~x t) is spectral wave energy density, depending on wave frequency, wave direction, position and time; c(f d) is the depth-dependent wave group speed; S in is wind energy input; S nl is non-linear wave-wave interaction; S ds is wave energy dissipation through wave breaking (white capping); S cu is wave-current interaction; and S bf is interaction with the sea bed through friction and wave refraction. For further information on WAM Cycle, please refer to [], [].. Model set-up DMI-WAM has four geographical domains, including a large part of the North Atlantic, the North Sea and Baltic Sea, the Transition Area (inner Danish waters), and the Mediterranean (cf. Table and Figure ). Figure. The four DMI wave model domains. From the large scale North Atlantic model, the Baltic and the Mediterranean are excluded. From the regional North Sea - Baltic model (or NW European Shelf model), the Mediterranean is excluded. The model open boundaries are chosen as follows. The coarse grid North Atlantic model uses the JONSWAP wind-sea spectrum (see [], []). The fine grid North Sea - Baltic model is nested into the North Atlantic model, and uses time/space interpolated boundary wave spectra calculated by that model. In the same way, the Transition Area mode uses boundary wave spectra calculated by the North Sea - Baltic model. The Mediterranean is treated as a closed basin, assuming no wave energy exchange with the Atlantic or the Black Sea.

7 DMI-WAM runs without current refraction (S cu =), and sea ice information is also not included. The wave forecasting system has been coldstarted once and for all using developed sea. Subsequent model runs are initialised using the sea state at analysis time, calculated by the previous run as a hour forecast. Model North Atlantic North Sea - Baltic Transition Area Mediterranean Space resol. / o / o / o / o Time step min min min min Frequencies Direction resol. o o o o Forcing model(s) Hirlam G Hirlam E Hirlam E Hirlam E+G - resolution of. o. o. o. o /. o Longitudes o W- o E o W- o E o E- o E o W- o E Latitudes o N- o N o N- o N o N- o N. o N- o N Open boundaries JONSWAP Nested Nested Closed basin Forecast range h h h h Output time step h h h h Schedule x daily x daily x daily x daily Table. DMI-WAM set-up. The wave model frequencies range from. Hz to. Hz in % steps. The Mediterranean model patches Hirlam E+G to get maximum resolution.. Weather model The forcing models are the DMI limited area numerical weather prediction models Hirlam-E ( km resolution) and Hirlam-G ( km resolution). The G model embeds the E model, and both are currently being used in the DMI weather forecasting service. The wind vector at m height is interpolated linearly in time and space, from the rotated spherical weather model grids onto the spherical wave model grids. Figure. DMI Hirlam. The outermost box is the G model, the box covering most of Europe is the E model.

8 Wave data The verification data consists of operational DMI-WAM wave forecasts, and wave ervations from a number of fixed positions (buoys, platforms).. Forecasts All wave forecasts are archived as hourly maps in the model s spatial resolution. Time series for verification stations are sampled using nearest model grid point. This is done for each parameter shown in Table. Out of scheduled forecasts, were produced on time and archived. Wave parameter stations H s Significant wave height H sw Height of swell - T Mean wave period T p Dominant wave period T sw Swell mean period - w Mean wave direction sw Swell direction - Table. DMI-WAM wave parameters, obtained by a suitable integral of the wave energy spectrum. T p is the discretized model frequency (inverse) containing the highest energy, picked from a set of predefined values. The second column shows the number of validation stations. None of the fixed stations record swell, but some record maximum wave height H m, which is not calculated by the wave model.. Observations A total of wave recorders are pre-selected for verification; station positions are shown in Fig. and comprehensive station information is given in Appendix.. Observed wave statistics are shown in Appendix.. Figure. Wave recorder locations.

9 The sampling rate is ususally hour, but please refer to Appendix.. Sampling accuracy is H s :.m, T :.s, T p :s, w : o, but it may be higher or lower at single buoys. The data coverage is % (see Fig. for missing data), At two stations no data were available during this three-month period. Missing data (cov=.).... almag oland truba arkon athos Figure. Missing data. St.,, and sample every hours, but every hour in storm situations. St., and Athos sample every hours. At these stations, the data coverage is based on hour sampling.

10 Error measures Model errors are calculated using a -d residual matrix, built from all available ervations and forecasts. With the general formula residual = forecast; ervation the matrix reads (brackets indicate a dependency) residual(station analysis range) with the number of stations depending on the parameter in question (cf. Table ), analysis every hours, and forecasts ranging from - hours in hour steps. The residual matrix has roughly.* data points. By averaging the residual over all analyses, we get the model bias or mean error: bias(station range) Further averaging gives the bias for each forecast range (averaged over all stations), for each station (averaged over the full forecast range), and as a grand average: bias(range) bias(station) BIAS In the same way, the root mean square error rms(station range) is calculated and averaged using the residual squared. For the wave height only, the bias and rms error are also calculated as a function of wave height. The residual is sorted into ervation bins.m wide and averaged for each bin. bias(station bin) rms(station bin) Averaging these parameters over all stations gives the model error dependency on wave height, calculated both as an absolute value and as a relative error in %. rms The scatter index si = is obtained by normalising rms with the erved mean value. si may <> be used to intercompare rms errors at stations with large differences in wave climate. Averaging is done as above. Correlation coefficients cc(station block) are calculated using forecast pseudo time series, established by concatenating forecasts in hour range blocks. This gives coefficients valid for each of the range blocks -, -,.., - hours. Range block and station-dependent values (cc cc), and a grand average (CC), are calculated. A special peak bias pbias(station block) is calculated using the most extreme events at each station, allowing for a forecast phase error of a few hours. Peak biases are calculated both as absolute and relative values.

11 Results This section describes wave verification results for the st quarter of, for significant wave height (H s ), mean and dominant wave period (T T p ), and mean wave direction ( w ). Swell data was not available. We discuss grand averages and averages for geographical regions, for each wave parameter in turn. Detailed results for each station are found in the Appendix at the end of the report.. Significant wave height Table shows bias and relative bias, rms error, scatter index and correlation coefficient, averaged over the full forecast range. Fig. on the front page shows the short range (-h) scatter diagram. Results for each single station are shown in Table, Appendix.. Data sheets are presented in Appendix.. Parameter #st bias rms si cc Region cm % cm Atlantic.. North Sea ;.. Br.Channel.. Irish Sea.. Scotland;Faroe ; ;.. Danish West Coast.. Kattegat;Baltic.. Mediterranean ; ;.. All Waters.. Table. Significant wave height results There is a small bias and an rms error of. m. There is some regional spread. A large positive bias is found only in the British Channel. The rms error is largest in regions with high waves (Atlantic, Shetland). Scatter index is low (.) and correlation coefficient high (.). In most regions, the scatter index is well below an acceptance level of.. The error dependency on forecast range and on wave height is shown in Fig.. There is a weak dependence on forecast range, with short range forecasts being slightly better than long-range (-day) forecasts. The rms error is significant already at analysis time since the model is initialised without any use of the erved sea state. Errors depend strongly on wave height. Small waves have positive bias, while higher waves most often are underestimated. The rms error increases with wave height. The relative rms error is -% except for very small waves.

12 bias=. rms=. Average residual error [m] Error distribution [%], all stations r.bias=. r.rms=. Observation distribution [m], all stations Average Expl.Var/Corr.Coeff. [%] cc=. ev=. forecast range [hrs/] bias=. rms=. Error distribution [m], all stations.... Average scatter index [%] Figure. Significant wave height

13 . Extreme wave height The error on the highest waves erved is calculated for the highest events at each station, using the forecast error allowing for a few hours phase displacement. Table below shows range-averaged peak biases. Peak biases for each station are shown in Table, Appendix.. Parameter #st peak bias Region cm % Atlantic ; ; North Sea ; ; Br.Channel Irish Sea ; ; Scotland;Faroe ; ; Danish West Coast Kattegat;Baltic ; ; Mediterranean ; ; All Waters ; ; Table. Extreme wave height results The highest waves are underestimated, except in the British Channel and along the Danish West Coast. The bias is about -.m, independent of forecast range (Fig. ) Peak bias. Average peak error [m] forecast range [hrs/] Figure. Peak wave height errors.

14 . Mean wave period The mean wave period T is recorded at stations. Grand averages are shown in Table, and a short-range scatter diagram in Fig.. Results for each station are shown in Table, Appendix.. Data sheets are presented in Appendix.. Parameter #st bias rms si cc Region sec. % sec. Danish West Coast.... Kattegat;Baltic.... Mediterranean.... All Waters.... Table. Mean wave period results At the Danish West Coast stations T is overestimated by almost %. The reason for this is still unresolved. At other stations T is slightly overestimated. The scatter index at these stations is well below the acceptancy level of.. forecast cc=. Scatter diagram h, all stations ervation Figure. Mean wave period, -h range.

15 . Dominant wave period The dominant (or peak) wave period T p is recorded at stations. Grand averages are shown in Table, short-range scatter diagrams in Fig.. Results for each station are found in Table, Appendix.. Data sheets for Mediterranean stations only in Appendix.. Parameter #st bias rms si cc Region sec. % sec. Atlantic.... North Sea.... Br.Channel ;. ;... Irish Sea.... Scotland;Faroe.... Danish West Coast.... Mediterranean.... All Waters.... Table. Dominant wave period results T p errors are large, due partly to low recording and forecasting accuracy, and partly to the nonsmoothness of the series, with T p shifting abruptly between a high and a low period peak. Even when the wave spectrum is rather well predicted, a small error in the shape of the spectrum may lead to very large T p errors in situations with a two-peaked spectrum (swell and wind sea). Scatter diagram h, all stations cc=. forecast ervation Figure. Dominant wave period, -h range.

16 . Mean wave direction The mean wave direction w is recorded at stations. The results are presented in Table and the scatter diagram in Fig.. Results for each station is found in Table, Appendix.. Data sheets are not shown. Parameter #st bias std cc Region deg. deg. Danish West Coast ;. Kattegat;Baltic. Mediterranean ;. All Waters. Table. Mean wave direction results The mean wave direction predictions fit the ervations well, with no bias, some scatter, and a high correlation coefficient. forecast Scatter diagram h, all stations cc=. ervation Figure. Mean wave direction, -h range.

17 Conclusion DMI wave forecasts valid for the st quarter of are verified, using wave data from buoys. Two buoys have not provided data in this period. Main conclusions are: Significant wave height H s and mean wave direction w are usually well predicted We have some problems predicting wave period T and T p There is a large regional spread in forecast quality The H s error depends on wave height; very high waves are slightly underestimated The forecast quality decreases a little with increasing forecast range The significant wave height is recorded at stations. The average bias is small, independent of forecast range, There is some geographical spread, and a pronounced dependency on wave height. Small waves are overpredicted, while high waves are underestimated by up to %. The average rms error is.m, increasing gradually with forecast range. For medium-sized and large waves the rms error is roughly %. The average scatter index SI=.. A few have si>. (sometimes used as an acceptance level), partly due to low recording accuracy and small average wave height. The ervation-forecast correlation is high,. on average. The highest waves are underestimated by a few percent (-.m on average). There is no forecast range dependence. The mean wave period is recorded at stations. of these have a data interpretation problem. At the remaining stations the model overestimates the mean wave period by more than.s. Dominant wave period is recorded at stations. The predictions are not good. Bias and rms errors range up to several seconds. This could be a data problem; a well predicted wave spectrum does not guarantee a correct dominant wave period in situations with two spectral maxima. Also, most stations sample only with s accuracy and so does the model; this in itself leads to large error measures. Mean wave direction is recorded at stations. The predictions have no bias, a standard deviation of about o, and a high correlation coefficient. Swell parameters are not recorded at any of the fixed positions. A few record maximum wave height but this is not predicted by the wave model.

18 Appendix This Appendix contains a wave recorder station table (below), ervation statistics tables, forecast statistics tables, and a plot sheet for each station and each parameter (H s T T p w ), arranged sequentially according to the station table.. Wave recorders Station ID Agency Region lat. lon. t parameters almag SMHI Baltic.N.E h H s H m T oland SMHI Baltic.N.E h H s H m T truba SMHI Baltic.N.E h H s H m T arkona BSH Baltic.N.E h H s H m T w KDI D. West Coast.N.E h H s H m T T p w KDI D. West Coast.N.E h H s H m T T p w KDI D. West Coast.N.E h H s H m T T p w KDI D. West Coast.N.E h H s H m T T p w NDBC Mediterranean.N.W h H s T p NDBC Mediterranean.N.W h H s T p NDBC Atlantic.N.W h H s T p NDBC North Sea.N.E h H s T p NDBC Atlantic.N.W h H s T p NDBC B.Channel.N.W h H s T p NDBC B.Channel.N.W h H s T p NDBC Atlantic.N.W h H s T p NDBC Atlantic.N.W h H s T p NDBC Atlantic.N.W h H s T p NDBC Atlantic.N.W h H s T p NDBC North Sea.N. h H s T p NDBC North Sea.N. h H s T p NDBC North Sea.N.E h H s T p NDBC Atlantic.N.W h H s T p NDBC Irish Sea.N.W h H s T p NDBC Irish Sea.N.W h H s T p NDBC B.Channel.N.E h H s T p NDBC B.Channel.N. h H s T p NDBC North Sea.N.E h H s NDBC Atlantic.N.W h H s T p NDBC Scotland.N.W h H s T p athos NCMR Mediterranean.N.E h H s T T p w Table. Wave stations. Station name/number, driving agency, position, and wave parameters. SMHI=Swedish Meteorological Institute, BSH=Bundesamt für Seeschiffahrt in Hamburg, KDI=Coastal Authorities (Denmark), NDBC=National Data Buoy Center (UK), NCMR=National Center for Marine Research (Greece). H s=significant wave height, H m=maximum wave height, T =mean wave period, T p=peak or dominant wave period, w=mean wave direction. t is the sampling rate in hours.

19 . Observed wave statistics Station min mean max stdev almag.... oland truba.... arkon athos.... Table. Observed wave height.

20 Station min mean max stdev almag.... oland truba.... arkon athos.... Table. Observed mean wave period Station min mean max stdev athos.... Table. Observed dominant wave period

21 . Wave forecast statistics Parameter bias rms si cc Station cm % cm almag.. oland truba.. arkon ; ; ; ;.. ; ;.. ; ;.. ; ;.. ; ; ; ; ; ;.. ; ;.... ; ; ; ;.. athos ; ;.. Table. Predicted significant wave height

22 Parameter Obs peak Station m m % almag. ;. ; oland truba.. arkon. ;. ; ;. ;. ;. ;. ;. ;. ;. ;. ;. ;. ; ;. ;. ;. ;. ;. ;. ;. ;..... ;. ;..... ;. ;..... ;. ;. ;. ;. ;. ; athos. ;. ; Table. Average of top wave events (peaks) and corresponding mean peak error (peak bias)

23 Parameter bias rms si cc Station sec % sec almag.... oland truba.... arkon athos.... Table. Predicted mean wave period Parameter bias rms si cc Station sec % sec ;. ;... ; ; ;. ;... ;. ; athos ;. ;... Table. Predicted dominant wave period

24 Parameter bias std cc Station deg deg arkon. ;. ;. ;.. athos ;. Table. Predicted mean wave direction

25 . Significant wave height The following pages show significant wave height error statistics for each station.

26 Obs/pred. wave height [m] at st. almag min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st. almag bias=. rms=. Residual error [m] at st. almag bias=. rms=. Error distribution [m] at st. almag. si=. Scatter index [%] at st. almag.. Error distribution [%] at st. almag r.bias=. r.rms= Figure. Significant wave height: Almagrundet

27 Obs/pred. wave height [m] at st. truba min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st. truba bias=. rms=. Residual error [m] at st. truba bias=. rms=. Error distribution [m] at st. truba. si=. Scatter index [%] at st. truba.. Error distribution [%] at st. truba r.bias=. r.rms= Figure. Significant wave height: Trubaduren

28 Obs/pred. wave height [m] at st. arkon min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st. arkon bias=. rms=. Residual error [m] at st. arkon bias=. rms=. Error distribution [m] at st. arkon. si=. Scatter index [%] at st. arkon.. Error distribution [%] at st. arkon r.bias=. r.rms= Figure. Significant wave height: Arkona

29 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The zig-zag curves are caused by irregular h sampling.

30 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The zig-zag curves are caused by irregular h sampling.

31 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The zig-zag curves are caused by irregular h sampling.

32 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The zig-zag curves are caused by irregular h sampling.

33 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

34 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

35 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

36 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

37 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

38 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

39 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:.

40 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:.

41 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

42 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

43 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

44 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:.

45 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

46 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

47 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The sampling accuracy is.m

48 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

49 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

50 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

51 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:. The zig-zag curves are caused by irregular h sampling.

52 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:.

53 Obs/pred. wave height [m] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st bias=. rms=. Residual error [m] at st bias=. rms=. Error distribution [m] at st.. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= Figure. Significant wave height:

54 Obs/pred. wave height [m] at st. athos min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [m] at st. athos bias=. rms=. Residual error [m] at st. athos bias=. rms=. Error distribution [m] at st. athos. si=. Scatter index [%] at st. athos.. Error distribution [%] at st. athos r.bias=. r.rms= Figure. Significant wave height: Athos

55 . Mean wave period The following pages show mean wave period error statistics for each station. Only stations with reasonable statistics are included.

56 Obs/pred. mean wave period [s] at st. almag min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. almag ervation [s] bias=. rms=. Residual error [s] at st. almag... bias=. rms=. Error distribution [s] at st. almag ervation [s]. si=. Scatter index [%] at st. almag.. Error distribution [%] at st. almag r.bias=. r.rms= ervation [s] Figure. Mean wave period: Almagrundet

57 Obs/pred. mean wave period [s] at st. truba min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. truba ervation [s] bias=. rms=. Residual error [s] at st. truba... bias=. rms=. Error distribution [s] at st. truba ervation [s]. si=. Scatter index [%] at st. truba.. Error distribution [%] at st. truba r.bias=. r.rms= ervation [s] Figure. Mean wave period: Trubaduren

58 Obs/pred. mean wave period [s] at st. arkon min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. arkon ervation [s] bias=. rms=. Residual error [s] at st. arkon... bias=. rms=. Error distribution [s] at st. arkon ervation [s]. si=. Scatter index [%] at st. arkon.. Error distribution [%] at st. arkon r.bias=. r.rms= ervation [s] Figure. Mean wave period: Arkona

59 Obs/pred. mean wave period [s] at st. athos min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. athos ervation [s] bias=. rms=. Residual error [s] at st. athos... bias=. rms=. Error distribution [s] at st. athos ervation [s]. si=. Scatter index [%] at st. athos.. Error distribution [%] at st. athos r.bias=. r.rms= ervation [s] Figure. Mean wave period: Athos

60 . Dominant wave period The following pages show dominant wave period error statistics for each station. Only stations with reasonable statistics are included.

61 Obs/pred. dominant wave period [s] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. ervation [s].. bias=. rms=. Residual error [s] at st.. bias=. rms=. Error distribution [s] at st..... ervation [s]. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= ervation [s] Figure. Dominant wave period:

62 Obs/pred. dominant wave period [s] at st. min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. ervation [s].. bias=. rms=. Residual error [s] at st.. bias=. rms=. Error distribution [s] at st..... ervation [s]. si=. Scatter index [%] at st... Error distribution [%] at st. r.bias=. r.rms= ervation [s] Figure. Dominant wave period:

63 Obs/pred. dominant wave period [s] at st. athos min=. max=. mean=. stdev=. prog h / / / / / / Observation distribution [s] at st. athos ervation [s].. bias=. rms=. Residual error [s] at st. athos. bias=. rms=. Error distribution [s] at st. athos.... ervation [s]. si=. Scatter index [%] at st. athos.. Error distribution [%] at st. athos r.bias=. r.rms= ervation [s] Figure. Dominant wave period: Athos

64 References [] G. Komen et al. Dynamics and Modelling of Ocean Waves. Cambridge University Press,. [] The SWAMP group. Ocean Wave Modelling. Plenum Press, New York,. [] H. Günther, S. Hasselmann, and P. Janssen. Wamodel cycle (revised version). Technical Report, Deutches Klimarechnenzentrum,. [] J. W. Nielsen. Verification of DMI wave forecasts: st quarter of. Technical Report -, Danish Meteorological Institute,. [] J. W. Nielsen. Verification of DMI wave forecasts: nd quarter of. Technical Report -, Danish Meteorological Institute,. [] J. W. Nielsen. Verification of DMI wave forecasts: rd quarter of. Technical Report -, Danish Meteorological Institute,. [] J. W. Nielsen. Verification of DMI wave forecasts: th quarter of. Technical Report -, Danish Meteorological Institute,. [] J. W. Nielsen, J. B. Jørgensen, and J. She. Verification of wave forecasts: DMI-WAM nov-dec. Technical Report -, Danish Meteorological Institute,. [] J. She. HIRLAM-WAM quality assessment on winds and waves in the North Sea. Technical Report -, Danish Meteorological Institute,. [] J. She and J.W. Nielsen. Operational wave forecasts in Baltic and North Sea. Scientific Report -, Danish Meteorological Institute,.

65 List of Tables Key numbers DMI-WAM operational set-up DMI-WAM wave parameters Significant wave height results Extreme wave height results Mean wave period results Dominant wave period results Mean wave direction results Wave stations and locations Observed wave height Observed mean wave period Observed dominant wave period Predicted significant wave height Predicted peak waves and errors Predicted mean wave period Predicted dominant wave period Predicted mean wave direction List of Figures Significant wave height: short range (-h) forecasts DMI wave model domains DMI Hirlam Wave recorders Missing data Significant wave height Peak wave height errors Mean wave period Dominant wave period Mean wave direction Significant wave height: Almagrundet Significant wave height: Trubaduren Significant wave height: Arkona Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height:

66 Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Significant wave height: Athos Mean wave period: Almagrundet Mean wave period: Trubaduren Mean wave period: Arkona Mean wave period: Athos Dominant wave period: Dominant wave period: Dominant wave period: Athos