TY - JOUR

T1 - Stochastic longshore current dynamics

AU - Restrepo, Juan M.

AU - Venkataramani, Shankar

N1 - Funding Information:
We received funding from GoMRI/BP. JR and SV also received funding from NSF-DMS-1109856. We wish to thank Prof. Falk Feddersen, for discussions on current longshore models. Several suggestions by the referees improved the paper. JR also thanks the J. T. Oden Fellowship program at U. Texas, Austin, and the Aspen Center for Physics. The Aspen Center of Physics is supported, in part, by the National Science Foundation under Grant No. PHYS-1066293.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We develop a stochastic parametrization, based on a ‘simple’ deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the “missing physics” to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.

AB - We develop a stochastic parametrization, based on a ‘simple’ deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the “missing physics” to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.

KW - Consistently of model sensitivity

KW - Data assimilation

KW - Longshore currents

KW - Parameter sensitivity

KW - Stochastic parametrization

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U2 - 10.1016/j.advwatres.2016.11.002

DO - 10.1016/j.advwatres.2016.11.002

M3 - Article

AN - SCOPUS:84995468531

VL - 98

SP - 186

EP - 197

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

ER -