Connecting Land and Sea Vertical Datums: A Data Evaluation for Developing Australia’s AUSHYDROID Model

Figures & data

Figure 1. Reference datums/surfaces for land and sea in relation to each other: ocean’s time-mean dynamic topography (MDT), mean sea level (MSL; at the tide gauge) or mean sea surface (MSS; in the open ocean), lowest astronomical tide (LAT), tide gauge zero (TGZ), chart datum (CD), ellipsoidal height ($\mathrm{h}$), geoid-ellipsoid separation (N) and physical height (H) on the land vertical datum. Note that $\mathrm{h}=\mathrm{H}+\mathrm{N}$ on land, and $\mathrm{h}=\mathrm{\text{MDT}}+\mathrm{N}$ over the ocean.

Figure 2. Locations of 10 WADoT tide gauges, 16 PPA tide gauges and 116 AHO tide gauges. The boxes (red in the online version) on the main plot at Ashburton, Dampier and Port Hedland relate to the inset boxes in the bottom row, showing the PPA tide gauges at these locations (numbered as per Table 1).

Figure 3. Summary of 10 WADoT and 16 PPA tide gauge observations for the WA study area. The circle size increases with more observations for a given year (e.g. due to an increase in sample rate). Missing circles are where there are no observations – small circles may represent some data missing and/or a lower sampling rate for the given year. Locations for these sites are shown in Figure 2.

Table 2. Details of the different models tested in this study to provide modelled ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ to compare with tide gauge ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ at the coast.

Model	Spatial res	Period	Source/availability (Download location)	References
MSS
CNES-CLS 2015 MSS	1’	1993–2012	Aviso+ at https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/mss.html	Schaeffer et al. (2016a, 2016b)
DTU18 MSS	1’	1993–2017	DTU at ftp://ftp.spacecenter.dk	Andersen et al. (2018b, 2018c)
MDT
CNES-CLS18 MDT	7.5’	1993–2017	Aviso+ at https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/mdt.html	Mulet et al. (2021)
DTU19MDT	1’	1993–2018	DTU, ftp://ftp.spacecenter.dk/pub/dtu19/mdt	Andersen and Knudsen (2009)
DTU15MDT	1’	1993–2014	DTU, ftp://ftp.spacecenter.dk/pub/dtu15/1_min	Andersen and Knudsen (2009)
Ocean tide
TPXO9v5	2’	1999–2010	Y. Erofeeva, pers. comm. (2021)	Egbert and Erofeeva (2002), Egbert, Erofeeva, and Ray (2010)
FES2014b	3.75’	1999–2014	Aviso+ at https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html	Lyard et al. (2021)
Geoid
AGQG 2017	1’	Variable	Curtin University	Featherstone et al. (2018)
EGM2008	5’	Variable	http://icgem.gfz-potsdam.de/home	Pavlis et al. (2012)
XGM2019e_2159	5’	Variable	http://icgem.gfz-potsdam.de/home	Zingerle et al. (2020)
EIGEN-6C4	5’	Variable	http://icgem.gfz-potsdam.de/home	Foerste et al. (2014)

Note that geoid models with 5’ spatial resolutions are computed from global gravity models to spherical harmonic degree/order 2190.

Table 1. Final 25 tide gauges used in this study for analysis. The tide gauges are ordered from west to east.

#	Tide gauge name	Latitude	Longitude	Observation period
1	Exmouth 02 [W]	–21.954861	114.140889	1997–2019
2	Ashburton MOF [P]	–21.681950	115.010296	2016–2021
3	Ashburton Beacon 10 [P]	–21.667018	115.012072	2016–2021
4	Ashburton Beacon 1 [P]	–21.524230	115.049039	2016–2021
5	Onslow Beadon Creek [W]	–21.649670	115.131530	1986–2019
6	Dampier South Reef [P]	–20.649312	116.649760	2015–2021
7	Dampier Beacon 1W Fairway [P]	–20.533512	116.703957	2015–2021
8	Dampier King Bay Beacon 08 [P]	–20.626825	116.746553	2015–2021
9	King Bay [W]	–20.623611	116.748889	1985–2015
10	Cape Lambert [W]	–20.587778	117.185833	1985–2016
11	Port Hedland Beacon C7 [P]	–20.073105	118.417199	2015–2021
12	Port Hedland Beacon C1 [P]	–19.986172	118.437051	2017–2021
13	Port Hedland Beacon 17 [P]	–20.188755	118.517284	2015–2021
14	Port Hedland Beacon E3 [P]	–20.053700	118.543567	2020–2021
15	Port Hedland Beacon 31 [P]	–20.244949	118.567829	2017–2021
16	Port Hedland Beacon 47 [P]	–20.304517	118.576296	2015–2021
17	Port Hedland Beacon 42 [P]	–20.295281	118.586819	2015–2021
18	Broome 02 [W]	–18.000600	122.218600	1986–2003
19	Derby [W]	–17.292252	123.606755	1996–2016
20	Troughton Island [A]	–13.7500	126.1500	13/05/2015–7/07/2015 (55 days)
21	Jar Island [A]	–14.1500	126.2500	17/04/2014–5/06/2014 (49 days)
22	Long Island (WA) [A]	–13.9667	126.3000	17/04/2014–5/06/2014 (49 days)
23	Carronade Island [A]	–13.9333	126.6000	29/03/2006–15/05/2006 (47 days)
24	Ila Point [A]	–13.9333	126.6830	29/06/2004–9/08/2004 (41 days)
25	Curran Point [A]	–13.9167	126.8000	29/06/2004–9/08/2004 (41 days)

Tide gauge record sources are: [W] = WADoT, [P] = PPA, [A] = AHO. A subset of 19 tide gauges (removing the six AHO tide gauges) was used for selected analyses.

Table 3. Treatment of corrections and transformations for models and observations.

Model/ observation	Tide system	Datum/TRF	Comment
GNSS	Tide free	GDA2020 (GRS80)
Levelling	NA	NA	Connects GNSS observed at the tide gauge benchmark to the tide gauge.
DTU18 MSS	Mean tide	TOPEX ellipsoid	Converted to tide free, transformed to GRS80 ellipsoid and IB effect restored.
CNES-CLS15 MSS	Mean tide	TOPEX ellipsoid	Converted to tide free, transformed to GRS80 ellipsoid and IB effect restored.
DTU19MDT	Mean tide*	NA	IB effect restored. See text for discussion on combination with geoid model.
CNES-CLS18MDT	Mean tide*	NA	IB effect restored. See text for discussion on combination with geoid model.
AGQG2017	Tide free	GRS80, zero degree term –0.704 m applied	Tide system and zero degree term tailored to fit the MDT.
EGM2008	Tide free	GRS80, zero degree term –0.704 m applied	Tide system and zero degree term tailored to fit the MDT.
EIGEN-6C4	Tide free	GRS80, zero degree term –0.704 m applied	Tide system and zero degree term tailored to fit the MDT.
XGM2019e_2159	Zero-tide	GRS80, zero-degree term –0.704 m applied	Converted to tide free in harmonic synthesis. Tide system and zero degree term tailored to fit the MDT.
Tide gauge observations	NA	Local TGZ	Transformed to GDA2020 (GRS80) using levelling connection and GNSS $h$

The combination of the MDT models with the geoid models to realise the MSS is explained in the text. *the concept of the MDT tide system is described in the text.

Figure 4. The difference between tide gauge ${\mathrm{h}}_{\mathrm{\text{MSL}}}$ and ${\mathrm{h}}_{\mathrm{\text{MSS}}}$ derived from geoid(N)+MDT and MSS models at 25 tide gauges. The modelled MSS in the differences are shown in the legend on the figure. The tide gauges are ordered from west to east, as listed in Table 1 and shown in Figure 2. Descriptive statistics are shown in Table 4.

Table 4. Descriptive statistics for differences between model ${\mathrm{h}}_{\mathrm{\text{MSS}}}$ from a range of N + MDT and MSS models and ${\mathrm{h}}_{\mathrm{\text{MSL}}}$ at tide gauges.

Model	Mean		Standard Deviation (SD)		RMS		Minimum		Maximum
AGQG17+DTU19MDT	–0.287	–0.062	0.536	0.096	0.608	0.114	–2.170	–0.184	0.149	0.149
AGQG17+CNES18MDT	–0.177	0.046	0.534	0.101	0.563	0.111	–2.056	–0.089	0.262	0.244
EGM2008+DTU19MDT	–0.299	–0.084	0.520	0.122	0.600	0.149	–2.089	–0.267	0.155	0.155
EGM2008+CNES18MDT	–0.189	0.024	0.518	0.122	0.551	0.125	–1.975	–0.172	0.250	0.250
EIGEN-6C4+DTU15MDT	–0.323	–0.127	0.492	0.103	0.588	0.163	–2.033	–0.280	0.151	0.076
EIGEN-6C4+DTU19MDT	–0.314	–0.117	0.492	0.103	0.584	0.156	–2.027	–0.264	0.158	0.079
EIGEN-6C4+CNES18MDT	–0.204	–0.009	0.490	0.104	0.531	0.105	–1.913	–0.168	0.278	0.174
XGM2019e+DTU15MDT	–0.321	–0.120	0.494	0.109	0.590	0.162	–2.046	–0.328	0.106	0.066
XGM2019e+DTU19MDT	–0.313	–0.110	0.495	0.108	0.585	0.154	–2.040	–0.312	0.113	0.069
XGM2019e+CNES18MDT	–0.202	–0.002	0.493	0.111	0.533	0.111	–1.926	–0.216	0.233	0.164
DTU18MSS	–0.204	–0.059	0.451	0.123	0.495	0.136	–1.701	–0.399	0.633	0.113
CNES15MSS	–0.199	0.005	0.531	0.201	0.567	0.201	–2.016	–0.231	0.647	0.647

The non-bold values are for all 25 tide gauges shown in Table 1 and used in Figure 4 while bold values are for the 19 tide gauges when all AHO tide gauges are removed (cf. Table 1). Units are metres.

Figure 5. Comparison of ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ derived from geoid(N)+MDT and MSS derived ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ at 25 tide gauges.

Table 5. Descriptive statistics for ${\Delta \mathrm{h}}_{\mathrm{\text{LAT}}}$ which is the difference between ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ computed from models, and h_LAT computed from tide gauge records at the tide gauge location.

Models	Mean		Standard Deviation		RMS
EIGEN-6C4(N)+DTU19MDT–FES2014(LAT)	–0.234	–0.048	0.495	0.158	0.547	0.165
EIGEN-6C4(N)+DTU19MDT–TPXO9(LAT)	–0.307	–0.130	0.484	0.164	0.573	0.209
EIGEN-6C4(N)+CNES18MDT–FES2014(LAT)	–0.124	0.060	0.500	0.185	0.515	0.195
EIGEN-6C4(N)+CNES18MDT–TPXO9(LAT)	–0.197	–0.022	0.478	0.145	0.517	0.146
XGM2019e(N)+DTU19MDT–FES2014(LAT)	–0.233	–0.042	0.497	0.158	0.548	0.164
XGM2019e(N)+DTU19MDT–TPXO9(LAT)	–0.306	–0.123	0.484	0.160	0.573	0.202
XGM2019e(N)+CNES18MDT–FES2014(LAT)	–0.122	0.067	0.502	0.187	0.517	0.198
XGM2019e(N)+CNES18MDT–TPXO9(LAT)	–0.196	–0.015	0.478	0.142	0.517	0.142
DTU18MSS–FES2014(LAT)	–0.124	0.010	0.451	0.125	0.468	0.125
DTU18MSS–TPXO9(LAT)	–0.197	–0.072	0.457	0.188	0.498	0.201
CNES15MSS-FES2014(LAT)	–0.119	0.073	0.553	0.279	0.566	0.288
CNES15MSS-TPXO9(LAT)	–0.193	–0.008	0.512	0.197	0.547	0.198

The non-bold values are for all 25 tide gauges shown in Table 1 and used in Figure 4 while bold values are for the 19 tide gauges when all AHO tide gauges are removed (cf. Table 1). Units are metres.

Figure 6. Top left is the difference between ${\mathrm{h}}_{\mathrm{\text{MSS}}}$ computed at 25 tide gauges from EIGEN-6C4(N)+CNES18MDT and ${\mathrm{h}}_{\mathrm{\text{MSL}}}$ computed from the tide gauge record. Top right is the difference between ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ computed from DTU18MSS and FES2014b(LAT) and ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ computed from the tide gauge record. The middle row shows enlargements for the four clusters of tide gauges (shown in boxes (red in the online version) in the top row plots) for model ${\mathrm{h}}_{\mathrm{\text{MSS}}}$ minus tide gauge computed ${\mathrm{h}}_{\mathrm{\text{MSL}}}$ (as per top left), with the bottom row showing those same enlargements with model ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ minus tide gauge computed ${\mathrm{h}}_{\mathrm{\text{LAT}}}$ (as per top right). The offshore dotted grey line in the inset boxes indicates the ∼10 km distance offshore adopted as the limit of reliable altimetry observations. Note the larger scale range for the enlargements on the right of rows 1 and 2 (Kalumburu) indicating the much larger differences for the northern-most AHO tide gauges.

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Data availability statement

Tide gauge data are available from the AHO, WADOT, PPA and BOM on request. AGQG2017 is available from Sten Claessens (Curtin University) on request. All other models are available as per the URL in Table 2, or by contacting the developers.