# Presentation: 396423

## AmeriFlux data assimilation and driver domain integration for regional carbon flux estimation

**AmeriFlux data assimilation and driver domain integration for regional carbon flux estimation**

- Lianhong Gu  Wilfre Mac Post III
- Anthony W. King  Thomas Boden
**Oak Ridge National Laboratory**
**Dennis Baldocchi**
**University of California - Berkeley**
**October 22, 2002**
**Boulder, CO**

- AmeriFlux

**Notes:**
I am honored to join you today to share some thoughts about the opportunities we have to address in a meaningful and lasting way both the energy challenges and environmental challenges for the nation and the southeast.

In some respects I have the best portion of the discussion.  While others have addressed the nature and dimension of the problem, I was asked to take a look at the longer term scenario.  Maybe it’s because at heart I’m a researcher, but for me this is the fun part—stepping back and looking at big problems, and then figuring out how to organize our resources and vast portfolio of technologies to solve those problems.

## A Challenge in Carbon Cycle Study

## Objectives

**To introduce the concept of ****data assimilation**** and how to apply it in the analysis of AmeriFlux data**
**To introduce the concept of ****driver domain integration**** and how to use it to estimate carbon exchanges on regional scales**

## What is data assimilation? 

**   ****“*****A quantitative, objective method to infer the state of the earth-atmosphere-ocean system from heterogeneous, irregularly distributed, and temporally inconsistent observational data with differing accuracies*****”**

- (in the context of Geophysics)

*- National research council (*1991*)*

- Full name: Model-based data assimilation

## Basic Elements of Data Assimilation

**Data (any information regarding the system and its behaviors can be useful) **
**Model that describes the system dynamics as accurately as possible**
**An assimilation methodology that integrates the measurements and model together**
**	****- Variational: model initial states are obtained by minimizing the difference between the observation and prediction over a period of time (using, for example, adjoint method)**
**	****- Sequential: model states are immediately updated whenever measurements are encountered (using, for example, Kalman filter theory)**

## Why Data Assimilation?

**Objective estimations of initial conditions and system parameters for the solution of the equations that govern the system dynamics**
**Reduction of the impacts of weaknesses in measurements and models on the prediction of system dynamics **
**Provision of spatially and temporally uniform and dynamically consistent high-quality datasets**
**Example: Dramatic improvement in the accuracy of numerical weather forecasts**

## Why Assimilating Eddy Covariance Flux Data?

**Flux measurements are gappy and have uncertainties (for example, nighttime fluxes, time registry, instrument shifts and drifts)**
**Process-based SVAT models have been developed but are hardly used beyond validation**
**SVAT models need not only environmental driving variables but also ****ecosystem state variables**** and ****relevant physiological parameters**** in order to do predictions. The latter two are often not measured.**
**Spatially and temporally consistent high-quality datasets are needed for spatial and temporal integration and for use in global change studies (such as atmospheric CO2 inversion)**
**Data assimilation is a critical component of Earth system modeling**

## Any initial value problem in terrestrial ecosystem science? YES!

## Any initial value problem in terrestrial ecosystem science? YES!

## Any initial value problem in terrestrial ecosystem science? YES!

## Evolution of Ecosystem State

## Variational Flux Data Assimilation

## A variational framework for assimilating flux and other (proxy) measurements at eddy covariance tower sites

- Soil-vegetation-atmosphere transfer model (biophysics and biogeochemistry, composed of a number of equations)
* *
**	****	****	****M**(**X, P, U, F) = 0****	****	****                                                           **(1)
**X**: Ecosystem state and parameter vector: LAI, Vcmax, Jmax, soil carbon stock, soil nitrogen stock, parameters in
-      biochemical photosynthetic models, parameters describing soil chemical and physical properties etc., often not
-      available
**P**: Ecosystem proxy state vector: Measurements of temperature, VPD, CO2 concentration profiles inside the canopy, soil
-     temperature and water content, etc, if available, can be very useful constraints in data assimilation
**F**: Ecosystem-atmosphere mass and energy exchange vector: Above-canopy fluxes of CO2, water vapor, sensible heat,
-      and momentum, reflected shortwave radiation, outgoing longwave radiation, any understory flux measurements, etc.
**U**: Ecosystem forcing variable vector: Temperature, humidity, incoming solar radiation, incoming shortwave radiation,
-      wind speed, etc
- Cost function: *J*
*	**	**	**J(***X**) = (**P** – **P**m)T**B**-1(**P** – **P**m) + (**F **– **F**m)T**(O+S)**-1(**F** – **F**m) 		           (2)
**B**: modeling error covariance matrix for proxy state variables
**S**: modeling error covariance matrix for mass and energy exchanges
**O**: observation error covariance matrix

## Slide 14

## Difficulties in Spatial Integration of Terrestrial Ecosystems

- Unlike geophysical fluid systems (atmosphere and ocean), no evolutionary equations are available for linking states of geographically distributed terrestrial ecosystems
- States of spatially distributed terrestrial ecosystems are often discontinuous and very diverse
- Ecological theories about spatial patterns tend to be qualitative, rather than quantitative (*but can be useful in guiding spatial integration*)
- Our ability to sample flux spatial distribution is limited
- Implication: Direct spatial integration is unlikely to be successful

## Global eddy covariance tower site distribution in the spatial domain

## Global eddy covariance tower site distribution in the P-T domain

## Slide 18

## Slide 19

## Philosophy

- Driver domain integration for regional flux estimation

***The difference or similarity between two ecosystems is not determined by the geographical distance between them, but by the distance in the driver space formed by those environmental variables that determine where the two ecosystems are located and how they function.***

## Integration Domain Transform

## Simple Demonstration - An Imagined Flux Field

## To get the total flux over the domain:

- (1) _Direct spatial integration_

*n*: the number of flux towers

- (2) _Driver domain integration_

*m*: the number of intervals in the driver domain (here PAR only)

- Determined from environmental sampling

## Slide 24

## x

- Environmental Gradient Sampling      (for the Jacobian)

*x*

*y*

- -100

- 100

- 100

## Slide 26

## Slide 27

## A scheme for regional carbon estimation

## Message

**Data assimilation**** is necessary for AmeriFlux to achieve its scientific objectives and actively contribute to Earth system modeling**
**The driver domain integration method ****may be used to provide bottom-up estimates of regional carbon exchanges**