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## Abstract

The statistical properties of the oceanic finescale strain field are investigated. Strain information is derived from a set of 9000 CTD profiles from the surface to 560-m depth, obtained from the Research Platform *FLIP* in the 1986 PATCHEX Experiment. Four hundred isopycnals, with mean vertical separation *z* = 1

The instantaneous separation, Δ*z*(*t*), between isopycnal pairs is found to be statistically independent of the mean position of the pair. The separation statistics demonstrate a number of the characteristic features of a Poisson process. If the number of isopycnals found in a given fixed-depth interval is simply tallied from profile to profile, the variability in the count, when properly rescaled, is given by a Poisson distribution. Probability density functions (pdfs) of separation are well described by the classical Gamma family.

A simple mechanistic model of the strain field is proposed as a guide for interpreting the Poisson-like observations. The model approximates the vertical profile of a passive scalar quantity as a series of constant gradient segments. The depth bounds of each segment are governed by Poisson statistics. Curiously, the strain variance is not an adjustable parameter in this model. The strain variance is 0.5 when statistics are collected in an Eulerian frame. Variance has value unity if the statistics are accumulated in an isapycnal-following frame.

The model vertical wavenumber spectrum of strain is a function of a single parameter, the Poisson scale constant κ_{0}. For κ_{0} = 1.1 m^{−1}, consistent with the observations, the spectrum has *k*
^{0} form at low wavenumber. Spectral form transitions to *a* ≈ *k*
^{−1.5} slope at vertical scales smaller than about 10 m. In contrast to spectral models based on linear dynamics, here the form of the spectrum is constrained to change with changing energy density. Also, skewness, kurtosis, and higher moments of the strain process can be inferred from observations of the second moment.

The moments of inverse separation,Δ*z*
^{−1}, are useful in predicting fluctuations in the vertical gradients of passive scalar quantities θ(*z*): ∂θ/∂*z* ≡ (θ(ρ_{1}) − θ(ρ_{2}))·Δ*z*
^{−1}. A family of probability density functions (pdfs) of vertical gradients is presented as a function of the vertical differencing interval *z*_{0} = 1.1 m^{−1} from PATCHEX, the model pdfs of gradients compare excellently with temperature gradient data obtained by Gregg in the central Pacific in 1977.

Small but significant discrepancies appear between the observations and the idealized Poisson model. These are ascribed to the tendency of isopycnals to gather into a “sheets and layer” configuration. When a number of isopycnals gather into a thin sheet, the chances of finding successive isopycnals in the adjoining water (layer) is reduced. A weak predictive ability is implied that is inconsistent with a Poisson process.

## Abstract

The statistical properties of the oceanic finescale strain field are investigated. Strain information is derived from a set of 9000 CTD profiles from the surface to 560-m depth, obtained from the Research Platform *FLIP* in the 1986 PATCHEX Experiment. Four hundred isopycnals, with mean vertical separation *z* = 1

The instantaneous separation, Δ*z*(*t*), between isopycnal pairs is found to be statistically independent of the mean position of the pair. The separation statistics demonstrate a number of the characteristic features of a Poisson process. If the number of isopycnals found in a given fixed-depth interval is simply tallied from profile to profile, the variability in the count, when properly rescaled, is given by a Poisson distribution. Probability density functions (pdfs) of separation are well described by the classical Gamma family.

A simple mechanistic model of the strain field is proposed as a guide for interpreting the Poisson-like observations. The model approximates the vertical profile of a passive scalar quantity as a series of constant gradient segments. The depth bounds of each segment are governed by Poisson statistics. Curiously, the strain variance is not an adjustable parameter in this model. The strain variance is 0.5 when statistics are collected in an Eulerian frame. Variance has value unity if the statistics are accumulated in an isapycnal-following frame.

The model vertical wavenumber spectrum of strain is a function of a single parameter, the Poisson scale constant κ_{0}. For κ_{0} = 1.1 m^{−1}, consistent with the observations, the spectrum has *k*
^{0} form at low wavenumber. Spectral form transitions to *a* ≈ *k*
^{−1.5} slope at vertical scales smaller than about 10 m. In contrast to spectral models based on linear dynamics, here the form of the spectrum is constrained to change with changing energy density. Also, skewness, kurtosis, and higher moments of the strain process can be inferred from observations of the second moment.

The moments of inverse separation,Δ*z*
^{−1}, are useful in predicting fluctuations in the vertical gradients of passive scalar quantities θ(*z*): ∂θ/∂*z* ≡ (θ(ρ_{1}) − θ(ρ_{2}))·Δ*z*
^{−1}. A family of probability density functions (pdfs) of vertical gradients is presented as a function of the vertical differencing interval *z*_{0} = 1.1 m^{−1} from PATCHEX, the model pdfs of gradients compare excellently with temperature gradient data obtained by Gregg in the central Pacific in 1977.

Small but significant discrepancies appear between the observations and the idealized Poisson model. These are ascribed to the tendency of isopycnals to gather into a “sheets and layer” configuration. When a number of isopycnals gather into a thin sheet, the chances of finding successive isopycnals in the adjoining water (layer) is reduced. A weak predictive ability is implied that is inconsistent with a Poisson process.

## Abstract

This paper presents surface meteorological data and boundary layer profiles from a single meridional transect across the equator along 125°W collected during the Pan American Climate Study mooring cruise in September of 1998. These observations are unique because they occurred at the start of a cold event in the eastern tropical Pacific when the SST gradients along the equatorial front were near their climatological maximum. In addition to the anomalous cold conditions encountered near the equator, an added benefit of this limited study is the relatively high station resolution across the front. The meridional minimum in SST, and center of the cold tongue, was 20.9°C and occurred at 0.4°N. An equatorial front was located to the north where SST increased linearly to 25.5°C at 2.0°N. The atmospheric boundary layer (ABL) was stable over the cold tongue. An unstable ABL developed over the warm side of the front in less than 55 km. The unstable ABL was found at two more stations over the warm side of the front and had a height of 350–450 m. Collocated with the formation of the unstable ABL was a rapid acceleration of the surface wind field. These observations are consistent with the hypothesis that the surface wind field is modulated by stability-dependent boundary layer effects. These observations also suggest that the spatial scale of the surface wind acceleration is less than the spatial scale of the SST front.

## Abstract

This paper presents surface meteorological data and boundary layer profiles from a single meridional transect across the equator along 125°W collected during the Pan American Climate Study mooring cruise in September of 1998. These observations are unique because they occurred at the start of a cold event in the eastern tropical Pacific when the SST gradients along the equatorial front were near their climatological maximum. In addition to the anomalous cold conditions encountered near the equator, an added benefit of this limited study is the relatively high station resolution across the front. The meridional minimum in SST, and center of the cold tongue, was 20.9°C and occurred at 0.4°N. An equatorial front was located to the north where SST increased linearly to 25.5°C at 2.0°N. The atmospheric boundary layer (ABL) was stable over the cold tongue. An unstable ABL developed over the warm side of the front in less than 55 km. The unstable ABL was found at two more stations over the warm side of the front and had a height of 350–450 m. Collocated with the formation of the unstable ABL was a rapid acceleration of the surface wind field. These observations are consistent with the hypothesis that the surface wind field is modulated by stability-dependent boundary layer effects. These observations also suggest that the spatial scale of the surface wind acceleration is less than the spatial scale of the SST front.

## Abstract

Quasi-continuous depth–time observations of shear (5.5-m, 6-min resolution) and strain, (∂*η*/∂*z,* (2-m, 2.1- min resolution) obtained from the R/P *FLIP* are applied to a study of Richardson number (Ri) statistics. Data were collected off the coast of central California in the 1990 Surface Waves Processes Experiment. Observations are presented in Eulerian and in isopycnal-following frames. In both frames, shear variance is found to scale as *N*^{2}

To model the Richardson number, the detailed interrelationship between shear and strain must be specified. Two contrasting hypotheses are considered: One (H I) holds that fluctuations in the cross-isopycnal shear are independent of isopycnal separation. The other (H II) states that the cross-isopycnal velocity difference is the quantity that is independent of separation. Model probability density functions for Ri are developed under both hypotheses. The consideration of strain as well as shear in the Richardson calculation increases the probability of occurrence of both extremely low and high values of Ri. The observations confirm this general prediction. They also indicate that, while neither hypothesis is strictly correct, H II appears to be a much better approximation over the most commonly observed values of Ri.

## Abstract

Quasi-continuous depth–time observations of shear (5.5-m, 6-min resolution) and strain, (∂*η*/∂*z,* (2-m, 2.1- min resolution) obtained from the R/P *FLIP* are applied to a study of Richardson number (Ri) statistics. Data were collected off the coast of central California in the 1990 Surface Waves Processes Experiment. Observations are presented in Eulerian and in isopycnal-following frames. In both frames, shear variance is found to scale as *N*^{2}

To model the Richardson number, the detailed interrelationship between shear and strain must be specified. Two contrasting hypotheses are considered: One (H I) holds that fluctuations in the cross-isopycnal shear are independent of isopycnal separation. The other (H II) states that the cross-isopycnal velocity difference is the quantity that is independent of separation. Model probability density functions for Ri are developed under both hypotheses. The consideration of strain as well as shear in the Richardson calculation increases the probability of occurrence of both extremely low and high values of Ri. The observations confirm this general prediction. They also indicate that, while neither hypothesis is strictly correct, H II appears to be a much better approximation over the most commonly observed values of Ri.

## Abstract

Gregg has provided observational evidence that averaged estimates of dissipation, *ϵ*, vary approximately as the square of the internal wave field energy level *ϵ* ∼ *E*
^{2}. He notes that the finding is consistent with a specific model for energy transfer in the internal wave field proposed by Henyey et al. If it is also consistent with a purely statistical breaking model, based on the random superposition of independent waves, support for any particular dynamic scenario vanishes.

However, most previous statistical models of the wave breaking process have demonstrated an extreme sensitivity of dissipation to energy level. Doubling *E* results in an increase of dissipation by a factor of 2 × 10^{5} in the early model of Garrett and Munk and by 10^{3} in the later model of Desaubies and Smith.

These mixing models are revisited, attempting to reconcile their predictions with the observations of Gregg. An extensive Doppler sonar (5.5-m vertical resolution) and CTD (5400 profiles to 420 m) dataset, obtained from the Research Platform *FLIP* during the SWAPP experiment, is applied to the problem. A model for the probability density function (pdf) of Richardson number is developed (Part I of this work), accounting for both shear and strain variability. This pdf is an explicit function of the vertical differencing scale, *z*

When this finite difference approach is pursued, dissipation levels are found to vary nearly as *E*
^{2} for a variety of contrasting internal wave spectral models. Gregg’s constant of proportionality is recovered, provided independent realizations of the Richardson number process are said to occur every 10–14 hours.

## Abstract

Gregg has provided observational evidence that averaged estimates of dissipation, *ϵ*, vary approximately as the square of the internal wave field energy level *ϵ* ∼ *E*
^{2}. He notes that the finding is consistent with a specific model for energy transfer in the internal wave field proposed by Henyey et al. If it is also consistent with a purely statistical breaking model, based on the random superposition of independent waves, support for any particular dynamic scenario vanishes.

However, most previous statistical models of the wave breaking process have demonstrated an extreme sensitivity of dissipation to energy level. Doubling *E* results in an increase of dissipation by a factor of 2 × 10^{5} in the early model of Garrett and Munk and by 10^{3} in the later model of Desaubies and Smith.

These mixing models are revisited, attempting to reconcile their predictions with the observations of Gregg. An extensive Doppler sonar (5.5-m vertical resolution) and CTD (5400 profiles to 420 m) dataset, obtained from the Research Platform *FLIP* during the SWAPP experiment, is applied to the problem. A model for the probability density function (pdf) of Richardson number is developed (Part I of this work), accounting for both shear and strain variability. This pdf is an explicit function of the vertical differencing scale, *z*

When this finite difference approach is pursued, dissipation levels are found to vary nearly as *E*
^{2} for a variety of contrasting internal wave spectral models. Gregg’s constant of proportionality is recovered, provided independent realizations of the Richardson number process are said to occur every 10–14 hours.

## Abstract

This study demonstrates that intraseasonal perturbations in sea surface temperature (SST′) in the western Pacific warm pool is very sensitive to the structure, as well as other characteristics, of the Madden–Julian oscillation (MJO). SST′ is simulated using a one-dimensional ocean mixed-layer model and idealized MJO surface forcing that mimics observations. The amplitude and phase of simulated SST′ and its sensitivity to precipitation all depend on the structure of the MJO. It is concluded that a realistic structure of simulated MJO in a coupled model is as vital as realistic phase speed and zonal scale to correctly interpreting the effect of air–sea interaction on the MJO.

## Abstract

This study demonstrates that intraseasonal perturbations in sea surface temperature (SST′) in the western Pacific warm pool is very sensitive to the structure, as well as other characteristics, of the Madden–Julian oscillation (MJO). SST′ is simulated using a one-dimensional ocean mixed-layer model and idealized MJO surface forcing that mimics observations. The amplitude and phase of simulated SST′ and its sensitivity to precipitation all depend on the structure of the MJO. It is concluded that a realistic structure of simulated MJO in a coupled model is as vital as realistic phase speed and zonal scale to correctly interpreting the effect of air–sea interaction on the MJO.

## Abstract

The tropical response to a localized thermal forcing with approximately 45-day period is investigated for several models of increasing complexity consisting of two equivalent shallow water system and two fully stratified systems. The fully stratified models appear to be able to reproduce a number of observed features of the tropical 40–50 day oscillation including the modulation of the subtropical jet and the eastward and poleward propagation of zonal wind anomalies.

## Abstract

The tropical response to a localized thermal forcing with approximately 45-day period is investigated for several models of increasing complexity consisting of two equivalent shallow water system and two fully stratified systems. The fully stratified models appear to be able to reproduce a number of observed features of the tropical 40–50 day oscillation including the modulation of the subtropical jet and the eastward and poleward propagation of zonal wind anomalies.

## Abstract

The linear, zonally symmetric modes of the basic state of a Hadley cell are examined. We find that the inclusion of the divergent basic state leads to the formation of a new class of slowly oscillating modes, some of which have periods in the range of 40–50 days. The modes have many features in common with the observed tropical 40–50-day oscillation; however, an explanation for the observed fluctuations in convective cloudiness remains a topic for future work.

## Abstract

The linear, zonally symmetric modes of the basic state of a Hadley cell are examined. We find that the inclusion of the divergent basic state leads to the formation of a new class of slowly oscillating modes, some of which have periods in the range of 40–50 days. The modes have many features in common with the observed tropical 40–50-day oscillation; however, an explanation for the observed fluctuations in convective cloudiness remains a topic for future work.

## Abstract

For some years, investigators have made measurements of downwelling longwave irradiance with the Eppley Precision Infrared Radiometer (PIR), recording the values of thermopile voltage and body and dome thermistor resistances and combining them in data processing. Part I of this paper reviews previous work on the processing equation and presents an improved equation. It establishes that the standard single-output Eppley has an inherent uncertainty of 5%. By measuring the three possible outputs separately and comparing them in the improved equation, the inherent accuracy can be improved to 1.5%. Part II presents a method of calibrating the Eppley PIR for the three-output equation using an easily constructed blackbody cavity in a temperature bath capable of a 0°–50°C temperature range. Calibration of PIR thermistors is recommended since occasionally one is found out of specifications.

An outdoor comparison of 15 PIRs calibrated with the technique was carried out in groups of four, with one PIR used in all of the groups as a standard of comparison. The mean differences and 1-min standard deviations between 12 individual PIRs and this standard over comparison periods of 10–22 days were less than 6.0 and 11 W m^{−2}, respectively. Only two of the PIRs and a standard single-output Eppley PIR (calibrated by Eppley) had mean differences and standard deviations greater than 7 and 11 W m^{−2}, respectively. Although the new calibration procedure yielded consistent results in the mean, at times the longwave measurements diverged by up to 45 W m^{−2} for several hours. Some of these events are attributable to confirmed pinholes in the dome filter, but others are left unexplained.

## Abstract

For some years, investigators have made measurements of downwelling longwave irradiance with the Eppley Precision Infrared Radiometer (PIR), recording the values of thermopile voltage and body and dome thermistor resistances and combining them in data processing. Part I of this paper reviews previous work on the processing equation and presents an improved equation. It establishes that the standard single-output Eppley has an inherent uncertainty of 5%. By measuring the three possible outputs separately and comparing them in the improved equation, the inherent accuracy can be improved to 1.5%. Part II presents a method of calibrating the Eppley PIR for the three-output equation using an easily constructed blackbody cavity in a temperature bath capable of a 0°–50°C temperature range. Calibration of PIR thermistors is recommended since occasionally one is found out of specifications.

An outdoor comparison of 15 PIRs calibrated with the technique was carried out in groups of four, with one PIR used in all of the groups as a standard of comparison. The mean differences and 1-min standard deviations between 12 individual PIRs and this standard over comparison periods of 10–22 days were less than 6.0 and 11 W m^{−2}, respectively. Only two of the PIRs and a standard single-output Eppley PIR (calibrated by Eppley) had mean differences and standard deviations greater than 7 and 11 W m^{−2}, respectively. Although the new calibration procedure yielded consistent results in the mean, at times the longwave measurements diverged by up to 45 W m^{−2} for several hours. Some of these events are attributable to confirmed pinholes in the dome filter, but others are left unexplained.

## Abstract

Solar radiative heating errors in buoy-mounted, naturally ventilated air temperature sensors are examined. Data from sensors with multiplate radiation shields and collocated, fan-aspirated air temperature sensors from three buoy deployments during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment) and the Arabian Sea Mixed Layer Dynamics Experiment are used to describe the errors in the naturally ventilated measurements. The naturally ventilated sensors have mean daytime errors of 0.27°C and maximum instantaneous errors of 3.4°C. The errors are at times larger than the difference between the air and sea surface temperatures. These errors lead to mean daytime biases in sensible and latent heat fluxes of 1–4 W m^{−2} and instantaneous errors up to 22 W m^{−2}. The heating errors increase with increasing shortwave radiation and diminish with increasing wind speed. The radiative heating is also found to be a function of sun elevation with maximum heating errors occurring at elevations of approximately 45°. A simple model of sensor heating that balances the radiative heating with convective and conductive cooling is presented. This model can be used with empirically determined coefficients and observations of wind speed and shortwave radiation to quantify the radiative heating errors in naturally ventilated air temperature sensors.

## Abstract

Solar radiative heating errors in buoy-mounted, naturally ventilated air temperature sensors are examined. Data from sensors with multiplate radiation shields and collocated, fan-aspirated air temperature sensors from three buoy deployments during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment) and the Arabian Sea Mixed Layer Dynamics Experiment are used to describe the errors in the naturally ventilated measurements. The naturally ventilated sensors have mean daytime errors of 0.27°C and maximum instantaneous errors of 3.4°C. The errors are at times larger than the difference between the air and sea surface temperatures. These errors lead to mean daytime biases in sensible and latent heat fluxes of 1–4 W m^{−2} and instantaneous errors up to 22 W m^{−2}. The heating errors increase with increasing shortwave radiation and diminish with increasing wind speed. The radiative heating is also found to be a function of sun elevation with maximum heating errors occurring at elevations of approximately 45°. A simple model of sensor heating that balances the radiative heating with convective and conductive cooling is presented. This model can be used with empirically determined coefficients and observations of wind speed and shortwave radiation to quantify the radiative heating errors in naturally ventilated air temperature sensors.

## Abstract

In recent years there has been a great deal of interest in a quasi-periodic tropical oscillation of zonal winds, which was first reported by Madden and Julian. An attempt to determine the temporal variation of the oscillation parameters is presented here. Using a 4-year duration global time series and a 25-year station time series, we find that although the nonseasonal variations are large, any seasonal cycle in the oscillation amplitude and frequency must be very small. The small seasonal signal in the oscillation frequency seems to argue against explanations for the time scale based on Doppler-shifted traveling waves.

## Abstract

In recent years there has been a great deal of interest in a quasi-periodic tropical oscillation of zonal winds, which was first reported by Madden and Julian. An attempt to determine the temporal variation of the oscillation parameters is presented here. Using a 4-year duration global time series and a 25-year station time series, we find that although the nonseasonal variations are large, any seasonal cycle in the oscillation amplitude and frequency must be very small. The small seasonal signal in the oscillation frequency seems to argue against explanations for the time scale based on Doppler-shifted traveling waves.