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Improving tide-estuary representation in MPAS-Ocean (Final Report)

The overarching goal of this research is to produce a skill-assessed tide-estuary representation, including BGC (biogeochemistry) components of the ecosystem, into the MPAS-O global climate modeling system. Specifically, in the original proposal we proposed one-way nesting, into global MPAS-O, of a high-resolution model for TES (tidal and estuary systems) including the coupling of the BGC components. We have completed the proposed tasks during the past 4 years. Specifically, after extensive consultation with the MPAS-O group during the first year, we have decided to go beyond the original proposal and to two-way nest SCHISM into MPAS-O. As a result, SCHISM-CoSiNE (with CoSiNE being the BGC model) is now fully integrated into MPAS-O as a subroutine (more precisely, an analysis member) and can be invoked as MPAS-O is running with two-way exchange of information between the TES and global models (with proper spatial interpolation done on the fly). As originally proposed, we have also developed the new finite-volume (FV) model MPAS-OI (aka ELCIRC-sub) for TES. We have conducted several tests using the coupled MPAS-SCHISM- CoSiNE model and also MPAS-OI for Columbia River, San Francisco Bay and Chesapeake Bay. Four journal publications have been produced so far as the result of the project and 1 is under review (cf. Publication section). With these achievements, we will be ready to conduct fully coupled simulations of TES and global ocean anywhere, as soon as some missing capabilities in MPAS-O (e.g. tides, improved ability to handle the boundary conditions, and streamlining of the global BGC model) are worked out. The significance of the outcome of this project cannot be overstated. It marks the first time, as far as we know, that a global climate model is tightly coupled to a bona fide nearshore and terrestrial model (SCHISM system); in fact SCHISM is the first bona fide compound flooding model that seamlessly covers the coastal ocean, estuaries, rivers and watersheds (Ye et al. 2020; Zhang et al. 2020). The coupled model will reduce the errors and uncertainties of the MPAS-O global climate model system. It also complements and extends on-going E3SM project, as the latter seeks in the long-term to include components required to simulate impacts of sea-level change and storm surge on coastal regions, including wave models and focusing resolution in coastal and storm-track regions, as an important component of the Cryosphere-ocean system. Note that a spectral wave model (the unstructured-grid version of Wave Watch III, aka Wind Wave Model) is already incorporated inside the SCHISM system and is therefore directly accessible in the coupled system.

58 GEOSCIENCES↗

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Here, we demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

97 MATHEMATICS AND COMPUTING↗

Storm Surge Modeling as an Application of Local Time-Stepping in MPAS-Ocean

This paper presents the first practical application of local time-stepping (LTS) schemes in the Model for Prediction Across Scales-Ocean (MPAS-O). We use LTS schemes in a single-layer, global ocean model that predicts the storm surge around the eastern coast of the United States during Hurricane Sandy. The variable-resolution meshes used are of unprecedentedly high resolution in MPAS-O, containing cells as small as 125 m wide in Delaware Bay. It is shown that a particular, third-order LTS scheme (LTS3) produces sea-surface height solutions that are of comparable quality to solutions produced by the classical four-stage, fourth-order Runge-Kutta method (RK4) with a uniform time step on the same meshes. Furthermore, LTS3 is up to 35% faster in the best cases considered, where the number of cells using the coarse time-step relative to those using the fine time-step is as low as 1:1. This shows that LTS schemes are viable for use in MPAS-O with the added benefit of substantially less computational cost. The results of these performance experiments inform us of the requirements for efficient mesh design and configuration of LTS regions for LTS schemes. In particular, we see that for LTS to be efficient on a given mesh, it is important to have enough cells using the coarse time-step relative to those using the fine time-step, typically at least 1:5 to see an increase in performance.

54 ENVIRONMENTAL SCIENCES↗

Computing eddy-driven effective diffusivity using Lagrangian particles

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is compared against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.

54 ENVIRONMENTAL SCIENCES↗

Effects of different vegetation drag parameterizations on the tidal propagation in coastal marshlands

Vegetation drag is a fundamental quantity directly affecting results for both long- and short-term coastal marsh and geomorphological studies. The vegetation drag in coastal marshland has been modeled by various two-dimensional (2D) and threedimensional (3D) numerical parameterizations. 2D parameterizations treat coastal marshes as bottom roughness elements, while 3D parameterizations resolve the vertically-variable vegetation drag through the water column. However, differences in tidal propagation arising from different drag parameterizations within a single model are largely unknown, and clear guidance on parameterization selection is still missing. In this study, we implemented four vegetation drag parameterizations into the Model for Prediction Across Scales-Ocean (MPAS-O), which include 1) a 2D parameterization using land-cover type-determined Manning’s n (2DLM); 2) a 2D parameterization using vegetation-determined Manning’s n (2DVM); 3) a 3D parameterization for stiff vegetation (3DSV); and 4) a 3D parameterization for flexible vegetation (3DFV). Estimates of the flow resistance effects from these parameterizations were compared using a series of idealized tidal propagation simulations. Given the same tidal condition, flooding depth and flooding distance are the largest in the 2DLM simulations and the smallest in the 3DSV simulations. 2DVM results are the closest to the 2DLM results. 3DFV results are the closest to the average of 2DVM, 3DSV, and 3DFV results. 2DVM and 3DSV results are the least and most sensitive to the vegetation aboveground biomass, respectively. Based on the input data requirement and computational efficiency of each parameterization, a comparison summary is provided to help inform parameterization selection for specific applications. Here, the effects of these parameterizations on coastal geomorphology are further discussed, and the results demonstrate that estimates of the long-term evolution of coastal marshes and coastal morphology depend upon the selection of the vegetation drag parameterization

54 ENVIRONMENTAL SCIENCES↗

Energy Exascale Earth System Model v2.1.0

First release of version 2.1 of the Energy Exascale Earth System Model. [ATM] The atmosphere component remains EAM. There are no major changes in the default configuration since 2.0. New features include: A semi-lagrangian tracer transport for theta-l dycore, a new algorithm for finding the tropopause, new RRM mesh configurations. Add and update SSP370 and SSP585 cases. Restore the FIDEAL case. [LAND] The land component is ELM. There are no major changes in the default configuration since 2.0. Several option features have been added including: implementation of topography-based subgrid structure (topounits) and accompanying parameterizations and atmospheric forcing downscaling methods; a new plant hydraulics scheme; two-way land-river hydrological coupling through the infiltration of floodplain water; an implementation of perennial crops; updates to the SNICAR-AD snow radiative transfer model; and implementation of soil erosion and sediment yield in ELM-Erosion. Each of these new changes is modular in design and can be turned on or off as the user specifies; they are currently being tested in different “BGC” configurations. [OCEAN] The ocean component remains MPAS-Ocean. Major change since version 2.0 include the addition of the Fox-Kemper et al. 2011 parameterization for submesocale eddies, a correction for barotropic thickness consistency that reduces divergence noise, and the addition of an ocean carbon conservation analysis member. [SEAICE] The sea-ice component remains MPAS-Seaice. Major changes since version 2.0 include: A correction to how shortwave parameters are interpolated in the snicar-ad 5-band radiation scheme, the addition of a sea ice carbon conservation analysis member, updates to the default sea ice biogeochemistry namelist parameters to be consistent with version 2.0 improvements to nitrogen cycling and a correction in the ice-ocean dissolved organic nitrogen coupling. [LAND ICE] The land-ice component remains MPAS-Albany-landIce (MALI). Major changes since 2.0 include an update to the MALI version and the Greenland mesh.[RIVER] The river model is MOSART. There are no major changes in the default configuration since 2.0. A major new optional feature is two-way river-ocean hydrological coupling between MOSART and MPAS-O. This change can be turned on or off as the user specifies, and is being tested in different configurations. [COUPLER] The coupler remains cpl7/MCT. Major changes since version 2.0 include: Carbon budget calculated when heat/water budgets active. Fix a bug in land-atm fluxes for tri-grid configurations. [OTHER] a small bug in the zenith angle calculation was fixed in the data models.

ECP↗

Structure-preserving numerical discretizations for domains with boundaries

This SAND report documents Exploratory Express LDRD Project 223790, "Structure-preserving numerical discretizations for domains with boundaries", which developed a method to incorporate consistent treatment of domain boundaries and arbitrary boundary conditions in discrete exterior calculus (DEC) for arbitrary polygonal (2D) and tensor-product structure prism (3D) grids. The new DEC required the development of novel discrete exterior derivatives, boundary operators, wedge products and Hodge stars. This was accomplished through the use of boundary extension and the blending of known 2D operators on the interior with 1D operators on the boundary. The Hodge star was based on the Voronoi Hodge star, and retained the limitation of a triangular circumcentric primal or dual grid along with low-order accuracy. In addition to the new DEC, two related software packages were written: one for the study of DEC operators on arbitrary polygonal and polyhedral grids using both symbolic and numerical approaches and one for a (thermal) shallow water testbed using TRiSK-type numerics. Immediately relevant (already funded, through CANGA) followup work is the development of a high-order, geometrically flexible Hodge star and structure-preserving, high-order, oscillation-limiting transport operators (using WENO) for n-forms on arbitrary 2D and 3D grids. This will provide all of the machinery required for a high-order version of TRiSK with boundaries on arbitrary 2D and tensor-product 3D grids, which is applicable to both the atmospheric (CRM in E3SM-MMF) and oceanic (MPAS-O) components of E3SM.

97 MATHEMATICS AND COMPUTING↗

Barotropic tides in MPAS-Ocean (E3SM V2): impact of ice shelf cavities

Abstract. Oceanic tides are seldom represented in Earth system models (ESMs) owing to the need for high horizontal resolution to accurately represent the associated barotropic waves close to coasts. This paper presents results of tides implemented in the Model for Prediction Across Scales–Ocean or MPAS-Ocean, which is the ocean component within the U.S. Department of Energy developed Energy Exascale Earth System Model (E3SM). MPAS-Ocean circumvents the limitation of low resolution using unstructured global meshing. We are at this stage simulating the largest semidiurnal (M2, S2, N2) and diurnal (K1, O1) tidal constituents in a single-layer version of MPAS-O. First, we show that the tidal constituents calculated using MPAS-Ocean closely agree with the results of the global tidal prediction model TPXO8 when suitably tuned topographic wave drag and bottom drag coefficients are employed. Thereafter, we present the sensitivity of global tidal evolution due to the presence of Antarctic ice shelf cavities. The effect of ice shelves on the amplitude and phase of tidal constituents are presented. Lower values of complex errors (with respect to TPXO8 results) for the M2 tidal constituents are observed when the ice shelf is added in the simulations, with particularly strong improvement in the Southern Ocean. Our work points towards future research with varying Antarctic ice shelf geometries and sea ice coupling that might lead to better comparison and prediction of tides and thus better prediction of sea-level rise and also the future climate variability.

58 GEOSCIENCES↗