The Impact of Initial Spread Calibration on the RELO Ensemble and Its Application to Lagrangian Dynamics

Abstract. A number of real-time ocean model forecasts were carried out successfully at Naval Research Laboratory (NRL) to provide modeling support and numerical guidance to the CARTHE GLAD at-sea experiment during summer 2012. Two RELO ensembles and three single models using NCOM and HYCOM with different resolutions were carried out. A calibrated ensemble system with enhanced spread and reliability was developed to better support this experiment. The calibrated ensemble is found to outperform the un-calibrated ensemble in forecasting accuracy, skill, and reliability for all the variables and observation spaces evaluated. The metrics used in this paper include RMS error, anomaly correlation, PECA, Brier score, spread reliability, and Talagrand rank histogram. It is also found that even the un-calibrated ensemble outperforms the single forecast from the model with the same resolution. The advantages of the ensembles are further extended to the Lagrangian framework. In contrast to a single model forecast, the RELO ensemble provides not only the most likely Lagrangian trajectory for a particle in the ocean, but also an uncertainty estimate that directly reflects the complicated ocean dynamics, which is valuable for decision makers. The examples show that the calibrated ensemble with more reliability can capture trajectories in different, even opposite, directions, which would be missed by the un-calibrated ensemble. The ensembles are applied to compute the repelling and attracting Lagrangian coherent structures (LCSs), and the uncertainties of the LCSs, which are hard to obtain from a single model forecast, are estimated. It is found that the spatial scales of the LCSs depend on the model resolution. The model with the highest resolution produces the finest, small-scale, LCS structures, while the model with lowest resolution generates only large-scale LCSs. The repelling and attracting LCSs are found to intersect at many locations and create complex mesoscale eddies. The fluid particles and drifters in the middle of these tangles are subject to attraction and repulsion simultaneously from these two kinds of LCSs. As a result, the movements of particles near the Deepwater Horizon (DWH) location are severely limited. This is also confirmed by the Lagrangian trajectories predicted by the ensembles.

[1]  George Haller,et al.  Optimal pollution mitigation in Monterey Bay based on coastal radar data and nonlinear dynamics. , 2007, Environmental science & technology.

[2]  Paul J. Martin,et al.  Description of the Navy Coastal Ocean Model Version 1.0 , 2000 .

[3]  Mathew E. Maltrud,et al.  On the possible long-term fate of oil released in the Deepwater Horizon incident, estimated using ensembles of dye release simulations , 2010 .

[4]  P. L. Houtekamer,et al.  A System Simulation Approach to Ensemble Prediction , 1996 .

[5]  George Haller,et al.  Forecasting sudden changes in environmental pollution patterns , 2012, Proceedings of the National Academy of Sciences.

[6]  J. Marsden,et al.  Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows , 2005 .

[7]  F. Beron-Vera,et al.  An Assessment of the Importance of Chaotic Stirring and Turbulent Mixing on the West Florida Shelf. , 2009, Journal of physical oceanography.

[8]  Gustavo Goni,et al.  Surface Ocean Mixing Inferred from Different Multisatellite Altimetry Measurements , 2010 .

[9]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[10]  Eugenia Kalnay,et al.  Ensemble Forecasting at NMC: The Generation of Perturbations , 1993 .

[11]  G. Haller,et al.  Lagrangian coherent structures and mixing in two-dimensional turbulence , 2000 .

[12]  F. Molteni,et al.  The ECMWF Ensemble Prediction System: Methodology and validation , 1996 .

[13]  Neill E. Bowler,et al.  The local ETKF and SKEB: Upgrades to the MOGREPS short‐range ensemble prediction system , 2009 .

[14]  Rainer Bleck,et al.  An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates , 2002 .

[15]  Robert H. Weisberg,et al.  Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record-Breaking Enterprise , 2011 .

[16]  H. Koçak,et al.  Tracing the Early Development of Harmful Algal Blooms on the West Florida Shelf with the Aid of Lagrangian Coherent Structures. , 2007, Journal of geophysical research.

[17]  Renate Hagedorn,et al.  Probabilistic Forecast Calibration Using ECMWF and GFS Ensemble Reforecasts. Part II: Precipitation , 2008 .

[18]  C. Schultz.  Monitoring and Modeling the Deepwater Horizon Oil Spill: A Record‐Breaking Enterprise , 2013 .

[19]  Mozheng Wei,et al.  A new measure of ensemble performance: Perturbation versus error correlation analysis (PECA) , 2003 .

[20]  George Haller,et al.  Lagrangian coherent structures and the smallest finite-time Lyapunov exponent. , 2011, Chaos.

[21]  Eric P. Chassignet,et al.  North Atlantic Simulations with the Hybrid Coordinate Ocean Model (HYCOM): Impact of the Vertical Coordinate Choice, Reference Pressure, and Thermobaricity , 2003 .

[22]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[23]  M. Olascoaga,et al.  Isolation on the West Florida Shelf with implications for red tides and pollutant dispersal in the Gulf of Mexico. , 2010, Nonlinear processes in geophysics.

[24]  Pierre F. J. Lermusiaux,et al.  Uncertainty estimation and prediction for interdisciplinary ocean dynamics , 2006, J. Comput. Phys..

[25]  C. Bishop,et al.  The ensemble‐transform scheme adapted for the generation of stochastic forecast perturbations , 2007 .

[26]  George Haller,et al.  Pollution release tied to invariant manifolds: A case study for the coast of Florida , 2005 .

[27]  A. J. Marianoa,et al.  Modeling the 2010 Gulf of Mexico oil spill , 2019, Mathematics for Social Justice.

[28]  Annalisa Griffa,et al.  On the Predictability of Lagrangian Trajectories in the Ocean , 2000 .

[29]  Gustavo Goni,et al.  Oceanic mesoscale eddies as revealed by Lagrangian coherent structures , 2008 .

[30]  Thomas M. Hamill,et al.  Hypothesis Tests for Evaluating Numerical Precipitation Forecasts , 1999 .

[31]  Yuejian Zhu,et al.  Analysis differences and error variance estimates from multi-centre analysis data , 2010 .

[32]  Yuejian Zhu,et al.  Initial perturbations based on the ensemble transform (ET) technique in the NCEP global operational forecast system , 2008 .

[33]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[34]  C. Bishop,et al.  Ensemble Transform Kalman Filter-based ensemble perturbations in an operational global prediction system at NCEP , 2006 .

[35]  Neill E. Bowler,et al.  Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model , 2006 .

[36]  Helga S. Huntley,et al.  Surface Drift Predictions of the Deepwater Horizon Spill: The Lagrangian Perspective , 2013 .

[37]  O. Talagrand,et al.  Evaluation of probabilistic prediction systems for a scalar variable , 2005 .

[38]  Carolyn A. Reynolds,et al.  Examination of parameter variations in the U. S. Navy Global Ensemble , 2011 .

[39]  George Haller,et al.  Uncovering the Lagrangian skeleton of turbulence. , 2007, Physical review letters.

[40]  Jerrold E. Marsden,et al.  The correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay , 2009 .

[41]  G. Halliwell,et al.  Evaluation of vertical coordinate and vertical mixing algorithms in the HYbrid-Coordinate Ocean Model (HYCOM) , 2004 .

[42]  Leonid I. Piterbarg,et al.  Predictability of Drifter Trajectories in the Tropical Pacific Ocean , 2001 .

[43]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[44]  Tim N. Palmer,et al.  Ensemble forecasting , 2008, J. Comput. Phys..

[45]  A. Kirwan,et al.  Lagrangian predictability assessed in the East China Sea , 2011 .

[46]  David F. Parrish,et al.  Estimation and calibration of observation impact signals using the Lanczos method in NOAA/NCEP data assimilation system , 2012 .

[47]  T. Hamill,et al.  A Comparison of Probabilistic Forecasts from Bred, Singular-Vector, and Perturbed Observation Ensembles , 2000 .

[48]  G. Mellor,et al.  A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers. , 1974 .

[49]  P. Durbin,et al.  The Structure and Dynamics of the Ocean Surface Mixed Layer , 1975 .

[50]  J. Sheinbaum,et al.  A Lagrangian approach to the Loop Current eddy separation , 2013 .

[51]  O. Talagrand,et al.  On Some Aspects of the Definition of Initial Conditions for Ensemble Prediction , 2007 .

[52]  Paul J. Martin,et al.  Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM) , 2006 .

[53]  J. Cummings,et al.  Operational multivariate ocean data assimilation , 2005 .

[54]  R. Buizza,et al.  A Comparison of the ECMWF, MSC, and NCEP Global Ensemble Prediction Systems , 2005 .

[55]  L. Magnusson,et al.  Flow-dependent versus flow-independent initial perturbations for ensemble prediction , 2009 .

[56]  Paul J. Martin,et al.  The US Navy's RELO ensemble prediction system and its performance in the Gulf of Mexico , 2014 .