- Email: [email protected]
Wind retrieval and ERS-1 scatterometer radar backscatter measurements
Adv. Space Res. Vol. 13, No. 5, pp. (5)53—(5)60, 1993 Printed in Great Britain. Allrights reserved.
0273—1177)93 $24.00 Copyright ~ 1993 COSPAR
WIND RETRIEVAL AND ERS-1 SCATTEROMETER RADAR BACKSCATTER MEASUREMENTS A. Stoffelen* and D. L. T. Anderson** European Centrefor Medium-Range Weather Forecasts, Reading, U.K. ** Departmentof Atmospheric, Oceanic and Surfacerary Physics, Clarendon Laboratory, University of Oxford, Oxford, U.K. *
ABSTRACT Calibration and validation activities for the ERS-l scatterometer have been carried out at ECMWF, complementary to the “Haltenbanken” field campaign. At a Numerical Weather Prediction (NWP) centre a wealth of verifying data is available both in time and space. By using the data and resources available at a NWP centre, it is possible to contribute extensively to a sateffite instrument calibration and validation exercise. We estimated noise, and characterised the scatterometer measurements in relation to wind speed and direction. The antennae configuration of the ERS-l scatterometer proved to be crucial for this work. It is shown that measurement noise is low and that a solution surface is generally well-defmed in 3D measurement space except at low wind speed at the inner edge of the swath. We reformulated ESA’s prelaunch transfer model CMOD2, and also propose revision of existing wind retrieval schemes. The changes implemented so far at ECMWF clearly improve the accuracy of wind retrieval from the scatterometer. 1. iNTRODUCTION At ECMWF there is an ongoing project to help in the calibration and validation of ERS-1 wind scatterometer data, complementary to the “Haltenbanken” field campaign held off the coast of Norway. This paper reports on our part in instrumental calibration, and characterisation ofthe norinalised radar cross sections, i.e. a°,as measured by the ERS-l scatterometer. We will briefly report on the dependence of a° on wind speed and direction, and other geophysical parameters, and the derivation of a a°-to-wind relationship using a maximum likelihood estimation procedure. For a more extensive description of this work we refer to Stoffelen et al. /1,2/. This paper addresses essential issues for the process of obtaining a unique wind speed and direction (wind retrieval and direction ambiguity removal). We will first discuss the operational ESA processing suite. 1.1 The Oierational Wind Retrieval Suite The ERS-l scatterometer has three independent antennae pointing in a horizontal surface towards a direction of 45, 90, and 135 ° with respect to satellite propagation. Therefore, a site in the scatterometer swath is illuminated three times, respectively by the fore, mid and aft beam. The incidence angle of the radar beam varies from 18 to 47 ° for the mid beam, and 25 to 57 ° for the fore and aft beams. The swath, approximately 500 km wide, is sampled every 25 km resulting in 19 measurement cells across the swath; along the swath the sampling distance also equals 25 km. The spatial resolution of the instrument on the earth’s surface is approximately 50 km. The C-band radar frequency used is 5.3 0Hz and its polarisation is vertical. From pre-launch field campaigns an empirical relationship between a°,and wind speed V and direction 4) for neutral stratification at 10 m height was found by Long, called CMOD2 /3/: (5)53
(5)54
A. Stoffelen and D. L. T. Anderson
00
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The coefficients B0, B1, and B2 depend on the radar beam incidence angle and wind speed. In this paper the largest term B0 will be referred to as “bias term”, the smaller harmonic coefficient B1 as “upwind/downwind amplitude”, and B2 as “upwind/crosswind amplitude”, although strictly latter phrase should be assigned a more complicated definition. Several research groups have found aO to be a function of other geophysical parameters rather than neutral 10 m wind speed and direction (e.g. /4/). Globally available fields on stability, SST, and wave parameters from the WAM model can be used at ECMWF to investigate these geophysical effects statistically. Our first aim is, however, to obtain as accurate a wind retrieval procedure as possible based on a 0°-to-wind relationship only. The transfer function is used inversely in the wind retrieval algorithm. ESA’s operational scheme called CREO performs several steps in order to obtain an unambiguous wind field: • Its first step is based on minimisation of the following maximum likelihood estimator (MLE) for varying wind speed and direction: MLE
-
iL
~
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where ø°mjis the measured value, and o°~ is obtained from the 0°-to-windtransfer function for a trial value of the wind vector. SD(a°~) is Kp1.a°,1,where K~is a constant in the search for a minimum, with a value of typically 0.05. The minimisation is done for each cell, i.e. triplet of measured 0°s(Also 0°pairs can be processed). Over the full wind domain this objective function will have several local minima, with the two most probable solutions in general approximately 180 “ degrees apart, due to the small upwind/downwind amplitude in the transfer function. These local minima are ranked in order of decreasing probability and stored as the possible solutions for wind speed and direction. • In the second step of CREO two fields are compiled across the full swath and a maximal distance of 3000 kin along the swath. The two fields are supposedly blowing in opposite directions. Information on potential skill in discrimination between upwind and downwind is used in this step. • The third step is called “autonomous dealiasing”, in which one of the two fields is selected on the basis of a sufficiently low MLE averaged over all cells. Optionally this third step can be circumvented. • If step 3 is unsuccessful, step four is to check which field is closest to a background wind field in some integral sense over an area typically 500 km X 3000 km. If the large scale fit of the closest field is not acceptable, no solution is given. The processed areas overlapby one-third in order to be able to check for consistency. 2.VISUALISATION OF 3D MEASUREMENT SPACE Each triplet of measurements can in principle be plotted in a 3D space spanned by an axis system representing the fore, mid, and aft beam measurements. Given a transfer function as in equation (1-3) one can show that for a particular cell position across the swath the triplets should lie close to a cone, here called solution surface, as shown in figure 1. To visualise this cone we made 2D cross sections through it, with a thickness comparable to instrumental noise. In figure 2(a) is shownaxis for triplets having of approximately a matching value for fore anda°~ aft 0°foesa=cross-section 0°~). The horizontal is the average 0°~ and 0°~, and the vertical represents beam 0° ( values. This type of section should reveal points lying around a lower curve, where the wind direction is approximately blowing perpendicular to the mid beam pointing direction, and two upper curves corresponding to wind directions blowing towards and away from the mid beam pointing direction. Thus the a~triplets constituting the “upwind” and “downwind” curves can easily be separated by using the ECMWF analysis wind direction. Analysis wind direction accuracy might not be sufficient for wind speeds below 5 m/s, and here the upwind/downwind separation will become less exact. Figure 2(a) and 2(b) show respectively the upwind and downwind 0°triplets. We further tagged (coloured) each triplet with the
(5)55
Wind Retrieval and ERS-1 Measurements
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FiRure 1: Solution surface in 3D measurement space. The solid line represents a constant wind speed at varying wind direction.
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FiRure 2: Cross-section through 3D measurement space at cell 11 (from inner.swath) with a thickness of 5 % of 00 and for a plane where 00,~,.= &,~. The horizontal represents the average of ~ and &~,and the vertical Is a°,,ed.The curves show a transferfunction fit in this plane (see text). 2(a) shows “upwind” 00 triplets, and 2(b) “downwind” triplets (The ECMWF analysis wind has a positive (2(a)) or negative (2(b)) component along the mid beam pointing direction).
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ECMWF analysis wind speed to be able to diagnose the wind speed dependence of the curves (grey tints here). The separation of the upper and lower curves is a measure of the upwind/crosswind amplitude at the mid beam incidence angle. The separation between the two upper curves is caused by a combination of the upwind/downwind amplitude of the mid, and the fore and aft beam. Therefore it is not possible to accurately quantify this separation in an upwind/downwind coefficient. However, this cross section is a very good diagnostic to fmd weaknesses in the fit of a transfer function to 0°triplets. 0°th versus 0°f~. Again a separation is made for the collocated ECMWF analysLs winds Figure 3a component shows having upwind, 3(a), and downwind, 3(b), to the mid beam, and triplets are tagged with the analysis wind speed (grey tints here). The upper and lower curves represent the triplets calculated from the transfer function which have the maximum distance from the line 0°~ = &~ and are approximately upwind and downwind to the aft and fore beam respectively. These scatter plots reveal ‘information on the upwind/crosswind term and the upwind/downwind tenn in the transfer function, for incidence angles corresponding to the fore or aft beam. (Essentially, this type of plot shows the behaviour of a 2-beam scauerometer like SEASAT). Again accurate quantative information is difficult to extract, but the projection is a powerful diagnostic to indicate transfer function problems. In /1/ we discussed a cross section at a surface for which the sum of 0°~ and 00th is constant. From this section we estimated the 0°noise perpendicular to solution surface, and the upwind/crosswind (B 2 in eq. 1) coefficient in the transfer function, as a function of wind speed and incidence angle.
(5)56
A. Stoffelen and D. L. T. Anderson
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We investigated the effect of sea surface temperature (SST) on triplets in the cross sections at wind speeds below 3 rn/s. By tagging (colouring) SST values from 0 to 30 °Cin 10 °Cbins, we did not find any difference in the scatter of 0°triplets across the plots. The noise contribution from geophysical parameters not included in the transfer function may be more significant in a direction parallel to solution surface. Or in other words, changing SST or another sea surface parameter might have the same effect as changing wind speed in our transfer function formulation. Therefore, we can conclude that any 0°SST dependency should be implementable as an “effective” wind speed. Plotting the above cross sections and projection over ice showed some anisotropy of backscattering over ice (0°~ + 0°c,),and the difficulty of separating ice from wave scattering (the oo triplets are not always in different domains of 3D measurement space). In this way these sections contribute to understanding the physics of radar backscattering. 3. WIND RETRIEVAL REVISION 3.1 a~normalisation Equation (2) computes for each 00 triplet the distance to the solution surface defined by the transfer function used in a 3D 00 space. The transformation of the 3D space is defined by the term SD(0°,1).In the definition as by CREO the three axis are scaled by a constant times 0°,~, i.e. the value of the solution o~ for each beam (axis). Other normalisations have been investigated /6/ such as by measured ~ or no normalisation at all. We also considered retrieval in ln(0°)rather than 0012/. From a theoretical point of view, nomialisation should be done by the square root of the best estimate of expected variance of ~ 0°,,. However, it is shown by Stoffelen et al. /2/that the answers from such a nonnalisation do not give the expected (true) solution, due to the non-linear shape of the solution surface and the proportionality of the expected variance Ofl 00. We investigated the effect of normalisation through visualisation ofare differently measurement 0°fo~ constant.scaled Figure3D4(a) shows no spaces. Figure and 4 shows sections for which 0°~ pluswith the o°,value at the centre of gravity of normalisation, figure cross 4(b) shows a scaling of each axis the plot. The latter scaling visualises approximately the space used to compute a distance, for a normalisation of equation (2) by either SD(0°m.) or SD(0°,,).In order to be able to retrieve wind directions accurately and obtain a realistic wind direction probability density function (PDF) after retrieval, it is desirable that equal portions of the 0°triplets are thrown onto equal wind direction intervals. This is the case if the solution surface has no edged shape and is circular rather than elliptic. With these constraints, normalisation by solution or measured 0°looks unfavourable, whilst no normalisation appears favourable. For the same reasons retrieval in ln(o°)in stead of 0°is also unfavourable (not shown). By performing wind retrievals using the different normalisations we found that using no normalisation gives the least number of local minima, whilst normalisation by solution 0°results in the highest number
Wind Retrieval and ERS-1 Measurements
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of minima. For all nonnailsations we found that wind directions associated with 3~’or 4th ranked local minima have on average a probability that is less than the average probability of any wind direction. So, the presence of these solutions depends on the nonnailsation, rather than a physical probability. In our earlier work 12/ we noted that the skill for discriminating between rank 1 and rank 2 is very low. To test the accuracy of wind retrieval for different nonnalisations we computed statistics for the wind direction of rank 1 and rank 2 solutions, whichever is closest to the ECMWF analysis wind direction. Additionally we included the possibility to exclude solutions that differ by more than 60 ° from the analysis. Doing so we found that indeed the wind direction PDF obtained when using a normalisation by measured or solution 00 has a bimodal shape, with minima corresponding to the wind directions at the sharp edges of figure 4(b). The wind direction PDF most closely resembles the analysis PDF when using no normalisation. Further, the standard deviation of the departures between retrieved and analysis wind direction is smallest in this case. In figure 5 we show a synoptic wind pattern as obtained using different normalisations in wind retrieval. Figure 5(a) shows no nonnalisation, and 5(b) the current CREO wind retrieval normalisation. No ambiguity removal is used here, rather the closest of rank 1 and 2 to a 24 hour ECMWF forecast is selected. The forecast is shown in figure 5(c). Consistently, we find that no normalisation produces the superior synoptic wind pattern. The scatterometer shows more synoptic detail than the 24 hour forecast. In line with the above, normalisation could be optimised using information on the upwind/downwind amplitudes and noise characteristics of mid, and fore and aft beams, and on the shape of the transfer function in the surroundings of a measured o~triplet. However it is thought that little could be gained by doing this exercise, since no normalisation seems close to optimal. 3.2 Ambiguity removal On average CREO manages to process 95 % of its wind directions closer than 90 ° to the ECMWF analysis. From our earlier work 12/however, we showed the difficulties of CREO in building up a synoptic wind field from the solutions given at each cell. Most problems occur near fronts and lows, and also tropical cyclones. So, the 5 % that does not match seems to result from CREO in most cases. We tried to improve the procedure, by introducing slightly different spatial filters to build up the two anti-parallel fields. We found howeverthat these filters solve some problems, but create others. Hoffinan carried out
A. Stoffelen and D. L. T. Anderson
(5)58
(c)
FiRure 5: Synoptic windpattern ascending swath (ERS-1 passes inatpart top ofan from to right) on 6 november 1991 at approximately 12 GMT. The upper right latitude is 45.5 N, and longitude 157.7 E.
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5(a) and 5(b) are ERS-1 retrieved winds by 0.05.&,~ using no normalisation, respectively and (seenormalisation text). Wind by is obtained by selecting the closest to 5(c) from rank 1 and 2 solutions.
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5(c) is the operational ECMWF 24 hour forecast
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an impact study assimilating CREO winds into the ECMWF meteorological model 17/. Not surprisingly, he found mixed results in the Southern Hemisphere, i.e. forecasts could be improved or degraded as a result of assimilating scatterometer data. In the Northern Hemisphere and Tropics no significant forecast impact was shown. As mentioned in the previous section, there is no physical reason to assign potential value to local minima in the MLE, when the probability of those solutions is very low. We further found that in cases where the probability of a rank 3 or 4 solution was high, we are dealing with either lower wind speeds, or with temporally variable wind directions athigher wind speeds. In both cases there is not much information in the 0°triplet concerning wind direction. These triplets can be found in figure 4(a) as lying close to the centre of gravity of the scatter plot, and can be accurately uncovered by computing, for a triplet, the average distance (probability) to the solution surface over all wind directions, and comparing this with the expected probability of the true solution. Additionally, this mean probability should be much lower than the rank 1 probability, and the rank 1 probability should itself be high. Using the above three constraints we should be able to distinguish triplets with clear wind direction information from triplets with less wind direction information content. In latter case we have to rely both on background wind direction information and scatterometer wind direction information to retrieve wind direction. The constraints should also be used for quality control, i.e. rejection of triplets.
Wind Retrieval and ERS-l Measurements
(5)59
Essential wind direction information is not lost when locally relying on the background (e.g. see Figure 5). We concluded from this that relying on a high quality meteorological background locally (for each cell) is better than trying to build up synoptic wind fields from ranked solutions, and rely only on the large scale background wind field. Given the above, we propose to use background wind direction information in the retrieval at each node, i.e. add a background wind direction term in equation (4). For purposes of data assimilation at our site this is sufficient, since for assimilation of wind speed in the analysis a direction has to be assigned. A spatial consistency filter selecting between a rank 1 and 2 solution, may still be applied to correct the background for misplacement of fronts and lows. Preliminary tests have shown that we are indeed able to exclude those cases in which the scatterometer wind direction information is insufficient. We have not as yet experimented with the inclusion of background wind direction infonnation. A difficultyhere arises in cases with relatively high wind speeds which do not lie close to the solution surface defined by our transfer function. We believe in these cases a confused sea state is present, where wave fetch is most relevant. The problem occurs in general over areas of typically 100-200 km. Since these cases will generally result in both unreliable wind direction and wind speed we have to refine our constraints in order to exclude these 0°triplets. 4. CONCLUSIONS A 3D measurement space can be defined using a~measurements from each antenna as a coordinate on one of the axis. Useful information can be retrieved from cross sections through and 2D projections of this space. We found that in general a very definite surface arises in this measurement space with only little 0°noise perpendicular to it. We were able to estimate wind direction sensitivity from the particular circular shape of this surface, and found that below incidence angles of 25 °wind direction sensitivity is very poor. At high incidence angles wind direction sensitivity is best. A shift of the swath towards higher incidence angles would therefore be beneficial. By fitting a 0°-to-windtransfer function to the solution surface we found that wind speed sensitivity is very good. We have indications that 0°saturation may be present for wind speeds above approximately 18 m/s. Visualisation of 3D measurement space appears to be a powerful tool in diagnosing problems with the fitting of a 00-to-wind transfer function in this space. It became obvious that ESA’s original transfer function had to be reformulated/l/. By collocationof ERS- 1 data with other geophysical fields, potentially a great deal can be learned about radar backscattering, using the visualisation techniques described in this paper. Normalisationof 0°in wind retrieval (Equation (2)) can also be visualised using proper scalings of the axis of 3D measurement space. In this way wind retrieval becomes a geometrical problem rather than just a statistical one. The ranking of local minima in residual beyond rank 2, when retrieving wind speed and direction is shown not to be very fruitful. Cases where ranks 3 and 4 are probable are in general cases where little directional information is present in the triplets. Geometrical considerations made us able to design constraints that only select those triplets with satisfactory wind vector solutions. 0~
The compilation of synoptic fields from the available ranked solutions in CREO often fails close to fronts, lows, and also tropical cyclones 12/. Attempts to improve CREO in those areas were not very successful. However, when using the closest of the available ranked solutions to an ECMWF forecast we found that in the above synoptic cases, the scatterometer wind field looks much better. Therefore, at locations where insufficient directional information from the scatterometer is present, we believe that using the forecast wind direction in a local retrieval is better than using forecast wind direction information only over larger scales, as CREO does. We believe that in all cases an accurate wind speed from the ERS-l scatterometer can be retrieved, unless a confused sea state is present as we observed for high wind speeds with a large temporal variability of the wind vector. This occurs typically over areas of 100-200 km. Using a variational method to retrieve a wind field over a larger area, using forecast wind and 0° measurements in the minimisation (e.g. /81) could in our opinion also improve upon CREO, but is a more
(5)~Ø
A. Stoffelen and D. L. T. Anderson
demanding approach. At ECMWF we will eventually use 00 measurements directly in a 3D-var assimilation scheme /9/. At a NWP centre a wealth of information is available, and we have shown that an important contribution is given to calibration and validation of satellite measurements. Using ECMWF analysis winds we were able to significantly improve the 0°-to-windrelationship 12/, indicate problems in scatterometer wind retrieval algorithms, and show how to improve ERS-l scatterometer wind retrieval. We believe that scatterometry has great potential for defining more accurately the atmosphere-ocean interface. Acknowledgements We would like to thank Peter Woiceshyn, Graeme Kelly, and other ECMWF staff members for their helpful discussions and time. Also the ESA analysis and experimenters team provided a sound framework for the research to take place. Last but not least we thank ESA and ECMWF for providing the resources for carrying out the work. REFERENCES 1. A.C.M. Stoffelen, D.L.T. Anderson, ERS- 1 scatterometer calibration and validation activities at ECMWF: A. The quality and characteristics of the radar backscatter measurements. Proc. European ‘International Space Year’ Conference, Munich, Germany, 30 March - 4 April 1992. 2. A.C.M. Stoffelen, D.L.T. Anderson, and P.M. Woiceshyn, ERS-l scatterometer calibration and validation activities atECMWF: B. From radar backscauer characteristics to wind vector solutions. Proc. European ‘International Space Year’ Conference, Munich, Germany, 30 March - 4 April 1992. 3. A.E. Long, Towards a C-Band radar sea echo model for the ERS-l scatterometer. Proceedings of a conference on spectral signatures, Les Arc, France, December 1985, ESA SP-247 4. M.A. Donelan, W.J. Pierson Jr., Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry, J. Geophys. Res., 92, # CS, 4971-5029, (1987)
- Study of a method to dealias winds from ERS-l data. Vol 2 - Wind retrieval and dealiasing subroutines, Final report of ESA contract No. 6874/87/CP-I(sc), ESTEC, Noordwijk, The Netherlands 5. A. Cavanid, P. Lecomte, Vol 1
6. R. Graham, D. Anderson, A. Hollingsworth, and H. Bottger, Evaluation of ERS-l wind extraction and ambiguity removal algorithms. Meteorological and statistical evaluation., Technical report, ECMWF, Reading, UK 7. R. Hoffman, A preliminary study of the impact of C-Band scatterometer wind data on global scale numerical weather prediction, Draft report, ECMWF, Reading, UK (July 1992). 8. H. Roquet and A. Ratier, Towards direct variational assimilation of scatterometer backscatter measurements into numerical weather prediction models, IGARSS 88 Proceedings. 9. J. Pailleux, W. Heckley, D. Vasiljevic, J.-N. Thdpaut, F. Rabier, C. Cardinal!, and E. Andersson, Development of a variational assimilation system., Technical memorandum 179, ECMWF, Reading, UK (1991).
0273—1177)93 $24.00 Copyright ~ 1993 COSPAR
WIND RETRIEVAL AND ERS-1 SCATTEROMETER RADAR BACKSCATTER MEASUREMENTS A. Stoffelen* and D. L. T. Anderson** European Centrefor Medium-Range Weather Forecasts, Reading, U.K. ** Departmentof Atmospheric, Oceanic and Surfacerary Physics, Clarendon Laboratory, University of Oxford, Oxford, U.K. *
ABSTRACT Calibration and validation activities for the ERS-l scatterometer have been carried out at ECMWF, complementary to the “Haltenbanken” field campaign. At a Numerical Weather Prediction (NWP) centre a wealth of verifying data is available both in time and space. By using the data and resources available at a NWP centre, it is possible to contribute extensively to a sateffite instrument calibration and validation exercise. We estimated noise, and characterised the scatterometer measurements in relation to wind speed and direction. The antennae configuration of the ERS-l scatterometer proved to be crucial for this work. It is shown that measurement noise is low and that a solution surface is generally well-defmed in 3D measurement space except at low wind speed at the inner edge of the swath. We reformulated ESA’s prelaunch transfer model CMOD2, and also propose revision of existing wind retrieval schemes. The changes implemented so far at ECMWF clearly improve the accuracy of wind retrieval from the scatterometer. 1. iNTRODUCTION At ECMWF there is an ongoing project to help in the calibration and validation of ERS-1 wind scatterometer data, complementary to the “Haltenbanken” field campaign held off the coast of Norway. This paper reports on our part in instrumental calibration, and characterisation ofthe norinalised radar cross sections, i.e. a°,as measured by the ERS-l scatterometer. We will briefly report on the dependence of a° on wind speed and direction, and other geophysical parameters, and the derivation of a a°-to-wind relationship using a maximum likelihood estimation procedure. For a more extensive description of this work we refer to Stoffelen et al. /1,2/. This paper addresses essential issues for the process of obtaining a unique wind speed and direction (wind retrieval and direction ambiguity removal). We will first discuss the operational ESA processing suite. 1.1 The Oierational Wind Retrieval Suite The ERS-l scatterometer has three independent antennae pointing in a horizontal surface towards a direction of 45, 90, and 135 ° with respect to satellite propagation. Therefore, a site in the scatterometer swath is illuminated three times, respectively by the fore, mid and aft beam. The incidence angle of the radar beam varies from 18 to 47 ° for the mid beam, and 25 to 57 ° for the fore and aft beams. The swath, approximately 500 km wide, is sampled every 25 km resulting in 19 measurement cells across the swath; along the swath the sampling distance also equals 25 km. The spatial resolution of the instrument on the earth’s surface is approximately 50 km. The C-band radar frequency used is 5.3 0Hz and its polarisation is vertical. From pre-launch field campaigns an empirical relationship between a°,and wind speed V and direction 4) for neutral stratification at 10 m height was found by Long, called CMOD2 /3/: (5)53
(5)54
A. Stoffelen and D. L. T. Anderson
00
—
B0
.
[1
+
B1 cos(4))
+
B2 cos(24))
1
(D
The coefficients B0, B1, and B2 depend on the radar beam incidence angle and wind speed. In this paper the largest term B0 will be referred to as “bias term”, the smaller harmonic coefficient B1 as “upwind/downwind amplitude”, and B2 as “upwind/crosswind amplitude”, although strictly latter phrase should be assigned a more complicated definition. Several research groups have found aO to be a function of other geophysical parameters rather than neutral 10 m wind speed and direction (e.g. /4/). Globally available fields on stability, SST, and wave parameters from the WAM model can be used at ECMWF to investigate these geophysical effects statistically. Our first aim is, however, to obtain as accurate a wind retrieval procedure as possible based on a 0°-to-wind relationship only. The transfer function is used inversely in the wind retrieval algorithm. ESA’s operational scheme called CREO performs several steps in order to obtain an unambiguous wind field: • Its first step is based on minimisation of the following maximum likelihood estimator (MLE) for varying wind speed and direction: MLE
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where ø°mjis the measured value, and o°~ is obtained from the 0°-to-windtransfer function for a trial value of the wind vector. SD(a°~) is Kp1.a°,1,where K~is a constant in the search for a minimum, with a value of typically 0.05. The minimisation is done for each cell, i.e. triplet of measured 0°s(Also 0°pairs can be processed). Over the full wind domain this objective function will have several local minima, with the two most probable solutions in general approximately 180 “ degrees apart, due to the small upwind/downwind amplitude in the transfer function. These local minima are ranked in order of decreasing probability and stored as the possible solutions for wind speed and direction. • In the second step of CREO two fields are compiled across the full swath and a maximal distance of 3000 kin along the swath. The two fields are supposedly blowing in opposite directions. Information on potential skill in discrimination between upwind and downwind is used in this step. • The third step is called “autonomous dealiasing”, in which one of the two fields is selected on the basis of a sufficiently low MLE averaged over all cells. Optionally this third step can be circumvented. • If step 3 is unsuccessful, step four is to check which field is closest to a background wind field in some integral sense over an area typically 500 km X 3000 km. If the large scale fit of the closest field is not acceptable, no solution is given. The processed areas overlapby one-third in order to be able to check for consistency. 2.VISUALISATION OF 3D MEASUREMENT SPACE Each triplet of measurements can in principle be plotted in a 3D space spanned by an axis system representing the fore, mid, and aft beam measurements. Given a transfer function as in equation (1-3) one can show that for a particular cell position across the swath the triplets should lie close to a cone, here called solution surface, as shown in figure 1. To visualise this cone we made 2D cross sections through it, with a thickness comparable to instrumental noise. In figure 2(a) is shownaxis for triplets having of approximately a matching value for fore anda°~ aft 0°foesa=cross-section 0°~). The horizontal is the average 0°~ and 0°~, and the vertical represents beam 0° ( values. This type of section should reveal points lying around a lower curve, where the wind direction is approximately blowing perpendicular to the mid beam pointing direction, and two upper curves corresponding to wind directions blowing towards and away from the mid beam pointing direction. Thus the a~triplets constituting the “upwind” and “downwind” curves can easily be separated by using the ECMWF analysis wind direction. Analysis wind direction accuracy might not be sufficient for wind speeds below 5 m/s, and here the upwind/downwind separation will become less exact. Figure 2(a) and 2(b) show respectively the upwind and downwind 0°triplets. We further tagged (coloured) each triplet with the
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Wind Retrieval and ERS-1 Measurements
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FiRure 1: Solution surface in 3D measurement space. The solid line represents a constant wind speed at varying wind direction.
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A. Stoffelen and D. L. T. Anderson
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We investigated the effect of sea surface temperature (SST) on triplets in the cross sections at wind speeds below 3 rn/s. By tagging (colouring) SST values from 0 to 30 °Cin 10 °Cbins, we did not find any difference in the scatter of 0°triplets across the plots. The noise contribution from geophysical parameters not included in the transfer function may be more significant in a direction parallel to solution surface. Or in other words, changing SST or another sea surface parameter might have the same effect as changing wind speed in our transfer function formulation. Therefore, we can conclude that any 0°SST dependency should be implementable as an “effective” wind speed. Plotting the above cross sections and projection over ice showed some anisotropy of backscattering over ice (0°~ + 0°c,),and the difficulty of separating ice from wave scattering (the oo triplets are not always in different domains of 3D measurement space). In this way these sections contribute to understanding the physics of radar backscattering. 3. WIND RETRIEVAL REVISION 3.1 a~normalisation Equation (2) computes for each 00 triplet the distance to the solution surface defined by the transfer function used in a 3D 00 space. The transformation of the 3D space is defined by the term SD(0°,1).In the definition as by CREO the three axis are scaled by a constant times 0°,~, i.e. the value of the solution o~ for each beam (axis). Other normalisations have been investigated /6/ such as by measured ~ or no normalisation at all. We also considered retrieval in ln(0°)rather than 0012/. From a theoretical point of view, nomialisation should be done by the square root of the best estimate of expected variance of ~ 0°,,. However, it is shown by Stoffelen et al. /2/that the answers from such a nonnalisation do not give the expected (true) solution, due to the non-linear shape of the solution surface and the proportionality of the expected variance Ofl 00. We investigated the effect of normalisation through visualisation ofare differently measurement 0°fo~ constant.scaled Figure3D4(a) shows no spaces. Figure and 4 shows sections for which 0°~ pluswith the o°,value at the centre of gravity of normalisation, figure cross 4(b) shows a scaling of each axis the plot. The latter scaling visualises approximately the space used to compute a distance, for a normalisation of equation (2) by either SD(0°m.) or SD(0°,,).In order to be able to retrieve wind directions accurately and obtain a realistic wind direction probability density function (PDF) after retrieval, it is desirable that equal portions of the 0°triplets are thrown onto equal wind direction intervals. This is the case if the solution surface has no edged shape and is circular rather than elliptic. With these constraints, normalisation by solution or measured 0°looks unfavourable, whilst no normalisation appears favourable. For the same reasons retrieval in ln(o°)in stead of 0°is also unfavourable (not shown). By performing wind retrievals using the different normalisations we found that using no normalisation gives the least number of local minima, whilst normalisation by solution 0°results in the highest number
Wind Retrieval and ERS-1 Measurements
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of minima. For all nonnailsations we found that wind directions associated with 3~’or 4th ranked local minima have on average a probability that is less than the average probability of any wind direction. So, the presence of these solutions depends on the nonnailsation, rather than a physical probability. In our earlier work 12/ we noted that the skill for discriminating between rank 1 and rank 2 is very low. To test the accuracy of wind retrieval for different nonnalisations we computed statistics for the wind direction of rank 1 and rank 2 solutions, whichever is closest to the ECMWF analysis wind direction. Additionally we included the possibility to exclude solutions that differ by more than 60 ° from the analysis. Doing so we found that indeed the wind direction PDF obtained when using a normalisation by measured or solution 00 has a bimodal shape, with minima corresponding to the wind directions at the sharp edges of figure 4(b). The wind direction PDF most closely resembles the analysis PDF when using no normalisation. Further, the standard deviation of the departures between retrieved and analysis wind direction is smallest in this case. In figure 5 we show a synoptic wind pattern as obtained using different normalisations in wind retrieval. Figure 5(a) shows no nonnalisation, and 5(b) the current CREO wind retrieval normalisation. No ambiguity removal is used here, rather the closest of rank 1 and 2 to a 24 hour ECMWF forecast is selected. The forecast is shown in figure 5(c). Consistently, we find that no normalisation produces the superior synoptic wind pattern. The scatterometer shows more synoptic detail than the 24 hour forecast. In line with the above, normalisation could be optimised using information on the upwind/downwind amplitudes and noise characteristics of mid, and fore and aft beams, and on the shape of the transfer function in the surroundings of a measured o~triplet. However it is thought that little could be gained by doing this exercise, since no normalisation seems close to optimal. 3.2 Ambiguity removal On average CREO manages to process 95 % of its wind directions closer than 90 ° to the ECMWF analysis. From our earlier work 12/however, we showed the difficulties of CREO in building up a synoptic wind field from the solutions given at each cell. Most problems occur near fronts and lows, and also tropical cyclones. So, the 5 % that does not match seems to result from CREO in most cases. We tried to improve the procedure, by introducing slightly different spatial filters to build up the two anti-parallel fields. We found howeverthat these filters solve some problems, but create others. Hoffinan carried out
A. Stoffelen and D. L. T. Anderson
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FiRure 5: Synoptic windpattern ascending swath (ERS-1 passes inatpart top ofan from to right) on 6 november 1991 at approximately 12 GMT. The upper right latitude is 45.5 N, and longitude 157.7 E.
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an impact study assimilating CREO winds into the ECMWF meteorological model 17/. Not surprisingly, he found mixed results in the Southern Hemisphere, i.e. forecasts could be improved or degraded as a result of assimilating scatterometer data. In the Northern Hemisphere and Tropics no significant forecast impact was shown. As mentioned in the previous section, there is no physical reason to assign potential value to local minima in the MLE, when the probability of those solutions is very low. We further found that in cases where the probability of a rank 3 or 4 solution was high, we are dealing with either lower wind speeds, or with temporally variable wind directions athigher wind speeds. In both cases there is not much information in the 0°triplet concerning wind direction. These triplets can be found in figure 4(a) as lying close to the centre of gravity of the scatter plot, and can be accurately uncovered by computing, for a triplet, the average distance (probability) to the solution surface over all wind directions, and comparing this with the expected probability of the true solution. Additionally, this mean probability should be much lower than the rank 1 probability, and the rank 1 probability should itself be high. Using the above three constraints we should be able to distinguish triplets with clear wind direction information from triplets with less wind direction information content. In latter case we have to rely both on background wind direction information and scatterometer wind direction information to retrieve wind direction. The constraints should also be used for quality control, i.e. rejection of triplets.
Wind Retrieval and ERS-l Measurements
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Essential wind direction information is not lost when locally relying on the background (e.g. see Figure 5). We concluded from this that relying on a high quality meteorological background locally (for each cell) is better than trying to build up synoptic wind fields from ranked solutions, and rely only on the large scale background wind field. Given the above, we propose to use background wind direction information in the retrieval at each node, i.e. add a background wind direction term in equation (4). For purposes of data assimilation at our site this is sufficient, since for assimilation of wind speed in the analysis a direction has to be assigned. A spatial consistency filter selecting between a rank 1 and 2 solution, may still be applied to correct the background for misplacement of fronts and lows. Preliminary tests have shown that we are indeed able to exclude those cases in which the scatterometer wind direction information is insufficient. We have not as yet experimented with the inclusion of background wind direction infonnation. A difficultyhere arises in cases with relatively high wind speeds which do not lie close to the solution surface defined by our transfer function. We believe in these cases a confused sea state is present, where wave fetch is most relevant. The problem occurs in general over areas of typically 100-200 km. Since these cases will generally result in both unreliable wind direction and wind speed we have to refine our constraints in order to exclude these 0°triplets. 4. CONCLUSIONS A 3D measurement space can be defined using a~measurements from each antenna as a coordinate on one of the axis. Useful information can be retrieved from cross sections through and 2D projections of this space. We found that in general a very definite surface arises in this measurement space with only little 0°noise perpendicular to it. We were able to estimate wind direction sensitivity from the particular circular shape of this surface, and found that below incidence angles of 25 °wind direction sensitivity is very poor. At high incidence angles wind direction sensitivity is best. A shift of the swath towards higher incidence angles would therefore be beneficial. By fitting a 0°-to-windtransfer function to the solution surface we found that wind speed sensitivity is very good. We have indications that 0°saturation may be present for wind speeds above approximately 18 m/s. Visualisation of 3D measurement space appears to be a powerful tool in diagnosing problems with the fitting of a 00-to-wind transfer function in this space. It became obvious that ESA’s original transfer function had to be reformulated/l/. By collocationof ERS- 1 data with other geophysical fields, potentially a great deal can be learned about radar backscattering, using the visualisation techniques described in this paper. Normalisationof 0°in wind retrieval (Equation (2)) can also be visualised using proper scalings of the axis of 3D measurement space. In this way wind retrieval becomes a geometrical problem rather than just a statistical one. The ranking of local minima in residual beyond rank 2, when retrieving wind speed and direction is shown not to be very fruitful. Cases where ranks 3 and 4 are probable are in general cases where little directional information is present in the triplets. Geometrical considerations made us able to design constraints that only select those triplets with satisfactory wind vector solutions. 0~
The compilation of synoptic fields from the available ranked solutions in CREO often fails close to fronts, lows, and also tropical cyclones 12/. Attempts to improve CREO in those areas were not very successful. However, when using the closest of the available ranked solutions to an ECMWF forecast we found that in the above synoptic cases, the scatterometer wind field looks much better. Therefore, at locations where insufficient directional information from the scatterometer is present, we believe that using the forecast wind direction in a local retrieval is better than using forecast wind direction information only over larger scales, as CREO does. We believe that in all cases an accurate wind speed from the ERS-l scatterometer can be retrieved, unless a confused sea state is present as we observed for high wind speeds with a large temporal variability of the wind vector. This occurs typically over areas of 100-200 km. Using a variational method to retrieve a wind field over a larger area, using forecast wind and 0° measurements in the minimisation (e.g. /81) could in our opinion also improve upon CREO, but is a more
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A. Stoffelen and D. L. T. Anderson
demanding approach. At ECMWF we will eventually use 00 measurements directly in a 3D-var assimilation scheme /9/. At a NWP centre a wealth of information is available, and we have shown that an important contribution is given to calibration and validation of satellite measurements. Using ECMWF analysis winds we were able to significantly improve the 0°-to-windrelationship 12/, indicate problems in scatterometer wind retrieval algorithms, and show how to improve ERS-l scatterometer wind retrieval. We believe that scatterometry has great potential for defining more accurately the atmosphere-ocean interface. Acknowledgements We would like to thank Peter Woiceshyn, Graeme Kelly, and other ECMWF staff members for their helpful discussions and time. Also the ESA analysis and experimenters team provided a sound framework for the research to take place. Last but not least we thank ESA and ECMWF for providing the resources for carrying out the work. REFERENCES 1. A.C.M. Stoffelen, D.L.T. Anderson, ERS- 1 scatterometer calibration and validation activities at ECMWF: A. The quality and characteristics of the radar backscatter measurements. Proc. European ‘International Space Year’ Conference, Munich, Germany, 30 March - 4 April 1992. 2. A.C.M. Stoffelen, D.L.T. Anderson, and P.M. Woiceshyn, ERS-l scatterometer calibration and validation activities atECMWF: B. From radar backscauer characteristics to wind vector solutions. Proc. European ‘International Space Year’ Conference, Munich, Germany, 30 March - 4 April 1992. 3. A.E. Long, Towards a C-Band radar sea echo model for the ERS-l scatterometer. Proceedings of a conference on spectral signatures, Les Arc, France, December 1985, ESA SP-247 4. M.A. Donelan, W.J. Pierson Jr., Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry, J. Geophys. Res., 92, # CS, 4971-5029, (1987)
- Study of a method to dealias winds from ERS-l data. Vol 2 - Wind retrieval and dealiasing subroutines, Final report of ESA contract No. 6874/87/CP-I(sc), ESTEC, Noordwijk, The Netherlands 5. A. Cavanid, P. Lecomte, Vol 1
6. R. Graham, D. Anderson, A. Hollingsworth, and H. Bottger, Evaluation of ERS-l wind extraction and ambiguity removal algorithms. Meteorological and statistical evaluation., Technical report, ECMWF, Reading, UK 7. R. Hoffman, A preliminary study of the impact of C-Band scatterometer wind data on global scale numerical weather prediction, Draft report, ECMWF, Reading, UK (July 1992). 8. H. Roquet and A. Ratier, Towards direct variational assimilation of scatterometer backscatter measurements into numerical weather prediction models, IGARSS 88 Proceedings. 9. J. Pailleux, W. Heckley, D. Vasiljevic, J.-N. Thdpaut, F. Rabier, C. Cardinal!, and E. Andersson, Development of a variational assimilation system., Technical memorandum 179, ECMWF, Reading, UK (1991).