Crop Ensemble Data Assimilation

J Gómez-Dans & Hongyuan Ma (UCL & NCEO)

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Objectives

1. Principle of the WOFOST model
2. Introduce ensemble crop DA method
3. Illustrate the crop model
4. Demonstrate its use on maize in Northern Ghana

The WOFOST crop model

1. Phenology​
2. Light interception​
3. Assimilation (Photosynthesis)​
4. Respiration​
5. Assimilate partitioning​
6. Leaf area dynamics (growth and decay)​
7. Evapotranspiration​
8. Soil water balance and drought response​

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⇒Crop models simulate how crops develop as a function of meteo, soils and crop characteristics

WOFOST parameterisation

• Use default tropical maize (Van Heemst 1988, Srivastava et al 2016)
• Adapt a few parameters to account for
• Low fertility soils
• Low nutrients
• We can only observe LAI & want yield
• Leaf life span (SPAN) & initial crop weight (TDWI) strong controls on LAI
• Max Leaf Assim rate: used to model stresses
• Also need to define sowing date
• Model used in water limited mode (WLM)

Uncertainty in models

• Models are not perfect
• (they are still useful! 😃)
• Models are simplifications of reality
• Incomplete understanding of processes
• Drivers lack adequate spatial/temporal scale
• Inherent variability of parameters (e.g. variation in genetics)
• Sensible to treat model output as uncertain
• Observations may reduce model uncertainty

⇒We cannot expect the crop model to perfectly predict every field. But to give us a rough idea

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Uncertainty

Huang et al (2019)

Martre et al (2019)

Models & observations: towards a happy marriage?

• Models produce uncertain predictions
• … use uncertain observations to improve model predictions
• Weight predictions if consistent with observations
• Probability is the tool to mix obs & model
• Bayesian approach: Combine
• Prior pdf (e.g, uncertain model)
• Likelihood (uncertainty observations)
• to update posterior pdf

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Update an educated guess with some new evidence. Robust statistical methods are available for this

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Variational methods (4DVAR) & Ensembles

• Approximation of Bayes posterior pdf calculations:
• Assume errors Gaussian
• Convert problem into cost function minimisation:
• Tweak model parameters to fit observations
• Also constrained by prior!
• “Tweaking”: gradient descent minimisation
• Efficient implementation using ensembles

Ensemble crop DA method

The prior model ensemble. Different realisations of the model with different parameters, meteo drivers, etc.

Each ensemble member has a parameter set associated to it.

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The observations of LAI over time

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Match the ensemble members with the observations (considering uncertainties).

Can calculate parameter pdf by weighting ensemble parameters

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Inferring parameters will also reduce uncertainty in yield predictions and other model outputs

The crop model ensemble

ERA5 meteo data drivers over study region

• ERA5 Land dataset
• Spatial resolution: ~10km
• Hourly data aggregated to daily
• A few grid cells cover area
• very similar meteo drivers
• Interfield crop variability
• Local soils
• Farm management practices
• Local meteo effects

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Effect of parameters

• TDWI: Initial build up of LAI, max LAI
• SPAN: length of LAI arc, max LAI
• AMAX: max LAI & yield
• SDOY: shift in time

Localise model so LAI is an effective constraint for yield

Try it out!

• You can run the WOFOST crop model interactively
• Change the parameters and see how the model predictions match up with
• Observations of LAI
• Observations of crop yield
• You can explore all the other outputs of WOFOST too!

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WOFOST parameter visualisation in yield/LAI space

WOFOST parameter visualisation in yield/LAI space

Application to maize in Ghana

The prior ensemble: LAI

Ensemble

Observations

The prior ensemble: Yield

Ensemble confronted with observations for one field

Yield prediction

• Selected ensemble members ⇒ associated weight
• Uncertainty of yield distribution ⇒ reduced
• Large update of the mean of prior yield distribution
• Assumption: the model encompasses LAI⇒yield relationship
• How unique over Ghana?
• How unique over different years?
• Limited validation!
• Model parameters need to be adapted to field data variations:
• Empirical linear yield correction
• Better model parameterisation

Linear yield transformation

TRAINING

VALIDATION

Parameter interpretation

• A posteriori parameters: what happened to the crop?
• ⇒low AMAX_SCALAR⇒Stress
• ⇒TDWI related to yield
• Lower yield for late-planted crops
• Parameter correlations complicate picture
• Can also look at other model outputs
• Canopy TRAnspiration (⇒ Photosynthesis)
• Above ground biomass (AGB)

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Biomass & canopy transpiration

Pixel-scale inversion: Yield & Yield Uncertainty

30 m

Pixel level results

• Up to now, only field-averaged results shown
• Planet data nominal spatial resolution: 3.7m
• This gives opportunity to look at within-field variability
• Each pixel is processed independently to give:
• Yield @ 4m resolution
• Parameters @4m resolution
• Uncertainty estimate

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Pixel inversion: Sowing date

Pixel inversion: Initial Seed Mass

Pixel inversion: Leaf lifespan

Pixel inversion: Assimilation scalar

Final remarks

• Pragmatic DA method for large areas
• Uses LAI as linkage between crop model & observations
• Importance of crop model localisation:
• Crop model parameter selection & calibration
• Questions on generality (need other locations, years, …)
• Update on crop model parameters due to LAI
• LAI trajectories reflect yield within the field
• Need to remove bias in the ensemble
• Possible to improve parameters in ensemble
• We explain crop development via 4 parameters
• Low/high yield spatial distribution very local -> local access to nutrients
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Spares

No linear correction, all fields

Remove outlier fields & apply linear correction

• Remove fields where retrieved LAI inconsistent with field LAI (7 fields)
• Apply empirically-derived linear correction factor
• Per pixel results are worse than field-averaged processing
• Within-field variability not well captured in field measurements?
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