Data assimilation in Marko Scholze

Strictly speaking, there are so far no DA activities in QUEST, but CCDAS (as part of core team activities) CPDAS and C4DAS (in the planning stage)

A Carbon Cycle Data Assimilation System (CCDAS) 2 FastOpt 3 1 Wolfgang Knorr and Marko Scholze in collaboration with Peter Rayner 1, Heinrich Widmann 2, Thomas Kaminski 3 & Ralf Giering 3

Carbon Cycle Data Assimilation System (CCDAS) current form BETHY+TM2 only Photosynthesis, Energy&Carbon Balance +Adjoint and Hessian code Globalview CO 2 + Uncert. Optimised Parameters + Uncert. Diagnostics + Uncert. Assimilation Step 2 (calibration) + Diagnostic Step Background CO 2 fluxes: ocean: Takahashi et al. (1999), LeQuere et al. (2000) emissions: Marland et al. (2001), Andres et al. (1996) land use: Houghton et al. (1990) veg. Index (AVHRR) + Uncert. full BETHY Phenology Hydrology Assimilation Step1 Parameter Priors + Uncert.

CCDAS calibration step Terrestrial biosphere model BETHY (Knorr 97) delivers CO2 fluxes to atmosphere Uncertainty in process parameters from laboratory measurements Global atmospheric network provides additional constraint covariance of uncertainty in measurements + model covariance of uncertainty in priors for parameters priors for parameters observed concentrations Terrestrial biosphere model BETHY (Knorr 97) delivers CO2 fluxes to atmosphere Uncertainty in process parameters from laboratory measurements Global atmospheric network provides additional constraint

Gradient of J(p) provides search directions for minimisation. Second Derivative (Hessian) of J(p) yields curvature of J, provides estimated uncertainty in p opt Figure taken from Tarantola '87 J(p) Minimisation and Parameter-Uncertainties Space of p (model parameters)

Optimisation (BFGS+ adjoint gradient)

Posterior uncertainties on parameters examples: Use inverse Hessian of objective function to approximate posterior uncertainties Relative reduction of uncertainties Observations resolve about directions in parameter space

CCDAS diagnostic step Global fluxes and their uncertainties Examples for diagnostics: Long term mean fluxes to atmosphere (gC/m2/year) and uncertainties Regional means

Extension of concept 1. More processes/components Have tested a version extended by an extremely simplified form of an ocean model: flux(x,t) =  coefficient(i) * pattern(i,x,t) Optimising coefficients for biosphere patterns would allow the optimisation to compensate for errors (e.g. missing processes) in biosphere model (weak constraint 4DVar, see,e.g., Zupanski (1993)) But it is always preferable to include a process model, e.g for fire, marine biogeochemistry Can also extend to weak constraint formulation for state of biosphere model: include state as unknown with prior uncertainty estimated from model error

J(p) = ½ (p-p 0 ) T C p -1 (p-p 0 ) + ½ (c mod (p)- c obs ) T C c -1 (c mod (p)- c obs ) + ½ (f mod (p)- f obs ) T C f -1 (f mod (p)- f obs ) + ½ (I mod (p)- I obs ) T C I -1 (I mod (p)- I obs ) + ½ (R mod (p)- R obs ) T C R -1 (R mod (p)- R obs ) + etc... Extension of concept 2. Adding more observations Flux Data Can add further constraints on any quantity that can be extracted from the model (possibly after extensions/modifications of model) Covariance matrices are crucial: Determine relative weights! Uses Gaussian assumption; can also use logarithm of quantity (lognormal distribution),... Inventories Atmospheric Isotope Ratios Atmospheric Concentrations (could also be column integrated)

Earth-System Predictions to build an adequate Earth System Model that is computationally efficient  QUEST’s Earth System Modelling Strategy to develop a tool that allows the assimilation of observations of various kinds that relate to the various Earth System components, such as climate variables, atmospheric tracers, vegetation, ice extent, etc.  CPDAS & C4DAS

Climate Prediction Data Assimilation System (CPDAS): Assimilate climate variables of the past 100 years to constrain predictions of the next 100 years, including error bars. Coupled Climate C-Cycle Data Assimilation System (C4DAS): Assimilate carbon cycle observations of the past 20 (flask network) and 100 years (ice core data), to constrain coupled climate-carbon cycle predictions of the next 100 years, including error bars. Step-wise approach, building on and enhancing existing activities such as CCDAS, C4MIP, QUEST-ESM (FAMOUS), GENIEfy, QUMP and possibly Paleo-QUMP. Using the adjoint (and Hessian, relying on automatic differentiation techniques) which allows – for the first time – to optimize parameters comprehensively in a climate or earth system model before making climate predictions. Scoping study to start next month (pot. users meeting).

CCDAS methodological aspects remarks: –CCDAS tests a given combination of observational data plus model formulation with uncertain parameters –CCDAS delivers optimal parameters, diagnostics/prognostics, and their a posteriori uncertainties –all derivative code (adjoint, Hessian, Jacobian) generated automatically from model code by compiler tool TAF: quick updates of CCDAS after change of model formulation –derivative code is highly efficient –CCDAS posterior flux field consistent with trajectory of process model rather than linear combination of prescribed flux patterns (as transport inversion) –CCDAS includes a prognostic mode (unlike transport inversion) some of the difficulties/problems: –Prognostic uncertainty (error bars) only reflect parameter uncertainty What about uncertainty in model formulation, driving fields…? –Uncertainty propagation only for means and covariances (specific PDFs), and only with a linearised model –Result depends on a priori information on parameters –Result depends on a single model –Two step assimilation procedure sub optimal –lots of other technical issues (bounds on parameters, driving data, Eigenvalues of Hessian...)

BETHY (Biosphere Energy-Transfer-Hydrology Scheme) GPP: C3 photosynthesis – Farquhar et al. (1980) C4 photosynthesis – Collatz et al. (1992) stomata – Knorr (1997) Plant respiration: maintenance resp. = f(N leaf, T) – Farquhar, Ryan (1991) growth resp. ~ NPP – Ryan (1991) Soil respiration: fast/slow pool resp., temperature (Q 10 formulation) and soil moisture dependant Carbon balance: average NPP = b average soil resp. (at each grid point)  <1: source  >1: sink  t=1h  t=1day  lat,  lon = 2 deg

Seasonal cycle Barrow Niwot Ridge observed seasonal cycle optimised modeled seasonal cycle

Parameters I 3 PFT specific parameters (J max, J max /V max and b) 18 global parameters 57 parameters in all plus 1 initial value (offset) ParamInitialPredictedPrior unc. (%)Unc. Reduction (%) fautleaf c-cost Q 10 (slow)  (fast)  (TrEv)  (TrDec)  (TmpDec)  (EvCn)  (DecCn)  (C4Gr)  (Crop)

Some values of global fluxes (prior) GPP Growth resp. Maint. resp. NPP Fast soil resp. Slow soil resp. NEP Value Gt C/yr

Global Growth Rate Calculated as: observed growth rate optimised modeled growth rate Atmospheric CO 2 growth rate

Including the ocean A 1 GtC/month pulse lasting for three months is used as a basis function for the optimisation Oceans are divided into the 11 TransCom-3 regions That means: 11 regions * 12 months * 21 yr / 3 months = 924 additional parameters Test case:  all 924 parameters have a prior of 0. (assuming that our background ocean flux is correct)  each pulse has an uncertainty of 0.1 GtC/month giving an annual uncertainty of ~2 GtC for the total ocean flux

Including the ocean Seasonality at MLO Global land flux Observations Low-res incl. ocean basis functions Low resolution model High resolution standard model