The breeding method for ensemble forecasting: application to ...

The breeding method for ensemble forecasting: application to ...

Alejandro Hermoso Advisor: Victor Homar Bred Vectors based tailored perturbations: application to mesoscale ensemble prediction system over the Western Mediterranean Meteorology Group, Physics Department, University of the Balearic Islands, Palma de Mallorca, Spain [email protected] Introduction Numerical weather forecasts are inherently uncertain Both system state and its uncertainty must be assessed

The uncertainty is quantified by means of probabilistic information expressed in terms of probability density functions (PDF) The perfect-model evolution of the system fulfils the Liouville equation (LE) The lack of analytical solution of the LE and the high dimensionality of the system restrain its application for the systems of interest 2 Introduction At operational centres, only an ensemble of discrete samples can be considered Choosing a sampling strategy is a key question for any ensemble prediction system (EPS) Different sampling strategies:

Monte Carlo Ensemble Data Assimilation (EDA) Based on system dynamics Singular vectors: Used at ECMWF. Adequate for synoptic scale Bred vectors: Used at NCEP. Better for mesoscale 3 Bred vectors Step 1: A random initial perturbation is added to the analysis Step 2: The model is integrated for the perturbed and unperturbed initial

conditions for a short integration period Step 3: The difference between the two forecasts is rescaled with some norm and added to the next analysis Kalnay, 2003 1 2 ; ( ) =

Arithmetic rescaling 4 Logarithmic bred vectors Primo et al., 2008 propose a new breeding method: Logarithmic Bred Vectors (LBV) BV are rescaled with a geometrical mean: This rescaling is coherent to the exponential growth of perturbations LBV perform better in terms of ensemble diversity in toy models 5

Characterization of perturbation The amplitude and scale of the perturbations can be defined with the following parameters: (Amplitude) (Localization) 6 Characterization of perturbation 2

log 7 Mediterranean severe weather Severe weather events are common in the Mediterranean region during fall Evaporation from the sea and interaction with orography are important mechanisms for its development Orography of the region contributes to enhance low-level convergence Many of these phenomena origin over the sea

8 Example Example of severe weather event: October 29 squall line (Romero et al. 2015) Rain intensities as high as 260 mm Hailstones of 2.5 cm diameter Losses of 15 M 9 Motivation and objectives

One of the main problems of EPS is the underdispersion Extreme events may not be represented In order to improve the high resolution short-range forecast of extreme events, ensemble spread must be controlled (typically increased) OBJECTIVES: 1) to explore the potential of LBVs to more efficiently initialize mesoscale EPS 2) to investigate options to increase ensemble diversity and obtain a seamless scale representation compared to traditional BV 10 Bred vectors in a limited area domain Bred vectors in an external domain:

40-km horizontal resolution external domain 5-km horizontal resolution forecast domain The model used is the WRF-ARW v3.9.1

A set of 5 arithmetic (ABV) and 5 LBV are generated for a 1 month test period (September 2014) Perturbed variables: potential temperature perturbation, wind components and specific humidity The rescaling period is 6h The amplitude of ABV is rescaled to a RMSD of 1K and the LBV are rescaled to a log of -1.1 1 2 ( ) =1

1 30 vertical levels Boundary conditions provided by ECMWF analysis External domain Forecast domain 11 New method to increase diversity: Bred vectors tailored ensemble perturbations

The scale of the perturbation can be changed: = 0.5 = 1.5 = 2.5 12 New method to increase diversity: Bred vectors tailored ensemble

perturbations This method enables to increase the size of the ensemble at no bred generation cost It also allows a seamless scale representation unlinking scales of forecast interest from bred generation strategy BVTEP are generated by combining different BV with different scales and amplitudes: 13 Ensemble experiments setup Same model configuration described for BV generation

11 ensemble members, 1 control and 5 twin perturbations 00 and 12 UTC forecast cycles are run daily over the test period, and have a lead time of 36 h Boundary conditions generated from BV perturbed forecasts in the external domain 14 Ensemble configurations CNTL: 5 ABV perturbations LOG: 5 LBV perturbations BVTEP1B: 1 ABV with prefixed for each perturbation BVTEP5B: Each perturbation consists of a combination of 1 to 5 ABVs

with prefixed 15 Bred vectors in a limited area domain Ensemble dimension is computed from the covariance matrix eigenvalues : Perturbations covariance matrix: Ensemble dimension 16

Results Variation of ensemble dimension with lead times for T at a model level close to 850 hPa 17 Results Wind speed Rank histograms 6h 12h

24h 18h 18 Results 3h accumulated precipitation Rank histograms 6h 12h

24h 18h 19 Conclusions The ensemble diversity is similar for forecasts perturbed with arithmetic and logarithmic rescaled bred vectors Modifying the scale of the initial perturbations increases ensemble diversity and skill The methodology should be tested in a severe weather event 20

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