Adjoint of the global Eulerian–Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com ), with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e−14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated into a variational inversion system designed to optimize surface fluxes of greenhouse gases.

[1]  Pauli Heikkinen,et al.  Inferring regional sources and sinks of atmospheric CO 2 from GOSAT XCO 2 data , 2013 .

[2]  A. McGuire,et al.  Is the northern high‐latitude land‐based CO2 sink weakening? , 2011 .

[3]  Stefan Reimann,et al.  An analytical inversion method for determining regional and global emissions of greenhouse gases: Sensitivity studies and application to halocarbons , 2008 .

[4]  A. Karion,et al.  Long-term greenhouse gas measurements from aircraft , 2012 .

[5]  R. Macdonald,et al.  Sensitivity of the carbon cycle in the Arctic to climate change , 2009 .

[6]  S. Kobayashi,et al.  The JRA-25 Reanalysis , 2007 .

[7]  Makoto Saito,et al.  Regional CO2 flux estimates for 2009–2010 based on GOSAT and ground-based CO2 observations , 2012 .

[8]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[9]  D. Jacob,et al.  Comparison of Adjoint and Analytical Bayesian Inversion Methods for Constraining Asian Sources of Carbon Monoxide Using Satellite (MOPITT) Measurements of CO Columns , 2009 .

[10]  Makoto Saito,et al.  Evaluation of Biases in JRA-25/JCDAS Precipitation and Their Impact on the Global Terrestrial Carbon Balance , 2011 .

[11]  Philippe Bousquet,et al.  Inferring CO2 sources and sinks from satellite observations: Method and application to TOVS data , 2005 .

[12]  Shamil Maksyutov,et al.  Mass-conserving tracer transport modelling on a reduced latitude-longitude grid with NIES-TM , 2011 .

[13]  Inez Y. Fung,et al.  Variations in modeled atmospheric transport of carbon dioxide and the consequences for CO2 inversions , 1996 .

[14]  P. Rasch,et al.  Description of the NCAR community climate model (CCM2), June 1993. Technical note , 1993 .

[15]  Kevin W. Bowman,et al.  Source‐receptor relationships of column‐average CO2 and implications for the impact of observations on flux inversions , 2015 .

[16]  Shamil Maksyutov,et al.  Carbon flux estimation for Siberia by inverse modeling constrained by aircraft and tower CO2 measurements , 2012 .

[17]  Shamil Maksyutov,et al.  TransCom model simulations of CH4 and related species: linking transport, surface flux and chemical loss with CH4 variability in the troposphere and lower stratosphere , 2011 .

[18]  Y. Niwa,et al.  Global atmospheric carbon budget: results from an ensemble of atmospheric CO2 inversions. , 2013 .

[19]  Wouter Peters,et al.  An improved Kalman Smoother for atmospheric inversions , 2005 .

[20]  Thomas Kaminski,et al.  A coarse grid three-dimensional global inverse model of the atmospheric transport 1. Adjoint model and Jacobian matrix , 1999 .

[21]  Shamil Maksyutov,et al.  Optimization of a prognostic biosphere model for terrestrial biomass and atmospheric CO2 variability , 2014 .

[22]  M. Buchwitz,et al.  SCIAMACHY: Mission Objectives and Measurement Modes , 1999 .

[23]  Shamil Maksyutov,et al.  Interannual variability of the air–sea CO2 flux in the north Indian Ocean , 2013, Ocean Dynamics.

[24]  Masakatsu Nakajima,et al.  Thermal and near infrared sensor for carbon observation Fourier-transform spectrometer on the Greenhouse Gases Observing Satellite for greenhouse gases monitoring. , 2009, Applied optics.

[25]  J. G. Esler,et al.  Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM) , 2014 .

[26]  Thomas Kaminski,et al.  On aggregation errors in atmospheric transport inversions , 2001 .

[27]  I. Enting,et al.  Seasonal sources and sinks of atmospheric CO2 Direct inversion of filtered data , 1989 .

[28]  Pierre Friedlingstein,et al.  Three-dimensional transport and concentration of SF6. A model intercomparison study (TransCom 2) , 1999 .

[29]  Adrian Sandu,et al.  On the properties of discrete adjoints of numerical methods for the advection equation , 2008 .

[30]  P. Haines.  Technical Note : Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework ( RETRO-TOM ) , 2014 .

[31]  Akihiko Ito,et al.  Changing ecophysiological processes and carbon budget in East Asian ecosystems under near-future changes in climate: implications for long-term monitoring from a process-based model , 2010, Journal of Plant Research.

[32]  Vincent R. Gray.  Climate Change 2007: The Physical Science Basis Summary for Policymakers , 2007 .

[33]  Kevin R. Gurney,et al.  TransCom 3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988–2003 , 2006 .

[34]  Shamil Maksyutov,et al.  Simulation and assimilation of global ocean pCO2 and air–sea CO2 fluxes using ship observations of surface ocean pCO2 in a simplified biogeochemical offline model , 2010, Tellus B: Chemical and Physical Meteorology.

[35]  Time-dependent atmospheric CO2 inversions based on interannually varying tracer transport , 2003 .

[36]  Philippe Bousquet,et al.  Daily CO2 flux estimates over Europe from continuous atmospheric measurements: 1, inverse methodology , 2005 .

[37]  Ian G. Enting,et al.  Inverse problems in atmospheric constituent transport , 2002 .

[38]  Clive D Rodgers,et al.  Inverse Methods for Atmospheric Sounding: Theory and Practice , 2000 .

[39]  R. Vautard,et al.  TransCom model simulations of hourly atmospheric CO2: Experimental overview and diurnal cycle results for 2002 , 2008, Global Biogeochemical Cycles.

[40]  G. Marland,et al.  Monthly, global emissions of carbon dioxide from fossil fuel consumption , 2011 .

[41]  S. Houweling,et al.  Global CO 2 fluxes estimated from GOSAT retrievals of total column CO 2 , 2013 .

[42]  Justus Notholt,et al.  Simulations of column-averaged CO 2 and CH 4 using the NIES TM with a hybrid sigma-isentropic (σ-θ) vertical coordinate , 2012 .

[43]  M. Ikegami,et al.  New technique to analyse global distributions of CO2 concentrations and fluxes from non-processed observational data , 2010 .

[44]  S. Maksyutov,et al.  Simulation of contribution of continental anthropogenic sources to variations in the CO2 concentration during winter period on Hateruma Island , 2013 .

[45]  Olivier Talagrand,et al.  Eulerian backtracking of atmospheric tracers. I: Adjoint derivation and parametrization of subgrid‐scale transport , 2006 .

[46]  Nicholas C. Parazoo,et al.  TransCom model simulations of hourly atmospheric CO2: Analysis of synoptic‐scale variations for the period 2002–2003 , 2008 .

[47]  Sander Houweling,et al.  CO 2 flux history 1982–2001 inferred from atmospheric data using a global inversion of atmospheric transport , 2003 .

[48]  P. Rayner,et al.  The utility of remotely sensed CO2 concentration data in surface source inversions , 2001 .

[49]  M. Chipperfield,et al.  Development of a variational flux inversion system (INVICAT v1.0) using the TOMCAT chemical transport model , 2013 .

[50]  Hartmut Boesch,et al.  Carbon Monitoring Satellite (CarbonSat): assessment of atmospheric CO 2 and CH 4 retrieval errors by error parameterization , 2013 .

[51]  M. Heimann,et al.  A two-step scheme for high-resolution regional atmospheric trace gas inversions based on independent models , 2009 .

[52]  J. Seinfeld,et al.  Development of the adjoint of GEOS-Chem , 2006 .

[53]  Shamil Maksyutov,et al.  Simulation of variability in atmospheric carbon dioxide using a global coupled Eulerian – Lagrangian transport model , 2011 .

[54]  R. Prinn,et al.  Inversion of long-lived trace gas emissions using combined Eulerian and Lagrangian chemical transport models , 2011 .

[55]  J. Randerson,et al.  Global fire emissions and the contribution of deforestation, savanna, forest, agricultural, and peat fires (1997-2009) , 2010 .

[56]  Philippe Ciais,et al.  Transcom 3 inversion intercomparison: Model mean results for the estimation of seasonal carbon sources and sinks , 2004, Global Biogeochemical Cycles.

[57]  David Crisp,et al.  The Orbiting Carbon Observatory (OCO) mission , 2004 .

[58]  Shamil Maksyutov,et al.  ENSO-related variability in latitudinal distribution of annual mean atmospheric potential oxygen (APO) in the equatorial Western Pacific , 2015 .

[59]  Guriĭ Ivanovich Marchuk,et al.  Adjoint Equations and Analysis of Complex Systems , 1995 .

[60]  D. Davydov,et al.  Continuous measurements of methane from a tower network over Siberia , 2010 .

[61]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[62]  Shamil Maksyutov,et al.  NIES/FRCGC Global Atmospheric Tracer Transport Model: Description, Validation, and Surface Sources and Sinks Inversion , 2008 .

[63]  Thomas Kaminski,et al.  A coarse grid three-dimensional global inverse model of the atmospheric transport. 2. Inversion of the transport of CO2 in the 1980s , 1999 .

[64]  Andreas Stohl,et al.  FLEXINVERT: an atmospheric Bayesian inversion framework for determining surface fluxes of trace species using an optimized grid , 2014 .

[65]  Michael Buchwitz,et al.  A remote sensing technique for global monitoring of power plant CO 2 emissions from space and related applications , 2010 .

[66]  A. Denning,et al.  Variations in modelled atmospheric transport of carbon dioxide and the consequences for CO inversions , 2012 .

[67]  Makoto Saito,et al.  A global coupled Eulerian-Lagrangian model and 1 × 1 km CO2 surface flux dataset for high-resolution atmospheric CO2 transport simulations , 2011 .

[68]  P. Tans,et al.  Latitudinal distribution of the sources and sinks of atmospheric carbon dioxide derived from surface observations and an atmospheric transport model , 1989 .

[69]  Philippe Ciais,et al.  Towards robust regional estimates of CO2 sources and sinks using atmospheric transport models , 2002, Nature.

[70]  Tatsuya Yokota,et al.  Global Concentrations of CO2 and CH4 Retrieved from GOSAT: First Preliminary Results , 2009 .

[71]  J. Randerson,et al.  An atmospheric perspective on North American carbon dioxide exchange: CarbonTracker , 2007, Proceedings of the National Academy of Sciences.

[72]  Dusanka Zupanski,et al.  An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations , 2005 .

[73]  Hendrik Elbern,et al.  Variational data assimilation for tropospheric chemistry modeling , 1997 .

[74]  Annual Fossil-Fuel CO2 Emissions: Mass of Emissions Gridded by One Degree Latitude by One Degree Longitude , 2009 .

[75]  Makoto Saito,et al.  On the Benefit of GOSAT Observations to the Estimation of Regional CO2 Fluxes , 2011 .

[76]  Martyn P. Chipperfield,et al.  Off-line algorithm for calculation of vertical tracer transport in the troposphere due to deep convection , 2012 .

[77]  Thomas Kaminski,et al.  Recipes for adjoint code construction , 1998, TOMS.

[78]  A. Stohl,et al.  Technical note: The Lagrangian particle dispersion model FLEXPART version 6.2 , 2005 .

[79]  Trissevgeni Stavrakou,et al.  Inversion of CO and NO x emissions using the adjoint of the IMAGES model , 2004 .

[80]  Peter Bergamaschi,et al.  Four‐dimensional variational data assimilation for inverse modeling of atmospheric methane emissions: Analysis of SCIAMACHY observations , 2008 .

[81]  Shamil Maksyutov,et al.  A very high-resolution (1 km×1 km) global fossil fuel CO2 emission inventory derived using a point source database and satellite observations of nighttime lights , 2011 .