## Abstract

Beaufort equivalent scales from the literature have been compared to find the scale that gives the most homogenous, internally consistent, combined anemometer and visual wind speed data from the Comprehensive Ocean–Atmosphere Data Set. Anemometer wind speeds have been height corrected using the individual anemometer height for each ship, where that could be identified, resulting in a more consistent dataset than that used in previous studies. Monthly mean 1° averages were constructed for visual and anemometer wind speeds separately from data between 1980 and 1990. The anemometer and visual means were compared where there were enough observations to give confidence in both means. The equivalent scale of Lindau was the most effective at giving similar anemometer and visual wind distributions from this mean dataset. The scale of daSilva et al. also performed well. The Lindau scale is, however, preferred because of its more rigorous derivation. The results for the different scales are in agreement with Lindau’s suggestion that the characteristic biases of earlier Beaufort scales could be explained by the statistical method of derivation.

## 1. Introduction

The visual estimation of winds, based on the Beaufort scale, remains the preferred method of wind speed determination on voluntary observing ships recruited by the United Kingdom and other meteorological agencies. In 1990, 60% of wind observations from the North Atlantic were visual estimates. However, the proportion of ships equipped with anemometers is increasing and these anemometers are, on average, mounted at increasingly greater heights as larger ships have been built. A significant but apparently spurious climatic trend toward increasing wind speeds (Ramage 1987; Wright 1988) has been attributed to these changes in estimation technique (Cardone et al. 1990). Thus, for studies of climate change and variability, it is important that a reliable method be available for merging visual and anemometer derived wind estimates into a consistent wind speed dataset.

This study has used the Comprehensive Ocean–Atmosphere Data Set (COADS; Slutz et al. 1985; Woodruff et al. 1987) to determine which of the many published Beaufort equivalent scales—WMO1100 (WMO 1970), CMMIV (WMO 1970), UWM (daSilva et al. 1995), Lindau (Lindau 1995), Isemer (Isemer 1992), Kaufeld (Kaufeld 1981), Cardone (Cardone 1969)—is the most successful in creating a homogeneous monthly mean wind dataset. That is, we wish to correct the visual wind reports (based on the WMO1100 scale) to give the same climatology as the anemometer winds. Specifically we will compare monthly mean 1° average wind speeds from anemometers and from visual reports.Comparisons between the two different wind speed estimates were made by way of a two-way regression of monthly mean wind speeds with equal error variability.

In previous studies, the dataset was either limited to ocean weather ship (OWS) or other data of known anemometer height (e.g., Quayle 1980; Graham 1982), or a mean anemometer height had to be assumed and applied to the entire voluntary observing ship (VOS) anemometer wind dataset (e.g., daSilva et al. 1995). Cardone et al. (1990) made an attempt to identify individual anemometer heights but only managed this for 8% of the data, the remainder had a constant height assumed, leaving little impact on the results. The present study only used VOS anemometer wind reports for the years 1980–90 where the anemometer height was available from the list of selected ships, “WMO47” (e.g., WMO 1980), and the height corrections could therefore be applied to individual reports. The dataset therefore represented the best quality anemometer wind dataset that may be derived from COADS at the present time.

The validity of correcting wind observations for the height of anemometers mounted on merchant ships is open to question. Indeed, Dobson (1981) concluded that height correction of marine winds is not useful until errors arising from airflow distortion around the ship could be quantified and corrected for at the same time. This is still not possible as wind flow patterns around merchant ships have not been studied in detail and there is no way of identifying a ship shape or anemometer location with a particular wind report in COADS. However, the results of the Voluntary observing ship Special Observing Project for the North Atlantic (VSOP-NA; Kent et al. 1993) showed that, for the subset of VOS studied, the anemometers were generally judged to be well exposed. Furthermore, the bias between ship wind reports and the U.K. Meteorological Office Fine Mesh Model depended on the ship anemometer height and could be reduced by height correction. On that evidence, height correction was used in this study to help to remove these biases in the wind data.

The next two sections will describe the different Beaufort scales to be compared and the comparison method that we have used. The results are presented in section 4 and discussed in section 5, where it is shown that the method by which the Beaufort scale was derived was the major factor determining the performance of the scale. Section 6 will provide our conclusions regarding the choice of scales.

## 2. Description of the Beaufort scales

### a. Introduction

Beaufort scales are defined either using ranges of wind speed for a Beaufort interval or a midpoint value for the interval. As not all the scales define ranges, Table 1 gives the midpoint values for each of the scales used in this study. Also given are the equivalent heights for the scales. This is simply the average height of the anemometer measurements used to derive the scale.

Of all the scales, the operationally used WMO1100 scale has the lowest equivalent winds at low Beaufort numbers and the highest at high Beaufort numbers. The crossover occurs at about Beaufort 7 (for the Cardone and CMMIV scales), Beaufort 9 (for the Kaufeld, Lindau, and UWM scales), and Beaufort 10 (for the Isemer scale). At moderate wind speeds, about Beaufort 4, the largest differences from the operational scale are the Kaufeld and Isemer scales, which have higher equivalent wind speeds than the WMO1100 scale by 2 m s^{−1}, the next largest difference is from the Cardone scale with a difference of 1.5 m s^{−1}. At highBeaufort numbers the Lindau scale equivalents are the closest to those of the WMO1100 scale, within 1 m s^{−1} above Beaufort 8. The Cardone scale has the lowest equivalents at wind speeds above Beaufort 7, the difference reaching 5 m s^{−1} by Beaufort 12. This trend is shown in the CMMIV, Kaufeld, Isemer, and UWM scales to a lesser extent. By Beaufort 12 the CMMIV and Kaufeld scales have lower equivalent wind speeds by about 2.5 m s^{−1} and the UWM and Isemer scales by about 1.5 m s^{−1}.

All the other scales indicate that the equivalent wind speeds of the WMO1100 scale are biased, there is disagreement as to the extent. In the following sections we shall first consider the two WMO-recommended scales (WMO1100, CMMIV); second, two recently proposed scales (UWM, Lindau); and finally, three scales that have been used in previous studies (Isemer, Kaufeld, and Cardone).

### b. WMO1100 (WMO 1970)

The WMO1100 wind scale was devised based on simultaneously measured and visually estimated wind speeds from five English coastal and inland stations by G. Simpson in 1906. The analysis was dominated by observations from a lighthouse station on the Scillies. The observations were used to determine the constant *c* in an empirical fit to the relationship:

where *v* (m s^{−1}) is the wind speed and *n* is the Beaufort force interval number. The large exponent of 3/2 chosen to represent the curvature of the graph was characteristic of the data from the Scillies station and was thought to result from the high vantage point and hence the large area of sea over which the observations were made (Verploegh 1967).

The applicability of this scale might be expected to be limited because the observations on which the scale is based were from land or coastal stations, none came from ship comparisons. Also, the height of the anemometers used was 6 m, considerably lower than the height of the anemometers used on ships in open waters.

### c. CMMIV (WMO 1970)

The data for the derivation of CMMIV came from simultaneous visual and anemometer wind speed reports from 12 ocean-going ships. No evidence was found for the very high wind speed previously attributed to the upper limit of force 11 in WMO1100. The scale was derived using the Beaufort wind speeds as the independent variable to give the mean anemometer wind speed for a given Beaufort force interval. The reference height for the new scale was 18 m ± 6 m (95% confidence interval).

### d. UWM (daSilva et al. 1995)

Working at the University of Wisconsin—Milwaukee (UWM), daSilva et al. derived separate wind speed climatologies (from the short report version of COADS) for estimated and measured reports differentiated using the CMR5 wind indicator flag. The CMR5 flag is set as 1 for an anemometer wind speed and as 0 if the report is visual or the method is unknown. (Note that any errors in the wind indicator flag will tend to make the measured and estimated reports seem more similar.) These two sets of reports were then objectively analyzed to give estimates of the global annual 1° latitude by 1° longitude mean wind speed field. To maintain consistency in the stress measurements, the correction was derived from a nonlinear regression of the two fields including the scatter of the observations that gave the relationship

where *U*_{1100} (m s^{−1}) is the WMO1100 wind speed and*U*_{UWM} is the UWM wind speed defined at 20 m. DaSilva et al. derived the scale assuming all the anemometer measurements were at 20-m height, then converted both anemometer and visual winds to 10 m using a stability-dependent correction when a 10-m value was required.

It will be argued in section 3b that it is not correct to apply a stability correction to visual winds in this manner and also that the height of the anemometer is important (although little bias is introduced by the use of a sensible estimate of the mean anemometer height, the scatter in the anemometer wind speeds will be increased). Also it is unclear how a scale derived and tested on objectively analyzed monthly mean values would perform when applied to individual values.

### e. Lindau (Lindau 1995)

Lindau argued that what is required from a Beaufort scale is not, for example, the mean wind speed for a given Beaufort interval, but rather a universal relationship between the Beaufort force and the wind speed. The latter can be achieved by an orthogonal (two way) regression, but only if both the natural and the measurement error variances are the same for each parameter. He carefully considered the natural variability and measurement variability of each type of measurement. Both must be equal for the technique to be valid. Lindau compared visual estimates from the short report version of COADS (identified using the CMR5 flag as described in section 2d) with anemometer data from OWS in the 1960s.

There were several stages in equalizing the error variance for the OWS and the VOS averages. First, the natural error variance of the VOS visual wind reports was determined. For the VOS he took pairs of simultaneous visual wind reports and plotted the squared difference (variance) of the two wind speeds as a function of their separation. If this mean squared wind speed difference against distance plot was extrapolated to zero distance, the intercept is the variability between two independent ship measurements if they were taken at the same place and at the same time, that is, the measurement error variance of the VOS visual wind speed. The value of the intercept was halved as there was variability contributed from both ships. Second, the measurement error variance of the OWS anemometer winds was calculated. This was done by extrapolating the variance of OWS–VOS simultaneous wind speed pairs to zero distance as for the VOS–VOS pairs described above. In this case, the intercept was the measurement variability of the OWS reports plus the measurement variability of the VOS reports (which was previously calculated and could be subtracted). Table 2 summarizes the error variances found in the study. Third, both VOS and OWS wind reports were averaged separately; each VOS average containing more reports than the OWS averages in order to equalize the measurement error variability for each average.

The next step was to assess the natural spatial and temporal variabilities. For the OWS anemometer winds, the differences were taken at the same position but for varying time differences. The mean squared difference as a function of the time between the measurements was extrapolated to zero time difference to give twice the measurement variability in the OWS wind measurements. The temporal variability within the averaging period (24 h) for the OWS data was the variance at 24 h minus the intercept (the variability in the measurement). The VOS visual winds (that have already been averaged to give the same measurement variability as the OWS reports) were then treated as described in the first step of this calculation. Only the aim was now to find the averaging radius that would give the same variability as was observed in the 24-h OWS average wind speed. This could be read from the graph of variance against distance once the measurement variability (the intercept atzero distance) was removed. The VOS data were averaged over a radius of about 300 km such that the natural variability for the averages within that area was approximately equal to the natural variability of the averages within 24 h at the OWS site. The scale was then derived from these twice-averaged wind speeds using the method of cumulative frequencies.

Considering Lindau’s analysis, it is not clear how much an effect the nonindependence of the time series of OWS wind speeds would have on the error variance. Also, it should be noted that there was only 1 observation in Beaufort interval 12, and only 15 at Beaufort 11.

### f. Isemer (Isemer 1992)

Isemer compared OWS anemometer winds from the period between 1951 and 1989 with estimated VOS wind reports if their separation was less than 150 nautical miles and the time difference was less than 1 h. To attempt to eliminate reports separated by an atmospheric front, the difference in the wind directions had to be less than 30°; however, Isemer suggested this might create a bias toward good VOS reports. The use of simultaneous values removed the possibility of fair-weather bias.

The resulting scale was similar to that of Kaufeld (1981, see following section) as the same data type and technique were used, but the high Beaufort numbers (above 8) have higher equivalent wind speeds, which may have been due to the larger dataset Isemer used.

Isemer derived different scales for different stability conditions and for day compared with night, but the resultant differences were small.

### g. Kaufeld (Kaufeld 1981)

Using data from the period 1951–75, Kaufeld compared measured winds from OWSs C, D, E, I, J, and K and estimated winds from ships in 150 nautical miles range where the observations were taken within 1.5 h of each other and the reported wind direction differed by less than 30°. The use of simultaneous values removed the possibility of fair-weather bias. A Beaufort equivalent scale was obtained from cumulative frequency analysis for each station separately. The results were similar for each OWS. An alternative method of deriving the relationship between measured and estimated wind speed used a correlation diagram. The average measured wind speed for a given Beaufort interval and the average Beaufort force for a given range of measured wind speeds were plotted. The curve representing a two-way conversion between the two one-way curves was constructed at the intersection point of lines of equal length at equal angles from each of the one-way curves. The results from this were similar to those obtained using cumulative frequency analysis.

The data were smoothed to remove the bias toward reporting even numbers for the wind speed value. The bias due to the nonlinear increase of the cumulative frequency distribution within a Beaufort interval was found to be small and was therefore neglected. The average anemometer height for the OWS was 25 m and this was therefore the height for the equivalent scale.

### h. Cardone (Cardone 1969)

Cardone developed a scale based on simultaneously measured and visually estimated wind speeds (5499 data pairs) from British and Canadian weather ships. The mean height of the anemometers in the study was 20 m. The scale was developed using a regression of anemometer wind speeds on the Beaufort visual wind speeds. Conversion from code 1100 to the Cardone scale is given by

where *U*_{1100} (kt) is the WMO1100 wind speed and *U*_{Cardone} is the Cardone wind speed.

## 3. Method of analysis

### a. Merging of COADS with WMO47

The WMO47 metadata (information about data) reportcontains information about the instrumentation carried by the VOS, including the height of any anemometer carried (e.g., WMO 1980). An electronic format version of this report as described by Kent and Oakley (1995) was used in this study. These metadata were merged onto the individual COADS reports as follows. For each report, the ship call sign was checked against the WMO47 list of ships corresponding to the year of the observation. If the call sign was found, the metadata were merged onto the COADS report. If the call sign was not found, the WMO47 lists for the following 2 years were checked, then that for the year before the correct year. Again if the call sign was present, the metadata were merged. An attempt was made to match any unmatched call signs that might have been jumbled by removing leading blanks and numbers, since this had been noted to be a common cause of nonmatching.

Figure 1 shows the matching success rate between 1980 and 1990. Although the number of reports has increased over the period, the number of ship reports in a particular month has decreased. The version of COADS used was compiled in 1991, and the drop in the number of ship reports in 1989 may be due to the lack of delayed log book data in the dataset. Some of the logbook data takes a number of years to be keyed in and added to the dataset, and not all of it would have been included after 2 years. The remainder of the reports come from buoys and fixed stations; these are not included in WMO47 and have not been used in this study. As only ship information is contained in WMO47, Fig. 1 shows that the matching rate achieved was high; after 1985 over 75% of the ship reports have been matched to metadata in WMO47. This should be compared with the matching rate of Cardone (1990) who achieved a rate of 8% for data in the 40 years up to 1987.

### b. Separation of anemometer and visual winds

Each wind speed long marine report in COADS has an associated wind indicator flag that gives the method of measurement, either estimated or measured (anemometer), and whether the original report was in knots or meters per second. If the method of measurement was unknown, the flag was unset. This flag from the full dataset therefore contains more information than the CMR5 flag from the compressed reports used by both Lindau (1995) and daSilva et al. (1995). The use of the CMR5 flag would result in an overestimate of the number of visual winds as reports from anemometers for which the method is unknown would be included in the visual wind dataset. This is in addition to any errors in the flags that would tend to make the visual and the anemometer datasets appear more similar. The accuracy of both these flags has been questioned (e.g., Cardone et al. 1990; daSilva et al. 1995). Cardone et al. (1990) found errors in the wind indicator flag for reports in the South China Sea before 1963. He found, however, that results from a rigorously quality-controlled subset of the data were similar to those from the entire dataset.

In this study, the wind indicator flag has been assumed to be correct; this is supported by the fact that the distributions of the visual and anemometer wind speeds for a sample month (January 1986) are different, as shown in Fig. 2. There was a preference for the ship officers to report wind speeds in multiples of two or five for both visual and anemometer wind speeds, and also the midpoint of a Beaufort interval was favored for visual winds (see Table 1). In particular, the Beaufort midpoints for the WMO1100 scale at 7, 9, 12, 15, and 19 m s^{−1} can be clearly seen as peaksin the visual distribution and not in the anemometer distribution, indicating that the flag was largely reliable. There were, however, conflicts between these preferences, for example, the peak in the visual distribution expected at 4 m s^{−1} as the midpoint of Beaufort interval 3 has been shifted to 5 m s^{−1}.

Figure 3 shows the proportion of anemometer wind speeds in, as an example, January 1986, for 2° × 2° areas derived from this flag. The Pacific can be seen to be dominated by anemometer wind reports whereas the visual winds were concentrated in the Atlantic. This resulted from the observing practices of different countries; ships recruited by the United Kingdom, the Netherlands, and Germany all reported predominantly visual winds, leading to the large number of visual wind reports in the Atlantic; those recruited by the United States and Japan predominantly used anemometers, leading to the large number of anemometer wind reports in the Pacific. This distribution of reports meant that the areas with enough anemometer and visual winds to enable a comparison to be made were limited as there were few regions with many reports from both sources. Table 3 gives the mean anemometer height and the proportion of anemometer winds in particular months for two regions, one in the North Atlantic and one in the North Pacific. The trend for increasing anemometer heights was clear in both these regions, but the anemometer heights in the Pacific region were about 10 m higher than in the Atlantic. The proportion of anemometer winds was also increasing in the Pacific region.

### c. Height correction

#### 1) Anemometer winds

The height correction of anemometer wind speeds to 10-m height and neutral stability was calculated following Smith (1980). To enable the maximum amount of data to be used, if the humidity was absent a value of 70% relative humidity was used and if the pressure was absent, a default of 1013 mb was used. The effects of humidity and pressure on the stability factor are small. Data were only used if the wind indicator flag was set, so only data flagged as anemometer measured was used. In addition, no default height was assumed. If no anemometer height was quoted in WMO47, the measurement was discarded. Figure 1 shows that more anemometer wind data will have been discarded in the early years of this study compared to the later years.

Having merged the anemometer height onto the COADS reports, we may plot the distribution of mean anemometer height for the observations received in a particular month. Figure 4 shows the distribution of 5° latitude by 5° longitude monthly mean anemometer height for the Northern Hemisphere Atlantic and Pacific for January 1986. The North Sea and Canadian oil fields are clearly visible as peaks in the anemometer height distribution for the Atlantic. The major shipping lane from northern Europe to the United States shows up as a region of high mean anemometer height with mean heights greater than 20 m, whereas much of the rest of the North Atlantic has mean anemometer heights lower than 20 m. The North Pacific distribution clearly shows the effect of the large Japanese merchant fleet that have very high anemometers. There are several areas with a mean anemometer height greater than 35 m and the shipping lanes again show up as regions of elevated anemometer height. It is striking to note the sharp boundary along the western side of the North Pacific between the region frequented by large merchant ships with high anemometers and the region of very low anemometer heights found close to the coast. The coastal observations are probably from small fishing vessels with low anemometer heights. This figure shows the very different character of the ships reportingfrom the two ocean basins and indicates that biases will result in the wind speed field if the anemometer height is assumed to be the same in both regions.

The mean anemometer heights for each of the 1° × 1° monthly means used in the analysis are aggregated in the histogram of Fig. 5. The overall mean anemometer height is 30 m with a standard deviation of 12 m. The large mean anemometer heights come from the northern North Sea and the region east of Newfoundland and are presumably associated with oil rigs or support vessels. These reports were still present in the COADS data even though it had been selected to only include reports with platform type “ship.” The reports with large anemometer heights were kept in the dataset and compose 3% of the monthly means. A typical value for the anemometer height neglecting these values is 25 m.

The height correction required for data under very stable conditions is uncertain. In this study, very stable data were defined as those for which the measurement height/Monin–Obukhov length ratio, denoted *z*/*L,* is greater than +1; see, for example, daSilva et al. (1994) for a definition of the Monin–Obukhov length. In these conditions, the height correction algorithm applies large corrections to the data, wind speeds as high as 4 m s^{−1} can be reduced to a zero 10-m neutral value. This is physically unrealistic since the near-surface flow would be reversed and it creates a large number of low wind speeds distorting the wind speed distribution. Since very stable conditions tend to only occur at low wind speeds, removal of very stable data will preferentially remove low wind speed data leading to an altered wind speed distribution. These very stable data have therefore been removed from both the anemometer and the visual wind speed datasets so that the distributions are comparable.

Figure 6 shows the effect of height correction on the anemometer wind speeds for January 1986. Figure 6a is a scatterplot of the individually height corrected mean wind speeds as described above, against the anemometer wind speed without any height correction. A reduction of about 10% in the wind speed would be expected [see tables in Dobson (1981) for a typical anemometer height of 25–30 m and a typical sea minus air temperature of 2°C]. Figure 6b shows the height corrected wind speed plotted against the 25-m (a typical height for this dataset) corrected wind speed; the slope of the regression line is 0.97. The 25-m corrected winds are on average biased 0.2 m s^{−1} high and the standard deviation is 0.5 m s^{−1}. These plots suggest that height correction using a constant height would be significantly better than no height correction, but that using a constant height adds up to 5 m s^{−1} scatter when compared to the individually height corrected wind speeds.

#### 2) Visual winds

Visual wind speed estimates are based on observations of the roughness of the sea surface. These observations have been calibrated using a Beaufort equivalent scale to be consistent with anemometer measurements of wind speed at a particular height; this height is then known as the equivalent height for the scale (see Table 1). Corrections are required to adjust the wind estimate to the equivalent value at 10-m height and also to take account of the effects of varying atmospheric stability on the appearance of the sea.

The magnitude of the correction needed to adjust the wind estimate to a 10-m value will depend on how the Beaufort scale was derived. If the anemometer wind data used in the derivation were adjusted to the neutral stabilityvalue before comparison with the visual estimates, then a neutral stability wind profile is appropriate for correcting the visual winds. However, if the anemometer winds had not been corrected for stability, then the profile to be used should represent the typical stability conditions under which the anemometer data were obtained. For want of that information, and since the stability over the ocean is typically near neutral, it would again seem best to assume a neutral wind profile.

The effect of stability on the appearance of the sea surface, and hence on the visual wind estimate, is fundamentally different from the effect of the stability on the vertical wind profile and hence the effect on anemometer winds [section 3c(1)]. Lindau (1995) has shown that Beaufort equivalent scales derived for different stabilities are different by less than 0.25 m s^{−1} for wind speeds up to Beaufort force 7, suggesting that stability effects do not greatly influence the wind values reported by the ship’s officers. The sense of the required adjustment is such that estimated winds under stable conditions should be converted to higher equivalent values than for unstable conditions. Thus, for stable conditions, visually estimated wind speeds are increased by stability correction, whereas anemometer-derived winds would be decreased.

It has been noted above (section 2c) that through their choice of analysis procedure, daSilva et al. (1995) applied a stability dependent height correction to the visual wind data. The effect of stability correcting visual winds in this way would be to increase wind speeds reported under unstable conditions by about 1 m s^{−1} or less. Under stable conditions the wind speeds would be decreased, with corrections of a few meters per second possible in light wind conditions. This is in the opposite sense to the effects observed by Lindau (1995) and again it must be emphasized that it is not correct to apply a stability correction to visual winds using the method used for anemometer wind speeds.

In summary, we have corrected visual wind observations from the equivalent height for each scale to 10 m assuming neutral stability, omitting a small correction for stability that could have been applied following Lindau (1995) or Isemer (1992).

### d. Processing

To produce a representative set of wind data for the decade 1980 to 1990 (including summer and winter conditions) while limiting the processing required, COADS data (with the platform type ship) from January and July 1980, 1982, 1984, 1986, 1988, and 1990 were selected. Each wind report was either height corrected taking into account stability effects (if an anemometer wind) or converted to each of the different visual Beaufort scales, then height corrected as appropriate (for visual winds). Only data for which the wind indicator flag was set were used, and for anemometer winds, an anemometer height merged from WMO47 had to be present. The dataset was then divided into an anemometer winds dataset and a visual dataset. Both datasets were then averaged to give 1° latitude by 1° longitude monthly means (hereafter referred to as monthly means). No interpolation of the resulting fields was carried out.

The number of monthly mean pairs available for comparison varied with year. Table 4 shows the number of monthly means, with greater than 10 observations contributing, available for analysis by year. The number of paired means (where there are more than ten anemometer and ten visual observations) was small because the preferences of each individual recruiting country for either visual or anemometer winds resulted in marked regional variations in the proportion of anemometerto visual winds [section 3b(1) and Fig. 3]. The trend in the proportion of anemometer reports given in Table 3 also affects the number of paired means shown in Table 4. Figure 7 shows the resulting geographical distribution of the paired monthly means used in the analysis. The paired means are limited to regions where the major shipping lanes converge approaching the coasts as the total number of reports must be high to get a large enough number of anemometer reports in the Atlantic and enough visual reports in the Pacific [see section 3b(1)]. However, comparison of Figs. 4 and 7 suggests that the ships reporting from these regions are, in general, the same ships that report from deep ocean regions. It is therefore expected that the results from these reports will be more generally applicable over most of the ocean.

## 4. Results

### a. Mean wind speed distributions

Figure 8 shows the distributions of the mean wind speed in 1 m s^{−1} ranges. The scales of Isemer, Kaufeld, and Cardone, and to some extent CMMIV, all underestimated the number of low wind speed reports compared to the 10-m neutral anemometer wind distribution; moderate mean wind speeds (about 6–9 m s^{−1} wind speed range) are overrepresented and the higher wind speeds occur at the correct rate.

The use of the WMO1100 scale results in too many low wind speed estimates, too few estimates between 7 and 11 m s^{−1}, and again the high wind speed tail is about right. The UWM (daSilva et al. 1995) and Lindau scales agree the best with the anemometer mean wind distribution. It should be noted, however, that it is difficult to compare the distributions because of the partially discrete nature of the raw visual wind data (see Fig. 2).

### b. Calculation of error variances for COADS data

In the present study we needed to ensure that the error variances of the VOS visual and anemometer winds were comparable so that a two-way regression would not be biased (Lindau 1995). January 1986 was selected as a month with a large amount of both visual and anemometer wind reports (see Table 4). The wind speed difference between pairs of simultaneous ship reports was calculated along with the separation of the ships. This was done separately for pairs of visual reports and pairs of anemometer reports.

Figure 9 shows a density plot of the number of pairs of reports with a particular separation and squared wind speed difference. The numbers of anemometer wind pairs have been scaled by a factor of 3.9 to give the same numbers as the visual pairs. The distributions can be seen to be very similar. The intercept and slope for the regressions of the mean squared wind speed difference as a function of ship separation were quoted in Table 2. The visual wind error variance (intercept values in Table 2) from this study was very similar to that found by Lindau. The anemometer error variance was less well defined due to the smaller number of pairs of ships but was comparable to the two visual error variance estimates. The regression coefficients were 0.98 for the visual winds and 0.93 for the anemometer winds. This analysis showed that the error variances for VOS anemometer winds and for visual winds are similar and that regressions could therefore be performed on the monthly mean values.

### c. Regressions

Now that the error variances of both methods of measurement have been shown to be similar, a two-way regression can be used. Table 5 shows the results of regressing mean winds from each of the visual scales against the mean winds from the anemometers. The Lindau scale gave the slope closest to unity (0.98) and also has the smallest intercept (−0.17 m s^{−1}). The UWM scale performed similarly (slope 0.95, intercept 0.36 m s^{−1}).

### d. Contoured distributions

Figure 10 shows density distributions for the WMO1100, CMMIV, UWM, and Lindau scales, which the regressions had shown to give the best equivalence between the anemometer and visual monthly mean wind distributions in COADS. WMO1100 can be seen to have given mean visual wind speeds too high for almost all the range (up to about 12 m s^{−1}). The use of the CMMIV scale overestimated the mean wind speeds below about 8 m s^{−1} and underestimated those above. While the use of the UWM scale resulted in the smallest differences between the visual and the anemometer mean winds, the regression line diverged from the line of agreement more rapidly than the Lindau scale regression line, which is therefore preferred. The differences between the mean wind speeds from the UWM and the Lindau scales were small, mean difference (UWM minus Lindau) is 0.3 m s^{−1} and individual differences for this monthly mean dataset ranged from −0.3 to 0.7 m s^{−1}.

## 5. Discussion

### a. Introduction

In this discussion we will consider how the performance of each of the scales might depend on the method used to derive the scale. Although there are considerable differences in the datasets used for the various scales (see section 2), the effect of the statistical method of derivation will be shown to be more important than variations in the datasets.

Following Lindau (1995) we note that if the error variances for two variables to be regressed are not equal, the effect on the slope can be predicted. A one-way regression of the data is only correct if the independent variable is error free; if it contains errors, the slope of the relationship will always be underestimated. This can be deduced if one considers that the error in an independent variable will lead to a larger range of independent variable. Given enough data, errors in the dependent variable should average to zero. The slope will therefore always be underestimated, resulting from what can be considered a stretching of the *x* axis. A one-way regression of the least accurate variable on the most accurate variable will give a better estimate of the slope than the opposite regression of the most accurate on the least accurate. In both cases, however, the slope will be underestimated.

As an example of one-way regression, we can use the example of comparing visual wind speeds from the VOS and OWS anemometer wind speeds. When considering slopes, the anemometer wind speeds will be on the *x* axis and the visual wind speeds on the *y* axis. Lindau has shown us that the OWS anemometer winds contain less measurement error than the VOS visual winds. The most accurate slope will therefore be found if the OWS anemometer winds are used as the independent variable. The slope will be underestimated, but the amount should be “small.” This will be called case 1. If the visual winds are used as the independent variable, the slope will again be underestimated, but as the errors in the independent variable are larger, the underestimate in the slope will be larger. This is case 2. When the axes are transposed in order to compare with case 1 (with the anemometer wind speed on the *x* axis), the result will be anoverestimate of the slope and this overestimate is “large.”

So, for variables containing errors, a two-way regression should be applied. A cumulative frequency analysis is in effect a two-way regression. The correct slope can only be found from a two-way regression if the errors in both variables are equal. This is case 3. In contrast to the one-way regression, either an overestimate or an underestimate of the slope can occur, depending only on the errors in the two variables. Using again the example of the VOS visual winds and the OWS anemometer winds, the slope will be overestimated (where the anemometers are on the *x* axis). The size of the overestimation will depend on the relative sizes of the errors. This is case 4.

### b. Case 1: Anemometer wind speed as the independent variable (WMO1100)

The WMO1100 scale was derived from a nonlinear regression of Beaufort winds on anemometer winds. If it is assumed that the error variance of the anemometer winds is smaller than that of the visual winds (i.e., that the error variances were comparable to those found by Lindau and quoted in Table 2) the regression used, the regression of visual on anemometer would underestimate the slope of the visual (*y* axis) against anemometer (*x* axis) graph. This underestimation would, however, be smaller than the overestimation that would have occurred had the opposite regression been used for the assumed error variances. Table 5 shows that the slope is overestimated by 12%. If the slope of the original relationship was underestimated, the resulting scale would compensate for this and the final graph would have a slope that is too high.

### c. Case 2: Visual wind speed as the independent variable (CMMIV, Cardone)

Both the CMMIV and Cardone scales used the anemometer wind speeds as the dependent variable and Beaufort wind speeds as the independent variable. Since the observations were from OWS (Cardone) or specially selected VOS (CMMIV), it will be assumed that the error variances were similar to those found by Lindau (Table 3). The slope of the visual (*y* axis) on the anemometer (*x* axis) graph (the opposite plot to that used to derive the regression) should be overestimated because the visual winds have been used as the independent variable. The error should therefore be of opposite sign to that for the WMO1100 scale and of greater magnitude because the visual error variance was larger than for anemometer winds from OWS. This is partially confirmed by Table 5, which shows that the slope is underestimated by 12% for CMMIV and 23% for Cardone (which would result from an overestimation of the original relationship).

### d. Case 4: Cumulative frequency analysis (Isemer, Kaufeld)

Cumulative frequency analysis was used to derive the scales; the error variances would be given by Lindau’s values in Table 3 as OWS anemometer winds were compared to VOS visual winds. The variable with the largest error would have the largest range, the slope of the visual (*y* axis) on anemometer (*x* axis) graph should therefore be overestimated. From Table 5 the Isemer scale underestimated the slope by 12% and Kaufeld by 16%, again as expected if the original relationship overestimated the slope.

### e. Case 3: Cumulative frequency analysis of variables with equal error variance (Lindau)

Lindau performed a cumulative frequency analysis on OWS anemometer and VOS visual mean wind speeds with equal error variances. The resulting slope should be close to the true value; Table 5 showsthat the slope is underestimated by 2%.

### f. Case 3: Two-way regression with equal error variance (UWM, case 3)

The UWM scale was derived from monthly mean interpolated COADS data that were regressed using a nonlinear fit. The scatter of the mean wind speeds was included in the regression analysis. It has been shown in section 3b(1) that the error variances of the anemometer means and the visual means are similar so this method should also give the true slope. Table 5 shows that the slope is underestimated by 5%. As this study used VOS anemometer winds with an assumed constant anemometer height of 20 m, it is possibly fortuitous that the agreement was so good between the anemometer and the visual winds. In addition, the use of the CMR5 flag would include anemometer winds for which the method was unknown, in with visual winds, which would tend to make the distributions more similar. The scale, however, seemed to perform well with this COADS dataset with the correct anemometer height conversion used. This test of the UWM scale was made using data comparable to that from which it was derived. No conclusions can be drawn on how it would perform with individual wind speed reports.

## 6. Conclusions

The scales of Kaufeld, Isemer, and Cardone did not produce mean wind speed distributions similar to that of the height corrected anemometer wind speeds in this study. This has been shown to result from the statistical method used to derive these scales. While the WMO1100 and CMMIV scales gave distributions more similar to those obtained for the associated height- and stability-corrected anemometer wind speed, a two-way regression indicated that in each case the slopes differed more than 10% from unity. The shortcomings in these scales can be attributed to the methods of derivation. Of these two WMO recommended scales, the operationally used WMO1100 seemed to be better than the CMMIV scale recommended for scientific use.

With regard to the choice of a scale for calculating monthly mean 1° area averages, the scales of Lindau and UWM gave the closest distribution to the anemometer winds. The Lindau scale had the slope closest to unity and the smallest offset. The slope of 0.98 and offset of −0.17 (anemometers on the *x* axis), however, combine to give a mean difference of −0.3 m s^{−1}, while the UWM slope of 0.95 combined with an offset of 0.4 gave a mean difference of close to 0. A mean difference of 0.3 m s^{−1} for the Lindau scale implies that, on average, the anemometer wind speeds in this study are biased low compared to the OWS data used to derive the scale. Figure 10 shows that for the range of mean wind speeds in this study, UWM gives the best result, but the errors will become larger as the range increases. Also a slope close to unity is likely to give a closer relationship between wind stresses calculated from visual observations and those calculated from anemometer measurements, but this has not been tested. There was little difference between the performance of these two scales in this study, but the scale of Lindau has been more rigorously derived and is therefore preferred.

Considering previous climate studies, a climatology that used the WMO1100 winds from COADS without conversion would, based on the results of the present study, give more realistic results than one that used say CMMIV. CMMIV would overcorrect the winds by more than twice the amount shown in this study to be needed. The wind climatology of Bunker (1976), which used WMO1100, should contain less bias than that of Isemer and Hasse (1987), which used the scale of Kaufeld. The climatology of daSilva et al. (1994) uses the UWM scale, which has been shown in this study toperform well, although in that study stability correction of the visual winds was applied in a similar manner to the anemometer winds, which is not thought to be appropriate.

Height correction of the individual anemometer wind speed reports has been important in removing uncertainties and scatter from the dataset of anemometer winds. However, whereas anemometer winds should be corrected using a stability dependant profile, visual wind speeds have been assumed to already represent neutral stability values.

In conclusion, the results of this study show that the Beaufort equivalent scale of Lindau (1995) is to be preferred when creating a homogeneous monthly mean wind dataset from anemometer and visual winds in COADS.

## Acknowledgments

We thank the COADS group for provision of the data and for the helpful advice and information that they provided. This study has been partially funded by a Commission from the Hadley Centre for Climate Prediction and Research, UK. Meteorological Office.

## REFERENCES

## Footnotes

*Corresponding author address:* Elizabeth C. Kent, James Rennell Division, Southampton Oceanography Centre, European Way, Southampton, S014 3ZH, United Kingdom.

Email: E.Kent@soc.soton.ac.uk