1. Introduction
One of the main challenges facing the offshore wind energy industry in North America is the generally poor ability of numerical weather prediction (NWP) models to predict wind speed and turbulence profiles over ocean (Olsen et al. 2015). Much of this has to do with atmospheric boundary layer (ABL) parameterization schemes in NWP models. Our understanding and modeling of the physics of the marine ABL simply lags behind that of the ABL over land because of the scarcity of high quality, long-term observations. In this study we propose to improve the representation of the marine ABL lower-level winds in the WRF Model (Skamarock et al. 2008).
The coupling of the atmosphere to the surface via fluxes of heat and momentum drives the spatial and temporal evolution of the ABL. Typically in NWP models these fluxes are estimated from the available mean quantities. A powerful set of statistical relationships was derived from Monin–Obukhov similarity theory (MOST; Obukhov 1946; Monin and Obukhov 1954; Lumley and Panofsky 1964; Wyngaard 1973) based on pioneering field campaigns held in the 1960s and 1970s, such as the 1968 Kansas experiment (Izumi 1971), which sought to improve our understanding of the turbulence characteristics in the atmospheric surface layer (i.e., the portion of the ABL closest to the ground).
Currently, MOST is still the basis of state-of-the-science NWP model surface and boundary layer formulations. The universality of its relationships is questionable when applied offshore, however, given that its formulation is based on (incomplete) land-based measurements. Indeed, several past studies have found evidence of deficiencies in MOST when applied to the marine ABL (e.g., Geernaert et al. 1986; Donelan et al. 1993; Rieder et al. 1994; Hare et al. 1997; Edson and Fairall 1998; Sjöblom and Smedman 2002, 2003; Smedman et al. 2003, 2009; Pichugina et al. 2012; Andreas et al. 2012).
A proper treatment of the marine ABL requires additional scaling parameters to account for the momentum production and dissipation generated by the highly variable ocean waves (Sullivan et al. 2008). Hanley and Belcher (2008) found that ocean wave momentum flux can affect the entire marine ABL wind profile. Following Edson and Fairall (1998), we can define a wave boundary layer (WBL), which is the portion of the surface layer in the marine ABL where the ocean wave contribution to the turbulence budget is present.
Observations of key quantities in the WBL are quite limited (Smedman et al. 2009) and, when available, are sparse in time and space (Pichugina et al. 2012). The state estimation problem, usually called data assimilation (DA) for the atmosphere, is the process by which prognostic variables in a model are estimated and updated using observations. This process can be extended to include parameter estimation [in this case via state augmentation; e.g., Aksoy et al. (2006); Golaz et al. (2007); Ruiz et al. (2013); Hacker and Angevine (2013); Bellsky et al. (2014)]. Thus, a DA system provides a theoretically optimal framework for combining observations and numerical simulations, filling the gaps in the observational datasets with model estimates while simultaneously optimizing model parameters.
As we describe in detail in section 2, joint state-parameter estimation allows new insights into model dynamics and errors. If implemented properly, very short-range predictions (minutes to hours) skillfully predict the future atmospheric state. The model, then, is representing the state of the system with the greatest fidelity achievable given its formulation and a set of observations. The model state can then be examined for internal balances, budgets, and error structures. By combining an atmospheric modeling system with observations of the surface layer in the marine ABL via a DA system, we can verify the positive impact of the parameter estimation techniques on low-level wind predictions, which are critical to reducing market barriers to offshore wind energy production.
The purpose of this study is to examine the impact on hub-height offshore wind 1-h forecasts that result from the estimation of a key parameter in the marine ABL using ensemble DA and a single-column model (SCM). Secondarily, we want to find out if estimation of this key parameter also improves the prediction of the momentum fluxes, which play an important role in ABL development. These findings will provide some indication of how much model error in the marine ABL is or is not explained via estimation of this parameter.
This paper is organized as follows. Section 2 describes joint state-parameter estimation. Section 3 provides information on the meteorological tower we use for observations. The experimental design is laid out in section 4. Results are presented in section 5, and section 6 contains a summary and concluding remarks.
2. Joint state-parameter estimation
a. Background
The covariance propagation is completed by an ensemble prediction beginning from the analysis, with perturbations according to 
Skillful short-range predictions lead to small corrections (increments) by the observations to the prior ensemble sample estimate. Those increments contain useful information about the model itself. This information results from the fact that in an EnKF the forecast state is temporally propagated with 
Over many updates, distributions of increments 
Assimilation of near-surface observations within an SCM and an ensemble filter has already been explored (Hacker and Snyder 2005; Hacker and Rostkier-Edelstein 2007; Hacker et al. 2007; Rostkier-Edelstein and Hacker 2010). Hacker and Angevine (2013) quantified model errors with short-range predictions and increments from the joint state-parameter estimation with the SCM version of the WRF NWP model, DART. Even though the results in that study were obtained for areas over land, we believe that the technical concept also applies to offshore simulations. The results of Hacker and Angevine (2013) suggested the complexity of model inadequacy; a model change can easily lead to improvement in one model variable and skill reduction in another.
Model error can take either a parametric or functional form. Each parameterization in an NWP model can generally be written as a series expansion of the parameterized term in the model equations (Nielsen-Gammon et al. 2010). Parametric errors exist because coefficients on terms in that series expansion are rarely known perfectly. More often, they are derived from a limited number of field experiments or are heuristically tuned within the NWP model. But the functional form of the series expansion can be incorrect; we refer to this as structural error, and its form is typically not known a priori.
State augmentation offers a straightforward and theoretically optimal way to quantify parametric errors. Parameters 
b. Sensitivity tests
We performed sensitivity tests with the WRF-SCM on various parameters to see which would impact the model wind speed in the marine ABL. We tested a multiplicative constant in the equation for the convective velocity scale 
c. Parameter estimation of 
In this study, for each experiment we initialized 
3. FINO1 platform
a. Tower description
We utilized meteorological observations from the Forschungsplattformen in Nord- und Ostsee 1 (FINO1; http://www.fino-offshore.de/en) tower. FINO1 is one of three instrumented, continuously operating measurement towers installed in the German bight. FINO1 and FINO3 are located in the North Sea while FINO2 is in the Baltic Sea. FINO1 is an approximately 80-m tower mounted on a platform 20 m above the lowest astronomical tide (LAT), giving measurements of atmospheric conditions to approximately 100 m above LAT. The FINO1 platform was constructed in autumn 2003, and is located in the North Sea approximately 50 km northwest of Emden, Germany, in a water depth of approximately 30 m (Fig. 1). FINO1 was built partly to quantify the wind characteristics before the Alpha Ventus offshore wind farm was built nearby. Construction of the Alpha Ventus wind farm started with the installation of the substation in July 2008. This analysis uses data from 2006, when the winds measured at the site represent the undisturbed flow.
(a) Location and (b) configuration of the FINO1 platform. [Images are from the FINO1 website (http://www.FINO1.de/en).]
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
A variety of data are collected at different heights on the tower, as listed in Table 1. There is only a single-cup anemometer and wind vane at each level on the tower, and booms are a similar length to the tower face width. The wind speed measurements are potentially impacted by flow speeding up or slowing down around the tower structure. The cup anemometers are mounted on booms that extend in the direction 127°–135°; when winds are from approximately 310° ± 30°, wind speed measurements should be considered potentially impacted (or “shadowed”) by wakes from the tower structure. For the wind and stability climatology analysis in section 3b, no filtering was done based on wind direction. For the period of October–December 2006, our analysis found that wind components could be derived for at least one height on the tower from nonmissing and nonshadowed wind speed and direction observations over 86% of all 10-min observations, with the vast majority of continuous periods without any valid wind component observations being less than 1 h in duration (not shown). For the DA experiments we excluded the shadowed wind observations.
Instrumentation heights on the FINO1 tower. Heights are given with respect to the LAT: WS, wind speed; WD, wind direction; SA, sonic anemometer; AT, air temperature; RH, relative humidity; AP, air pressure; and PRCP, precipitation rate.
The FINO1 tower has three sonic anemometers, located at 40, 60, and 80 m above LAT, to measure the 3D velocity components at a frequency of 10 Hz. Although measurements from the sonic anemometers were available throughout 2006, the 60-m sensor was not operational during the last half of the year. Leveraging the previous work of Sanz Rodrigo (2011), turbulent fluxes were obtained by averaging the velocity covariances over a 1-h period to reduce random flux errors. Some additional details about the flux measurements and calculation of the covariances are included in appendix A.
b. Climatology of wind and atmospheric stability conditions
Atmospheric stability at the FINO1 location shows a slight relationship to wind speed (Fig. 2). In Fig. 2 data have been categorized according to ranges of stability that are typically used for the ABL:
- strongly stable,
- stable, 0.05 <
- neutral, −0.05 <
- unstable, −10 <
- strongly unstable,
Monthly distributions of wind speed and stability. Stability data are plotted as a function of the 81.5-m wind speed. Stability is classified into strongly unstable (red), unstable (orange), neutral (light yellow), stable (light blue), and strongly stable (dark blue). Data in this plot were not filtered by either wind direction or wind speed.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
A goal of this study was to identify when conditions were neutral or slightly convective, which is when we can expect MOST to be most appropriate. This is why we chose a conservative threshold for the strongly stable conditions above, to safely avoid periods where those conditions predominated. The time series of binned Richardson numbers is plotted in Fig. 3, from which it can be seen that there are several periods when the marine ABL stability was neutral for 24 h or more. These occurred on 6–7 February, 28 March, and 5, 13–15, and 30 December 2006. Figure 3 also shows that stable conditions predominated from April through July, while the months where mainly neutral and slightly convective conditions were observed were January, February, October, November, and December.
Time series of stability classes. Data are 10-min bulk Richardson number binned according to the scale at the bottom of the plot (same scale as Fig. 2). White areas indicate intervals where the data required for the calculation were not available. Data in this plot were not filtered by either wind direction or wind speed.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
Wind speed profiles, grouped by stability class, are similar to what would be expected from theory (not shown). In unstable conditions, there is little variation of wind speed with height, while stable conditions show a steeper, positive gradient to the wind speed.
Based on these results, and the desirability for the simulations to be conducted over continuous periods, the selected periods at FINO1 were from October to December 2006.
4. Experiment design
The WRF-SCM provides a platform for more rapid testing than would be available with the WRF 3D model. In cases where the marine ABL is weakly forced by horizontal mesoscale gradients, the SCM is also broadly applicable as a representative model of the local conditions in horizontally homogeneous terrain. Because the FINO1 tower is located approximately 50 km offshore, we can also assume that the effects from the land–sea interface are limited. Simulations with the WRF-SCM are relevant to the marine ABL because the subgrid scale can be isolated. To ensure results remain relevant to 3D dynamics, the 3D WRF is used to provide vertical velocity tendencies, geostrophic wind components, and advective tendencies. Thermal profiles and clouds can advect through the SCM domain, and realistic treatment of those may be necessary to achieve the most accurate energy balances at the surface (Wulfmeyer and Janjić 2005; LaCasse et al. 2008). But whether this is the case is unknown for micro and mesoscale interaction, especially when performing DA (e.g., Rostkier-Edelstein and Hacker 2010).
a. WRF 3D runs for SCM forcing
Version 3.5.1 of the Advanced Research version of WRF (WRF-ARW) was set up over northern Europe, centered over the FINO1 platform, to provide lateral forcing for the SCM–DART experiments from 1 October to 31 December 2006. One 3D run did not use any DA (“Baseline”) while the other (“FDDA”) used NCAR’s community four-dimensional data assimilation (FDDA) system, which has been extensively tested over the years and is known to provide a good fit with the available observations (Stauffer and Seaman 1990, 1994; Stauffer et al. 1991; Jonassen et al. 2012). The assimilated observations were from NCEP Automated Data Processing data streams stored in NCAR Research Data Archive datasets 353.4 and 461.0 (NCAR 1980, 2004). The observation types that were assimilated in those experiments include radiosondes, surface stations, buoys, ships, and aircraft reports. Figure 4 shows the location of the FINO1 platform (54.014861°N, 6.587639°E) and the 3D WRF computational domains. Additional details about the 3D WRF Model setup are contained in appendix B.
The 3D WRF domain configuration centered over the FINO1 tower location (blue crisscross). The horizontal grid spacings are 30, 10, and 3.3 km for the three domains, respectively.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
b. SCM–DART ensemble forcing description
Previously, common strategies for generating initialization and lateral forcing data for SCM experiments relied upon a large climatology of input data to randomly draw from (e.g., Hacker and Rostkier-Edelstein 2007). The new EOF approach that we describe below is attractive because it requires that only a single 3D WRF run be made for the same period of the SCM experiment to provide the forcing, rather than several years of (in this case) October–December simulations.
Lateral forcing conditions for the 100-member SCM–DART ensembles were produced with mean forcing from the WRF 3D runs and ensemble perturbations derived by empirical orthogonal functions (EOFs) of each relevant variable from 3D WRF output over each monthly period. Unique EOFs for each hour of the day were found for each monthly simulation period. These perturbations’ magnitude roughly matches the RMSE of the 3D WRF at the location of the FINO1 tower for the monthly time period selected in order to assure statistical consistency of the lateral information driving the SCM (i.e., that the perturbation magnitudes were, on average, comparable to the error magnitudes in the 3D WRF simulation that month). The appropriate size of the perturbation magnitudes was determined prior to running SCM–DART. The perturbations were a linear combination of the first several EOFs, whose coefficients were random numbers constrained by an autoregressive [AR(1)] process, to ensure temporal consistency. Perturbations were only made to the atmospheric variables; all 100 SCM–DART members used identical, unperturbed SST and subsurface forcing conditions. These subsurface forcing files were also generated from the WRF 3D simulation. From these subsurface, SST, and atmospheric forcing files, an ensemble of “wrfinput” files were generated for the SCM–DART simulations. When running the SCM, however, we turned off the advection of wind, temperature, and moisture so as not to wipe out the effects of the assimilation. However, we kept the vertical advection on, which meant that, effectively, the only relevant perturbations in this study are to the geostrophic wind field.
Additionally, we made some code improvements to the WRF-SCM for use over ocean grid points, as described in appendix C.
c. SCM–DART experiments
With the goal of reducing wind speed error by joint state-parameter estimation and understanding the sources of these errors, the following experiments were conducted with the coupled WRF-SCM–DART system for month-long periods covering October–December 2006, using WRF version 3.5.1 and modifications to both WRF and DART that allow parameter estimation of the time-varying surface roughness length 
- “Baseline”—SCM–DART runs with forcing from 3D WRF without FDDA and with
- “Baseline+ZNT_est”—SCM–DART runs with forcing from 3D WRF without FDDA and with
- “FDDA”—SCM–DART runs with forcing from 3D WRF with FDDA and with
- “FDDA+ZNT_est”—SCM–DART runs with forcing from 3D WRF with FDDA and with
Our hypothesis was that both the higher quality boundary conditions and the estimation with DA of 
For all experiments we used 1-h DA cycling with the EAKF implemented in DART. Each SCM–DART ensemble had 100 members. The WRF prognostic variables updated by DART were all three wind components, as well as the geopotential height, potential temperature, pressure, and water vapor mixing ratio. We assimilated the 10-min observations of the u and υ wind components, temperature, and dewpoint temperature from multiple levels on the FINO1 tower, valid at the top of every hour ±10 min. Observations outside of that 20-min window surrounding the top of the hour were discarded.
We conducted several month-long sensitivity tests to tune the observation error variances for each observation type. The goal of this tuning was to identify the observation error variances that led to RMSE values that roughly equaled the total spread (the sum of the ensemble spread and the observation error). When the RMSE and total spread equal each other, the ensemble is statistically consistent. We set the observation errors to be 1.0 m s−1 for wind components, 0.25°C for air temperature, and 0.5°C for dewpoint temperature (square those values to get the observation error variances). These observation error variances were used in all experiments.
For nearly all geophysical models using ensemble Kalman filters for DA, covariance localization is required in both the horizontal and vertical. This localization process sets a cutoff or maximum distance beyond which an observation is not allowed to influence the state variables (Houtekamer and Mitchell 1998; Anderson 2012). Here, we use the Gaspari–Cohn fifth-order piecewise rational correlation function of space [Eq. 4.10 in Gaspari and Cohn (1999)] for localization, which is the default localization function in DART. Vertical covariance localization in the EAKF algorithm was set to 4 km after several sensitivity tests. Horizontal covariance localization, meanwhile, of course has no impact on DA in SCM experiments. Additionally, DART’s standard spatially varying state space inflation was applied to the prior state in order to increase the ensemble spread at every assimilation time. The namelist settings guiding the inflation were chosen according to prior experience with DART and were not tuned in this study.
Examples of a monthly time series of SCM–DART ensemble mean 1-h forecasts of wind speed and temperature at FINO1 compared against observations and the 3D WRF simulation that drove the SCM–DART ensemble are shown in Fig. 5 for the FDDA+ZNT_est experiment. For the wind speed plot in Fig. 5a, the 1-h ensemble mean forecasts (red) are on average of similar accuracy as the 3D WRF analysis wind speed at FINO1 (black), and the model predictions track the observations reasonably well. For the temperature plot in Fig. 5b, the ensemble mean forecasts closely match the observations and have smaller errors than the 3D WRF analysis. We would expect the SCM–DART ensemble mean 1-h forecasts to match the observations at FINO1 more closely than the 3D WRF analysis matched them because the SCM–DART runs assimilated FINO1 data, while the 3D WRF assimilated a different set of observations that did not include FINO1 data. That said, the only forcing to the SCM was provided by geostrophic winds. Thus, for winds, the perturbed forcing fields imposed an additional tendency away from the observations. The SCM–DART ensemble mean for temperature hewed close to the observations because there was no perturbed forcing for temperature.
Time series of (a) wind speed and (b) temperature forecasts and observations (blue) at the FINO1 tower, averaged over the tower depth, for the FDDA+ZNT_est experiment for November 2006. The SCM–DART ensemble mean 1-h forecasts are in red, and this experiment’s corresponding 3D WRF prediction at FINO1 is in black.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
d. Verification metrics
5. Results
An example time series of the evolution of 
Time series of the ensemble mean sea surface roughness length 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
Performance metrics for the four SCM–DART experiments described above (Baseline, Baseline+ZNT_est, FDDA, and FDDA+ZNT_est) are shown in Figs. 7–9 for wind speed, the u-wind component, and the υ-wind component, respectively. For the month of October 2006, the results reflect the initial hypothesis, that is, that both the higher quality boundary conditions and the estimation with DA of a key parameter, the surface roughness 
(top left) RMSE, (top right) bias error, (bottom left) centered RMSE, and (bottom right) correlation of 1-h wind speed predictions for the months of October, November, and December 2006. Shown are values for the Baseline (blue), Baseline+ZNT_est (red), FDDA (green), and FDDA+ZNT_est (orange) experiments. See main text for description of the four experiments.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
As in Fig. 7, but for the zonal wind component 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
As in Fig. 7, but for the meridional wind component υ.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
Figure 10 shows, for the month of October 2006 only, an analysis of the same experiments presented in Figs. 7–9, but by looking at the vertical profile of the same metrics at FINO1 (RMSE, blue; bias, black; and CRMSE, green), with the addition of total spread (red), which is the sum of the ensemble spread and the observation error. When the total spread is roughly equivalent to the RMSE of the ensemble mean, it indicates that the probabilistic prediction system is able to quantify the prediction uncertainty. Aside from indicating a more optimal DA system, predicting this uncertainty is a key factor in supporting cost-effective decision-making. Results are shown for the zonal (u) component for all four experiments during October 2006. Similar results were obtained for the meridional (υ) component, wind speed, temperature, and dewpoint temperature, and also for the months of November and December (not shown). Also shown in Fig. 10 is the number of available observations across the different vertical levels (cyan) over the entire month and the number of assimilated observations (magenta).
Vertical profiles at FINO1 of RMSE (blue), bias (black), centered RMSE (green), total spread (red), number of available observations (cyan), and assimilated observations (magenta). Shown values are for 1-h predictions of the zonal wind component 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
The first aspect to notice in Fig. 10 is the limited vertical variability of the metrics, which makes the analysis shown in Figs. 7–9 of averages across the entire tower representative of the whole column. Also, no wind component data were available at 61 m because of the 61-m wind vane being nonoperational during the last half of 2006. When 
We compared these modeled stresses to observed stresses from sonic anemometers on the FINO1 tower located at heights of 40 and 80 m (the 60-m sonic anemometer was not operational during October–December 2006). Figures 11 and 12 show the same statistics as Figs. 7–9, but for the turbulent stress 
As in Fig. 7, but for turbulent stress 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
As in Fig. 7, but for the turbulent stress 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
Time series of the turbulent stress 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
As in Fig. 13, but for the turbulent stress 
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
In Fig. 11 the RMSE for 
Overall, these results confirm one of the hypotheses of this project: 1-h forecasts of low-level winds in the marine ABL are improved by using our joint state-parameter estimation procedure. These improvements will positively impact the offshore wind energy industry. That is, estimating uncertain parameters of NWP boundary layer schemes over water for neutral-to-unstable conditions within a DA framework, even with a single-column model, leads to noticeable improvements in short-range wind predictions.
While the hub-height wind predictions improved with joint state-parameter estimation, the turbulent stress predictions did not. This result means there are still structural sources of error that are unaccounted for by our method of estimating 
6. Summary and conclusions
In this study we have improved NWP analyses and forecasts of low-level winds in the marine boundary layer as estimated and predicted with an SCM and ensemble DA system. This has been accomplished using the WRF single-column model (WRF-SCM), state estimation algorithms from DART, and observations of key quantities of the lower marine ABL at the FINO1 tower in the North Sea, including temperature and winds at multiple levels above the sea surface.
We modified the WRF-SCM to run properly, not just over land points but over water points as well; developed a new lateral forcing and perturbation strategy for SCM ensemble experiments; and created 100-member WRF-SCM ensembles using the ensemble adjustment Kalman filter from the DART toolkit. For each month of October, November, and December 2006, we performed four ensemble experiments. These four experiments used two different 3D WRF datasets to provide the lateral forcing for the SCM ensemble (first, a baseline run without any DA and, second, a run with FDDA), as well as two different techniques to determine the sea surface roughness length, 
We found that regardless of the forcing data, the wind speed RMSE was lower in every month by 4%–22% when 
The lack of improvement in the prediction of the turbulent fluxes indicates that there is potentially a structural problem with the parameterization of surface effects in the marine ABL. Parameterization of wave effects using the simple Charnock–Fairall relation, where the assumption is that the wind and waves are in equilibrium, may be problematic because there is no way to account for the effects of swell. Thus, new parameterizations accounting for the swell or other wind–wave nonequilibrium effects are likely necessary to improve offshore wind predictions further.
The experiments with the WRF-SCM–DART system have led to large improvements with respect to a standard WRF configuration, which is currently used by the wind energy industry. The WRF-SCM appears to be a tool particularly suitable for offshore wind energy short-range (1 h) forecasting applications given its accuracy, the ability to quantify uncertainty, and the minimal computational resource requirements. For resource assessment applications, where one needs to predict turbulence levels in addition to the wind, it is unclear whether parameter estimation would be the most appropriate approach, however. In situations where the impact of an upwind wind farm may be of interest in a downwind location, a 3D modeling approach is suitable. Work to apply similar joint state-parameter estimation techniques to a 3D WRF–DART ensemble and examine its suitability is ongoing.
This project was funded by the U.S. Department of Energy under Contract DE-EE0005374. We would like to acknowledge high-performance computing support on Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory, which is sponsored by the National Science Foundation. Additionally, several of the analysis and plotting scripts were coded using the NCAR Command Language (NCL; doi:10.5065/D6WD3XH5). FINO1 data were provided by the German Bundesamt für Seeschifffahrt und Hydrographie under agreements with the National Renewable Energy Laboratory (NREL) and NCAR. We thank the Danish Meteorological Institute (DMI) for providing the high-resolution SST analyses for the region around northern Europe. The authors also thank Sue Ellen Haupt (NCAR), Terri Marshburn (NREL), and two anonymous reviewers for helpful comments that improved the manuscript.
APPENDIX A
FINO1 Flux Measurements
Using the planar fit method, measurements from the sonic anemometers were rotated to the mean streamline coordinate system (Wilczak et al. 2001). Because the mean streamline plane and the sea surface must be parallel to each other, the mounted tilt angles can be inferred and corrected for. During an evaluation period in the first half of 2006, tilt angles from 1.0° to 1.8° were found for the three sonics (Sanz Rodrigo 2011). Using the eddy-correlation technique over a time scale of 5 min, variances and covariances of detrended velocity and sonic temperature perturbations were computed.
APPENDIX B
3D WRF Model Setup
For the 3D WRF Model described in section 4a that provided the forcing conditions for the SCM ensemble, there were three one-way nested domains (Fig. 4) with horizontal grid spacing of 30, 10, and 3.3 km, respectively, with 132 × 132 × 41 grid points for each domain. There were 41 vertical levels, with eight levels in the first 500 m above MSL at approximately 15, 45, 75, 100, 130, 195, 315, and 490 m.
The physical parameterizations chosen follow work presented by Draxl et al. (2014). This configuration was developed for North Sea applications by the Department of Wind Energy at the Technical University of Denmark (DTU). The physics options include the Thompson microphysics scheme (Thompson et al. 2008), the Kain–Fritsch cumulus scheme (Kain 2004) for domains 1 and 2 only (with explicit convection on domain 3), sixth-order numerical diffusion, and positive-definite advection of moisture and scalars. The Rapid Radiative Transfer Model (Mlawer et al. 1997) and Dudhia schemes (Dudhia 1989) are used for longwave and shortwave radiation calculations, respectively. The 2.5-level Nakanishi and Niino (2006) ABL and its companion surface-layer scheme (MYNN) were selected.
The model was initialized with global data from the NOAA Climate Forecast System Reanalysis (CFSR) project (Saha et al. 2010). The CFSR data are 6-hourly global reanalyses at 0.5° grid spacing, valid from 1979 to 2010. The 6-hourly data are also used for lateral boundary conditions along the outermost domain. In addition, daily SST data from the NCEP Optimum Interpolation Sea Surface Temperature (OISST) project (https://www.ncdc.noaa.gov/oisst) were used. Where available over the North Sea and North Atlantic, SST analyses from the Danish Meteorological Institute (DMI) were used. The DMI SST product (http://www.myocean.edu) is at 1/30° grid spacing, and was blended with the 1/12° NCEP OISST data near the DMI SST dataset’s outer boundary (Fig. B1). Land-use categories come from MODIS.
An example of regional 1/30° SST data from DMI overlaid onto WRF domain 1.
Citation: Monthly Weather Review 145, 1; 10.1175/MWR-D-16-0063.1
APPENDIX C
WRF-SCM Improvements
The WRF-SCM had originally been designed for use over land, so we made several updates to the community-distributed code in order to use it over water. WRF-SCM users can now specify a set of eta levels in the WRF namelist, rather than allowing the model to generate its own set of eta levels based on a specified number of vertical levels (in this project we used 10 levels from 30 to 210 m with 20-m spacing, and 50 more levels above 210 m). The WRF-SCM now sets the land-use category according to the value read in from the 3D WRF output files that drive the SCM simulations, instead of assuming a land point. Additionally, the WRF-SCM now uses SST for subsurface initialization if the SCM point is over water. These improvements and modifications will be made available to the community in an upcoming release of WRF.
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