Phil Woodworth, Christian Le Provost and C.K. Shum
6 February 1995
BACKGROUND
In reference to the broadcast messages to the T/P SWT by L. Fu (16 Dec 94) and by P. Woodworth et al. (25 Dec 94), the tide model recommendation for T/P GDR is being conducted in two phases. The interim phase is the subject of this report. The second phase will evaluate and recommend a tide model by the May SWT Meeting from all available tide models ('black box' modules and data files) submitted to the T/P Tides Committee by 15 March 1995. The current activity intends to recommend a deep ocean (depth > 800 m) tide model, in addition to the consensus recommendation of the Grenoble FES94.1 model as the shallow (depth < 800 m) ocean tide model. The candidate models for the interim phase recommendation is discussed in the next section.
CANDIDATE TIDE MODELS
The identified candidate tide models to be evaluated for the interim phase are: Desai/Wahr (CU), Grenoble (FES94.1), Egbert/Bennett/Foreman TPXO2 (OSU), Sanchez/Pavlis (GSFC94A), Ray/Sanchez/Cartwright (RSC), and Eanes (CSR2.0) models. Three additional models were evaluated for some of the criteria in the study: the Schrama/Ray model (SR94), the Andersen-Grenoble (AG) model and an revised version of RSC (RSC2.0) model. The SR94 model and its updated version were presented at the T/P SWT meeting and has 4 major tidal harmonics plus Schwiderski for the other major tidal lines. The AG model adjusted M2 and S2 of the Grenoble (FES94.1) model using T/P data. It was presented at the T/P SWT meeting and has been available since mid-December 1994. The RSC2.0 model provided 'minor' adjustments to the RSC model (with no additional T/P data) in the tropical Atlantic off NE Brazil, in the N. Atlantic near S. Greenland, Gulf of Alaska, and along the coast of S. Chile. These models, some of which have been published, and used techniques which can be categorized into pure hydrodynamical, empirical, assimilation methods. All of the models were computed using GDR orbit/data, except CSR2.0 which used an orbit computed with an improved dynamical tide model and gravity model (JGM-3). The specific descriptions of techniques and data used in producing each of these models are omitted here.
EVALUATION TEAM
The evaluation work was performed with volunteering help from a group of individuals, including O. Andersen, R. Eanes, D. Chambers, X. Li, F. Lyard, J. Molines, M. Parke, J. Ries, D. Stammer, and C. Tierney. In particular, O. Andersen, J. Molines, M. Parke and D. Stammer have been very helpful in performing data analysis and providing results and insight to the evaluation process. Their efforts are gratefully acknowledged. The evaluation is based primarily on email Jexchanges and on reports/notes, e.g., Andersen et al., report (Nov. version), and on relevant papers published in the T/P Special Issue.
EVALUATION METHOD AND DATA
The tide models were evaluated by (1) comparing tidal height predictions to tidal constants from pelagic tide gauge data (islands and coastal gauges), (2) comparing geocentric tidal height predictions to T/P altimeter crossover residuals (deep ocean, i.e., depth > 800 m, and shallow ocean, depth <= 800 m), (3) comparing sea level anomalies using different models in the tropical Pacific Ocean, (4) comparing with sea level time series from tide gauges (island/pelagic and coastal gauges) [evaluation results provided by J. Molines], and (5) comparing sea level spectra computed using different tide models and global T/P sea level time series [results provided by D. Stammer]. An additional evaluation is conducted for (5) comparing the sea level spectra computed using the GDR orbit (JGM-2) and using the improved JGM-3 orbit for the CSR2.0 tide model. The last evaluation was conducted to assess the effect of the improved orbit on tide model solutions.
The tide gauge data used are subsets of the 103 gauge pelagic data set compiled by C. Le Provost et al. O. Andersen used a subset consisting of 95 gauges [Andersen et al. report, Nov. 1994 version] and M. Parke used a subset consisting of 86 gauges for some of their evaluations. The Parke data set was created by editing the 103 gauge set to remove all shallow water bottom pressure gauges, all short island records and all island gauges where the geometry of the gauge location and magnitude of the M2 tide suggested differences between the gauge and surrounding deep water are > 3 cm rms. J. Molines used filtered hourly tide gauge sea level time series for his study which consists of 65 island/pelagic gauges and 19 coastal gauges collected through WOCE/GLOSS, TOGA, POL and LEGI data centers from 1985-1994. D. Chambers used T/P cycle 74 sea level anomalies data in the tropical Pacific and Indian Ocean to examine several tide models. C. Shum used crossover residuals computed with the JGM-3 orbit and limiting the crossover time differences to within 3.5 days for T/P (130 days), ERS-1 (140 days), and Geosat (105 days), to test the candidate models. D. Stammer used more than two years (77 cycles) of global T/P sea level data to perform his evaluation of tide models. J. Ries provided a set of JGM-3 orbit corrections (to the GDR orbit) to enable some of the sea level tests to be conducted.
EVALUATION CRITERIA
A list of evaluation criteria was chosen during the T/P SWT meeting: including criteria such as the tide model must include at least 8 major tidal lines and/or use orthotides representation; the model must be defined globally and include coastal/shallow/inland seas; and the model must 'pass' minimum tide gauge and crossover residual comparison tests. In this study, we attempt to 'rank' tide models for each one of these tests and perform qualitative and other analyses to hope to distinguish between the models which are ranked closer to each other. Other criteria such as efficiency of coding is considered. However, there is not an objective standard at present to test the computational efficiency and ease of use for these tide models.
RESULTS
Tide Gauges Comparisons
Table 1 and Table 2 contains results of comparison with the 95 and 86 pelagic tide constants for 4 major constituents. The 86 gauge comparison can be considered a test for performance of the tide models in relatively deep oceans. The models tested are also ranked accordingly in both Tables with the lowest residual rss being the highest rank model. The differences between the CU, RSC, RCS2.0 and the CSR2.0 models may be statistically insignificant for the 95 gauge comparison case. The 95 gauge test favors the SR94 and the AG models. Using the 86 gauge case, the differences between the models seem to be statistically insignificant with the exception of FES94.1 model. The 86 gauge comparison favors the CU and the AG models (the SR94 model was not tested in this case).
Table 1. Comparison with 95 Tide Gauges
Model RSS of 4 Major Constituents (cm)
----- --------------------------------
SR94# 2.69
AG* 2.73
CU 2.83
RSC 2.87
RSC2.0* 2.88
CSR2.0 2.90
GSFC94A 2.98
OSU 3.00
FES94.1 3.72
*Models not among the original 6 candidate models.
#Not considered because it contains less than 8 major constituents.
Table 2. Comparison with 86 Tide Gauges
Model RSS of 4 Major Constituents (cm)
----- --------------------------------
CU 2.26
AG* 2.32
OSU 2.37
RSC 2.39
GSFC94A 2.39
CSR2.0 2.55
FES94.1 3.34
*Models are among the original 6 candidate models.
Tide Gauge Time Series Comparisons J. Molines performed comparisons of predicted tidal heights from tidal models to filtered hourly tide gauge sea level time series for a set of island/pelagic gauges and coastal gauges. Table 3 presents the results of the ranking of the models based on scores according to appropriate variance reduction using 65 island tide gauges. The higher the score, the closer is the comparison of tidal heights predicted by the tide model to the tide gauge time series. The RSC (or RSC2.0) tide model is undefined in some of the 65 gauge locations. The GSFC94A tide model was not tested because of an apparent inconsistency in the coding and a bug-fix version of the software was not available at the time of the evaluation. Again, Table 3 shows that all models except FES94.1 are quite close in ranking statistically.
Table 3. Comparison with 65 Island Tide Gauges Model Score ----- ----- AG* 36 CSR2.0 35 OSU 35 RSC 33 RSC2.0* 33 CU 32 FES94.1 29 *Models not among the original 6 candidate models.Crossover Comparisons
Although the shallow ocean and global ocean cases were also conducted, the deep ocean comparison case is shown here. Table 4 shows the results of comparing deep ocean T/P altimeter crossover residuals computed using the JGM-3 orbits and with different tide models. Table 4 shows the crossover residual rms with the models ranked accordingly, i.e., the smallest crossover rms has the highest rank for the model. This test favors CSR2.0, CU, and RSC models.
Table 4. T/P Crossover Residual Comparisons Model Rms of Deep Ocean Crossovers (cm) ----- --------------------------------- CSR2.0 6.6 CU 6.7 RSC 6.9 RSC2.0* 6.9 OSU 7.5 GSFC94A 7.8 FES94.1 8.2 AG* 8.2 *Models not among the original 6 candidate models. Note: Some models (e.g., RSC2.0 and GSFC94A) are not defined in certain regions and are therefore not tested in these regions.Sea Level Anomaly Comparisons
This test was conducted on the CSR2.0, CU, and the RSC models in the tropical Pacific using T/P cycle 74. The sea level anomalies computed using CSR2.0, RSC and CU models have rms differences of about 7 cm. Large-scale features in the CSR2.0 and RSC sea level anomalies agree very well. The CU sea level shows small scale variations which are not present in the RSC and CSR2.0 sea level anomaly maps. Spectral Analysis of Global Sea Level
D. Stammer performed this test and the results of 4 cases are presented in Table 5. In each case, tide models and different orbits were used to compute the sea level and the variances for each case were computed and ranked accordingly. The CSR1.4 and the CU models were computed using JGM-2 orbits, and the CSR2.0 model was computed using JGM-3 orbits. Table 5 shows that relative sea level variance reduces with the improvement of the tide models (CSR1.4 to CSR2.0) and the orbits (JGM-2 to JGM-3). The orbit difference variance is 6.8 cm^2, but not all of this are affecting tides or sea level differences, as the majority of the variances is due to gravity model differences, which are eliminated in sea level averaging. It is encouraging to note the respective improvement when the improved orbit is used. This test favors the CSR2.0 model.
Table 5. Variance of Sea Level Averaging
Model Variance (cm^2)
----- ---------------
CSR2.0/JGM3 131.85
CSR2.0/JGM2 133.74
CSR1.4/JGM2 135.10
CU/JGM2 136.19
STATISTICAL RANKING OF TIDE MODELS In light of the fact that some of the above tests show different ranking for different tide models, a simple averaging technique suggested by M. Parke is used here to quantify some of the tests conducted. The tide gauge test cases (the 95- and 86-gauge cases) are combined into one ranking by averaging the two rankings. The rankings for tide gauge sea level test and for deep ocean crossover test were also tabulated, and added to the combined tide gauge ranking, to form a composite ranking for all the tide models (Table 6). The SR94 model is not considered here since the model does not contain at least 8 major constituents. Note that there is no weighting used for each of the tests (two tide gauge test and one altimeter test). In this case, the lower the number, the better is the performance of the model and the higher is the ranking. Table 6 shows that the CSR2.0 and the CU models tie for first place with a composite ranking of 7.5.
Table 6. Composite Ranking of Tide Models Model Combined TG TG Sea Level Crossover Composite Ranking ----- ----------- ------------ --------- ----------------- CSR2.0 4.5 2 1 7.5 CU 1.5 4 2 7.5 AG* 1.5 1 6 8.5 RSC2.0* 3.5 3 3 9.5 GSFC94A 4.5 - 5 >9.5# OSU 4.5 2 4 10.5 FES94.1 6.5 5 6 17.5 *Models not among the original 6 candidate models. #Tide gauge sea level test was not performed for this model, therefore, the composite ranking for this model will be worse than 9.5 if this test was performed. Note: Some models (e.g., RSC2.0 and GSFC94A) are not defined in certain regions and are therefore not tested in these regions.SUMMARY AND RECOMMENDATIONS
This report summarized the activities conducted by the TOPEX/POSEIDON (T/P) Tides Committee for the action item issued during the T/P SWT December 94 Meeting to provide an interim recommendation of the T/P ocean tide model by 31 January 1995. During the SWT Meeting, six models were identified as the candidates for this interim recommendation exercise. Three additional models were evaluated for some of the test cases as well. They are the Andersen-Grenoble (AG) model, the RSC December (RSC2.0) model, and the SR94 model. The SR94 model was eliminated because it does not satisfy the criteria of including at least 8 major tidal constituents. We choose to consider the AG and the RSC2.0 models for this exercise. The Tide Committee has already reached a consensus to recommend the FES94.1 model for coastal ocean and geodetic applications. The objective in this report is to provide an interim recommendation of a model for deep ocean applications. Some of the candidate models (e.g., RSC2.0 and GSFC94A) are not defined in the Mediterranean Sea nor in some of the coastal areas. The tide gauge tests (pelagic and time series analysis) provide a ranking for several models which favors the AG, CU, and the RSC2.0 models. The sea level anomaly test in tropical Pacific for the models compared (RSC, CSR2.0 and CU) favors the RSC and the CSR2.0 models. The crossover test favors the CSR2.0, CU, OSU, and the RSC models. It is curious that the AG model performs poorly in the crossover test, while it performs well in the tide gauge tests. A composite ranking for all the tide models was computed by summing up the rankings for the tide gauge test, the tide gauge sea level test and the crossover test. This simple statistical exercise results in the CSR2.0 and the CU models tied for first place. The sea level variance test for these two models were performed and the results favors the CSR2.0 model over the CU model. The CSR2.0 model is the only model computed using the improved orbit, and further analysis indicates the use of inconsistent orbits (JGM-2) and tide model (CSR2.0 model was computed using JGM-3 orbits) did not prevent it to perform better than the CU model in the sea level variance test. An additional test performed using the improved JGM-3 orbit along with the consistent tide model (CSR2.0) indicates further reduction in the sea level variance.
In summary, the interim recommendation for the T/P tide model for deep ocean applications is the CSR2.0 model. However, the reason for this selection is not overwhelming. Results conducted also show a reduction in sea level variances (3.25 cm^2) when the improved JGM-3 orbit was used, along with a consistent tide model developed using this orbit (CSR2.0). It is further recommended that the appropriate loading tides for CSR2.0 model to be computed and make available, and that a proposal of "patching" the deep ocean T/P tide model (CSR2.0) and the shallow ocean T/P tide model (FES94.1) into a single software module be studied. The various techniques developed by individuals during this exercise will be used and expanded upon in the next phase of tide model evaluations.