In a cycling system where data assimilation (DA) and model simulation are executed consecutively, the model forecasts initialized from the analysis (or data assimilation) can be systematically affected by dynamic imbalances generated during the analysis process. The high-frequency noise arising from the imbalances in the initial conditions can impose constraints on computational stability and efficiency during subsequent model simulations and can potentially become the low-frequency waves of physical significance. To mitigate these initial imbalances, the incremental analysis update (IAU) has long been utilized in the cycling context. This study introduces our recent implementation of the IAU in the Model for Prediction Across Scales – Atmospheric (MPAS-A) coupled with the Joint Effort for Data assimilation Integration (JEDI) through the cycling system called MPAS-Workflow. During the integration of the compressible nonhydrostatic equations in MPAS-A, analysis increments are distributed over a predefined time window (e.g., 6 h) as fractional forcing at each time step. In a real case study with the assimilation of all conventional and satellite radiance observations every 6 h for 1 month, starting from mid-April 2018, model forecasts with the IAU show that the initial noise illustrated by surface pressure tendency becomes well constrained throughout the forecast lead times, enhancing the system reliability. The month-long cycling with the assimilation of real observations demonstrates the successful implementation of the IAU capability in the MPAS–JEDI cycling system. Along with the comparison between the forecasts with and without the IAU, several aspects regarding the implementation in MPAS–JEDI are discussed. Corresponding updates have been incorporated into the MPAS-A model (originally based on version 7.1), which is now publicly available in MPAS–JEDI and MPAS-Workflow version 2.0.0.

Data assimilation (DA) is a mathematical or statistical procedure that incorporates observations, unevenly distributed in time and space, into adjacent grids in the model forecast (or background) using relative weights based on the error statistics of the forecasts and observations. It is not required to account for dynamical or physical balances across model grids or variables, nor does it ensure the conservation of mass, momentum, or energy. Consequently, the initial balance of the atmospheric flow can be disrupted by data assimilation when the initial state is replaced by the analysis state. Such imbalances can introduce artificial high-frequency noise, which is amplified and propagated throughout the model simulation.

In the cycling system that alternates between analysis and forecast, noise can continuously accumulate through cycles, which can degrade numerical stability and efficiency (with the time step smaller than 6

To mitigate abrupt changes (or shocks) originating from inconsistencies or imbalances in the initial state, the incremental analysis update (IAU) method was introduced by

The Model for Prediction Across Scales – Atmosphere (MPAS-A or MPAS, hereafter) utilizes centroidal Voronoi tessellations for its horizontal meshes and terrain-following height as a vertical coordinate and employs a fully compressible nonhydrostatic model with the capability of high-resolution forecasting over a local area for both global and regional applications

Through the collaborative work with the Joint Effort for Data assimilation Integration (JEDI) team, an interface between MPAS and JEDI has been recently developed for a new community data assimilation system based on the variational approach

Since all of the analysis variables in MPAS–JEDI are either derived or diagnostic variables in the MPAS model, their analysis increments need to be converted back to the model's prognostic variables after the minimization so that the analysis updates can be reflected in the model forecast. The variable transformations of mass fields are carried out based on the reconstructed pressure coordinate derived from surface pressure, assuming hydrostatic balance and an ideal gas state. The recent version of MPAS–JEDI is updated to transform analysis increments to the increments of the model's prognostic variables (instead of their full fields), as stated in

This article reports on our new implementation of the IAU feature in MPAS–JEDI using the cycling system called MPAS-Workflow (

The MPAS-A model uses a height-based coordinate following

In the MPAS model, the nonhydrostatic compressible equation is formulated for conserved quantities (mass, momentum, and moisture) represented in the flux form using the split-explicit time integration techniques introduced in

The nonhydrostatic equations are integrated by updating total tendencies computed from each component of the modeling process. In the default configuration without the IAU, the model is simply integrated from the initial condition updated with analysis variables at the initial time. However, if the IAU is activated in the forecast (e.g., config_IAU_option

In MPAS–JEDI, analysis variables are defined as temperature (

While the nonhydrostatic MPAS-A model solves a prognostic equation for

As the dry density multiplied by the vertical coordinate Jacobian (

The tendency for edge wind (

In the IAU module, analysis increments (

A diagram for cycling with the IAU.

Our open-source MPAS-Workflow was introduced in

Once the IAU is activated in MPAS-Workflow, the model initial and run times are automatically adjusted to

MPAS–JEDI employs its own customized version of the MPAS-A model, using a two-stream I/O (input/output) approach by default to run DA cycling more efficiently. The two-stream (or split) I/O approach was originally developed for DA cycling in a restart mode to avoid writing time-invariant fields in every restart file while ensuring the model forecasts are reproducible. In the restart mode, the MPAS-A model produces a restart file with about 230 variables, among which only

The variational approach essentially linearizes the model and constructs a static background (or forecast) error covariance to find an analysis solution closest to observations iteratively (e.g., through a minimization process). Although the static background error covariance only represents the climatological information (e.g., with no temporal variations), it is a key component of variational data assimilation algorithms, modeling the relationships between control variables through physical transformation or balance operators as well as spatial auto-correlations of each control variable to determine how to propagate the observed information across model grids and variables

In the JEDI system, the Unified Forward Operator (UFO) not only provides observation operators (named “HofX”) to compute innovations (e.g., differences between observations and the corresponding forecasts, O

After the new implementation of the IAU in MPAS v7, global analysis and forecast cycling was conducted over a global 120 km quasi-uniform mesh every 6 h for 1 month, starting from 15 April 2018, using MPAS-Workflow for the hybrid 3DEnVar in the MPAS–JEDI system. During the cycling, all the conventional observations, satellite winds, and clear-sky microwave radiances from six Advanced Microwave Sounding Unit-A (AMSU-A) sensors aboard NOAA-15, NOAA-18, NOAA-19, Aqua, Metop-A, and Metop-B were assimilated together, using diagonal observation error covariances and a pure ensemble background error covariance (computed from GEFS), like in

In the model simulation, a “mesoscale_reference” physics suite is used that includes WSM6 (WRF single-moment 6-class) microphysics, new Tiedtke cumulus, YSU PBL (Yonsei University planetary boundary layer), YSU gravity wave drag over orography (GWDO), RRTMG SW and LW (Rapid Radiative Transfer Model for general circulation models shortwave and longwave), and Noah LSM (land surface model) variables. Ozone climatology is activated, and radiation effective radii for cloud water (

Time series of the globally averaged absolute value of the surface pressure tendency (

The 2-month-long cycling experiments are conducted with and without the IAU, named IAU and CTRL (control), respectively. Figure

Horizontal distribution of

Time series of the difference in the total number of surface pressure observations assimilated in CTRL and IAU (red) and the total number of the observations available at each cycle (gray).

In DA cycling, it is common to monitor the total number of observations assimilated at each cycle. A time series with a declining trend might be indicative of the analysis with poor quality, rejecting more observations with cycles. As shown in Fig.

Time series of

To examine the performance of cycling DA, Fig.

Percent difference of rms (O

In the sounding verification over the globe, the percentage difference of rms errors in IAU with respect to the one in CTRL for the entire cycling period also shows slight but systematic improvements in the background forecasts, as depicted in Fig.

The rms errors in 5 d forecasts in surface pressure at different latitudes relative to the GFS analysis are displayed

We also run 5 d forecasts from the 00:00 UTC analysis every day and compute forecast errors with respect to the Global Forecast System (GFS) analysis. Figure

The overall results from the cycling experiments are promising, showing the reliability throughout the month-long period. We can examine the impact of the IAU option through more extensive diagnostics against other observation types and variables and through the evaluation of longer forecasts in the future. As a proof of concept, only 3DIAU on a 120 km global mesh was tested here, but it was implemented in a way to make it extensible with different weighting functions or even to 4DIAU in the MPAS model. Also, it is applicable to variable-resolution meshes in case one would want to examine the impact of the IAU over the area with mesh refinement.

This study introduces the incremental analysis update (IAU) implemented in the MPAS–JEDI cycling system operated by MPAS-Workflow. Through a real case study for 1 month, starting from mid-April 2018, assimilating all conventional, aircraft, and satellite radiance observations, we demonstrate that the IAU is successfully implemented on the model's unstructured mesh, effectively suppressing the artificial noise produced by initial imbalances during the analysis process. Although the current implementation is a simple three-dimensional IAU (3DIAU) with the same fractional forcing applied to each time step, there are several aspects that might be worth pointing out in regards to our development effort in MPAS–JEDI. (i) Computational stability and efficiency might be critical to any numerical weather prediction (NWP) models, but special attention was taken regarding the MPAS-A model which solves the compressible nonhydrostatic equations employing an unstructured mesh based on centroidal Voronoi tessellations. In the model integration, a time step is set based on the smallest grid spacing of a given unstructured mesh and is then uniformly applied across the entire mesh (e.g., regardless of the nominal grid spacing of individual grid cells). To ensure numerical stability even for the unstructured mesh applications, various filtering techniques are carefully designed and applied to the model numerics

MPAS–JEDI is an interface between the MPAS-A model and the JEDI data assimilation system, including all the model-specific components such as variable transformation and HofX, which computes analysis increments in the MPAS variables. To cycle MPAS–JEDI over a period of time in a synthetic way, MPAS-Workflow controls the entire data stream as well as all the configurations for data assimilation and model forecasts. As the IAU changes the input/output file stream and the model configuration, they are all accounted for in MPAS-Workflow (mostly through various YAML configurations).

MPAS-Workflow offers high flexibility for a number of applications such as data assimilation with 3DVar, pure 3/4DEnVar, hybrid 3DEnVar with dual resolution, ensemble data assimilation, and more recently the local ensemble transform Kalman filter (LETKF) algorithm in MPAS–JEDI. In addition, it can generate observations in the IODA format, the GFS analyses in MPAS initial-condition format, and free deterministic forecasts from the GFS analyses using specific Cylc suites (no cycling). Observations and GFS analyses can be obtained from the NCAR Research Data Archive (RDA) or the NCEP FTP server. With all of these capabilities, it has been tested for near-real-time cycling runs using the 3DVar algorithm.

At the time of writing, MPAS-Workflow does not build either MPAS or JEDI, which should be built separately after downloading the source codes from

To run a cycling experiment with the IAU, all users need to do is edit a single YAML file. Each section controls the specific configuration to build up the YAML file of the MPAS–JEDI application (i.e., pure 3DEnVar) and other components of the workflow to construct the Cylc suite that will orchestrate the cycling experiment. For the IAU, a new logical parameter has to be added in a new line as “IAU: True”. Here is the configuration employed this study.

<MPAS-Workflow/scenarios/3denvar_OIE120km_ WarmStart_IAU.yaml>

workflow:

first cycle point: 20180414T18

final cycle point: 20180510T00

experiment:

suffix: “_IAU”

observations:

resource: PANDACArchive

members:

n: 1

model:

outerMesh: 120 km

innerMesh: 120 km

ensembleMesh: 120 km

firstbackground:

resource: “PANDAC.GFS”

externalanalyses:

resource: “GFS.PANDAC”

variational:

DAType: 3denvar

ensemble:

forecasts:

resource: “PANDAC.GEFS”

forecast:

IAU: True

The YAML file used to run MPAS–JEDI with 3DEnVar is built by adding the observers snippets to the application sections (see MPAS-Workflow/config/jedi/applications/3denvar.yaml). Here we also provide two more sample YAML configurations used in this study for assimilating surface observations.

MPAS-Workflow/config/jedi/ObsPlugs/da/filters/sfc.yaml (The following is for the data QC flag.)

obs filters:

filter: PreQC

maxvalue: 3

filter: Difference Check

reference: MetaData/stationElevation value: GeoVaLs/surface_altitude

threshold: 100.0

filter: Background Check

threshold: 3.0

MPAS-Workflow/config/jedi/ObsPlugs/da/base/sfc.yaml (The following are options for an observation operator for surface observations.)

obs space:

name: SfcPCorrected

_obsdatain: &ObsDataIn

engine:

type: H5File

obsfile: InDBDir/sfc_obs_thisValidDate.h5

_obsdataout: &ObsDataOut

engine:

type: H5File

obsfile: OutDBDirMemberDir/obsPrefix_sfcObsOutSuffix.h5

obsdatain: *ObsDataIn

ObsDataOut

simulated variables: [stationPressure]

obs error: *ObsErrorDiagonal

obs operator:

name: SfcPCorrected

da_psfc_scheme: WRFDA

linear obs operator:

name: Identity

observation alias file: obsop_name_map.yaml

As described in Sect. 2, MPAS–JEDI first computes the analysis through the iterative minimization procedure and then converts the increments in the analysis variables to the model's prognostic fields. Based on Eq. (

The increments in dry-air density (

The exact version of MPAS–JEDI, including its Python-based post-processing package, is archived on Zenodo

The supplement related to this article is available online at:

SH implemented the IAU in MPAS–JEDI, conducting experiments, analyzing the results, and writing the manuscript. JJG updated MPAS-Workflow for the IAU capability. IHB helped with producing plots and comprehensively edited Appendix A. WCS and MGD worked with SH on the implementation of the IAU and the two-stream I/O in the MPAS-A model. All the co-authors edited the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The National Center for Atmospheric Research is sponsored by the National Science Foundation of the United States. We would like to acknowledge high-performance computing support from Cheyenne (

This research has been supported by the National Science Foundation (grant no. 1852977) and the United States Air Force (grant no. NA21OAR4310383).

This paper was edited by Shu-Chih Yang and reviewed by two anonymous referees.