Providing distributed forecasts of precipitation using a Bayesian nowcast scheme

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Providing distributed forecasts of precipitation
using a Bayesian nowcast scheme

• Neil I. Fox Chris K. Wikle
• University of Missouri - Columbia

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Contents

• Reasoning
• Method / model
• Statistical method
• Dynamics
• More reasoning
• Products
• Case study example
• Development

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Reasoning

• Need realistic representation of uncertainty in
  precipitation forecasts
• 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

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Hierarchical Model

• 5 stage model
• Data
• Process
• Spatial distributions
• Parameters

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Spatio-Temporal Dynamic Models
Hierarchical Space-Time Framework

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Used in

• Ecology e.g. Model species dispersion
• Data sparse obs e.g. Scatterometer winds
• Long-term modeling e.g. SST prediction

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Model formulation

• Stage 3 The integro-difference equation (IDE)

ks(r?s) is a redistribution kernel that
describes how the process Y at time t is
redistributed spatially at time t1.
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IDE Kernel Parameterization
For 2-D space, consider the multivariate Gaussian
kernel for location s
The kernel is centered at s µ(?s) and thus the
µ parameters control the translation and the
covariance parameters control the dilation and
orientation. These parameters can be given
spatial distributions at the next level of the
hierarchy!! Alternative kernel parameterization
ellipse foci, e.g., Higdon et al. 1999
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Spatial distribution

• Model the ?s parameters with a spatial
  distribution at the next level of the hierarchy
• Gaussian random field

• Diffusive wave fronts shape and speed of
  diffusion depend on kernel width and tail
  behavior (dilation) (e.g., Kot et al. 1996)
• Non-diffusive propagation via relative
  displacement of kernel (translation) e.g., Wikle
  (2001 2002)

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Model implementation MCMC

• Markov Chain Monte-Carlo
• Gibbs sampler

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Things this can do

• 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)

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More things we can do

• Incorporation of physics
• ? can become a spatially varying growth parameter
• Kernel can incorporate windfield information

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Products - domain

• Nowcast fields
• Mean nowcast
• to T60 (10 minute intervals at present)
• Variance fields
• Uncertainty

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Mean nowcast fields
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Indication of uncertainty in space
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Products - point / catchment

• Nowcast reflectivity
• 10 minute intervals to T60
• With variance
• Nowcast Rainfall
• Point or group of points
• Mean or median nowcast rainfall or accumulation
  out to T60
• Cumulative frequency / probability distributions

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Rainrate distribution
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Cumulative frequency of nowcast rainrate
Pixel 1
Pixel 2
Pixel 3
3 pixel aggreg
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Cumulative frequency of nowcast rain accumulations
Pixel 1
Pixel 2
Pixel 3
3 pixel aggreg
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In the future

• Verification and adjustment
• Incorporation of physics
• Computational efficiency
• Hydrology
• lumped model probabilities
• distributed probabilistic input

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References

• Wikle, C.K., Berliner, L.M., and Cressie, N.
  (1998). Hierarchical Bayesian space-time models.
  Environmental and Ecological Statistics, 5,
  117-154.
• Wikle, C.K., Milliff, R.F., Nychka, D., and L.M.
  Berliner, 2001 Spatiotemporal hierarchical
  Bayesian modeling Tropical ocean surface winds,
  Journal of the American Statistical Association,
  96, 382-397.
• Berliner, L.M., Wikle, C.K., and Cressie, N.,
  2000 Long-lead prediction of Pacific SSTs via
  Bayesian dynamic modeling. Journal of Climate,
  13, 3953-3968.
• Xu, B., Wikle, C.K., and N.I. Fox, 2003 A
  kernel-based spatio-temporal dynamical model for
  nowcasting radar precipitation. Journal of the
  American Statistical Association. In review.
  Available at http//solberg.snr.missouri.edu/Peop
  le/fox/research/xuetal2003.pdf