Hierarchical Bayesian Modeling of Multisite Daily Rainfall Occurrence

Transcription

1 The First Henry Krumb Sustainable Engineering Symposium Hierarchical Bayesian Modeling of Multisite Daily Rainfall Occurrence Carlos Henrique Ribeiro Lima Prof. Upmanu Lall March 2009

2 Agenda 1) Motivation 2) Modeling of Rainfall Season Onset, Duration and End 3) A Hierarchical Bayesian Model for Parameter Estimates 4) Seasonal Rainfall Occurrence Results 5) Temporal Trends, Climate Teleconnections and Forecasts 6) Conclusions and Future Research

3 Motivation 1) Rainfed agriculture as a social element for self subsistence and economical development of several regions (e.g. Northeast Brazil) 2) Every year millions of farms lose entire plantations ($) due to wrong planning of seeding time: they plant, expect rain but no rain. 3) If they know in advance (even some days) when the rain season begins, can they mitigate losses? 4) But current climate models do a poor job in predicting the rain season onset, duration and end.

4 Motivation Main goal: use modern statistical tools associated with climate understanding to model and potentially forecast the timings of the rainfall season: application to Northeast Brazil, characterized by a distinguish rain season period.

5 1) Benefits: Motivation Rainfed agriculture & Crop models Multiple and competing uses of water: Irrigation versus Hydropower increasing the efficiency and reducing losses: Sustainable Development!! Support further development of spatiotemporal rainfall models (e.g. weather generation models, simulation of scenarios under global climate changes, etc)

6 Modeling of Rainfall Season onset, duration and end First question: How do we define the rain season timings? What criteria should we use? Needs of a parametric model that allows us to model the interannual variability of rain season timings: identify major climate sources of variability and build a forecast model! High intra and interannual rainfall variability makes hard the use of models to identify rain season timings

7 Modeling of Rainfall Season onset, duration and end Daily Rainfall 60 day accumulated rainfall Accumulated # of rainy days Difficulties in identify the rain season timings Difficulties in fitting a parametric model: function? # of parameters?

8 Modeling of Rainfall Season onset, duration and end Proposed alternative: Modeling of rainfall occurrence (0 =dry, 1 = rain) probabilistic model Rain season Crop period Irrigation

9 Modeling of Rainfall Season onset, Advantages: duration and end Relatively simple, natural way to model seasonal cycles Non-homogenous Binomial Distribution (GLM) for rainfall occurrence Fits well observed proportion of wet days with only 3 parameters

10 Modeling of Rainfall Season onset, duration and end Advantages: 3) Can define the rain season onset and end based on the probability of rain (e.g. p =0.5) or water needs 4) Can address interannual variability in rainfall amounts as well as shifts in the rainy season onset, duration and end temporal trends; 5) Able to correlate time varying Fourier parameters with climate predictors (SST, NINO, PDO,...) possibility of a real time forecast model for rain season timings!!

11 Modeling of Rainfall Season onset, duration and end

12 Modeling of Rainfall Season onset, duration and end Main issues: Missing data: several gaps, sometimes not sparse (clustered) Cannot always trust data: period in which missing data was filled with 0 s (rather than -999 or any other symbol), difficulty to measure rain during extreme events, etc Both can lead to bad estimates of parameters:

13 Modeling of Rainfall Season onset, duration and end Outlier?

14 A Hierarchical Bayesian Model for Solution: Hierarchical Bayesian Modeling Structured, elegant Model; Parameter Estimates Shrink parameters towards a common mean reduce uncertainty since we are use more information to estimate model parameters; Parameter uncertainties are fully accounted during simulations

15 A Hierarchical Bayesian Model for Parameter Estimates General Description of Bayesian Model 1) Shrinkage in time then in space; 3) Partial modeling of spatial structure 4) MCMC to estimate posterior distribution of parameters

16 Seasonal Rainfall Occurrence Results

17 Seasonal Rainfall Occurrence Results

18 Temporal Trends, Climate Teleconnections and Forecasts Slope of a linear curve fitted to the series of maximum probability of rainfall Slope of a linear curve fitted to the series of day of year of maximum probability of rainfall

19 Temporal Trends, Climate Teleconnections and Forecasts

20 Temporal Trends, Climate Teleconnections and Forecasts NINO3 (DEC) Atlantic SST Dipole (JAN) South Atlantic SST (MAR) Can include climate indexes here

21 5) Other applications: spatio-temporal weather generation model Conclusions and Future Research 1) Able to modeling rainfall season timings as well as intensity 2) Identification of potential climate predictors 3) More complete modeling of spatial structure: change the order of shrinkage (first space then time) and use of a full covariance matrix for the spatial coefficients 4) Use of climate predictors to further shrink the parameters real time forecast model;

22 Many Thanks!!! In particular for the EAEE Department for all support along the last 4 years And to my PhD advisor Prof. Lall