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Hans Hersbach

Abstract

Near the surface, it is commonly believed that the behavior of the (turbulent) atmospheric flow can be well described by a constant stress layer. In the case of a neutrally stratified surface layer, this leads to the well-known logarithmic wind profile that determines the relation between near-surface wind speed and magnitude of stress. The profile is set by a surface roughness length, which, over the ocean surface, is not constant; rather, it depends on the underlying (ocean wave) sea state. For instance, at the European Centre for Medium-Range Weather Forecasts this relation is parameterized in terms of surface stress itself, where the scale is set by kinematic viscosity for light wind and a Charnock parameter for strong wind. For given wind speed at a given height, the determination of the relation between surface wind and stress (expressed by a drag coefficient) leads to an implicit equation that is to be solved in an iterative way.

In this paper a fit is presented that directly expresses the neutral drag coefficient and surface roughness in terms of wind speed without the need for iteration. Since the fit is formulated in purely dimensionless quantities, it is able to produce accurate results over the entire range in wind speed, level height, and values for the Charnock parameter for which the implicit set of equations is believed to be valid.

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Hans Hersbach

Abstract

Some time ago, the continuous ranked probability score (CRPS) was proposed as a new verification tool for (probabilistic) forecast systems. Its focus is on the entire permissible range of a certain (weather) parameter. The CRPS can be seen as a ranked probability score with an infinite number of classes, each of zero width. Alternatively, it can be interpreted as the integral of the Brier score over all possible threshold values for the parameter under consideration. For a deterministic forecast system the CRPS reduces to the mean absolute error.

In this paper it is shown that for an ensemble prediction system the CRPS can be decomposed into a reliability part and a resolution/uncertainty part, in a way that is similar to the decomposition of the Brier score. The reliability part of the CRPS is closely connected to the rank histogram of the ensemble, while the resolution/uncertainty part can be related to the average spread within the ensemble and the behavior of its outliers. The usefulness of such a decomposition is illustrated for the ensemble prediction system running at the European Centre for Medium-Range Weather Forecasts. The evaluation of the CRPS and its decomposition proposed in this paper can be extended to systems issuing continuous probability forecasts, by realizing that these can be interpreted as the limit of ensemble forecasts with an infinite number of members.

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Hans Hersbach

Abstract

This article describes the evaluation of a C-band geophysical model function called C-band model 5.N (CMOD5.N). It is used to provide an empirical relation between backscatter as sensed by the spaceborne European Remote Sensing Satellite-2 (ERS-2) and Advanced Scatterometer (ASCAT) scatterometers and equivalent neutral ocean vector wind at 10-m height (neutral surface wind) as function of scatterometer incidence angle.

CMOD5.N embodies a refit of CMOD5, a C-band model function, which was previously derived to obtain nonneutral surface wind, in such a way that its 28 tunable coefficients lead, for a given backscatter observation, to an enhancement of 0.7 m s−1 in wind speed. The value of 0.7 m s−1 is chosen to be independent of wind speed and incidence angle, and it incorporates the average difference between neutral and nonneutral wind (∼0.2 m s−1) and for a known bias of CMOD5 (∼0.5 m s−1) when compared to buoy wind data. The quality of the CMOD5.N fit is successfully tested for the Active Microwave Instrument (AMI) scatterometer on ERS-2 and ASCAT instrument on Meteorological Operational-A (MetOp-A) for July 2007 and January 2008.

ASCAT and ERS-2 wind speed obtained from CMOD5.N compares well on average with operational neutral wind from the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with nonneutral wind, the local, seasonally dependent biases between scatterometer and ECMWF model are reduced. Besides effects introduced by sea state, orography, and ocean currents, a residual stability-dependent bias between scatterometer and neutral wind remains, which is likely connected to a nonoptimality in the ECMWF boundary layer formalism that is reported in the literature.

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Hans Hersbach and Peter A. E. M. Janssen
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Øyvind Saetra, Hans Hersbach, Jean-Raymond Bidlot, and David S. Richardson

Abstract

The effects of observation errors on rank histograms and reliability diagrams are investigated using a perfect model approach. The three-variable Lorenz-63 model was used to simulate an idealized ensemble prediction system (EPS) with 50 perturbed ensemble members and one control forecast. Observation errors at verification time were introduced by adding normally distributed noise to the true state at verification time. Besides these simulations, a theoretical analysis was also performed. One of the major findings was that rank histograms are very sensitive to the presence of observation errors, leading to overpopulated upper- and lowermost ranks. This sensitivity was shown to grow for larger ensemble sizes. Reliability diagrams were far less sensitive in this respect. The resulting u-shaped rank histograms can easily be misinterpreted as indicating too little spread in the ensemble prediction system. To account for this effect when real observations are used to assess an ensemble prediction system, normally distributed noise based on the verifying observation error can be added to the ensemble members before the statistics are calculated. The method has been tested for the ECMWF ensemble forecasts of ocean waves and forecasts of the geopotential at 500 hPa. The EPS waves were compared with buoy observations from the Global Telecommunication System (GTS) for a period of almost 3 yr. When the buoy observations were taken as the true value, more than 25% of the observations appeared in the two extreme ranks for the day 3 forecast range. This number was reduced to less than 10% when observation errors were added to the ensemble members. Ensemble forecasts of the 500-hPa geopotential were verified against the ECMWF analysis. When analysis errors were neglected, the maximum number of outliers was more than 10% for most areas except for Europe, where the analysis errors are relatively smaller. Introducing noise to the ensemble members, based on estimates of analysis errors, reduced the number of outliers, particularly in the short range, where a peak around day 1 more or less vanished.

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H. K. Johnson, H. J. Vested, Hans Hersbach, J. Højstrup, and S. E. Larsen

Abstract

The reliability of the wave model (WAM, cycle 4) for predicting waves and wind stress in restricted fetches is investigated using measured data obtained during the Risø Air–Sea Experiment (RASEX) at Vindeby, Denmark. The WAM model includes Janssen’s theory for calculating sea roughness as a function of wave spectra. RASEX is characterized by being located in relatively shallow waters (depths of about 3 to 4 m in an area where the waves are predominantly fetch limited, with a maximum fetch of about 20 km).

Comparison between WAM results and measured data (integral wave parameters and friction velocities) shows fair agreement for moderate winds (U 10 ≃ 10 m s−1) but significant overprediction for strong winds. Analysis of the WAM results for sea roughness yields a trend of increasing dimensionless roughness with inverse wave age, as obtained from field data; however, the WAM values are generally higher than that obtained from field data.

It is shown that inclusion of depth-induced wave breaking does not explain the overprediction of measured wind stress and associated wave heights. Furthermore, it is shown that using the measured wind friction velocities to force the WAM model significantly reduces the wave height overprediction for strong winds.

These investigations indicate that further improvements are required before the WAM model can be reliably used in shallow and fetch-limited areas, such as Vindeby.

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Peter A. E. M. Janssen, Saleh Abdalla, Hans Hersbach, and Jean-Raymond Bidlot

Abstract

Triple collocation is a powerful method to estimate the rms error in each of three collocated datasets, provided the errors are not correlated. Wave height analyses from the operational European Centre for Medium-Range Weather Forecasts (ECMWF) wave forecasting system over a 4-yr period are compared with independent buoy data and dependent European Remote Sensing Satellite-2 (ERS-2) altimeter wave height data, which have been used in the wave analysis. To apply the triple-collocation method, a fourth, independent dataset is obtained from a wave model hindcast without assimilation of altimeter wave observations. The seasonal dependence of the respective errors is discussed and, while in agreement with the properties of the analysis scheme, the wave height analysis is found to have the smallest error.

In this comparison the altimeter wave height data have been obtained from an average over N individual observations. By comparing model wave height with the altimeter superobservations for different values of N, alternative estimates of altimeter and model error are obtained. There is only agreement with the estimates from the triple collocation when the correlation between individual altimeter observations is taken into account.

The collocation method is also applied to estimate the error in Environmental Satellite (ENVISAT), ERS-2 altimeter, buoy, model first-guess, and analyzed wave heights. It is shown that there is a high correlation between ENVISAT and ERS-2 wave height error, while the quality of ENVISAT altimeter wave height is high.

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James B. Edson, Venkata Jampana, Robert A. Weller, Sebastien P. Bigorre, Albert J. Plueddemann, Christopher W. Fairall, Scott D. Miller, Larry Mahrt, Dean Vickers, and Hans Hersbach
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James B. Edson, Venkata Jampana, Robert A. Weller, Sebastien P. Bigorre, Albert J. Plueddemann, Christopher W. Fairall, Scott D. Miller, Larry Mahrt, Dean Vickers, and Hans Hersbach

Abstract

This study investigates the exchange of momentum between the atmosphere and ocean using data collected from four oceanic field experiments. Direct covariance estimates of momentum fluxes were collected in all four experiments and wind profiles were collected during three of them. The objective of the investigation is to improve parameterizations of the surface roughness and drag coefficient used to estimate the surface stress from bulk formulas. Specifically, the Coupled Ocean–Atmosphere Response Experiment (COARE) 3.0 bulk flux algorithm is refined to create COARE 3.5. Oversea measurements of dimensionless shear are used to investigate the stability function under stable and convective conditions. The behavior of surface roughness is then investigated over a wider range of wind speeds (up to 25 m s−1) and wave conditions than have been available from previous oversea field studies. The wind speed dependence of the Charnock coefficient α in the COARE algorithm is modified to , where m = 0.017 m−1 s and b = −0.005. When combined with a parameterization for smooth flow, this formulation gives better agreement with the stress estimates from all of the field programs at all winds speeds with significant improvement for wind speeds over 13 m s−1. Wave age– and wave slope–dependent parameterizations of the surface roughness are also investigated, but the COARE 3.5 wind speed–dependent formulation matches the observations well without any wave information. The available data provide a simple reason for why wind speed–, wave age–, and wave slope–dependent formulations give similar results—the inverse wave age varies nearly linearly with wind speed in long-fetch conditions for wind speeds up to 25 m s−1.

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Paul Poli, Hans Hersbach, Dick P. Dee, Paul Berrisford, Adrian J. Simmons, Frédéric Vitart, Patrick Laloyaux, David G. H. Tan, Carole Peubey, Jean-Noël Thépaut, Yannick Trémolet, Elías V. Hólm, Massimo Bonavita, Lars Isaksen, and Michael Fisher

Abstract

The ECMWF twentieth century reanalysis (ERA-20C; 1900–2010) assimilates surface pressure and marine wind observations. The reanalysis is single-member, and the background errors are spatiotemporally varying, derived from an ensemble. The atmospheric general circulation model uses the same configuration as the control member of the ERA-20CM ensemble, forced by observationally based analyses of sea surface temperature, sea ice cover, atmospheric composition changes, and solar forcing. The resulting climate trend estimations resemble ERA-20CM for temperature and the water cycle. The ERA-20C water cycle features stable precipitation minus evaporation global averages and no spurious jumps or trends. The assimilation of observations adds realism on synoptic time scales as compared to ERA-20CM in regions that are sufficiently well observed. Comparing to nighttime ship observations, ERA-20C air temperatures are 1 K colder. Generally, the synoptic quality of the product and the agreement in terms of climate indices with other products improve with the availability of observations. The MJO mean amplitude in ERA-20C is larger than in 20CR version 2c throughout the century, and in agreement with other reanalyses such as JRA-55. A novelty in ERA-20C is the availability of observation feedback information. As shown, this information can help assess the product’s quality on selected time scales and regions.

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