Bayesian Hierarchical Modelling: Incorporating spatial information in water resources assessment and accounting

Transcription

1 Bayesian Hierarchical Modelling: Incorporating spatial information in water resources assessment and accounting Grace Chiu & Eric Lehmann (CSIRO Mathematics, Informatics and Statistics) A water information R & D alliance between the Bureau of Meteorology and CSIRO s Water for a Healthy Country Flagship

2 Presentation outline Background National water accounting WIRADA research alliance Model-data fusion Soil moisture data Soil moisture in the Murrumbidgee River Catchment Ground probes vs. remote sensing vs. modelled estimates Data assimilation Bayesian hierarchical model Rationale Model structure definition Results: data blending & evaluation Summary & conclusions

3 Background National water accounting and assessment under WIRADA / AWRA Water Information Research and Development Alliance Alliance between CSIRO and the Bureau of Meteorology (BoM) Monitor status of Australia s water resources + forecasting of availability Australian Water Resources Assessment (AWRA): BoM activity component, system of models, model-data fusion Observational data in AWRA-L: used in model development, (global) parameter estimation, forcing (e.g. precipitation) Additional datasets exist with new/other characteristics Need to reconcile or integrate observed and modelled estimates.

4 Focus of this Research Soil moisture (SM) one of the possible variables of interest in WIRADA / AWRA availability of SM products: ground-based remote sensing case-study: could be replaced with any other variable... Murrumbidgee River Catchment (MRC) km 2, southern NSW, Australia availability of ground probes for benchmark SM measurements (OzNet monitoring network) case-study with aim to up-scale nationally

5 Measuring Soil Moisture 1) In-situ ground probes: OzNet, point-level SM at depth of ~ 0 5cm 2) Remote sensors, e.g. AMSR-E, ASCAT, ASAR, etc.: deterministic retrievals from brightness temperature, SM at depth of ~1 2cm 3) Physics models: e.g. AWRA-L, CABLE, etc.... not considered in our preliminary model... different temporal & spatial resolutions!

6 Data Assimilation How to reconcile/consolidate SM products and assess uncertainty? Data assimilation: via Kalman filter, particle filter, 3D-KF, etc. model-based temporal smoothing typically ignore spatial correlation (no spatial smoothing), or use nonmodel-based estimation of spatial correlation usually require manual alignment of pixels (space) and time intervals

7 Bayesian Hierarchical Modelling How to reconcile/consolidate SM products and assess uncertainty? Proposed approach: statistical spatio-temporal modelling model-based temporal smoothing model-based spatial smoothing model-based spatial alignment model-based imputation for missing data single hierarchical model for unified inference... temporal aspect not considered in current work preliminary model!

8 Proposed Bayesian Hierarchical Model Model-based spatial smoothing: at fixed time t Product q ground probes Product p AMSR-E Covariate x (driver of SM) AWAP (precip.) time 08/01/2007

9 Proposed Bayesian Hierarchical Model Model-based spatial alignment (preliminary model): linking the spatial datasets at different resolutions Product q RESPONSE Product p INFLUENCE State s Aim: benchmark AMSR-E product vs. probes... Covariate x

10 Proposed Bayesian Hierarchical Model Preliminary spatial model for SM (Murrumbidgee Catchment): every quantity is related to each other through a single model ground probes: AMSR-E SM: latent SM: AWAP: spatial patterns: explicit modelling of spatial correlation

11 Proposed Bayesian Hierarchical Model Conditional auto-regression (CAR): a form of 5 th nearestneighbour dependence with exponential decay models spatial dependence beyond one but less than two AMSR-E pixels (so that SM state is representative of AMSR-E pixels) AWAP pixel AMSR-E pixel

12 Proposed Bayesian Hierarchical Model Given model structure, the latent soil moisture (and other variables) is estimated / fitted via MCMC Gibbs sampling: ~ iterations average over last 2500 iterations basic convergence diagnostics runs in ~3.5 4 hours on standard PC (non-optimised code) implementation can be heavily parallelised

13 Spatial Model Fit: 18/01/2007 Model hierarchy (at fixed time): (p,q) s x φ Model fit for OzNet ground probes: q and

14 Spatial Model Fit: 18/01/2007 Model hierarchy (at fixed time): (p,q) s x φ p, estimate of latent SM : influence of AMSR-E, AWAP & OzNet inferring missing AMSR-E pixels : some residual bias apparent (due to influence of precipitation) posterior mean of spatial random effects : spatial autocorrelation clearly visible (motivation for proposed framework) x

15 Spatial Model Fit: 20/01/2007 Latent soil moisture: 95% credible interval (CI): (for white pixels above)... issue with SM<0 in CI due to assumptions of instruments specs (e.g. probe accuracy of ± X units)

16 Evaluating AMSR-E vs. Ground Probes model-based comparison of AMSR-E performance vs. benchmark: interpret as: AMSR-E is less precise than m-th probe by factor R m conditional variance is from a single level of model hierarchy 08/01/ /01/2007 AMSR-E is more precise...

17 Summary Preliminary Bayesian hierarchical model for SM over Murrumbidgee River Catchment:... work in progress... demonstration of statistical modelling framework unified model-based inference for SM assimilation & evaluation currently under research: investigation of bias issues review of assumptions leading to SM<0 need for additional / different covariates Future developments: addition of temporal component look at further / other datasets (OzNet contribution to SM map is minimal), including modelled estimates (e.g., AWRA-L) extension to larger and/or national scale parallelisation of implementation code

18 CSIRO Mathematics, Informatics and Statistics Eric Lehmann (presenter) Research Scientist Phone: eric.lehmann@csiro.au Web: CSIRO Mathematics, Informatics and Statistics Grace Chiu (corresponding author) Senior Research Scientist Phone: grace.chiu@csiro.au Web: Thank you Contact Us Phone: or Enquiries@csiro.au Web: