Impact of numerical choices on water conservation in the E3SM Atmosphere Model version 1 (EAMv1)

Abstract

The conservation of total water is an important numerical feature for global Earth system models. Even small conservation problems in the water budget can lead to systematic errors in century-long simulations. This study quantifies and reduces various sources of water conservation error in the atmosphere component of the Energy Exascale Earth System Model.Several sources of water conservation error have been identified during the development of the version 1 (V1) model. The largest errors result from the numerical coupling between the resolved dynamics and the parameterized subgrid physics. A hybrid coupling using different methods for fluid dynamics and tracer transport provides a reduction of water conservation error by a factor of 50 at 1 • horizontal resolution as well as consistent improvements at other resolutions. The second largest error source is the use of an overly simplified relationship between the surface moisture flux and latent heat flux at the interface between the host model and the turbulence parameterization. This error can be prevented by applying the same (correct) relationship throughout the entire model. Two additional types of conservation error that result from correcting the surface moisture flux and clipping negative water concentrations can be avoided by using massconserving fixers. With all four error sources addressed, the water conservation error in the V1 model becomes negligible and insensitive to the horizontal resolution. The associated changes in the long-term statistics of the main atmospheric features are small.A sensitivity analysis is carried out to show that the magnitudes of the conservation errors in early V1 versions decrease strongly with temporal resolution but increase with horizontal resolution. The increased vertical resolution in V1 results in a very thin model layer at the Earth's surface, which amplifies the conservation error associated with the surface moisture flux correction. We note that for some of the identified error sources, the proposed fixers are remedies rather than solutions to the problems at their roots. Future improvements in time integration would be beneficial for V1.

A Total Energy Error Analysis of Dynamical Cores and Physics‐Dynamics Coupling in the Community Atmosphere Model (CAM)

“…Although the average source of mass is small each time step, it always has the same sign (i.e., it is a bias) and therefore accumulates. Zhang et al () estimated that this spurious source of mass is equivalent to ∼10‐cm sea‐level rise per decade in coupled climate simulation experiments.…”

The DOE E3SM Coupled Model Version 1: Overview and Evaluation at Standard Resolution

“…Water conservation is also important for a global Earth system model. During the early development of the E3SMv1 model, we identified a number of computational problems, leading to water conservation errors in the atmosphere component (Zhang et al, ). These problems were all considered and suitable remedies applied (e.g., borrowing from adjacent cells to avoid more drastic nonconservative fixers) so that in the 500‐year piControl simulation, the relative water conservation error (as defined in Zhang et al, ) in the atmosphere component is about 0.00226%, equivalent to a computational sea level rise of about 2 mm per century.…”

An Overview of the Atmospheric Component of the Energy Exascale Earth System Model

“…These choices make the discretization formally fourth-order accurate in the horizontal dimension and first-order accurate in time. A hybrid physics-dynamics coupling that uses different methods for fluid dynamics and tracer transport (Lauritzen et al, 2014) is used in EAMv1 to ensure water conservation (K. Zhang, Rasch, et al, 2018).…”