XIAOXU TIAN http://xiaoxutian.com Meteorological Researcher at Earth System Science Interdisciplinary Center, University of Maryland Fri, 16 Oct 2020 19:59:42 +0000 en-US hourly 1 https://wordpress.org/?v=5.7.9 Development of the tangent linear and adjoint models of the MPAS-Atmosphere dynamic core and applications in adjoint relative sensitivity studies http://xiaoxutian.com/mpas-adjoint-sensitivity/ Thu, 15 Oct 2020 20:18:58 +0000 http://xiaoxutian.com/?p=379

Tangent linear and adjoint models for the MPAS-Atmosphere is available!

      The MPAS-A is an advanced global numerical weather prediction model with a hexagonal mesh that can be compressed for higher resolutions in some targeted regions of interest and smoothly transitioned to coarse resolutions in others. In this study, a Python-driven MPAS-A model is first developed, combining a flexible Python driver and Fortran’s fast computation, making the MPAS-A model exceedingly user- and platform- friendly. The tangent linear and adjoint models of the MPAS-A dynamical core are then developed, both of which are required for various sensitivity studies. They are also indispensable components of a future MPAS- based global four-dimensional variational (4D-Var) data assimilation system. Finally, the relative sensitivity of a baroclinic instability wave development is obtained and shown using the MPAS-A adjoint model.

The MPAS-Atmosphere tangent linear model can well approximate the evolutions of perturbations of small magnitudes (10^-3) in the figure below.

Sensitivity analyses to a wide variety of user-defined quantities at the forecast time is accurate and efficient with the adjoint model.

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Evolutions of Errors in the Global Multiresolution Model for Prediction Across Scales – Shallow Water (MPAS-SW) http://xiaoxutian.com/evolutions-of-errors-in-the-global-multiresolution-model-for-prediction-across-scales-shallow-water-mpas-sw/ Thu, 15 Oct 2020 18:10:30 +0000 http://xiaoxutian.com/?p=357

how would simulation errors evolve in a multi resolution global model

      The global MPAS with the shallow water (SW) dynamics is taken as the forecast model to characterize the errors under a variable resolution (VR) mesh. An idealized experiment featuring gravity and Rossby waves triggered by orography is conducted with two meshes consisting of the same number of grid cells, which directly indicates the computational costs. One mesh is of 120 km uniform resolution (UR), the other of 53-210 km VR. Both simulations are compared with the solutions from a 60 km uniform high-resolution (HR) mesh serving as the reference.

      The differences with respect to the HR results from both the UR and VR experiments are manifested as rapidly propagating gravity waves circling the Earth about every two days. These signals are regarded as errors due to insufficient resolutions. Over the most part of the Earth, the resolutions in the VR mesh is coarser than the UR mesh. The magnitudes of the errors in the VR experiment are found to grow larger than in the UR case shortly after the simulation started. The sensitivities to the errors in the eight-day forecast calculated with the MPAS-SW adjoint model show similar propagating patterns following the nonlinear state trajectory. The sensitivities under VR suggest that little contribution to the errors throughout the simulation process is made within the finely resolved areas. In the initial conditions under VR, the error signals primarily come from the coarse resolutions immediately outside the areas with enhanced resolutions. The finding implies that, in simulations under VR, error signals generated in the coarsely resolved regions can be propagated into the finely resolved areas conveyed by wave types allowed in the model, i.e., gravity waves in the case of this study, the rate of which depends on the fluid mean height.

Voronoi grid distribution in uniform (top left) and variable (top right) resolution meshes. The adjoint sensitivity of errors in the 8-day forecasts to the initial conditions in experiments with uniform (middle) and variable (bottom) resolution meshes.

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NCAR MMM Seminar http://xiaoxutian.com/ncar-mmm-seminar/ Wed, 27 Nov 2019 16:12:44 +0000 http://xiaoxutian.com/?p=327

Date and Time: Thursday, 30 January 2020; 15:30 – 16:30
Location: FL2-1001 Small Seminar Room

A 4D-Var vortex initialization based on a nonhydrostatic axisymmetric hurricane model with ATMS measurements assimilated to improve hurricane intensity forecast

Xiaoxu Tian
Cooperative Institute for Climate and Satellites, Earth System Science Interdisciplinary Center,
University of Maryland, College Park, MD 20740

Abstract

A four-dimensional variational (4D-Var) vortex initialization (VI) system is developed for a nonhydrostatic axisymmetric numerical model with convection accounted for (the RE87 model). Derivations of the tangent linear and adjoint models of the RE87 model and the correctness checks are presented. As an initial evaluation of the 4D-Var VI system, a cost function that measures the model fit to satellite microwave retrievals of tropical cyclone (TC), warm-core temperatures and total precipitable water (TPW) from the following four polar-orbiting satellites within a slightly longer than 1-h assimilation window is minimized using the limited-memory quasi-Newton minimization algorithm: the Suomi National Polar-orbiting Partnership, NOAA-20, Fengyun-3D and Global Change Observation Mission—Water Satellite 1. An azimuthal spectral analysis in cylindrical coordinates centred on the TC centres shows that the warm core and TPW fields within TCs are dominated by the axisymmetric component. The 4D-Var VI results assimilating the axisymmetric component of the above satellite retrievals produced a significant reduction in the cost function and the norm of the gradient as the minimization process is completed. The gradient of the cost function is accurately computed by a single integration of the RE87 adjoint model. In the cases of Hurricane Florence and Typhoon Mangkhut, improved forecast of intensifications and more realistic vertical structures of all model state variables (e.g. temperature, water vapour mixing ratio, liquid water content mixing ratio, tangential and radial wind components and vertical velocity) are obtained when compared with a parallel run initialized simply by the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis.

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FengYun Satellite MWTS Instrument Limb Corrections http://xiaoxutian.com/fengyun-satellite-mwts-instrument-limb-corrections/ Sat, 01 Dec 2018 15:54:42 +0000 http://xiaoxutian.com/?p=255

uncovering weather signals in microwave temperature sounder data hidden by the limb effect

      It’s been 40 years since microwave temperature sounders started to observe the Earth. Observations from microwave temperature sounders are critical for various areas of basic and applied science, including climatological studies, numerical weather forecasting, and extreme-weather monitoring. However, the cross-track scanning approach of temperature sounders can conceal weather signals in raw observations, which is problematic.
      Professor Xiaolei Zou and Dr. Xiaoxu Tian from the Earth System Science Interdisciplinary Center at the University of Maryland, with Dr. Shengpeng Yang from Nanjing University of Information Science and Technology, propose a limb correction algorithm for observations from MWTS-2. Their findings are published in Advances in Atmospheric Sciences.
      The limb correction method helps to uncover the underlying weather signals behind the scan-dependent features in observations. After limb correction, the observed brightness temperatures can be directly applied in analyzing large-scale weather patterns at a global range, as well as monitoring smaller-scale weather events such as typhoons or even convection systems.

      Taking Super Typhoon Neoguri in 2014 as an example, the authors compare the brightness temperatures covering the storm before and after limb correction, as shown in Fig. 1. In the brightness temperature before limb correction, the typhoon structures can be vaguely seen, only with the more dominant scan-dependent features due to the varying scan angles within each scan line. In comparison, the storm structure as well as the temperature distribution of the ambient environment looks a lot clearer in the limb-corrected results (Fig. 1b). After comparing the MWTS-2 observations against geophysical variables including atmospheric temperature and liquid water path, the authors found the correlations between the observations and atmospheric temperature reached as high as 0.982, while the correlations with liquid water path increased by 30% to 55%.
      The authors argue that there is considerable potential for more weather applications by using the limb-corrected brightness temperatures, like studying climatological trends and direct assimilation into numerical weather prediction models. In the meantime, the proposed algorithm is readily applicable to microwave temperature sounders carried by the future FengYun satellite series.

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AMS 2021 http://xiaoxutian.com/ams-2021/ Wed, 21 Nov 2018 19:59:19 +0000 http://xiaoxutian.com/?p=239

Date and Time: TBD
Session: TBD
Location: The Convention Center of Zoom

Development of the tangent linear and adjoint models of the MPAS-Atmosphere dynamic core and applications in adjoint relative sensitivity studies

Xiaoxu Tian and Xiaolei Zou
Department of Atmospheric and Oceanic Science,
University of Maryland, College Park, MD 20740

Abstract

This study develops and tests a version of the Python-driven, non-hydrostatic Model for Prediction Across Scales – Atmosphere (MPAS-A) dynamic model, as well as its tangent linear and adjoint models. The non-linear, non-hydrostatic dynamic core of the MPAS-A is restructured to have a Python driver for the convenience of parsing namelists, manipulating matrices, controlling simulation time flows, reading model inputs, and writing outputs, while the heavy-duty mediation and model layers are retained in Fortran for computational efficiency. Under the same Python-driving structure, developed are the tangent linear and adjoint models for the dynamic core of the MPAS-A model with verified correctness. The case of Jablonowski and Williamson’s baroclinic wave is used for demonstrating the approximation accuracy of the MPAS-A tangent linear model and the applicability of the MPAS-A adjoint model to relative sensitivity studies. Numerical experimental results show that the tangent linear model can well approximate the temporal evolutions of non-linear model perturbations for all model variables over a four-day forecast period. Employing the MPAS-A adjoint model, it is shown that the most sensitive regions of the 24-h forecast of surface pressure are weather dependent. An interesting westward vertical tilting is also found in the relative sensitivity results of a 24-h forecast of surface pressure at a point located within a trough to model initial conditions. This functionality of the MPAS-A adjoint model is highly essential in understanding dynamics and variational data assimilation.

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