slide1
Download
Skip this Video
Download Presentation
Michael Raupach, Cathy Trudinger, Peter Briggs, Luigi Renzullo, Damian Barrett, Peter Rayner

Loading in 2 Seconds...

play fullscreen
1 / 29

Michael Raupach, Cathy Trudinger, Peter Briggs, Luigi Renzullo, Damian Barrett, Peter Rayner - PowerPoint PPT Presentation


  • 147 Views
  • Uploaded on

Data assimilation in terrestrial biosphere models: exploiting mutual constraints among the carbon, water and energy cycles. Michael Raupach, Cathy Trudinger, Peter Briggs, Luigi Renzullo, Damian Barrett, Peter Rayner

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Michael Raupach, Cathy Trudinger, Peter Briggs, Luigi Renzullo, Damian Barrett, Peter Rayner' - zihna


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Data assimilation in terrestrial biosphere models: exploiting mutual constraints among the carbon, water and energy cycles

Michael Raupach, Cathy Trudinger, Peter Briggs, Luigi Renzullo, Damian Barrett, Peter Rayner

Thanks: colleagues in the Australian Water Availability Project (CSIRO, BRS, BoM); participants in OptIC project

CarbonFusion (Edinburgh, 9-11 May 2006)

outline
Outline
  • Data assimilation challenges for carbon and water
  • Multiple-constraint data assimilation
  • Using water fluxes (especially streamflow) to constrain carbon fluxes
  • Observation models for streamflow (with more general thoughts on scale)
  • Example: Murrumbidgee basin
  • Model-data fusion: comparison of two methods
carbon da
Carbon DA
  • Challenges for carbon cycle science (including data assimilation)
    • Science: finding state, evolution, vulnerabilities in C cycle and CCH system
    • Policy: supporting role: IPCC-SBSTA-UNFCCC, national policy
    • Management: trend detection, source attribution ("natural", anthropogenic)
  • Terrestrial carbon balance
  • Required characteristics of an observation system
    • pools (Ci(t)), fluxes (GPP, NPP, NBP, respiration, disturbance)
    • Long time scales (to detect trends)
    • Fine space scales (to resolve management and attribute sources)
    • Good process resolution (to detect vulnerabilities, eg respiration, nutrients)
    • Demonstrated consistency from plot to globe
water da
Water DA
  • Challenges for hydrology (including water data assimilation)
    • Science: state, evolution, vulnerabilities in water as a limiting resource
    • Policy: supporting role at national and regional level
    • Management: providing tools (forecasting, allocation, trading)
  • Terrestrial water balance (without snow)
  • Required characteristics of an observation system
    • W(t) and fluxes for soil water balance (also rivers, groundwater, reservoirs)
    • Accurately enough to support regulation, trading, warning (flood, drought)
    • With forecast ability from days to seasons
coupled terrestrial cycles of energy water carbon and nutrients
Coupled terrestrial cycles of energy, water, carbon and nutrients

Water flow

C flow

N flow

P flow

Energy

ATMOSPHERE

Photosynthesis

Soil evap

Rain

WaterCycle

N fixation,N deposition,N volatilisation

C Cycle

Transpiration

PLANTLeaves, Wood, Roots

Disturbance

Respiration

Fertiliser inputs

N,P Cycles

ORGANIC MATTER

Litter: Leafy, Woody

Soil: Active (microbial)

Slow (humic)

Passive (inert)

SOIL

Soil water

Mineral N, P

Fluvial, aeolian transport

Runoff

Leaching

confluences of carbon water energy nutrient cycles
Confluences of carbon, water, energy, nutrient cycles
  • Carbon and water:
    • (Photosynthesis, transpiration) involve diffusion of (CO2, H2O) through stomata
    • => (leaf scale): (CO2 flux) / (water flux) = (CsCi) / (leaf surface deficit)
    • => (canopy scale): Transpiration of water ~ GPP ~ NPP
  • Carbon and energy:
    • Quantum flux of photosynthetically active radiation (PAR) regulates photosynthesis (provided water and nutrients are abundant)
  • Water and energy:
    • Evaporation is controlled by (energy, water) supply in (moist, dry) conditions
    • Priestley and Taylor (1972): evaporation = 1.26 [available energy][Conditions: moist surface, quasi-equilibrium boundary layer]
  • Carbon and nutrients:
    • P:N:C ratios in biomass (and soil organic matter pools) are tightly constrained
    • 500 PgC of increased biomass requires ~ (5 to 15) PgN
    • Estimated available N (2000 to 2100) ~ (1 to 6) PgN (Hungate et al 2003)
the carbon water linkage
The carbon-water linkage
  • Terrestrial water balance (without snow):
  • Residence time of water in soil column ~ (10 to 100) days, so over averaging times much longer than this, dW/dt is small compared with fluxes
  • In an "unimpaired" catchment with constant water store: [streamflow] = [runoff] + [drainage]
  • Chain of constraints:
    • Streamflow (constrains (total) evaporation
    • Total evaporation (= transpiration + interception loss + soil evaporation) constrains transpiration
    • Transpiration constrains GPP and NPP
    • GPP, NPP control the rest of the terrestrial carbon cycle
streamflow observation model
Streamflow: observation model
  • Basic principle
    • In an unimpaired catchment,
      • d[water store]/dt = [runoff] + [drainage]  [streamflow]
    • If d[water store]/dt can be neglected (small store or long averaging time):
      • [streamflow] = [runoff] + [drainage]
    • [water store] includes groundwater within catchment, rivers, ponds ...
  • Requirements for unimpaired catchment
    • All runoff and drainage finds its way to the river (no farm dams)
    • No other water fluxes from the river (eg irrigation, urban water use)
    • No major dams (otherwise d[store]/dt dominates streamflow)
    • Groundwater does not leak horizontally through catchment boundaries
  • Snow
    • needs a separate balance
streamflow and other data issues
Streamflow (and other) data issues
  • Requirements on catchments
    • Unimpaired, gauged at outlet
    • Catchment boundary must be known
  • Requirements on measurement record
    • Well maintained gauge
    • The water agency must be prepared to give you the data
  • Requirements on other data
    • Need spatial distribution of met forcing (precip, radiation, temperature, humidity)
    • Need spatial distribution of soil properties (depth, water holding capacity ...)
    • Catchments are hilly:
      • Downside: everything varies
      • Upside: exploit covariation of met and soil properties with elevation (eg: d(Precipitation)/d(elevation) ~ 1 to 2 mm/y per metre
      • ANUSplin package (Mike Hutchinson, ANU)
modelling at multiple scales
Modelling at multiple scales

Raupach, Barrett, Briggs, Kirby (2006)

  • We often have to predict large-scale behaviour from given small-scale laws:

Small-scale dynamics Large-scale dynamics

  • Four generic ways of approaching this problem:

1. Full solution: Forget about F, integrate dx/dt = f(x,u) directly

2. Bulk model: Forget about f, find F directly from data or theory

3. Upscaling: Find a probabilistic relationship between small scales (f) and large scales (F), for example by:

4. Stochastic-dynamic modelling: Solve a stochastic differential equation for PDF of x (small scale), and thence find large-scale F:

steady state water balance bulk approach
Steady-state water balance: bulk approach

Fu (1981)Zhang et al (2004)

  • Steady state water balance:
  • Dependent variables: E = total evaporation, R = runoff
  • Independent variables: P = precipitation, EP = potential evaporation
  • Similarity assumptions (Fu 1981, Zhang et al 2004)
  • Solution finds E and R (with parameter a)(Fu 1981, Zhang et al 2004)
steady water balance bulk approach
Steady water balance: bulk approach

dry wet

wet dry

  • Normalise with potential evap EP:plot E/EP against P/EP
  • Normalise with precipitation P:plot E/EP against EP/P

E/EP

a=2,3,4,5

P/EP

a=2,3,4,5

Fu (1981)Zhang et al (2004)

EP/P

stochastic dynamic modelling
Stochastic-dynamic modelling
  • Forcing (u) on small-scale process (x(t)) is often random, and dynamics (dx/dt = f(x,u)) often has strong nonlinearities such as thresholds
  • Examples: soil moisture, dust uplift, fire, many other BGC processes
  • If we can find rx(x), the PDF of x, we can find any average (large-scale) property
stochastic dynamic modelling1
Stochastic-dynamic modelling
  • Forcing (u) on small-scale process (x(t)) is often random, and dynamics (dx/dt = f(x,u)) often has strong nonlinearities such as thresholds
  • Examples: soil moisture, dust uplift, fire, many other BGC processes
  • If we can find rx(x), the PDF of x, we can find any average (large-scale) property
steady state water balance stochastic dynamic approach
Steady-state water balance: stochastic-dynamic approach

rw(w)

<w>

increasing precipitation event frequency

increasing precipitation event frequency

dry wet

w = relative soil water

P/EP

Rodriguez-Iturbe et al (1999)Porporato et al (2004)

  • Dynamic water balance for a single water store w(t):
  • Then:
    • Let precipitation p(t) be a random forcing variable with known statistical properties (Poisson process in time, exponential distribution for p in a storm)
    • Find and solve the stochastic Liouville equation for rw(w), the PDF of w
    • Thence find time-averages: <w>, E = <e(w)>, R = <r(w)>
water and carbon balances dynamic model
Water and carbon balances: dynamic model
  • Dynamic model is of general form dx/dt = f(x, u, p)
  • All fluxes (fi) are functions fi(state vector, met forcing, params)
  • Governing equations for state vector x = (W, Ci):
  • Soil water W:
  • Carbon pools Ci:
  • Simple (and conventional) phenomenological equations specify all f(x, u, p)
  • Carbon allocation (ai) specified by an analytic solution to optimisation of NPP
slide19

J

F

M

A

M

J

J

A

S

O

N

D

81

82

83

84

Murrumbidgee Relative Soil Moisture (0 to 1)

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

00

01

02

03

04

05

slide20

J

F

M

A

M

J

J

A

S

O

N

D

81

82

83

84

Murrumbidgee

Total Evaporation

(mm d-1)

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

00

01

02

03

04

05

predicted and observed discharge 11 unimpaired catchments in murrumbidgee basin
Predicted and observed discharge 11 unimpaired catchments in Murrumbidgee basin
  • 25-year mean: Jan 1981 to December 2005Prior model parameters set roughly for Adelong, no spatial variation

Goobarragandra:410057

Adelong:410061

predicted and observed discharge 11 unimpaired catchments in murrumbidgee basin1
Predicted and observed discharge 11 unimpaired catchments in Murrumbidgee basin
  • 25-year time series: Jan 1981 to December 2005
model data fusion
Model-data fusion

Prior information

Observations

Measurements

Prior information about target variables

Cost function

Model prediction of observations

Target variables

Covariance matrix of prior information error

Covariance matrix of observation error

  • Basic components
    • Model: containing adjustable "target variables" (y)
    • Data: observations (z) and/or prior constraints on the model
    • Cost function: to quantify the model-data mismatch z – h(y)
    • Search strategy: to minimise cost function and find "best" target variables
  • Quadratic cost function:
kalman filter
Kalman Filter
  • Estimates the time-evolving hidden state of a system governed by known but noisy dynamical laws, using data with a known but noisy relationship with the state.
  • Dynamic model:
    • Evolves hidden system state (x) from one step to the next
    • Dynamics depend also on forcing (u) and parameters (p)
  • Observation model:
    • Relates observations (z) to state (x)
  • Target variables (y): might be any of state (x), parameters (p) or forcings (u)
  • Kalman filter steps through time, using prediction followed by analysis
    • Prediction: obtain prior estimates at step n from posterior estimates at step n-1
    • Analysis: Correct prior estimates, using model-data mismatch z – h(y)
parameter estimation with the kalman filter
Parameter estimation with the Kalman Filter
  • Dynamic model includes parameters p = pk (k=1,…K) which may be poorly known:
  • Include parameters in the state vector, to produce an "augmented state vector"
  • The dynamic model for the augmented state vector is
parameter estimation from runoff data
Parameter estimation from runoff data
  • Compare 2 estimation methods
    • EnKF with augmented state vector (sequential: estimates of p and Cov(p) are functions of time)
    • Levenberg-Marquardt (PEST)(non-sequntial: yields just one estimate of p and Cov(p))
  • Model runoff predictions with parameter estimates from EnKF
final thoughts
Final thoughts
  • Applications of "Multiple constraints"
    • Data sense: atmospheric CO2, remote sensing, flux towers, C inventories ...
    • Process sense: measuring one cycle (eg water) to learn about another (eg C)
  • Requirement for multiple constraints (in process sense)
    • "Confluence of cycles"
      • Fluxes: cycles share a process pathway controlled by similar parameters
      • Pools: cycles have constrained ratios among pools (eg C:N:P)
  • Streamflow as a constraint on water cycle, thence carbon cycle
    • Strength: Independent constraint on water-carbon (and energy-water) cycles (strongest in temperate environments with P/EP ~ 1)
    • Limitation 1: obs model = full hydrological model (sometimes can be simplified)
    • Limitation 2: streamflow data (availability, quality, access)
  • Model-data fusion
    • Several methods work (focus on EnKF in parameter estimation mode)
    • OptIC (Optimisation InterComparison) project: see poster by Trudinger et al.
ad