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- Author or Editor: Jochem Marotzke x

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## Abstract

Boundary mixing is implemented in an ocean general circulation model such that the vertical mixing coefficient *k*
_{
υ
} is nonzero only near side boundaries and in convection regions. The model is used in a highly idealized configuration with no wind forcing and very nearly fixed surface density to investigate the three-dimensional dynamics of the thermohaline circulation. For *k*
_{
υ
} = 20 × 10^{−4} m^{2} s^{−1} and lower, the meridional overturning strength to great accuracy is proportional to *k*
^{2/3}
_{
υ
}
*k*
^{1/2}
_{
υ
}

For *k*
_{
υ
} = 30 × 10^{−4} m^{2} s^{−1} and higher, no steady solutions have been found; the meridional overturning oscillates on a timescale of about 25 years. A time-averaged thermally direct overturning cell is not supported dynamically because convection extends longitudinally across the entire basin, and upwelling near the western boundary does not lead to densities higher than at the eastern boundary.

Assuming uniform upwelling in the west, level isopycnals near the equator, and level isopycnals along the eastern boundary south of the outcropping latitude permits the analytic determination of convection depth at the eastern wall and hence the density difference between the eastern and western walls. This difference is at most one-quarter the surface density difference between high and low latitudes, and agrees in magnitude and latitudinal dependence with the numerical experiments. Scaling arguments estimate overturning strength as of the order of 10 × 10^{6} m^{3} s^{−1} and confirm the 2/3 power dependence on *k*
_{
υ
}. The derivation also gives a dependence of overturning strength with latitude that agrees qualitatively with the numerical results. The scaling for the dependence of meridional heat transport on latitude agrees well with the model results; scaling for heat transport amplitude agrees less well but correctly predicts a weaker dependence on *k*
_{
υ
} than maximum overturning.

## Abstract

Boundary mixing is implemented in an ocean general circulation model such that the vertical mixing coefficient *k*
_{
υ
} is nonzero only near side boundaries and in convection regions. The model is used in a highly idealized configuration with no wind forcing and very nearly fixed surface density to investigate the three-dimensional dynamics of the thermohaline circulation. For *k*
_{
υ
} = 20 × 10^{−4} m^{2} s^{−1} and lower, the meridional overturning strength to great accuracy is proportional to *k*
^{2/3}
_{
υ
}
*k*
^{1/2}
_{
υ
}

For *k*
_{
υ
} = 30 × 10^{−4} m^{2} s^{−1} and higher, no steady solutions have been found; the meridional overturning oscillates on a timescale of about 25 years. A time-averaged thermally direct overturning cell is not supported dynamically because convection extends longitudinally across the entire basin, and upwelling near the western boundary does not lead to densities higher than at the eastern boundary.

Assuming uniform upwelling in the west, level isopycnals near the equator, and level isopycnals along the eastern boundary south of the outcropping latitude permits the analytic determination of convection depth at the eastern wall and hence the density difference between the eastern and western walls. This difference is at most one-quarter the surface density difference between high and low latitudes, and agrees in magnitude and latitudinal dependence with the numerical experiments. Scaling arguments estimate overturning strength as of the order of 10 × 10^{6} m^{3} s^{−1} and confirm the 2/3 power dependence on *k*
_{
υ
}. The derivation also gives a dependence of overturning strength with latitude that agrees qualitatively with the numerical results. The scaling for the dependence of meridional heat transport on latitude agrees well with the model results; scaling for heat transport amplitude agrees less well but correctly predicts a weaker dependence on *k*
_{
υ
} than maximum overturning.

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## Abstract

The length of time an ocean model and its adjoint should be integrated in determining a steady state compatible with observed data is investigated. The starting point is based upon a suggestion that only one time step is required. This method fails to converge to an acceptable solution when applied to a general circulation model (GCM) of the North Atlantic. Using a very coarse resolution GCM in an idealized geometry, the problem is traced to the interplay of convective adjustment and the very short integration time.

The general assimilation technique is explored using a very simple model, a linear first-order equation with forcing and damping. The model is unable to provide a dynamical coupling between the forcing and the model response, owing to a mismatch of integration time and adjustment time scale. Coupling can be enforced in the simple linear model through a careful choice of weighting factors, a strategy excluded in the GCM due to the presence of very fast processes like convective adjustment. An integration over a sufficiently long time can avoid the problems encountered. Experiments with the idealized GCM prove successful for longer integrations, and a tentative upper limit of 50 years is given for inversions aiming at the main thermocline structure.

## Abstract

The length of time an ocean model and its adjoint should be integrated in determining a steady state compatible with observed data is investigated. The starting point is based upon a suggestion that only one time step is required. This method fails to converge to an acceptable solution when applied to a general circulation model (GCM) of the North Atlantic. Using a very coarse resolution GCM in an idealized geometry, the problem is traced to the interplay of convective adjustment and the very short integration time.

The general assimilation technique is explored using a very simple model, a linear first-order equation with forcing and damping. The model is unable to provide a dynamical coupling between the forcing and the model response, owing to a mismatch of integration time and adjustment time scale. Coupling can be enforced in the simple linear model through a careful choice of weighting factors, a strategy excluded in the GCM due to the presence of very fast processes like convective adjustment. An integration over a sufficiently long time can avoid the problems encountered. Experiments with the idealized GCM prove successful for longer integrations, and a tentative upper limit of 50 years is given for inversions aiming at the main thermocline structure.

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## Abstract

Three different convective adjustment schemes are employed in the GFDL GCM to investigate if the spontaneous collapse of the thermohaline circulation under mixed boundary conditions, as observed by F. Bryan, depends on the parameterization of convective overturning. It is found that both a procedure guaranteeing complete static stability and Cox's implicit vertical diffusion scheme avoid the spontaneous collapse. Both schemes are also insensitive to the choice of time step, whereas the standard GFDL convection algorithm in conjunction with mixed boundary conditions produces results that differ qualitatively from each other when different time steps are used.

## Abstract

Three different convective adjustment schemes are employed in the GFDL GCM to investigate if the spontaneous collapse of the thermohaline circulation under mixed boundary conditions, as observed by F. Bryan, depends on the parameterization of convective overturning. It is found that both a procedure guaranteeing complete static stability and Cox's implicit vertical diffusion scheme avoid the spontaneous collapse. Both schemes are also insensitive to the choice of time step, whereas the standard GFDL convection algorithm in conjunction with mixed boundary conditions produces results that differ qualitatively from each other when different time steps are used.

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## Abstract

A general circulation model of the Indian Ocean is fitted to monthly averaged climatological temperatures, salinities, and surface fluxes using the adjoint method. Interannual variability is minimized by penalizing the temporal drift from one seasonal cycle to another during a two-year integration. The resultant meridional overturning and heat transport display large seasonal variations, with maximum amplitudes of 18 and 22 (× 10^{6} m^{3} s^{−1}) for the overturning and 1.8 and 1.4 (× 10^{15} W) for heat transport near 10°S and 10°N, respectively. A dynamical decomposition of the overturning and heat transport shows that the time-varying Ekman flow plus its barotropic compensation can explain a large part of the seasonal variations in overturning and heat transport. The maximum variations at 10°N and 10°S are associated with monsoon reversal over the northern Indian Ocean and changes of the easterlies over the southern Indian Ocean. An external mode with variable topography has a moderate contribution where the Somali Current and the corresponding gyre reverse direction seasonally. Contribution from vertical shear (thermal wind and ageostrophic shear) is dominant near the southern boundary and large near the Somali Current latitudes. The dominant balance in the zonally integrated heat budget is between heat storage change and heat transport convergence except south of 15°S.

Optimization with seasonal forcings improves estimates of sea surface temperatures, but the annual average overturning and heat transport are very similar to previous results with annual mean forcings. The annual average heat transport consists of roughly equal contributions from time-mean and time-varying fields of meridional velocities and temperatures in the northern Indian Ocean, indicating a significant rectification to the heat transport due to the time-varying fields. The time-mean and time-varying contributions are primarily due to the overturning and horizontal gyre, respectively.

Inclusion of TOPEX data enhances the seasonal cycles of the estimated overturning and heat transport in the central Indian Ocean significantly and improves the estimated equatorial zonal flows but leads to unrealistic estimates of the velocity structure near the Indonesian Throughflow region, most likely owing to the deficiencies in the lateral boundary conditions.

## Abstract

A general circulation model of the Indian Ocean is fitted to monthly averaged climatological temperatures, salinities, and surface fluxes using the adjoint method. Interannual variability is minimized by penalizing the temporal drift from one seasonal cycle to another during a two-year integration. The resultant meridional overturning and heat transport display large seasonal variations, with maximum amplitudes of 18 and 22 (× 10^{6} m^{3} s^{−1}) for the overturning and 1.8 and 1.4 (× 10^{15} W) for heat transport near 10°S and 10°N, respectively. A dynamical decomposition of the overturning and heat transport shows that the time-varying Ekman flow plus its barotropic compensation can explain a large part of the seasonal variations in overturning and heat transport. The maximum variations at 10°N and 10°S are associated with monsoon reversal over the northern Indian Ocean and changes of the easterlies over the southern Indian Ocean. An external mode with variable topography has a moderate contribution where the Somali Current and the corresponding gyre reverse direction seasonally. Contribution from vertical shear (thermal wind and ageostrophic shear) is dominant near the southern boundary and large near the Somali Current latitudes. The dominant balance in the zonally integrated heat budget is between heat storage change and heat transport convergence except south of 15°S.

Optimization with seasonal forcings improves estimates of sea surface temperatures, but the annual average overturning and heat transport are very similar to previous results with annual mean forcings. The annual average heat transport consists of roughly equal contributions from time-mean and time-varying fields of meridional velocities and temperatures in the northern Indian Ocean, indicating a significant rectification to the heat transport due to the time-varying fields. The time-mean and time-varying contributions are primarily due to the overturning and horizontal gyre, respectively.

Inclusion of TOPEX data enhances the seasonal cycles of the estimated overturning and heat transport in the central Indian Ocean significantly and improves the estimated equatorial zonal flows but leads to unrealistic estimates of the velocity structure near the Indonesian Throughflow region, most likely owing to the deficiencies in the lateral boundary conditions.

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## Abstract

A general circulation model with a highly idealized geometry is used to investigate which fundamentally different equilibria of the global thermohaline circulation may exist. The model comprises two identical basins representing the Atlantic and Pacific oceans, which are connected by a circumpolar channel in the south. The model circulation is driven, in addition to wind forcing by restoring the sea surface temperature to prescribed values and specified freshwater fluxes in the surface salinity budget (mixed boundary conditions). The boundary conditions are symmetric with respect to the equator and identical for both oceans.

Four fundamentally different, stable steady states are found under the same set of boundary conditions. Two of the equilibria show both oceans in the same state, with high-altitude deep-water formation occuring either in both northern or in both southern oceans, respectively. Two additional equilibria exist in which the thermohaline circulations of the basins differ fundamentally from each other: one ocean forms deep water at northern high latitudes, while the other has a much weaker circulation with sinking in the Southern Hemisphere. One of these equilibria qualitatively corresponds to today's global thermohaline circulation pattern (conveyor belt).

It is demonstrated that a transition from one equilibrium to another can be accomplished by relatively small differences in the freshwater fluxes. The preference and sensitivity of the steady states depends critically on the freshwater forcing applied.

## Abstract

A general circulation model with a highly idealized geometry is used to investigate which fundamentally different equilibria of the global thermohaline circulation may exist. The model comprises two identical basins representing the Atlantic and Pacific oceans, which are connected by a circumpolar channel in the south. The model circulation is driven, in addition to wind forcing by restoring the sea surface temperature to prescribed values and specified freshwater fluxes in the surface salinity budget (mixed boundary conditions). The boundary conditions are symmetric with respect to the equator and identical for both oceans.

Four fundamentally different, stable steady states are found under the same set of boundary conditions. Two of the equilibria show both oceans in the same state, with high-altitude deep-water formation occuring either in both northern or in both southern oceans, respectively. Two additional equilibria exist in which the thermohaline circulations of the basins differ fundamentally from each other: one ocean forms deep water at northern high latitudes, while the other has a much weaker circulation with sinking in the Southern Hemisphere. One of these equilibria qualitatively corresponds to today's global thermohaline circulation pattern (conveyor belt).

It is demonstrated that a transition from one equilibrium to another can be accomplished by relatively small differences in the freshwater fluxes. The preference and sensitivity of the steady states depends critically on the freshwater forcing applied.

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## Abstract

An idealized three-dimensional model of buoyancy-driven flow in a single hemisphere is used to investigate the relationship between the meridional overturning and the efficiency by which convective mixing eliminates static instability. In the “fast” limit (mixing timescale hours to weeks), the meridional overturning is not rate limited by the efficiency of convective mixing. If convective mixing is made less efficient, the model’s meridional overturning strength *increases.* Moreover, the dominant downwelling occurs not at the highest surface density;hence the deep ocean is relatively buoyant. The numerical results are explained by the different influences of convective mixing and downward advection on the deep-ocean heat budget; they underscore the fundamentally three-dimensional nature of the meridional overturning. In addition, the narrowness of deep downwelling is related to the geostrophic dynamics of deep temperature anomalies near the eastern wall. The model results presented here are in contrast to the expectation that deep-water formation by convective mixing is a necessary, if not rate-limiting, ingredient to the existence of a thermohaline circulation.

## Abstract

An idealized three-dimensional model of buoyancy-driven flow in a single hemisphere is used to investigate the relationship between the meridional overturning and the efficiency by which convective mixing eliminates static instability. In the “fast” limit (mixing timescale hours to weeks), the meridional overturning is not rate limited by the efficiency of convective mixing. If convective mixing is made less efficient, the model’s meridional overturning strength *increases.* Moreover, the dominant downwelling occurs not at the highest surface density;hence the deep ocean is relatively buoyant. The numerical results are explained by the different influences of convective mixing and downward advection on the deep-ocean heat budget; they underscore the fundamentally three-dimensional nature of the meridional overturning. In addition, the narrowness of deep downwelling is related to the geostrophic dynamics of deep temperature anomalies near the eastern wall. The model results presented here are in contrast to the expectation that deep-water formation by convective mixing is a necessary, if not rate-limiting, ingredient to the existence of a thermohaline circulation.

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## Abstract

The wind-driven circulation adds a significant contribution to poleward meridional heat transport. Numerical models indicate that equatorward of *ϕ*
_{0}, the zero wind stress latitude (30° lat), most of the wind-induced heat transport is due to the meridional overturning circulation known as the subtropical cell. The volume transport of this overturning is approximately given by the surface Ekman transport. By combining this fact with the assumption that Ekman-downwelled water approximately follows isotherms except near the equator, the authors derive an expression for the meridional heat transport that depends only on wind stress and surface temperature. The expression is confirmed in numerical models with simplified geometry and forcing. Numerical results indicate that peak heat transport due to the subtropical cell is about 0.1 × 10^{15} W for the North Atlantic and 0.3 × 10^{15} W for the North Pacific.

## Abstract

The wind-driven circulation adds a significant contribution to poleward meridional heat transport. Numerical models indicate that equatorward of *ϕ*
_{0}, the zero wind stress latitude (30° lat), most of the wind-induced heat transport is due to the meridional overturning circulation known as the subtropical cell. The volume transport of this overturning is approximately given by the surface Ekman transport. By combining this fact with the assumption that Ekman-downwelled water approximately follows isotherms except near the equator, the authors derive an expression for the meridional heat transport that depends only on wind stress and surface temperature. The expression is confirmed in numerical models with simplified geometry and forcing. Numerical results indicate that peak heat transport due to the subtropical cell is about 0.1 × 10^{15} W for the North Atlantic and 0.3 × 10^{15} W for the North Pacific.

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## Abstract

A coarse resolution, three-dimensional numerical model is used to study how external parameters control the existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin. Initially, the meridional surface density gradient is directly set to be larger in a “dominant” hemisphere than in a “subordinate” hemisphere. The two-hemisphere system has a broader thermocline and weaker upwelling than the same model with the dominant hemisphere only. This behavior is in accord with classical scaling arguments, providing that the continuity equation is employed, rather than the linear vorticity equation.

The dominant overturning cell, analogous to North Atlantic Deep Water formation, is primarily controlled by the surface density contrast in the dominant hemisphere, which in turn is largely set by temperature. Consequently, in experiments with mixed boundary conditions, the dominant cell strength is relatively insensitive to the magnitude *Q*
_{
S
} of the salinity forcing. However, *Q*
_{
S
} strongly influences subordinate hemisphere properties, including the volume transport of a shallow overturning cell and the meridional extent of a tongue of low-salinity intermediate water reminiscent of Antarctic Intermediate Water.

The minimum *Q*
_{
S
} is identified for which the steady, asymmetric flow is stable; below this value, a steady, equatorially symmetric, temperature-dominated overturning occurs. For high salt flux, the asymmetric circulation becomes oscillatory and eventually gives way to an unsteady, symmetric, salt-dominated overturning. For given boundary conditions, it is possible to have at least three different asymmetric states, with significantly different large-scale properties. An expression for the meridional salt transport allows one to roughly predict the surface salinity and density profile and stability of the asymmetric state as a function of *Q*
_{
S
} and other external parameters.

## Abstract

A coarse resolution, three-dimensional numerical model is used to study how external parameters control the existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin. Initially, the meridional surface density gradient is directly set to be larger in a “dominant” hemisphere than in a “subordinate” hemisphere. The two-hemisphere system has a broader thermocline and weaker upwelling than the same model with the dominant hemisphere only. This behavior is in accord with classical scaling arguments, providing that the continuity equation is employed, rather than the linear vorticity equation.

The dominant overturning cell, analogous to North Atlantic Deep Water formation, is primarily controlled by the surface density contrast in the dominant hemisphere, which in turn is largely set by temperature. Consequently, in experiments with mixed boundary conditions, the dominant cell strength is relatively insensitive to the magnitude *Q*
_{
S
} of the salinity forcing. However, *Q*
_{
S
} strongly influences subordinate hemisphere properties, including the volume transport of a shallow overturning cell and the meridional extent of a tongue of low-salinity intermediate water reminiscent of Antarctic Intermediate Water.

The minimum *Q*
_{
S
} is identified for which the steady, asymmetric flow is stable; below this value, a steady, equatorially symmetric, temperature-dominated overturning occurs. For high salt flux, the asymmetric circulation becomes oscillatory and eventually gives way to an unsteady, symmetric, salt-dominated overturning. For given boundary conditions, it is possible to have at least three different asymmetric states, with significantly different large-scale properties. An expression for the meridional salt transport allows one to roughly predict the surface salinity and density profile and stability of the asymmetric state as a function of *Q*
_{
S
} and other external parameters.

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## Abstract

A theoretical analysis of the interactions between atmospheric meridional transports and the thermohaline circulation is presented, using a four-box ocean-atmosphere model in one hemisphere. The model is a simplified version of that developed by Nakamura Stone, and Marotzke and is amenable to analytical solutions. The ocean model is Stommel's; the atmospheric model gives the surface heat and freshwater fluxes as residuals of the atmospheric energy and moisture budgets, assumed in balance. Radiation at the top of the atmosphere depends linearly on surface temperature; atmospheric meridional heat and moisture transports are proportional to the meridional temperature gradient.

A Newtonian cooling law is derived for differential surface heat flux. The restoring coefficient is proportional to the efficiency of atmospheric transports and inversely proportional to the relative ocean area compared to total surface area. Surface freshwater flux increases with increasing temperature gradient and is inversely proportional to the ratio of ocean area to catchment area. The range of stable solutions with high-latitude sinking is smaller than in related, uncoupled box models due to the dependence of freshwater flux on the temperature gradient, which leads to a positive feedback with the thermohaline circulation. A strong control of the temperature gradient by atmospheric transports enhances the positive feedback between the salinity gradient and thermohaline Circulation simultaneously, it weakens the positive feedback between atmospheric moisture transport and the thermohaline circulation.

Overestimating the atmospheric moisture transport and underestimating oceanic mass transport both artificially destabilize the high-latitude sinking state. Overestimating the atmospheric heat transport and hence the Newtonian restoring coefficient can be artificially stabilizing or destabilizing. These erroneous sensitivities ate not alleviated if flux adjustments are added to obtain the correct mean climate, and then held fixed in climate change experiments. We derive alternate flux adjustment schemes, which do preserve the model's stability properties for particular sources of error.

## Abstract

A theoretical analysis of the interactions between atmospheric meridional transports and the thermohaline circulation is presented, using a four-box ocean-atmosphere model in one hemisphere. The model is a simplified version of that developed by Nakamura Stone, and Marotzke and is amenable to analytical solutions. The ocean model is Stommel's; the atmospheric model gives the surface heat and freshwater fluxes as residuals of the atmospheric energy and moisture budgets, assumed in balance. Radiation at the top of the atmosphere depends linearly on surface temperature; atmospheric meridional heat and moisture transports are proportional to the meridional temperature gradient.

A Newtonian cooling law is derived for differential surface heat flux. The restoring coefficient is proportional to the efficiency of atmospheric transports and inversely proportional to the relative ocean area compared to total surface area. Surface freshwater flux increases with increasing temperature gradient and is inversely proportional to the ratio of ocean area to catchment area. The range of stable solutions with high-latitude sinking is smaller than in related, uncoupled box models due to the dependence of freshwater flux on the temperature gradient, which leads to a positive feedback with the thermohaline circulation. A strong control of the temperature gradient by atmospheric transports enhances the positive feedback between the salinity gradient and thermohaline Circulation simultaneously, it weakens the positive feedback between atmospheric moisture transport and the thermohaline circulation.

Overestimating the atmospheric moisture transport and underestimating oceanic mass transport both artificially destabilize the high-latitude sinking state. Overestimating the atmospheric heat transport and hence the Newtonian restoring coefficient can be artificially stabilizing or destabilizing. These erroneous sensitivities ate not alleviated if flux adjustments are added to obtain the correct mean climate, and then held fixed in climate change experiments. We derive alternate flux adjustment schemes, which do preserve the model's stability properties for particular sources of error.

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## Abstract

The authors identify spatial and temporal scales in a one-dimensional linear, diffusive atmospheric energy balance model coupled everywhere to a slab mixed layer of fixed depth. Mathematically, the model is identical to a heat conducting rod, which over its entire length both radiates and is in contact with a large but finite“reservoir.” Three characteristic timescales mark, respectively, the atmosphere’s adjustment to a sea surface temperature (SST) anomaly, the decay of a pointwise SST anomaly, and the radiative decay of a large-scale SST anomaly. The first and the third of these timescales are associated with diffusive length scales characterizing, respectively, the distance over which heat is diffused in the atmosphere before being lost to the ocean beneath, and the distance over which heat is diffused in the coupled system before being radiated to space. For spatial scales between the two diffusive lengths, the SST anomaly does not decay exponentially but with the square root of time; this regime has not previously been identified. Apparent discrepancies between published discussions of diffusive length scales are reconciled.

## Abstract

The authors identify spatial and temporal scales in a one-dimensional linear, diffusive atmospheric energy balance model coupled everywhere to a slab mixed layer of fixed depth. Mathematically, the model is identical to a heat conducting rod, which over its entire length both radiates and is in contact with a large but finite“reservoir.” Three characteristic timescales mark, respectively, the atmosphere’s adjustment to a sea surface temperature (SST) anomaly, the decay of a pointwise SST anomaly, and the radiative decay of a large-scale SST anomaly. The first and the third of these timescales are associated with diffusive length scales characterizing, respectively, the distance over which heat is diffused in the atmosphere before being lost to the ocean beneath, and the distance over which heat is diffused in the coupled system before being radiated to space. For spatial scales between the two diffusive lengths, the SST anomaly does not decay exponentially but with the square root of time; this regime has not previously been identified. Apparent discrepancies between published discussions of diffusive length scales are reconciled.