Data Assimilative Physical Modeling of the

California Current System (experimental)

with Forecast Observational Impact Assesments and

High Frequency Radar Radial Observations

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Our assimilation procedure currently runs over 4-day cycles. Every day, a data assimilation run is performed for the previous 4 days, producing an estimate of the physical ocean state in which the model initial conditions have been modified. Several physical data sets are assimilated. AVISO Sea Level Anomalies and subtidally averaged NOAA tide-gauge data provide information of the sea surface height. OSTIA Sea Surface Temperature and AQUARIUS Sea Surface Salinity provide additional sea surface information. Subsurface hydrography derives from several platforms: Argo buoys provide subsurface information broadly throughout our domain. In addition, glider lines in the central and southern California regions are supported by SCCOOS and CeNCOOS. Glider information off the Washington coast is supported by NANOOS. We are grateful to the agencies and individuals who have made this data available for use in this ocean state estimate.

We note that not all data mentioned above is generally assimilated into every cycle. Some platforms (e.g., Argo) do not necessarily collect information within our domain during every assimilation cycle. In addition, AQUARIUS data is presently only available in delayed-time mode and not in real-time. However, this information is useful for reanalyses, which we run occasionally to update our historical estimates.

The ** California Current System (CCS)** refers to the multiple
oceanographic features of the northeast Pacific Ocean circulation off
the U.S. west coast. It includes the broad equatorward surface motion
that represents the easternmost portion of the North Pacific subtropical
gyre spanning the breadth of the ocean basin, a narrow subsurface
poleward flow (the California Undercurrent) often found between about
100 and 300 m depth along the continental slope, and occasionally a
narrow surface nearshore countercurrent, seasonally varying in intensity
and often strongest in fall. Superposed on these slowly varying motions
are intense mesoscale eddies of tens to 100 km in scale that vary
position on weekly to monthly time-scales, as well as smaller
submesoscale and smaller motions that fluctuate on still shorter
time-scales.
**CCS Physical Model:**
The ocean circulation is modeled using the Regional Ocean Modeling System (ROMS).
Our domain extends from midway down the Baja Peninsula to the southern tip
of Vancouver Island at 1/10 degree (roughly 10 km) resolution, with 42
terrain-following levels resolving vertical structure in ocean
properties. The model is forced at the surface by atmospheric fields
produced by the Coupled Ocean
Atmosphere Mesoscale Prediction System (COAMPS) which
is run in near-real-time by the Naval
Research Laboratory. Oceanic fields at the
lateral boundaries are obtained from a larger,
basin-scale data assimilative model,
HYCOM.
The model does not include freshwater forcing by rivers, and
it neglects tidal motion. Ocean model fields are stored as daily
snapshots at midnight GMT.

Despite tremendous advances in **ocean circulation models ** over the
last several decades, many sources of error exist and are in fact
unavoidable when trying to accurately represent or predict the complex
evolution of the true ocean state (i.e., the full physical structure of
temperature, salinity and velocity fields). For example, the initial
ocean state from which a simulation evolves is never known with 100%
accuracy. In addition, ocean models themselves involve approximations
of the true fluid dynamics for many reasons, such as limited resolution
or imperfect representation of unresolved processes like small-scale
turbulence. Finally, forcing fields (such as wind stress or heat flux)
and conditions applied at the lateral (open) boundaries of the regional
ocean model are themselves model solutions also with their own
uncertainties.
**Assimilation Approach**
The solution shown on this page applies the Incremental,
Strong-Constraint 4-D Variational Assimilation (4DVar) method. This
approach finds changes to the initial ocean state during an assimilation
cycle that minimize a cost function representing the sum of squared
model-data differences and squared deviations of a background model
ocean state. This method can also expand the control-space to include
changes in the surface forcing and lateral boundary conditions, though
such changes are not included in the shown solution. This approach is
referred to as incremental as it determines increments to the background
ocean state that are assumed to be small. The phrase strong-constraint
means that errors in ocean dynamics are neglected (i.e., model dynamics
are applied as a strong constraint).

What impact does any given observation have on the system's ability to forecast the future ocean state? We can compare the improvement of a forecast based on a 4D-Var data-assimilative solution with a forecast based on the non-assimilative case. Observation forecast impact calculations allow for the computation of the contribution of each individual observation that is assimilated during 4D-Var process to the forecast error reduction in a given metric of interest, such as coastal SST in central California. The observations can be grouped by state variable (salinity, velocity, etc.), or measurement platform (glider, satellite, etc.), to show the aggregate effects of any type of observation. The metrics are time-averaged over each 2-day forecast. Each forecast is based on a previous 4-day analysis window. For more information on a given metric, click a figure below, or see a more detailed description here.

The Eddy Kinetic Energy (EKE) represents the energy in the difference between the horizontal ocean velocities and some mean background flow state, in this case a monthly climatology. This energy metric, 0.5(

The EKE evolves from cycle to cycle, as shown in the top panel below. The bottom panel reveals changes, or increments, in the metric due to the 4D-Var assimilation. Two estimates of the increments are given, one from a direct differencing of the prior and posterior model solutions (blue), and the other from the summation of all the individual observation impacts (red).

The impacts for different groupings of observation type are shown in the figure at the top of the page.

The Vertical Transport represents the net volume flux through an imaginary horizontal surface at 40 m depth. The metric is derived from the vertical velocity at 40 m. A time-average of the velocity for one 4-day cycle is shown below. The velocity at each ROMS grid cell is multiplied by the cell's area, and then the flux for all cells in the central California coastal region (within 50 km of shore, outlined in black) is summed to form a scalar metric.

The Vertical Transport evolves from cycle to cycle, as shown in the top panel below. The bottom panel reveals changes, or increments, in the metric due to the 4D-Var assimilation. Two estimates of the increments are given, one from a direct differencing of the prior and posterior model solutions (blue), and the other from the summation of all the individual observation impacts (red).

The impacts for different groupings of observation type are shown in the figure at the top of the page.

The Northward Transport represents the flux through an imaginary vertical surface extending along 37°N, from -127°E shoreward, and from the surface down to 500 m, or the bottom, whichever is encountered first. The metric is derived from the depth-averaged northward velocity at 37°N. A time-average of the velocity for one 4-day cycle is shown below. The northward velocity at each ROMS grid cell along 37°N is multiplied by the cell's width and thickness, and then the flux for all oceanic cells shoreward of -127°E is summed to form a scalar metric.

The Northward Transport evolves from cycle to cycle, as shown in the top panel below. The bottom panel reveals changes, or increments, in the metric due to the 4D-Var assimilation. Two estimates of the increments are given, one from a direct differencing of the prior and posterior model solutions (blue), and the other from the summation of all the individual observation impacts (red).

The impacts for different groupings of observation type are shown in the figure at the top of the page.

Density increases with depth in the ocean. The depth at which the density reaches a specific value can give insights into the ocean's circulation. The time average depth of the 1026 kg m

The Isopycnal Depth evolves from cycle to cycle, as shown in the top panel below. The bottom panel reveals changes, or increments, in the metric due to the 4D-Var assimilation. Two estimates of the increments are given, one from a direct differencing of the prior and posterior model solutions (blue), and the other from the summation of all the individual observation impacts (red).

The impacts for different groupings of observation type are shown in the figure at the top of the page.

The Energy Density represents the sum of the available gravitational potential and kinetic energy in the ocean. The metric is dominated by the available gravitational potential energy. This statistic gives the energy stored in the density structure of the ocean that could be converted into the kinetic energy of ocean currents. Near-surface values of the available potential energy for one 4-day cycle are shown below. The energy per unit volume is integrated over the entire model domain to give a scalar Energy Density metric.

The Energy Density evolves from cycle to cycle, as shown in the top panel below. The bottom panel reveals changes, or increments, in the metric due to the 4D-Var assimilation. Two estimates of the increments are given, one from a direct differencing of the prior and posterior model solutions (blue), and the other from the summation of all the individual observation impacts (red).

The impacts for different groupings of observation type are shown in the figure at the top of the page.

**
SST Mean Square Forecast Error **

The accuracy of the forecast can be evaluated by specific metrics, such as the disagreement between the forecast and observed SST in the central California region, the black box in the figure below, which extends 200 km offshore. This error is shown for a particular 2-day forecast in September 2020 when the previous cycle is non-assimilative (prior case, top panel) and assimilative (posterior case, bottom panel).

The SST forecast mean square error evolves from cycle to cycle, and the effect of the assimilation on the error can be quantified by differencing the error of forecasts based on assimilative non-assimilative cycles. This difference is shown in the top panel below, where a negative value indicates the assimilation has improved the forecast (as in the figure above). Two estimates of the difference are given, one from a direct differencing of the prior and posterior model forecasts errors (blue), and the other from the summation of all the individual observation forecast impacts (red).

The forecast impacts for different groupings of observation type are shown in the bottom panel of the figure above.

**
SST Mean Square Forecast Error **

The accuracy of the forecast can be evaluated by specific metrics, such as the disagreement between the forecast and observed SST in the central California region, the black box in the figure below, which extends 200 km offshore. This error is shown for a particular 2-day forecast in September 2020 when the previous cycle is non-assimilative (prior case, top panel) and assimilative (posterior case, bottom panel).

The SST forecast mean square error evolves from cycle to cycle, and the effect of the assimilation on the error can be quantified by differencing the error of forecasts based on assimilative non-assimilative cycles. This difference is shown in the top panel below, where a negative value indicates the assimilation has improved the forecast (as in the figure above). Two estimates of the difference are given, one from a direct differencing of the prior and posterior model forecasts errors (blue), and the other from the summation of all the individual observation forecast sensitivities (red).

The forecast sensitivity for different groupings of observation type are shown in the bottom panel of the figure above.

**
HF Radar Radials Mean Square Forecast Error **

The accuracy of the forecast can be evaluated by specific metrics, such as the disagreement between the forecast and observed HF radar radial velocity in the central California region, the black box in the figure below, which extends 200 km offshore. This error is shown for a particular 2-day forecast in September 2020 when the previous cycle is non-assimilative (prior case, top panel) and assimilative (posterior case, bottom panel).

The HF radar radials forecast mean square error evolves from cycle to cycle, and the effect of the assimilation on the error can be quantified by differencing the error of forecasts based on assimilative non-assimilative cycles. This difference is shown in the top panel below, where a negative value indicates the assimilation has improved the forecast (as in the figure above). Two estimates of the difference are given, one from a direct differencing of the prior and posterior model forecasts errors (blue), and the other from the summation of all the individual observation forecast impacts (red).

The forecast impacts for different groupings of observation type are shown in the bottom panel of the figure above.

**
HF Radar Radials Mean Square Forecast Error **

The accuracy of the forecast can be evaluated by specific metrics, such as the disagreement between the forecast and observed HF radar radial velocity in the central California region, the black box in the figure below, which extends 200 km offshore. This error is shown for a particular 2-day forecast in September 2020 when the previous cycle is non-assimilative (prior case, top panel) and assimilative (posterior case, bottom panel).

The HF radar radials forecast mean square error evolves from cycle to cycle, and the effect of the assimilation on the error can be quantified by differencing the error of forecasts based on assimilative non-assimilative cycles. This difference is shown in the top panel below, where a negative value indicates the assimilation has improved the forecast (as in the figure above). Two estimates of the difference are given, one from a direct differencing of the prior and posterior model forecasts errors (blue), and the other from the summation of all the individual observation forecast sensitivities (red).

The forecast sensitivity for different groupings of observation type are shown in the bottom panel of the figure above.

The Northward Transport represents the flux through an imaginary vertical surface extending along 37°N, from -127°E shoreward, and from the surface down to 500 m, or the bottom, whichever is encountered first. The metric is derived from the depth-averaged northward velocity at 37°N. A time-average of the velocity for one 4-day cycle is shown below. The northward velocity at each ROMS grid cell along 37°N is multiplied by the cell's width and thickness, and then the flux for all oceanic cells shoreward of -127°E is summed to form a scalar metric.

The Vertical Transport represents the net volume flux through an imaginary horizontal surface at 40 m depth. The metric is derived from the vertical velocity at 40 m. A time-average of the velocity for one 4-day cycle is shown below. The velocity at each ROMS grid cell is multiplied by the cell's area, and then the flux for all cells in the central California coastal region (within 50 km of shore, outlined in black) is summed to form a scalar metric.

Access to the model fields is not currently available for this run.

Many people are responsible for various aspects of ROMS and the overall data assimilation code. Major contributors to UCSC data assimilation projects are listed below.

Andrew M. Moore

Hernan Arango

Hajoon Song

Milena Veneziani

Nicole Goebel

Christopher A. Edwards

Patrick Drake

Paul Mattern

Jerome Fiechter

Gregoire Broquet

We are grateful to Dan Rudnick (UCSD/SIO) and Craig Lee (UW) for providing
access to their west coast glider data for assimilation.

James Doyle (NRL) has provided considerable assistance in our use of the COAMPS atmospheric fields.

We are also indebted to Brian Powell (UH) and John Wilkin (Rutgers) who have written and kindly shared outstanding scripts to carry out various ROMS-related operations.

- Veneziani, M., C. A. Edwards, J. D. Doyle, and D. Foley (2009), A central California coastal ocean modeling study: 1. Forward model and the influence of realistic versus climatological forcing, J. Geophys. Res., 114, C04015, doi:10.1029/2008JC004774.
- Veneziani ,M., C. A. Edwards and A. M. Moore (2009). A central California coastal ocean modeling study: 2. Adjoint sensitivities to local and remote forcing mechanisms. J Geophys Res, 114, doi:10.1029/2008JC004775.
- Broquet G., C. A. Edwards, A. M. Moore, B. S. Powell, M. Veneziani and J. D. Doyle, (2009), Application of 4D-Variational data assimilation to the California Current System, Dyn. Atmos. Oceans, doi:10.1016/j.dynatmoce.2009.03.001.
- Broquet G., A. M. Moore, H. G. Arango, C. A. Edwards, and B. S. Powell (2009), Ocean state and surface forcing correction using the ROMS-IS4DVAR data assimilation system, Mercator Ocean Quarterly Newsletter, Mercator Ocean Quarterly Newsletter, 34, pp. 5-13.
- Broquet, G., A. M. Moore, H. G. Arango, and C.A. Edwards (2010), Corrections to ocean surface forcing in the California Current System using 4D variational data assimilation, Ocean Mod. 36, doi:10.1016/j.ocemod.2010.10.005.
- Moore, A.M., Arango, H.G., Broquet, G., Powell, B.S., Zavala-Garay, J., Weaver, A.T., in press-a. The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems. I: System overview and formulation. Prog. Oceanogr. doi:10.1016/j.pocean.2011.05.004.
- Moore, A.M., Arango, H.G., Broquet, G., Edwards, C.A., Veneziani, M., Powell, B.S., Foley, D., Doyle, J.D., Costa, D., Robinson, P., in press b. The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems. II: Performance and application to the California current system. Prog. Oceanogr.doi:10.1016/j.pocean.2011.05.003.
- Moore, A.M., Arango, H.G., Broquet, G., Edwards, C.A., Veneziani, M., Powell, B.S., Foley, D., Doyle, J.D., Costa, D., Robinson, P., in press-b. The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems: III Observation impact and observation sensitivity in the California Current system. Prog. Oceanogr. doi:10.1016/j.pocean.2011.05.005.

Thisweb-pageand the near-real-time ocean state estimation system is supported by the National Oceanographic and Atmospheric Administration (NOAA) through a grant from the Central and Northern California Ocean Observing System (CeNCOOS).We

gratefully acknowledge financial supportfor various elements of this data assimilative system by the National Oceanographic Partnership Program (NOPP) , the Office of Naval Research (ONR), the National Oceanographic and Atmospheric Administration (NOAA) , the National Science Foundation (NSF), and the Gordon and Betty Moore Foundation .