Abstract

Satellite altimetry provides an immensely valuable source of operational significant wave height (Hs) data. Currently, altimeters on board Jason-1 and Envisat provide global Hs observations, available within 3–5 h of real time. In this work, Hs data from these altimeters are validated against in situ buoy data from the National Data Buoy Center (NDBC) and Marine Environmental Data Service (MEDS) buoy networks. Data cover a period of three years for Envisat and more than four years for Jason-1.

Collocation criteria of 50 km and 30 min yield 3452 and 2157 collocations for Jason-1 and Envisat, respectively. Jason-1 is found to be in no need of correction, performing well throughout the range of wave heights, although it is notably noisier than Envisat. An overall RMS difference between Jason-1 and buoy data of 0.227 m is found. Envisat has a tendency to overestimate low Hs and underestimate high Hs. A linear correction reduces the RMS difference by 7%, from 0.219 to 0.203 m.

In addition to wave height–dependent biases in the altimeter Hs estimate, a wave state–dependent bias is also identified, with steep (smooth) waves producing a negative (positive) bias relative to buoys.

A systematic difference in the Hs being reported by MEDS and NDBC buoy networks is also noted. Using the altimeter data as a common reference, it is estimated that MEDS buoys are underestimating Hs relative to NDBC buoys by about 10%.

1. Introduction

Wave height measurements are used for a variety of purposes. These range from studies to improve the understanding of the physical processes responsible for wind–wave evolution to the validation and calibration of models for waves and other ocean processes as well as wave climate investigations, which have implications for shipping and offshore engineering projects.

Traditionally, data coverage over the ocean has been poor. Wave observations have come from ships and moored buoys clustered around coastlines. In recent times, the advent of satellite remote sensing instruments has facilitated a significant increase in the amount of data available. The global coverage makes these observations ideal for assimilation into global wave models, model evaluation, and the construction of wave climatologies. The fast delivery (FD) altimeter products examined here (see section 2) are generally received at the major centers within 3 h of observation, with Jason-1 currently being assimilated into the operational wave model at the Australian Bureau of Meteorology (the Bureau). Previous work has shown that FD data typically contain systematic errors (e.g., Cotton and Carter 1994), although the precise nature of these errors has also been found to vary somewhat from mission to mission. Careful calibration of these data is thus required before they can be used with confidence.

In this work, FD significant wave height (Hs) from both the Jason-1 and Envisat altimeters is validated against in situ buoy data. A number of correction schemes are then investigated with the aim of minimizing the overall RMS difference. Section 2 examines the previous validation work for each altimeter. Section 3 describes the data and method used, followed by a discussion of the results in section 4, and finally section 5 states some conclusions.

2. Previous work

Seven satellite altimeters have been deployed since 1985, providing the first long-term global observation of sea level, wind speed, and wave height. Steady improvement has been made with each subsequent satellite, though characteristic biases have tended to vary somewhat from one to the next. Careful calibration of altimeter estimates against in situ measurements is thus important for accurate global estimation of Hs.

Altimeter validation studies, in general, attempt to obtain a set of collocated altimeter and buoy observations and find an appropriate adjustment for the altimeter, which results in the best fit with the in situ buoy data. Comparisons between buoy and altimeter-derived Hs data are complicated by the fact that each is measuring different aspects of the temporally and spatially varying wave field, and hence may differ, even in the case that both instruments are making perfectly accurate estimates (Monaldo 1988).

Differences can be divided into three categories: temporal proximity, spatial proximity, and sampling variability associated with time and space averaging. Because of the frequency of satellite passes, altimeter–buoy measurements cannot always be made simultaneously. Usually, a temporal window of acceptability is established—a maximum time difference for measurements to be considered a comparable altimeter–buoy pair. Similarly, an acceptable spatial separation between the altimeter track and the buoy location must be established. Sampling variability occurs because altimeter measurements are essentially an instantaneous spatial average of Hs over the altimeter footprint area, which increases from a diameter of about 3 km for small wave conditions to about 10 km for large wave conditions, whereas buoy measurements are time-averaged measurements of Hs at a point location.

Based on assessments of the spatial and temporal variation of the wave field, Monaldo (1988) proposes collocation criteria of observations occurring within 50 km and 30 min of one another. Since then these criteria have been widely adopted and now provide the standard for this type of work.

The two altimeters examined in this study are on board the currently flying Jason-1 and Envisat satellites. Launched in December 2001, Jason-1 is a jointly operated project between the French and U.S. space agencies, the Centre National d’Etudes Spatiales (CNES), and the National Aeronautics and Space Administration (NASA), respectively. It follows on from the enormously successful Ocean Topography Experiment (TOPEX)/Poseidon mission, sharing the same orbital parameters and following in the same ground tracks as its predecessor (see Fig. 1a). It flies in a non-sun-synchronous orbit at an altitude of 1336 km and an inclination angle of 66°. It carries a Poseidon-2 altimeter, derived from the experimental Poseidon-1 instrument carried on the TOPEX mission. Detailed descriptions of the mission and the Poseidon-2 altimeter can be found in Ménard et al. (2003) and Carayon et al. (2003), respectively. Envisat, launched March 2002, is operated by the European Space Agency (ESA). This mission follows on from European Remote Sensing Satellites 1 (ERS-1) and 2 (ERS-2), carrying the radar altimeter, RA-2, derived from these earlier missions. Envisat flies in a sun-synchronous orbit at an altitude of 800 km. In contrast to the prograde orbit of Jason-1, Envisat has a retrograde orbit of 98°; this angle allows for measurement closer to the poles (see Fig. 1b). More detail can be found in Resti et al. (1999).

Fig. 1.

Altimeter ground tracks from one day for (a) Jason-1 and (b) Envisat

Fig. 1.

Altimeter ground tracks from one day for (a) Jason-1 and (b) Envisat

Multiple datastreams are available from these satellites. These can be divided into operational, or so-called FD streams, and higher accuracy, offline (OL) streams. The former is used primarily for operational data assimilation and is available within 2–3 h of observation, whereas the latter is typically available several days later. Radar altimeters are active microwave sensors that infer Hs directly from the shape of the radar pulse, or waveform, returning to the nadir-looking altimeter. For FD products, processing of these waveforms is carried out on board, whereas ground-based processing is performed for the offline stream. In this work, the FD stream is validated, referred to as the operational sensor data record (OSDR) for Jason-1 and the near–real time (NRT) stream for Envisat.

Although both Jason-1 and Envisat have been in orbit for a number of years, there is little published work on the validation of Hs data from these satellites, especially the FD products. The following subsections summarize the published validation studies for each altimeter.

a. Jason-1

Although there is little validation work available for FD Jason-1 data, there has been some work examining the offline product. For these studies to be used as a context for the work presented here, it must be known how the FD and offline products compare. Desai and Vincent (2003) investigated precisely this, comparing 40 days of data from each stream. Inclusion of sea-state bias calculations based on, among other things, wind and wave conditions in the offline product, results in significant differences between these streams for sea surface height data. For Hs though, they conclude that although the FD product does show slightly less scatter, only small systematic differences exist between the FD and offline (OL) products, which appear to be well described by the linear relationship,

 
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Assuming the validity of this result, some work validating offline Hs data with in situ buoy data can now be considered. One of the earliest studies was performed by Ray and Beckley (2003) using six months of offline data from February to August 2002. They find a 7-cm negative bias, suggesting a correction of (with 95% confidence levels indicated)

 
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This study is of limited reliability, however, as conclusions are based on only 368 collocations.

In an attempt to provide a homogeneous dataset spanning several satellites, Queffeulou (2004) validates Hs data from six altimeters, using cross-altimeter and buoy comparisons. Using 50-km along track averages and a collocation separation criterion of 30 min, his study covers the period January 2002–September 2003 and resulted in 2853 collocations for Jason-1. Overall, he found a 5-cm negative bias in the altimeter data relative to the buoy data, finding the following linear relation:

 
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Substituting Eq. (1) into Eqs. (2) and (3) gives the following corrections to FD data, respectively:

 
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It must be stressed that Eqs. (4) and (5) are inferred from relationships between offline data and buoy data, and offline data and FD data found in different studies, and hence cannot be relied upon to provide quality validations. Despite this, they suggest that little correction to this data is required. This is consistent with work done at Météo-France (J. M. Lefevre 2006, personal communication), where biases have been shown to be small, and FD data are not corrected prior to assimilation. The European Centre for Medium-Range Weather Forecasts (ECMWF) applies a reduction of 4%, based on comparisons with buoy and model data (Abdalla et al. 2005).

b. Envisat

Queffeulou (2004) performed a validation of Envisat Hs data, using 30-min temporal and 50-km spatial windows, from April 2003 to February 2004, yielding 1280 collocations. He proposes a correction of

 
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However, this is using the offline product, and although the results of Desai and Vincent (2003) mentioned above regarding comparisons between FD and offline data for Jason-1 are encouraging, the relationship between these two streams for Envisat remains unknown.

Abdalla (2006) carried out a thorough investigation on Envisat FD wind–wave performance based on data from July 2002 to October 2003. Although no correction is proposed, they estimate that the altimeter overestimates Hs about 9 cm relative to buoy data. As a result of this work, ECMWF applies the same correction to Envisat as is applied to the Jason-1 data—that is, a bulk reduction of 4% (J. Bidlot et al. 2006, personal communication).

Overall, there is a distinct lack of work validating the FD data for both of these altimeters. Those that do exist have often been obtained through informal validations in an operational environment. As such, the need exists for a documented validation of these datastreams.

3. Method

a. Data

Buoy data are generally assumed to be of high quality and have been used in numerous studies for validation of model data (e.g., Janssen et al. 1997; Caires and Sterl 2003; Caires et al. 2004) and altimeter data (e.g., Tolman 2002; Queffeulou 2004; Faugere et al. 2006). Buoy data used in this work are obtained from two buoy networks: the National Data Buoy Center (NDBC) network operated by the United States and the Marine Environmental Data Service (MEDS) network operated by Environment Canada. Buoy data from the Australian network was considered but buoy locations were too close to the coast, or the reporting frequency was too low to be of value. With both selected networks, rigorous quality control is undertaken by these institutions, with bad data being either flagged or removed completely from the dataset. These networks are a dynamic set, with new buoys regularly being added and others being removed.

Altimeter data was obtained from several sources. Near-real-time data from both Jason-1 and Envisat are received at the Bureau through the Global Telecommunication System (GTS) and archived. Envisat data was extracted from this archive for the period from September 2004 to April 2006, with earlier data from April 2003 being obtained from CNES. Similarly, Jason-1 data was extracted for the period from September 2004 to the end of March 2006, with data from January 2002 obtained from Météo-France. For each altimeter, a month of overlapping data was analyzed to ensure consistency and accurate decoding from the two sources. This gave datasets covering a period of 3 yr for Envisat, and 4½ yr for Jason-1.

b. Method

Though a 50-km spatial proximity criterion, or thereabouts, is widely used for altimeter validation studies, it is often replaced by a latitude–longitude proximity to ease calculation (e.g., Janssen et al. 1997; Caires and Sterl 2003; Greenslade and Young 2004). The obvious shortcoming of this method is that zonal proximity varies with latitude. It could be argued, as is evident by its widespread use, that this will not greatly affect validation conclusions. However, using this technique, it was found that the latitude dependence of the error characteristics varied for each altimeter, a result arising from their differing inclination angles. Hence, a strict 50-km great arc proximity requirement was adopted.

At each buoy, consecutive altimeter observations crossing an area within a 50-km radius of the buoy location were grouped together. Passes took less than a minute to traverse this area, with each pass typically resulting in 15–18 individual observations that can be assumed to be simultaneous. These data were quality controlled by removing individual observations greater than ± two standard deviations away from the mean for that pass. Hourly buoy data were then linearly interpolated to the altimeter overpass time, with the additional criterion that there be at least one buoy observation within 1 h before and 1 h after the time of the altimeter overpass. This interpolated buoy data and the mean of the quality controlled altimeter observations made up a single collocation.

To eliminate interference from land, buoys were required to be greater than 50 km offshore. This condition is included because if buoys are too close to the coast, altimeter overpasses will generally occur seaward of the buoy location, thus sampling generally higher wave conditions (Greenslade and Young 2004). This will affect the collocation statistics, particularly the bias. Excluding buoys that are too close to the coast mitigates this problem. To ensure that 50 km was sufficiently strict, the buoys were divided into two groups: those between 50 and 150 km offshore and those greater than 150 km offshore. Collocation statistics were compiled for the two groups separately and the results were found to be consistent, suggesting that 50 km is a sufficient distance to avoid coastal contamination. The set of buoys included in this analysis are shown in Fig. 2.

Fig. 2.

Buoys from the NDBC are marked with squares and those from the MEDS network are marked with triangles.

Fig. 2.

Buoys from the NDBC are marked with squares and those from the MEDS network are marked with triangles.

During the early altimeter missions, errors associated with buoy data were small relative to those of the altimeter. As such, buoy data were generally regarded as “truth” and hence the correct procedure was to regress the altimeter data onto the buoy data—that is, perform an ordinary least squares (OLS) regression with the altimeter data as the independent variable and the buoy data as the dependent variable. As the relative error of altimeters has reduced over time, more sophisticated regression techniques have been applied to the problem, which account for errors in both variables (e.g., orthogonal regression, errors in variables, and principal component regression). These techniques generally require knowledge of the error variances of the two datasets. Caires and Sterl (2003) conclude that error variances for altimeter and buoy data are approximately equal. This has since been adopted by many others (e.g., Queffeulou 2003; Ray and Beckley 2003; Soukissian and Kechris 2007) and is assumed here. The derivation of appropriate corrections is calculated using total least squares (TLS) methods (also known as errors in variables). The merits of the TLS methods are discussed in many papers (e.g., Isobe et al. 1990; Soukissian and Kechris 2007).

The statistics used here are the bias, root-mean-square (RMS) difference, scatter index (SI), and linear correlation coefficient (R), defined as follows:

 
formula
 
formula
 
formula
 
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where Ai is the altimeter Hs, Bi is buoy Hs, N is the number of collocations, and an overbar represents the mean value.

4. Results

a. MEDS and NDBC buoy network differences

The initial collation of the collocated data revealed an apparent systematic difference between Hs estimates from the MEDS and NDBC buoy networks. Figure 3 shows scatterplots of collocations for both altimeters for both NDBC and MEDS buoys. With both satellites, it is clear that the MEDS buoys are underestimating buoy Hs measurements relative to the altimeter. Jason-1 shows little bias relative to NDBC buoys but a 28-cm bias relative to the MEDS buoys. Similarly for Envisat, a small bias of 3 cm relative to NDBC buoys compares to 28 cm for the MEDS collocations. This systematic underestimation appears to be linearly related to Hs. The SI indicates a similar amount of noise for comparisons with both altimeters, suggesting a comparable level of noise for the buoy networks relative to each other.

Fig. 3.

Scatterplots of collocated Hs observations for (a), (b) Jason-1 and (c), (d) Envisat for both the NDBC and MEDS buoy networks. (a), (c) Collocations with NDBC buoys only. (b), (d) Collocations with MEDS buoys only. The number of collocations in each 0.5-m bin has been contoured.

Fig. 3.

Scatterplots of collocated Hs observations for (a), (b) Jason-1 and (c), (d) Envisat for both the NDBC and MEDS buoy networks. (a), (c) Collocations with NDBC buoys only. (b), (d) Collocations with MEDS buoys only. The number of collocations in each 0.5-m bin has been contoured.

To quantify the difference between buoy networks, altimeter Hs estimates were taken as a reference against which buoy networks could be compared. Reference to the altimeter Hs as truth is deliberately avoided here. As discussed in section 3, neither buoy nor altimeter measurements can be regarded as truth and both must be assumed to contain errors. However, under the assumption that the altimeter provides self-consistent and repeatable measurements, it is valid to employ it as a common reference.

For each network, an OLS regression is performed with buoy data as the independent variable and the altimeter data as the dependent variable. This provides altimeter Hs as a linear function of both NDBC and MEDS buoys, given by Eqs. (11) and (12) for Jason-1 and (13) and (14) for Envisat, respectively,

 
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Then these expressions are equated to give a relationship between the two buoy networks. It is stressed here that these expressions do not present proposed corrections. Corrections are derived in the next section using TLS regressions, rather than the OLS regressions used here. Equating Eqs. (11) and (12), and (13) and (14) yields the following linear relationships between the MEDS and NDBC buoy Hs estimates as determined from Jason-1 (15) and Envisat (16) as a reference:

 
formula
 
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This suggests that MEDS buoys are underestimating Hs relative to NDBC buoys by about 10%. To test the significance of this difference, a set of normalized differences was calculated using collocations with each buoy network. Then a Student’s t test was applied to these two datasets to determine whether they had significantly different means. Results for each altimeter separately showed these means to be different at the 99% significance level in both cases.

This presents a significant point of note, which, to the authors’ knowledge, does not appear in the peer-reviewed literature. It has, however, been noted previously, with several conference proceedings indicating similar findings. Most recently, in examining TOPEX, and Jason-1 and Envisat wave heights, Queffeulou (2006) showed that the validation results are different according to the buoy network and in the same way for the three altimeters. For instance, the TOPEX-buoy mean bias is −0.01 m for the NDBC network and 0.19 m for the MEDS network, with similar results reported for the other satellites. Examining 2 yr of altimeter data, Cotton et al. (2004) also identify significant differences in validation results for Envisat and ERS-2 in reference to different buoy networks, with results again showing a greater altimeter bias when compared to MEDS buoys than for that of NDBC buoys. Similar results are also noted in the work of Challenor and Cotton (2003). They present altimeter verification results for all altimeters since Geosat versus several buoy networks. They show that the Japanese buoys measured Hs highest (+6% cf. NDBC), then the U.K. buoy network (+4%), then NDBC (as the reference), with the Canadian network buoys measuring the lowest (−5%). However, it is noted that the errors in these analyses were quite high because at the time, the Hs data supplied by the Met Office and Japan Meteorological Agency were only provided to the nearest 0.5 m. The size of the buoy platform was investigated as a possible cause of the discrepancy but no significant dependency was identified. They conclude that the differences are likely largely due to different reporting standards and quality control.

The source of this discrepancy remains unclear, although work is currently underway to investigate this further (J. Bidlot et al. 2006, unpublished manuscript). Initial investigations suggest that it is not environmental. Examining each buoy individually reveals consistent biases among buoys in the same network, regardless of their position. Buoy size is also unlikely to be the cause. Again, the consistency within each network, despite each being made up of buoys of various makes and sizes, suggests this is not a significant contributor. Although no evidence is presented here, it is suggested that differences in data processing are likely the primary cause.

Given the prevalence of the use of these buoys, often together as a presumed consistent dataset, a discrepancy of this magnitude warrants the attention not only of the data providers but also the community of users.

b. Validation results

To ensure a consistent reference dataset based on the discussion above, only NDBC buoys were used for altimeter validation. This choice was motivated by the NDBC dataset being much larger than the MEDS dataset. NDBC data has also been more extensively used for this type of work, thereby providing the logical choice in the interests of providing a consistent dataset across several satellites.

Using only NDBC buoys yielded 3452 collocations for Jason-1 and 2157 for Envisat. These collocated data points are shown in Fig. 4. Table 1 provides the proposed corrections and the statistics for both raw and corrected data.

Fig. 4.

Collocated satellite and buoy data, and the same data with the number of collocations in each 0.5-m bin contoured for (a),(b) Jason-1 and (c),(d) Envisat.

Fig. 4.

Collocated satellite and buoy data, and the same data with the number of collocations in each 0.5-m bin contoured for (a),(b) Jason-1 and (c),(d) Envisat.

Table 1.

Validation statistics for raw and linearly corrected data based on NDBC buoy comparisons for both Jason-1 and Envisat. For linearly corrected data, regression coefficients are given based on the relationship Hscorrected = αHsraw + β.

Validation statistics for raw and linearly corrected data based on NDBC buoy comparisons for both Jason-1 and Envisat. For linearly corrected data, regression coefficients are given based on the relationship Hscorrected = αHsraw + β.
Validation statistics for raw and linearly corrected data based on NDBC buoy comparisons for both Jason-1 and Envisat. For linearly corrected data, regression coefficients are given based on the relationship Hscorrected = αHsraw + β.

The uncorrected Jason-1 data shows a negative bias of only 1 cm and an RMS of 23 cm. The correction found with the TLS regressions results in no improvements to the RMS error, suggesting that Jason-1 does not require correction. As discussed in section 2, results inferred from Ray and Beckley (2003) and Queffeulou (2004) found small negative biases, whereas the findings of Abdalla (2006) suggest a small positive bias. Overall, all these studies propose minor corrections and are consistent with the findings of this work. These perspectives are also in line with those of Météo-France, who currently do not apply a correction to Jason-1 fast delivery data prior to assimilation.

For Envisat a small overall bias of 3.6 cm is present in the uncorrected data, with the altimeter overestimating Hs. It is apparent from Fig. 4 that Envisat is overestimating low Hs and underestimating high Hs. Linear correction produces more improvement than seen for Jason-1, decreasing the RMS by 7% and the SI by 6%.

In terms of the need for bias corrections, Jason-1 seems to outperform Envisat. However, Jason-1 is the noisier of the two, with the RMS difference being slightly higher than Envisat, despite its biases. Once Envisat is corrected, its RMS is 0.203 compared to 0.227 m for Jason-1. This relative noise between the two altimeters has also been noted by Abdalla et al. (2005). Similarly, several previous studies have noted an increased level of noise for Jason-1 relative to its predecessor TOPEX (e.g., Cotton et al. 2001; Ray and Beckley 2003; Queffeulou 2006). This suggests that the Jason-1 instrument, rather than differences in the data processing, is the cause of this difference.

Envisat appears to have shown significant improvements over its predecessor ERS-2, which suffered from systematic errors at low Hs (Greenslade and Young 2004). It is worth noting, however, that once a branched linear correction was applied, the RMS error reported by Greenslade and Young (2004) for ERS-2 was similar to that found here for the Envisat corrected data. This suggests that while the systematic biases are still being reduced with each altimeter mission, random error—or noise—is leveling out. This also suggests that a large proportion of the RMS error seen in these results is from the sampling issues discussed in section 2. The previously mentioned work of Monaldo (1988), upon which much of the validity of studies of this nature are predicated, states an expected buoy–altimeter RMS error of 0.4 m assuming perfect measurements from both instruments due to these sampling issues alone. The fact that these results are now better than these theoretical limits suggests that that estimate is in need of revision.

The apparent difference between the variance for each altimeter suggests that the assumption of equal error variances between buoy and altimeter, used in the TLS regressions, is perhaps a generous one. The use of a third independent dataset—model data, for example—could be used to overcome the need for such an a priori assumption. So-called triple collocation techniques—first used by Stoffelen (1998) in application to marine winds and later by Caires and Sterl (2003) and Janssen (2007) for the validation of waves—employ an iterative approach whereby a relative error between the three datasets is assumed then new estimates are calculated. This is then repeated based on these new estimates until stable values are reached. This is a powerful technique in the presence of a third dataset. Because the corrections found here are small, the assumption of equal error variance is unlikely to have a significant affect on results.

c. Wave state influence

Two main classes of gravity waves exist in the ocean, namely, wind wave (or wind sea) and swell. The former refers to young waves under growth, or in equilibrium with local wind, whereas the latter is defined as waves generated elsewhere that have propagated some distance. This section examines whether altimeter Hs estimates are influenced by the dominance of either wind sea or swell.

The idea that the wave state may have an influence on the accuracy of altimeter-derived Hs was examined by Janssen (2000) in relation to the ERS-2 FD data. He argues that the “peakiness” of the waves will affect the retrieval of altimeter wave heights, with the assumption of a Gaussian distribution of sea surface height being invalid for steep wave conditions. It was shown that by adjusting the ERS-2 Hs according to the Phillips parameter αp, better agreement could be found between altimeter and buoy Hs observations; αp is obtained from wave spectra by parameterizing the spectrum as

 
formula

where k is the wavenumber. This is speculative, however, and the authors note the need for further investigation. Challenor and Cotton (2003) also examined this idea by comparing the normalized altimeter–buoy error in Hs against wave age. In that study no relationship was found.

A similar approach is taken here, examining the direct effects of wave steepness. Specifically, significant wave steepness (Ss) (Tucker and Pitt 2001) is used, defined in terms of the integral wave characteristics, which are reported by the buoys,

 
formula

where Lp and Tp are wavelength and period, respectively, corresponding to the spectral peak frequency. This is also referred to as significant slope by Huang et al. (1981).

It is expected that the effect of wave state on altimeter Hs retrievals would apply similarly to both altimeters. Hence, the datasets have been combined here to increase the total number of observations and increase confidence in the results. Unless otherwise stated, altimeter data have been linearly corrected, with the corrections given in Table 1.

Figure 5 shows the mean bias (altimeter minus buoy) plotted against the wave steepness. The size of the ellipses gives the number of collocations in each bin. This shows a significant decreasing bias with increasing steepness, adding weight to the findings of Janssen (2000).

Fig. 5.

Altimeter bias as a function of wave steepness. The size of the ellipses gives the number of collocations in each bin.

Fig. 5.

Altimeter bias as a function of wave steepness. The size of the ellipses gives the number of collocations in each bin.

However, in examining this plot alone, some care must be taken in the attribution of the cause of these bias characteristics. Figure 6 shows mean Hs against wave steepness. It is apparent from this that larger waves tend to be steeper than smaller ones. As discussed in section 2, altimeters tend to contain wave height–dependent biases that are easily removed with linear corrections. Hence, it is possible that biases associated with wave height could be responsible—at least in part—for these wave steepness–dependent biases. In addition, use of Hs-corrected data here could be masking some of the wave steepness–dependent bias.

Fig. 6.

Same as in Fig. 5, but for mean Hs as a function of wave steepness. The size of the ellipses gives the number of collocations in each bin.

Fig. 6.

Same as in Fig. 5, but for mean Hs as a function of wave steepness. The size of the ellipses gives the number of collocations in each bin.

Figure 7 shows altimeter bias as a function of Hs (Fig. 7a) and wave steepness (Fig. 7b) for both corrected and uncorrected altimeter data. Focusing first on the Hs case in the uncorrected data, a positive bias is seen for low wave heights and a negative bias for high, as discussed in section 4. This bias is, not surprisingly, almost eliminated by the Hs-dependent correction. A qualitative assessment of how much of this bias is due to wave steepness can be gained by looking at how this correction affects the bias relative to wave steepness. Examining the second plot for the uncorrected data, a large positive bias is seen for relatively smooth waves, whereas steep waves yield a negative bias, a result that could be consistent with both trends having the same origins. However, correcting the data according to Hs does not eliminate the wave steepness bias. Although there is a reduction in the positive bias in the case of relatively smooth waves, little difference is seen for steeper waves, with a decreasing bias with increasing wave steepness remaining clearly evident. This suggests that altimeter Hs retrievals suffer from systematic biases associated with both wave height and wave steepness.

Fig. 7.

Altimeter bias as a function of (a) Hs and (b) wave steepness for both corrected and uncorrected altimeter data [note that the uncorrected data in (b) are the same as those of Fig. 5].

Fig. 7.

Altimeter bias as a function of (a) Hs and (b) wave steepness for both corrected and uncorrected altimeter data [note that the uncorrected data in (b) are the same as those of Fig. 5].

Partial correlation (Wilks 1995) provides a means of isolating these effects. Table 2 shows the Pearson correlation coefficients for the altimeter Hs bias against Hs and wave steepness, as well as the partial correlations of each variable with the effects of the other removed. With a correlation of −0.36, Hs-dependent bias is stronger than that apparent from wave steepness with a correlation of −0.21. Removing the effects of wave steepness has little affect on the Hs correlation. Removing the effects of Hs does reduce the steepness correlation somewhat, though it remains significant. This suggests that both effects apply.

Table 2.

Correlations (R) between altimeter Hs bias (altimeter minus buoy) and both Hs and wave steepness as well as partial correlations for each variable with the effects of the other removed.

Correlations (R) between altimeter Hs bias (altimeter minus buoy) and both Hs and wave steepness as well as partial correlations for each variable with the effects of the other removed.
Correlations (R) between altimeter Hs bias (altimeter minus buoy) and both Hs and wave steepness as well as partial correlations for each variable with the effects of the other removed.

There are obvious limitations to using mean wave characteristics to define wave steepness. This analysis would certainly benefit from the use of buoy data, which contains spectral information; however, it is left here for future work. Given this apparent wave steepness bias dependence, the opportunity also exists to extend this work to develop a correction scheme based on both wave height and wave steepness. Although peak period information would be required, which is not directly reported by altimeters, there is some work investigating the use of semiempirical functions to determine period information from altimeter data (e.g., Hwang et al. 1998; Quilfen et al. 2004) that shows good agreement with buoys. It is also possible to obtain this information from first-guess model estimates prior to assimilation, or simply using climatological values.

This work suggests that wave state has an influence on altimeter estimates of Hs. Although no explanation is put forward here, the hypothesis of Janssen (2000) regarding the breakdown of the assumption of a Gaussian distribution in steep wave conditions would certainly warrant further investigation. Given the potential value of a better understanding of wave steepness effects for both validation studies, and wave model assimilation, it is hoped that this initial work will stimulate further research in this important area.

5. Conclusions

Fast delivery Hs data from both the Jason-1 and Envisat altimeters have been validated against in situ buoy data. Jason-1 is found to be performing consistently throughout the range of wave heights and requires no correction. Consistent with previous work, it is found to be rather noisy, certainly more so than Envisat. The RMS difference between Jason-1 and buoy data is 0.227 m. Envisat is overestimating low Hs and underestimates high Hs. A linear correction reduces the RMS from 0.219 to 0.203 m, a 7% reduction. This lower-corrected RMS relative to Jason-1 is a reflection of the noise in the Jason-1 data.

A systematic difference in the Hs being reported by MEDS and NDBC buoy networks is noted. Using the altimeter data as a common reference, it is estimated that MEDS buoys are underestimating Hs relative to NDBC buoys by about 10%.

The influence of sea state on the accuracy of altimeter Hs retrievals has been examined. Specifically, the relationship between altimeter Hs bias and wave steepness is explored. This work suggests a positive bias is present in altimeter-reported Hs for smooth conditions and a negative bias for steep waves. This characteristic bias is found to be in addition to, rather than because of, Hs-dependent biases.

Future work will involve the use of bias-corrected (where appropriate) altimeter data for verification of the Bureau’s operational wave model. An extension to the wave model assimilation scheme (Greenslade and Young 2005), which currently assimilates Jason-1 data, to include Envisat-corrected data is also planned.

Acknowledgments

The authors thank a number of people for contributing to this work, including Jean-Michel Lefevre (Météo-France) and the European Space Agency for providing some Jason-1 and Envisat data, respectively; and Graham Warren and Mikhail Entel for their help in retrieving archived data at the Bureau. Comments made on the manuscript by Eric Schulz, Jeff Kepert, and three anonymous reviewers also were greatly appreciated.

REFERENCES

REFERENCES
Abdalla
,
S.
,
2006
:
Global validation of ENVISAT wind, wave and water vapour products from RA-2, MWR, ASA and MERIS.
ECMWF, ESA Contract Rep. 17585, 81 pp
.
Abdalla
,
S.
,
J.
Bidlot
, and
P.
Janssen
,
2005
:
Jason altimeter wave height verification and assimilation.
Proc. Seventh Int. Conf. on the Mediterranean Coastal Environment (MEDCOAST 2005), Kusadasi, Turkey, 1179–1185
.
Caires
,
S.
, and
A.
Sterl
,
2003
:
Validation of ocean wind and wave data using triple collocation.
J. Geophys. Res.
,
108
,
3098
.
doi:10.1029/2002JC001491
.
Caires
,
S.
,
A.
Sterl
,
J. R.
Bidlot
,
N.
Graham
, and
V.
Swail
,
2004
:
Intercomparison of different wind-wave reanalyses.
J. Climate
,
17
,
1893
1913
.
Carayon
,
G.
,
N.
Steunou
,
J.
Courrière
, and
P.
Thibaut
,
2003
:
Poseidon-2 radar altimeter design and results of in-flight performances.
Mar. Geod.
,
26
,
159
165
.
Challenor
,
P. G.
, and
P. D.
Cotton
,
2003
:
The joint calibration of altimeter and in situ wave heights.
Advances in the applications of marine climatology—The dynamic part of the WMO guide to the applications of marine climatology, WMO Tech. Doc. 1081, JCOMM Tech. Rep. 13, 139–148
.
Cotton
,
P. D.
,
D. J. T.
Carter
,
P. G.
Challenor
, and
V. Yu
Kareev
,
2001
:
A co-ordinated programme for global calibration/validation of altimeter sea state data.
AVISO Newsletter, Vol. 8, CNES, Ramonville St. Agne, France, 41–42
.
Cotton
,
P. D.
,
P. G.
Challenor
, and
J-M.
Lefevre
,
2004
:
Calibration of ENVISAT and ERS2 wind and wave data through comparison with in situ data and wave model analysis fields.
ENVISAT ERS Symp., Salzburg, Austria, European Space Agency SP-572. [Available online at http://earth.esa.int/workshops/salzburg04/papers_posters/3P09_1_cotton_341.pdf.]
.
Cotton
,
P. D.
, and
D. J. T.
Carter
,
1994
:
Cross calibration of TOPEX, ERS-1, and Geosat wave heights.
J. Geophys. Res.
,
99
,
25 025
25 033
.
Desai
,
S. D.
, and
P.
Vincent
,
2003
:
Statistical evaluation of the Jason-1 Operational Sensor Data Record.
Mar. Geod.
,
26
,
187
199
.
Faugere
,
Y.
,
J.
Dorandeu
,
F.
Lefevre
,
N.
Picot
, and
P.
Femenias
,
2006
:
Envisat ocean altimetry performance assessment and cross-calibration.
Sensors
,
6
,
100
130
.
Greenslade
,
D. J. M.
, and
I. R.
Young
,
2004
:
A validation of ERS-2 Fast Delivery Significant Wave Height.
Bureau of Meteorology Research Centre, BMRC Research Rep. 97, 35 pp
.
Greenslade
,
D. J. M.
, and
I. R.
Young
,
2005
:
The impact of inhomogenous background errors on a global wave data assimilation system.
J.Atmos. Ocean Sci.
,
10
,
61
93
.
Huang
,
N.
,
S.
Long
, and
L.
Bliven
,
1981
:
On the importance of the significant slope in empirical wind-wave studies.
J. Phys. Oceanogr.
,
11
,
569
573
.
Hwang
,
P.
,
W.
Teague
,
G.
Jacobs
, and
D.
Wang
,
1998
:
A statistical comparison of wind speed, wave height, and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region.
J. Geophys. Res.
,
103
,
10 451
10 468
.
Isobe
,
T.
,
E. D.
Feigelson
,
M. G.
Akritas
, and
G. J.
Babu
,
1990
:
Linear regression in astronomy.
Astrophys. J.
,
364
,
104
113
.
Janssen
,
P. A. E. M.
,
2000
:
ECMWF wave modeling and satellite altimeter wave data.
Satellites, Oceanography, and Society, D. Halpern, Ed., Oceanography Series, Vol. 3, Elsevier, 2639–2640
.
Janssen
,
P. A. E. M.
,
2007
:
Progress in ocean wave forecasting.
ECMWF Tech. Memo 529, 29 pp
.
Janssen
,
P. A. E. M.
,
B.
Hansen
, and
J. R.
Bidlot
,
1997
:
Verification of the ECMWF wave forecasting system against buoy and altimeter data.
Wea. Forecasting
,
12
,
763
784
.
Ménard
,
Y.
, and
Coauthors
,
2003
:
The Jason-1 Mission.
Mar. Geod.
,
26
,
131
146
.
Monaldo
,
F.
,
1988
:
Expected differences between buoy and radar altimeter estimates of wind speed and significant wave height and their implications on buoy altimeter comparisons.
J. Geophys. Res.
,
93
,
2285
2302
.
Queffeulou
,
P.
,
2003
:
Cross validation of ENVISAT RA-2 significant wave height, sigma0 and wind speed.
Cross-Calibration and Validation Team Plenary Meeting #17 Final Rep., 7 pp
.
Queffeulou
,
P.
,
2004
:
Long-term validation of wave height measurements from altimeters.
Mar. Geod.
,
27
,
495
510
.
Queffeulou
,
P.
,
cited
.
2006
:
Altimeter wave height validation: An update.
Ocean Surface Topography Science Team (OSTST) Meeting, Int. Doris Service (IDS) Workshop, Venice, Italy, ESA, CNES. [Available online at http://argonautica.jason.oceanobs.com/documents/swt/posters2006/queffeulou.pdf.]
.
Quilfen
,
Y.
,
B.
Chapron
,
F.
Collard
, and
M.
Serre
,
2004
:
Calibration/validation of an altimeter wave period model and application to TOPEX/Poseidon and Jason-1 altimeters.
Mar. Geod.
,
27
,
535
549
.
Ray
,
R.
, and
B.
Beckley
,
2003
:
Simultaneous ocean wave measurements by the Jason and Topex satellites, with buoy and model comparisons.
Mar. Geod.
,
26
,
367
382
.
Resti
,
A.
,
J.
Benveniste
,
M.
Roca
,
G.
Levrini
, and
J.
Johannessen
,
1999
:
The Envisat Radar Altimeter System (RA-2).
ESA Bull.
,
98
,
94
101
.
Soukissian
,
T.
, and
C.
Kechris
,
2007
:
About applying linear structural method on ocean data: Adjustment of satellite wave data.
Ocean Eng.
,
34
,
371
389
.
Stoffelen
,
A.
,
1998
:
Toward the true near-surface wind speed-error modeling and calibration using triple collocation.
J. Geophys. Res.
,
103
,
7755
7766
.
Tolman
,
H. L.
,
2002
:
Validation of WAVEWATCH III version 1.15 for a global domain.
NCEP Tech. Note 213, 33 pp
.
Tucker
,
M.
, and
E.
Pitt
,
2001
:
Waves in Ocean Engineering.
Elsevier, 521 pp
.
Wilks
,
D. S.
,
1995
:
Statistical Methods in the Atmospheric Sciences: An Introduction.
Academic Press, 467 pp
.

Footnotes

Corresponding author address: T. H. Durrant, Centre for Australian Weather and Climate Research, Bureau of Meteorology, GPO Box 1289, Melbourne, VIC 3001 Australia. Email: t.durrant@bom.gov.au