The Sensitivity of Relocatable Local Area Models to Temporal Interpolation Noise at Open Boundaries

Sylvia J. Murphy Naval Research Laboratory, Oceanography Division, Stennis Space Center, Mississippi

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Timothy R. Keen Naval Research Laboratory, Oceanography Division, Stennis Space Center, Mississippi

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Abstract

The feasibility of utilizing regional model data to force the open boundaries of a relocatable local area model (RLAM) is investigated mathematically and numerically. The error associated with the interpolation in time of a periodic signal at the open boundaries of a numerical ocean circulation model can generate high-frequency noise in the interior of the model domain. This error is investigated for a tidal signal represented by a sine wave with a period of 12 h and an amplitude of 1 m. The original time series is subsampled and reconstructed using first- and third-order polynomial interpolations. The power spectra of the reconstructed time series contain additional peaks, regardless of sample interval or interpolation order. The pattern of error growth with increasing sample interval is examined.

Several suites of numerical model simulations are described. These include an idealized basin forced at the open boundaries by semidiurnal tide and residual (storm surge) water-level time series. Also presented is a realistic representation of the southern Middle Atlantic Bight forced with the semidiurnal tide plus residual used for the idealized basin, and a multiconstituent tide plus storm surge. In all of the numerical experiments, the error increases by one order of magnitude with each sample interval increase. The spectral periods at which error is introduced into the model are examined. The use of a multiconstituent tide significantly increases the error magnitudes as well as the overall variability. Neither rotational nor frictional effects change the pattern of interpolation error growth.

Corresponding author address: Sylvia J. Murphy, Climate Dynamics Division, NCAR, 1850 Table Mesa Drive, Boulder, CO 80303.

Email: murphys@ucar.edu

Abstract

The feasibility of utilizing regional model data to force the open boundaries of a relocatable local area model (RLAM) is investigated mathematically and numerically. The error associated with the interpolation in time of a periodic signal at the open boundaries of a numerical ocean circulation model can generate high-frequency noise in the interior of the model domain. This error is investigated for a tidal signal represented by a sine wave with a period of 12 h and an amplitude of 1 m. The original time series is subsampled and reconstructed using first- and third-order polynomial interpolations. The power spectra of the reconstructed time series contain additional peaks, regardless of sample interval or interpolation order. The pattern of error growth with increasing sample interval is examined.

Several suites of numerical model simulations are described. These include an idealized basin forced at the open boundaries by semidiurnal tide and residual (storm surge) water-level time series. Also presented is a realistic representation of the southern Middle Atlantic Bight forced with the semidiurnal tide plus residual used for the idealized basin, and a multiconstituent tide plus storm surge. In all of the numerical experiments, the error increases by one order of magnitude with each sample interval increase. The spectral periods at which error is introduced into the model are examined. The use of a multiconstituent tide significantly increases the error magnitudes as well as the overall variability. Neither rotational nor frictional effects change the pattern of interpolation error growth.

Corresponding author address: Sylvia J. Murphy, Climate Dynamics Division, NCAR, 1850 Table Mesa Drive, Boulder, CO 80303.

Email: murphys@ucar.edu

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