Biases in land surface models

Yingping Wang

CSIRO Marine and Atmospheric Research

Model residuals

• Differences between predictions and data, and result from errors

– Data: representation and precision

– Model formulation

– State (time varying)

– Parameters (time independent)

Errors in state space

• Total errors:

• Errors due to model structure:

• Errors due to incorrect state and parameters values

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How big are those errors?

Abramowitz et al. 2006Averaging window size (day)

Parameter error

Systematic error

Random error

Some errors can not be accounted for by parameter tuning

Use the improved CBM (CABLE)

Eight parameters varied within their reasonable ranges

Grey region shows PDF of ensemble predictions

From Abramowitz et al. 2008

Model errors

If systematic model errors are not modeled

• the SE of optimized model parameters can are too optimistic;

• Estimates of model parameters can be biased;

Systematic model errors

• Inaccurate inputs

• Missing processes

• Low sensitivities

• Incorrect formulations

Incorrect inputs of LW to the model

Why does CABLE predict incorrect energy partitioning?

Haverd unpublished data

Observed E(MJ m-2 d-1)

-5 0 5 10 15 20

Obs

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d E

(MJ

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-10

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15CABLECABEL wiith litterRegression line

Observed H (MJ m-2 d-1)

-10 -5 0 5 10 15 20

Obs

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d H

(MJ

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-10

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CABLE:y=0.43+0.74x r2=0.36

CABLE+littery=-0.66+0.91x r2=0.72

CABLE:y=-0.83+1.05x r2=0.61

CABLE+littery=-0.52+0.95x r2=0.73

Modeling variance in the data statistically

Braswell et al. 2005

8 of 11 optimized photosynthesis parameters are well constrained. But the model still failed capturing a significant fraction of seasonal and inter-annual variations in NEE data.

Analyzing errors in frequency domain

From Braswell et al. 2005

Inter-annual

Seasonal

Daily

S

ET/ETm

Katual et al. 2007

Incorrect response to soil water

Explaining the variance in the data

• Any variability that can not be modeled deterministically .. must be .. modeled statistically (Enting 2002)

• Analysis model residuals in both time and frequency domains

Analyzing model residual in t and f domains

Time domain (t) Frequency domain (f)

Residual plots

SOFM

Wavelet analysis

Intuitive

Clues for when and why models failed

Separation of what the models should and should not explain at different time scales

Difficult to resolve some complex interactions at different time scales

Little information about why the models fail

Conclusions

• How many models should be calibrated? One or many? – Many.

• How do we address the initial condition problem? – Treat initial state values as model parameters.

• How do we detect and address model flaws? – SOFM, – State-space formulation– Analysis model residuals in both t and f domain, – data-model fusion as a sensitivity analysis tool – etc.

Deficiencies in land surface models

• Inadequate representation of canopy and soil

• Inaccurate formulations

Deficiencies in land surface models

• Overestimate heat fluxes, and because of– insulation by litter– canopy heat storage

• Incorrect response to soil water, and because of – incorrect model parameters– model structure

The Kalman-gain (g)

• Kalman gain (g) cov(x)/cov(z);

• Larger errors in data give smaller g;

• Lower sensitivity to z to x gives smaller gain;

• We need to separate model structural errors and from state and parameter errors

• Errors must be accounted by statistical models

Fast vs slow process

• Variance in EC data is dominated by the variation at diurnal and seasonal scales. Fitting LSM to EC data then gives better constraints on parameters for fast process than those for slow processes

Analyzing model residuals in frequency domain: the Bayesian approach

A consistent framework for studying model residuals

Fast biophysical processes

Canopy conductancephotosynthesis, leaf respiration

Carbon transfer,Soil temp. & moistureavailibity

Slow biogeographicalprocesses

Vegetation dynamics & disturbance

Land-use and land-cover change

Vegetation change

Autotrophic andHeterotrophic

respiration

Allocation

Intermediate timescalebiogeochemical processes

Phenology

Turnoover

Nutrient cycle

Solution of SEB;canopy and ground

temperatures and fluxes

Soil heat and moisture

Surface water balance

Update LAI,Photosyn-thesis capacity

Physical-chemical forcingT,u,Pr,q, Rs, Rl,

CO2

Radiationwater, heat, & CO2 fluxes

day years

Biogeo-chemicalforcing

Time scale of biosphere-atmosphere interactions

Atmosphere

hour

Limitations of current land surface models

• What is PFT?

• Do all plants in the same PFT truly have same parameter values?

• Mismatch between model and data, soil T and for example.

• Spatial heterogeneity in canopy and soil

• Litter layer

Why EC data cannot constrain soil BGC processes?

• Sensitivity of turnover rate of slow pools to C fluxes is low;

• Soil C has a spectrum of turnover rate as substrate quality changes with time;

• Soil C has long memory (disturbance history, weather history etc)

• The parameters you obtained have limited applicability in predicting response to future climate change

State and parameter estimation

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What eddy flux data can constrain effectively?

• Sensitivity of Biogeochemical processes (particularly slow pools)

• Plant phenology

• Vegetation dynamics

Schimel’s Figure