a. Data preprocessing

The triplet of calibrated backscatter (σ₀) measurements can be related to wind speed and direction using an empirical transfer function (Stoffelen and Anderson 1993). Because of the cyclical nature of the transfer function with wind direction, the result of such a retrieval is four ambiguous wind directions of which the upwind and downwind directions usually have a high (but nearly equal) likelihood. Extra information, such as a meteorological background field, is necessary to enable a choice to be made between these ambiguous wind directions. We have chosen to do the wind retrieval in-house so that we can make use of the most up-to-date 10-m winds from our model background in the ambiguity removal procedure.

Details of the processing are given in Offiler (1994). In brief, the three-stage procedure starts with the ambiguous winds being ranked according to their “goodness of fit” or residual to the σ₀ transfer function—this is the weighted sum of squares of the difference between the measured σ₀ values and those given by the transfer function for that particular wind vector. The model background 10-m winds, linearly interpolated in time to the observation time, are used during the second stage to help choose the best solution. The rank 1 solution is retained if it is nearest background, otherwise other solutions are considered. In practice we find that the rank 1 or 2 solution nearest to the background is chosen on most occasions. The rank 3 or 4 solutions are preferred less than 1% of the time and this is usually in a low–wind speed case where we ignore the wind direction in the assimilation (see section 3b below). The final stage consists of a nearest neighbor test to check for local consistency. This consistency check proceeds through the swath iteratively looking at each direction in comparison with a 5 × 5 average.

The σ₀-to-wind processing implicitly includes some quality control by virtue of its use of a model background and local consistency checks. Prior to assimilation, a further check, using a Bayesian methodology (Lorenc and Hammon 1988), is included which uses a more timely background field. In our tests, a further 1% of the data are flagged in this final quality control check.

We are careful not to include any data from areas thought to be ice covered (based on the Washington Joint Ice Center ice analyses). The ice-edge data is processed to provide information on the grid scale of our forecast model (90 km) and observations where the associated model grid point is deemed to be ice covered are ignored. We also eliminate all reports based on less than three look directions.

b. Coverage

The final product of the data preprocessing is a 500-km-wide swath of wind vectors, with 19 overlapping 50-km cells across the swath at a separation of 25 km. With this swath width, one-third of the earth’s ocean area is observed in a day. In reality the coverage is somewhat less than this because an important part of the ERS-1 mission is dedicated to another instrument, the synthetic aperture radar, which cannot operate in tandem with the scatterometer. This reduced the data coverage in the northern latitudes (north of 30°N) and particularly the North Atlantic (see section 4a). Average data volumes during our trial were some 17000 reports per day in the Northern Hemisphere extratropics (90°–30°N), 74000 reports per day in the tropical band (30°N–30°S), and 67000 reports per day south of 30°S. It is worth noting that in these three areas, the ice-free sea area as a percent of the global area is 6%, 37%, and 20%, respectively, during March.

Figure 1 shows the cumulative observation data density during the full 10 days of the trial as a percentage of the maximum data density. Note the density nearest the poles is typically twice that in the equatorial latitudes because the swathes converge near the poles. Also note that the gaps in the orbits to the west of the United Kingdom were a persistent feature during the trial period.

c. Quality

Maps of the scatterometer winds derived at the United Kingdom Meteorological Office (UKMO) are routinely examined in the Central Forecast Office. The wind charts are well received, although lack of data over meteorologically important features has caused some frustration. Small-scale low pressure systems (both extratropical and tropical) and trough lines have been identified with considerable extra detail compared with model background plots. The forecasters are satisfied that the mean speed bias at high wind strengths is not a cause for concern. The subjective assessment has been backed up by a comprehensive monitoring exercise which has been ongoing since launch. Observation differences from model background, broken down by speed, latitude, and swath position, have yielded important feedback to the algorithm calibration as well as demonstrating the quality of the product relative to ship data.

As the World Meteorological Organization lead center for monitoring marine observations, the UKMO undertakes a continuous and comprehensive study of ship and buoy data. Our monitoring of scatterometer wind data fits naturally with this activity and enables an indirect intercomparison between the different components of the global observing system. Since January 1993, after the postlaunch calibration period, UKMO retrieved scatterometer winds have consistently bettered ship winds in all respects. Results for the period of the preoperational trial are given in Table 1, where scatterometer data is compared indirectly with ship data. Only a subset of all the available ship data has been chosen for this statistical comparison. We imposed a strict quality control whereby only ships reporting at least seven times per month with a root-mean-square vector wind difference from background of less than 6 m s⁻¹ are used. This sample of “good” ships includes half of all ship reports. The cutoff of 6 m s⁻¹ was chosen to be 50% greater than the annual difference from background of ocean weather ship GACA (and approximately equal to the largest monthly difference for this ship in the stormiest months). The background values are at 10 m for the scatterometer and 25 m for the ships, which correspond approximately with the observation heights.

In Table 1, we break the statistics down into five speed bins and give global figures. In the lowest speed bin, the direction statistics are not calculated for speeds less than 4 m s⁻¹. One interesting feature is that at all but the lowest speed range the scatterometer winds are weaker than the model background, whereas the ship winds are stronger, even after accounting for possible differences in reporting height. We suspect that even our sample of “good” ships tend to overreport wind speed, perhaps due to poor exposure or a bias toward gust speeds. Nevertheless, it does seem that at the highest wind speeds the scatterometer might be biased low. The standard deviations of wind speed and wind direction differences from model background and the rms vector wind difference are lower for the scatterometer data at all wind speeds. The global speed bias is close to 0 for the scatterometer data, whereas ship data are 0.5 m s⁻¹ stronger than background on average.

Table 1 also highlights the large difference in data volumes between the two observing systems. This is more marked when we look at a geographical breakdown where we see the scatterometer providing 15 times more data in the Northern Hemisphere and 100 times more data in the Southern Hemisphere than the “good” ships.

We have also examined the rms vector difference of scatterometer winds from model background as monthly time series throughout 1995 (not shown). We note that the values are lower at the end of the period than they were during our trial. This can be attributed to several factors, including a gradual improvement in model performance, better preprocessing of the observations, and of course the fact that after 4 August 1993 the background fields were generated from analyses making use of the scatterometer wind data. We also note a seasonal effect.

a. Assimilation tuning

Atmospheric assimilation is performed using the UKMO operational analysis correction scheme (Lorenc et al. 1991). This is an iterative analysis, with each variable being analyzed in turn. Each iteration is interleaved with a time step of the full forecast model to keep the analysis close to the preferred model solution. Observations are introduced into this continuous assimilation over a period around their validity time, with a peak weighting at their validity time. Thus, the model field relaxes toward the observations gradually to minimize any dynamical imbalances. Horizontal spreading of the observations is determined by a continuous background error correlation function that has a time dependence such that progressively smaller scales are fitted as the observation nears its validity time. This univariate approach is given a multivariate character by using appropriate dynamical balance equations to generate increments to other analysis variables from the analyzed univariate increment. One such routine that was developed specifically to improve the use of wind-only observations and which was found to be highly beneficial for the assimilation of ERS-1 scatterometer wind data is described in section 3b.

The characteristics of the scatterometer wind observations differ significantly from conventional sources of marine surface wind data. There is the obvious geographical distribution difference: ships provide a rather haphazard distribution with a focus on coastal waters and regular shipping lanes, and a tendency to avoid areas of high wind speeds and large wave height. The scatterometer, however, provides a regular high density of information within the swath and no information outside the swath. There is also a difference in the nominal height of the report. The scatterometer wind retrieval algorithms have been tuned to give winds at a nominal 10 m, whereas the ships may or may not have been reduced to 10 m depending on the observing practice (typically we find that ships are better fitted at 25 m). We also need to consider the light wind regime where the scatterometer is unable to provide reliable directional information. Revisions to the data assimilation system have been introduced to account for these different characteristics.

The increments at the observation position are calculated using a modeled 10-m wind. The interpolation to 10 m in the model boundary layer is performed in a manner consistent with the calculation of surface turbulent fluxes, which yields interpolation coefficients that depend on stability and surface roughness. Below a threshold observed wind speed of 4 m s⁻¹ the assimilation makes no use of the observed directional information. Horizontal correlation scales have been reduced in response to the higher data density. The values chosen are 240 km at the start of the iteration, reducing to 120 km at the observation time. These values are a compromise between our desire to analyze small-scale features where they are observed and our desire to spread information into the data voids beyond the swath. The vertical correlation scale has been revised following a reexamination of (o − b) radiosonde statistics and, for surface data, it is defined such that the correlation drops to about 0.7 at 900 hPa and 0.2 at 800 hPa. All observations surviving quality control are used in the assimilation, but at global scales where the model resolution is 90 km, observation data at the density provided by the scatterometer are not required. Our thinning strategy avoids a preliminary sort or averaging by choosing a different subset (one-fifth) of the data at each iteration (model time step) of our assimilation. At each iteration, a surface wind increment field is generated from all surface observation types: that is, the current scatterometer subset plus all other surface-based reports. It was determined that (with the thinning option in place), this was a better strategy than calculating independent increment fields from the different observing systems. The reduced horizontal correlation scales together with the data-thinning strategy reduces the density of scatterometer reports to an extent where they do not swamp the ship observations. Both of these measures also contributed to a significant computing-cost savings and have helped to make operational use of the data a viable proposition. With these measures the computational cost overhead of assimilating the scatterometer data is no more than 10%, even though data volumes exceed the sum of all other observing systems combined.

b. The WINDBAL balance step

Analyzed wind increments are available at all model levels from nonsurface wind data because of the broad vertical structure function used in the analysis correction scheme. We can thus use Eqs. (1) and (2) to obtain a balanced geopotential increment at each model level. Given the formulation of the Unified Model [the UKMO’s atmospheric model used for global and mesoscale numerical weather prediction and climate modeling, Cullen (1993)], we then need to use these balanced geopotential increments to calculate a balanced surface pressure increment (Δp∗) and balanced potential temperature increments (Δθ) at each model level. This is done by making use of the hydrostatic equation together with an additional closure constraint. We note that, because of radiative and subgrid-scale boundary layer processes, the temperature of the lowest model level has little to do with the rotational wind component at that level. We therefore choose the closure constraint to be that the temperature increment for the lowest model level is zero (note that the potential temperature increment for this model level will usually be nonzero because of the contribution to it from the balanced surface pressure increment). Hence, we obtain the expression for the balanced surface pressure increment of Eq. (3). Here, Π is the Exner pressure; B is a term in the definition of the model’s pressure levels (p_n = A_n + B_np∗, where p∗ is the surface pressure and A_n, B_n are constants). The integer subscripts label the true model levels (1 being the model level nearest to the surface), with the half-integer subscripts labeling the interpolated levels between them. Finally, R is the universal gas constant. Thus,

View Expanded

This balanced surface pressure increment, Δp∗, is then used in Eq. (4) (where C_p is the specific heat of air at constant pressure) together with the balanced geopotential increments to calculate the balanced potential temperature increment at each model level:

View Expanded

In tests, the correlations obtained from comparison of the derived balanced increments with the true increments (determined by subtracting two model dumps with the same validity time) were an impressive 0.8 in the extratropics for the surface pressure increments but were lower for the low-level potential temperature increments. These correlations were empirically modeled using a latitudinally varying correlation function that reduced as sin(1.5|latitude|) equatorward of 60° and, for the potential temperature increments, a vertically varying function zero outside of set lower (n) and upper (m) model levels: 0.333 at levels n and m, 0.666 at levels n + 1 and m − 1, and 1.0 everywhere else. During this trial, using a 19-level model, n and m were set to 3 and 17, respectively. The derived balanced surface pressure and potential temperature increments are scaled by this model of the correlation function before being used in the assimilation scheme.

For surface wind data, including the scatterometer wind data, we only have significantly nonzero components of the vertical structure function within the boundary layer, that is, the five model levels below 700 hPa. Thus, we cannot use the method of Eq. (4) to generate balanced potential temperature increments throughout the troposphere (as we do not know the balanced geopotential increments). Instead, we use the balanced surface pressure increment obtained from Eq. (3) and scaled as above as input to our existing HYDRST balance step and use this to generate balanced potential temperature increments throughout the troposphere.

We anticipated that this provision of balanced surface pressure and temperature increments would significantly enhance the assimilation of surface wind data by the analysis correction scheme.

a. A parallel trial

A global data assimilation trial was run in parallel with the operational assimilation for an 11-day period from 18 to 28 March 1993. The trial differed from the control in two respects. Scatterometer winds were included and WINDBAL was switched on during the assimilation. Ideally a longer trial period would be preferable but constraints on computer availability precluded this. Our hope was that the very large volume of additional observational data available to us in the trial would enable a clear signal to be obtained from this relatively short period.

An observation processing database entry was generated, giving diagnostics from the global data assimilation cycle. Forecast verification was available from the 5-day forecast that ran from a 1200 UTC analysis. Output was provided to drive a parallel wave model.

The mean data coverage given in Fig. 1 was typical of the trial period except for data losses at 0600 UTC 22 March and from 0600 UTC 23 March to 0600 UTC 24 March due to data processing problems. As we noted in section 2b, we obtained three-and-a-half times the number of scatterometer wind observations in the extratropical Southern Hemisphere than in the extratropical Northern Hemisphere. We therefore expected to see a much larger impact in the Southern Hemisphere than in the Northern Hemisphere, particularly given the value of accurate observations in an otherwise data-sparse region. The data loss for one day was unfortunate as any positive impact obtained from the data would be weaker than it would have been with a complete sample.

b. Fit to the background

The best measure of the performance of a data assimilation system is the fit of a short-period forecast to the next set of observations. We examined these “observation minus model background” (o − b) statistics for all observation types common to both trial and control. The only nonzero differences were in the extratropical Southern Hemisphere and were mostly restricted to the lower levels of the atmosphere. They all presented a positive signal as we see in Table 2, which contains statistics of the fit of observations to the model background fields valid at both 0000 and 1200 UTC. We see the typical reduction in rms (o − b) is 3%. To obtain this degree of improvement in the short-period forecasts, we must presume that the scatterometer winds are contributing toward an improved analysis.

For areas north of 30°S most statistics (not shown) were the same and where differences did occur they were so small that no significance could be attached to them.

c. Objective forecast verification

Forecasts were verified at 24-h intervals by comparison against surface reports and radiosondes of the 1200 UTC forecast, meaned over standard latitude band verification areas (60° bands labeled NH for 90°–30°N, TR for 30°N–30°S and SH for 30°–90°S). In Table 3 we present the results for the Southern Hemisphere expressed as a percentage change in rms error to simplify the comparison, with trial improvements shown as positive values. (Note that these results are not directly comparable to the data assimilation statistics presented in section 4b as they were based on forecasts from 0600 and 1800 UTC.)

The improvements in the Southern Hemisphere are substantial. The surface pressure and height fields show improvements in forecast scores of between 6% and 10% at all forecast ranges out to day 4. The temperature and wind fields show improvements of between 2% and 4%. Improvements are greatest at the shortest forecast ranges, but much of the improvement is retained out to the medium range. It is interesting to see a bigger signal at the surface at 24 h in Table 3 than we saw at 6 h in Table 2. One possible explanation for this is that in data-sparse regions 6-h forecast errors might be correlated with observation errors. To place this improvement in context, it should be noted that historically the performance of our numerical weather prediction system has improved by 3% per annum (measured as an average decrease in a basket of rms scores). For the Southern Hemisphere at least, this change makes a substantial contribution.

Differences were minimal in the Northern Hemisphere and Tropics. Overall we saw differences in magnitude of less than 0.5%, with the control being marginally better in the northern latitudes and the trial being marginally better in the Tropics. No significance can be attached to such small differences. It might be argued that a null result outside the Southern Hemisphere implies that there is no call for scatterometer wind data north of 30°S. Clearly, the model background is better in the Northern Hemisphere, so on average, the observations are less valuable. Other data sources (e.g., ships) are more likely to make scatterometer wind observations redundant and, as pointed out in section 2b, at best, the impact would be only a quarter of that found in the Southern Hemisphere based on data volume considerations. However, even if it is difficult to see an impact in the Northern Hemisphere statistics, we should still expect improvements in occasional cases where the scatterometer winds (which are clearly of good quality) identify and correct substantial errors in the model background in areas lacking conventional data sources. Breivik et al. (1994) demonstrated such an impact from scatterometer assimilation in the Norwegian Sea.

d. A global assessment

Figure 2 gives the rms difference in analyzed vector wind between the trial and control experiments at the 10-m level averaged over 10 days of assimilation. We see immediately that the largest rms differences are south of 45°S, with largest values of order 6 m s⁻¹. We also see that the differences are not confined to the lines of the satellite swath, which implies that the data assimilation system is both spreading the information away from the source of the data and is retaining information from past times. Figure 3 shows the equivalent rms difference at 850 hPa. The differences between Figs. 3 and 4 are, for the most part, reasonably well correlated. In some areas, differences at 10 m, as in parts of the Pacific, become negligible at the higher level. In other areas, as in the Indian Ocean and parts of the North Atlantic, the 850-hPa differences are as large, if not larger than, the lower-level differences. Zonal mean height–latitude cross sections (not shown) showed that the vector wind differences propagate throughout the troposphere while the temperature differences are more obviously confined to the lower troposphere.

The equivalent surface pressure rms difference is given in Fig. 4. Here we see that major differences are confined to the area south of 45°S with a maximum difference of 12 hPa. It is rare that analysis errors exceed 2 hPa in the Northern Hemisphere, so we would not expect large areas to differ by more than 1 hPa. As one might expect these differences grew during the forecast and in the Southern Hemisphere differences become more widespread, mostly through eastward advection. However, in the Northern Hemisphere, the forecast differences rarely exceeded 4 hPa.

As part of the trial, the resultant forecast surface winds were fed into a parallel run of our ocean wave model system. Because equilibrium wave height is proportional to wind speed squared, and because wave models retain a memory of the past wind field through the presence of swell wave energy, the wave model is a sensitive indicator to changes in the surface wind field of the atmospheric model. Typically trial wave heights in the southern Tropics were up to 0.5 m higher because of the differing evolution of systems in the Southern Hemisphere storm belt. In the storm belt itself there were major differences coincident with the wind speed differences associated with the displacement of the synoptic features. Unfortunately there were no wave observations to enable any verification of these features.

e. South Atlantic impact

Subjective assessment is a problem because in the Southern Hemisphere, where differences between trial and control are largest, the truth is difficult to determine. Further, as we have seen, the differences outside the Southern Hemisphere storm belt were rather small. The southwest Atlantic is one sector of the Southern Hemisphere where some reliance can be placed on the objective analysis as there are a reasonable number of surface reports from ships, islands, the southern tip of South America, and the Antarctic peninsula farther south. It is also an area where forecast differences were largest, being downstream of the South Pacific data void. Figure 5 compares the rms surface pressure difference of trial and control T + 72 h forecasts from verifying operational objective analyses for this area. We see the trial “winning” on 8 occasions out of 10 and in 5 of these cases the trial shows a reduction of rms scores in excess of 10%. We have performed a Bayesian test to objectively estimate the probability that the trial is better than the control. Assuming Gaussian probability density functions for the rms scores, and using the control run as the prior estimate for the trial run, we obtain a probability of 73% that the trial rms scores are better than those of the control run.

In our experience, differences in the synoptic evolution are only readily apparent in cases where the objective scores show a reduction of rms error in excess of 10%. Even in such cases, the two forecasts are often more like each other than they are like the verification. A subjective judgement of the forecast charts for this South Atlantic sector confirms the results of the objective assessment. Figure 6 gives results from the forecast from 22 March to highlight the degree of improvement obtained. Figures 6a–c show trial and control T + 72 forecasts of surface pressure plus the verifying control analysis. The trial correctly positions the low south of the Falklands, with better direction to the flow south of Tierra del Fuego. The trial also has a better low over the Antarctic peninsula. It is generally felt that correct positioning of systems in the Southern Hemisphere is the most important aspect to achieve. Even at analysis time the depths of systems cannot be determined with any precision. Bell (1994) discusses the subjective impact for all 10 cases and includes a full set of charts with differences from verifying analyses.