The KMS04 Multi-Mission Mean Sea Surface.

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1 The KMS04 Multi-Mission Mean Sea Surface. Ole B. Andersen, Anne L. Vest and P. Knudsen Danish National Space Center. Juliane Maries Vej 30, DK-100 Copenhagen, Denmark. Abstract. The KMS04 Mean Sea Surface (MSS) is the physically observed time-averaged height of the ocean s surface derived from a total of 5 different satellites and a total of 8 different satellite missions like the T/P, T/P Tandem Mission, ERS1 ERM+GM, ERS ERM, GEOSAT GM, and GFO-ERM data. For all mission the MSS have been derived with what is believed to be the best available geophysical and range corrections. JASON-1 data have been used to validate and compare various recent mean sea surface models. An intercomparison with existing mean sea surface models demonstrate that parts of the difference between the KMS04 mean sea surface and older mean sea surfaces can actually be subscribed to the way that interannual ocean variability have been folded into the different mean sea surfaces. Keywords: Satellite Altimetry, Mean sea surface, Inter-annual ocean variability. signals like the large ENSO/El-Nino event will be visible to a larger or smaller extend in these temporal averaging used to derive these different MSS. Table 1. Recent mean sea surfaces models. GSFC (Wang, 000; 001), CLS (Hernandez and Schaeffer, 00), KMS (Andersen and Knudsen, 001), NTU (Hwang et al, 00), CSR (Kim et al., 1995), OSU (Rapp and Yi, 1997) Model KMS04 NCU01 CLS01 KMS01 GSFC00 / GSFC98 CLS-SHOM 98, KMS98 CSR95 OSU95 T/P data Years 9 (93-01) 7.5 (93-00) 7 ( (93-99) 6 (93-98) (93-94) 1 (93-93) Res (min) Introduction The mean sea surface is one of the key parameters in geodesy and physical oceanography. It is the physically observed time-averaged height of the ocean s surface. In principle a complete separation of the oceans mean and variable part requires uninterrupted infinite sampling in both time and space. The challenge in mean sea surface mapping from satellite altimetry is to achieve the most accurate filtering of the temporal variability due to the limited time span of the observations along with resolving the highest spatial resolution. Over the past decade several mean sea surfaces have been published. A summary of these recent mean sea surfaces is shown in Table 1. These global mean sea surfaces are all based on different time-epoch for the TOPEX/POSEIDON (T/P) altimetry used in their derivation. Consequently, large inter-annual ocean All available MSS models have been derived by merging repeat observations (i.e., T/P) with nonrepeating data from the ERS-1 and Geosat Geodetic Mission (GM). Ocean variability is efficient averaged out along the Exact Repeat Mission (ERM) s. However, only sparse information about the mean is available in-between these tracks. Therefore the ERM mean tracks are merged with the non-repeating geodetic mission data providing very dense and homogeneous coverage. The non-repeating GM observations contains the full oceanographic signal which needs to be removed using i.e. crossover techniques.. Satellite Altimeter Data. The satellite altimeter data is a combination of ERM data from the Ocean Altimeter pathfinder Project and

2 non-repeating GM data from the Radar Altimetry Data Base (RADS) maintained at the Department of Earth Observation and Space Systems, TU Delft (Scharroo, 003). Both archives strive to provide the most up to date altimetric products with the best available suite of corrections applied. For details se (Pathfinder), or /altim/rads/rads.shtml (RADS). Table. Summary of all the datasets used to compute the KMS04 Mean Sea Surface Model. The standard deviation reflects the accuracy on the data and the number of available repeats. Satellite Time Period Std. Dev. (cm) / number of repeats T/P mean (cyc ) ERS mean (cyc. 1-74) y ears years T/P TDM mean GFO mean ERS-1 GM days Geosat GM years Ground Track Spacing 0.6 / km 1.5 / km.0 / km.0 / km 6.5 / 1 8 km 7.0 / 1 6 km Table summarizes the altimetric data used to derive the KMS04 mean sea surface along with the spatial coverage, standard deviation, and ground-track spacing. Version 9. of the NASA Pathfinder T/P dataset was used. In this dataset the TOPEX Microwave Radiometer (TMR) drift have been corrected and the sea state bias have been recomputed for side A and B employing Gaspar BM4 parametric algorithm (Gaspar et al., 1994). For more than nine years T/P produced superior and uninterrupted mapping of the sea surface along its ground-tracks, before it was shifted into its new interlaced ground-tracks in August 00. All ERS and GFO ERM data was therefore adjusted into the T/P reference frame employing technique similar to LeTraon, et al. (1998). Version 5.4 of the ERS- data and version 1.3 of the GFO datasets were used. These had radial offsets of 6.5 cm and 5.5 cm applied for ERS- and GFO respectively. All altimetric observations were processed using a slightly modified version of the GOT00. ocean tide model. (Ray, 1999). The modified version (called GOT00.X) is extended in coverage towards and onto the coast to avoid coastal observations being erroneous or being edited out because of no ocean tide correction. For ERS-1 observations, the Microwave Radiometer (MWR) based troposphere and ionosphere range corrections was substituted by the ECMWF model correction to avoid degradation and data-loss close to the coast. The physical MSS can be transformed into the somewhat hypothetical IB corrected MSS. For many oceanographic applications it is desirable to have the ocean static response to the atmosphere removed. To account for this effect the KMS04 MSS have been derived as both a physical MSS and an IB corrected MSS based on a global mean pressure of 1013 millibars (Dorandeau, and Le Traon, 1999). 3. The KMS04 Mean Sea Surface The KMS04 MSS was derived using a 3-steps remove/restore procedure designed to map the different spatial scales in the MSS. Initially the long wavelength are mapped (longer than 500 km). Then the medium wavelength ( km) are mapped and added and finally the fine scales (0-100 km) are mapped and added to give the final MSS. 3.1 Long wavelength MSS. The long wavelength part of the MSS model was derived from T/P ERM data supplemented with the adjusted ERS- data outside 66 latitudes. A minimum of 00 T/P observations was required at each georeferenced observation point. The analysis was carried out by solving for four parameters in each point representing the largest variation in sea level. These are the mean value, the trend (sea level change over 9 years) and the annual variations like: h obs = h 0 + h 1 t+h cos(? ann t) +h 3 sin (? ann t), where? ann is the annual frequency. The estimated mean value h 0 was interpolated onto a regular grid of resolution 0.15 using least squares collocation and a second-order Gauss-Markov covariance

3 function with a correlation length of 500 km taking the error on the mean track observations in Table 1 into account. 3. Medium wavelength contribution At this stage the globe is divided into 8 latitude by 0 longitude blocks with all ERM mean s being individually fitted to the low-resolution mean sea surface by estimating bias and tilt terms to each track (Knudsen, 1993), thus removing all signals with a wavelength longer than about 8. Within 30 of the Equator the GM data were introduced as 0.5 spatial averaged values to provide observation in-between the ground-tracks of the ERM data. Inclusion of the GM data highly improved the representation of the shorter wavelength of the MSS close to the Equator where the tracks become almost North-south going. This step contributes up to 3 meters to the MSS over various seamounts in the western Pacific Ocean. 3.3 High resolution Mean Sea Surface. Using all available altimetric ERM+GM observations the final high-resolution part of the MSS is then computed and added. The process is similar to deriving the medium wavelength MSS above, but this time the block size is decreased to latitude by 10 longitude, and the computation is performed in a remove restore way to the medium wavelength MSS. All tracks were crossover adjusted, and to avoid problems with rank deficiency, a minimum variance criterion was applied. Data are then interpolated onto a regular grid with a resolution of 1/30 by 1/30 ( min) using similar techniques to Andersen and Knudsen (1998) Figure 1. Estimated mapping error for the KMS04 Mean sea surface in the Northeast Atlantic region. The location of the highly accurate T/P track is clearly seen. The colorscale is in meters. The estimated mapping error for the high-resolution mean sea surface is shown in Figure 1 for the northeast Atlantic Ocean. The mapping error is the combined mapping error of all three steps in the mean sea surface procedure. The location of the highly accurate T/P mean tracks in clearly shown along with the transition to the less accurate zone north of 66N derived from ERS- data. On average the mapping error is around 4-5 cm globally. 4 Inter-annual variability and sea surface trend associated with KMS04. The simultaneous four parameter estimation of mean value, trend and annual signal enables the study of inter-annual variability during the 9 years of T/P data relative to the KMS04 MSS and how these are mapped into the MSS (Rapp and Yi, 1997).

4 CLS GSFC Figure. Difference between the CLS01 and KMS04 MSS in the upper figure, and the difference in inter-annual sea level signal computed over 7 and over 9 years in the lower figure. The colorscale is in cm. Figure shows the difference between the CLS01 and KMS04 MSS. The difference between the two MSS are generally very few centimetres even though the data have been processed by different institutions. The large discrepancies seen at high latitude most likely stems from a combination of the amount of ERS-1+ data entering the solution, and the fact that data in the KMS04 have been iterative edited/removed (Andersen and Knudsen 005) relative to the GRACE geoid GGM01. The lower part of Figure shows the difference in the T/P derived mean sea-surface height computed over 7 and 9 years corresponding to the two periods used to compute the CLS01 MSS ( , 7 years) and the KMS04 ( , 9 years). Besides a constant offset of less than 1 cm, the major difference can be subscribed to the averaging of inter-annual sea level variations over 7 years versus 9 years. This is particularly clear in the ENSO region of the tropical Pacific Ocean. 5 Validation with JASON-1 data The CLS01, GSFC00 and the KMS04 mean sea surfaces have been validated against a -year mean Jason-1. This data covers cycle 1-76 (January 00 to January 004) and is not a subset of any of the three mean sea surfaces periods. The comparison has been performed along the Jason-1 track, extending from the Hudson Bay to Antarctica running through the whole Atlantic Ocean. Table 3. Evaluation of the CLS01, GSFC00 and the KMS04 mean sea surfaces with a -year mean Jason-1. The 154 mm offset between JASON-1 and T/P has been applied prior to the comparison. RMS Mean Standard Deviation KMS The validation in Table 3 does not gives any conclusive signs to which MSS is more accurate than the other. It is important to notice that MSS are in principle only representative of the period in which data have been averaged (1993 to max 001). And as such, all three mean sea surfaces equally well represents a year mean from Conclusions The KMS04 9-year Mean Sea Surface (MSS) have been presented, described and validated in this paper along with its error file. A comparison with other existing mean sea surface models revealed that the difference is largely dominated by the temporal averaging of large interannual signals. In particular the averating of the large El Nino event in could clearly be seen in the difference between a 7-year mean used to derive the CLS MSS and the 9-year mean used to derive the KMS04 mean sea surface. Comparisons between the three most recent mean sea surfaces (KMS04, CLS01 and GSFC00) yielded virtually identical comparisons with more recent JASON-1 mean s. Acknowledgment. This analysis is partly sponsored by the Danish Research Agency and the EU and is a contribution to the GOCINA project. The authors would like to thank Brian Beckley for providing the best available Pathfinder altimetry and Remko Scharroo for providing the RADS software and data. Information. The KMSS04 mean sea surface and associated inter-annual correction is available from the authors on CD- ROM (oa@spacecenter.dk) or from anonymous ftp at: ftp://ftp.spacecenter.dk/pub/mssh. References Andersen, O. B. Shallow water tides on the northwest European shelf from TOPEX/POSEIDON altimetry. J. Geophys. Res, 104, , Andersen O. B. and P. Knudsen, Global Marine Gravity Field from the ERS-1 and GEOSAT Geodetic Mission Altimetry, J. Geophys. Res., 103(C4), , Andersen, O. B. and P. Knudsen, The role of Satellite Altimetry in Gravity Field modelling in Coastal Areas, Phys. Chem. Earth, 5 (1), 17-4, 000.

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