A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 1: Offline forward and adjoint transport models

Abstract

Abstract. A four-dimensional variational (4D-Var) method is a popular algorithm for inverting atmospheric greenhouse gas (GHG) measurements. In order to meet the computationally intense 4D-Var iterative calculation, offline forward and adjoint transport models are developed based on the Nonhydrostatic ICosahedral Atmospheric Model (NICAM). By introducing flexibility into the temporal resolution of the input meteorological data, the forward model developed in this study is not only computationally efficient, it is also found to nearly match the transport performance of the online model. In a transport simulation of atmospheric carbon dioxide (CO 2 ), the data-thinning error (error resulting from reduction in the time resolution of the meteorological data used to drive the offline transport model) is minimized by employing high temporal resolution data of the vertical diffusion coefficient; with a low 6-hourly temporal resolution, significant concentration biases near the surface are introduced. The new adjoint model can be run in discrete or continuous adjoint mode for the advection process. The discrete adjoint is characterized by perfect adjoint relationship with the forward model that switches off the flux limiter, while the continuous adjoint is characterized by an imperfect but reasonable adjoint relationship with its corresponding forward model. In the latter case, both the forward and adjoint models use the flux limiter to ensure the monotonicity of tracer concentrations and sensitivities. Trajectory analysis for high CO 2 concentration events are performed to test adjoint sensitivities. We also demonstrate the potential usefulness of our adjoint model for diagnosing tracer transport. Both the offline forward and adjoint models have computational efficiency about 10 times higher than the online model. A description of our new 4D-Var system that includes an optimization method, along with its application in an atmospheric CO 2 inversion and the effects of using either the discrete or continuous adjoint method, is presented in an accompanying paper (Niwa et al., 2016).

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 2: Optimization scheme and identical twin experiment of atmospheric CO<sub>2</sub> inversion

“…The archived meteorological data consist of air mass densities, three-dimensional air mass fluxes, vertical diffusion coefficients, mixing ratios of water substances, temperatures, and cumulus base mass fluxes. These data are consistent with the dynamical calculation of NICAM, though their temporal resolutions are decreased from the original model time step (20 min) to 1-to 3-hourly steps in the offline model calculations (Niwa et al, 2017). The horizontal resolution is set at glevel-5 ("5" denotes the number of division from the original icosahedron; see Fig.…”

“…Detailed descriptions of the offline forward and adjoint models of NICAM-TM are found in the accompanying paper of Niwa et al (2017). Reanalysis data used with nudging in the online calculation are from the 6-hourly Japan Meteorological Agency Climate Data Assimilation System (JC-DAS) reanalysis (Onogi et al, 2007).…”

“…Both the forward and adjoint models are driven by archived meteorological data (e.g., mass fluxes, temperatures, turbulent coefficients, cumulus base mass fluxes; details are found in Niwa et al, 2017). The meteorological data are prepared by a GCM run of NICAM, in which horizontal winds are nudged towards reanalysis data to simulate real atmospheric flow fields.…”

“…For the new inversion system, we have employed the NICAM-based Transport Model (NICAM-TM), naming our inversion system as NICAM-TM 4D-Var. The previous accompanying paper of Niwa et al (2017) derived and evaluated the offline forward and adjoint models of NICAM-TM. This paper describes the entire NICAM-TM 4D-Var system, including the optimization scheme POpULar.…”

“…As described in Niwa et al (2017), NICAM-TM has two types of adjoint models: one is a discrete adjoint model and the other is a continuous one. The discrete adjoint model ensures model linearity and maintains an exact adjoint relationship with its corresponding forward model, while the continuous adjoint model is nonlinear and consequently loses the exact adjoint relationship but has less model errors.…”