On transit-time distributions in unsteady circulation models

Haine, Thomas W. N.; Zhang, H.; Waugh, Darryn W.; Holzer, Mark

doi:10.1016/j.ocemod.2007.11.004

Cited by 41 publications

(91 citation statements)

References 13 publications

(24 reference statements)

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“…Figure 9 suggests that any larger ensemble that could have practically been simulated (say, 10 or 15 members) would not have increased our confidence by a tremendous amount. Further, the 40-member simulations performed by Haine et al [8] clearly show that a much smaller number of ensemble members are necessary at times sufficiently greater than the peak. On the other hand, Fig.…”

Section: Discussionmentioning

confidence: 94%

“…The result of a single forward integration of the transport equation with an impulse boundary condition, formally referred to as the Boundary Impulse Response (BIR), can no longer be interpreted as a true probability distribution function of transit times, as is the case with steady flow. However, Haine et al [8] (hereafter referred to as HZWH08) have shown that even for unsteady flow, the BIR and TTD share the same statistical moments under certain conditions. We exploit this property to estimate the TTD as the average of a (modest sized) ensemble of BIRs, which are directly simulated in a global eddying simulation.…”

Section: Introductionmentioning

confidence: 99%

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Boundary impulse response functions in a century-long eddying global ocean simulation

2009

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Results are presented from a century-long 1/10 • global ocean simulation that included a suite of age-related passive tracers. In particular, an ensemble of five global Boundary Impulse Response functions (BIRs, which are statistically related to the more fundamental Transit Time Distributions, TTDs) was included to quantify the character of the TTD when mesoscale eddies are explicitly simulated rather than parameterized. We also seek to characterize the level of variability in water mass ventilation timescales arising from eddy motions. The statistics of the BIR timeseries are described, and it is shown that the greatest variability occurs at early times, followed by a remarkable conformity between ensemble members at longer timescales. The statistics of the first moment of the BIRs are presented, and the upper-ocean spatial distribution of the standard deviation of the first moment of the BIRs discussed. It is shown that variations in the BIR first moment with respect to the ensemble average are typically only a few percent, and that the variability slightly decreases with increasing ensemble size, implying that only a few ensemble members may be necessary for a reasonable estimate of the TTD. The completeness of the estimated TTD, i.e., the degree to which the century long BIRs capture the range of global ocean ventilation timescales is discussed, and the potential for extrapolation of the BIR to longer times is briefly explored. Several regional BIRs were also simulated in order to quantify the relative abundance of fluid parcels that originate in specific geographical locations.

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Section: Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Boundary impulse response functions in a century-long eddying global ocean simulation

2009

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“…Our approach is based on the boundary impulse response (BIR) method (e.g. Haine et al, 2008;Li et al, 2012a), generalized to transient simulations using quasi-observational winds, and is therefore more appropriately termed the Boundary Impulse (time-)Evolving Response (BIER) method.…”

Section: Discussionmentioning

confidence: 99%

“…In general, as a function of transit time τ the BIR is not equal to the age spectrum, because the τ -dependency occurs in different arguments of G. Only for stationary flow the boundary propagator is time translation invariant and depends only on the transit time τ , such that the age spectrum and BIR are equal (e.g. Haine et al, 2008). Equation (2) provides a method to calculate the boundary propagator G by using N different pulse tracers χ i (i = 1, .…”

Section: Age Spectrum Calculationmentioning

confidence: 99%

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Seasonal and inter-annual variability of lower stratospheric age of air spectra

2016

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Abstract. Trace gas transport in the lower stratosphere is investigated by analysing seasonal and inter-annual variations of the age of air spectrum -the probability distribution of stratospheric transit times. Age spectra are obtained using the Chemical Lagrangian Model of the Stratosphere (CLaMS) driven by ERA-Interim winds and total diabatic heating rates, and using a time-evolving boundary-impulseresponse (BIER) method based on multiple tracer pulses. Seasonal age spectra show large deviations from an idealized stationary uni-modal shape. Multiple modes emerge in the spectrum throughout the stratosphere, strongest at high latitudes, caused by the interplay of seasonally varying tropical upward mass flux, stratospheric transport barriers and recirculation. Inter-annual variations in transport (e.g. quasibiennial oscillation) cause significant modulations of the age spectrum shape. In fact, one particular QBO phase may determine the spectrum's mode during the following 2-3 years.

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Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed

2015

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Transport processes and pathways through many hydrodynamic systems vary over time, often driven by variations in total water storage. This paper develops a very general approach to modeling unsteady transport through an arbitrary control volume (such as a watershed) that accounts for temporal variability in the underlying transport dynamics. Controls on the selection of discharge from stored water are encapsulated in probability distributions X Q ðS T ; tÞ of age-ranked storage S T (the volume of water in storage ranked from youngest to oldest). This framework is applied to a long-term record of rainfall and streamflow chloride in a small, humid watershed at Plynlimon, UK. While a time-invariant gamma distribution for X Q produced a good fit to data, the fit was significantly improved when the distribution was allowed to vary with catchment storage. However, the variation was inverse to that of a ''well-mixed'' system where storage has a pure dilution effect. Discharge at high storage was predicted to contain a larger fraction of recent event water than at low storage. The effective volume of storage involved in transport was 3411 mm at mean catchment wetness, but declined by 71 mm per 1 mm of additional catchment storage, while the fraction of event water in discharge increased by 1.4%. This ''inverse storage effect'' is sufficient to reproduce the observed long-memory 1=f fractal spectral structure of stream chloride. Metrics quantifying the strength and direction of storage effects are proposed as useful signatures, and point toward a unified framework for observing and modeling coupled watershed flow and transport.

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On transit-time distributions in unsteady circulation models

Cited by 41 publications

References 13 publications

Boundary impulse response functions in a century-long eddying global ocean simulation

Boundary impulse response functions in a century-long eddying global ocean simulation

Seasonal and inter-annual variability of lower stratospheric age of air spectra

Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed

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