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Validation of Two-Dimensional Variational Ambiguity Removal on SeaWinds Scatterometer Data JUR VOGELZANG, AD STOFFELEN, ANTON VERHOEF, AND JOHN DE VRIES Royal Netherlands Meteorological Institute, De Bilt, Netherlands
HANS BONEKAMP European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT), Darmstadt, Germany (Manuscript received 23 September 2008, in final form 17 December 2008) ABSTRACT A two-dimensional variational ambiguity removal technique (2DVAR) is presented. It first makes an analysis based on the ambiguous scatterometer wind vector solutions and a model forecast, and next selects the ambiguity closest to the analysis as solution. 2DVAR is applied on SeaWinds scatterometer data and its merits for nowcasting applications are shown in a general statistical comparison with model forecasts and buoy observations, and in a number of case studies. The sensitivity of 2DVAR to changes in the parameters of its underlying error model is studied. It is shown that observational noise in the nadir swath of SeaWinds is effectively suppressed by application of 2DVAR in combination with the multisolution scheme (MSS). MSS retains the local wind vector probability density function after inversion, rather than only a limited number of ambiguous solutions. As a consequence, the influence of the background increases, but this can be mitigated by switching off variational quality control. A case study on an extratropical cyclone of hurricane force intensity observed with SeaWinds at 25-km resolution shows that reliable wind estimates can be obtained for wind speeds up to 40 m s21 and more. At 25 km, the results of 2DVAR with MSS compare better with buoy measurements than with the ECMWF model. At 100-km resolution this is reversed, proving that 2DVAR retrieves small-scale features absent in the ECMWF model.
1. Introduction Wind scatterometry is a widely used technique for measuring global ocean surface winds from space. Current operational applications include assimilation into global models for numerical weather prediction like that of the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach 2007) and detection of tropical and extratropical hurricane force cyclones for marine nowcasting (Sienkiewicz et al. 2007). Table 1 gives an overview of present operational scatterometers. Scatterometers measure the radar cross section of the ocean surface. A geophysical model function (GMF) gives the radar cross section as a function of the wind vector at 10-m anemometer height, incidence angle,
Corresponding author address: Jur Vogelzang, Royal Netherlands Meteorological Institute, Wilhelminalaan 10, 3732 GK De Bilt, Netherlands. E-mail:
[email protected] DOI: 10.1175/2008JTECHA1232.1 Ó 2009 American Meteorological Society
azimuth angle, radar frequency, and polarization (Wentz and Smith 1999; Hersbach et al. 2007). Numerical inversion of the GMF yields the scatterometer wind measurement. Because of the nature of radar backscatter from the ocean surface, this procedure generally yields more than one solution. These multiple solutions are referred to as ambiguities. If the scatterometer observations are to be assimilated in a numerical weather prediction (NWP) model, the ambiguities and their a priori probabilities can be fed into the variational data assimilation scheme of that model to be combined with other observations (Stoffelen and Anderson 1997). If, on the other hand, the scatterometer observations are intended as a stand-alone information source for nowcasting, it is necessary to select the solution that is most likely the correct one. This is done in the ambiguity removal (AR) step. A number of ambiguity removal methods have been proposed. These methods can be divided into three groups: the naı¨ve methods, the spatial filters, and the variational methods. Naı¨ve methods are the first-rank
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TABLE 1. Operational scatterometers (May 2008). HH and VV stand for horizontally and vertically polarized emitted and received microwave radiation, respectively. Name SCAT
SeaWinds ASCAT
Satellite European Remote Sensing Satellite-2 Quick Scatterometer MetOp-A
Operator
Launch
Radar band and polarization
Incidence angle (8)
Type
European Space Agency
1995
C-VV
34–64 (fore) 25–53 (mid) 34–64 (aft)
Single trio of fanbeams
NOAA
1998
Ku-HH-VV
EUMETSAT
2007
C-VV
45 (HH) 54 (VV) 34–64 (fore) 25–53 (mid) 34–64 (aft)
Rotating pencil beam Double trio of fanbeams
method that selects the solution with the highest a priori probability and the closest-to-background method that selects the solution closest to a model prediction (background wind field). More sophisticated AR schemes are based on spatial filtering (see, e.g., Cavanie´ and Offiler 1986; Graham et al. 1989; Cavanie´ and Lecomte 1987; Stoffelen and Anderson 1997; Stiles et al. 2002). The ambiguity removal problem can also be solved in two steps following a variational approach. The first step requires availability of a model prediction of the wind field (background). An analysis wind field is constructed from the observations and the background by minimizing a cost function, which may contain constraints on smoothness, statistical consistency, physical consistency, etc. In the second step, the solution closest to the analysis is selected (so such methods may as well be referred to as closest to analysis). The Variational Ambiguity Removal for the Scatterometer Online Processing (VARscat) algorithm was developed for processing scatterometer measurements (Roquet and Ratier 1988; Leru 1999) and to improve the operational scheme used at the Institute Francxais de Recherche pour l’Exploitation de la Mer (IFREMER) (Quilfen and Cavanie´ 1991). It is a variational method minimizing a heuristic cost function. Another variational method is the successive corrections ambiguity removal (SCAR) developed at the Norwegian Meteorological Institute (DNMI). Hoffman et al. (2003) present a twodimensional variational method with a cost function consisting of seven terms for filtering and dynamical consistency. It is also possible to input measured radar cross sections, so inversion may be included in this method. It compares well to a median filter ambiguity removal technique when applied to data from the National Aeronautics and Space Administration (NASA) Scatterometer (NSCAT), as shown by Henderson et al. (2003). In this paper, we present a two-dimensional variational ambiguity removal technique (2DVAR) developed at the Royal Netherlands Meteorological Institute (KNMI) from the mid-1990s onward. 2DVAR is al-
ready used in present operational wind products disseminated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) through the Ocean and Sea Ice Satellite Application Facility (OSI SAF; see http://www.knmi.nl/scatterometer/ osisaf). It provides a simplified framework to test improvements to more complete three- and fourdimensional variational data assimilations (3D- or 4DVAR) of ambiguous scatterometer data. 2DVAR may further be used to process winds from the forthcoming Indian and Chinese scatterometers (e.g., to aid in marine and coastal warnings). Portabella and Stoffelen (2004) have shown that the distance between a scatterometer observation and a corresponding ambiguous solution on the GMF can be related to an a priori probability for that particular ambiguity being the correct solution. 2DVAR takes these a priori probabilities as well as the known error characteristics of observations and background into account. Therefore it leads to wind fields that are not only spatially consistent and meteorologically balanced, but also statistically consistent: an ambiguity with high a priori probability is more likely to be selected than one with low probability. The main differences of 2DVAR with respect to other similar methods are that d
d
d
d
the cost function contains two terms: an observational and a background term; minimalization is performed in spectral space, thus optimizing all spatial scales simultaneously; the problem is preconditioned, so inversion of the background error correlation matrix is trivial; the a priori probabilities of the ambiguities are properly accounted for in the observation term of the cost function.
The observation geometry of SeaWinds changes along the swath. In the nadir part, this leads to broad minima when inverting the GMF (see, e.g., Fig. 1 from Hoffmann et al. 2003). The minima are no longer good representations of the ambiguities, resulting in considerable
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noise in the final wind solution. The multisolution scheme (MSS) retains the local wind vector probability density function after inversion, rather than only a limited number of ambiguous solutions at the local minima (Portabella 2002). This yields a better representation of the ambiguities, and 2DVAR in combination with the MSS effectively reduces the noise in the SeaWinds measurements. The noise level is estimated quantitatively for each wind vector cell (WVC) by extrapolating the autocorrelation function. Without MSS the background has little effect, but with MSS it gets more weight. It will be shown here that this can best be mitigated by switching off variational quality control. Good results are obtained for a hurricane force cyclone in the northern Pacific with wind speeds over 40 m s21. The scatterometer measurements at 25-km resolution compare better to buoy observations than those at 100 km, while this is reversed for comparison with the ECMWF prediction. This proves that 2DVAR retains small-scale information from SeaWinds measurements that is present in buoy observations but absent in the ECMWF model. The aim of the paper is twofold: presentation of the 2DVAR method and investigation of its behavior and sensitivity to changes in the underlying error model. The 2DVAR method is described in section 2, but more details can be found in Vogelzang (2007). Section 3 describes two tests for the correctness of the current 2DVAR implementation: the single observation test and the so-called edge analysis. Section 4 contains the statistical analysis of a dataset consisting of one month of SeaWinds data. Section 5 contains two case studies about the effect of the parameters in the 2DVAR error model. The paper ends with the conclusions in section 6.
2. 2DVAR a. Formulation of the problem The basic idea behind 2DVAR is first to combine the scatterometer observations and a model prediction (background) in a weighted field (analysis), and then to select that local ambiguous solution that lies closest to the analysis. Such a procedure, basically following the approach of Daley (1991), requires knowledge on the error characteristics of observations (in terms of error variances) and background (in terms of full error covariances). The observation error has been treated by Stoffelen (1998). Moreover, Portabella and Stoffelen (2004) show how local scatterometer wind vector ambiguities can be assigned an a priori probability based on their distance to the GMF (inversion residual). The
error characteristics of the background are known and monitored on a routine basis at centers for numerical weather prediction (NWP; see http://www.nwpsaf.org). 2DVAR operates on a so-called batch grid that encompasses a set of scatterometer measurements. The batch grid has its x axis perpendicular to the satellitemoving direction and its y axis parallel to it. The wind vector components perpendicular and parallel to the satellite direction are denoted by t and l, respectively. The local rotation angle of the 2DVAR batch grid can be found with sufficient precision from the known positions of the WVCs (Vogelzang 2006b). Suppose that inversion and quality control resulted in a set of possible scatterometer wind solutions (ambiguities) at all WVC grid points stored in a state vector vko with ambiguity index k. Suppose also that the background information is contained in a state vector xb. The analysis state vector x minimizes the cost function J(vk , x) 5 J o (vk , x) 1 J b (x),
(1)
with Jo as the observational term and Jb as the background term. For each scatterometer observation the background field is assumed to be known at the same position and time, if necessary from interpolation. Note that the situation here is opposite to that of assimilating data into a numerical weather model: here the abundant observations have the largest weight and define the grid on which the analysis is made. To increase the computational efficiency of 2DVAR, analysis increments dx are used rather than the state vector x itself (incremental formulation): dx 5 x xb ,
dvk 5 vko xb .
(2)
b. Definition of the cost function The observation cost function reads (Stoffelen and Anderson 1997) 9l 11/l 0 Mij 8
