Atmospheric Inventories for Regional Biogeochemistry Scott Denning Colorado State University.

Slides:



Advertisements
Similar presentations
2ª aula Evolution Equation. The Finite Volume Method.
Advertisements

Component Analysis (Review)
Atmospheric inversion of CO 2 sources and sinks Northern Hemisphere sink Jay S. Gregg.
Improving Understanding of Global and Regional Carbon Dioxide Flux Variability through Assimilation of in Situ and Remote Sensing Data in a Geostatistical.
CmpE 104 SOFTWARE STATISTICAL TOOLS & METHODS MEASURING & ESTIMATING SOFTWARE SIZE AND RESOURCE & SCHEDULE ESTIMATING.
Tropical vs. extratropical terrestrial CO 2 uptake and implications for carbon-climate feedbacks Outline: How we track the fate of anthropogenic CO 2 Historic.
Classification and Prediction: Regression Via Gradient Descent Optimization Bamshad Mobasher DePaul University.
Slides for IPCC. Inverse Modeling of CO 2 Air Parcel Sources Sinks wind Sample Changes in CO 2 in the air tell us about sources and sinks Atmospheric.
Chapter 3 Space, Time, and Motion. (1) Wind Observations Vectors have both magnitude and direction. Wind is a vector quantity. The components of wind.
Estimating parameters in inversions for regional carbon fluxes Nir Y Krakauer 1*, Tapio Schneider 1, James T Randerson 2 1. California Institute of Technology.
The Global Carbon Cycle Humans Atmosphere /yr Ocean 38,000 Land 2000 ~90 ~120 7 GtC/yr ~90 About half the CO 2 released by humans is absorbed by.
Evaluating Spatial, Temporal, and Clear-Sky Errors in Satellite CO 2 Measurements Katherine Corbin, A. Scott Denning, Ian Baker, Aaron Wang, Lixin Lu TransCom.
Andrew Schuh, Scott Denning, Marek Ulliasz Kathy Corbin, Nick Parazoo A Case Study in Regional Inverse Modeling.
Geostatistical structural analysis of TransCom data for development of time-dependent inversion Erwan Gloaguen, Emanuel Gloor, Jorge Sarmiento and TransCom.
Compatibility of surface and aircraft station networks for inferring carbon fluxes TransCom Meeting, 2005 Nir Krakauer California Institute of Technology.
Evaluating the Impact of the Atmospheric “ Chemical Pump ” on CO 2 Inverse Analyses P. Suntharalingam GEOS-CHEM Meeting, April 4-6, 2005 Acknowledgements.
Retrieval Theory Mar 23, 2008 Vijay Natraj. The Inverse Modeling Problem Optimize values of an ensemble of variables (state vector x ) using observations:
NOCES meeting Plymouth, 2005 June Top-down v.s. bottom-up estimates of air-sea CO 2 fluxes : No winner so far … P. Bousquet, A. Idelkadi, C. Carouge,
Investigating Synoptic Variations in Atmospheric CO2 Using Continuous Observations and a Global Transport Model Nicholas Parazoo, Scott Denning, Randy.
Modeling approach to regional flux inversions at WLEF Modeling approach to regional flux inversions at WLEF Marek Uliasz Department of Atmospheric Science.
Basic Mathematics for Portfolio Management. Statistics Variables x, y, z Constants a, b Observations {x n, y n |n=1,…N} Mean.
3D Tracer Transport Modeling and the Carbon Cycle Please read: Tans, P. P., I. Y. Fung, and T. Takahashi, Observational constraints on the atmospheric.
Application of Geostatistical Inverse Modeling for Data-driven Atmospheric Trace Gas Flux Estimation Anna M. Michalak UCAR VSP Visiting Scientist NOAA.
Modeling framework for estimation of regional CO2 fluxes using concentration measurements from a ring of towers Modeling framework for estimation of regional.
Interannual inversions with continuous data and recent inversions with the CSIRO CC model Rachel Law, CSIRO Atmospheric Research Another set of pseudodata.
Today Wrap up of probability Vectors, Matrices. Calculus
1 Oceanic sources and sinks for atmospheric CO 2 The Ocean Inversion Contribution Nicolas Gruber 1, Sara Mikaloff Fletcher 2, and Kay Steinkamp 1 1 Environmental.
Principles of the Global Positioning System Lecture 11 Prof. Thomas Herring Room A;
An Assimilating Tidal Model for the Bering Sea Mike Foreman, Josef Cherniawsky, Patrick Cummins Institute of Ocean Sciences, Sidney BC, Canada Outline:
T Jing M. Chen 1, Baozhang Chen 1, Gang Mo 1, and Doug Worthy 2 1 Department of Geography, University of Toronto, 100 St. George Street, Toronto, Ontario,
PATTERN RECOGNITION AND MACHINE LEARNING
The seasonal and interannual variability in atmospheric CO 2 is simulated using best available estimates of surface carbon fluxes and the MATCH atmospheric.
Page 1© Crown copyright WP4 Development of a System for Carbon Cycle Data Assimilation Richard Betts.
O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 1 Vegetation/Ecosystem Modeling and Analysis Project (VEMAP) Lessons Learned or How to Do.
J.-F. Müller and T. Stavrakou IASB-BIRA Avenue Circulaire 3, 1180 Brussels AGU Fall meeting, Dec Multi-year emission inversion for.
Results from the Carbon Cycle Data Assimilation System (CCDAS) 3 FastOpt 4 2 Marko Scholze 1, Peter Rayner 2, Wolfgang Knorr 1 Heinrich Widmann 3, Thomas.
ECE 8443 – Pattern Recognition ECE 8423 – Adaptive Signal Processing Objectives: Deterministic vs. Random Maximum A Posteriori Maximum Likelihood Minimum.
Regional Inversion of continuous atmospheric CO 2 measurements A first attempt ! P., P., P., P., and P. Philippe Peylin, Peter Rayner, Philippe Bousquet,
Computer Animation Rick Parent Computer Animation Algorithms and Techniques Optimization & Constraints Add mention of global techiques Add mention of calculus.
Integration of biosphere and atmosphere observations Yingping Wang 1, Gabriel Abramowitz 1, Rachel Law 1, Bernard Pak 1, Cathy Trudinger 1, Ian Enting.
Research Vignette: The TransCom3 Time-Dependent Global CO 2 Flux Inversion … and More David F. Baker NCAR 12 July 2007 David F. Baker NCAR 12 July 2007.
A direct carbon budgeting approach to study CO 2 sources and sinks ICDC7 Broomfield, September 2005 C. Crevoisier 1 E. Gloor 1, J. Sarmiento 1, L.
# # # # An Application of Maximum Likelihood Ensemble Filter (MLEF) to Carbon Problems Ravindra Lokupitiya 1, Scott Denning 1, Dusanka Zupanski 2, Kevin.
Cambiamento attuale: Biogeochimica CLIMATOLOGIA Prof. Carlo Bisci.
INVERSE MODELING TECHNIQUES Daniel J. Jacob. GENERAL APPROACH FOR COMPLEX SYSTEM ANALYSIS Construct mathematical “forward” model describing system As.
Quality of model and Error Analysis in Variational Data Assimilation François-Xavier LE DIMET Victor SHUTYAEV Université Joseph Fourier+INRIA Projet IDOPT,
CarboEurope: The Big Research Lines Annette Freibauer Ivan Janssens.
Lagrangian particle models are three-dimensional models for the simulation of airborne pollutant dispersion, able to account for flow and turbulence space-time.
Discretization Methods Chapter 2. Training Manual May 15, 2001 Inventory # Discretization Methods Topics Equations and The Goal Brief overview.
CO 2 retrievals from IR sounding measurements and its influence on temperature retrievals By Graeme L Stephens and Richard Engelen Pose two questions:
Observing and Modeling Requirements for the BARCA Project Scott Denning 1, Marek Uliasz 1, Saulo Freitas 2, Marcos Longo 2, Ian Baker 1, Maria Assunçao.
Cheas 2006 Meeting Marek Uliasz: Estimation of regional fluxes of CO 2 … Cheas 2006 Meeting Marek Uliasz: Estimation of regional fluxes of CO 2 …
Inverse Modeling of Surface Carbon Fluxes Please read Peters et al (2007) and Explore the CarbonTracker website.
Earth Observation Data and Carbon Cycle Modelling Marko Scholze QUEST, Department of Earth Sciences University of Bristol GAIM/AIMES Task Force Meeting,
Retrieving sources of fine aerosols from MODIS/AERONET observations by inverting GOCART model INVERSION: Oleg Dubovik 1 Tatyana Lapyonok 1 Tatyana Lapyonok.
Comparison of adjoint and analytical approaches for solving atmospheric chemistry inverse problems Monika Kopacz 1, Daniel J. Jacob 1, Daven Henze 2, Colette.
Dimension reduction (2) EDR space Sliced inverse regression Multi-dimensional LDA Partial Least Squares Network Component analysis.
27-28/10/2005IGBP-QUEST Fire Fast Track Initiative Workshop Inverse Modeling of CO Emissions Results for Biomass Burning Gabrielle Pétron National Center.
Carbon Cycle Data Assimilation with a Variational Approach (“4-D Var”) David Baker CGD/TSS with Scott Doney, Dave Schimel, Britt Stephens, and Roger Dargaville.
CO2 sources and sinks in China as seen from the global atmosphere
(Towards) anthropogenic CO2 emissions through inverse modelling
LECTURE 10: DISCRIMINANT ANALYSIS
Advisor: Michael McElroy
CH 5: Multivariate Methods
CarboEurope Open Science Conference
Monika Kopacz, Daniel Jacob, Jenny Fisher, Meghan Purdy
Ensemble variance loss in transport models:
Models of atmospheric chemistry
Principles of the Global Positioning System Lecture 11
LECTURE 09: DISCRIMINANT ANALYSIS
Presentation transcript:

Atmospheric Inventories for Regional Biogeochemistry Scott Denning Colorado State University

The Global Carbon Cycle Atmosphere /yr Ocean 38,000 Plants and Soils 2000 Fossil Fuel ~90 ~120 6 ~90

Global trend known very accurately Provides an integral constraint on the total carbon budget Interannual variability is of the same order as anthropogenic emissions!

Meridional Gradients (Tans et al, 1990) Simulated gradient way too steep for most emission scenarios

Diurnal Variations Diurnal cycle of 70 ppm over an active forest is 5x as strong as seasonal cycle Vertical gradient at sunrise is 15x as strong as pole-to-pole gradient Vertical gradient reverses in daytime, much weaker

Diurnal Variations

Advection: –Stuff that was “upstream” moves here with the wind: –To predict the future amount of q, we simply need to keep track of gradients and wind speed in each direction Turbulence –Tracer transport by “unresolved” eddies –Behaves like down-gradient diffusion or “mixing” Moist (cumulus) convection –Vertical transport by updrafts and downdrafts in clouds Atmospheric Transport

Cumulus Transport (example) Cloud “types” defined by lateral entrainment Separate in-cloud CO2 soundings for each type Detrainment back into environment at cloud top

Inverse Modeling of Atmospheric CO 2 Air Parcel Sources Sinks transport (model) (solve for) concentration transport sources and sinks (observe) Sample

Synthesis Inversion Procedure (“Divide and Conquer”) 1.Divide carbon fluxes into subsets based on processes, geographic regions, or some combination 1.Spatial patterns of fluxes within regions? 2.Temporal phasing (e.g., seasonal, diurnal, interannual?) 2.Prescribe emissions of unit strength from each “basis function” as lower boundary forcing to a global tracer transport model 3.Integrate the model for three years (“spin-up”) from initially uniform conditions to obtain equilibrium with sources and sinks 4.Each resulting simulated concentration field shows the “influence” of the particular emissions pattern 5.Combine these fields to “synthesize” a concentration field that agrees with observations

Consider Linear Regression Given N measurements y i for different values of the independent variable x i, find a slope ( m ) and intercept ( b ) that describe the “best” line through the observations –Why a line? –What do we mean by “best” –How do we find m and b ? Compare predicted values to observations, and find m and b that fit best Define a total error (difference between model and observations) and minimize it!

Our model is Error at any point is just Could just add the error up: Problem: positive and negative errors cancel … we need to penalize signs equally Define the total error as the sum of the Euclidean distance between the model and observations (sum of square of the errors): Defining the Total Error

Minimizing Total Error (Least Squares) Take partial derivs Set to zero Solve for m and b

Geometric View of Linear Regression Any vector can be written as a linear combination of the orthonormal basis set This is accomplished by taking the dot product (or inner product) of the vector with each basis vector to determine the components in each basis direction Linear regression involves a 2D mapping of an observation vector into a different vector space More generally, this can involve an arbitrary number of basis vectors (dimensions)

Generalized Least Squares The G's can be thought of as partial derivatives and the whole matrix as a Jacobian.

“Determinedness” Even-determined –Exact solution, zero prediction error Over-determined –Single "best" solution, finite prediction error Underdetermined –Infinite solutions, zero prediction error Mixed-determined –Many solutions, finite prediction error

TransCom Inversion Intercomparison Discretize world into 11 land regions (by vegetation type) and 11 ocean regions (by circulation features) Release tracer with unit flux from each region during each month into a set of 16 different transport models Produce timeseries of tracer concentrations at each observing station for 3 simulated years

Synthesis Inversion Decompose total emissions into M “basis functions” Use atmospheric transport model to generate G –Fill by columns using forward model, or –Fill by rows using backward (adjoint) model Observe d at N locations Invert G to find m datatransport fluxes d 1 = G 11 m 1 + G 12 m 2 + … + G 1N m N CO 2 sampled at location 1Strength of emissions of type 2 partial derivative of CO 2 at location 1 with respect to emissions of type 2

Rubber Bands Inversion seeks a compromise between detailed reproduction of the data and fidelity to what we think we know about fluxes The elasticity of these two “rubber bands” is adjustable Prior estimates of regional fluxes Observational Data Solution: Fluxes, Concentrations

MODEL a priori emission a priori emission uncertainty concentration data concentration data uncertainty emission estimate emission estimate uncertainty Bayesian Inversion Technique

MODEL a priori emission a priori emission uncertainty reduction concentration data concentration data uncertainty emission estimate emission estimate uncertainty Bayesian Inversion Technique

Our problem is ill-conditioned. Apply prior constraints and minimize a more generalized cost function: Bayesian Inversion Formalism Solution is given by Inferred flux Prior Guess Data Uncertainty Flux Uncertainty observations data constraintprior constraint

Uncertainty in Flux Estimates A posteriori estimate of uncertainty in the estimated fluxes Depends on transport (G) and a priori uncertainties in fluxes (C m ) and data (C d ) Does not depend on the observations per se!

Covariance Matrices Inverse of a diagonal matrix is obtained by taking reciprocal of diagonal elements How do we set these? (It’s an art!)

Accounting for “Error” Sampling, contamination, analytical accuracy (small) Representativeness error (large in some areas, small in others) Model-data mismatch (large and variable) Transport simulation error (large for specific cases, smaller for “climatological” transport) All of these require a “looser” fit to the data

Regional Problem is Harder! Higher density of observations over central US or Europe allows more detailed analysis High-resolution transport modeling typically requires specifying inflow! How to treat tracer variations on lateral boundaries? Can “nest” models of various scales, but how to treat errors? The smaller the region, the less trace gas variations are determined inside it!

Ingredients for Inversions Observations! Choices of domain, spatial & temporal structure of solution to seek Transport model to specify winds, turbulence, cloud motions Source-receptor matrix linking fluxes to observable concentrations An optimization scheme Error covariance statistics for expected model- data mismatch Numerical matrix algebra