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PPRO: Parameterized Polarimetric Radar Operator Library

Overview

PPRO is an independent, standalone library for computing dual-polarization radar variables from atmospheric model state variables. The library provides a modular, reusable implementation of the Parameterized Polarimetric Radar Operator (P-PRO) that can be used in any numerical weather prediction or data assimilation system.

This library can be used independently or integrated into data assimilation frameworks such as JEDI-UFO.

Scientific Background

The P-PRO operator is based on the parameterized forward operators for polarimetric radar data:

Zhang21 Method (Zhang et al. 2021): Assumes double-moment microphysics schemes with exponential particle size distribution (PSD). Dual-pol radar quantities are parameterized as polynomial functions of mean diameter (Dm) and mass content of hydrometeors (Wx), by fitting to integral of T-matrix-based backscattering amplitude over the PSD. Two Melting models are implemented in this operator.

TCWA2 Method (Tsai et al. 2026): Similar to Zhang21, but assumes a gamma PSD. Dual-pol radar quantities are parameterized as more complex functions of gamma-PSD parameters (λ, α) (or equivalently bulk moments qx and Ntx with derived size metrics such as Dx). Environmental state (e.g., T), density and shape of particles, and model-provided melting fractions (smlf/gmlf) are also used in the simulation. The single scattering calculation is based on the Rayleigh approximation,following Ryzhkov et al., 2011.

Operator Comparison: Zhang21 vs TCWA2

Feature Zhang21 TCWA2
PSD assumption Exponential Gamma
Scattering method T-matrix Rayleigh approximation
Fitted functions Polynomials of Dm and Wx (mass content) Complex functions of more parameters
Microphysics Thompson, WSM6, NSSL, TCWA2 TCWA2 (Taiwan CWA)
Melting treatment Melting models (Zhang21 or Liu et al. 2024) Melted fraction from TCWA2 MP scheme
Required inputs qr, qs, qg [+ qh, nr, ns, ng, nh, vg, vh for NSSL] qr, qs, qg, qc, qi, nr, ns, ng, ni, smlf, gmlf
Ice crystal Not used Explicit (qi, ni)
Cloud water Not used Explicit (qc)

Key Algorithmic Differences:

  • Zhang21: Exponential PSD + T-matrix scattering → Dm, Wx → Polynomial evaluation → Zh, ZDR, KDP, ρhv
  • TCWA2: Gamma PSD + Rayleigh scattering → λ, α, Dx, smlf/gmlf → Fitted analytic functions → Zh, ZDR, KDP

Recommendation:

  • Use Zhang21 for multiple microphysics schemes (e.g., Thompson, WSM6, NSSL, TCWA2)
  • Use TCWA2 for Taiwan CWA double-moment microphysics scheme TCWA2

The operator computes dual-polarization radar variables including:

  • Zhh: Horizontal reflectivity (dBZ)
  • ZDR: Differential reflectivity (dB)
  • KDP: Specific differential phase (deg/km)
  • ρhv: Copolar correlation coefficient

Features

  • Multiple Polarimetric Operators:

    • Zhang21: Exponential PSD, T-matrix scattering, polynomial functions (Zhang et al. 2021)
    • TCWA2: Gamma PSD, Rayleigh scattering, complex functions (Tsai et al. 2026)

  • Microphysics Schemes:

    • Thompson: Double-moment for rain (with Zhang21 operator)
    • WSM6: Single-moment (with Zhang21 operator)
    • NSSL: Double-moment with hail (with Zhang21 operator)
    • TCWA2: Taiwan CWA double-moment miscrophysics scheme (Tsai et al. 2026, work with both TCWA2 and Zhang21 operator)

  • Radar Frequencies:

    • S-band (11 cm wavelength) and C-band (5.3 cm wavelength) support

  • Advanced Physics:

    • Melting layer treatment (Zhang21: melting model, Liu et al. 2024; TCWA2: melting fraction from TCWA2 MP scheme)
    • Pure and melting hydrometeor categories (rain, snow, graupel, hail, ice)
    • Gamma PSD (Particle Size Distribution) parameterization (TCWA2)

Directory Structure

ppro/
├── CMakeLists.txt          # Main CMake build configuration
├── VERSION.cmake           # Version information
├── ppro-config.cmake.in    # CMake package config template
├── README.md              # This file
├── LICENSE                # License information
├── cmake/                 # CMake modules
│   ├── ppro_compiler_flags.cmake
│   ├── compiler_flags_GNU_Fortran.cmake
│   ├── compiler_flags_Intel_Fortran.cmake
│   └── compiler_flags_IntelLLVM_Fortran.cmake
├── src/                   # Source code
│   ├── CMakeLists.txt
│   ├── dualpol_op_mod.f90       # Main interface (operator dispatch)
│   ├── zhang21/                 # Zhang21 operator
│   │   ├── zhang21_forward_mod.f90 # Zhang21 forward operator
│   │   ├── zhang21_tlad_mod.f90   # Zhang21 TL/AD
│   │   └── CMakeLists.txt
│   └── tcwa2/                   # TCWA2 operator
│       ├── tcwa2_forward_mod.f90   # TCWA2 forward operator
│       └── CMakeLists.txt
├── examples/              # Standalone example programs
│   ├── CMakeLists.txt
│   ├── standalone_test.f90      # Comprehensive test/demo program
│   └── README.md                # Examples documentation
└── fix/                   # Coefficient data files for Zhang21/Kong26
    ├── README.txt
    ├── sband_rain_coefs.txt
    ├── sband_snow_coefs.txt
    ├── sband_graupel_coefs.txt
    ├── sband_hail_coefs.txt
    ├── cband_rain_coefs.txt
    ├── cband_snow_coefs.txt
    ├── cband_graupel_coefs.txt
    └── cband_hail_coefs.txt

Building

Prerequisites

  • CMake 3.20 or higher
  • Fortran compiler (GNU, Intel, or IntelLLVM)
  • Optional: OpenMP for parallel computation

Build Instructions

# Clone or copy the ppro directory
cd ppro

# Create build directory
mkdir build
cd build

# Configure with CMake
cmake ..

# Build the library
make

# Install (optional)
make install

CMake Options

  • OPENMP: Enable OpenMP support (default: ON)
  • BUILD_SHARED_LIBS: Build shared libraries instead of static (default: OFF)
  • BUILD_EXAMPLES: Build standalone example programs (default: ON)
  • CMAKE_INSTALL_PREFIX: Installation prefix

Example with custom options:

cmake -DOPENMP=OFF -DBUILD_EXAMPLES=OFF -DCMAKE_INSTALL_PREFIX=/path/to/install ..

Running Examples

After building, run the standalone test:

cd build/bin
./ppro_standalone_test

See examples/README.md for more details on examples and how to write your own programs using PPRO.

Usage

Standalone Usage

The library can be used independently in any Fortran-based numerical weather prediction model:

Using Zhang21 operator (exponential PSD + T-matrix):

use dualpol_op_mod, only: ppro_init_coefs, ppro_compute_point

! Initialize with Zhang21 operator (reads polynomial coefficient files)
call ppro_init_coefs(operator_name='Zhang21')

! Compute dual-pol variables using polynomial functions of Dm and Wx
call ppro_compute_point(iband, 'THOMPSON', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv, nr=nr)

Using TCWA2 operator (gamma PSD + Rayleigh scattering):

use dualpol_op_mod, only: ppro_init_coefs, ppro_compute_point

! Initialize with TCWA2 operator (no coefficient files required)
call ppro_init_coefs(operator_name='TCWA2')

! Compute dual-pol variables (TCWA2 requires additional parameters)
! Note: TCWA2 needs cloud ice (qi, ni), cloud water (qc), and melting fractions (smlf, gmlf)
call ppro_compute_point(iband, 'THOMPSON', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv, &
                        nr=nr, ns=ns, ng=ng, ni=ni, qi=qi, qc=qc, &
                        smlf=smlf, gmlf=gmlf)

Integration with JEDI-UFO

The library can also be integrated into JEDI-UFO for data assimilation applications:

Option 1: Using find_package (Recommended for production)

After installing ppro, configure UFO with:

find_package(PPRO REQUIRED)
target_link_libraries(ufo PUBLIC ppro)

Option 2: Using add_subdirectory (Recommended for development)

Place ppro in your JEDI bundle and use:

ecbuild_bundle(PROJECT ppro SOURCE ${CMAKE_CURRENT_SOURCE_DIR}/ppro)
target_link_libraries(ufo PUBLIC ppro)

Coefficient Files

The Zhang21 operator requires coefficient files for S-band and C-band radars, which should be placed in the fix/ directory. See fix/README.txt for details. The TCWA2 operator has all coefficients hard-coded in the source and requires no external files.

Module Structure

Main Interface (dualpol_op_mod.f90)

Unified interface providing:

  • ppro_init_coefs(): Initialize library with operator selection
  • ppro_compute_point(): Main computation (dispatches to selected operator)
  • ppro_set_operator(): Switch between operators
  • ppro_finalize(): Cleanup

Zhang21 Operator (zhang21/)

zhang21_forward_mod.f90 - Exponential PSD + T-matrix polynomial operator:

  • zhang21_init_coefs(): Load polynomial coefficients (S-band/C-band)
  • zhang21_compute_point(): Compute using polynomial functions of Dm and Wx
  • melting_model_liu24(): Melting layer treatment
  • dualpol_op_rain/icephase/total(): Individual hydrometeor calculations

zhang21_tlad_mod.f90 - Tangent-linear and adjoint for Variational DA applications

TCWA2 Operator (tcwa2/)

tcwa2_forward_mod.f90 - Gamma PSD + Rayleigh scattering fitted formulations:

  • dualpol_op_rain_tcwa2(): Rain using fitted analytic formulas
  • dualpol_op_ice_tcwa2(): Ice using fitted analytic formulas
  • dualpol_op_snow_tcwa2(): Snow with melting treatment
  • dualpol_op_graup_tcwa2(): Graupel with melting treatment
  • GAMLN(): Gamma function computation

Detailed Operator Usage

Zhang21 Operator with Multiple Microphysics Schemes

Method: Exponential PSD; polynomial functions of Dm (mean diameter) and Wx (mass content) fitted from T-matrix scattering simulations

Compatible Schemes: WSM6, Thompson, NSSL, TCWA2

WSM6 (Single-moment, 7 variables):

use dualpol_op_mod

call ppro_init_coefs(operator_name='Zhang21')
call ppro_compute_point(iband, 'WSM6', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv)

Thompson (Double-moment for rain, 8 variables):

use dualpol_op_mod

call ppro_init_coefs(operator_name='Zhang21')
call ppro_compute_point(iband, 'THOMPSON', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv, nr=nr)

NSSL (Double-moment with hail, 14 variables):

use dualpol_op_mod

call ppro_init_coefs(operator_name='Zhang21')
call ppro_compute_point(iband, 'NSSL', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv, &
                        qh=qh, nr=nr, ns=ns, ng=ng, nh=nh, vg=vg, vh=vh)

TCWA2 Operator

Method: Gamma PSD; fitted analytic parameterizations derived from bin-based scattering under the Rayleigh approximation

Compatible Scheme: TCWA2 only

TCWA2 (15 variables with melting fractions):

use dualpol_op_mod

! Initialize TCWA2 operator (no coefficient files needed)
call ppro_init_coefs(operator_name='TCWA2')

! Compute dual-pol variables with TCWA2-specific inputs
! Note: Requires qi, ni (ice), qc (cloud water), smlf, gmlf (melting fractions)
call ppro_compute_point(iband, 'TCWA2', density_air, temp_air, &
                        qr, qs, qg, zh, zdr, kdp, phv, &
                        nr=nr, ns=ns, ng=ng, ni=ni, qi=qi, qc=qc, &
                        smlf=smlf, gmlf=gmlf)

Key Differences:

  • Zhang21:

    • PSD: Exponential; Scattering: T-matrix
    • Initialization: Read polynomial coefficients from files (one-time)
    • Runtime: Polynomial evaluation only—no table lookup
    • Melting: Melting model (Liu et al. 2024)
    • Schemes: WSM6, Thompson, NSSL, TCWA2

  • TCWA2:

    • PSD: Gamma; Scattering: Rayleigh approximation
    • Initialization: Coefficients hard-coded in source
    • Runtime: Fitted analytic evaluation (as functions of gamma-PSD parameters)
    • Melting: Explicit melted fraction fields (smlf, gmlf) from model
    • Schemes: TCWA2 only

Version History

  • v1.0.0 (2025): Initial modularized release
    • Multi-operator architecture (Zhang21 + TCWA2)
    • Modular directory structure (zhang21/ and tcwa2/ subdirectories)
    • Support for Thompson, WSM6, NSSL, and TCWA2 microphysics
    • S-band and C-band radar support
    • Standalone examples and documentation

Authors

Core Development:

  • Rong Kong (NCAR/MMM) - Library architecture, modularization, multi-operator framework, testing and maintenance

Operator Implementation:

  • Zhiquan (Jake) Liu (NCAR/MMM) - Zhang21 operator implementation
  • Tzu-Chin Tsai (CWA) - TCWA2 operator implementation

Extensions and Integration:

  • Hejun Xie - tangent linear and adjoint of Zhang21 operator
  • Tao Sun - Hail categories and extended microphysics support

License

This software is licensed under the terms of the Apache Licence Version 2.0 which can be obtained at http://www.apache.org/licenses/LICENSE-2.0.

References

  1. Zhang21 Operator:
    Zhang, G., J. Gao, and M. Du, 2021: Parameterized forward operators for simulation and assimilation of polarimetric radar data with numerical weather predictions. Adv. Atmos. Sci., 38(5), 737−754.

  2. Zhang21 Melting Scheme:
    Liu, et al., 2024: A New Melting Model and Its Implementation in Parameterized Forward Operators for Polarimetric Radar Data Simulation With Double Moment Microphysics Schemes. JGR Atmospheres, 129.

  3. Application of Zhang21 Operator in MPAS-JEDI:
    Kong et al., 2026: Assimilation of Radar Radial Velocity and Polarimetric Observations Using LETKF within MPAS-JEDI: A Case Study of an Afternoon Thunderstorm in Taiwan. Mon. Wea. Rev., submitted.

  4. TCWA2 Operator:
    Tsai, T.-C., J.-P. Chen, Z. Liu, S.-Y. Jiang, R. Kong, Y.-J. Wu, J. Ban, L.-F. Hsiao, Y.-S. Tang, P.-L. Chang, and J.-S. Hong, 2026: Development of the TCWA2 Bulk Cloud Microphysics Scheme and Its Integration with a Dual-Polarization Radar Operator for Forecasting Applications. J. Adv. Model. Earth Syst., submitted.

Contact

For questions, issues, or contributions:

  • Technical Lead: Rong Kong (rkong@ucar.edu)
  • Issues: Please open an issue in the repository

Acknowledgments

This work was developed at the National Center for Atmospheric Research (NCAR), Mesoscale and Microscale Meteorology Laboratory (MMM).

PPRO is designed to be used for a general-purpose, standalone dual-polarization radar operator library or be incorporated into a data assimilation framework such as JEDI.

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PPRO dual-polarization radar operator library for JEDI

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