Space-borne scatterometers provide information on near-surface atmospheric flows over large water bodies by measuring the microwave energy backscattered to the satellite by centimetre-scale gravity-capillary waves generated on the ocean surface by wind stress. Even though backscatter correlates with this turbulent stress (Weissman et al., 1994; Chelton et al., 2001; Stoffelen, 2002), the scarcity of accurate turbulence measurements over the oceans provides an incentive for the transformation of observed scatterometer backscatter into more standard wind information at a height of 10 m for the generation of well-calibrated remotely sensed ocean surface wind products. However, to consider a variable more akin to the stress measured by the instrument while preserving the speed and direction observable properties of wind, the concept of an equivalent neutral wind was introduced. The definition proposed by Ross et al. (1985) and Liu and Tang (1996) is particularly consistent with scatterometry and corresponds to the wind speed calculated by using the stress and related surface roughness length consistent with the atmospheric stratification but neglecting the term representing the effect of stability in the expression of the modified log-wind profile.
Scatterometer wind retrievals are estimated through geophysical model functions (GMF) derived empirically from collocated measurements of backscatter with readily available in situ buoy and/or numerical weather prediction (NWP) model wind data (Hersbach et al., 2007). Geophysical model functions developed for Ku-band scatterometers such as the NASA scatterometer (NSCAT) launched on the Advanced Earth Observing Satellite (ADEOS) (Naderi et al., 1991) and SeaWinds onboard the QuikSCAT satellite (Hoffman and Leidner, 2005), e.g. NSCAT-1 (Wentz and Smith, 1999; Freilich and Dunbar, 1999), NSCAT-2 (Ebuchi, 2000) and QSCAT-1 (Ebuchi et al., 2002) GMF, were calibrated against equivalent neutral winds. On the other hand, the CMOD family of GMF initially developed for C-band scatterometers, e.g. AMI sensor onboard ERS-1 and ERS-2 satellites and the Advanced SCATterometer (ASCAT) onboard the MetOp-A satellite (Figa-Saldaña et al., 2002), were designed to provide retrievals of real (stability-dependent) winds (Offiler, 1994; Hersbach et al., 2007). However, the CMOD5.n GMF was developed more recently to provide equivalent neutral winds (Hersbach, 2010; Verspeek et al., 2010) and is now used to produce the operational ASCAT level 2 wind products at the Royal Netherlands Meteorological Institute (KNMI).
relatively low spatial and temporal coverage of assimilated observations;
artefacts of data thinning procedure;
artefacts of method used for resolving the inherent directional ambiguity of scatterometer wind vector solutions (Price, 1976);
use of suboptimal observation error statistics;
use of static background error covariances not allowing flow-dependent propagation of information from near-surface increments to upper-level dynamics;
characteristics of the NWP model leading to systematic errors in the surface wind field;
neglect of possible sea-state dependencies on scatterometer observations (Quilfen et al., 2004);
neglect of air density effects in the interpretation of scatterometer wind retrievals (Bourassa et al., 2010);
lack of proper consideration of the equivalent neutral calibration of scatterometer winds.
This paper focuses on the last item in this list.
A key aspect of data assimilation is the accurate calculation of innovations, i.e. differences between the assimilated observations and their model counterpart, assumed unbiased and preferably of small amplitude. Errors that may lead to biases therefore should be minimized. As pointed out earlier, a subtle difference exists in the definition of real versus equivalent neutral winds. This subtlety in the definition of scatterometer winds has been largely ignored in the calculation of the NWP model counterpart to scatterometer observations, with innovations calculated as differences between scatterometer equivalent neutral winds and the 10 m stability-dependent wind diagnostics from the model. To partly circumvent this inconsistency, a simple correction may be applied by subtracting 0.2 m s^{−1} to scatterometer wind retrievals, a value corresponding to the average difference between equivalent neutral and stability-dependent wind speeds (Portabella and Stoffelen, 2009). The aim of this correction is to eliminate a source of bias in scatterometer wind innovation calculations.
In this article, an observation operator providing a more consistent evaluation of equivalent neutral (hereafter abbreviated as EN) wind innovations is developed. The aim is to not only eliminate the bias related to the average difference between EN and real winds, but also to better represent the variability of EN ocean surface winds in the calculation of innovations for improved scatterometer ocean surface wind data assimilation. The variational data assimilation perspective on remotely sensed ocean surface winds is outlined in section 2. The new EN observation forward operator is presented in section 3. Various implementations of the corresponding tangent linear model and adjoint are developed and their impact on the calculation of analysis increments is assessed. Results from trial data assimilation experiments are presented in section 4, showing the impact of the new observation operator. Section 5 presents a summary and discussion.
2. The variational data assimilation perspective on scatterometer winds
The data assimilation process aims to blend together observations from various sources and prior information of the atmospheric state from a numerical model to produce a best linear unbiased estimate of the actual state of the atmosphere. For a given assimilation window, observations are collected and compared with the background state through a cost function J representing a normalized scalar measure of the quadratic departure of a given state to both the background state and to observations. In an incremental formulation (Courtier et al., 1994), minimization of the cost function is performed with respect to increments correcting the background state to produce an analysis corresponding to the state with minimum distances to the background and to observations, taking into account their respective error statistics. The 3D-Var cost function is thus the sum of a background term (J_{b}) and an observation term (J_{o}), which may be written as
(1)
where H is the tangent linear (TL) model of observation operators projecting analysis increments into observation space, and B and R are the background and observation error covariance matrices respectively. δx is the vector of increments representing corrections to the model background x^{b}
(2)
where x is the model state vector. Considering the subset of model state x corresponding to wind components at the lowest model level (denoted by vector u), the innovation vector d represents the departure of observations from the background u^{b}
(3)
where u° is the vector of observed scatterometer winds. The model counterpart to observations is estimated using H, the nonlinear observation operator projecting the background state into observation-space. For near-surface winds, H deals in large part with the vertical interpolation of wind vectors from the lowest model level down to the usual 10 m observation height. In this context, H is used to map perturbations in model state variables to perturbations in the 10 m wind components. The adjoint (AD) (transpose of the TL model) is used to propagate wind sensitivity information from the observation space to the model state during the minimization of J. Therefore, the effectiveness with which observations are assimilated depends in part on accurate calculations of innovations and proper representation of the sensitivities of H by the TL and AD operators.
3. Observation operator for the 10 m equivalent neutral wind
3.1. Nonlinear (forward) operator
For near-surface winds, because most NWP models have their lowest level located higher than the usual 10 m observation height, the main role of the observation operator H is to vertically interpolate model wind information through the surface layer (SL) downward to 10 m. This typically is done using the well-known logarithmic wind profile and Monin–Obukhov similarity functions as described in Geleyn (1988). Formally, the diagnosed wind vector at 10 m can be expressed as
(4)
where ψ_{m} is the stability function for momentum, z_{0m} is the momentum roughness length, L is the Obukhov length
(5)
In Eq. (5), k is the von Karman constant, g is the acceleration due to gravity, θ_{∗} is the SL temperature scale and u_{∗} is the friction velocity vector, related to the wind stress vector τ through
(6)
where ρ_{a} is the air density at the surface. The friction velocity vector can be calculated from
(7)
where z_{M} is the height of the lowest model level.
For scatterometer winds, the observation operator taking into account the EN definition of the wind vector (u_{en}) can be written as
(8)
where the stability correction to the logarithmic profile (second term within parentheses in Eq. (4)) has been neglected. It should be emphasized that scatterometer wind observations are relative to ocean surface currents (Cornillon and Park, 2001; Kelly et al., 2001; Chelton et al., 2004) and may be further modified by surface wave motion (Bourassa, 2006). These effects are neglected here, however, with Eq. (8) describing Earth-relative EN winds. Substituting Eq. (7) into Eq. (8), we obtain
(9)
Now recognizing that the wind vector at height z_{M} can be expressed as
(10)
where α is the wind direction at z_{M}, the final expression for the 10 m EN wind vector is obtained by substituting Eq. (10) into Eq. (9):
(11)
where Δα represents the rotation of the wind vector between level z_{M} and 10 m height in the stable SL (see below). The momentum roughness length over the ocean is formulated using the classic Charnock expression (Charnock, 1955)
(12)
where C_{ch} is a constant equal to 0.018.
As seen in Eq. (11), the representation of stability effects remains important in the evaluation of the 10 m EN wind. The parametrization of SL turbulent momentum transfer within the Canadian Global Environmental Multiscale (GEM) NWP model (Côté et al., 1998; Bélair et al., 2009) includes three distinct formulations for ψ_{m}, the integrated form of the flux-gradient relations φ_{m}. For the unstable SL, Delage and Girard (1992) proposed the relation
(13)
Turbulent transfer within the stable SL is represented using two distinct formulations representing the marginally and strongly stable regimes as described in Delage (1997). For the marginally stable SL, the log-linear formulation of Webb (1970) is used
(14)
while a modified version of the Louis (1979) relation is used for the more strongly stratified SL
(15)
where Ri_{B} is the bulk Richardson number estimated from the background state using the well-known finite-difference equation described in Stull (1988). The usual hypothesis of constant momentum flux in the SL is relaxed by assuming a vertical linear decrease of the friction velocity from a surface value u_{∗0} (obtained from Eq. (7)) to zero at the top of the stable layer (h_{BL})
(16)
This leads to an Ekman rotation of the wind vector between the lowest model level and the observation height, determined from
(17)
where Δα_{max} is the maximum rotation angle allowed (taken as 49°), and lat is the latitude. The value of h_{BL} is estimated following Zilitinkevich (1972)
(18)
where f is the Coriolis parameter.
The forward operator is thus composed of a highly nonlinear coupled system of equations. This has significant implications for the derivation of the tangent linear operator as will be discussed in section 3.2.
3.1.1. Stability effects on 10 m wind diagnostics
The forward operator described above has been used to estimate 10 m EN winds from GEM model short-term forecasts produced over January 2009. In the current model configuration, the height of the lowest model level (z_{M}) is typically found at about 40 m over the oceans. Differences between these estimates and the usual stability-dependent 10 m winds are shown in Figure 1 as a function of SL stability (i.e. bulk Richardson number Ri_{B}). The monthly average difference is approximately equal to +0.2 m s^{−1} as expected (see section 1), representative of near-neutral conditions most commonly found over the oceans. However, significant departures from the average are observed, particularly under stable stratification (Ri_{B} > 0) for which negative differences are obtained. Departures up to about 1 m s^{−1} may also take place under unstable conditions depending on ambient conditions. Figure 2 shows the spatial distribution of EN versus stability-dependent wind differences. Values near the +0.2 m s^{−1} average are found over large portions of the oceans, but departures from this average are observed over well-defined regions. Large positive departures characterize regions east of the North American and Asian continents associated with unstable conditions prevailing in the marine boundary layer during continental cold outflow events. On the other hand, negative differences are found over the northeastern Pacific and over a significant portion of the Southern Ocean under the influence of transient weather patterns leading to warm air flowing over cold sea surfaces (i.e. stably stratified marine SLs). These results, quantifying the influence of the flow-dependent thermodynamic conditions in the marine boundary layer on EN versus real wind differences, are consistent with the studies of Kara et al.(2008) and Hersbach (2010).
3.1.2. Stability effects on innovations
Departures between observed and model background winds estimated using two distinct configurations of the scatterometer wind forward operator are contrasted. Values obtained with the configuration currently implemented in the operational NWP system are used as reference. In this configuration, the 10 m real wind is first calculated on the model grid (Figure 3) using an iterative procedure solving simultaneously for |u_{∗}|, z_{0m} and L using Eqs (7), (5) and (12). The 10 m stability-dependent wind vectors are then calculated using Eqs (4) and (10). Results are subsequently linearly interpolated to the observation location to define the model counterpart to scatterometer winds. As background estimates are real winds, scatterometer EN observations (u) are corrected into pseudoreal winds (u) by simply applying a correction corresponding to the mean difference between real and equivalent neutral winds: u m s^{−1}. In contrast, EN retrievals are used without any transformation in the new operator and model EN winds are obtained from the background state using Eq. (11). It is also noted that the sequence with which linear horizontal and nonlinear vertical interpolations are applied is reversed (see Figure 3). This has significant implications for the calculation of increments as will be described later.
Table 1 shows global innovation statistics obtained from the two operator configurations, applied on output from the same short-term GEM forecasts (i.e. same background) produced in January 2009. All assimilated scatterometer observations (from SeaWinds and ASCAT) are considered. As expected, no change is observed in wind speed bias. Only slight increases in the meridional wind velocity bias and standard deviations of both components are obtained with the new EN operator. More importantly, the new operator leads to a 27% reduction in the zonal wind velocity bias and a 4% reduction in the standard deviation of wind speed innovations.
Table 1. Global innovation statistics obtained with the operational and new equivalent neutral configurations of the scatterometer wind observation operator applied on the same set of 128 GEM short-term forecasts produced over January 2009. Statistics are compiled over the same set of 2060958 observations for both experiments.
Parameter
Operational
Equivalent neutral
Bias
Standard deviation
Bias
Standard deviation
(m s^{−1})
(m s^{−1})
(m s^{−1})
(m s^{−1})
Speed
−0.03
1.24
−0.03
1.19
Zonal
−0.22
1.52
−0.16
1.53
Meridional
−0.06
1.61
−0.08
1.63
Beyond the global statistics, Figure 4 shows the spatial distribution of monthly averaged differences in wind speed innovations calculated with the EN versus operational forward operator configurations. This difference can be decomposed as
(19)
and represents the sum of the bias factor applied to EN observations in the operational configuration and the difference in forward operators. The average of the term in parentheses in Eq. (19) is equal to 0.2 m s^{−1} (see previous section) thus the average difference is equal to zero. Small differences in Figure 4 thus delineate areas where the new operator does not provide significant changes to the calculation of innovations over the operational configuration. The new EN operator has a significant impact on innovations over large portions of the global ocean as shown by larger differences observed over well-defined areas. These areas are characterized by more strongly unstable and stable SL conditions, consistent with results shown in Figure 2. To ascertain whether the new operator leads to an improved fit to observations, innovation statistics on wind speed as a function of SL stability (i.e. bulk Richardson number) are shown for both operator configurations in Figure 5b and c, along with the corresponding difference (Figure 5d). Positive innovations (model winds too weak) characterizing unstable SLs are reduced on average by about 30–40% when the EN operator is used, while the small negative bias (model winds too strong) under neutral and weakly stable conditions is practically eliminated when EN innovations are considered. On the other hand, the significant underestimation of model winds in more strongly stable SLs is exacerbated with the EN operator. It should be noted that wind direction innovations are largely unaffected by the EN operator (results not shown). These results suggest that taking into account the difference between equivalent neutral and real winds further highlights a significant bias in GEM's representation of momentum turbulent transfer in stable SLs. This result should, however, be interpreted with caution due to the small number of data found in that stability regime for the period considered (see Figure 5a). It should be noted, however, that the presence of stable stratification over the oceans is known to be more prominent in summer when warm continental air flows over the relatively cold oceans (Hersbach, 2010). As will be shown in section 4, the innovation differences discussed above feed into the data assimilation process, leading to appreciable changes in analysed atmospheric states.
3.2. Tangent linear and adjoint operators
Analysis increments resulting from the variational assimilation of scatterometer wind data are determined by the minimization of the cost function (Eq. (1)). This minimization is performed using an iterative descent algorithm, which requires several evaluations of the cost function and its gradient. Gradient information and its propagation back and forth in the form of perturbations between the observed variable (i.e. 10 m wind) and control variables (i.e. model state) are determined through the tangent linear (TL) and adjoint (AD) operators.
The TL is obtained by taking the derivative of the nonlinear operator (Eq. (11)) with respect to its control variables (i.e. the Jacobian). This can be done analytically or by numerically estimating the Jacobian using finite differences by applying small perturbations to the background state as input to the nonlinear operator. This perturbation method has been applied previously to radiative transfer (Chevallier and Mahfouf, 2001; Garand et al., 2001) and cloud models (Fillion and Mahfouf, 2003) for the sensitivity characterization of parametrization schemes. Rüdiger et al. (2010) have also tested this approach for the assimilation of remotely sensed observations of vegetation biomass into a land surface model. Using the perturbation approach has the distinct advantage of not having to perform the tedious task of determining the algebraic expressions of the derivatives of a series of complex nonlinear equations, such as the integrated form of the flux-gradient stability functions of Eqs (13), (14) and (15). The main disadvantages are the potentially prohibitive computational cost of estimating the Jacobian depending on the number of control variables and the possible introduction of noise into the TL due to errors inherent to the use of finite differences in estimating the derivatives of nonlinear functions.
3.2.1. Jacobian formulation and estimation
The parameters controlling the turbulent transfer of momentum within the SL are the wind shear and virtual potential temperature gradient between the lowest prognostic model level and the surface. Therefore the control vector is composed of the wind components at the lowest model level (), the height of that level (z_{m}) and the virtual potential temperature at that level () and at the sea surface (θ_{v,sfc}). The TL can be expressed in matrix form as
(20)
where the symbol δ indicates a perturbation on the associated variable. The Jacobian (matrix on the right-hand side of Eq. (20)) represents the sensitivity of the 10 m EN wind to perturbations on the model background state. The small number of control variables combined with the complexity of the functions used in the operator renders the estimation of the Jacobian using the perturbation method attractive, with the advantages arguably outweighing the disadvantages in the context of the present study. The AD operator is based on the transpose of the Jacobian matrix and is expressed as
(21)
where the symbol ∧ denotes adjoint variables representing sensitivities with respect to the associated control variables. The partial derivatives found in Eqs (20) and (21) are estimated at every observation location using the perturbation method. Small positive and negative perturbations around the background state are successively applied to each control variable and the corresponding 10 m equivalent neutral wind components are estimated with the nonlinear operator. Partial derivatives are finally estimated from the perturbed EN wind values using a centred finite difference scheme. A magnitude of 1× 10^{−3} was found appropriate for perturbations applied to all control variables through results from sensitivity experiments.
Sensitivities of the 10 m EN operator are illustrated in Figure 6 through their dependence on SL stability. Data points represent values of the Jacobian of the zonal wind with respect to the control variables. Values were obtained using the perturbation method applied to GEM model background states sampled at the location of all scatterometer wind observations assimilated over the month of January 2009. Curves representing various percentiles, estimated using data within intervals (bins) of the bulk Richardson number, are also shown to provide information on the distribution of sensitivities. It should be noted that similar results are obtained for the meridional wind component (not shown). We also point out that the derivative with respect to θ_{v,sfc} (not shown) is simply equal to the negative of the derivative with respect to . The relative importance of sensitivities is discussed from the point of view of the magnitude of perturbations calculated with the TL (Eq. (20)). Keeping in mind that typical analysis increments of near-surface wind components and virtual temperature are of the order of unity, while height increments are generally two orders of magnitude smaller, the following can be observed. The sensitivity of the 10 m EN wind with respect to the model level height is small and can be neglected (Figure6c). The sensitivity of EN wind components in unstable conditions (Ri_{B} < 0) is dominated by the dependence on the corresponding model wind component at height z_{m} (Figure 6a). Other Jacobian terms lead to perturbations that are smaller by at least an order of magnitude (Figure 6b and d). A slight decrease in the magnitude of the dominant term is observed with increasing Richardson number (e.g. weakening momentum turbulent transfer), along with an increase in the magnitude of other sensitivities. The sensitivity with respect to the orthogonal wind component becomes significant only under stable conditions (Figure 6b) due to the rotation of the wind vector across the SL considered in the nonlinear operator (section 3.1). Sensitivity to virtual temperature is generally small, except for some estimates in neutral and stably stratified SLs (Figure 6d). In particular, large values are observed in near neutral (Ri_{B} ≈ 0) and slightly stable conditions, due to the sensitive response of the parametrized turbulent transfer to changes in stability regimes between unstable and stable and between slightly stable and more stable conditions induced by slight changes in the vertical gradient of virtual potential temperature across the SL.
3.2.2. Temperature increments from near-surface wind data assimilation
As suggested by the number and nature of the control variables, the complete inverse problem of surface wind data assimilation is multivariate and ill-posed as no unique solutions strictly exist. Various combinations of wind shear and atmospheric stratification lead to the same surface stress and hence the same EN wind. This is referred to as the stability ambiguity by Hoffman and Louis (1990). Assessing the impact of considering this ambiguity, these authors concluded that, in an idealized context of perfect observations and model, neglecting the sensitivity on virtual temperature leads to small but systematic errors in surface wind analyses. However, from the more practical point of view adopted in NWP systems, realistic estimates of observation and background error statistics are needed, including correlations between control variables, to address the complete inverse problem as defined by Eqs (20) and (21). Noting that θ_{v,sfc} and sea surface temperature (T_{SST}) are related through
(22)
where r_{v,sat} is the water vapour mixing ratio corresponding to saturated conditions at T_{SST},p_{sfc} is the pressure at the surface and p_{0} is a reference pressure typically taken as 1000 hPa, the relevant statistics can be determined properly only in the context of a coupled atmosphere–ocean modelling system. With an uncoupled system in which T_{SST} is specified using a separate analysis procedure (Brasnett, 1997, 2008), the air temperature at the lowest model level becomes the sole controlling parameter in the determination of SL stratification during the analysis procedure.
To assess the impact of retaining this partial representation of the controlling factors on SL state, assimilation experiments in which a single scatterometer wind vector is assimilated were performed with various configurations of TL and AD operators. The resulting profiles of increments of important dynamical variables provide insights into the impact of the TL/AD operators on the resulting analysis. Experiments were carried out on various scatterometer observations, chosen to represent specific background SL stability regimes (see Table 2), namely weakly unstable and near-neutral conditions, most commonly found over the oceans (Figure 5a), and slightly stable conditions for which particular characteristics of the Jacobian exist as discussed in the previous subsection. The various TL/AD configurations are listed in Table 3 and consist of gradually simplifying the TL/AD by neglecting an increasing number of Jacobian terms. To carry out the experiment using the complete form of the Jacobian (COMPLETE experiment), estimates of background error statistics involving the sea-surface temperature are required. It is assumed here that the covariances between state variables at prognostic model levels and the temperature at the diagnostic 2 m level (an analysis level in the current assimilation system) approximately describe covariances with respect to sea-surface temperature. This is believed to be an appropriate approximation on the basis of the strong coupling between the surface layer air and the surface. The statistics were derived previously using the so-called NMC (National Meteorological Center) method (Parrish and Derber, 1992; Derber and Bouttier, 1999) and correspond to the statistics used in the current operational global NWP system.
Table 2. List of observations used in the single-observation assimilation experiments and associated characteristics of model background state.
Observation
(Latitude,longitude)
Observation
Background
Background
Innovations
ID
(u_{en},v_{en}) (m s^{−1})
(u_{en},v_{en}) (m s^{−1})
Ri_{B}
(m s^{−1})
84724
(−37.7,324.6)
(−4.0,−0.3)
(0.5,1.2)
−0.1387
(−4.5,−1.5)
80863
(−51.7,120.2)
(2.4,−7.7)
(8.7,−5.4)
−0.0003
(−6.3,−2.3)
76550
(35.5,181.1)
(−0.2,−5.8)
(1.3,−2.5)
+0.0166
(−1.5,−3.3)
Table 3. Configurations of the tangent linear of the scatterometer equivalent neutral wind observation operator used in the single-observation assimilation experiments.
Experiment
Tangent linear model
Description
COMPLETE
All sensitivities taken into account
noSFC
No sensitivity on sea-surface virtual potential temperature
noSTRAT
No sensitivity on surface-layer stratification
//COMPonly
Sensitivity only on wind component parallel to the component
being assimilated
Figures 7–9 show profiles of analysis increments obtained using the various TL/AD configurations. These were taken at the grid point nearest to the assimilated observation. Although observations were taken under different meteorological conditions, profiles are shown with a surface pressure set at 1000 hPa for easier comparison of results. Wind increments are relatively insensitive to the formulation of the TL/AD in the case of unstable SLs, with variations in near-surface increments of only 3% obtained whether sensitivity to the SL vertical temperature gradient, either controlled through both and θ_{v,sfc} (COMPLETE configuration) or through only (noSFC configuration), is activated or not (Figure7). However, noticeable differences in temperature increments arise in the lower troposphere. Temperature increments are produced even when sensitivities on and θ_{v,sfc} are neglected (noSTRAT and //COMPonly configurations), due to the multivariate relationships between variables defined through background error covariances (i.e. matrix B in Eq. (1)) (Buehner, 2002). Larger temperature increments are generated when including sensitivities on temperature, particularly when the SL stratification is controlled only with (noSFC configuration). Modifying the SL temperature gradient through changes in temperature at the lowest model level induces a 325% increase in the temperature increment only at that level compared with increments obtained with the noSTRAT and //COMPonly configurations (Figure 7c). A 50% increase is obtained when the COMPLETE TL/AD is used. This signal is propagated in the vertical throughout the lower troposphere from correlations specified in the background error statistics. In turn, larger geopotential height increments are observed up to the model lid (Figure 7d), consistent with the hydrostatic balance.
Similar increment responses are observed for a scatterometer wind vector assimilated in a near-neutral SL (Figure 8). A slightly enhanced sensitivity of wind increments to the TL/AD configuration is observed, however. A reduction of 0.3 m s^{−1} in the near-surface zonal wind increment and an equivalent increase in the meridional wind increment are obtained when the noSFC TL/AD configuration is used. These represent about a 10% change compared with increments obtained with the other configurations. This sensitivity is largest in the experiment corresponding to a slightly stable SL (Figure 9a and b), with smaller zonal wind increments by 13% for the COMPLETE and noSFC configurations, and by up to 33% for the meridional wind with the noSFC configuration, when compared with increments obtained with the noSTRAT and//COMPonly configurations. Also noteworthy are the differences in related temperature and geopotential height increments. Increments obtained with the TL/AD including sensitivities on the SL temperature gradient are of opposite sign and of much larger amplitudes compared with the case where the influence of stratification is not taken into account. In this particular case, the background model wind is weaker compared with the scatterometer observation. Therefore the assimilation of the observed wind vector will generate increments contributing to an acceleration of the 10 m EN wind through a combination of an increased wind shear (stronger wind speed at the lowest model level, i.e. negative increments on negative background wind components) and by increasing the magnitude of the negative vertical temperature gradient (decrease in stability) by cooling the temperature at the lowest model level (i.e. negative temperature increment).
The single-observation assimilation experiments have shown that temperature and geopotential height increments are significantly sensitive to the TL/AD formulation of the scatterometer wind observation operator. Enhanced responses to the analysed temperature and mass field are generated when SL stratification is allowed to vary through the assimilation of scatterometer wind data. This suggests that it is preferable to neglect the sensitivity on SL temperature in the TL/AD, particularly in the absence of other assimilated observations providing independent constraints on the SL stratification during the analysis process. In such cases, there is the potential to exacerbate the impact of model wind biases by projecting the related innovation signals on the analysed large-scale mass field. These biases may be due to deficiencies in boundary layer parametrizations, which are particularly suspected in stable conditions (see section 3.1.2 above). This undesired effect would particularly be important when the SL vertical temperature gradient is controlled only through the temperature at the lowest model level, as is possible in an uncoupled atmospheric model. In this context, our results justify the use of a simplified form of the TL/AD in which sensitivity to SL stratification is neglected (i.e. the noSTRAT configuration). Use of the COMPLETE TL/AD should be considered and further tested in the context of a coupled ocean–atmosphere data assimilation and forecast system.
4. Impact on NWP
4.1. Assimilation experiments
Numerical weather prediction experiments were carried out to assess the impact of the new scatterometer observation operator on global atmospheric analyses and forecasts. The Canadian operational Global Deterministic Prediction System (GDPS) is composed of the GEM model and an incremental 4D-Var data assimilation system (Gauthier et al., 2007; Laroche et al., 2007). The global configuration of the GEM model is characterized by a horizontal grid spacing of 33 km (exact value at 49°N) with 80 hybrid vertical levels (terrain-following near the surface relaxing to pressure at higher altitudes) extending from the surface to 0.1 hPa (Charron et al., 2012). Analysis increments are produced on model levels on a 1.5° horizontal grid. In contrast to the operational system, the 3D-Var First-Guess at Appropriate Time (FGAT) data assimilation system (Gauthier et al., 2007) has been used in this study. Although 4D-Var is known to provide enhanced projection of low-level increments in the vertical, comparison of results between 3D- and 4D-Var over a subset of cases (results not shown) have shown that the impact of the EN operator is well represented in 3D-Var. 3D-Var therefore provides a suitable and computationally efficient framework for the assessment of the relative impact on analyses of enhancements to the ocean surface wind observation operator.
Two 3D-Var FGAT assimilation experiments were performed providing global analyses every 6 h over the period from 0000 UTC 15 December 2008 to 0000 UTC 1 February 2009. Only results generated over January 2009 are examined to allow a 2 week adjustment period at the beginning of each experiment. A control experiment (CNTL) was performed using the currently operational configuration of the SL observation operator used for the assimilation of near-surface in situ wind observations from land surface stations, buoys and ships and remotely sensed scatterometer winds. A trial experiment (referred to as ENSW) has been performed in which the EN operator was used. The same set of observations was assimilated in both experiments, corresponding to observations that passed the background check of the operational data assimilation system.
Assimilated scatterometer data consist of wind retrievals from the SeaWinds and Advanced Scatterometer (ASCAT) sensors. Observations are obtained from the European Organization for the Exploitation of Meteorological Satellites Ocean and Sea Ice Satellite Application Facility located at KNMI. Quality controlled 100 km SeaWinds and 25 km ASCAT retrievals are used. As part of the quality control, the ambiguity of wind vector retrievals is resolved by using the most probable solution as determined by a two-dimensional variational scheme (Vogelzang et al., 2009) using prior information from the European Centre for Medium-range Weather Forecasts (ECMWF) products. Observations flagged for contamination by land, ice or precipitation are discarded, as well as retrievals with speeds lower than 4 m s^{−1}. ASCAT data are further thinned to a resolution of 100 km by choosing quality controlled observations closest to the centre of fixed geographical boxes. Such a dual-scatterometer configuration provides for significant observation coverage of the global ocean (Figure 10). Between 8000 and 9000 wind vector observations are assimilated from each sensor per analysis.
Other than scatterometer winds, assimilated observations were taken from radiosondes, dropsondes, aircraft, land stations, buoys, ships and National Oceanic and Atmospheric Administration (NOAA) wind profilers; along with atmospheric motion vectors (AMVs) from geostationary satellites and from the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Aqua and Terra polar-orbiting satellites, Global Positioning System Radio Occultation (GPS-RO) data and radiances from Geostationary Operational Environmental Satellite (GOES) imagers, the Atmospheric Infrared Sounder (AIRS), and Advanced Microwave Sounding Unit (AMSU) A and B sensors.
4.2. Impact on analyses
The impact of considering the EN character of scatterometer winds in the calculation of innovations is described from the perspective of the resulting global analyses. A comparison of the monthly averaged analyses from the CNTL and ENSW experiments confirms the presence of systematic differences, not only in the surface wind field itself, but also in other analysis variables. The EN observation operator leads to a weakening of the strong wind speeds in the unstable atmospheric boundary layer over the Gulf Stream, Labrador Sea and Kuroshio extension (Figure 11a and d). A reduction of the weaker winds over the subtropical southern oceans is also observed. In contrast, a slight acceleration takes place in regions of moderate winds in the Southern Ocean, particularly north of the Ross Sea, over the Drake Passage and over the southwestern Atlantic. A large region of strong winds over the northeastern Pacific is also characterized by increased wind speeds as a result of using the EN operator. These regions are characterized by the presence of stable SLs as described in section 3. Impacts of the operator on wind components are also apparent. Use of the EN operator leads to slight increases in the extratropical westerlies, particularly in the Northern Hemisphere, and weakened subtropical easterlies (Figure 11b and e). Monthly averaged differences in the meridional wind component exhibit a greater spatial variability, which hampers the identification of a trend. However, enhanced meridional circulation over northeastern Pacific and stronger equatorward flow in the southern portion of the intertropical convergence zone are noticeable features (Figure 11c and f).
The analysed 1000 hPa geopotential height (variable strongly linked to surface pressure) is examined to assess how changes in surface wind increments propagate onto the entire atmospheric state (Figure12). Use of the EN operator leads to a weakening of subtropical highs, notably the Azores High, along the band of high pressures extending across the Pacific between the Siberian and Pacific Highs, and for systems over the Indian Ocean and southeastern Pacific. Weakening of extratropical lows is also observed, particularly the Aleutian and Icelandic Lows and the low pressure systems along the Antarctic Circumpolar current. These changes result in a weakening of the mean meridional pressure gradient between subtropical and extratropical regions in both hemispheres. Therefore, subtle changes to the assimilation of surface observations lead to changes in key features in the analyses, which can affect global forecasts.
4.3. Impact on forecasts
Global forecasts with lead times up to 5 days (120 hours) were initialized with the 0000 UTC and 1200 UTC analyses from the CNTL and ENSW data assimilation experiments, totalling 62 sets of forecast runs from each experiment available for verification.
Statistics characterizing scatterometer innovations are examined to determine whether the EN operator brings improvements in the skill of ocean surface wind short-term forecasts (3 to 9 h lead times). In contrast to the discussion in section 3.1.2, the EN operator has an effect on the analysis as well as on the following background field and subsequent analyses through the data assimilation cycling process. Beyond the average difference, mostly reflecting the change of background winds from real to EN winds as described in section 3.1, the impact of the EN operator on the representation of ocean surface winds is assessed by examining changes in the variance of innovations. Figure 13 shows the spatial distribution of monthly standard deviations of innovations corresponding to ASCAT observations from the CNTL experiment and the corresponding differences between ENSW and CNTL experiments. Small reductions in error variance are obtained with the new EN operator over large areas corresponding to 30% of the ocean's surface. This is in comparison with larger variances observed over 13% of the global ocean. The most significant error reductions are found in the Northern Hemisphere in areas of enhanced error variance over the central Pacific and western and mid-Atlantic regions. A greater variability is found over the tropical oceans, particularly along the South Pacific convergence zone and tropical Indian Ocean south of the Equator. Larger increases in error variance are found over these areas, interspersed with reductions of similar magnitudes. The combination of these competing features leads to a small overall reduction of 0.03 m s^{−1} in global wind speed error standard deviation. It should be pointed out that little impact is obtained on wind direction (not shown). It is also noted that similar impact from the change in the observation operator is obtained with respect to SeaWinds observations (not shown).
The impact of the EN operator on longer-range forecasting is examined by assessing forecast accuracy against observations from the global radiosonde network. Global error statistics for geopotential heights are presented in Figure 14 as a function of forecast horizon. No significant differences are seen between the two sets of forecasts in terms of biases and standard deviation of forecast errors for the pressure levels shown. A very slight reduction in the standard deviations of errors can, however, be seen at 850 hPa and 500 hPa for the 120 h forecasts. Figure 15 shows the corresponding vertical profiles of error statistics for the main dynamical variables for that lead time. Also shown are the confidence intervals for both bias and standard deviation, estimated using the Student and Fisher significance tests respectively. The largest difference in forecast error for wind occurs in the zonal component near the upper tropospheric jet (i.e. maximum error at 300 hPa) and corresponds to a small decrease in error standard deviation when the new operator is used to generate the analyses. The difference is, however, not statistically significant at the 90% confidence level. Statistically significant differences are obtained for geopotential height forecasts, however, for which the use of the new operator leads to small reductions in error standard deviations below 300 hPa.
5. Summary and Discussion
A novel forward observation operator has been developed to improve the consistency between the 10 m wind diagnosed from gridded model output and the remotely sensed equivalent neutral (EN) ocean surface wind observations for the purpose of enhancing the assimilation of scatterometer wind data. This consistency ensures more accurate calculations of innovations, a key aspect in data assimilation. The corresponding tangent linear and adjoint (TL/AD) operators were developed for the direct calculation of analysis increments at the lowest prognostic model level based on SL turbulent transfer functions, rather than simply using the adjoint of a horizontal interpolation operator combined with background error statistics as in the Canadian operational GDPS system. A simplified configuration of the TL/AD was derived, adapted to the limitations associated with marine surface layer data assimilation in the context of a stand-alone atmospheric NWP system.
Results from 3D-Var FGAT data assimilation experiments indicate an improved correspondence between background and scatterometer winds resulting from the introduction of the EN operator. Similar results were found by Hersbach (2010) with the ECMWF model. The new EN operator leads to significant changes to ocean surface wind innovations, particularly in some regions where local differences of several tenths of metres per second are obtained, which then propagate into the resulting analyses. The impact is observed not only in the analysed ocean surface winds, but other key variables are affected, including notably the geopotential heights characterizing large-scale weather systems. An evaluation of forecast results has shown that differences in analyses lead to a relatively modest but generally positive impact on forecast skill. Mean forecast errors are mostly unaffected by the use of the EN operator, however, small but significant reductions in the global forecast error variance are obtained. In particular, small but widespread reductions in error variances characterizing short-term forecasts of ocean surface winds and medium-range forecasts of geopotential heights in the extratropical troposphere may be ascribed to the new EN operator.
The relatively subtle contributions to forecast skill can be attributed partially to the relatively modest volume of assimilated scatterometer observations compared with the large number of other observations that largely constrain the analyses. Also, the impact of bringing more physics into the TL/AD operators is limited by uncertainties in the underlying parametrizations of surface layer turbulent transfer and their linearized counterparts. In spite of their relative complexities, such parametrizations remain simplified representations of complex multiscale processes, which may limit our ability to represent the complete spectrum of physical sensitivities required for comprehensive assimilation of near-surface observations. Another possible limiting factor is the use of static background error statistics, in which the flow-dependency of errors, such as the contrasting vertical correlations characterizing unstable and stable boundary layers (Hacker and Snyder, 2005), is not taken fully into account. Providing further perspective on the results, it should be pointed out that a single issue only among several in scatterometer data assimilation has been addressed here. As listed in the introduction and also discussed in Hersbach (2010), other issues may limit the impact of scatterometer wind data assimilation. Neglecting the fact that remotely sensed winds are relative to the underlying ocean surface currents as well as neglecting possible air density and sea state effects in the interpretation of scatterometer winds may lead to errors of the same order as those related to differences between EN and stability-dependent winds.
Despite such limitations, this study has shown that the use of equivalent neutral (EN) rather than stability-dependent (real) background winds, combined with the use of a more complex determination of SL increments based on linearized parametrizations of momentum turbulent transfer, brings a modest but beneficial impact to global atmospheric analyses and forecasts generated with the Canadian GDPS. This suggests that properly taking into account the differences between EN and real winds in the evaluation of the model counterpart to scatterometer wind retrievals should not be overlooked in the assimilation of scatterometer data. This is in apparent contradiction with the study of Portabella and Stoffelen (2009), who found that scatterometer retrievals are as close to real as to EN winds due to uncertainties in SL parametrizations and their inputs. As pointed out by Hersbach (2010), differences in findings may be attributed to a wider sampling of EN versus real wind differences in our global model data compared with a dataset limited to buoy locations as in Portabella and Stoffelen (2009). More importantly, the effect of considering EN versus real winds has been tracked through the entire NWP process, in which subtle differences in surface wind innovations are allowed to influence the analysed large-scale atmospheric state through a dynamically consistent multivariate propagation of innovation information. Therefore, subtle but fundamental enhancements to ocean surface wind data assimilation can have beneficial impacts on a global atmospheric data assimilation and prediction system.
Acknowledgement
This research was funded by the Canadian Search and Rescue New Initiatives Fund (SAR-NIF). R. Tardif benefited from a NSERC (Natural Sciences and Engineering Research Council of Canada) Visiting Scientist fellowship. The authors would like to thank Mark Buehner for providing insights on forecast error statistics and insightful comments contributing to the significant improvement of the manuscript, as well as Judy St-James and Mateusz Reszka of the Meteorological Service of Canada for their contributions to research and development efforts performed in the context of this project and their valuable comments on the manuscript.