CMEMS General Assembly, 23 May 2019 RENUMERATE: Reducing numerical mixing resulting from applying tides explicitly in a global ocean model Alex Megann1 and Maria Luneva2 (1) National Oceanography Centre, Southampton, UK (2) National Oceanography Centre, Liverpool, UK CMEMS General Assembly, 23 May 2019

Project objectives and team presentation Adding tides to ocean models Motivation: benefits and downsides The global tidally forced model Preliminary mixing analysis Numerical mixing in fixed-coordinate models The z~ coordinate Further alleviation of numerical mixing Summary and next steps Projected impacts on CMEMS MFCs and TACs

Overall objectives of RENUMERATE project Objective 1: To add explicit tidal forcing to the GO8.0 global ¼° NEMO configuration and evaluate the effects on water mass characteristics and mixing.

Overall objectives of RENUMERATE project Objective 1: To add explicit tidal forcing to the GO8.0 global ¼° NEMO configuration and evaluate the effects on water mass characteristics and mixing. Objective 2: To add the z-tilde semi-lagrangian coordinate to this configuration and evaluate the effects on water mass characteristics and mixing, in particular to assess its effect in ameliorating numerical mixing from tidal and other high frequency motions.

Overall objectives of RENUMERATE project Objective 1: To add explicit tidal forcing to the GO8.0 global ¼° NEMO configuration and evaluate the effects on water mass characteristics and mixing. Objective 2: To add the z-tilde semi-lagrangian coordinate to this configuration and evaluate the effects on water mass characteristics and mixing, in particular to assess its effect in ameliorating numerical mixing from tidal and other high frequency motions. Objective 3 To investigate the effects of tides on large-scale ocean circulation, including global stratification, overturning and gyre circulations; shelf slope exchange, seasonal mixed layers, deep and bottom waters, and polar sea ice.

The RENUMERATE team Alex Megann Maria Luneva Interests: Interests: Model development, numerical mixing, vertical coordinate issues, ocean heat uptake Role in project: Overall PI; carry out model runs and evaluate them; lead on project deliverables Maria Luneva Interests: High latitude oceans, ocean mixing schemes, tides, vertical coordinate issues Role in project: Test tidal configurations and diagnostics; advice on tides and mixing; contribute to reports and papers

Why add tides to a global ocean model? Tidal motions close to ridges and rough bathymetry, along with breaking internal tides, cause strong mixing in the ocean; standard parameterisations of tidal mixing can only be an approximation, neglecting spatial distributions and link to circulation.

Why add tides to a global ocean model? Tidal motions close to ridges and rough bathymetry, along with breaking internal tides, cause strong mixing in the ocean; standard parameterisations of tidal mixing can only be an approximation, neglecting spatial distributions and link to circulation. Tidal flows are dominant source of mixing on shelves.

Why add tides to a global ocean model? Tidal motions close to ridges and rough bathymetry, along with breaking internal tides, cause strong mixing in the ocean; standard parameterisations of tidal mixing can only be an approximation, neglecting spatial distributions and link to circulation. Tidal flows are dominant source of mixing on shelves. Tides are responsible for a large part of transport of nutrients on and off shelves.

Potential downsides to including tidal forcing Large tidal velocities will stress stability of model numerics, especially in shallow shelf regions and over slopes.

Potential downsides to including tidal forcing Large tidal velocities will stress stability of model numerics, especially in shallow shelf regions and over slopes. Vertical motions from tides have potential to cause significant levels of numerical mixing in a depth-coordinate ocean model

Potential downsides to including tidal forcing Large tidal velocities will stress stability of model numerics, especially in shallow shelf regions and over slopes. Vertical motions from tides have potential to cause significant levels of numerical mixing in a depth-coordinate ocean model Most global models, with horizontal resolutions of 20-80 km and with 40-80 vertical levels, cannot realistically simulate the internal tide, and certainly not the explicit mixing from the latter.

Potential downsides to including tidal forcing Large tidal velocities will stress stability of model numerics, especially in shallow shelf regions and over slopes. Vertical motions from tides have potential to cause significant levels of numerical mixing in a depth-coordinate ocean model Most global models, with horizontal resolutions of 20-80 km and with 40-80 vertical levels, cannot realistically simulate the internal tide, and certainly not the explicit mixing from the latter. … but it’s still worth doing!

Adding tides to the GO8p0.1 global model Global NEMO configuration: horizontal resolution ¼° (10-27km) and 75 vertical levels. Closely related to ocean component of GC3.1 coupled model (used in CMIP6). Forced with M2, S2, N2, K1 and O1 tidal components. This is, to our knowledge, the first tidally-forced NEMO simulation in a realistic, eddy-permitting global domain.

First assessment of tidal motions GO8p0 tidal experiment GESLA analysis RMS hourly surface elevation excursion from the mean (metres) over three months in tidally-forced simulation (left) and M2 amplitude in GESLA analysis (right)

Numerical mixing in fixed-coordinate models Default vertical coordinate in NEMO is nonlinear free surface (z*): vertical levels are allowed to flex with external mode, but internal waves and internal tides will cause advection across coordinate surfaces. Advection schemes have a diffusive component, which leads to spurious numerical mixing (Griffies et al, 2000). This constitutes a substantial contribution to mixing in global ¼° NEMO configurations (Megann, Ocean Modelling, 2018) So we need to address numerical mixing to avoid tides adding to this

Quantification of numerical mixing We estimate effective diapycnal diffusivity keff in latitude bins and in density classes from the rate of watermass transformation (Lee et al, 2002; and Megann, 2018). To assess magnitude of numerical mixing, we compare keff in each experiment with: explicit vertical diffusivity kexp from model mixing scheme; and with diagnosed diffusivity keff in control. Augment this with global temperature drifts at each depth level. As expected, effective diffusivity is generally higher with tides than in control, particularly in intermediate and bottom water densities.

Tackling numerical mixing Introduce elasticity in vertical coordinate (z~) that flexes with disturbances of isopycnals on timescales less than a few days. Leclair and Madec (2011) found this reduced numerical mixing by a factor of ~5 in an idealized model. Have implemented z~ in the the global GO8p0 configuration. Vertical grid distortion associated with passage of large internal wave in NEMO with z~ scheme enabled (from Leclair and Madec, 2011)

Effects of z~ on mixing Adding z~ alone gives an unequivocal, though small (5-10%), reduction in effective diffusivity relative to control. Other changes to numerical scheme are being evaluated: More accurate (4th order) horizontal advection scheme; Increased viscosity to suppress poorly resolved, but persistent mesoscale features at higher latitudes, which are known to produce numerical mixing (Megann and Storkey, 2019); Increased filter cutoff time for z~ from 5 to 10 days

Preliminary results from sensitivity experiments All changes give reductions in effective diffusivity and in T drifts Largest improvements are from higher-order horizontal advection and increased viscosity Ratio of keff to keff in control Global mean temperature change between years 1 and 30

Achievements to date We have built and demonstrated the first global 3-D tidal model using NEMO at eddy-permitting resolution.

Achievements to date We have built and demonstrated the first global 3-D tidal model using NEMO at eddy-permitting resolution. The simulated barotropic tide is realistic in amplitude and spatial distribution.

Achievements to date We have built and demonstrated the first global 3-D tidal model using NEMO at eddy-permitting resolution. The simulated barotropic tide is realistic in amplitude and spatial distribution. We have installed and tested the novel z~ flexible vertical coordinate for the first time in a global model.

Achievements to date We have built and demonstrated the first global 3-D tidal model using NEMO at eddy-permitting resolution. The simulated barotropic tide is realistic in amplitude and spatial distribution. We have installed and tested the novel z~ flexible vertical coordinate for the first time in a global model. Preliminary analysis confirms that z~ offers a clear reduction in numerical mixing at little computational cost; other changes in numerical schemes offer promising further improvements.

Next steps Build improved tidal simulation with realistic shelf depths Complete 2-D and 3-D harmonic analysis of tidal simulation Evaluate shelf transports from tidal motions

Next steps Build improved tidal simulation with realistic shelf depths Complete 2-D and 3-D harmonic analysis of tidal simulation Evaluate shelf transports from tidal motions Quantify effect on run speed of numerical improvements

Next steps Build improved tidal simulation with realistic shelf depths Complete 2-D and 3-D harmonic analysis of tidal simulation Evaluate shelf transports from tidal motions Quantify effect on run speed of numerical improvements Combine numerical improvements with z~ to give optimised configuration

Next steps Build improved tidal simulation with realistic shelf depths Complete 2-D and 3-D harmonic analysis of tidal simulation Evaluate shelf transports from tidal motions Quantify effect on run speed of numerical improvements Combine numerical improvements with z~ to give optimised configuration Add tidal forcing to the latter, then repeat the above!

Benefits to Monitoring and Forecasting Centres (1) The work here is developing improvements to the NEMO ocean model, used in CMEMS operational systems, so results (in principle) are directly transferable to MFCs…

Benefits to Monitoring and Forecasting Centres (2) The simulation of tides will improve realism of ocean circulation in operational models, and hence will improve accuracy of forecasts. Specific examples include: Interaction between tides and sea ice has potential to enhance forecasting ability of the Arctic MFC. The presence of tidal transports on ocean shelves will improve the representation of shelf seas and biogeochemical fields (all MFCs)

Benefits to Monitoring and Forecasting Centres (3) The addition of the z~ coordinate and the optimisation of numerical schemes around it will further improve accuracy of forecasts. Specifically: We work closely with Mercator Ocean in Toulouse on improving the numerical performance of NEMO: this will feed directly into improvements in global models in the Global MFC. Minimising the numerical mixing associated with tidal motions will benefit all MFCs.

Benefits to Thematic Assembly Centres The development of a global, relatively high resolution 3-D ocean model with tides will be of interest to the Sea Level TAC