PROVIDING DISTRIBUTED FORECASTS OF PRECIPITATION USING A STATISTICAL NOWCAST SCHEME Neil I. Fox and Chris K. Wikle University of Missouri- Columbia

Reasoning Need realistic representation of uncertainty in precipitation forecasts Need realistic representation of uncertainty in precipitation forecasts Previous methods too deterministic (no measure of uncertainty) or too probabilistic (stochastic) Previous methods too deterministic (no measure of uncertainty) or too probabilistic (stochastic) This methodology allows for the integration of some real physics with a realistic statistical formulation that can provide genuine information on forecast uncertainty This methodology allows for the integration of some real physics with a realistic statistical formulation that can provide genuine information on forecast uncertainty

What I’ll show today Not much theory Not much theory The future of nowcasting The future of nowcasting Examples of products Examples of products The future of this nowcasting method The future of this nowcasting method

Nowcasting techniques - current Extrapolation techniques Extrapolation techniques –Mostly linear extrapolation –Do not account for development Modeling approaches Modeling approaches –Forecasts motion and development –Lack of knowledge of: Storm scale dynamics (model accuracy) Storm scale dynamics (model accuracy) Atmospheric environment (observation limitation) Atmospheric environment (observation limitation)

Limitations of Current Nowcasting Only good for very short periods Only good for very short periods Poor at simulating development Poor at simulating development –Predict position but not characteristics of storms –No estimation of forecast rainfall Tend to smooth high intensity features Tend to smooth high intensity features Little or no indication of forecast uncertainty Little or no indication of forecast uncertainty Computationally intensive Computationally intensive

Nowcast formulation where s and r are spatial locations in the domain of interest, k s (r; θ s ) is a redistribution kernel that describes how the process at time t is redistributed in space at time t+1. η represents the noise and γ is a growth / stationarity parameter Stochastic integro-difference equation Continuous in space Discrete in time The nowcast field (y t+1 ) is related to the current field (y t ) by

Model implementation: MCMC Markov Chain Monte-Carlo Markov Chain Monte-Carlo Gibbs sampler Gibbs sampler

Things this can do Full spatial variance field Full spatial variance field –Where do we have least confidence in the forecast –Quantitative uncertainty for defined points and areas (i.e. catchment QPF uncertainty) Incorporation of physics Incorporation of physics – γ (growth/decay) conditioned on convergence – Spatial kernel conditioned on winds

Advantages of Statistical Approach Provide full distribution of forecasts allowing realistic assessment of uncertainty Provide full distribution of forecasts allowing realistic assessment of uncertainty Avoid detailed physical modeling of atmosphere Avoid detailed physical modeling of atmosphere Can ‘train’ system Can ‘train’ system Can incorporate further observations to constrain equation parameters Can incorporate further observations to constrain equation parameters

Example Nowcast of supercell motion from 11/03/00 Nowcast of supercell motion from 11/03/00 Sydney, Australia (to prove we can cope with any hemisphere) Sydney, Australia (to prove we can cope with any hemisphere) Storm produced localized flooding, F1 tornadoes, damaging large hail Storm produced localized flooding, F1 tornadoes, damaging large hail Very complex situation Very complex situation Other nowcast systems did okay Other nowcast systems did okay

Products - domain Nowcast fields Nowcast fields –Mean nowcast – to T+60 (10 minute intervals at present) Variance fields Variance fields –Uncertainty

Mean nowcast fields

Indication of uncertainty in space

How this could appear in ops

Example validation

Products - point / catchment Nowcast reflectivity Nowcast reflectivity –10 minute intervals to T+60 –With variance Nowcast Rainfall Nowcast Rainfall –Point or group of points –Mean or median nowcast rainfall or accumulation out to T+60 –Cumulative frequency / probability distributions

Rainrate distribution

Cumulative frequency of nowcast rainrate Pixel 1Pixel 2Pixel 3 3 pixel aggreg

Cumulative frequency of nowcast rain accumulation Pixel 1Pixel 2Pixel 3 3 pixel aggreg

In the future Verification and adjustment Verification and adjustment Incorporation of physics Incorporation of physics Computational efficiency Computational efficiency Hydrology Hydrology –lumped model probabilities –distributed probabilistic input