# Search Results

## You are looking at 1 - 9 of 9 items for

- Author or Editor: Harold O. Mofjeld x

- Refine by Access: All Content x

## Abstract

We study theoretically the effects of linear (Rayleigh) friction on free internal waves in the equatorial wayeguide. The waves may be vertically propagating or in standing vertical modes. Analytic solutions on a beta-plane show that the meridional scale of the wayeguide becomes significantly larger than the inviscid value only when the frequency is much less than the friction coefficient. In the limit of zero frequency, the meridional scale grows without bound. The amount of zonal damping depends on the wave type. Kelvin, high-frequency Yanai (mixed Rossby-gravity), inertial-gravity and low-wavenumber (non-dispersive) Rossby waves decay relatively slowly while low-frequency Yanai and high-wavenumber (short) Rossby waves are much more strongly attenuated. With friction, transitions to evanescence are spread over frequency bands; waves that had zero group velocity without friction are zonally evanescent with friction. Off the equator, friction changes amplitude nodes into non-zero minima and smooths sharp phase shifts; phase lines slant backward relative to the direction of phase propagation. By symmetry, nodes and phase shifts of π are preserved on the equator. Friction alters the relative amplitudes and phases of the dynamic variables. When the frequency is much less than the friction coefficient, the motion obeys diffusion-dynamics rather than wave-dynamics.

## Abstract

We study theoretically the effects of linear (Rayleigh) friction on free internal waves in the equatorial wayeguide. The waves may be vertically propagating or in standing vertical modes. Analytic solutions on a beta-plane show that the meridional scale of the wayeguide becomes significantly larger than the inviscid value only when the frequency is much less than the friction coefficient. In the limit of zero frequency, the meridional scale grows without bound. The amount of zonal damping depends on the wave type. Kelvin, high-frequency Yanai (mixed Rossby-gravity), inertial-gravity and low-wavenumber (non-dispersive) Rossby waves decay relatively slowly while low-frequency Yanai and high-wavenumber (short) Rossby waves are much more strongly attenuated. With friction, transitions to evanescence are spread over frequency bands; waves that had zero group velocity without friction are zonally evanescent with friction. Off the equator, friction changes amplitude nodes into non-zero minima and smooths sharp phase shifts; phase lines slant backward relative to the direction of phase propagation. By symmetry, nodes and phase shifts of π are preserved on the equator. Friction alters the relative amplitudes and phases of the dynamic variables. When the frequency is much less than the friction coefficient, the motion obeys diffusion-dynamics rather than wave-dynamics.

## Abstract

An analytic theory is presented for free, barotropic Kelvin waves subject to constant, vertical eddy viscosity on a semi-infinite, *f*-plane shelf of constant depth bordering a straight, vertical coast. A coastal boundary condition closes the solutions of Sverdrup (1927) and Fjeldstad (1929) by requiring that the component of vertically integrated, volume transport normal to the coast be zero just seaward of coastal boundary layers. This condition on offshore transport is then found to hold everywhere seaward of the coastal layers. One condition on the complex wavenumber components is the dispersion relation in which frictional bottom stress appears in an equivalent depth. The coastal boundary condition then fixes the wavenumber components. The effects of vertical viscosity are found to depend on the frequency ω′ relative to the inertial frequency and on the Ekman number *E* or, more conveniently, the vertical scale *E*½ of steady, bottom Ekman layers. Below a frequency dependent on *E*½, low-frequency Kelvin waves are diffusive, rather than wavelike. These Kelvin “waves” have backward slanting cophase lines which at very low frequencies make the same angle to the coast as do the corresponding lines for steady flow. The offshore decay scale at low frequencies is greater than the Rossby radius, and the alongshore wavelengths are significantly shorter than the inviscid wavelength. There is no special behavior near the inertial frequency except that the cophase lines slant slightly forward at small *E*½, and that the bottom boundary layer extends to the surface. In general, the alongshore attenuation per unit distance increases with increasing ω′ or *E*½. For ω′ ≪ 1 the water motion forms narrow ellipses with Ekman veering in the quasi-steady bottom boundary layer. Near ω′ ≈ 1, the ellipses are broader with a counter-clockwise sense (Northern Hemisphere) near the bottom and clockwise near the surface; there is still some veering of the ellipses, and the motion at depth tends to lead that above. For ω′ ≫ 1, the ellipses are again narrow but tend to parallel the coast with little veering. The bottom boundary layer is thinner with a Stokes, rather than an Ekman, scale; and motion at depth loads significantly that above.

## Abstract

An analytic theory is presented for free, barotropic Kelvin waves subject to constant, vertical eddy viscosity on a semi-infinite, *f*-plane shelf of constant depth bordering a straight, vertical coast. A coastal boundary condition closes the solutions of Sverdrup (1927) and Fjeldstad (1929) by requiring that the component of vertically integrated, volume transport normal to the coast be zero just seaward of coastal boundary layers. This condition on offshore transport is then found to hold everywhere seaward of the coastal layers. One condition on the complex wavenumber components is the dispersion relation in which frictional bottom stress appears in an equivalent depth. The coastal boundary condition then fixes the wavenumber components. The effects of vertical viscosity are found to depend on the frequency ω′ relative to the inertial frequency and on the Ekman number *E* or, more conveniently, the vertical scale *E*½ of steady, bottom Ekman layers. Below a frequency dependent on *E*½, low-frequency Kelvin waves are diffusive, rather than wavelike. These Kelvin “waves” have backward slanting cophase lines which at very low frequencies make the same angle to the coast as do the corresponding lines for steady flow. The offshore decay scale at low frequencies is greater than the Rossby radius, and the alongshore wavelengths are significantly shorter than the inviscid wavelength. There is no special behavior near the inertial frequency except that the cophase lines slant slightly forward at small *E*½, and that the bottom boundary layer extends to the surface. In general, the alongshore attenuation per unit distance increases with increasing ω′ or *E*½. For ω′ ≪ 1 the water motion forms narrow ellipses with Ekman veering in the quasi-steady bottom boundary layer. Near ω′ ≈ 1, the ellipses are broader with a counter-clockwise sense (Northern Hemisphere) near the bottom and clockwise near the surface; there is still some veering of the ellipses, and the motion at depth tends to lead that above. For ω′ ≫ 1, the ellipses are again narrow but tend to parallel the coast with little veering. The bottom boundary layer is thinner with a Stokes, rather than an Ekman, scale; and motion at depth loads significantly that above.

## Abstract

The behavior of a barotropic Rossby wave in a zonal current is studied theoretically using a beta-plane ocean of constant depth in which the current depends only on latitude. The wave may be reflected or absorbed, depending on whether the relative frequency as detected in the moving water increases or decreases, respectively, as the wave penetrates into the current. An eastward-flowing current can reflect a Rossby wave with little transfer of zonal momentum or energy to the current, even in the presence of lateral viscosity. It does transfer meridional momentum. A westward-flowing current can absorb a Rossby wave, receiving all the wave momentum and much of its energy. Near the absorption velocity there is a balance between viscous diffusion and advection of vorticity, and relative accelerators are insignificant.

## Abstract

The behavior of a barotropic Rossby wave in a zonal current is studied theoretically using a beta-plane ocean of constant depth in which the current depends only on latitude. The wave may be reflected or absorbed, depending on whether the relative frequency as detected in the moving water increases or decreases, respectively, as the wave penetrates into the current. An eastward-flowing current can reflect a Rossby wave with little transfer of zonal momentum or energy to the current, even in the presence of lateral viscosity. It does transfer meridional momentum. A westward-flowing current can absorb a Rossby wave, receiving all the wave momentum and much of its energy. Near the absorption velocity there is a balance between viscous diffusion and advection of vorticity, and relative accelerators are insignificant.

## Abstract

On 10 August 1976 Hurricane Belle passed rapidly over the highly stratified shelf of the New York Bight. Records from Aanderaa current-meter moorings show that the response to the hurricane depended strongly on bathymetry. At deeper stations (∼70 m depth), intense, first-mode, internal near-inertial oscillations were generated at frequencies ∼1% less than the local inertial frequency. At shallower stations (∼50 m depth), only weak, heavily damped second-mode oscillations were observed in the current records, with no corresponding inertial signals in temperature. In the Hudson Shelf Valley, inertial motion occurred only near the surface. This was probably due to topographic effects. The divergence and curl of the wind stress contributed equally to the forcing. The response at the deeper stations is consistent with Geisler's (1970) theory for the open ocean in which a hurricane leaves a wake of internal-inertial oscillations if it travels faster than the internal phase speed and if its horizontal scale is comparable to the internal Rossby radius. The observed frequency shifts (subinertial motion) and observed relative vorticity are consistent with Mooer's (1975a) theory that relative and planetary vorticities combine to give an effective inertial frequency. Here it is suggested that lack of strong inertial motion at the shallower stations is due to a lack of resonance and the likelihood that frictional effects are more important in shallower water, resulting in a more heavily damped response.

## Abstract

On 10 August 1976 Hurricane Belle passed rapidly over the highly stratified shelf of the New York Bight. Records from Aanderaa current-meter moorings show that the response to the hurricane depended strongly on bathymetry. At deeper stations (∼70 m depth), intense, first-mode, internal near-inertial oscillations were generated at frequencies ∼1% less than the local inertial frequency. At shallower stations (∼50 m depth), only weak, heavily damped second-mode oscillations were observed in the current records, with no corresponding inertial signals in temperature. In the Hudson Shelf Valley, inertial motion occurred only near the surface. This was probably due to topographic effects. The divergence and curl of the wind stress contributed equally to the forcing. The response at the deeper stations is consistent with Geisler's (1970) theory for the open ocean in which a hurricane leaves a wake of internal-inertial oscillations if it travels faster than the internal phase speed and if its horizontal scale is comparable to the internal Rossby radius. The observed frequency shifts (subinertial motion) and observed relative vorticity are consistent with Mooer's (1975a) theory that relative and planetary vorticities combine to give an effective inertial frequency. Here it is suggested that lack of strong inertial motion at the shallower stations is due to a lack of resonance and the likelihood that frictional effects are more important in shallower water, resulting in a more heavily damped response.

## Abstract

A major difficulty in investigating the nature of interdecadal variability of climatic time series is their shortness. An approach to this problem is through comparison of models. In this paper a first-order autoregressive [AR(1)] model is contrasted with a fractionally differenced (FD) model as applied to the winter-averaged sea level pressure time series for the Aleutian low [the North Pacific (NP) index] and the Sitka winter air temperature record. Both models fit the same number of parameters. The AR(1) model is a “short-memory” model in that it has a rapidly decaying autocovariance sequence, whereas an FD model exhibits “long memory” because its autocovariance sequence decays more slowly.

Statistical tests cannot distinguish the superiority of one model over the other when fit with 100 NP or 146 Sitka data points. The FD model does equally well for short-term prediction and has potentially important implications for long-term behavior. In particular, the zero crossings of the FD model tend to be farther apart, so they have more of a “regimelike” character; a quarter century interval between zero crossings is 4 times more likely with the FD than the AR(1) model. The long-memory parameter *δ* for the FD model can be used as a characterization of regimelike behavior. The estimated *δ*s for the NP index (spanning 100 yr) and the Sitka time series (168 yr) are virtually identical, and their size implies moderate long-memory behavior. Although the NP index and the Sitka series have broadband low-frequency variability and modest long-memory behavior, temporal irregularities in their zero crossings are still prevalent. Comparison of the FD and AR(1) models indicates that regimelike behavior cannot be ruled out for North Pacific processes.

## Abstract

A major difficulty in investigating the nature of interdecadal variability of climatic time series is their shortness. An approach to this problem is through comparison of models. In this paper a first-order autoregressive [AR(1)] model is contrasted with a fractionally differenced (FD) model as applied to the winter-averaged sea level pressure time series for the Aleutian low [the North Pacific (NP) index] and the Sitka winter air temperature record. Both models fit the same number of parameters. The AR(1) model is a “short-memory” model in that it has a rapidly decaying autocovariance sequence, whereas an FD model exhibits “long memory” because its autocovariance sequence decays more slowly.

Statistical tests cannot distinguish the superiority of one model over the other when fit with 100 NP or 146 Sitka data points. The FD model does equally well for short-term prediction and has potentially important implications for long-term behavior. In particular, the zero crossings of the FD model tend to be farther apart, so they have more of a “regimelike” character; a quarter century interval between zero crossings is 4 times more likely with the FD than the AR(1) model. The long-memory parameter *δ* for the FD model can be used as a characterization of regimelike behavior. The estimated *δ*s for the NP index (spanning 100 yr) and the Sitka time series (168 yr) are virtually identical, and their size implies moderate long-memory behavior. Although the NP index and the Sitka series have broadband low-frequency variability and modest long-memory behavior, temporal irregularities in their zero crossings are still prevalent. Comparison of the FD and AR(1) models indicates that regimelike behavior cannot be ruled out for North Pacific processes.

## Abstract

The harmonic constant datum (HCD) method is a computationally efficient way of estimating tidal datums relative to mean sea level, without the need to compute long time series. However, datum discontinuities can occur between mixed and diurnal tidal regimes using this method. Solutions to this problem are investigated, with a hypothetical strait that contains a semidiurnal node, using three different procedures: algorithms specifically designed for diurnal tides (DTA), mixed tidal algorithms (MTA) throughout, and cubic polynomial interpolation (CPI) across the diurnal region. DTA creates small discontinuities (≤11% for the strait) in mean higher high water and mean lower low water but does not provide estimates of mean high water or mean low water. MTA gives continuous datums but creates artificial structures in the middle of the diurnal region. CPI provides smooth, continuous datums but does not use the tidal information within the diurnal regions. Which procedure works best depends on the size of the diurnal region and the application. The standard time series method can be used for limited transitional regions requiring high accuracy, with the efficient HCD method used elsewhere. However, the discontinuity issues still exist. Global distributions of datums computed by the HCD method are shown, based on the 0.5° × 0.5° Oregon State University (OSU) TPXO 5.0 tide model.

## Abstract

The harmonic constant datum (HCD) method is a computationally efficient way of estimating tidal datums relative to mean sea level, without the need to compute long time series. However, datum discontinuities can occur between mixed and diurnal tidal regimes using this method. Solutions to this problem are investigated, with a hypothetical strait that contains a semidiurnal node, using three different procedures: algorithms specifically designed for diurnal tides (DTA), mixed tidal algorithms (MTA) throughout, and cubic polynomial interpolation (CPI) across the diurnal region. DTA creates small discontinuities (≤11% for the strait) in mean higher high water and mean lower low water but does not provide estimates of mean high water or mean low water. MTA gives continuous datums but creates artificial structures in the middle of the diurnal region. CPI provides smooth, continuous datums but does not use the tidal information within the diurnal regions. Which procedure works best depends on the size of the diurnal region and the application. The standard time series method can be used for limited transitional regions requiring high accuracy, with the efficient HCD method used elsewhere. However, the discontinuity issues still exist. Global distributions of datums computed by the HCD method are shown, based on the 0.5° × 0.5° Oregon State University (OSU) TPXO 5.0 tide model.

## Abstract

A theoretical study was carried out to understand how the probability distribution for maximum wave heights (*η _{m}*) during tsunamis depends on the initial tsunami amplitude (

*A*) and the tides. It was assumed that the total wave height is the linear sum of the tides and tsunami time series in which the latter is decaying exponentially in amplitude with an

*e*-folding time of 2.0 days, based on the behavior of observed Pacific-wide tsunamis. Direct computations were made to determine the statistics of maximum height for a suite of different arrival times and initial tsunami amplitudes. Using predicted tides for 1992 when the lunar nodal

*f*factors were near unity during the present National Tidal Datum Epoch 1983–2001, the results show that when

*A*is small compared with the tidal range the probability density function (PDF) of the difference

*η*−

_{m}*A*is closely confined in height near mean higher high water (MHHW). The

*η*−

_{m}*A*PDF spreads in height and its mean height

*η*−

_{o}*A*decreases, approaching the PDF of the tides and MSL, respectively, when

*A*becomes large compared with the tidal range. A Gaussian form is found to be a close approximation to the

*η*−

_{m}*A*PDF over much of the amplitude range; associated parameters for 30 coastal stations along the U.S. West Coast, Alaska, and Hawaii are given in the paper. The formula should prove useful in probabilistic mapping of coastal tsunami flooding.

## Abstract

A theoretical study was carried out to understand how the probability distribution for maximum wave heights (*η _{m}*) during tsunamis depends on the initial tsunami amplitude (

*A*) and the tides. It was assumed that the total wave height is the linear sum of the tides and tsunami time series in which the latter is decaying exponentially in amplitude with an

*e*-folding time of 2.0 days, based on the behavior of observed Pacific-wide tsunamis. Direct computations were made to determine the statistics of maximum height for a suite of different arrival times and initial tsunami amplitudes. Using predicted tides for 1992 when the lunar nodal

*f*factors were near unity during the present National Tidal Datum Epoch 1983–2001, the results show that when

*A*is small compared with the tidal range the probability density function (PDF) of the difference

*η*−

_{m}*A*is closely confined in height near mean higher high water (MHHW). The

*η*−

_{m}*A*PDF spreads in height and its mean height

*η*−

_{o}*A*decreases, approaching the PDF of the tides and MSL, respectively, when

*A*becomes large compared with the tidal range. A Gaussian form is found to be a close approximation to the

*η*−

_{m}*A*PDF over much of the amplitude range; associated parameters for 30 coastal stations along the U.S. West Coast, Alaska, and Hawaii are given in the paper. The formula should prove useful in probabilistic mapping of coastal tsunami flooding.

## Abstract

Instrumental surface air temperature (SAT) records beginning in the late 1800s from 59 Arctic stations north of 64°N show monthly mean anomalies of several degrees and large spatial teleconnectivity, yet there are systematic seasonal and regional differences. Analyses are based on time–longitude plots of SAT anomalies and principal component analysis (PCA). Using monthly station data rather than gridded fields for this analysis highlights the importance of considering record length in calculating reliable Arctic change estimates; for example, the contrast of PCA performed on 11 stations beginning in 1886, 20 stations beginning in 1912, and 45 stations beginning in 1936 is illustrated. While often there is a well-known interdecadal negative covariability in winter between northern Europe and Baffin Bay, long-term changes in the remainder of the Arctic are most evident in spring, with cool temperature anomalies before 1920 and Arctic-wide warm temperatures in the 1990s. Summer anomalies are generally weaker than spring or winter but tend to mirror spring conditions before 1920 and in recent decades. Temperature advection in the trough–ridge structure in the positive phase of the Arctic Oscillation (AO) in the North Atlantic establishes wintertime temperature anomalies in adjacent regions, while the zonal/annular nature of the AO in the remainder of the Arctic must break down in spring to promote meridional temperature advection. There were regional/decadal warm events during winter and spring in the 1930s to 1950s, but meteorological analysis suggests that these SAT anomalies are the result of intrinsic variability in regional flow patterns. These midcentury events contrast with the recent Arctic-wide AO influence in the 1990s. The preponderance of evidence supports the conclusion that warm SAT anomalies in spring for the recent decade are unique in the instrumental record, both in having the greatest longitudinal extent and in their associated patterns of warm air advection.

## Abstract

Instrumental surface air temperature (SAT) records beginning in the late 1800s from 59 Arctic stations north of 64°N show monthly mean anomalies of several degrees and large spatial teleconnectivity, yet there are systematic seasonal and regional differences. Analyses are based on time–longitude plots of SAT anomalies and principal component analysis (PCA). Using monthly station data rather than gridded fields for this analysis highlights the importance of considering record length in calculating reliable Arctic change estimates; for example, the contrast of PCA performed on 11 stations beginning in 1886, 20 stations beginning in 1912, and 45 stations beginning in 1936 is illustrated. While often there is a well-known interdecadal negative covariability in winter between northern Europe and Baffin Bay, long-term changes in the remainder of the Arctic are most evident in spring, with cool temperature anomalies before 1920 and Arctic-wide warm temperatures in the 1990s. Summer anomalies are generally weaker than spring or winter but tend to mirror spring conditions before 1920 and in recent decades. Temperature advection in the trough–ridge structure in the positive phase of the Arctic Oscillation (AO) in the North Atlantic establishes wintertime temperature anomalies in adjacent regions, while the zonal/annular nature of the AO in the remainder of the Arctic must break down in spring to promote meridional temperature advection. There were regional/decadal warm events during winter and spring in the 1930s to 1950s, but meteorological analysis suggests that these SAT anomalies are the result of intrinsic variability in regional flow patterns. These midcentury events contrast with the recent Arctic-wide AO influence in the 1990s. The preponderance of evidence supports the conclusion that warm SAT anomalies in spring for the recent decade are unique in the instrumental record, both in having the greatest longitudinal extent and in their associated patterns of warm air advection.

## Abstract

This study describes winter climate during the last 500 yr for the greater Baltic Sea region through an examination of well-documented time series of ice cover, sea level pressure, and winter surface air temperatures. These time series have been the focus of previous studies, but here their covariation over different time scales is analyzed based on two modern descriptive statistical techniques, matching pursuit and wavelet analysis. Independently, 15 time periods were found during the last 500 yr with different climatic signatures with respect to winter severity, circulation patterns, and interannual variability. The onsets of these periods are presumably caused largely by perturbations within the system, although correspondences with solar and volcanic activity can be identified for certain of the periods. The Baltic region climate has changes on both centennial and decadal time scales, often with rapid transitions. Major warmer periods were the first half of the eighteenth century and the twentieth century. A common feature for warm (cold) periods is low (high) variability on shorter time scales. Century-scale variability and the modulation of interannual and decadal signals are quite diverse in the temporal records and do not suggest strong periodicities. An “event” type conceptual model therefore appears adequate for characterizing Baltic climate variability.

## Abstract

This study describes winter climate during the last 500 yr for the greater Baltic Sea region through an examination of well-documented time series of ice cover, sea level pressure, and winter surface air temperatures. These time series have been the focus of previous studies, but here their covariation over different time scales is analyzed based on two modern descriptive statistical techniques, matching pursuit and wavelet analysis. Independently, 15 time periods were found during the last 500 yr with different climatic signatures with respect to winter severity, circulation patterns, and interannual variability. The onsets of these periods are presumably caused largely by perturbations within the system, although correspondences with solar and volcanic activity can be identified for certain of the periods. The Baltic region climate has changes on both centennial and decadal time scales, often with rapid transitions. Major warmer periods were the first half of the eighteenth century and the twentieth century. A common feature for warm (cold) periods is low (high) variability on shorter time scales. Century-scale variability and the modulation of interannual and decadal signals are quite diverse in the temporal records and do not suggest strong periodicities. An “event” type conceptual model therefore appears adequate for characterizing Baltic climate variability.