Topographic-dependent modelling of surface climate for earth system modelling and assessment

Michael Hutchinson, Jennifer Kesteven, Tingbao XuAustralian National University

e-MAST’s objectives

DEVELOP research infrastructure to integrate TERN (and external) data streamsENABLE benchmarking, evaluation, optimization of ecosystem modelsSUPPORT ecosystem science, impact assessment and management

What e-MAST will provide

Top-level drivers and targets (from TERN and elsewhere) for modelsSoftware for benchmarking (based on PALS)Data-assimilation for optimizationTools for interpolation, downscaling, upscaling, hindcasting, forecastingHigh-resolution products: climate, canopy conductance, water use, primary production

Climate data sets (1 km)Tmin Tmax vp Precip pan

evapwet days

solar rad

wind speed

daily1970-2011

✔ ✔ ✔ ✔

monthly 1970-2011

✔ ✔ ✔ ✔ ✔ ✔

monthly mean

✔ ✔ ✔ ✔ ✔ ✔ ✔

High-resolution climate surfaces

Daily Rainfall Data Network

Anomaly-based daily interpolation

Background field can be calibrated on full historical data

Can be extended to sites with modest numbers of records – beyond what is available day by day

Topographic dependence can be (largely) incorporated into the background field parameters

Anomalies from the background field have broader scale spatial patterns, with little or no dependence on topography – supports day by day interpolation from limited numbers of sites

How to do this for daily rainfall?

Censored power of normal distribution

Rainα = μ + σz

α 0.3 – 0.9

z standard normal variable, z ≥ -μ/σ

μ/σ -3.0 to 2.0 P(W) = Φ(μ/σ)

α vs -μ/σ 1976-2005

Power Parameter 1976-2005 Jan, July

Parameterisation

Two parameters – calibrated on a monthly basis:

Mean daily rainfall = f(μ/σ).σ2

(σ ranges from 5 to 6)

P(W) = Φ(μ/σ) (μ/σ ranges from -3.0 to 2.0)

μ/σ 1976-2005 Jan, July

Mean daily rain mm/day 1976-2005 Jan, July

Regression extension of short period records – for 1976-2005

6400 stations with at least 20 years of record

Additional 3200 stations with at least 10 years of record

Without regression RMSE = 20%

With regression RMSE = 10%

Cross validation RMSE of interpolated long period stns = 15%Cross validation MAE of interpolated long period stns = 7% (3172 stations, at least 28 years of record)

Defining the anomalies

For positive rainfall – the z value of the underlying normal distribution - z = (Rainα - μ)/σ

For zero rainfall – invent a latent negative anomaly by placing the normalised value “mid-way” in the zero (dry day) probability region

Interpolation of anomaliesAdaptive thin plate smoothing spline interpolation of anomalies

More knots for positive rainfall, fewer for latent negatives: – up to 5000 for positives (amounts)– 1500 for negatives (occurrence)

Tune the placement and relative weighting of the latent negatives to minimise the RMS of cross validated normalised rainfall values

Placement: 0.25, weighting: 4.0

Monitor cross validation of occurrence structure

Monitor goodness of fit – amounts and occurrence

Statistics for 6 Representative Days

Statistic Cross Validation Residuals of Fit

RMS of normalised values

0.223 0.300

MAE (mm) 1.43 0.940

RMS (mm) 3.62 2.25

MAE of positive rain (mm)

2.9 1.80

Class average of occurrence

82.2% 90.6%

Kappa statistic of occurrence

0.668 0.810

Daily rainfall 5 Jan 1970

Daily rainfall 5 Jan 1970

ANUClimate - Interrogation of Elevation Dependent Climate Surfaces

Monthly Mean Daily Maximum Temperature for 2001-2010

Cairns

N

Low : 19.0

High : 28.7

Temperature (C)

Daily Maximum Temperature over NE Qld on 12/02/1999

Cairns

N

High : 460

Low : 113

Rainfall (mm)

Daily Rainfall over NE Qld on 12/02/1999

Conclusion

Censored square of normal distribution provides a stable parameterisation of the background daily rainfall distribution

Provides stable assessment of residual interpolation statistics

The anomalies, for both positive and zero rainfall, can be effectively interpolated by a TPS with adaptive complexity

Possible to incorporate additional fine scale predictors – radar, cloud data, etc

Cross validation and goodness of fit statistics show modest, but significant, improvements over some existing methods

Further assessment of accuracy, and of the tuning of the adaptive interpolation procedure, is in progress

Conclusion

Censored square of normal distribution provides a stable parameterisation of the background daily rainfall distributionCensored square of normal distribution a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoffCompute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid

Tools

Connect inputs and targets via a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoff

Compute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid

Tools

Connect inputs and targets via a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoff

Compute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid

Tools

Connect inputs and targets via a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoff

Compute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid

Tools

Connect inputs and targets via a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoff

Compute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid

Tools

Connect inputs and targets via a model“Spread” fluxes across the landscape via a modelConnect observed [CO2] and streamflow to modelled CO2 flux and runoff

Compute data-model comparison statisticsDerive re-analysis productsDownscale climate drivers to any pointDownscale climate change scenarios to a grid