The performance of the scatterometer simulator on actual wind field is a good means to establish the validity of the simulation model. SeaWinds is chosen to compare real data with simulated data because it is the only scatterometer for which real data are available among the three scatterometers here. In total 14 orbits (one day) of data are included in the validation. The maximum collocation distance between real and simulated data points is set to 10 km, and the number of collocated data is 75 867; Fig. 9 shows the collocated wind retrieval result. The simulated wind speed and wind direction give a good correlation with the real SeaWinds data, which means the simulation model has a good performance as compared to the real scatterometer, and it is suitable for the comparison among the different types of scatterometers.

The most important differences between SCAT, WindRad, and SeaWinds are the shape of the antenna and the number of antennas, directly leading to a different distribution of the number of views across the swath. SeaWinds, as a rotating pencil-beam instrument, has four views in each WVC across the swath, where the fore and aft views in the outer swath are each split in two views. The number of slices in each view varies across the swath though. For rotating fan-beam instruments, the view number varies across the swath, with the feature of fewer views in the outer and nadir swath and more views in the parts of the swath in between (Fig. 10). It can be observed that both SCAT and WindRad contain more views than SeaWinds for all WVCs, with a saddle shape in the view count. Moreover, the number of views of WindRad is about twice the number of views of SCAT.

The instrument noise (Kpc) of the simulator for SCAT, WindRad, and SeaWinds is estimated at various wind speeds (4, 9, and 16 ms-1) on slice level and WVC level. The Kpc for each view is aggregated by weighting the Kpc of the slices in this view, and the Kpc on WVC level is derived by averaging the Kpc for all the views in the corresponding WVC.

Figure 11a shows the slice Kpc of SCAT as a function of incidence angle. The slices with low wind speed and high incidence angle contain high Kpc, and Kpc for VV polarization overall is lower than for HH, except for the slices with incidence angle lower than 30.25∘ (indicated by the dashed line in Fig. 11a). The Kpc in a WVC for SCAT (Fig. 11b) is much lower than the Kpc on slice level, as expected due to the aggregation of the slices in a WVC. The outer swath contains relatively high instrument noise as compared to sweet and nadir swath. Low wind speed leads to a higher Kpc. On the WVC level, the instrument noise is lower than 20 % except for low wind speed.

WindRad has two frequencies at the Ku and C band. As illustrated in Fig. 12a and b, the VV Kpc is lower than the HH Kpc for the Ku and C band, and the C-band Kpc is much lower than the Ku-band Kpc. On the WVC level (Fig. 12c), it shows a similar pattern to SCAT, and generally the instrument noise is lower than 10 % if the outer swath and low wind speeds are excluded.

The SeaWinds Kpc on slice level (Fig. 13a, b) is more constant at a wind speed of 9 and 16 ms-1, while it is increasing along with the incidence angle at a low wind speed of 4 ms-1. On WVC level, the Kpc is lower than 20 % except for wind speeds below 4 ms-1. We note that a random error of 20 % at 4 ms-1 is still acceptable in terms of absolute random wind error after wind retrieval.

In general, low wind speeds cause high instrument noise, as expected, and the instrument noise on WVC level is less than 20 % for SCAT, less than 10 % for WindRad, and less than 20 % for SeaWinds, when the outer swath and low wind speeds are excluded. All three scatterometers have a pattern of higher Kpc at the outer swath as compared to the other parts of the swath.

As already known, the first rank wind solution is not always the best solution. However, the more often the first rank solution is chosen to be the best solution, the lower the ambiguity in the inverted instrument wind solutions. The quality of the first rank solution thus reflects the ambiguity in the wind measurement system. So, it is chosen for the comparison of the wind retrieval performance on SCAT, WindRad, and SeaWinds. The difference between first rank solution and 2DVAR performance provides insight into the effects of the wind direction ambiguities on the final selected wind field, which may depend on measurement geometry. 2DVAR with MSS (Multiple Solution Scheme) (Vogelzang, 2013) has been applied in our simulation. A weighted analysis field is constructed by combining the scatterometer observations and a model prediction, and then the one lying closest to the analysis field is selected as the output solution. The problem is solved by minimizing a total cost function that combines both observation and NWP information: J=Jobs+JNWP=-2lnPvk|x+ln⁡Px|xb, where x is the true state of the surface wind field, vk is the possible ambiguous wind solutions, Pvk|x is the conditional probability of the vk observed given x, and Px|xb is the conditional probability of surface wind field x given xb. Details of the method can be found in de Vries et al. (2005), Vogelzang et al. (2009), Vogelzang (2013).

Comparisons of first rank solution and 2DVAR performances of SCAT, WindRad, and SeaWinds are shown in Figs. 14, 15, and 16. For SCAT, the first rank solution wind field (Fig. 14a) shows poor retrieval quality in the nadir and outer swath, while 2DVAR (Fig. 14b) effectively improves the retrieval results here; a similar improvement occurs for SeaWinds (Fig. 16). The nadir swath of WindRad shows worse wind retrieval quality than the other parts of the swath (Fig. 15a), and 2DVAR is able to correct the false solutions appearing in the first rank solution. Note that the rotation sampling pattern of WindRad is visible as regular disturbances along the swath. This implies that for the same WVC number, different sets of views are collected, depending on the phase of the antenna rotation; hence the wind retrieval performance may vary, e.g., the expected MLE. One aspect needs to be noted: the 2DVAR with MSS works properly in our simulation, but the input wind field of the simulation is ECMWF model data, which is consistent with the 2DVAR background field. Even though a Gaussian-distributed geophysical noise has been added in the input wind field, it still might lead to a selection of wind solutions that tends to be close to the model wind field, and hence it may somewhat overestimate the performance.

Four orbits of data on 17 December 2011 have been generated to be used for the wind retrieval simulation. The contoured histograms in Figs. 17, 18, and 19 provide statistics of the wind speed, wind direction with respect to a wind blowing from the north, and wind components u (eastward) and v (northward) versus the variable “true” input wind field for SCAT, WindRad, and SeaWinds. We note that opposing wind solutions will have opposite u and v signs and similar amplitude, and therefore such common ambiguity appears as a cross pattern in the u and v histograms. This ambiguity is directly related to the main double harmonic dependency of the GMF (Wang et al., 2019).

For SCAT (Fig. 17a), the first rank solution of all WVCs across the swath is included. It shows rather poor statistics when compared with the input wind field. However, by simply excluding the WVCs located in the outer swath, the first rank solution quality improves substantially (Fig. 17b). The spread in the wind speeds is reduced, and some derived false wind directions, which are shown as parallel and perpendicular lobes to the true value in the plots, are removed. When the nadir-swath WVCs are also excluded (Fig. 17c), then the wind speed collocation statistics stay almost unchanged as compared to Fig. 17b, while most of the false wind directions perpendicular to the true value are removed. This means that the outer swath contains the most ambiguous wind vector results, while the nadir swath ambiguities cause mainly wind direction errors.

Figure 18a shows the first rank wind retrieval for WindRad with all WVCs, and it shows much better statistics as compared to SCAT (Fig. 17a), due to the availability of twice the number of views in each WVC. Excluding outer WVCs (Fig. 18b) has less effect on the wind retrieval quality for WindRad than for SCAT. The retrieved wind speed shows slightly better statistics, but wind direction statistics stay almost unchanged, which means that the outer WVCs do not have a much larger wind direction ambiguity. On the other hand, when we only exclude nadir WVCs (Fig. 18c), the wind direction retrieval is improved. The average wind speed bias is 0.42 ms-1, and the standard deviation of wind direction is 32.21∘ (Fig. 18c), while they are 0.51 ms-1 and 41.30∘ for Fig. 18b, respectively. The last experiment shown for WindRad is with the exclusion of both outer and nadir WVCs (Fig. 18d), with an averaged wind speed bias of 0.44 ms-1 and a standard deviation of wind direction of 35.61∘. The largest performance improvement of WindRad occurs when excluding nadir WVCs. The outer swath mainly influences the wind speed retrieval skill, while the nadir swath provides wind direction ambiguity.

SeaWinds's outer swath contains only two views (fore-VV and aft-VV), and in order to process outer swath winds, each of these two views is split into two views based on their azimuth angle (four views in total in the end). Even though there are four views at the outer swath, the limited azimuth diversity leads to more ambiguous wind retrieval results (Fig. 19). The wind retrieval quality of SeaWinds is the poorest one among these three instruments.

The averaged wind retrieval statistics against the input wind field are dominated by the lack of ambiguity removal and nonlinearity. In practice these issues are successfully dealt with in the ambiguity removal step, using prior background information. In the next section we determine figures of merit (FoMs) to compare scatterometer performances with and without such prior information.

The first rank solutions contain ambiguities and because the input wind field is the ECMWF model wind, but without spatially correlated error, it leads to a nearly perfect 2DVAR result, which is unrealistic. In order to further evaluate the wind retrieval performance, the ambiguity of the solutions may be statistically evaluated in the context of generally available background (NWP) information. Figures of merit (FoMs) are a set of parameters to evaluate the wind retrieval quality of different scatterometer concepts, taking into account imprecise, ambiguous, and biased wind solutions. Three FoMs, which are the normalized wind vector rms (root mean square) (VRMS) error, ambiguity susceptibility (AMBI), and systematic error (BIAS), are introduced here based on Rivas et al. (2009). A brief description is given first.

The VRMS FoM is defined to quantify the ability of the scatterometer wind retrieval to handle ambiguous solutions with a priori NWP model information, such as in 2DVAR, but without actually simulating realistic spatially correlated errors. The input wind field to our simulation is considered as true winds (denoted with vt). VRMS quantifies the total simulated wind retrieval error with respect to vt. It is, however, calculated by down-weighting ambiguous wind vector solutions that are very distant from vt, since in practice it is easiest for 2DVAR and other applications to discard such solutions. The down-weighting involves the common prior knowledge in these applications, which is the general NWP background wind component uncertainty, denoted σNWP and assumed equal for u and v. The ambiguous retrieved wind vector distribution, expressed in the wind probability Pobsv|vt, is multiplied by a Gaussian probability distribution PNWPv-vt centered at the input wind field and with a variance σNWP2∼5 m2s-2 in both wind components. The VRMS FoM is subsequently obtained by normalizing this expression by the prior NWP VRMS error: 2FoMVRMS=rmsobsrmsNWP, where rmsobs=∫v-vt2Pobsv|vt×PNWPv-vtd2v and rmsNWP=∫v-vt2PNWPv-vtd2v=2σNWP. VRMS quantifies the wind solution's relative rms about the true wind with respect to the general prior background uncertainty. If its value is 1, then the wind retrieval failed to provide new and useful information in the wind field, i.e., corresponding to Pobsv|vt=constant.

On the other hand, AMBI is defined to quantify the ability of the scatterometer and its processing to handle ambiguous solutions without a priori NWP model information. It is a ratio of the wind solution output falling outside the general prior wind field constraint, relative to the output falling inside the prior wind field constraint. The lower the ratio, the better the AMBI FoM, where PNWP,max is the maximum probability of PNWPv-vt. 3FoMAMBI=∫Pobsv|vt×PNWP,max-PNWPv-vtd2v∫Pobsv|vt×PNWPv-vtd2v BIAS quantifies the systematic vector wind bias, again in the context of the background prior, which is the shift of the average location of the output wind solution away from the location of the prior wind caused by skewness in the output wind solutions (Eq. 4). 4FoMBIAS=∫v-vt⋅Pobsv|vt×PNWPv-vtd2v The wind retrieval is a nonlinear problem, and the output wind error depends on the true wind vector (wind speed and direction distribution). In order to minimize this dependence, the calculated FoMs are averaged over a climatology of wind inputs with uniformly distributed directions and wind speeds (3 to 16 ms-1) following a Weibull distribution with a maximum around 8 ms-1 (Liu et al., 2008). The input wind speeds are from 3 to 16 ms-1 with steps of 1 ms-1, and the input wind directions are from 0 to 360∘ with steps of 10∘. Each wind speed and wind direction combination contains the equivalent number of WVCs from the same orbit.

Figure 20 gives the three FoM comparisons of SCAT, WindRad, and SeaWinds as a function of the WVC positions in the swath. Overall, the wind retrieval performance of the rotating fan-beam instruments is better than the pencil-beam instrument, while the outer and nadir swaths of the three instrument types yield a poorer performance than the sweet swaths. The outer swath of SeaWinds only has two independent views, which result in very ambiguous winds and the worst simulated wind retrieval quality. The wind retrieval quality across the swath strongly depends on the location of the WVC; it degrades substantially in the outer and nadir swaths as expected. The outer swath has worse quality than the nadir swath for both SCAT and SeaWinds, whereas these two regions show comparable wind retrieval quality for WindRad. Although the number of views in the sweet swath for WindRad is twice the number for SCAT (Fig. 10), the wind retrieval quality is not improved as expected, but it shows very similar quality to SCAT. The elevated values for AMBI and BIAS indicate that, despite the high number of views, the wind retrieval tends to be not well determined and slightly nonlinear. At the same time, the quality in the outer swath of WindRad shows very pronounced improvement with respect to SCAT, due to the increased number of available views.

Figure 21 illustrates the VRMS as a function of wind direction and WVC location at 9 ms-1 wind speed. The wind retrieval performance across the swath for all wind directions gives the same pattern as described above with some modulations at different wind direction. There is one different feature occurring for WindRad. The VRMS at nadir swath shows higher values than in the outer swath, which is opposite to SCAT and SeaWinds. AMBI and BIAS (not shown here) have similar patterns to VRMS.

Wind direction bias between the wind retrieval result (2DVAR result) and the ECMWF model wind has been evaluated as a function of WVC and relative wind direction, using 15 orbits. The relative wind direction means the retrieved wind direction relative to the satellite motion direction. In this evaluation, we are able to see the wind direction bias with respect to the true direction at all the WVCs (Fig. 22). No matter whether the biases are negative or positive, both signs indicate that the wind directions have a tendency to be closer to the satellite motion direction, and if the wind direction bias is averaged over all the relative wind directions, a small value of the bias remains.

SeaWinds gives stronger bias both on the outer swath and nadir swath (Fig. 22b), while the nadir swath of SCAT gives weaker bias compared to the outer swath due to the increased number of views (Fig. 22a). For WindRad, when the retrieved wind direction is close to satellite motion direction (relative wind direction is 0), it shows rather strong negative and positive bias, but the nonbiased area for WindRad is larger than it is in SCAT and SeaWinds. This phenomenon can also be observed with real data from SCATSAT (Wang et al., 2019). This retrieved wind direction preference might be caused by the retrieval method.