Authors: Sergey K. Gulev, Vika Grigorieva and Andreas Sterl
This Atlas is the result of a co-operative project, funded by European Union (INTAS grant 96-2089) "Intercomparison of ocean waves from in-situ measurements, voluntary observing ship data, remote sensing, and modelling". The main goal of this project is to quantify biases between wave fields available from different sources. Project participants are P.P.Shirshov Institute of Oceanology, Russian Academy of Science (Moscow), Southampton Oceanography Centre (Southampton) and Royal Netherlands Meteorological Institute (De Bilt).
The current version of the Atlas covers the globe from 80S to 80N for the period 1970-2015. Beside the basic meteorological variables, we derived the records of visually observed heights, periods and wind sea and swell directions. The reported accuracies are 0.5 m for heights, 1 sec for periods and 10 deg for the directions.We used the latest update of the global archive of visual wind wave data based on the ICOADS (International Comprehensive Ocean-Atmosphere Data Set, Freeman et al., 2017) collection of marine meteorological observations. These data span over the period from 1662 onwards with wave information appearing starting from 1880. However, the homogeneous global data coverage is provided for the period starting from 1970 (of about 100000 records per month). During the earlier decades, wave data are concentrated primaraly along the major ship routes with spatially and temporary varying sampling. The main advantage of visual wave observations is separate estimates of the wind sea and swell height since 1950. In the decades prior to 1950, officers reported only the highest wave component. Comprehensive description of the data processing, coding systems, changes in data formats, ad-hoc corrections of biases and estimates of the uncertainties can be found in Gulev et al. (2003) and Gulev and Grigorieva (2006). The major biases in basic wave characteristics have been considerably reduced in the global wave climatology. Along with the climatologoical distributions of the wave parameters, the Atlas also includes the global estimates of random observational errors in wind sea and swell, day-night differences and evaluation of sampling uncertainties. Climatological maps of wave characteristics are accompanied by corresponding 2°x2° matrices of monthly means (80x180). Left upper corner coordinates are 79N and 01E. Original data represent climatological averages based on original VOS data, which passed multistage Quality Control, analyzed data provide interpolated and smoothed fields of wave characteristics.
Preprocessing and variable corrections:
Visual wave data were a subject a numerous quality checks, variable corrections, and preprocessing. The most important procedures applied to the initial data are the following.
- 1. Computation of significant wave height
In order to derive the best estimate of SWH Gulev and Hasse [1998, 1999] recommended to use a combined approach, first introduced by Barratt , who suggested to apply square root of the sum of squares of sea and swell when sea and swell are within the same 45° directional sector, and to take maximum of the two components in all other cases. Analyzing directional sectors within the range from 30° to 60°, Gulev and Hasse  found the optimal directional sector to be 30°. Thus, the formulation for SWH applied in this study is the following:
- 2. Correction of small wave heights
Systematic underestimation of small waves in VOS results from the use in COADS LMR of the code figure "1" for coding all waves smaller than 0.5 m. All wave heights coded as "1" in fact are ranged within 0.5 m, but, for instance in COADS LMR they are decoded as single height of 0.5 m. We considered 2-dimensional frequency distributions of wind speed and wave height for small waves, computed using instrumental data from NDBC buoys and from the VOS reports which report "1" for the wave height and were sampled simultaneously with buoy measurements within the radius of 50 km. For the wind speed range from 1.2 to 6 m/s and wave height smaller than 0.5 we derived a simple formula which can be used for the correction of the VOS wave height. The corrected sea height, reported with the code figure "1" has to be derived as:
hs = 0.5-exp(-0.658V) (4)
where 1.2<V<6 is a wind speed. This formula allows to correct small sea height with the accuracy better than 20%.
- 3. Separation of sea and swell in visual estimates
In this study, analyzing the separation between sea and swell, we gave higher priority to the consideration of joint probability distributions and considered estimates of wave age to be a second priority. We computed joint distributions of wave height and wind speed for different regions and excluded from the consideration all wind seas, which are not captured by the JONSWAP curve corresponding to the duration 24 hours, and all swells, which are captured by the JONSWAP curve 6 hours. The number of the omitted reports varies from 0.1 to 3% of wave reports with the local maxima in the North Atlantic and North Pacific mid latitudes and in the Southern Ocean, where sea and swell have close to each other directional characteristics. Then the retained data were analyzed with respect to the wave age. This check resulted in elimination of additional 0.05 to 1.5% of observations, which reported seas with a > 1.2. The highest percentages of the omitted reports are observed in the mid-latitudinal regions, where up to 5% of reports were excluded from consideration.
- 4. Correction of the wave periods and computation of the dominant period
Wave periods are known to be systematically underestimated in visual VOS data. Gulev and Hasse , fitting the distributions of significant wave heights and dominant periods (h|p) for the locations of NDBC buoys and ship recorders in the North Atlantic developed an empirical method for the correction of individual observations of periods. Their relationships between the corrected (pw', ps') and uncorrected (pw, ps) sea and swell periods:
pw' = Aw ln(pw + Bw) + Cw ln(hw),
ps ' = As ln(ps + Bs) + Cs ln(hw) (8)
include wind sea height and a number of empirical coefficients, which are different for the cases of sea and swell propagation within and without the same directional sector, and for hw > hs and hs > hw. numerical values of the coefficients are given in Gulev and Hasse .
Development of global fields of wave parameters:
The pre-processed and corrected individual visual observations of ocean wave parameters were used for the production of wave climatology on a global scale. Individual monthly means of sea and swell heights and periods as well as of significant wave height, resultant period and characteristics of directional steadiness were computed for the World Ocean from 80S to 80N including all marginal and semi-enclosed seas for a 46-year period from 1970 to 2015. Climatology of wave parameters was developed for 2 by 2 degree spatial resolution. Most of recently developed global climatologies of basic meteorological variables and sea-air fluxes were derived for 1-degree spatial resolution [da Silva et al. 1994, Josey et al. 1999, Lindau2000]. However, the use of 1-degree resolution results in considerable undersampling, especially in poorly sampled regions, first of all in the Southern Ocean. Undersampling has two major effects on the climatology. First, monthly means for the poorly sampled boxes are influenced by inadequate sampling error, which results in high spatial noise in the poorly sampled regions, and requires spatial smoothing. Second, for the large number of fully unsampled boxes values have to be produced by the procedures of spatial interpolation. Sea-air flux field producers use different procedures, such as successive correction (SOC [Josey et al. 1999] and UWM [da Silva et al. 1994]), krigging (IFM [Lindau 2000]) and the Akima  method of local procedures [Gulev et al. 2001b]. More advanced methods, developed primarily for the SST and SLP fields and based on EOF reconstruction and Kalman filtering [e.g. Reynolds and Smith 1994, Kaplan et al. 2000] are not adopted yet to the analysis of other variables. Recently Kent et al.  analysed the SST fields from VOS and showed that the successive correction results in the noise in poorly sampled regions and may also affect well sampled regions neighboring with poorly sampled ones. She quoted, that approximately 90% of all grid monthly values in the SOC climatology have 3 to 5 degree spatial resolution, and for only less than 1% of points actual resolution is 1 degree. Comparing 7 different procedures of onterpolation, Gulev et al. [2001b] concluded that neither of them allows to avoid fully the sampling bias. Taking into accout, that wave variables have even worse sampling density than most of basic meteorological variables, we decided to use 2-degree spatial resolution for our climatology. For spatial interpolation over the unstapled locations we used the modified method of local procedures [Akima 1970], recently adopted for the analysis of sea-air interaction fields by Gulev et al. [2001b] in combination with 2-dimensional Lanczos filtering [Lanczos 1956, Duchon 1979]. Intramonthly trimming was based on 4.5s limits.