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  • View in gallery
    Fig. 1.

    Zonal mean climatological (1979–93) wind stress curl and wind divergence based on FSU and (height adjusted) ECMWF ERA and NCEP–NCAR reanalysis pseudostress products: (a) wind divergence for the Pacific Ocean region (120°E–70°W); (b) wind stress curl for the Pacific Ocean region (120°E–70°W). The wind stress was calculated based on a constant bulk formula drag coefficient of 1.2 × 10−3.

  • View in gallery
    Fig. 2.

    Zonal mean climatological (1979–93) pseudostress components for FSU and (height adjusted) ECMWF ERA and NCEP–NCAR reanalysis products: (a) north–south component for the Pacific Ocean region (120°E–70°W); (b) east–west component for the Pacific Ocean region (120°E–70°W).

  • View in gallery
    Fig. 3.

    Spatial distribution of a priori chosen weights in the functional for the FSU constraint, αx,y (top), and the NCEP–NCAR constraint, βx,y (bottom). Contour intervals are 2 for the FSU weight and 0.2 for the NCEP–NCAR weight. Note FSU (NCEP–NCAR) weight outside these contours is 0.0 (1.0), and inside the contours is 10.0 (0.0).

  • View in gallery
    Fig. 4.

    Aug 1991 pseudostress magnitude response function for the 135°W long band as a function of the curl weight. The curl weight is varied from 0.0 to 12.0 in the functional, keeping all other weights constant at 1.0. The magnitude at each weight is subtracted from the magnitude for a weight of 0.0 to determine the response. Positive values indicate increasing pseudostress magnitude with increasing curl weight. The contour interval is 0.1 m2 s−2 (dashed contours are negative).

  • View in gallery
    Fig. 5.

    Combined solution pseudostress with vectors for Aug 1991. The contours indicate magnitude; interval is 10 m2 s−2. Note there are vectors over land because the NCEP–NCAR analysis includes the entire globe.

  • View in gallery
    Fig. 6.

    The first spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 22.20% of the variance. Contour values are unitless, with an interval of 0.2.

  • View in gallery
    Fig. 7.

    The amplitude (top) and rotation angle (bottom) for the first eigenvector, and JMA SST index (dash–dot). Amplitudes greater than 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

  • View in gallery
    Fig. 8.

    The first spatial function from the CEOF analysis using NCEP–NCAR data only (no combination of FSU and NCEP–NCAR) after having applied a 90° counterclockwise rotation angle. This field represents 23.0% of the variance. Contour values are unitless, with an interval of 0.2. The associated time series is very similar to that for the FSU–NCEP–NCAR analysis, i.e., Fig. 7.

  • View in gallery
    Fig. 9.

    The second spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 11.58% of the variance. Contour values are unitless, with an interval of 0.2.

  • View in gallery
    Fig. 10.

    The amplitude (top) and rotation angle (bottom) for the second eigenvector, and JMA SST index (dash–dot). Amplitudes greater 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

  • View in gallery
    Fig. 11.

    The third spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 9.61% of the variance. Contour values are unitless, with an interval of 0.2.

  • View in gallery
    Fig. 12.

    The amplitude (top) and rotation angle (bottom) for the third eigenvector, and JMA SST index (dash–dot). Amplitudes greater than 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

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Interannual Variability of Synthesized FSU and NCEP-NCAR Reanalysis Pseudostress Products over the Pacific Ocean

William M. PutmanCenter for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

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David M. LeglerCenter for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

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James J. O’BrienCenter for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

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Abstract

A technique is applied to seamlessly blend height-adjusted Florida State University (FSU) surface wind pseudostress with National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis-based pseudostress over the Pacific Ocean. The FSU pseudostress is shown to be of higher quality in the equatorial Pacific and thus dominates the analysis in that region, while the NCEP–NCAR reanalysis-based pseudostress is used outside the equatorial region. The blending technique is based on a direct minimization approach. The functional to minimize consists of five constraints; each constraint is given a weight that determines its influence on the solution. The first two constraints are misfits for the FSU and NCEP–NCAR reanalysis datasets. A spatially dependent weighting that highlights the regional strengths of each dataset is designed for these misfit constraints. Climatological structure information is used as a weak smoothing constraint on the solution through Laplacian and kinematic (divergence and curl) constraints. The weights for the smoothing constraints are selected using a sensitivity analysis and evaluation of solution fields. The resulting 37 yr of monthly pseudostress fields are suitable for use in a variety of modeling and climate variability studies.

The monthly mean analyses are produced for 1961 through 1997, over the domain 40°S–40°N, 125°E–70°W. NCEP–NCAR reanalysis data, from 40° to 60°N, are added to the minimization solution fields, and the monthly mean climatologies, based on the solution fields, are removed from the combined fields. The resulting pseudostress anomalies are filtered with an 18-month low-pass filter to focus on interannual and ENSO timescales, and a complex empirical orthogonal function (CEOF) analysis is performed on the filtered anomalies. The CEOF analysis reveals tropical and extratropical linkages, for example, the presence of a strengthening of the Aleutian low in the North Pacific, coincident with the anomalous westerlies along the equator associated with El Niño events. The analysis also reveals a weakening of the Aleutian low during the winter–spring preceding the El Niño events of 1973 and 1983, and during the peak period of El Viejo, the cold phase of ENSO. A change in the nature of the tropical and extratropical linkages is observed from the warm events of the 1960s to those of the 1980s. These linkages are not found using NCEP–NCAR reanalysis data alone.

* Current affiliation: Computational Climate Dynamics Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Corresponding author address: Dr. David M. Legler, USCLIVAR Office, 400 Virginia Ave. SW, Suite 750, Washington, DC 20024.

Email: legler@usclivar.org

Abstract

A technique is applied to seamlessly blend height-adjusted Florida State University (FSU) surface wind pseudostress with National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis-based pseudostress over the Pacific Ocean. The FSU pseudostress is shown to be of higher quality in the equatorial Pacific and thus dominates the analysis in that region, while the NCEP–NCAR reanalysis-based pseudostress is used outside the equatorial region. The blending technique is based on a direct minimization approach. The functional to minimize consists of five constraints; each constraint is given a weight that determines its influence on the solution. The first two constraints are misfits for the FSU and NCEP–NCAR reanalysis datasets. A spatially dependent weighting that highlights the regional strengths of each dataset is designed for these misfit constraints. Climatological structure information is used as a weak smoothing constraint on the solution through Laplacian and kinematic (divergence and curl) constraints. The weights for the smoothing constraints are selected using a sensitivity analysis and evaluation of solution fields. The resulting 37 yr of monthly pseudostress fields are suitable for use in a variety of modeling and climate variability studies.

The monthly mean analyses are produced for 1961 through 1997, over the domain 40°S–40°N, 125°E–70°W. NCEP–NCAR reanalysis data, from 40° to 60°N, are added to the minimization solution fields, and the monthly mean climatologies, based on the solution fields, are removed from the combined fields. The resulting pseudostress anomalies are filtered with an 18-month low-pass filter to focus on interannual and ENSO timescales, and a complex empirical orthogonal function (CEOF) analysis is performed on the filtered anomalies. The CEOF analysis reveals tropical and extratropical linkages, for example, the presence of a strengthening of the Aleutian low in the North Pacific, coincident with the anomalous westerlies along the equator associated with El Niño events. The analysis also reveals a weakening of the Aleutian low during the winter–spring preceding the El Niño events of 1973 and 1983, and during the peak period of El Viejo, the cold phase of ENSO. A change in the nature of the tropical and extratropical linkages is observed from the warm events of the 1960s to those of the 1980s. These linkages are not found using NCEP–NCAR reanalysis data alone.

* Current affiliation: Computational Climate Dynamics Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Corresponding author address: Dr. David M. Legler, USCLIVAR Office, 400 Virginia Ave. SW, Suite 750, Washington, DC 20024.

Email: legler@usclivar.org

1. Introduction

Accurate surface wind stress fields over the Pacific Ocean are vital in ocean modeling for studies of seasonal and interannual variability of the ocean–atmosphere system. The accuracy of these products over the tropical Pacific has been the subject of many studies. One of the most popular datasets is the Florida State University (FSU) monthly mean tropical Pacific pseudostress (defined as the magnitude of the wind times its component;units m2 s2) analyses. Modeling experiments, forced with the FSU pseudostress product, have produced high coherence with observed dynamic height in the western and central tropical Pacific (McPhaden et al. 1988). The FSU product also performs well in studies of model forced ocean circulations compared to observations (Landsteiner et al. 1990).

The National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) produced a global reanalysis of atmospheric fields, including surface winds, from 1958 to the present (Kalnay et al 1996). This gridded product should have numerous advantages over the FSU analysis such as higher spatial and temporal resolution, better analysis approach, etc. However, as outlined in later sections, the NCEP–NCAR reanalysis wind fields are clearly deficient over the tropical Pacific region.

For climate variability analyses, there are advantages to developing an improved, combination pseudostress product, that is, FSU in the tropical Pacific region and NCEP–NCAR reanalysis values elsewhere. This study describes the methodology in developing such a product. Using the resulting 37-yr dataset, we also explore the relationship between tropical and extratropical Pacific regions on interannual time periods. Other reanalysis products do not extend far enough in time (e.g., that of the European Centre for Medium-Range Weather Forecasts is only from 1979 to 1993) to facilitate a similar analysis.

The simplest approach to combining these two datasets would be to insert the FSU products into the reanalysis product and smooth in the region of the border between the two products. This approach is limited in two ways. First, it does not consider the difference in the reference height of the two products (∼20 m for FSU and 10 m for NCEP–NCAR). Significant wind shear can exist between 10 and 20 m above the ocean (da Silva et al. 1994). This shear can have seasonal and interannual variations that must be accounted for. The simplest approach could also lead to generation of artificial signals in the derivative (e.g., curl, divergence) fields of the combined fields along the blending border. Our approach explicitly addresses the limitation of a piecewise combined NCEP–NCAR–FSU product.

The technique we use, direct minimization, is based on a variational approach. In this technique, one minimizes a nonlinear combination of constraints operating on observations, background information, and other dynamical or physical expectations (Laplacian, curl, divergence, etc.). This approach has been utilized previously for gridding irregularly spaced observations into smoothed analyses (Hoffman 1984). Likewise, a direct minimization approach has been applied to produce monthly pseudostress vector fields from in situ surface marine observations and climatological information over the Indian Ocean (Legler et al. 1989). The direct minimization approach has also been employed to blend two fields (Ramamurthy and Navon 1992), as it can maintain realistic physical properties in the kinematic (derivative) fields of the solution. This study applies a similar direct minimization approach in combining pseudostress analyses from the FSU and the NCEP–NCAR reanalysis, over the Pacific Ocean from 1961 through 1997. Alternatively, one could use our approach to combine anomaly fields (rather than full fields). As some (Thiébaux 1997) have shown, objective analysis of anomaly fields can be more skillful (relies on better knowledge of the statistical characteristics of the anomalies). We focus on the full fields to allow a broader use of the resulting fields.

The methodology will address important issues previously mentioned regarding the two combined products. The FSU products will be first adjusted to a 10-m reference height. Through the minimization of a strategically designed functional, we combine the positive aspects of the FSU and NCEP–NCAR reanalysis datasets while maintaining realistic physical characteristics in the derivative fields such as divergence and curl. This is accomplished with spatially dependent weighting functions, determined a priori, based on the regional characteristics of the respective products. Determining the appropriate weights for the other constraints (i.e., the kinematic and smoothing constraints) of the functional is much more challenging. Exhaustive sensitivity analysis provides measures of sensitivity of the resulting field to the weights (Meyers et al. 1994), thereby guiding the subjective decision.

In summary, the FSU and NCEP–NCAR reanalysis pseudostress fields are combined using a direct minimization approach. This resulting 37-yr monthly mean pseudostress product reflects the desired presence of the FSU tropical products within the combined FSU–NCEP–NCAR product, minimizing artificial noise in the curl and divergence fields.

This product has direct applications to improving research of El Niño–Southern Oscillation (ENSO). The ability to examine interactions between tropical and extratropical winds over the Pacific Ocean is greatly improved by the existence of this combined product. We explore this new dataset using a complex empirical orthogonal function (CEOF) analysis. The CEOF analysis reveals the interannual variability between tropical and extratropical systems, particularly on timescales associated with ENSO.

2. Data

The FSU, NCEP–NCAR reanalysis, and University of Wisconsin—Milwaukee Comprehensive Ocean–Atmosphere Data Set (UWM COADS) climatology pseudostress fields are required for the direct minimization approach. The direct minimization process is designed to accentuate the strengths of each dataset. For this reason, emphasis will be placed on the regional strengths and weaknesses of each dataset.

a. FSU tropical Pacific pseudostress

The FSU dataset (Stricherz et al. 1997) is a set of monthly mean pseudostress vectors resulting from a subjective analysis of monthly ship observations over the tropical Pacific, 30°N–30°S, 120°E–70°W. These monthly fields are available from 1961 to the present. The process utilizes an average of 25 000 wind observations each month. These individual wind observations are converted to pseudostress, binned into 2° lat by 10° long rectangles, and subjectively analyzed and digitized onto a 2° by 2° lat–long grid. The subjective analysis includes subjective weighting according to the number of observations and also considers climatological information in data void regions. Data coverage, defined as the number of available observations, is good for the Northern Hemisphere. However, areas of the Southern Hemisphere and equatorial regions near the date line suffer from poor data coverage for a large portion of the period. The region off the coast of South America from about 12° to 30°S and extending to 120°W is a particularly data-sparse area.

Other studies have examined the success of the FSU product in forcing ocean models to resemble observations of sea level and dynamic height (McPhaden et al. 1988), as well as comparisons to other surface wind products (Reynolds et al. 1989; Landsteiner et al. 1990). Dynamic evaluation of the winds (Zebiak 1990) indicate that the quality of the product in the data-sparse regions, particularly in the southeast Pacific off the coast of South America, is less than the quality of the Northern Hemisphere. The approach we use minimizes the role of the FSU products in these regions of poor data availability and hence places more weight on the NCEP–NCAR reanalysis.

The in situ observations, on which the FSU analyses are based, are recorded over a wide range of heights. The normal mean height is ∼20 m. Under stable conditions at low wind speeds significant wind shear can exist between 10 and 20 m above the ocean surface (da Silva et al. 1994). Winds measured at 10 m could be as little as 20%–40% of a measurement taken at a height of 20 m. The shear between 10 and 20 m has seasonal as well as interannual variations. These variations are accounted for by adjusting the monthly mean FSU pseudostress fields (∼20 m) to a reference height of 10 m. For convenience, the serially complete monthly mean FSU pseudostress analyses were first bilinearly interpolated to the NCEP–NCAR Gaussian grid prior to the height adjustment. Then, using a boundary layer model (Smith 1988) and fields of atmospheric moisture and temperature from the NCEP–NCAR reanalysis, height adjustment coefficients for each grid point for each month of the study period were calculated and applied to the FSU analyses. The mean reduction for the 37-yr period is ∼7% (standard deviation about this mean reduction is 1.2%).

b. NCEP–NCAR reanalysis

The NCEP–NCAR Reanalysis Project is a 40-yr global assimilation of land surface, ship, buoy, and other data and resulted in fields of atmospheric data for the period 1958–present. Specifics of the NCEP–NCAR reanalysis scheme can be found in Kalnay et al. (1996).

The 10-m u and υ wind components from the surface Gaussian grid NCEP–NCAR reanalysis dataset, available every 6 h, are converted to pseudostress and averaged to create monthly mean NCEP–NCAR reanalysis pseudostress fields from 1961 to 1997. NCEP–NCAR classifies the u and υ wind components as class A variables, that is, those greatly influenced by observational data as opposed to model derived quantities. Pseudostress values from the NCEP–NCAR reanalysis are extracted for the region 40°S–40°N, 125°E–70°W.

In comparing the NCEP–NCAR reanalysis to height-adjusted FSU products as well as to European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA) for the tropical Pacific, it is clearly evident the NCEP–NCAR fields are markedly different from both FSU and ERA (Legler 1999, manuscript submitted to J. Phys. Oceanogr.), thus questioning their validity in this region. For example, the divergence fields illuminate a well-defined intertropical convergence zone in the FSU and ERA products, but it is practically nonexistent in the NCEP–NCAR reanalysis (Fig. 1). Additionally, climatologically, the NCEP–NCAR winds are weaker along the equator, but show unusually strong southerlies in the east (Fig. 2). Anomalous NCEP–NCAR winds fail to have strength and duration of anomalous wind events associated with ENSO events that are clearly depicted in the FSU and ERA products. Thus the equatorial Pacific (∼10°N–10°S) is a suspect region for the NCEP–NCAR reanalysis wind speed and direction. Thus there is sufficient motivation to combine the FSU and NCEP–NCAR reanalysis products.

c. UWM COADS climatology

A climatological pseudostress product with suitable coverage for the analysis region is required for the kinematic and smoothing constraints. COADS provides monthly mean fields of surface marine climate data for the years 1945–89, including u and υ wind components. Biases in wind measurements from the use of an old Beaufort equivalent scale for estimating wind speeds based on sea state and from variations in anemometer use are inherent. The Department of Geosciences at UWM collaborated with the National Oceanographic Data Center to correct the biases in visual observations by determining a new Beaufort equivalent scale. This collaboration lead to the UWM COADS monthly mean summaries (da Silva et al. 1994), which are considered to be an improved COADS.

The UWM COADS fields are serially complete monthly mean u and υ wind components on a 1° by 1° grid (they used a successive correction technique). We have extracted these fields for the Pacific region (40°S–40°N, 125°E–70°W). These u and υ wind components are converted to monthly mean pseudostress and then bilinearly interpolated onto the NCEP–NCAR Gaussian grid. The choice of this particular climatology is purely for convenience. Using a number of different climatologies, we found that the results from the direct minimization blending are not sensitive to the choice of climatology.

3. Methodology

The desired product of this study is a synthesis of the FSU and NCEP–NCAR reanalysis pseudostress into realistic (i.e., showing no artifacts of synthesis methodology) fields of monthly mean pseudostress from 1961 to 1997. There are many methods that could be used for this purpose. They range from straightforward piecewise construction to more sophisticated approaches using data assimilation [see Lorenc (1986) and Daley (1991) for good comparison of many of these approaches]. The direct minimization approach we use combines fields of pseudostress products in a nonlinear least squares framework, that is, the solution is the field of pseudostress vectors that best minimizes a functional that expresses several constraints or “lack of fit.” The key of this approach is the functional to be minimized. For this analysis, we wish to simply piece together two datasets using existing knowledge as a guide for relative weighting in regions of overlap. The direct minimization approach is efficient and straightforward, and addresses concerns highlighted previously. It has been used for similar purposes (e.g., Ramamurthy and Navon 1992). Future developments in the use of direct minimization/variational approaches to objective analysis may take advantage of more refined expressions of the wind field (divergent and rotational parts) and alternative approaches of data mapping. For this study, the functional includes weighted misfit constraints for the FSU and NCEP–NCAR reanalysis datasets, and Laplacian, divergence, and curl constraints that are intended to weakly smooth the solution field and ensure smooth derivative fields.

Each constraint of the functional is weighted with a coefficient that controls the impact on the solution fields. The functional is weighted with regards to the regional strengths and weaknesses of each dataset. The following sections will describe the details of the functional, its minimization, and the sensitivity analysis performed to determine suitable weights for each of the kinematic terms.

a. The functional

The functional to be minimized, F(V), is designed to combine the two datasets into a seamless pseudostress field:
i1520-0442-13-16-3003-eq1
where u, υ, are pseudostress vector components, and vector; uFSU, υFSU are FSU pseudostress components; uNCEPR, υNCEPR are NCEP–NCAR pseudostress components; uC, υC, c are climatological pseudostress components, and vector (daSilva 1994); and αx,y, βx,y, γ, θ, λ are weights.

Each of the kinematic terms are multiplied by a power of the length scale L (L = 1°, latitude) such that all terms of F are dimensionally uniform. The coefficients αx,y, βx,y, γ, θ, λ, specified a priori, control the influence of each term on the resulting solution.

The first two terms of F represent the misfit of the FSU and NCEP–NCAR fields with respect to the solution pseudostress field. These terms have different spatially dependent weighting functions (Fig. 3), subjectively determined a priori based on each dataset’s strengths and weaknesses as described in section 2. The FSU constraint dominates from 20°S to 20°N, where the FSU weight is set to 10.0 and the NCEP–NCAR weight is zero, with the exception of the southeast corner of this region. Smooth transition zones are defined by a gradual change in the weights from 0.0 to their maximum value, between 20° and 30° both north and south. The southeast corner has a larger transition zone to accommodate the dramatic differences between the two datasets. Thus α, β control the influence of FSU and NCEP–NCAR analyses in the solution fields. We chose FSU to dominate in the tropical (20°N–20°S) region and NCEP–NCAR elsewhere.

The direct minimization approach described here can also be cast as a statistical estimation problem where the weights are expressions of the inverse error covariances. Our weight selection (described later) for the first two terms establishes these error magnitudes to be geographically dependent but homogenous within each specified geographical region. The ratio of these weights determines the weighted average of NCEP–NCAR and FSU wind values that compose the solution wind value. These weights could in theory be much more complicated, for example, incorporating detailed spatial correlation structure. However, our objective was simply to meld the two analyses, not dramatically alter the overall structure. The explicit ratio selected (implying the FSU winds have errors 10 times smaller than NCEP–NCAR analyses in the equatorial region and reaching parity outside the equatorial band) were based on several factors including sufficient weighting to retain completely the FSU product in the central Tropics, the relatively large errors in NCEP–NCAR winds in the tropical Pacific as determined through comparisons to FSU and ECMWF reanalysis winds, and finally the sensitivity experiments (described earlier). More detailed and exact error estimates (i.e., weights) would be desirable;however, it is not clear how this might be achieved (see comments later).

The third term of F is the Laplacian or smoothing term. This term smooths the solution field. The fourth and fifth terms of F are kinematic constraints that indirectly impose climatological structure information on the output. These terms alter slightly the solution to smooth divergence and curl fields. The degree to which the Laplacian and kinematic constraints influence the solution is determined by the selection of the γ, θ, λ weights. A sensitivity analysis (discussed in a later section) aides in determining suitable values for them. The values of the smoothing and kinematic weights are uniform for all grid points within the analysis domain. Within the FSU region (30°S–30°N, 140°E–85°W) the functional analyzes the misfit of the analysis to the UWM COADS climatology. Outside of this region and in regions over land, the Laplacian, divergence, and curl terms of the functional are analyzed using misfits to the NCEP–NCAR reanalysis with the same weights, γ, θ, λ (i.e., the NCEP–NCAR reanalysis acts as the climatology). This is done to ensure that the values at the edges of the solution domain do not differ from the NCEP–NCAR reanalysis values. Thus, the solution analysis can be inserted seamlessly into the global NCEP–NCAR reanalysis.

b. Minimization with the conjugate–gradient method

The conjugate–gradient method has been shown to be the optimal method that minimizes a functional in a large-scale variational analysis (Navon and Legler 1987). We use the subroutine CONMIN, a Beale restarted limited-memory quasi-Newton conjugate–gradient method described in Shanno and Phuo (1980).

The conjugate–gradient method is an iterative method requiring an initial guess field, a functional, and the gradient of that functional. For this study, the initial guess field (V) is a rough combination of the FSU and NCEP–NCAR pseudostress fields. The fields are simply pieced together and smoothed along the border with a weighted interpolation,
i1520-0442-13-16-3003-eq2
based on the weights (Fig. 3). This eliminates problems for the minimization subroutine where the FSU and NCEP–NCAR data differ dramatically.

The subroutine CONMIN requires development of suitable code to compute the gradient of the functional, F. The functional and its gradient are written in finite difference form in spherical coordinates. A solution is obtained when the norm of the gradient is reduced by 1.5 × 102. The behavior of the gradient and functional values were carefully monitored and behaved normally. Solutions typically were found after 10–15 iterations.

4. Sensitivity results

The weights γ, θ, λ are subjectively chosen parameters that can have a significant impact on the solution fields. Analysis of the sensitivity of the weights, that is, the change in the solution per change in the weight, provides insight in selecting suitable values (Meyers et al. 1994). This approach identifies the most sensitive weights and respective ranges of sensitivity, that is, changes in solution characteristics (i.e., pseudostress magnitude, divergence, curl) with respect to changes in the weights. We defined response functions to quantify integrated characteristics of the solution fields solution. The response functions describe the magnitude, divergence, and curl of the resulting fields for a specific set of weights (α . . . ):
i1520-0442-13-16-3003-eq3

Each response function is integrated over a specified region. Each of the weights are varied individually and their impact on the three response functions were noted. Many such analyses were completed. A representative sample of the results is presented here. We also examine closely the solution fields to ensure results represent underlying inputs and reflect realistic characteristics of pseudostress fields.

The Laplacian weight, γ, has the relatively largest (of all the smoothing and kinematic weights) impact on the solution. In general RM is ±3–7 m2 s−2 (meaning the magnitude of the initial guess field is altered by ±3–7 m2 s−2 in various regions of the domain) within a range of weight values from 0.5 to 12.0. Values of RM are very similar above a value of γ = 1.0, thus indicating that the analysis changes similarly irrespective of the specific weight within this range of weights. In other words, the solution is fairly insensitive to the specific selection of γ (within the tested range). Similarly, for RD and RC the γ weight has a relatively large impact, but again the sensitivity of RD and RC to specific choices of γ is very small within the ranges of tested values. Selecting a small weight, γ = 1.0, produces a notable impact on the solution fields and thus, wanting to guard against oversmoothing of the results, we choose γ = 1.0. Suitable values for the Laplacian and kinematic weights are chosen to be within the ranges where the solutions are fairly insensitive to changes of the weight. Additionally, an acceptable weight must result in a solution field that reflects the underlying inputs as well as indicate no artifacts of the combination process (assessed through numerical comparisons of the solution fields to the input fields).

The divergence and curl weights, θ and λ, have less of an impact on the response functions than that of the Laplacian weight; typically, the responses to the kinematic constraints is two orders of magnitude smaller than that of the Laplacian constraint. The sensitivity of the response functions, though small, varies considerably over the tested range of weight values from 0 to 12. Values of RM are constant for values of λ greater than 10.0 (Fig. 4). Therefore, λ is selected to be 11.0 in the middle of this constant response region. For θ, there was no range of values where the response functions were consistent, but a value of 9.5 was deemed acceptable.

In summary, we found the smoothing weight had the greatest impact on the solution (when compared to cases where the constraint was not included), but the solution was insensitive to the specific value. For the kinematic weights, the response was two orders of magnitude smaller than that for the smoothing constraint, but the response was somewhat sensitive to specific values for the weights. Optimal values for the weights are not easily defined. The selections made here are suitable by our criteria of low sensitivity and evaluation of resulting fields and relevant kinematic fields of divergence and curl. The subjective nature of our weight selection process injects questions of robustness regarding the results; however, the relative insensitivity of the solutions to the smoothing weight as well as the relatively low impact of the kinematic terms suggests that the solutions should be invariable across the tested range of weights. Cross-validation techniques (e.g., Legler et al. 1998) may offer hope in the future for more objective weight selection.

5. Direct minimization results

The direct minimization produces a combined FSU–NCEP–NCAR pseudostress product. Analysis of difference fields between the combined solution (e.g., Fig. 5) and the FSU and NCEP–NCAR products reveals the contrasts between these datasets. The differences in the magnitude, as well as the derivative fields, clearly reveal the effect of the weighting by region. The transition zones are sites of a gradual change in the differences from one region of influence to the other, producing a smooth product of the FSU and NCEP–NCAR fields along the blending border.

Smoothing effects are observed within the FSU weighting region (20°N–20°S), a direct result of the Laplacian and kinematic constraints. Variability on scales smaller than the original 2° lat by 10° long rectangles for the FSU analysis should be considered noise and hence many users of the FSU products smooth the data to remove these spurious signals. The smoothing effects are observed in the pseudostress as well as the divergence and curl patterns.

6. CEOF analysis

Empirical orthogonal function (EOF) analysis has been used to study the interannual variability of sea surface temperature (SST) (Tourre and White 1995) and other scalar fields. Vector fields can be analyzed in a similar manner using CEOF analysis (Horel 1984). CEOF analysis is applied to the resulting combined fields (nonland values only) in this study to explore the relationship between tropical and extratropical regions on interannual time periods.

Before the CEOF analysis is performed, the monthly mean climatologies (based on the solution fields) are removed from the pseudostress fields to form monthly anomalies. To focus on interannual (e.g., ENSO and decadal timescales), the data are then filtered in time with an 18-month low-pass Kaylor filter (Kaylor 1977). CEOF analysis, also called complex principal component analysis, treats the vector field represented as a set of complex numbers, the u and υ components placed into real and imaginary parts, respectively.

Due to the large latitudinal extent of this dataset, 40°S–60°N, care was taken to eliminate the geometrical effects of the grid spacing that results from the decreasing area of grid boxes at higher latitudes. We also account for the variable latitudinal spacing in the Gaussian grid. We define the second moment as follows:
i1520-0442-13-16-3003-eq4
where υ is a wind component at a grid location, and dA is the size of the grid box that υ represents. This scaling is necessary to represent correctly the true (continuous) EOFs regardless of the grid (North et al. 1982).
A Hermitian covariance matrix is calculated and normalized by the area of the entire domain. In this case, K = 3911 spatial grid points were analyzed from January 1962 through December 1996 (due to the filtering, we remove nine months from the ends of the filtered time series at each point, therefore we analyze the period from 1962 to 1996 in the CEOF analysis, a total of J = 419 months). The M = J eigenvalues and associated eigenvectors of the covariance matrix are calculated. The eigenvectors are then used to create principal components (i.e., spatial fields) from the data using the following relationship:
SETV
where S is an M × K matrix of principal components, E is a J × M matrix of eigenvectors, and V is the J × K matrix of solution vectors (columns are time series at each location).

The CEOF analysis results in 419 principal component (spatial patterns) and eigenvector (time series) pairs, each representing a certain percentage of the spatiotemporal variance (as determined by the eigenvalues). A scree test (Wilks 1995) reveals the first four principal components to be statistically significant, accounting for a combined 51% of the explained variance. The complex eigenvectors (time series) are expressed here as amplitude and rotation angle, which modulate the spatial fields, S. The rotation angle represents the counterclockwise rotation of each of the vectors in the principal component (spatial field). The following sections discuss prominent patterns during various phases of the ENSO events of the period, focusing on the extratropical response of the Aleutian low in the north Pacific.

a. The first principal component

The first spatial function represents 22.20% of the variance (Fig. 6). In the Tropics, this pattern is consistent with the mature phase of the canonical warm event anomaly composite as described in Rasmusson and Carpenter (1982). The striking presence of a strengthening of the Aleutian low, centered near its climatological position at 50°N, 167°W, accompanies the strengthened westerlies in the equatorial region. As expected, this pattern occurs during the mature phase of the warm events of 1973, 1983, 1987, and 1992 (Fig. 7). For each of these years, with the exception of 1987, the peak amplitude occurs during the Northern Hemisphere winter, that is, December–February, of the warm event. The 1987 event is not phase locked with the annual cycle and has its peak from March to June.

The strengthening of the Aleutian low during warm event winters has been observed in geopotential height fields (Horel and Wallace 1981), as well as model-derived height fields over the North Pacific (Lau 1997). The increased latitudinal extent of our combined pseudostress product allows us to observe this extratropical connection in fields of surface pseudostress. It is interesting to note the relationship of the first eigenvector with the Japan Meteorological Agency (JMA) index (based on monthly mean SST anomalies averaged for the area 4°N–4°S, 150°–90°W). After 1970, the first eigenvector is clearly in phase with the JMA index, having amplitude peaks accompanied by 90° (270°) rotation angles during warm (cold) SST conditions. Prior to 1970 the first principal component is relatively insignificant during the warm events of the 1960s, even though the orientations of the vector field are consistent to that in the post-1970 period.

Modeling results have shown that the warm events of the 1960s are a result of the cessation of the normal semiannual variability of the central Pacific easterlies, rather than an anomalous relaxation of the easterlies (Busalacchi and O’Brien 1981). This conclusion provides a possible explanation for the relatively small amplitudes observed in the first mode during these events;this normal semiannual variability will not appear in the filtered pseudostress fields. Therefore, the anomalous relaxation of the westerlies in the central equatorial Pacific, represented by the first mode, will not appear as a significant peak during these events.

The years of 1968, 1971, 1974, 1976, and 1988 are represented by a 270° counterclockwise rotation of the first spatial function coincident with amplitude peaks, from December to February, in the first eigenvector. These peaks occur in phase with the negative values of the JMA index, denoting an El Viejo year (the cold phase of ENSO). The spatial pattern for these time periods is dominated by easterly anomalies in the equatorial Pacific and strengthened southeast trades, along with a weakening of the Aleutian low, centered near its climatological position.

Finally it is interesting to question if similar findings would be found if using NCEP–NCAR reanalysis winds only (no FSU product insertion). Such a CEOF analysis indicates the NCEP–NCAR wind fields fail to indicate linkages between Pacific winds, 20°N–20°S and winds at higher latitudes (Fig. 8).

b. The second principal component

The second CEOF spatial function, representing 11.58% of the variance, has its largest response associated with the Aleutian low (Fig. 9). In contrast to the first principal component, the Aleutian low is weakened and shifted southeast of its normal position to 48°N and 155°W. There is significant northeasterly flow associated with the Aleutian low through the 30°N longitude band from 170°E to 145°W. North of the equator up to 10°N from 140°E to 160°W, there are anomalous westerlies. This pattern appears in winter–spring before the moderate to strong warm events of 1969, 1973, and 1983 (Fig. 10), preceding the warm SST anomalies peaks by 8–12 months. This timing is slightly lagged with respect to the findings of Emery and Hamilton (1985) in which seasonal mean atmospheric sea level pressure charts showed a weakened Aleutian low the winter before the 1973 and 1983 warm events.

When the second spatial function is rotated 270° (e.g., mid-1970s) the Aleutian low is strengthened, and there are easterly anomalies present north of the equator in the western Pacific. This occurs after the peak phase of the 1983 warm event, June–July, and (less significantly) after the peak phase of the 1973 warm event (Fig. 10). This pattern slowly decreases in amplitude through the weakening phases of the 1983 event, as the anomalies return to easterlies over the western equatorial Pacific and the strength of the Aleutian low diminishes. This pattern also precedes the cold events of 1971, 1974, 1976, and 1988 (negative peaks in the JMA index) by 3–4 months.

c. The third principal component

The third CEOF spatial function, representing 9.61% of the variance, shows significant values east of the date line just south of the equator (Fig. 11). These anomalies are westerly stretching from 160° to 100°W. Southwesterly anomalies are seen in the region of the northeast trades, just south of Hawaii, indicating these trade winds are weakened. There are northeasterly anomalies south of the Aleutian Islands in the North Pacific. This pattern is dominant during the weak warm events of 1963, 1965, and 1969 (Fig. 12), preceding SST anomaly peaks in the JMA index by 6–8 months.

Recalling the lack of significance the first principal component revealed during the warm events of the 1960s, it is an interesting finding that the third component peaks as a precursor to the positive SST anomalies prior to 1970. Westerly anomalies first appear south of the equator for the warm events of the 1960s, as opposed to north of the equator in the western Pacific after 1970. The north Pacific connections, with respect to the Aleutian low, are inconsistent prior to 1970. There is little organized connection in the North Pacific during the precursor stages of the 1963, 1965, and 1969 warm events. From December to February of these events, the mature phase, the intensity of the Aleutian low varies; there is no organized response during the 1963 event, a weakening during the 1965 event, and a strengthening during the 1969 event.

Previous studies of the interannual and interdecadal variability of SST in the Pacific basin have shown that variability in the background SST state feeds back on the tropical and midlatitude atmospheric circulations (Tourre et al. 1999). In particular, changes in the polarity of the subarctic and subtropical oceanic fronts [shift from a cold (warm) state in the subtropical (subarctic) front to a warm (cold) state] in the early 1970s have been shown to influence the developmental stages of the warm events prior to and following 1977 (Wang 1995). The changes in the tropical wind anomalies in the western equatorial Pacific are similar to those observed in our analysis. However, the onset phase of the 1973 event is more similar to that of the 1983 event in our analysis. Further investigation of the connection between the interdecadal SST state and the north Pacific atmospheric connections is needed to determine if the variable response of the Aleutian low observed in our analysis is a product of these feedback processes or simply the natural variability of the ENSO cycle.

7. Discussion

A direct minimization method is applied to combine monthly mean NCEP–NCAR reanalysis and height-adjusted FSU pseudostress fields over the Pacific Ocean. This is accomplished through the minimization of a strategically designed functional, consisting of weighted misfit constraints for the FSU and NCEP–NCAR reanalysis fields, as well as Laplacian and kinematic terms included to ensure smoothness in the derivative fields of the solution. A sensitivity analysis reveals that the Laplacian weight introduces the largest changes in the solution fields. However, over a relatively large range of nonzero weight values, the solution is fairly consistent. In contrast, the sensitivity of the solution to changes in the divergence and curl weights varies considerably over the range of weight values though these constraints have only minor effects on the solution. The final selection of the weight values was based on our criteria of low sensitivity and qualitative evaluation of resulting fields and relevant kinematic fields of divergence and curl. The spatially dependent weighting functions for the FSU and NCEP–NCAR constraints allow us to produce a combination of the two fields based on each dataset’s regional strengths.

The direct minimization approach produces satisfactory solution fields as evidenced by ocean model integrations and comparisons to the original fields. The solution fields in the tropical Pacific (20°N–20°S, i.e., the FSU region of influence) are a smoothed version of the FSU pseudostress fields. The solution fields gradually change through the transition zone into the NCEP–NCAR reanalysis region of influence. The divergence and curl fields of the solution fields maintain the physical properties of the FSU and NCEP–NCAR analyses without producing artificial noise along the border between the two fields. This is due in part to the gradual transition zones in the weighting functions, but primarily due to the smoothing effects of the Laplacian and kinematic constraints.

Additionally, the combination product maintains the integrity of the FSU pseudostress over the tropical Pacific. Identical runs of a reduced gravity, nonlinear shallow water transport model of the tropical Pacific Ocean (Kamachi and O’Brien 1995) forced with the FSU and the combined products produce similar upper-layer thickness results (not presented here), highly correlated with observed sea level height anomalies in the eastern and western equatorial Pacific. Correlation coefficients at Santa Cruz, Ecuador, and Callao, Peru, stations are 0.99 and 0.95, respectively. At these stations, the root-mean-squared difference between the combined and FSU thermocline positions are 3.9% and 9.5%, respectively. As with the FSU product, the combined product reproduces the physical ocean dynamics of the region, including the rise and fall of the thermocline position as dictated by anomalous wind patterns associated with ENSO and the passage of internal Kelvin and Rossby waves as described by Busalacchi et al. (1983).

The broad extent of these fields allows us to examine the interannual variability of tropical and extratropical pseudostress over the Pacific Ocean through a CEOF analysis. Analysis of the anomaly fields (with NCEP–NCAR reanalysis pseudostress 40°–60°N added to the northern edge of the domain) highlights significant interannual variability over the Pacific from 1962 to 1997.

The first mode of a CEOF analysis of the combined fields represents the typical mature phase of El Niño events exhibiting westerly pseudostress anomalies over the tropical Pacific linked to a strengthening of the Aleutian low during the mature phases of the El Niños of 1973, 1983, 1987, and 1992. The pattern is reversed for El Viejo events and is preceded by the combined effects of the second and third modes. In summary, this mode links the strengthening of the Aleutian low to the classic El Niño pseudostress anomaly pattern. This link exists in observed geopotential height, as well as model height fields, over the North Pacific during El Niño winters in the Northern Hemisphere (Horel and Wallace 1981; Lau 1997).

The second mode represents the precursor modes during the winter–spring prior to the 1973 and 1983 El Niños, that is, northwesterly anomalies develop in the western Pacific, north of the equator, and weakened northeast trades, coincident with a weakening of the Aleutian low. Surface pressure analyses have shown that the Aleutian low is weakened in the winter preceding an El Niño event (Emery and Hamilton 1985); the second mode provides further evidence of this in our pseudostress analyses. The second mode also appears during the end of these two El Niño events, marking the return to normal of the equatorial anomalies in the western Pacific. At the same time, these modes contribute to the strengthened Aleutian low, which is shifted southeast of its normal position.

The third mode appears during the 1983 event representing westerly anomalies in the eastern equatorial Pacific, after the peak of the first mode. This mode also appears during the onset of the El Niños of the 1960s. The combined contributions of the second and third modes explain the sequence of events for the 1963, 1965, and 1969 El Niños; the first mode is not significant during these weak events. The El Niños of the 1960s differ from those after 1970. The onset phase of these events are characterized by westerly anomalies developing south of the equator in the western Pacific; the connections in the North Pacific are inconsistent, with variable strengthening and weakening of the Aleutian low from one event to the next.

Each ENSO event has its own individual characteristics. Some generalizations regarding development and extratropical connections are possible; however, no two events are completely identical. The CEOF analysis in this study reveals many similarities between events (e.g., 1973 and 1983 events), as well as significant variability between events (e.g., the El Niños of the 1960s).

Acknowledgments

Thanks are extended to T. N. Krishnamurti, James B. Elsner, and Jon Ahlquist for their constructive comments. Thanks also to Mark Bourassa for helping with the minimization code. Improvements suggested by two anonymous reviewers are also acknowledged.

This research was supported by the National Science Foundation supporting the WOCE Center for Surface Meteorology and Fluxes (OCE-9314515), as well as by NASA (NAG5-7254). Base support of COAPS is provided by the Office of Naval Research. NCEP–NCAR reanalysis data were provided by NOAA Climate Diagnostics Center, Boulder, Colorado; UWM/COADS climatology provided courtesy of Dr. Arlindo da Silva.

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Fig. 1.
Fig. 1.

Zonal mean climatological (1979–93) wind stress curl and wind divergence based on FSU and (height adjusted) ECMWF ERA and NCEP–NCAR reanalysis pseudostress products: (a) wind divergence for the Pacific Ocean region (120°E–70°W); (b) wind stress curl for the Pacific Ocean region (120°E–70°W). The wind stress was calculated based on a constant bulk formula drag coefficient of 1.2 × 10−3.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 2.
Fig. 2.

Zonal mean climatological (1979–93) pseudostress components for FSU and (height adjusted) ECMWF ERA and NCEP–NCAR reanalysis products: (a) north–south component for the Pacific Ocean region (120°E–70°W); (b) east–west component for the Pacific Ocean region (120°E–70°W).

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 3.
Fig. 3.

Spatial distribution of a priori chosen weights in the functional for the FSU constraint, αx,y (top), and the NCEP–NCAR constraint, βx,y (bottom). Contour intervals are 2 for the FSU weight and 0.2 for the NCEP–NCAR weight. Note FSU (NCEP–NCAR) weight outside these contours is 0.0 (1.0), and inside the contours is 10.0 (0.0).

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 4.
Fig. 4.

Aug 1991 pseudostress magnitude response function for the 135°W long band as a function of the curl weight. The curl weight is varied from 0.0 to 12.0 in the functional, keeping all other weights constant at 1.0. The magnitude at each weight is subtracted from the magnitude for a weight of 0.0 to determine the response. Positive values indicate increasing pseudostress magnitude with increasing curl weight. The contour interval is 0.1 m2 s−2 (dashed contours are negative).

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 5.
Fig. 5.

Combined solution pseudostress with vectors for Aug 1991. The contours indicate magnitude; interval is 10 m2 s−2. Note there are vectors over land because the NCEP–NCAR analysis includes the entire globe.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 6.
Fig. 6.

The first spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 22.20% of the variance. Contour values are unitless, with an interval of 0.2.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 7.
Fig. 7.

The amplitude (top) and rotation angle (bottom) for the first eigenvector, and JMA SST index (dash–dot). Amplitudes greater than 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 8.
Fig. 8.

The first spatial function from the CEOF analysis using NCEP–NCAR data only (no combination of FSU and NCEP–NCAR) after having applied a 90° counterclockwise rotation angle. This field represents 23.0% of the variance. Contour values are unitless, with an interval of 0.2. The associated time series is very similar to that for the FSU–NCEP–NCAR analysis, i.e., Fig. 7.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 9.
Fig. 9.

The second spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 11.58% of the variance. Contour values are unitless, with an interval of 0.2.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 10.
Fig. 10.

The amplitude (top) and rotation angle (bottom) for the second eigenvector, and JMA SST index (dash–dot). Amplitudes greater 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 11.
Fig. 11.

The third spatial function from the CEOF analysis after having applied a 90° counterclockwise rotation angle. This field represents 9.61% of the variance. Contour values are unitless, with an interval of 0.2.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

Fig. 12.
Fig. 12.

The amplitude (top) and rotation angle (bottom) for the third eigenvector, and JMA SST index (dash–dot). Amplitudes greater than 6 m2 s−2, approximately the largest 20% of the amplitudes, are highlighted with a thick line. The rotation angle is in the counterclockwise direction.

Citation: Journal of Climate 13, 16; 10.1175/1520-0442(2000)013<3003:IVOSFA>2.0.CO;2

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