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Biases in land surface models
Yingping Wang
CSIRO Marine and Atmospheric Research
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Model residuals
• Differences between predictions and data, and result from errors
– Data: representation and precision
– Model formulation
– State (time varying)
– Parameters (time independent)
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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
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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
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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;
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Systematic model errors
• Inaccurate inputs
• Missing processes
• Low sensitivities
• Incorrect formulations
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Incorrect inputs of LW to the model
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Why does CABLE predict incorrect energy partitioning?
Haverd unpublished data
Observed E(MJ m-2 d-1)
-5 0 5 10 15 20
Obs
erv
ed
-mo
delle
d E
(MJ
m-2
d-1
)
-15
-10
-5
0
5
10
15CABLECABEL wiith litterRegression line
Observed H (MJ m-2 d-1)
-10 -5 0 5 10 15 20
Obs
erv
ed
-mo
delle
d H
(MJ
m-2
d-1
)
-15
-10
-5
0
5
10
15
-5 0 5 10 15 20 25
Mo
del
led
E
(M
J m
-2 d
-1)
-5
0
5
10
15
20
25
-10 -5 0 5 10 15 20 25
Mo
del
led
H (
MJ
m-2
d-1
)
-10
-5
0
5
10
15
20
25
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
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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.
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Analyzing errors in frequency domain
From Braswell et al. 2005
Inter-annual
Seasonal
Daily
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S
ET/ETm
Katual et al. 2007
Incorrect response to soil water
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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
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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
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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.
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Deficiencies in land surface models
• Inadequate representation of canopy and soil
• Inaccurate formulations
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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
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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
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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
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Analyzing model residuals in frequency domain: the Bayesian approach
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A consistent framework for studying model residuals
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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
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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
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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
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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
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Schimel’s Figure