The relationship between sea level and bottom pressure in an eddy permitting ocean model Rory Bingham and Chris Hughes Proudman Oceanographic Laboratory

Introduction Motivation: Clearer understanding on dynamics; Separation of barotropic and baroclinic components To what extent can altimetry be used to infer bottom pressure and validate GRACE Statistical properties of bottom pressure for assimilation into ocean models Outline: Variability of sea level and bottom pressure Co-variability of sea level and bottom pressure: geographic and frequency partitions EOF analysis: high and low frequencies, and Arctic Ocean. OCCAM: 0.25 ° eddy permitting resolution 66 vertical levels ECMWF 6hrly forcing 5 day mean fields period after spin up

The variability of bottom pressure and sea level Sea level Bottom pressure standard deviation maps power spectra sea level bottom pressure

The co-variability of bottom pressure and sea level: all frequencies Correlation of sea level and bottom pressure Percent of total sea level variance “appearing” as bottom pressure

The co-variability of BP and SL: geographical partitions To investigate how the relationship between bottom pressure and sea level depends on frequency for a particular geographical partition we compute the admittance: h, anomalous sea level p, anomalous bottom pressure ^ signifies Fourier transform * signifies the complex conjugate Summation is performed over some geographic region for each frequency component Z(   )=1 implies bottom pressure and sea level variability averaged over region is identical for frequency  0

Partition according to depth: 1.Shallow (<1000m) 2.Deep (>1000m) 3.Deep averaged over 1,2,4,8 degree bins The co-variability of BP and SL: geographical partitions Partition according to latitude: 1.Low (0-15°) 2.Mid (45°-65°) 3.High (65°-80°) Partition according to latitude and sea level variance: 1.Mid (45°-65°) 2.High (65°-80°) sd<5cm sd>10cm

The co-variability of BP and SL: frequency partitions To investigate how the relationship between bottom pressure and sea level depends on geographical location for a particular frequency band we compute the admittance: h, anomalous sea level p, anomalous bottom pressure ^ signifies Fourier transform * signifies the complex conjugate Summation is performed over some frequency band at each location Z(  0  0 )=1 implies bottom pressure and sea level variability in frequency band is identical at location  0, 0

The co-variability of BP and SL: frequency partitions 10-20cpd 20-60cpd annual interannual zero phase difference given by eastward pointing vector

EOFs of high frequency (T<100days) bottom pressure and sea level variability BP EOF1 (22%) BP EOF3 (3%) BP EOF2 (7%) SL EOF1 (15%) SL EOF3 (2%) SL EOF2 (5%) cor=0.91 cor=0.87

The variance accounted for the leading HF mode bottom pressure EOF1 sea level EOF1 % %

bottom pressure sea level EOFs of interannual (400days<T) BP and SL variability: Arctic basin POV (80%)POV (30%)EOF1 EOF2 POV (14%) BP1 SL1+SL2 correlation =0.85

bottom pressure sea level EOFs of interannual (400days<T) BP and SL variability: Arctic basin POV (3%)POV (4%)EOF2EOF3 BP2 SL3 correlation =0.79

Summary Sea level power much greater than bottom pressure Sea level and bottom pressure relationship highly dependent on timescale and geography Good correspondence at high frequencies where ocean behaves barotropically. Basin scale modes account for most of HF variance globally, but outside tropics smaller scale processes are more important. In most of deep ocean correspondence falls off rapidly with increasing timescale so little similarity at annual. Relationship disrupted to the presence of small scale energetic eddies, particularly in boundary currents The Arctic is an exception. Single basinwide mode dominants BP and SL at interannual timescales. Interannual relationship also on shelf seas.

Composites based on the transport through Drake passage

BP and SSH variability at 42N BP SSH

Low frequency BP and SSH variability at 42N bottom pressure sea level EB WB MAR 300m 1300m 3000m

Leading EOFs of interannual sea-surface height and bottom pressure BP EOF1 SSH BP SSH EOF1Strong association between leading bottom pressure and sea-level EOFs and low frequency MOC mode Pressure signal strongly constrained by bathymetry Consistent with geostrophic relationship Both account for most of variance on shelf and upper slope but little in the deeper ocean. Signal weakens to the south

Leading EOFs of interannual sea-surface height and bottom pressure BP EOF1SSH EOF1

The geostrophic calculation at 42N Upper layer transport RMS error: 0.28Sv Lower layer transport RMS error: 0.31Sv Actual Inferred from western boundary pressure

Observed low frequency SSH variability at 42N Eastern boundary Western boundary Mid-Atlantic Ridge

Leading EOFs of interannual sea-surface height AltimetryOCCAM Altimetry OCCAM

Global BP EOFs