1. Topographic-dependent modelling
of surface climate for earth system
modelling and assessment
Michael Hutchinson, Jennifer Kesteven, Tingbao Xu
Australian National University

2. e-MAST’s objectives
DEVELOP research infrastructure to integrate
TERN (and external) data streams
ENABLE benchmarking, evaluation, optimization
of ecosystem models
SUPPORT ecosystem science, impact assessment
and management

3. ANU_Climate - Interrogation of Elevation Dependent Climate Surfaces

4. Climate data sets (1 km)
Tmin Tmax vp Precip pan wet solar wind
evap days rad speed
daily ✔ ✔ ✔ ✔
1970-2011
monthly ✔ ✔ ✔ ✔ ✔ ✔
1970-2011
monthly ✔ ✔ ✔ ✔ ✔ ✔ ✔
mean

5. High-resolution climate surfaces

6. Daily Rainfall Data Network

7. 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?

8. 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)

10. α vs -μ/σ 1976-2005

11. Change in 99% daily rainfall January, July
1946-75 to 1976-2005

12. 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)

13. μ/σ 1976-2005 Jan, July

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

15. 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)

16. Interpolation of anomalies
Adaptive 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

17. Statistics for 6 Representative Days
Statistic Cross Validation Residuals of Fit
RMS of normalised 0.223
values
MAE (mm) 1.43 0.940
RMS (mm) 3.62 2.25
MAE of positive rain 2.9
(mm)
Class average of 82.2% 90.6%
occurrence
Kappa statistic of 0.668 0.810
occurrence

18. Daily rainfall 5 Jan 1970

19. Daily Rainfall over NE Qld on 12/02/1999
Rainfall (mm)
High : 460
Low : 113

20. Daily Maximum Temperature over NE Qld on 12/02/1999
Temperature (C)
High : 28.7
Low : 19.0

21. Conclusion
Censored square of normal distribution provides a stable parameterisation of
the background daily rainfall distribution
Also provides stable statistical assessment of rainfall extremes and of various
interpolation statistics – applications
Not perfect – smoothed interpolation of actual daily extremes – seasonal
aggregations reasonable
Anomaly-based interpolation is being applied to the other daily and monthly
variables
Downscale climate drivers to any point
Downscale climate change scenarios to a grid