Parametrizing the projected wind fields of ultra-hot Jupiters in thermal emission: An application to GCM spectra of WASP-76b

High-resolution thermal emission spectroscopy provides a powerful probe of atmospheric circulation in ultra-hot Jupiters (UHJs), with Doppler shifts encoding information about the 3D wind field across the planet disk. Retrieving these wind properties from phase-dependent emission spectra requires a forward model that is both physically motivated and computationally tractable. We aim to investigate what 3D wind information is contained in the thermal emission spectra of UHJs in the first place, and whether the complicated 3D atmospheric structure of these planets can be captured by a simplified forward model with a small number of parameters. We present , a new forward model that parametrizes the projected line-of-sight velocity field on the planet disk using four wind parameters (an equatorial jet speed v_ dopplerkernel and width σ_ a source-to-sink flow speed v_ and a flow convergence longitude ̌arphi_ and constructs a broadening kernel via weighted kernel-density estimation. We applied this framework in a Bayesian retrieval to synthetic K-band emission spectra of WASP-76b generated from three global circulation models (GCMs) that span a range of atmospheric drag strengths. We performed retrievals across multiple spectral resolutions and orbital phase coverages. Our retrievals successfully recovered the equatorial jet in the drag-free GCM to within ∼1 km/s of the zonal mean and infer day-to-night wind speeds in good agreement with GCM averages at 1--10 mbar for all three drag regimes. We find that spectral resolutions of R ∼ 100 , 000 offer an optimal trade-off: sufficient to resolve global wind features while avoiding spurious detections caused by model--data mismatches at higher resolution. Combining pre- and post-eclipse phases yields more reliable constraints than either alone, particularly on the orientation of the source-to-sink flow. Experiments with more complex weight functions reveal a degeneracy between the velocity field and the thermal weighting, cautioning against overparametrization. A parametric broadening-kernel model with a small number of physically interpretable parameters can accurately reproduce the phase-dependent line shifts, shapes, and strengths in UHJ emission spectra. However, the fundamental degeneracy between the velocity distribution and the thermal weight function means that adding model complexity does not necessarily improve wind inference and may introduce spurious features. Bayesian model comparison is essential when applying this framework to real observations.