Harmonic constants | National Tidal and Sea Level Facility

Tidal variations can be represented by summing a series of harmonic terms. Listed below are the four largest harmonic constants (or tidal constituents) M₂, S₂, O₁ and K₁ together with the mean value Z₀.

Each harmonic term has the form

H_n cos (σ_nt − g_n)

where H_n is an amplitude in metres, g_n is a phase lag on the Equilibrium Tide at Greenwich in degrees, σ_n is an angular speed and t is time.

To produce a full accurate tidal prediction it is often necessary to use more than a hundred of these harmonic terms. These results were generated by tidal analysis using tide gauge data spanning the dates listed.

Port	Date span	Days	Z₀	O₁		K₁		M₂		S₂
Port	Date span	Days	Z₀	H	g	H	g	H	g	H	g
St. Mary’s	1998–2007	3581	3.180	0.055	340.39	0.058	101.27	1.758	130.93	0.605	172.53
Newlyn	1989–2007	6805	3.195	0.054	341.80	0.064	109.43	1.716	133.37	0.573	177.75
Plymouth	1998–2007	3389	3.395	0.056	346.40	0.076	112.11	1.684	153.26	0.607	205.93
Weymouth	1998–2007	3592	1.169	0.049	348.70	0.089	111.85	0.595	190.69	0.309	242.06
Bournemouth	1998–2007	3611	1.593	0.041	348.21	0.090	112.38	0.411	273.42	0.182	292.42
Southampton	1957–1965	2922	2.865	0.034	5.20	0.087	114.20	1.359	329.20	0.407	15.10
Portsmouth	1997–2007	3541	2.879	0.027	345.21	0.087	113.01	1.409	326.66	0.437	13.19
Newhaven	1985–2007	6648	3.629	0.010	332.40	0.075	103.68	2.249	321.12	0.729	10.79
Dover	1989–2007	6758	3.750	0.058	180.58	0.050	40.33	2.250	331.83	0.706	23.85
Sheerness	1989–2007	6683	3.028	0.133	190.54	0.113	10.88	2.015	353.78	0.576	50.92
Harwich	2004–2007	1331	2.178	0.130	176.74	0.109	353.42	1.330	324.48	0.372	17.43
Felixstowe	1988–2007	6800	2.067	0.131	174.13	0.109	349.54	1.257	321.41	0.348	13.53
Lowestoft	1989–2007	6808	1.637	0.137	160.78	0.119	330.84	0.688	259.63	0.207	298.73
Cromer	1998–2007	3491	2.920	0.158	132.54	0.145	300.95	1.568	188.11	0.533	234.18
Immingham	1989–2007	6785	4.196	0.171	114.69	0.155	281.17	2.260	161.85	0.741	212.42
Whitby	1988–2007	6777	3.351	0.146	88.28	0.129	250.79	1.659	104.15	0.558	147.00
North Shields	1989–2007	6706	2.954	0.140	81.75	0.120	242.37	1.603	89.03	0.537	131.09
Leith	1996–2007	3643	3.187	0.142	65.12	0.121	220.89	1.795	55.34	0.614	95.66
Aberdeen	1989–2007	6726	2.557	0.127	51.10	0.113	204.56	1.301	24.57	0.440	62.88
Moray Firth	1994–2004	3034	2.552	0.122	34.43	0.115	181.72	1.298	336.94	0.454	15.05
Wick	1989–2007	6778	2.057	0.114	27.89	0.109	175.85	1.016	322.30	0.348	0.28
Lerwick	1987–2007	6910	1.296	0.079	31.85	0.075	164.76	0.581	311.84	0.210	346.95
Kinlochbervie	1997–2007	3403	2.883	0.081	340.69	0.119	125.97	1.434	207.93	0.548	241.83
Stornoway	1988–2007	6787	2.893	0.092	350.12	0.131	135.34	1.390	197.54	0.545	231.25
Ullapool	1987–2007	6937	3.093	0.077	345.81	0.108	128.78	1.503	200.75	0.584	234.99
Tobermory	1987–2007	6561	2.725	0.062	23.41	0.063	168.81	1.300	168.53	0.529	204.93
Port Ellen	1998–2007	3611	0.469	0.084	40.13	0.093	187.84	0.160	88.64	0.141	153.68
Millport	1987–2007	6909	1.996	0.098	43.89	0.109	192.72	1.119	342.67	0.296	35.17
Portpatrick	1987–2007	7005	2.161	0.100	42.20	0.108	190.94	1.339	332.14	0.375	16.63
Workington	1998–2007	3530	4.520	0.111	44.82	0.122	194.64	2.737	331.94	0.876	15.36
Heysham	1988–2007	6838	5.176	0.114	42.42	0.123	192.45	3.166	325.68	1.027	8.72
Liverpool	1998–2007	3423	5.263	0.115	40.74	0.123	191.03	3.041	320.62	0.981	4.55
Hilbre	1964–1965	380	5.140	0.104	38.70	0.112	189.10	2.923	317.50	0.947	0.10
Port Erin	1998–2007	3505	2.873	0.102	40.99	0.110	188.91	1.833	321.72	0.559	1.16
Llandudno	1997–2007	3505	4.061	0.111	34.60	0.119	184.67	2.690	309.87	0.868	351.05
Holyhead	1986–2007	6623	3.261	0.101	29.01	0.106	176.80	1.805	291.88	0.592	328.69
Barmouth	1996–2007	3588	2.705	0.082	21.21	0.082	166.45	1.451	238.81	0.543	277.26
Fishguard	1988–2007	6961	2.708	0.079	10.09	0.078	152.32	1.353	207.33	0.529	248.38
Milford Haven	1988–2007	6969	3.837	0.066	355.02	0.065	131.70	2.217	172.67	0.805	217.30
Mumbles	1998–2007	3385	5.222	0.069	352.99	0.066	130.62	3.120	172.07	1.120	219.70
Newport	1998–2007	3422	6.099	0.073	1.26	0.069	141.25	4.139	194.71	1.474	252.34
Avonmouth	1987–2007	6834	6.955	0.075	3.35	0.069	144.06	4.269	200.53	1.513	259.91
Hinkley Point	1998–2007	3480	6.235	0.073	355.95	0.069	134.72	3.915	182.40	1.402	236.50
Ilfracombe	1986–2007	6876	4.951	0.067	349.01	0.065	125.32	3.043	162.21	1.104	209.22
Dublin	1986–1987	365	2.457	0.101	44.90	0.096	189.50	1.325	326.60	0.393	358.80
Bangor	1997–2007	3540	2.045	0.100	39.00	0.108	187.12	1.168	317.66	0.295	359.65
Portrush	1998–2007	3547	1.285	0.086	27.25	0.093	174.63	0.536	197.61	0.233	211.42
Londonderry	1982–1982	365	1.646	0.085	41.00	0.098	192.00	0.757	236.80	0.295	263.70
Cobh	1906–1907	365	2.255	0.034	45.80	0.021	155.50	1.381	149.60	0.433	194.20
Rosslare	1972–1973	319	1.047	0.071	34.38	0.060	180.50	0.559	157.07	0.245	219.73
St. Helier	1998–2007	3639	6.025	0.081	346.46	0.093	97.67	3.336	181.88	1.303	231.28