App endix - DMI · App endix A Sea Lev el Calculations at Horns Rev Observ ations from the oshore...

Appendix A

Sea Level Calculations at Horns Rev

Observations from the o��shore tide gauge at Horns Rev �� N� � �� E� have beenobtained for the two periods�

�� period�� period�

August �� December ��

��December �� April ��

At the instrument inspection and data collection at �� a new instrument was re�mountedat a slightly di�erent position resulting in an o��set of approximately �� m in the water depth�and the two data periods have been analyzed separately�

The instrument measures at the sea bed the total pressure caused by the weight of the overlayingwater column plus the atmospheric pressure� By assuming hydrostatic pressure the relationbetween the observed bottom pressure and the sea level variations is given by�

pobs� � pwater � patm� � ��w�S� T� p� g z � patm�

where z � ��H�� is the negative water depth consisting of the height of the water column H atMean Sea Level �MSL�� and � the actual deviation from MSL� The bottom pressure instrumentmeasures the temperature T ��C�� the conductivity �� ohm��cm�� and the pressure �psi��The conversion from the pressure unit psi ��lb�in�� to the SI pressure unit Pa is�

� psi � �� Pa �

The total height of the water column� z is calculated by�

z � �� Pa

psi �pobs� � patm�psi

�w�T� S� p� g�

where g is the acceleration of gravity in m�s�� p and patm the total pressure and the atmosphericpressure� respectively� both measured in psi� and �w�T� S� p� the density of the water �kg�m��depending of the water temperature T �Co�� salinity S �Practical Salinity Units �PSU�� and

�� A Sea Level Calculations at Horns Rev

pressure p �hPa�� The density of the water �w is calculated as �UNESCO � ��

�w � �� T � �� T �

� �� T � � �� T � � �� T �

� S � �� T � �� T � � �� T � � �� T � �

� S�� T � �� T ��

� S� ��

In general the density of the water also depends on the pressure� but at �� m depth the pressureonly e�ects the density with less than �� and the pressure dependency in the water densityhas been neglected�

The water temperature measured at the sea bed at approximately �� m is used as representingthe temperature in the whole water column� The conductivity sensor at the instrument failedduring both data periods� and a constant value for the salinity of �� PSU have been used for thesea level calculations� These uncertainties in the water salinity and temperature have introducederrors in the calculations of the sea level� An estimate of the size of the error can be obtainedfrom statistical data from the Vyl light vessels that until � � did operate at the position ��N� �� E� approximately �� km SSE of the location of the instrument at Horns Rev� The lightvessel data show an annual variation in the salinity of approximately � PSU at the surface inthe interval �� PSU and at �� m water depth a variation in the interval of �� PSU�Sparre� ��b�� The temperature data show a depth variation of approximately � �C betweensurface and �� m �Sparre� ��a�� The errors in the water depth calculation caused by thesetemperature and salinity variations may therefore be estimated to be of the order of a few cm�

The In�uence from the Atmospheric Pressure

For calculation of the sea level the atmospheric pressure has been removed from the observations�The nearest observations of the atmospheric pressure are obtained from the meteorologicalstation at Bl�avands Huk �� N� �� E� operated by DMI� This synop station is located atthe Danish North Sea coast �� m above the sea surface and �� km east of the o��shore instrumentat Horns Rev� The atmospheric pressure observations are available at a sampling rate of � hours�and a cubic spline interpolation has been used to interpolate to hourly values� These atmosphericpressure observations have been used to remove the in�uence from the atmospheric load inthe sea level calculations� The distance between the o��shore station at Horns Rev and themeteorological synop station may introduce an error in the calculated sea level� The magnitudeof this error is highly dependent on the weather situation� A worst case pressure di�erencebetween the two stations is � hPa which may introduce an error in the sea level calculation ofapproximately � cm� For more calm weather situations the sea level error will be of the orderof � cm� To estimate the in�uence from the distance between the o��shore observations and thecoastal atmospheric observations� model simulated values for the atmospheric surface pressurefrom the HIgh Resolution Limited Area Model �HIRLAM� have been included� A scatter plotof the Horns Rev water depth time series calculated with the atmospheric pressure from theobservations from Bl�avands Huk and the model simulated values is shown in Figure A�� No

��

Figure A�� Scatter plot between Horns Rev water depth calculations� where the atmosphericpressure has been removed with observations from the synop station at Bl�avands Huk �BVH�and HIRLAM simulated values� respectively�

in�uence on the sea level calculations is found by using the HIRLAM data instead of the coastalobservations for removal of the atmospheric load� A third water depth time series have beencalculated by assuming a constant atmospheric pressure of �� hPa� This time series havebeen constructed to test the in�uence to the atmospheric pressure variations on the sea leveland the ocean tides� The standard deviations for the calculated sea level time series are shown inTable A�� for the three di�erent time series with and without the atmospheric pressure variationsremoved� A larger variation in the sea level is seen for the time series where the atmosphericpressure variations have been removed�

Scatter plots of the calculated total water depth at Horns Rev for the three di�erent atmosphericpressure calculations are seen in Figures A�� and A�� for the two data periods as function of sealevels from the coastal tide gauge station at Esbjerg �� km E of Horns Rev� A linear correlationcoe�cient has been estimated to be in the interval r�� with the lowest correlation forthe Horns Rev data where the atmospheric pressure variations have not been removed� Theinclination of the linear �t shows the shoaling e�ect on a factor of approximately � in the sealevel variations from Horns Rev towards the coast�

Data period�St� dev��patm�� hPa�

St� dev��patm��obs��

St� dev��patm��model�

��

�� cm�� cm

�� cm�� cm

�� cm�� cm

Table A�� The standard deviations for the sea level time series calculated without the atmo�spheric pressure variations removed �patm� � �� and with the atmospheric pressure variationsremoved by using observations and model simulations�


Sea level residuals from Horns Rev for the two time series calculated with constant and observedatmospheric pressure are shown in Figure A�� together with the corresponding residuals fromthe Esbjerg tide gauge station� A larger correlation between the residuals at Horns Rev andEsbjerg is seen for the Horns Rev data where the atmospheric pressure variations have beenremoved from the observed sea level variability�

An estimation of the IB e�ect �see Section �� for the Horns Rev data is shown in Figure A�� asfunction of the atmospheric pressure observations from Bl�avands Huk� The IB e�ect is estimatedfor the Horns Rev data set calculated with the atmospheric pressure contribution represented asthe constant values of �� hPa� and with the observations obtained from the synop station atBl�avands Huk� respectively� A signi�cant di�erent residual pattern is observed for the two dataperiods� and for the two calculated sea level records� with the IB e�ect estimated in the rangefrom no e�ect to �� cm�hPa� For the Horns Rev sea level residuals where the atmosphericpressure variability has been removed� the IB e�ects are estimated to be �� cm�hPa and�� cm�hPa for the two data sampling periods� respectively�

��

Figure A�� Scatter plot between Horns Rev water depths and corresponding sea level data fromEsbjerg� Shown for data period ��


Figure A�� As Fig� A�� but for data period ��

��

Figure A�� Scatter plot of Horns Rev residuals calculated with atmospheric pressure observationsfrom the synop station at Bl�avands Huk �BVH� as function of residuals from the coastal tidegauge station at Esbjerg�


Figure A�� Scatter plot of Horns Rev residuals plotted as function of the atmospheric pressureobservations from Bl�avands Huk� The sea level residuals are plotted for data period � at top�and data period � at bottom�

Appendix B

The M� Modulation Wave

A linear combination of the harmonics for the M� constituent and its two neighbouring con�stituents MA� and MB� gives �the nodal corrections are ignored��

h�t� � AM�ei�M�

t�gM�VM�

� � AMA�ei�MA� t�gMA�VMA�� AMB�

ei�MB� t�gMB�VMB��

� ei�M�t�gM�

VM��

hAM�

� AMA�ei��tgM�

�gMA�VMA��VM��

� AMB�ei��MB� t��M�

tgM��gMB�VMB��VM�

�i

where A� �� g and V are the amplitude� frequency� phase lag and the astronomical argument�respectively� for each of the three constituents� and �� M�

� �MA�� MB�

� �M�� Taking

the real part of the expression gives

h�t� � cos��M�t � gM�

� VM�� h

AM�� AMA�

cos��t� gM�� gMA�

� VMA�� VM�

�

� AMB�cos��t� gM�

� gMB�� VMB�

� VM��i

� sin��M�t� gM�

� VM�� h

AMA�sin��t� gM�

� gMA�� VMA�

� VM��

� AMB�sin��t� gM�

� gMB�� VMB�

� VM��i

�hAM�

� S�t�i� cos��M�

t� gM�� VM�

� � R�t�� sin��M�t� gM�

� VM��

where S�t� is given by

S�t� � AMA�cos��t � �gMA�

� gM�� VMA�

� VM��

�AMB�cos��t� �gMB�

� gM�� VMB�

� VM��

�� B The M� Modulation Wave

and R�t� by

R�t� � AMA�sin��t� �gMA�

� gM�� VMA�

� VM��

�AMB�sin��t� �gMB�

� gM�� VMB�

� VM��

The linear combination of the M�� MA� and MB� harmonics is seen to result in a M� carrierwave with a modulation in the amplitude at a period of T � � year� plus a small term at theM� frequency but with the phase lag shifted �� The modulation wave S�t� has been usedin Chapter � to investigate the annual modulation of the M� constituent� The sine term isconsidered as a small perturbation term to the annual modulation of the M� wave due to the�� phase shift� and has not been included in the investigations�

Appendix C

Vector Root�Sum�Square

The total error of the di�erence between two vectors is given by the length of the vector di�erenceintegrated over one period�

RSSvector �h �

N

NXi �

�

T

Z T

�k ATG ei�t�gTG� � A�D ei�t�g�D� k� dt

i��

�h �

N

NXi �

�

T

Z T

�

� �ATG cos��t� gTG� � A�D cos��t� g�D�

��

��ATG sin��t� gTG� � A�D sin��t� g�D�

�� dti��

�h �

N

NXi �

�

T

Z T

�

�A�TG �A�

�D � �ATGA�D cos��t� gTG� cos��t� g�D�

� �ATGA�D sin��t� gTG� sin��t� g�D��dti��

�h �

N

NXi �

�

T

Z T

�� A�

TG � A��D � ATGA�D

hcos��gTG � g�D� � cos��t� gTG � g�D�

i

� ATGA�D �cos��gTG � g�D�� cos��t� gTG � g�D��dti��

�h �

N

NXi �

�

T

Z T

��A�

TG � A��D � �ATGA�D cos�gTG � g�D�

�dti��

�h �

N

NXi �

�A�TG � A�

�D � �ATGA�D cos�gTG � g�D�� i��

�h �N

NXi �

�

�

h �ATG cos�gTG��A�D cos�g�D�

��ATG sin�gTG��A�D sin�g�D�

�� i i��

where the sum i is made over the total set of data� N �

Appendix D

The Modulation Wave from the

NEAC �D�model T runs

The modulation wave calculated from the NEAC �D�model T runs are shown below for the years�� for the model grid points corresponding to the location of the tide gauge stationsaround the North Sea� The amplitude of the modulation wave are shown in absolute values�cm� and relative to the M� amplitude� Also shown is the phase lag for the M� maximum with�� corresponding to January � and �� to December �� These tables are to be compared withTable �� for the T�S runs�

��

�� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��

North Shields ��

Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

�� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��


Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

�� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��


Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

�� D The Modulation Wave from the NEAC �Dmodel T runs

�� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��


Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

�� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��


Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

� M� �cm� S�t� �cm� S�t� �� S�t� ��

Wick ��

Leith ��


Lowestoft ��

Sheerness ��

Esbjerg ��

Hvide Sande ��

Hanstholm ��

Hirtshals ��

Appendix E

Plots of the NEAC �D�model

Modulation Wave

On the following pages are shown the modulation wave� S�t� calculated from the �D barotropicnumerical model �described in Section �� The amplitude for the modulation wave is givenin cm and the time in the year for this maximum is given in degrees and plotted for the years�� for runs forced with tides only �T runs� and forced with both tides and atmosphericforcing �elds �T�S runs��

��

EPlotsoftheNEAC�DmodelModulationWave

10o W 5o W 0o 5o E 10o E 15o E 20o E 25o E


50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.20

0.30

0.20

0.300.20

0.200.30

0.40

0.20 0.30

0.10

0.10

0

210

180

180

180

300

240

330

NEAC Model (POL): T run 1992M2−modulation Amplitude [cm]



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.150

0.225

0.250

0.275

0.2250.250

0.175

0.200 0.200

0.15

0

0.22

5

0.20

0

0.17

5 0.15

0

0.20

0

0.30

0

0.175

0.17

5

0.275

0.250

0.300

0.3250.3500.375

0.4000.225

0.25

0 0.35

00.

325

0.30

0

0.27

5

0.100

0.125

0.050

0.075

0.050

0.050

0.025

0.075

0.075

0.02

5

0.075

0.100

0.125

0

200210

190

180

170

170

170190

200

180

170

190200

190

180

250260

300

350280

220230

240250

290

310 320330340

220

NEAC Model (POL): T run 1992M2−modulation Phase [deg.]

��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.20

0.20

0.600.50

0.10

0.40

0.300.30

0.30

0.70

0.80

0.901.001.10

0.800.50

0.50

0.60

1.000.900.600.70

0.50

0.60

0.70 1.

00

1.10

1.200.80

0.90

0.20

0.40

0.30

0.20

0.30

0.10

0.20

0.40

0.10

0.10

0.400

0

0

609030

180

180

180

180

180

180

150

180150

180

180180

210

180

210

300

330

300

NEAC Model (POL): T+S run 1992M2−modulation Amplitude [cm]



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.2

0.2

0.2

0.2

0.4

0.6

1.00.6

0.60.2

0.4

0.60.8

1.00.8

0.8

0.8

1.0

1.2

1.40.6

0.4

0.2

0.40

0

0

405060708090

10

20

30

190

180

180

180

190

190

200

180

190

170

180

170

180

130140150

160

180

160

140150170

180

190

200

200

190

200

180

180

200

210

190

190

180

170

190

210

200

290300310 300

310330340

220

23025

0

NEAC Model (POL): T+S run 1992M2−modulation Phase

��




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.200.30

0.40

0.50

0.60

0.70

0.70

0.900.70

1.101.20

1.30

0.600.50

0.50

0.40

0.30

0.30

0.20

0.80

0.80 1.10

0.70

0.50

0.800.700.600.70

0.60

0.80

0.901.001.10

1.00

0.90

0.20

0.10

0.20

0.30

0.10

0.10

030150

180




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

02030

160 160

170

170

180

190 200

140150

160170

160

170

170

170

170

170

170

170


��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.20

0.20

0.10

0.20

0.20

0.30

0.30

0.30

0.70

0.60

0.50

0.40

0.80

0.90

1.00

1.10

1.301.20

1.30

1.50

1.40

0.800.90

0.80

1.30

1.000.90

1.10

1.20

1.40

1.50

1.60

1.70

1.60

1.50

2.001.10

0.90

1.001.201.301.902.10

1.00

1.10

1.20

0.50

0.40

0.30

0.20

0.40

1.30

1.40

1.50

1.60 2.

001.

901.70

1.80

1.60

1.801.70

2.101.90

2.002.202.302.40

0.70

0.70

0.40

0.400.40

0.50

0.60

0.30

0.30

0.10

60300

90

0

180

180

180

180

180

120150

180180

330




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

2.5

500 1020

80504030

60

70 90

0

160

170

160

180

180170

180

180

170

170

170

170

190200

160

150

130120140

180

170

180

170

170

170

170

170

180

170

170

340

330


��




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.30

0.80

1.30

1.10

1.20

1.40

1.50

0.901.00

0.90

0.80

0.70

0.50

1.40

1.00

0.50

0.40

0.50

0.60

0.60

0.70

0.80

0.90

0.90

0.60

0.70

0.900.70

0.80

0.40

0.30

0.20

0.10

0.20

0.20

0.40

0.60

0.10

180

180

150

180

210240270

240




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

40

180

170180

190200210

170

140150

160180

190

24023022025

0

260270

280290

230240


��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.30

0.40

0.50

0.60

0.70

0.70

0.70

0.80

0.80

1.00

0.90

1.20 1.

401.

50

1.401.201.300.700.800.901.00

0.90

0.80

0.40

0.30

0.50

0.60

0.70

0.40

0.30

0.400.50

0.60

0.30

1.30

1.401.801.90

1.501.601.70

1.00

1.10

1.20

0.10

0.20

0.20

0.30

0.20

0.90

1.00

1.10

1.20 1.501.30

1.40

1.50

1.10

1.60

1.50

1.30

1.40

1.70

1.80

1.90

0.30

0.10

0.10

0.20

300

3060

0

180

180 180

180

180

180

180180180

180180

180

180

180

180

210

300270




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

20020

0

10304050

1030 405060

180

190

180

180

200

170

190

180

190

170

180

180180

170

180

180

180

180

180

180

160180170

200210

180

290 300270280310320


��




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.90

0.90

0.80

0.90

1.00

1.20

1.20

1.20

1.10

1.30

1.40

1.501.

60

1.70

1.10

0.800.7

0

1.10

1.001.00

0.30

0.10

0.20

0.40

0.30

0.40

0.30

0.60

0.50

0.400.30

0.20

0.10

0.50

0.700.80

1.00

0.901.00

1.00 0.10

0

330

270

240300330

300

300

NEAC Model (POL): T run 1995

M2-modulation Amplitude [cm]



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.8

1.0

0.8 1.0

1.0

1.2

1.2

1.2

1.0 1.0

1.6

1.81.4

1.0

0.60.4

0.4

0.2

0.4

0.2

0.6

0.6

1.0

0.8

1.0

0

330

270

240300330

300

300

NEAC Model (POL): T run 1995

M2-modulation Phase

��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.70

0.60

0.50

0.400.30

0.20

0.10

0.20

0.40

0.400.30

0.40

0.30

0.200.40

0.50

0.60

0.90 1.00

1.10

1.200.

80

0.70

0.30

0.20

0.20

0.40

0.400.30

0.40

0.50

0.80

0.90

0.800.700.6

0

0.90

0.90 1.00

1.10

1.10 1.20

0.700.60

0.80

0.600.50

0.500.700.60

0.60

0.70

0.20

0

0

0

0

0

0

0

300

330

270

300

330

300270240330

240

270

330

NEAC Model (POL): T + S run 1995

M2-modulation wave

Amplitude [cm]



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.8

0.6

0.40.2

0.2

0.4

0.4

0.4

0.61.2

0.4

0.6

0.8 0.4

0.4

0.2

0.6

0.60.8

0.6

1.2

0.81.0

1.0 1.2

1.40.

8

0.4

0.2

0.20.4

0.6

0.2

0

0

0

0

0

0

0300

330

270

300

330

300270240330

240

270

330

NEAC Model (POL): T + S run 1995

M2-modulation Phase

��




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.30

0.30

0.300.30

0.40

0.30

0.30 0.20

0.40

0.20

0.10

0.10

0.10

0.20

0.10

0.10

0.20

180

180

180

180

180

180

180

180

180

180

180

180

180

180

180

180

180

240

30027

0




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.325

0.300

0.275

0.2500.325

0.32

5

0.37

5

0.3500.225

0.325 0.275

0.300

0.325

0.350

0.375

0.400

0.425 0.4500.475

0.2500.225

0.12

5

0.150 0.17

5

0.20

0

0.15

0

0.150

0.125

0.35

0

0.3750.400

0.3000.325

0.175

0.1250.100

0.05

0

0.150

0.17

5

0.075

0.125

0.07

5

0.100

0.050

0.0250.125

0.100

0.07

5

0.200

0.300

0.1500.175 0.200

0.075

200

190

180

180

180

190

180

190

180

180

180

190

170

170

200

170

180

180

180

180

180

180

180

180

180

180

280220

230240

250

26027

029

0

300

310


��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.70

0.80

0.40

0.50

0.60

0.40

0.30

0.40

0.40

0.30

0.30 0.

40

0.70

0.80

0.90 1.

001.

10

0.50

0.60

0.30

0.70

0.90

0.80

1.001.10

0.50

0.60

0.40

0.50

0.20

0.10

0.20

0.100.20

0.20

0.90

0.20

306090

180

150

180

180

180

120

150

150

180

180

180

180

180

180 180

180

180

270 240300330




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

30204050607090

180

190

190

160160

150170

180

190

170

120

130

160

140

150

180

190

180

170

180

180

180

180

190

180

190200

180

200

170160

180

190

150

170

170

180

180

190

25022023024

0260270280 290300310320330340350

220

230


��




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.20

0.30

0.50

0.60

0.700.80

0.30

0.40

0.500.70

0.80

0.901.001.10

0.50

0.60

0.500.600.90

1.000.900.80

1.20

1.30

1.40

1.501.

10

0.80

0.40

0.30

0.30

0.10

0.20

0.700.600.

500.10

0.20

0.10

0.30

0.40




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

170

170170

170

170

170

170

170

170

170


��



50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

0.20

0.20

0.30

0.40

0.30

0.80

0.60

0.70

0.50

0.60

0.40

0.30

0.40

0.30

0.40

0.60

0.70

0.80

0.90

1.00

1.201.001.101.5

0

1.60

1.70

1.80

1.30

1.40

0.50

0.701.40

1.30

1.10

1.00

0.90

1.001.20

1.401.601.701.50

0.700.800.901.001.301.401.501.60

0.70

0.80

0.90

1.00

1.10

1.40

1.50

1.60

1.30

1.20

0.30

0.200.30

0.10

0.10

906030

180

120

180150

180

210180

180

180

180

180

180

240




50o N

55o N

60o N

65o N

70o N

50o N

55o N

60o N

65o N

70o N

70403050608090

170

170

170

170 190 18

0

180

120

110 13

0

140

180

170

170

170

180

170

180170

190

200

210

150160180170190

180190

180

180

160

220230240250260

280


Appendix F

Paper submitted to Geophysical

Research Letters

The enclosed paper has been accepted by Geophysical Research Letters� November �� and ispublished in Geophysical Research Letters� Vol� �� N�� pages �� February ��

�

Seasonal Variation in the Main Tidal Constituent from Altimetry

V� Huess

Danish Meteorological Institute� Copenhagen� Denmark

O� B� Andersen

National Survey and Cadastre� Copenhagen� Denmark

Abstract

The existence of seasonal variations in the main tidal constituents has been known for a long

time from coastal tide gauges� In this paper we extend the amount of observations from the

relatively limited number of coastal tide gauge observations to also include the large amount of

o�shore information that have become available from altimetry� These observations are

compared with results from a hydrodynamical model applied for the north�west European shelf�

The model clearly identi�es the seasonal variation in the M� constituent as a shallow water e�ect

with a large part of the variation explained as a barotropic signal having high dependency on the

meteorological �eld over the area�

�

Introduction

Seasonal variation in the main tidal constituentshave been known for a long time� In �� R� H�Corkan investigated tide gauge data from the stationin Liverpool� U�K�� and observed less tidal range inthe winter period than predicted� and higher tidalrange in the summer period than predicted �Corkan�� To account for this observed annual perturbation� Corkan included two small semidiurnal constituents� MA� and MB�� that loses and gains approximately �� in the phase lag per day on M�� respectively� Cartwright� �� identi ed two causesto the existence of the MA� and MB� constituents�and de ned an annual modulation in M� caused bya pure gravitational e�ect �the anomalistic year withthe period T�� days�� and a seasonal modulation caused by the solar inclination �the tropicalyear with the period T�� days�� The annual contribution to the constituents MA� and MB�

are calculated from the gravity potential corresponding to �� and �� of the M� amplitude� respectively �Cartwright and Taylor� �� The distribution and cause of the observed MA� and MB�

amplitudes on several percent of the M� wave� havepreviously been investigated from coastal tide gaugedata mainly located around the British Isles �Bakerand Alcock� �� Pugh and Vassie� �� Pugh and

Vassie� �� New information about shallow water tides have recently been obtained from altimetrydata in the northwest European shelf region �An�dersen� �� We extend the previous investigationsof the seasonal modulation of the M� constituent toinclude the large amount of o�shore sea level observations from altimetry �see Figure �� This combinedFigure �o�shore and onshore data set is compared with resultsfrom a hydrodynamical model� with the objective toinvestigate the main factors responsible for the seasonal variation in M��

Seasonal Variation in the M�

Constituent

A linear combination of the three harmonics M��MA� and MB� can be shown to give a main contribution that can be interpreted as a M� carrier wave plusa modulation wave with a modulation in the M� amplitude at a period of T � �

�� year �Woodworth

et al� ��

h�t� � �HM�� S�t� ei��M�

t�gM��VM�

��

where the modulation wave S�t� is given by

S�t� � HMA�ei��t�gMA��gM�

��

� HMB�ei��t�gMB��gM�

��

where H is the amplitude� � the frequency� g the phaselag� and V the astronomical argument for the threeconstituents� Nodal corrections are ignored� The seasonal variation in the M� constituent is calculated bythe modulation wave S�t�� Note� that a separationof the annual and the seasonal contributions according to Cartwrights de nitions is not possible due tothe very small seperation in the frequency band� andthe name seasonal variation will be used throughoutthis paper to designate the total variation� where thisterm then includes the annual contribution�

Altimeter Data

Five years of TOPEX�POSEIDON altimetry ��cycles� were used to provide o�shore observations ofthe sea level height variations� Data were providedby the NASA Path nder Data� The altimetric observations were processed using the set of providedstandard geophysical� media and instrumental corrections� A special version without tidal correction wereprovided� Subsequently data within �� by �� latitudeby longitude bins were analysed for the tidal signalusing a harmonic analysis for the largest four constituents� Information about the time of observationwithin the year were taken into account by selectingdata in a � month data window� shifted by �� daysthrough the year computing ocean tide parametersfor each �� days shift� The choice of a � month datawindow was chosen to ensure an adequate numberof observations within each time shift� Plate � shows Plate �the maximumdeviation from the mean M� amplitude�top�� and the corresponding phase in the year for thismaximum �bottom�� with �� at January �st� TheT�P data identify an annual signal in the M� amplitude in the south eastern part of the North Sea ranging up to �� cm in July� This corresponds to deviations of up to �� of the M� amplitude� and indicatesa strong seasonal variation in this region� Harmonicanalysis of ve years of tide gauge data from Esbjergand Cuxhaven is shown in Figure � �for location see Figure �Figure �� Calculations of the seasonal variation S�t�for Esbjerg and Cuxhaven for the investigated yearsgives maximum deviations in May of �� cm and ��cm corresponding to �� and �� of the M� amplitude�respectively� This corresponds relatively well with thealtimetric results in Plate ��

�

Model Data

Five years of model simulations �� fromthe � km barotropic and non linear shallow waterhydrodynamical model developed by R A Flather�Proudman Oceanographic Laboratory �POL�� UK�Flather� �� were used to investigate the causingfactors of the seasonal variation in M� To investigatethe e�ect from the interaction with the meteorologi�cal �eld� data from model runs forced with tides onlyand model runs forced with both tides and meteo�rological �elds were analyzed The tidal forcing con�sists of a tidal wave generated by �� tidal constituents�MA� and MB� are not included in the forcing� at theopen boundaries The meteorological forcing consistsof reanalyzed �elds from the Norwegian Meteorologi�cal Institute �Reistad and Iden� �� The seasonalmodulation wave S�t� simulated by the model for oneyear �� is shown in Plate � Maximum amplitudePlate �

and corresponding phase lag for S�t� are shown Themaximum deviation for �� is a little more than �cm For �� a maximum of more than � cm is foundin German Bight The seasonal variation is in thetidal run caused by a non linear combination betweenthe tidal frequencies� but the model does not resolvewhich constituents interact to give the e�ect By com�paring the two model runs� the seasonal variation canbe identi�ed as a shallow water e�ect with a signi��cant dependence on the meteorological forcing

Model Results and Validation

The strong signal in the south eastern part of theNorth Sea� having a maximum M� deviation in theboreal summer period is observed from both altimetryand the hydrodynamical model The di�erent spatialshape of the model and the T�P derived signal maybe explained by the poor spatial resolution of the T�Pdata �processed in �� by �� bins� This is also theexplanation for the missing seasonal modulation inthe T�P observations along the British east coastResults from the �ve years model simulations havebeen validated by �� tide gauges along the North Seacoast �Wick� Leith� North Shields� Lowestoft� Sheer�ness� Rosco�� Cherbourg� Oostende� Esbjerg� Tors�minde� Hanstholm and Hirtshals� The model forcedwith both tides and meteorological �elds captures onaverage �� of the M� seasonal variation at these tidegauges Without the meteorological forcing� �� ofthe variation was explained by the non linear tidalinteraction in the model This identi�es a strong de�pendence to both the tidal interaction and the tidal�

meteorological interaction Furthermore the modelcaptures the large inter annual variations observedover the period �� from the tide gauges

Conclusion

The current accuracy of the T�P altimeters en�able observations of annual deviations in the mainconstituent M� This new knowledge about thespatial behaviour of the signal in the North Seawas compared with output from a hydrodynamicalmodel The barotropic model con�rmed that the sea�sonal variation is a shallow water phenomena� whichwas previously indicated from investigations based oncoastal tide gauge data alone The non linear interac�tion between the tides and the surges is seen to be animportant factor for the seasonal variation Despitethe relatively poor spatial resolution of the model� themain part of the seasonal variation is still seen as abarotropic phenomenon Future investigations with amodel on a �ner grid would include more of the verynear coastal shoaling e�ects� and give a more preciseestimate of the magnitude of the barotropic e�ects�and indicate the possible existence of baroclinic ef�fects of the seasonal variation in M�

Acknowledgments� This work is a contribution tothe GEOSONAR project under the Danish Earth Ob�servation Programme supported by the Danish ResearchCouncils� The authors wish to thank the NASA AltimeterPath�nder project� the British� French� Belgium� Germanand Danish hydrographic data providers for data� R� A�Flather� J� A� Williams and P� L� Woodworth� POL� UKfor kindly providing model data and for valuable discus�sions�

References

Andersen� O� B�� Shallow water tides in the northwest Eu�ropean shelf region from TOPEX�POSEIDON altime�try� Journal of Geophysical Research� �� C��

Baker� T� F� and G� A� Alcock� Time variations of oceantides� in Proc� �th Int� Symp� Earth Tides� edited by J�T� Kuo� pp� �� Schweizerbart� Stuttgart� ��

Cartwright� D� E�� A uni�ed analysis of tides and surgesround north and east Britain� Phil� Trans� R� Soc��

London� A ��

Cartwright� D� E� and R� J� Taylor� New computations ofthe tide�generating potential� Geophys� J� R� Astron�Soc��

Corkan� R� H�� An annual perturbation in the range oftide� Proc� R� Soc� London� A ��

�

Flather� R� A�� A tidal model of the north�west European

continental shelf�M�emoires Soci�et�e Royale des Sciences

de Li�ege� �e s�erie� tome X� ��

Pugh� D� T� and J� M� Vassie� Tide and Surge Propaga�

tion O��shore in the Dowsing Region of the North Sea�

Deutsche Hydrographische Zeitschrift� ��

��

Pugh� D� T� and J� M� Vassie� Seasonal Modulations of

the Principal Semidiurnal Lunar Tide� in Mixing and

Transport in the Environment� edited by K� J� Beven�

P� C� Chatwin and J� H� Milbank� �� John Wiley

� Sons Ltd��

Reistad� M� and K� Iden� Updating� correction and evalu�

ation of a hindcast data base of air pressure� wind and

waves for the North Sea� the Norwegian Sea and the

Barents Sea� Research Report No� �� Norwegian Mete�

orological Institute� Oslo� Norway� ��

Woodworth� P� L�� S� M� Shaw and D� L� Blackman� Sec�

ular trends in the mean tidal range around the British

Isles and along the adjacent European coastline� Geo�

phys� J� Int��

V� Huess� Danish Meteorological Institute� Lyng�byvej �� DK�� Copenhagen� Denmark� �emailvhdmi�dk�O� B� Andersen� National Survey and Cadastre�

Rentemestervej �� DK�� Copenhagen� Denmark��email oakms�dk�

Received June �� accepted November ��

This preprint was prepared with AGU�s LATEX macros

v�� File accepteretHUESSTEXT formatted December ��

��

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+ +

+

+++++++++

++++++++

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

++

++++++

++++++

+++

++++++

++++++

++++++

++++++

++++++

++++++

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+++++

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50

52

54

56

58

−2 0 2 4 6 8 10

Esbjerg

Cuxhaven

Figure F�� Figure �� Ground tracks for the T�P altimeters�

Figure F�� Figure �� Maximum deviations in the M� constituent from tide gauge data fromCuxhaven and Esbjerg�

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00 50 100 150 200

0

50

100

0.51.0

0.5 1.0

1.0

1.0

0.5

0.5

0.5

1.5

1.0

1.5

1.5 2.0

2.0

0.5

2.0

1.0

1.0

0.5

0.5

2.5

0 50 100 150 2000

50

100

3.03.5

4.0

4.55.0

0 50 100 150 2000

50

100

0

0−60

−120

0

0

0 50 100 150 2000

50

100

60

120

120

120

120

60

60

180

180

120 180

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

48

50

52

54

56

58

60

−10 −5 0 5 10

48

50

52

54

56

58

60

−10 −5 0 5 10

Figure F�� Plate �� Maximum deviations in the M� constituent from T�P data� Maximumamplitude �cm� �top� and phase lag �deg�� bottom��

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00 50 100 150 200

0

50

100

2.5

5.0

2.5

2.5

7.5

7.55.0

5.05.0

2.5

2.5

2.5

2.5

10.0

12.5

15.0

2.5

2.5

5.07.5 10.012.515.0

7.510.012.515.0

0 50 100 150 2000

50

100

17.5

20.0

17.520.0

17.520.0

0 50 100 150 2000

50

100

0 50 100 150 2000

50

100

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

48

50

52

54

56

58

−4 −2 0 2 4 6 8 10

−180

−90

0

90

180 Phase (degree)

48

50

52

54

56

58

−4 −2 0 2 4 6 8 10

0.0

2.5

5.0

7.5

10.0 Amplitude (mm)

Model: Tidal forcing

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.00 50 100 150 200

0

50

100

5.0

7.5

5.02.5

7.5

7.5

7.5

5.0

5.0

2.5

2.5

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10.0

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12.512

.5

15.0

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12.512.5

15.0

2.5

0 50 100 150 2000

50

100

17.5

17.5

17.520.0

20.0

20.0

17.520.0

0 50 100 150 2000

50

100

0 50 100 150 2000

50

100

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

48

50

52

54

56

58

−4 −2 0 2 4 6 8 10

−180

−90

0

90

180 Phase (degree)

48

50

52

54

56

58

−4 −2 0 2 4 6 8 10

0.0

2.5

5.0

7.5

10.0 Amplitude (mm)

Model: Tidal+met. forcing

Figure F�� Plate �� Model simulated M� modulation wave for �� Maximum amplitude �cm��top� and phase lags �bottom�� Results from a tidal run �left� and a tidal�met� run �right��

DANISH METEOROLOGICAL INSTITUTE Scientific Reports Scientific reports from the Danish Meteorological Institute cover a variety of geophysical fields,

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Reports in the series within the last five years:

No. 96-1 Poul Frich (co-ordinator), H. Alexandersson, J. Ashcroft, B. Dahlström, G.R. Demarée, A. Drebs, A.F.V. van Engelen, E.J. Førland, I. Hanssen-Bauer, R. Heino, T. Jónsson, K. Jonasson, L. Keegan, P.Ø. Nordli, T. Schmith, P. Steffensen, H. Tuomenvirta, O.E. Tveito: North Atlantic Clima-tological Dataset (NACD Version 1) - Final report No. 96-2 Georg Kjærgaard Andreasen: Daily response of high-latitude current systems to solar wind varia-tions: application of robust multiple regression. Methods on Godhavn magnetometer data No. 96-3 Jacob Woge Nielsen, Karsten Bolding Kris-tensen, Lonny Hansen: Extreme sea level highs: a statistical tide gauge data study No. 96-4 Jens Hesselbjerg Christensen, Ole Bøssing Christensen, Philippe Lopez, Erik van Meijgaard, Michael Botzet: The HIRLAM4 Regional Atmos-pheric Climate Model No. 96-5 Xiang-Yu Huang: Horizontal diffusion and filter-ing in a mesoscale numerical weather prediction model No. 96-6 Henrik Svensmark and Eigil Friis-Christensen: Variation of cosmic ray flux and global cloud cov-erage - a missing link in solar-climate relationships No. 96-7 Jens Havskov Sørensen and Christian Ødum Jensen: A computer system for the management of epidemiological data and prediction of risk and economic consequences during outbreaks of foot-and-mouth disease. CEC AIR Programme. Contract No. AIR3 - CT92-0652

No. 96-8 Jens Havskov Sørensen: Quasi-automatic of input for LINCOM and RIMPUFF, and output conver-sion. CEC AIR Programme. Contract No. AIR3 - CT92-0652 No. 96-9 Rashpal S. Gill and Hans H. Valeur: Evaluation of the radarsat imagery for the opera-tional mapping of sea ice around Greenland No. 96-10 Jens Hesselbjerg Christensen, Bennert Machen-hauer, Richard G. Jones, Christoph Schär, Paolo Michele Ruti, Manuel Castro and Guido Visconti: Validation of present-day regional climate simula-tions over Europe: LAM simulations with observed boundary conditions No. 96-11 Niels Larsen, Bjørn Knudsen, Paul Eriksen, Ib Steen Mikkelsen, Signe Bech Andersen and Tor-ben Stockflet Jørgensen: European Stratospheric Monitoring Stations in the Artic: An European con-tribution to the Network for Detection of Strato-spheric Change (NDSC): CEC Environment Pro-gramme Contract EV5V-CT93-0333: DMI contri-bution to the final report No. 96-12 Niels Larsen: Effects of heterogeneous chemistry on the composition of the stratosphere: CEC Envi-ronment Programme Contract EV5V-CT93-0349: DMI contribution to the final report No. 97-1 E. Friis Christensen og C. Skøtt: Contributions from the International Science Team. The Ørsted Mission - a pre-launch compendium No. 97-2 Alix Rasmussen, Sissi Kiilsholm, Jens Havskov Sørensen, Ib Steen Mikkelsen: Analysis of tropo-spheric ozone measurements in Greenland: Contract No. EV5V-CT93-0318 (DG 12 DTEE): DMI’s contribution to CEC Final Report Arctic Tro-phospheric Ozone Chemistry ARCTOC

No. 97-3 Peter Thejll: A search for effects of external events on terrestrial atmospheric pressure: cosmic rays No. 97-4 Peter Thejll: A search for effects of external events on terrestrial atmospheric pressure: sector boundary crossings No. 97-5 Knud Lassen: Twentieth century retreat of sea-ice in the Greenland Sea No. 98-1 Niels Woetman Nielsen, Bjarne Amstrup, Jess U. Jørgensen: HIRLAM 2.5 parallel tests at DMI: sensitivity to type of schemes for turbulence, moist processes and advection No. 98-2 Per Høeg, Georg Bergeton Larsen, Hans-Henrik Benzon, Stig Syndergaard, Mette Dahl Morten-sen: The GPSOS project Algorithm functional design and analysis of iono-sphere, stratosphere and troposphere observations No. 98-3 Mette Dahl Mortensen, Per Høeg: Satellite atmosphere profiling retrieval in a nonlin-ear troposphere Previously entitled: Limitations induced by Multi-path No. 98-4 Mette Dahl Mortensen, Per Høeg: Resolution properties in atmospheric profiling with GPS No. 98-5 R.S. Gill and M. K. Rosengren Evaluation of the Radarsat imagery for the opera-tional mapping of sea ice around Greenland in 1997 No. 98-6 R.S. Gill, H.H. Valeur, P. Nielsen and K.Q. Han-sen: Using ERS SAR images in the operational mapping of sea ice in the Greenland waters: final report for ESA-ESRIN’s: pilot projekt no. PP2.PP2.DK2 and 2nd announcement of opportunity for the exploitation of ERS data projekt No. AO2..DK 102 No. 98-7 Per Høeg et al.: GPS Atmosphere profiling meth-ods and error assessments

No. 98-8 H. Svensmark, N. Woetmann Nielsen and A.M. Sempreviva: Large scale soft and hard turbulent states of the atmosphere No. 98-9 Philippe Lopez, Eigil Kaas and Annette Guld-berg: The full particle-in-cell advection scheme in spherical geometry No. 98-10 H. Svensmark: Influence of cosmic rays on earth’s climate No. 98-11 Peter Thejll and Henrik Svensmark: Notes on the method of normalized multivariate regression No. 98-12 K. Lassen: Extent of sea ice in the Greenland Sea 1877-1997: an extension of DMI Scientific Report 97-5 No. 98-13 Niels Larsen, Alberto Adriani and Guido DiDon-francesco: Microphysical analysis of polar strato-spheric clouds observed by lidar at McMurdo, Ant-arctica No.98-14 Mette Dahl Mortensen: The back-propagation method for inversion of radio occultation data No. 98-15 Xiang-Yu Huang: Variational analysis using spatial filters No. 99-1 Henrik Feddersen: Project on prediction of cli-mate variations on seasonel to interannual time-scales (PROVOST) EU contract ENVA4-CT95-0109: DMI contribution to the final re-port:Statistical analysis and post-processing of uncoupled PROVOST simulations No. 99-2 Wilhelm May: A time-slice experiment with the ECHAM4 A-GCM at high resolution: the ex-perimental design and the assessment of climate change as compared to a greenhouse gas experi-ment with ECHAM4/OPYC at low resolution No. 99-3 Niels Larsen et al.: European stratospheric monitoring stations in the Artic II: CEC Envi-ronment and Climate Programme Contract ENV4-CT95-0136. DMI Contributions to the project

No. 99-4 Alexander Baklanov: Parameterisation of the deposition processes and radioactive decay: a re-view and some preliminary results with the DERMA model No. 99-5 Mette Dahl Mortensen: Non-linear high resolu-tion inversion of radio occultation data No. 99-6 Stig Syndergaard: Retrieval analysis and meth-odologies in atmospheric limb sounding using the GNSS radio occultation technique No. 99-7 Jun She, Jacob Woge Nielsen: Operational wave forecasts over the Baltic and North Sea No. 99-8 Henrik Feddersen: Monthly temperature fore-casts for Denmark - statistical or dynamical? No. 99-9 P. Thejll, K. Lassen: Solar forcing of the Northern hemisphere air temperature: new data No. 99-10 Torben Stockflet Jørgensen, Aksel Walløe Hansen: Comment on “Variation of cosmic ray flux and global coverage - a missing link in solar-climate relationships” by Henrik Svensmark and Eigil Friis-Christensen No. 99-11 Mette Dahl Meincke: Inversion methods for at-mospheric profiling with GPS occultations No. 99-12 Hans-Henrik Benzon; Laust Olsen; Per Høeg: Simulations of current density measurements with a Faraday Current Meter and a magnetome-ter No. 00-01 Per Høeg; G. Leppelmeier: ACE - Atmosphere Climate Experiment No. 00-02 Per Høeg: FACE-IT: Field-Aligned Current Ex-periment in the Ionosphere and Thermosphere No. 00-03 Allan Gross: Surface ozone and tropospheric chemistry with applications to regional air quality modeling. PhD thesis

No. 00-04 Henrik Vedel: Conversion of WGS84 geometric heights to NWP model HIRLAM geopotential heights No. 00-05 Jérôme Chenevez: Advection experiments with DMI-Hirlam-Tracer No. 00-06 Niels Larsen: Polar stratospheric clouds microphysical and optical models No. 00-07 Alix Rasmussen: “Uncertainty of meteorological parameters from DMI-HIRLAM” No. 00-08 A.L. Morozova: Solar activity and Earth’s weather. Effect of the forced atmospheric trans-parency changes on the troposphere temperature profile studied with atmospheric models No. 00-09 Niels Larsen, Bjørn M. Knudsen, Michael Gauss, Giovanni Pitari: Effects from high-speed civil traffic aircraft emissions on polar strato-spheric clouds No. 00-10 Søren Andersen: Evaluation of SSM/I sea ice algorithms for use in the SAF on ocean and sea ice, July 2000 No. 00-11 Claus Petersen, Niels Woetmann Nielsen: Di-agnosis of visibility in DMI-HIRLAM No. 00-12 Erik Buch: A monograph on the physical ocean-ography of the Greenland waters No. 00-13 M. Steffensen: Stability indices as indicators of lightning and thunder No. 00-14 Bjarne Amstrup, Kristian S. Mogensen, Xiang-Yu Huang: Use of GPS observations in an optimum interpolation based data assimilation system No. 00-15 Mads Hvid Nielsen: Dynamisk beskrivelse og hydrografisk klassifikation af den jyske kyst-strøm

No. 00-16 Kristian S. Mogensen, Jess U. Jørgensen, Bjarne Amstrup, Xiaohua Yang and Xiang-Yu Huang: Towards an operational implementation of HIRLAM 3D-VAR at DMI No. 00-17 Sattler, Kai; Huang, Xiang-Yu: Structure func-tion characteristics for 2 meter temperature and relative humidity in different horizontal resolu-tions No. 00-18 Niels Larsen, Ib Steen Mikkelsen, Bjørn M. Knudsen m.fl.: In-situ analysis of aerosols and gases in the polar stratosphere. A contribution to THESEO. Environment and climate research programme. Contract no. ENV4-CT97-0523. Fi-nal report No. 00-19 Amstrup, Bjarne: EUCOS observing system experiments with the DMI HIRLAM optimum in-terpolation analysis and forecasting system No. 01-01 V.O. Papitashvili, L.I. Gromova, V.A. Popov and O. Rasmussen: Northern polar cap magnetic activity index PCN: Effective area, universal time, seasonal, and solar cycle variations No. 01-02 M.E. Gorbunov: Radioholographic methods for processing radio occultation data in multipath re-gions No. 01-03 Niels Woetmann Nielsen; Claus Petersen: Cal-culation of wind gusts in DMI-HIRLAM No. 01-04 Vladimir Penenko; Alexander Baklanov: Methods of sensitivity theory and inverse model-ing for estimation of source parameter and risk/vulnerability areas No. 01-05 Sergej Zilitinkevich; Alexander Baklanov; Jutta Rost; Ann-Sofi Smedman, Vasiliy Lykosov and Pierluigi Calanca: Diagnostic and prognostic equations for the depth of the stably stratified Ekman boundary layer No. 01-06 Bjarne Amstrup: Impact of ATOVS AMSU-A radiance data in the DMI-HIRLAM 3D-Var analysis and forecasting system

No. 01-07 Sergej Zilitinkevich and Alexander Baklanov: Calculation of the height of stable boundary lay-ers in operational models. No. 01-08 Vibeke Huess: Sea level variations in the North Sea - from tide gauges, altimetry and modelling.

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