A machine learning emulator for Lagrangian particle dispersion model footprints - a case study using NAME

Aug 5, 2026

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Lagrangian particle dispersion models (LPDMs) compute source-receptor “footprints” used in greenhouse gas (GHG) flux inversions, but they scale poorly to large observational datasets because each data point requires a full model simulation. This work presents a proof-of-concept machine learning emulator that predicts LPDM footprints over a 350 km by 230 km domain using only meteorological inputs, emulating each grid cell via gradient-boosted regression trees. Trained on NAME footprints (2014–2015), it is evaluated against hourly NAME output (2016 and 2020), achieving mean R-squared of 0.69 across sites and predicting footprints in ~10 ms versus ~10 minutes for the 3D simulator.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Introduction

Motivation: scaling limits in GHG flux inference

LPDMs vs Eulerian transport models

Footprint definition and computational burden

Geosci. Model Dev., 16, 1997–2009, 2023 [https://doi.org/10.5194/gmd-16-1997-2023](https://doi.org/10.5194/gmd-16-1997-2023)[ ](https://doi.org/10.5194/gmd-16-1997-2023)© Author(s) 2023 . This work is distributed under the Creative Commons Attribution 4 .0 License. A machine learning emulator for Lagrangian particle dispersion model footprints: a case study using NAME Elena Fillola 1 , Raul Santos-Rodriguez 1 , Alistair Manning2 , Simon O'Doherty3 , and Matt Rigby3 1Department of Engineering Mathematics, University of Bristol, Bristol, UK 2Hadley Centre, Met Ofﬁce, Exeter, UK 3 School of Chemistry, University of Bristol, Bristol, UK Correspondence: Elena Fillola (elena.ﬁ[llolamayoral@bristol.ac.uk](llolamayoral@bristol.ac.uk)) Received: 27 October 2022 – Discussion started: 7 November 2022 Revised: 9 February 2023 – Accepted: 12 March 2023 – Published: 12 April 2023 Abstract. Lagrangian particle dispersion models (LPDMs) have been used extensively to calculate source-receptor relationships (“footprints”) for use in applications such as greenhouse gas (GHG) ﬂux inversions. Because a single model simulation is required for each data point, LPDMs do not scale well to applications with large data sets such as ﬂux inversions using satellite observations. Here, we develop a proof-of-concept machine learning emulator for LPDM footprints over a 􀀘 350 km 􀀂 230 km region around an observation point, and test it for a range of in situ measurement sites from around the world. As opposed to previous approaches to footprint approximation, it does not require the interpolation or smoothing of footprints produced by the LPDM. Instead, the footprint is emulated entirely from meteorological inputs. This is achieved by independently emulating the footprint magnitude at each grid cell in the domain using gradient-boosted regression trees with aselection of meteorological variables as inputs. The emulator is trained based on footprints from the UK Met Ofﬁce's Numerical Atmospheric-dispersion Modelling Environment (NAME) for 2014 and 2015, and the emulated footprints are evaluated against hourly NAME output from 2016 and 2020. When compared to CH 4 concentration time series generated by NAME, we show that our emulator achieves a mean R-squared score of 0.69 across all sites investigated between 2016 and 2020 . The emulator can predict a footprint in around 10 ms, compared to around 10 min for the 3D simulator. This simple and interpretable proof-of-concept emulator demonstrates the potential of machine learning for LPDM emulation. 1 Introduction To monitor the efﬁcacy of climate agreements and understand climate feedbacks, there is an urgent need to quantify changing greenhouse gas (GHG) ﬂuxes. Flux inference or inverse modelling systems are becoming increasingly popular for GHG ﬂux quantiﬁcation as they produce estimates of the spatial distribution of methane sources from atmospheric observations using an atmospheric transport model and statistical inversion framework. They have been used, for example, to evaluate methane emissions of the UK and Europe using in situ sensors (Lunt et al., 2021 ; Bergamaschi et al., 2018), for the investigation of regional CFC-11 emissions from eastern China (Rigby et al., 2019), and for many other applications. Flux inference inverse methods were traditionally designed for relatively small data sets based on high-precision ground-based measurements (tens of sites globally that together collect 􀀘 thousands of observations per month) . However, the growth of surface networks and space-based observations mean that the volume of GHG data has increased by several orders of magnitude in recent years and will continue to grow in the next decade. For example, the TROPOMI instrument onboard the Sentinel-5 precursor, which was launched in 2017, collects around 7 million CH 4 soundings per day (Butz et al., 2012), compared to 10 000 per day from the GOSAT instrument that was launched in 2009 (Taylor et a

FAQs

Why are LPDM footprints difficult to scale for large GHG flux inversion datasets?

Each observation data point typically requires a separate LPDM simulation to compute the source-receptor footprint, creating severe computational bottlenecks when dataset sizes grow rapidly.

How does the proposed emulator generate LPDM footprints?

It emulates the footprint magnitude at every grid cell directly from meteorological inputs, using gradient-boosted regression trees, without interpolating or smoothing LPDM-produced footprints.

What data and evaluation periods are used for training and testing?

The emulator is trained using UK Met Office NAME footprints from 2014 and 2015, then evaluated against hourly NAME outputs from 2016 and 2020 across multiple in situ sites.

Aug 5, 2026

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