JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. D3, PAGES 5133-5142, MARCH 20, 1995
Space and time aliasing structure in monthly mean polar-orbiting satellite data Lixin Zeng Department of Atmospheric Sciences, AK-40, University of Washington, Seattle
Gad Levy1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis
Abstract. Monthly mean wind fields from the European Remote Sensing Satellite (ERS1) scatterometer are presented. A banded structure which resembles the satellite subtrack is clearly and consistently apparent in the isotachs as well as the u and v components of the routinely produced fields. The structure also appears in the means of data from other polar-orbiting satellites and instruments. An experiment is designed to trace the cause of the banded structure. The European Centre for Medium-Range Weather Forecasts gridded surface wind analyses are used as a control set. These analyses are also sampled with the ERS1 temporalspatial sampling pattern to form a simulated scatterometer wind set. Both sets are used to create monthly averages. The banded structures appear in the monthly mean simulated data but do not appear in the control set. It is concluded that the source of the banded structure lies in the spatial and temporal sampling of the polar-orbiting satellite which results in undersampling. The problem involves multiple timescales and space scales, oversampling and undersampling in space, aliasing in the time and space domains, and preferentially sampled variability. It is shown that commonly used spatial smoothers (or filters), while producing visually pleasing results, also significantly bias the true mean. A three-dimensional spatialtemporal interpolator is designed and used to determine the mean field. It is found to produce satisfactory monthly means from both simulated and real ERS1 data. The implications to climate studies involving polar-orbiting satellite data are discussed.
1. Introduction Data from polar-orbiting satellites are increasingly being used to complement “conventional” climatological and general circulation model (GCM) estimates of mean atmospheric variables. The sampling frequency and coverage of satellite data make them an invaluable and often the sole source of observations in the sparsely observed oceans (e.g., the tropical and southern oceans). One of the basic fields needed for general circulation and climate studies is the wind vector. Near the ocean surface the vector wind field can be monitored remotely from space by scatterometers. The scatterometer is an instrument that retrieves the near surface wind from measurements of the radar backscatter cross section over the ocean [e.g., Freilich and Dunbar, 1992]. The first scatterometer in space was aboard the Seasat satellite (July 7, 1978 to October 10, 1978). During its 96day mission, the Seasat scatterometer provided data from two parallel swaths of wind measurements at the ocean surface, each approximately 500 km wide, separated by a gap
__________ 1Also at Department of Atmospheric Sciences, University of Washington, Seattle Copyright 1995 by the American Geophysical Union. Paper number 94JDO3252 0148-0227/95/94JD-03252$05.00
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of up to 400 km. These data were used in numerous studies involving data assimilation experiments [e.g., Legler and O’Brien, 1985; Atlas et al., 1987], synoptic and subsynoptic scale analyses [e.g., McMurdie et al., 1987; Levy, 1989; Levy and Brown, 1991], and general circulation studies [e.g., Levy and Tiu, 1990; Levy, 1994]. Since July 1991 the ERS1 scatterometer has provided almost continuous data from a single swath, approximately 500 km wide, which is offset about 225 km from the nadir track. The ERS1 winds have also been assimilated into numerical weather prediction models [e.g., Hoffman, 1993] and used for storm analyses [e.g., Brown and Zeng, 1994]. A continuing series of scatterometers is scheduled (e.g., ERS2 in 1995 and NASA scatterometer in 1996), making future climate studies involving long-term averages feasible. Traditionally, averaging schemes were designed for the interpolation and gridding of a few observations over vast areas. Data from polar-orbiting satellites have alleviated the data sparsity problem in some areas, but use of the data has introduced new complications because the data have special distributions in space and time. In the course of a day, there are dense observations along the satellite subtrack and no observations whatsoever in the wide gaps between swaths. The information is often redundant in the data-dense areas. The temporal sampling pattern is asynoptic as well, resulting in areas that are sampled only during certain parts of the averaging period. The undersampling of any data in space and/or time can lead to aliasing errors. These errors, unlike other analysis errors, are often overlooked in the meteorological and clima-
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tological literature. However, as was noted by Edwards [1987] and Ooyama [1987] for conventional data, failure to dealias the observed information properly may lead to serious problems in interpretation and analyses. We use the term dealiasing to mean the elimination of errors in the time-mean which stem from aliasing, as opposed to its use in scatterometry to mean wind ambiguity removal. Salby [1989] discusses how higher-frequency signals undersampled by polar-orbiting satellites can be aliased into scales which are of interest in climate studies. He concludes that time mean quantities, adequate for many purposes, are immune to aliasing from unresolved random variability because of cancellation of aliases in the averaging process provided that the undersampled variability is stationary. He also points out, however, that achieving this result in practice is limited by the length of averaging period and nonstationarity usually needs to be considered. The main purpose of this study is to propose a methodology for the proper use and analysis of satellite data in climate studies. We show that while polar orbiting satellite data provide an unprecedented source of information for climate studies, they can also lead to serious errors if not carefully and properly analyzed. We investigate, analyze, and quantify the amount of aliasing present in monthly mean sea surface wind fields due to the special temporal and spatial sampling pattern of the European Remote Sensing (ERS1) polar orbiting satellite. We show that on the monthly timescale, the presumption of stationarity in the undersampled variabilities is not fulfilled and aliasing still poses a serious difficulty. In practice, monthly mean wind fields are commonly subjected to spatial smoothers which produce visually pleasing results. However, as was noted by Salby [1989], and is shown here for the ERS1 data, extreme caution should be exercised when trying to interpret such longer term averages. In fact, we show that the use of an improper filter may obscure the aliasing problem and introduce biases which will not be detected. Although we limit our experiment and analysis to an example of a single month of the
ERS1 data, our results can be applied to different polar-orbiting data and timescales. We explore the structure and cause of aliasing in the monthly mean wind field in section 2. The commonly used bicubic spline spatial filter is applied to the mean fields and its dealiasing capability is tested and discussed in section 3. In section 4 we introduce a simple yet effective spatial-temporal interpolator for dealiasing and evaluate its performance. We conclude with a discussion and a brief summary in section 5.
2. Aliasing in Monthly Mean Wind Fields Monthly mean surface wind fields have been produced from the ERS1 observations since January 1992 [Halpern et al., 1994]. The observations are binned and averaged in 1/3˚ x 1/3˚ grid boxes on a daily basis, and then averaged to form the monthly means. Another common and even simpler method is to collect all observations that fall into 1˚ x 1˚ grid boxes during a month and average them directly. In this study, the monthly mean is obtained by the latter method (The authors have tested both the methods and found that the results are not significantly different). Figure 1 is an example of the mean zonal component of the ERS1 wind for September 1992. Banded structures which resemble the satellite tracks are present, notably in the tropical Atlantic, the subtropical Pacific (e.g., around 30˚N, 175˚E), and the southern Indian Ocean. A typical spatial variation of 4 m s-1 is associated with these structures. Although we limit our discussion to an example from September 1992, these structures are ubiquitous to most of the monthly mean maps obtained in similar ways [Halpern et al., 1994]. In fact, careful inspection of the maps provided by Halpern et al. [1994] reveals similar structures in the annual mean for 1992, as well as in the monthly mean wind speeds maps from the special sensor microwave imager (SSMI), which has a 1400-km measurement swath. For the Seasat data and for much shorter averaging periods, Legler and O’Brien [1985] have
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Figure 1. Monthly mean ERS1 zonal wind (in meters per second), September 1992.
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Figure 2. Monthly mean ECMWF surface zonal wind (in meters per second), September 1992. noted a similar structure in their objective analysis scheme applied to 2-day averages, while McMurdie et al. [1987] have noted the spatial distortion of a front when using the successive correction objective analysis scheme of Levy and Brown [1986] for a single storm analysis. These observations strongly imply that the structure is caused by the sampling rather than by an instrument error. An experiment is designed here to confirm that the banded structure is indeed a result of the satellite sampling. The European Centre for Medium-Range Weather Forecasts (ECMWF) surface wind analyses during September 1992 are used as the “ground truth” to generate simulated ERS1 obser-
vations. At each scatterometer observation point, ECMWF data are linearly interpolated from the analysis grid points and times. This results in simulated observations which are the ECMWF winds sampled with the ERS1 sampling pattern. Then the monthly mean is obtained in the same manner described above, and its deviation from the ECMWF monthly mean field (Figure 2, hereafter referred to as the control set) is calculated, and shown in Figure 3. A banded structure resembling that seen in Figure 1 for the ERS1 data, which is absent from the control set, is generated by this procedure. The difference between the control set and monthly mean simulated data field is thus attributed to the satellite sampling pattern.
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Figure 3. The difference between the simulated scatterometer and ECMWF zonal wind monthly means (in meters per second), September 1992.
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.
Table 1. Monthly mean zonal wind (m s-1) on selected grid points. Point
Longitude
Latitude
Us
UE
A
175˚E
26˚N
-3.19
-4.68
B
170˚E
26˚N
-9.08
-5.44
C
150˚W
26˚N
-6.77
-6.31
Winds are in meters per second. Us: simulated wind. UE: control set.
In order to understand the actual cause of the banded structure, we turn our attention to the sampling of individual grid points. Three grid points from Figure 3 are chosen (Table 1) to illustrate the temporal sampling pattern of the satellite. Points A and B are located approximately 500 km
apart, where the banded structure exhibits maxima and minima, respectively. Figure 4a is the time series of ECMWF zonal wind at these points. Figure 4b shows the number of satellite observations in the 1˚ x 1˚ box centered at A versus the time (day of the month) of sampling. Although the total number of observations is large, they are all taken in only eight satellite passes. Moreover, certain parts of the averaging period are heavily weighted in the time mean, while others have little or no effect, because the time mean is the arithmetic average of these data. At point B the ECMWF time series is similar, but the temporal sampling is significantly different (Figure 4c) from that at A. Thus, even though the time series at A and B are almost identical, the monthly means constructed from satellite sampling at each point are distinctly different (Table 1). On a given latitude circle the temporal sampling pattern varies with longitude periodically. Consequently, the horizontal scale of the banded structure is approximately the width of the satellite swath, and its orientation is the same as that of the ascending
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Figure 4. (a) Time series of ECMWF zonal winds (in meters per second) at A, B, and C during September 1992. (b) Number of ERS1 observations in the 1˚x1˚ box centered at A versus time. (c) Same as Figure 4b except at point B. (d) Same as Figure 4b except at point C. The total numbers of satellite passes and observations during the month of September 1992 are printed on the top portion of Figures 4b-4d.
ZENG AND LEVY: ALIASING STRUCTURE IN MEAN SATELLITE DATA
or descending satellite tracks, depending on the location and time series of the sampled process. It is not surprising, therefore, that spectral analysis (not presented here) performed on a latitude circle yields significant spurious spectral peaks at the corresponding wavelengths. Since spectral analysis is one of the most commonly used analysis techniques in climatological studies, one should proceed with extreme caution when employing spectral methods in the analysis of polarorbiting satellite data. Although the temporal-spatial sampling pattern discussed above is global, aliasing is not present everywhere. This is because, in addition to the observing pattern, aliasing depends on the actual signal being sampled. When the temporal change of the underlying signal is small, unevenly distributed samples will be adequate and give a fairly accurate mean. Compared with points A and B, the ECMWF wind at C, a point taken from a region where the banded structure is not apparent, has less variability (Figure 4a), and the temporal sampling pattern is more even (Figure 4d). As a result, the calculated monthly mean is much more accurate (Table 1). It should be noted that the control set (ECMWF analysis) is different from the real ERS1 data. In addition to differences due to resolution and instrument/analysis overestimation and underestimation, the control set does not contain high frequency oscillations with temporal scale shorter than the 6-hour analysis interval or spatial scale smaller than the grid spacing, which may appear in real satellite data. However, the magnitude of these higher-frequency (temporal and spatial) oscillations is believed to be much smaller than that of the larger-scale variations represented in the control set. The discussion in this and the following sections demonstrates that, given the satellite sampling pattern, the variability responsible for the aliasing structure has scales much greater than the shortest resolvable scale in the control set. Thus, we believe that the data simulation using ECMWF analysis is sufficient to address this problem. To quantify the effect that the aliasing has on the mean fields, a parameter r is defined as follows. Let σE be the spatial standard deviation of the monthly means of the ECMWF analysis in a given domain, and ε be the spatial root mean square (rms) difference between the control set (i.e., monthly mean ECMWF) and monthly mean simulated field in the same spatial domain. As σE represents the variability of the ECMWF field and ε measures the amount of added variability, their ratio r = ε/σE gives an estimate of the degree of deterioration of the underlying field. The parameter is calculated in regions I and II in Figure 3 and for the entire domain (the global ocean between 60˚S and 60˚N). The results are summarized in the third column of Table 2. As expected, r is much larger in areas where the banded structure is most
Table 2. Statistical Parameters σE, m s-1
r, %
rSmooth, %
rInterplolated, %
I
1.6
138
63
24
II
1.2
50
33
33
Global
4.5
29
20
16
Region
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apparent (e.g., region I) than in other areas. A scatterplot of the monthly mean simulated wind versus the control set (zonal components) in this region illustrates that the aliasing impairs the true field seriously, adding both variance and bias (Figure 5a). In the scatterplot, the data points tend to stay on lines that are almost vertical. Tracing the coordinates of the points on each of the lines reveals that they are usually neighboring grid points on a latitude circle. This is consistent with the fact that the banded structure is almost meridionally oriented. Thus the errors are mostly functions of longitude, while the true field is mostly a function of latitude in this region. A very similar picture emerges when a scatterplot of the true ERS1 data vs. the control set is generated. Since this area is usually dynamically active and of great research interest, precaution must be taken when the data are applied in further analysis or modeling. The rms error added to the global monthly mean due to the satellite sampling is about 30% of the standard deviation of the underlying field (Table 2). While for certain applications, an error of 30% may be tolerable, we note that the structure and distribution of the added error are not random and thus introduce biases which may be much more serious. For example, the bias of the monthly mean simulated zonal wind from the control set is -1.3 m s-1 in region I (Figure 5a). Globally, the bias can be up to -1 m s-1, which may put flux calculations in error. It is therefore desirable to design a filter to control the aliasing.
3. A Spatial Filter/Smoother A common method used to remove sampling errors is to apply a spatial smoother or filter to the field studied. One of the most widely used spatial filters is a low pass filter called the bicubic spline filter [Press et al., 1992]. Because of its widespread use in various applications, it is likely to be the filter of choice of many users for dealiasing the monthly mean fields. We therefore evaluate its performance on the simulated data. Since the spatial scale of the aliasing (about 1000 km) may be also of interest to climate studies, smoothing would remove both the aliasing and some valuable signals. Application of the bicubic spline filter to the monthly mean simulated data results in a field which is usually free of the banded structure. The deviation of the smoothed field from the control set is shown in Figure 6. We see that large biases of up to 3 m s-1 remain in several areas (e.g., northern and western Pacific and northern Atlantic). Application of the bicubic spline filter to the simulated data has not reproduced a satisfactory representation of the control set. The ratio r defined in section 2 is again calculated here, except that ε is now the rms difference between the smoothed field and control set (the fourth column of Table 2). Although the visible banded structure is removed, there is no significant improvement in r in areas where the aliasing was most apparent, for example, region I. The scatterplot of the smoothed field versus the control set demonstrates that the smoothed field has less variance but is still seriously biased from the control set (Figure 5b). As was noted in section 2, the data points tend to stay in almost vertical lines due to the orientation of the banded structure. A similar pattern is seen here, except that the vertical segments of the data points are “compressed” and shifted (biased) as a result of smoothing. The bias in region I is about -0.5 m s-1
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Figure 5. Scatter plots of (a) simulated, (b) smoothed simulated, (c) spatially-temporally interpolated simulated, and (d) spatially-temporally interpolated actual ERS1 monthly mean zonal wind (y coordinate) versus the control set (x coordinate) in region I (in meters per second). The solid lines are the perfect fit lines, and dashed lines are the least square fits of the data points. and -1 m s-1 for higher and lower winds, respectively. Globally, the bias is about 0.5 m s-1. The spectral analysis performed on a latitude circle (not presented here) shows that the peak corresponding to the banded structure is eliminated and the first and strongest peak in the wavelength space is retained. However, the next peak is shifted by 500 km in wavelength space from that in the control set. Thus the use of such smoothers could give misleading results. However, it should be realized that the poor performance of the bicubic spline smoother is not due to its formulation. Rather, it is because large biases exist in the smoother’s input, i.e., the mean field calculated by “binning and averag-
ing” procedure (e.g., at points like A and B in section 2). Spatial smoothers, usually designed to remove small perturbations from a presumably accurate underlying trend, are not capable of correcting such large biases. Other spatial-only smoothers/filters are expected to suffer from the same disadvantage. In fact, applying spatial smoother is equivalent to a “binning and averaging” with a larger spatial scale. Therefore, it does not address the problem caused by the uneven distribution of observations in time. We also note that the use of spatial smoothers can be difficult in practice because there is usually no well-defined criterion for selecting the “resolvable” scale. Such a scale maintains an optimal bal-
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Figure 6. Same as Figure 3 except that the simulated wind field is smoothed by a bicubic spline smoother. ance between retention of the physical signal of interest and removing the undesired aliasing [Ooyama, 1987].
where wk is a weight function 2
4. A Spatial-Temporal Interpolator To overcome the difficulties encountered by the spatial smoother, a three-dimensional spatial-temporal interpolator is designed. In designing this scheme, we are looking for an optimal interpolation solution that will make use of both the temporal and spatial sampling pattern of the satellite. It substitutes temporal information where spatial information is missing, and vice versa, thus fully utilizing the data. We further require the scheme to be simple to implement and computationally efficient. First, the satellite observations for the month are binned into 30 daily fields on the same grid. Instead of estimating the monthly mean by averaging the nonmissing data at each of the grid points, as is done in the simple “binning and averaging” method described in section 2, the new scheme is intended to estimate the local values of the missing data before averaging. The nonmissing values are unevenly distributed temporally, as illustrated in Figure 4, and there exist long periods with missing data. However, there are usually nonmissing values around a missing value when both the time and space dimensions are considered. We may then perform a spatial-temporal interpolation: If a datum is missing at a certain location x0, y0 and time t0, the scheme will search for nonmissing values within a horizontal (spatial) range D, and a temporal range T. Then the missing value at (x0,y0,t0) is estimated as a linear combination of the N nonmissing values found, namely ,
=1 u estimate = k------------------------
T0
N
∑ wk
k=1
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and xk, yk, and tk are the location and time of the non-missing (i.e. observed) value uk within the range defined by D and T, which are selected as 300 km and 1 day in this study. Ideally, the selection of the weight function would be based on the knowledge of the error structure and spatial correlations of the field. Since those are not known, we have opted for a simpler scheme which relies on fewer (unknown) assumptions. Here the parameters D and T are selected on the basis of the ERS1 orbit but can be replaced by other scales and weights according to the specific goal of a study and the sampling pattern of a satellite instrument. No fine tuning of the interpolator was done with respect to the simulated data because such tuning may produce suboptimal results with the actual satellite data. Sensitivity tests performed on the interpolator show that while adjusting the weights can control the amount of smoothing, the resulting field is only slightly sensitive to the choice of D and T. With most of the missing values estimated, the monthly mean is calculated at each grid point. The temporal mean u at a grid point is estimated by
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∑ wk uk
2
( xk – x0) + ( yk – y0) ( tk – t0) 2 – ------------------------------------------------------------ + -----------------------2 2 D T w k = ------------------------------------------------------------------------------------------------------------ (2) 2 2 2 ( xk – x0) + ( yk – y0) ( tk – t0) 2 + ------------------------------------------------------------ + -----------------------2 2 D T
1 u = -----T0
∫ 0
1 u ( t ) dt ≈ -----T0
M – 1 u' + u' j j+1
( tj + 1 – tj) ∑ -------------------------2
(3)
j=1
where T0 is the averaging period, M is the number of input
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60˚
6.0 5.0 4.0 3.0
30˚
2.0 1.0 0.0
0˚
-1.0 -2.0
30˚
-3.0 -4.0 -5.0 -6.0
60˚ 90˚E
180˚
90˚W
Figure 7. Same as Figure 3 except that the simulated wind field is processed by the spatial-temporal interpolator, September, 1992. points between time 0 and T0, and u’j is either an observed value (when available) or estimated value (from equation (2)) at time tj and at the same grid point. The difference between the resulting field and the control set is shown in Figure 7, and the retrieved monthly mean is presented in Figure 8. The banded structure is removed, and the underlying ECMWF monthly mean is well retrieved. It is noted that the remaining errors are mostly along the boundaries (e.g., the ocean-land boundaries), where the number of surrounding nonmissing data is greatly reduced. This suggests the potential benefit of incorporating land observations and specifying boundary conditions.
To quantify this scheme’s effect on the mean field, the ratio r is calculated again, with ε being the rms difference between the monthly mean interpolated field and the control set. The results are summarized in the fifth column of Table 2. In region I, where the banded structure was most apparent, the spatial-temporal interpolating reduces r dramatically to 24% from the 138% of the monthly mean simulated field obtained by “binning and averaging” method (section 2). In addition to its noticeable improvement in the banded structure regions, this method also provides a better global value of r, reducing it by half. In regions where the aliasing was not present (e.g., region II), the spatial-temporal interpolator
60˚
14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 -12.0 -14.0
30˚
0˚ 30˚
60˚ 90˚E
180˚
90˚W
Figure 8. Monthly mean zonal wind (in meters per second) retrieved by the spatial-temporal interpolator from the simulated data.
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60˚
14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 -12.0 -14.0
30˚
0˚
30˚
60˚ 90˚E
180˚
90˚W
Figure 9. Monthly mean zonal wind (in meters per second) retrieved by the spatial-temporal interpolator from the actual ERS1 data, September 1992. provides the same result as the bicubic spline filter does. The scatterplot of the average spatial-temporally interpolated field versus the control set shows that the bias is successfully removed in region I (Figure 5c). Further analysis shows that the bias is also entirely removed globally. In addition, spectral analysis performed on a latitude circle (not presented here) retains the first two peaks at the same wavelengths as in the control set. Finally, the scheme is applied to the real ERS1 data, and the result is shown in Figure 9. Compared with Figure 1, the banded structure is removed successfully. Compared with the ECMWF (Figures 2 and 5d), more variability and details are seen in the ERS1 field. Except for boundary effects discussed earlier, the largest differences are in the tropics and in the southern hemisphere, where much fewer observations are available to the ECMWF analysis. These differences are in agreement with observations of previous studies [e.g., Levy and Brown, 1991; Brown and Zeng, 1994]. We thus believe that these differences reflect true differences between the ERS1 measurements and the control analysis. We further conclude that the ERS1 field was successfully retrieved and that the residual bias in Figure 5d is not due to aliasing. Unfortunately, there is no control set to verify the result in an absolute sense or to test whether the interpolator weights are optimal for the true ERS1 field.
5. Discussion and Summary While an outstanding source of climate information in the otherwise poorly observed oceans, data from polar orbiting satellites require caution in the binning, averaging, and interpretation of the product fields. With the aid of a data simulation experiment and examples from the ERS1 monthly mean wind field observation, it is shown how irregular sampling and undersampling at higher frequencies by the ERS1 polar-orbiting satellite can lead to aliasing at scales which are of interest to climate studies requiring monthly means. Commonly used smoothers (e.g., bicubic
spline filter) can generate visually satisfactory maps but may remove physical features of interest along with the aliased signal. Even more seriously, they may also introduce undetectable bias after the visual warning (e.g., the banded structure in this study) is removed. As was pointed out by Halpern [1988] and Ramage [1984], an error of 0.5 m s-1 in surface wind in the tropics may lead to an uncertainty of about 12 W m-2 in surface heat flux. The implication of this amount of flux uncertainty are illustrated by Randall et al. [1992]. In their study, the sensitivities of 19 GCMs to a 4˚K increase in global sea surface temperature are tested. Such a significant global warming is associated with a change of surface latent heat flux and sensible heat flux of -12.2 W m-2 and 1.8 W m-2, respectively (mean of the 19 GCMs). These values are comparable to the error in flux calculations introduced by aliased as well as improperly smoothed surface winds described in sections 2 and 3. Taylor [1983] also indicates that precision of monthly mean surface heat flux needs to be of 10 W m-2 over 5˚ square regions for climate studies. Thus, the errors present in the monthly mean of real (Figure 1) and simulated ERS1 wind discussed in section 2, and the spatially smoothed monthly mean fields (section 3) are not acceptable for climate studies. The three-dimensional spatial-temporal interpolator proposed in this study provides an effective yet simple approach to form monthly mean fields. It addresses the cause of the aliasing, namely, the uneven spatial-temporal sampling, and minimizes its ill effects without biasing the true mean. Thus its performance is much better than direct “binning and averaging” (section 2) and spatial smoothers such as the bicubic spline filter tested in section 3. There are some possible improvements to our proposed interpolator. For example, establishing a systematical approach to determine the optimal weight function for specific satellite instruments or study goals would make the interpolator more robust. Methods for reducing boundary errors should also be investigated. Since multiple satellite
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observations will be available in the near future (e.g., ERS1 and ERS2 will be in orbit simultaneously in 1995), it is desirable to extend the interpolator so that it can incorporate multisatellite data (e.g., similar to the method used in Salby et al. [1991]). Finally, we would like to stress that it is of utmost importance that the researchers thoroughly study the effects of any filter or interpolator used on their data before interpreting the products. Acknowledgments. The authors would like to thank Robert A. Brown for his support and advice. We also express our thanks to Ralph Foster and Petra Udelhofen for helpful discussions. This work is supported by NASA under grants JPL NSCAT/Seawinds and NAGW 1770 and by NOAA under grant NA36GP0115.
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Levy, G., Southern hemisphere low level wind circulation statistics from the Seasat scatterometer, Ann. Geophys., 12, 65-79, 1994. Levy, G., Surface dynamics of observed maritime fronts, J. Atmos. Sci., 46, 1219-1232, 1989. Levy G., and R. A. Brown, A simple objective analysis scheme for scatterometer data, J. Geophys. Res., 91, 5153-5158, 1986. Levy, G., and R. A. Brown, Southern hemisphere synoptic weather from a satellite scatterometer, Mon. Weather Rev., 119, 2803-2813, 1991. Levy, G., and F.S. Tiu, Thermal advection and stratification effects on surface winds and the low level meridional mass transport, J. Geophys. Res., 95, 20,247-20,257, 1990. McMurdie, L. A., G. Levy, and K. B. Katsaros, On the relationship between scatterometer derived convergences and atmospheric moisture. Mon. Weather Rev., 115, 1281-1294, 1987. Ooyama, K.V., Scale-controlled objective analysis, Mon. Weather Rev., 115, 2479-2506, 1987. Press, W. H., S. A. Teukosky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed., 963 pp., Cambridge University Press, New York, 1992. Ramage, C.S., Can shipboard measurements reveal secular changes in tropical air-sea heat flux?, J. Clim. Appl. Meteorol., 23, 187-193, 1984. Randall, D.A., et al., Intercomparison and interpretation of surface energy fluxes in atmospheric general circulation models, J. Geophys. Res., 97, 3711-3724, 1992 Salby, M. L., Climate monitoring from space: Asynoptic sampling considerations, J. Clim., 2, 1091-1105, 1989. Salby, M. L., H. H. Hendon, K. Woodberry, and K. Tanaka, Analysis of global cloud imagery from multiple satellites, Bull. Am. Meteorol. Soc., 72(4). 467-80, 1991. Taylor, P.K., The determination of surface fluxes of heat and water by satellite microwave radiometry and in situ measurements, in Large-Scale Oceanographic Experiments and Satellites, edited by C. Gautier and M. Fieux, pp. 223-246, Reidel, Norwell, Mass., 1983. __________ G. Levy and L. Zeng, Department of Atmospheric Sciences, AK-40, University of Washington, WA 98195. (e-mail:
[email protected],
[email protected]) (Received August 5, 1994; revised November 2, 1994; accepted December, 5, 1994.)
