Verification of DMI wave forecasts 2nd quarter of 2002

Transcription

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

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

3 Verification of DMI wave forecasts nd quarter of Jacob Woge Nielsen The Danish Meteorological Institute, Copenhagen, Denmark

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 height vs. wave period Wave forecast statistics Significant wave height station plots Mean wave period station plots Dominant wave period station plots

5 Introduction with Key Numbers We analyse the quality of wave forecasts valid for the nd quarter of, produced by DMI-WAM - DMI s operational set-up of the rd generation wave model WAM Cycle. The significant wave height H s is of primary interest, but other wave parameters (wave period, direction, swell parameters) are examined where the data material is adequate. Standard error measures (bias, rms error,..) are calculated both as a function of forecast range and of wave height. Special statistics are done for extreme waves. Grand averages are calculated as mean values over all stations, over all ranges, and for separate geographical regions. All model results are forecasts. This means that errors in the parameters do not necessarily imply errors of the model, but may reflect errors in the meteorological forcing data and initial conditions. DMI has produced short-range operational wave forecasts since. A pre-operational validation study was carried out in [], a combined wave-wind validation in for a month hindcast period [], and a verification pilot study in []. Previous report(s) are []. Outline: Ch. briefly 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. For convenience, the Table below shows Key Numbers pertaining to the full model system. Please refer to the Results section (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 for Danish waters since, using the rd generation wave model WAM Cycle (described in detail in [], []) forced by DMI s numerical weather prediction model HIRLAM. In, the geographical model domain includes a large part of the North Atlantic, the North Sea and Baltic Sea, and the Mediterranean. The DMI-WAM model set-up is described in detail below.. 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 ) is the 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; S bf is interaction with the sea bed through friction and wave refraction. DMI-WAM still lacks current data (S cu =) and information about sea ice.. Model set-up DMI provides wave forecasts in three geographical domains as shown below: Figure. DMI wave models. North Atlantic, North Sea-Baltic, and Mediterranean model 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 spatially interpolated wave spectra calculated by that model. The Mediterranean is treated as a closed basin, assuming no wave energy exchange with the Atlantic or the Black Sea. Please refer to Table for a model set-up summary. The wave forecasting system was coldstarted using developed sea. Subsequent model runs are initialised using the sea state at analysis time, calculated by the previous run.

7 Model North Atlantic North Sea - Baltic Mediterranean Space res. Time step min min min Frequencies Direction resol. o o o Forcing model(s) Hirlam G Hirlam E Hirlam E+G - resolution of. o. o. o /. o Longitudes o W- o E o W- o E o W- o E Latitudes o N- o N o N- o N. o N- o N Open boundaries JONSWAP Nested Closed basin Forecast range h h h Output time step h h h Schedule 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. The directional resolution is o (in previous reports erroneously stated as o ). Changes to the model set-up usually require a new coldstart.. Weather model The forcing models are the DMI limited area numerical weather prediction models Hirlam-E and Hirlam-G. Both are currently being used in the DMI weather forecasting service. The G model covers a larger area than the E model, but in coarser spatial resolution (km vs. km on a rotated latitude-longitude grid). The wind vector at m height is interpolated linearly in time and space to match 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 and platforms).. Forecasts Wave parameters output from DMI-WAM are shown in Table. H s H sw T T p T sw w sw DMI-WAM output Significant wave height Height of swell Mean wave period Dominant wave period Swell mean period Mean wave direction Swell direction Table. DMI-WAM wave parameters The forecasts are stored as hourly maps in model resolution. Time series for each station are sampled using nearest model grid point. This is done for each analysis and each parameter. During the nd quarter of, forecasts were produced, of which were archived successfully on tape. Most wave parameters are obtained by a suitable integral of the wave energy spectrum F. In contrast, the dominant wave period T p is the discretized model frequency (inverse) containing the highest energy, picked from the predefined values. In cases with two competing wave energy maxima (wind sea and swell), T p may flip between the two, as first one, then the other has the highest energy. This means that T p is a non-smooth function of time or space, sampled with low accuracy.. Observations The wave recorder positions are shown in Fig. below. A total of stations that record more or less regularly are selected for verification. Comprehensive station information is found in Appendix., Table. Wave data is obtained from a number of sources, as indicated in table. SMHI, KDI and NCMR data are kindly provided by each agency in question. NDBC data is retrieved via the GTS. Table shows the number of stations for each wave parameter, and for each of geographical domains. NDBC SMHI KDI NCMR Wave Data providers National Data Buoy Center (UK) Swedish Meteorological Institute Danish Coastal Authority National Center for Marine Research (Greece) Table. Wave data providers.

9 Figure. Wave recorder locations. Parameter H s T T p w H m Atlantic Scotland-Faroe Irish Sea Br. Channel North Sea Danish West Coast Kattegat - Baltic Sea - - Mediterranean - Total Table. Number of wave stations in each domain, and for each wave parameter. Maximum wave height H m, recorded at Baltic and Danish West Coast stations only, is forecasted by the wave model. Swell parameters are not recorded at any fixed location. The mean data coverage is % (see Fig. for missing data). The sampling rate is hour, with stations (cf. Table ) sampling every hours. At these stations, we consider steady hour sampling as full data coverage. The sampling accuracy is H s :.m, T p :s, T :.s, w : o. Two buoys (, ) use low.m H s accuracy. Four buoys (Danish West Coast) use variable T p accuracy of.-.s, while one (Athos) uses high.s T p accuracy. Statistics on the erved wave parameters, and wave period vs. wave height plots, are shown in Appendices. and..

10 Missing data (cov=)... almag oland truba athos Figure. Missing data. St.,, and sample every rd hour, but revert to h sampling in storm situations. St.,,, and Athos sample every rd hour.

11 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. With stations, the matrix has elements. By averaging the residual over all analyses, we get the model bias or mean error: bias(station range) Further linear 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 s.m wide and averaged for each bin. bias(station bin) rms(station bin) Averaging 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.

12 Results This section describes wave verification results for the nd quarter of, for significant wave height (H s ), mean and dominant wave period (T T p ), and mean wave direction ( w ). In the sections below, we discuss grand averages and regional averages 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. shows the short range (-h) scatter diagram. The error estimates are sorted out on geographical regions. Parameter #st bias rms si cc Region cm % cm Atlantic ; ;.. Scotland;Faroe ; ;.. Irish Sea ; ;.. Br.Channel. North Sea ; ;. Danish West Coast. Kattegat;Baltic Mediterranean ; ;.. All Waters ;. Table. Significant wave height results forecast Scatter diagram h, all stations cc= ervation Figure. Significant wave height: short range (-h) scatter diagram The wave model has almost no bias on average and an rms error of. m. Scatter index is low (.) and correlation coefficient high (). There is some regional spread. Waves are underestimated on average (negative bias) at the Atlantic, Irish Sea, Shetland and Mediterranean stations, and overestimated (positive bias) in the British Channel and in the Baltic Sea. RMS errors range roughly from a quarter to half a metre. The scatter index is well below an acceptance level of. in most

13 regions, but exceeds in the British Channel, in the Baltic and in the Mediterranean. Fig. shows the scatter index at each station. Scatter index (avg=.), h... almag oland truba athos Figure. Significant wave height: scatter index The error dependency on forecast range and on wave height is shown in Fig.. The model bias is almost independent of forecast range, while the rms error/scatter index increase slowly. The rms error is significant already at analysis time since the model is initialised without any use of the erved sea state. Conversely, the correlation coefficient decreases, from at short range to at long range. There is a strong dependency on wave height. Very small waves are slightly overestimated, while higher waves are underestimated by up to about.m on average. The rms error increases steadily with increasing wave height. Except for very small waves (less than m), the relative bias and rms error only depend weakly on wave height. The relative rms error decreases slowly with wave height, with a standard level of about %. For waves >m the data material is too sparse to produce reliable statistics. Results on significant wave height for each single station is shown in Table, Appendix.. Data sheets are presented in Appendix..

14 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

15 . Extreme wave height The error on extreme waves is calculated by singling out the highest events at each station, and then calculate the forecast error, allowing for a few hours phase displacement. Table shows peak biases for each of the geographical domains, averaged over all forecast ranges. Parameter #st peak bias Region cm % Atlantic ; ; Scotland;Faroe ; ; Irish Sea Br.Channel North Sea ; Danish West Coast ; ; Kattegat;Baltic ; ; Mediterranean ; ; All Waters ; ; Table. Extreme wave height results There is a negative peak bias in most regions, with the British Channel as an exception. On average, the system has a small negative peak bias of -cm or -%. The dependency of the peak bias on forecast range is shown in Fig.. The peak bias is small at short range (day ), but increases on day and beyond Peak bias. Average peak error [m] forecast range [hrs/] Figure. Extreme wave height Table in Appendix. shows peak biases for each single station.

16 . 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.. 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 unresolved. At the stations in the Baltic and the Meditteranean T is only slightly overestimated. The scatter index at these stations is well below the acceptancy level of.. forecast cc= Scatter diagram h, all stations ervation forecast Scatter diagram h, Kattegat Baltic stations cc=. ervation Figure. Mean wave period, -h range. Left panel: all stations, right panel: Baltic stations only Results on mean wave period for each station are shown i Table, Appendix.. Data sheets are presented in Appendix..

17 . 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.. Parameter #st bias rms si cc Region sec. % sec. Atlantic.... Scotland;Faroe.... Irish Sea.... Br.Channel.... North Sea.... Danish West Coast.... Mediterranean ;. ;.. All Waters.... Table. Dominant wave period results T p shows very bad verification results due partly to low recording and forecasting accuracy, and partly to the non-smoothness 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 forecast ervation Scatter diagram h, Mediterranean stations cc=. ervation Figure. Dominant wave period, -h range. Left panel: all stations, right panel: Mediterranean stations only Results on dominant wave period for each stations is found in Table, Appendix.. Data sheets in Appendix..

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

19 Conclusion DMI wave forecasts valid for the nd quarter of are verified, using wave data from buoys. A Key Number Table is put right after the Introduction in the beginning of the report (Table ). Main conclusions are: The significant wave height H s and mean wave direction w are well predicted, but we have some problems predicting wave period There is a large regional spread in forecast quality The H s model error depends mainly on wave height. Extreme waves are usually underestimated The forecast quality decreases slowly with increasing forecast range The significant wave height is recorded at all stations. The error distribution is examined in terms of forecast range, as a function of erved wave height, and for separate geographical regions. The ervation-forecast correlation is high, on average. This falls off a bit as the prediction range increases. The bias is very small on average, but there is a large geographical spread, and some dependency on wave height. Low waves are overpredicted, while the highest waves are underestimated by about %. The bias does not depend on forecast range. The average rms error is.m, increasing gradually with forecast range. Except for situations with almost calm sea, waves have a relative rms error of about %. An average scatter index SI=. is acceptable. stations have si>. (sometimes used as an acceptance level) due to low recording accuracy or small average wave height. Extreme waves are underestimated in most regions, with an average ;% peak bias. An exception is the British Channel, where the highest waves are overestimated by about %. The negative bias increases on day and beyond. Two types of wave period are recorded; mean and dominant (peak) wave period. The mean wave period is recorded at locations, half of which have a data interpretation problem. At the remaining stations the model overestimates the mean wave period by roughly half a second, with a scatter index of. and a correlation coefficient of.. Dominant wave period predictions are not good. This is 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. Only the Meditteranean stations show good results, with no bias and a scatter index of. Mean wave direction predictions have a small bias, a standard deviation of 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.

20 Appendix This Appendix contains a wave recorder station table (below), ervation statistics tables, forecast statistics tables, wave height/period plots, 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 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, NDBC=National Data Buoy Center (UK), NCMR=National Center for Marine Research (Greece), KDI=Coastal Authorities (Denmark). 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.

21 . Observed wave statistics Station min mean max stdev almag.... oland.... truba athos.... Table. Observed wave height. The fraction of missing data is shown in Fig.

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

23 . Wave height vs. wave period The relation between significant wave height H s and mean wave period T is shown on the diagrams, below, for those stations that record both quantities. At each station, there is a fair linear correlation between H s and T, superimposed by a weak swell component. st. oland, cc= st. almag, cc=. st. truba, cc=. Mean wave period [s] Mean wave period [s] Mean wave period [s] Significant wave height [m] st., cc=. Significant wave height [m] st., cc=. Significant wave height [m] st., cc= Mean wave period [s] Mean wave period [s] Mean wave period [s] Significant wave height [m] st., cc= Significant wave height [m] st. athos, cc=. Significant wave height [m] Mean wave period [s] Mean wave period [s] Significant wave height [m] Significant wave height [m] Figure. Significant wave height vs. mean wave period

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

25 Parameter Obs peak Station m m % almag. ;. ; oland. ;. ; truba... ;. ;.... ;. ;. ;... ;. ;. ;. ;. ;. ;. ;. ;.... ;. ;. ;. ;. ;. ;. ;. ;..... ;. ;. ;. ;.. ;... ;. ;. ;. ;..... ;. ; athos. ;. ; Table. Average of top wave events (peaks) and corresponding mean peak error (peak bias) Parameter bias rms si cc Station sec % sec almag.... oland.... truba athos.... Table. Predicted mean wave period

26 Parameter bias rms si cc Station sec % sec ;. ;... ;. ; ;. ;... ;. ; athos.... Table. Predicted dominant wave period Parameter bias std cc Station deg deg ; athos Table. Predicted mean wave direction

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

28 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

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

30 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

31 min=. max=. mean=. stdev=. Obs/pred. wave height [m] at st. 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:

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:. The zig-zag curves are caused by irregular h sampling.

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:. The sampling accuracy is.m

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:. A single event (June th) is grossly overpredicted on short range due to error in the wind forecast.

43 Obs/pred. wave height [m] at st. min=. prog h max=. mean=. stdev=. / / / / / / / 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:. A single event (June th) is grossly overpredicted on short range due to error in the wind forecast.

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=. prog h max=. mean=. stdev=. / / / / / / / 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 min=. max=. mean=. stdev=. Obs/pred. wave height [m] at st. 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.

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:. The sampling accuracy is.m

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:

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 min=. max=. mean=. stdev=. Obs/pred. wave height [m] at st. 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.

55 Obs/pred. wave height [m] at st. min=. prog h max=. mean=. stdev=. / / / / / / / 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:. A single event (June th) is grossly overpredicted on short range due to error in the wind forecast.

56 Obs/pred. wave height [m] at st. min= prog h max=. mean=. stdev=. / / / / / / / 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:

57 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

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

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

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

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

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

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

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

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

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

67 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 Meteorologiacl Institute,. [] J. W. Nielsen, J. B. Jørgensen, and J. She. Verification of wave forecasts: DMI-WAM nov-dec. Technical Report -, Danish Meteorologiacl Institute,. [] J. She. HIRLAM-WAM quality assessment on winds and waves in the North Sea. Scientific Report -, Danish Meteorological Institute,. [] J. She and J.W. Nielsen. Operational wave forecasts in Baltic and North Sea. Scientific Report -, Danish Meteorological Institute,.

68 List of Tables Key numbers DMI-WAM operational set-up DMI-WAM wave parameters Wave data providers Wave stations in each domain 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 DMI wave models DMI Hirlam Wave recorders Missing data Significant wave height: short range (-h) scatter diagram Significant wave height: scatter index Significant wave height Extreme wave height Mean wave period Dominant wave period Mean wave direction Significant wave height vs. mean wave period Significant wave height: Almagrundet Significant wave height: Øland Significant wave height: Trubaduren 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:

69 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: Significant wave height: Significant wave height: Significant wave height: Athos Mean wave period: Almagrundet Mean wave period: Øland Mean wave period: Trubaduren Mean wave period: Athos Dominant wave period: Dominant wave period: Dominant wave period: Athos