Quality control of time-series seawater temperature and wave data adapted to the regional conditions of the Baltic Sea

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Proposed and determined new limit values for the non-storm season in the open waters of the Baltic Sea, based on measurement data from the Pomeranian Bay point

	Proposed value (Copernicus)	99th percentile of result	Proposed value	Number of records	Percentage of measurements flagged (%)
Hs	3	0.52	0.55 m	64	0.787
Tp	10	3.6	4.0 s	235	2.889

Number of flagged measurements in the Dixon’s 4σ result at the Petrobaltic point

Sezon sztormowy (n = 28667)					Sezon bezsztormowy (n = 20540)
	Sr−4Q	Sr + 4Q	Number of records flagged	Percentage of records flagged (%)		Sr−4Q	Sr + 4Q	Number of records flagged	Percentage of records flagged (%)
Hs	−1.88	4.67	41	0.14	Hs	−1.48	3.04	101	0.49
Tm	0.52	7.32	2	0.01	Tm	0.49	6.1	4	0.02
Tp	0.24	11.24	5	0.02	Tp	−0.2	9.76	1	0.00

Proposed and determined new limit values for the storm season in the open waters of the Baltic Sea, based on measurement data from the Petrobaltic point

	Proposed value (Copernicus)	99th percentile of result	Proposed value	Number of records	Percentage of measurements flagged (%)
Hs	3	5.49	5.5 m	37	0.129
Tm	4	9.97	10.0 s	12	0.042
Tp	10	17.37	18.0 s	4	0.014

The total number of outlier measurements for the tests performed for the significant wave height parameter

Test	Spike	Dixon’s 4σ	Hampel	Quartile
Spike	129	38	126	118
Dixon’s 4σ	38	226	29	117
Hampel	126	29	211	207
Quartile	118	117	207	380

Proposed and determined new limit values for the non-storm season in the open waters of the Baltic Sea, based on measurement data from the Petrobaltic point

	Proposed value (Copernicus)	99th percentile of result	Proposed value	Number of records	Percentage of measurements flagged (%)
Hs	3	3.54	3.5 m	1	0.005
Tm	4	4.69	5.0 s	685	3.335
Tp	10	19.29	20.0 s	71	0.346

The results of outlier identification at open sea stations—Dixon’s 4σ

Name of the stations	Measurement date	Season	Depth	The temperature measurement result	Dixon’s 4σ
					Control range		Assessment result
					μ − 4σ	μ + 4σ
L7	28.05.2007	Spring	2.5	15.5	−5.9	14.9	Attention
L7	28.05.2007	Spring	5	15.6	−5.9	14.9	Attention
P1	07.08.1961	Summer	50	13.4	−3.9	12.5	Attention
P1	17.10.1990	Autumn	70	12.8	−2.1	11.5	Attention
P110	29.07.1984	Summer	68	12.5	−2.3	11.0	Attention
P110	10.09.1985	Autumn	68	15.4	−3.9	15.2	Attention
P110	24.07.1990	Summer	60	16.6	−6.2	14.8	Attention
P110	09.07.1993	Summer	68	14.3	−2.3	11.0	Attention
P110	12.08.2005	Summer	60	14.9	−6.2	14.8	Attention
P110	07.09.2006	Autumn	67	16.6	−3.9	15.2	Attention
P116	27.09.1978	Autumn	70	13.1	−2.0	11.9	Attention
P116	29.07.1984	Summer	50	13.4	−4.2	12.9	Attention
P116	09.07.1993	Summer	50	13.7	−4.2	12.9	Attention
P116	09.07.1993	Summer	60	13.4	−3.1	10.5	Attention
P116	09.07.1993	Summer	70	12.2	−1.1	9.0	Attention
P116	07.09.2006	Autumn	60	17.1	−5.9	16.6	Attention
P140	06.08.2007	Summer	40	9.9	−0.5	9.5	Attention
P140	31.05.2016	Spring	2.5	13.8	−5.7	13.6	Attention
P140	31.05.2016	Spring	5	13.8	−5.7	13.6	Attention
P140	31.05.2016	Spring	10	13.8	−5.7	13.6	Attention
R4	28.05.2007	Spring	1	17.0	−7.0	16.5	Attention
R4	28.05.2007	Spring	2.5	17.0	−6.4	15.3	Attention
R4	28.05.2007	Spring	5	16.9	−6.4	15.3	Attention

Number of flagged measurements in the Dixon’s 4σ result at the Pomeranian Bay point

Sezon sztormowy (n = 9452)					Sezon bezsztormowy (n = 8133)
	Sr−4Q	Sr + 4Q	Number of records flagged	Percentage of records flagged (%)		Sr−4Q	Sr + 4Q	Number of records flagged	Percentage of records flagged (%)
Hs	−2.19	4.13	67	0.71	Hs	−1.72	3.6	17	0.21
Tp	−2.07	9.89	76	0.80	Tp	−1.37	9.21	83	1.02

The impact of identifying outlier measurements on the results of statistical analyses in relation to temperature measurements at the Kołobrzeg station in August 2006

Parameter	Test	Number of observations			Statistical values
		All	Outliers	Used to calculate statistical values	Mean	Median	Standard deviation
Temperature of water in coastal station Kołobrzeg in August 2006	Zero trial	31	0	31	19.96	20	0.76
	Spike, Hampel, Q-Dixon and Quartile		2	29	19.95	20	0.53

Proposed spike test limits for temperature results at southern Baltic coast stations

	Limit value for the test	99th percentile score	Proposed limit value	Number of records flagged	Percent of records flagged (%)
Temperature measurements at coastal stations	6	1.5	2	703	0.37

The results of outlier identification at coastal stations—Dixon’s 4σ

Name of the stations	Measurement date	Season	The temperature measurement result	Dixon’s 4σ
				Control range		Assessment result
				μ − 4σ	μ + 4σ
Gdynia	01.06.1962	Summer	5.9	6.01	29.14	Attention
Gdynia	12.06.1978	Summer	5.5	6.01	29.14	Attention
Hel	01.06.1980	Summer	4.6	5.86	27.76	Attention
Międzyzdroje	10.06.1955	Summer	8.6	9.13	26.70	Attention
Puck	01.06.1976	Summer	9	9.09	29.42	Attention
Puck	17.06.1982	Summer	8.9	9.09	29.42	Attention
Puck	23.06.1982	Summer	8.6	9.09	29.42	Attention
Świnoujście	04.12.1960	Winter	8.4	−4.54	8.02	Attention

The impact of identifying outlier measurements on the results of statistical analyses in relation to temperature measurements at coastal stations in the years 1946–2019

Parameter	Test	Number of observations			Statistical values
		All	Outliers	Used to calculate statistical values	Mean	Median	Standard deviation
Temperature of water in coastal stations	Zero trial	190,967	0	190967	9.47	8.80	6.64
	Spike		703	190264	9.46	8.80	6.64
	Dixon’s 4σ		8	190959	9.47	8.80	6.64
	Q-Dixon		282	190685	9.48	8.80	6.64
	Hampel		7649	183318	9.56	9.00	6.61
	Quartile		931	190036	9.48	8.80	6.64

Area and range of analyses

Area of tests	Research period	Parameter	Number of stations	Number of analysed results
Coastal stations	1946–2019	Water temperature	8	190,967
Open sea stations	1959–2019	Water temperature	18	40,651
	2018–2021	Wave	2	66,792

The impact of identifying outlier measurements on the results of statistical analyses in relation to temperature measurements at open sea stations from 1959 to 2019

Parameter	Test	Number of observations			Statistical values
		All	Outliers	Used to calculate statistical values	Mean	Median	Standard deviation
Temperature of water in open sea stations	Zero trial	40.651	0	40.651	7.57	5.65	5.20
	Gradient		304	40.347	7.55	5.64	5.18

Summary of the results of the spike test formula according to Copernicus for the entire Baltic Sea area

test value = | V2 − (V3 + V1)/2 | − | (V3 − V1)/2 | Wave parameter:	Spike test result according to Copernicus for the entire Baltic Sea area:
Hs		3
Tm	4
Tp	10

Proposed and determined new limit values for the storm season in the open waters of the Baltic Sea, based on measurement data from the Pomeranian Bay point

	Proposed value (Copernicus)	99th percentile of result	Proposed value	Number of records	Percentage of measurements flagged (%)
Hs	3	0.74	0.8 m	27	0.286
Tp	10	4.35	4.5 s	174	1.841

The number of outlier measurements common to the tests

Type of test	Spike	Dixon’s 4σ	Q-Dixon	Hampel	Quartile
Spike	703	2	51	137	32
Dixon’s 4σ	2	8	0	3	0
Q-Dixon	51	0	282	246	118
Hampel	137	3	246	7649	922
Quartile	32	0	118	922	931

Proposed gradient test limits for temperature results at southern Baltic open sea stations

	Limit value for the test	99th percentile score	Proposed limit value	Number of records flagged	Percent of records flagged (%)
Temperature measurements at open sea stations	9	4.7	5	304	0.75

The total number of outlier measurements for the tests performed for the mean wave period parameter

Test	Spike	Dixon’s 4σ	Hampel	Quartile
Spike	484	47	198	377
Dixon’s 4σ	47	165	151	162
Hampel	198	151	211	209
Quartile	377	162	209	380