Ulrike Wacker

Clumped isotope analysis of carbonates: comparison of two different acid digestion techniques

RATIONALE The kinetic nature of the phosphoric acid digestion reaction enables clumped isotope analysis of carbonates using gas source isotope ratio mass spectrometry (IRMS). In most laboratories acid digestions are performed at 25°C in sealed vessels or at 90°C in a common acid bath. Here we show that different Δ47 results are obtained depending on the digestion technique employed. METHODS Several replicates of a biogenic aragonite and NBS 19 were reacted with 104% H3 PO4 in sealed vessels at 25°C and at 90°C using a common acid bath. The sample size varied between 4 mg and 14 mg. Purification methods that are standard for clumped isotope analyses were applied to the evolved CO2 before measuring the abundances of masses 44 to 49 relative to a reference gas by IRMS. RESULTS A systematic trend to lower and more consistent Δ47 values is observed for reactions at 25°C if the sample size is increased. We suggest that secondary re-equilibration of evolved CO2 or reaction intermediates with free water molecules preferentially occurs for relatively small samples (4-7 mg), finally yielding elevated Δ47 values compared with >7 mg aliquots. In contrast, no such sample size effect on Δ47 values is observed for carbonates that are digested at 90°C using the common acid bath. CONCLUSIONS The determination of Δ47 values of carbonate samples smaller than 7 mg becomes more precise and accurate if digestions are performed at 90°C. Based on our results we propose that the difference in phosphoric acid fractionation factor between 25°C and 90°C is 0.07‰ for both calcite and aragonite.

Evolution of rain water profiles resulting from pure sedimentation: Spectral vs. parameterized description

The paper focuses on a comparison of solutions of the budget equations for specific moments of a hydrometeor size distribution, simplified to the problem of pure drop sedimentation, as following from models with a one-moment or a two-moment parameterization of microphysical processes and from a reference model based on spectral treatment of sedimentation. The solutions for the transient vertical profiles of liquid water content show remarkable differences in their spatial structure: starting from an idealized, discontinuous initial profile in form of a square wave, shock and rarefaction waves evolve in the parameterized models, while the reference solution describes a smooth distribution. These principle differences follow from the fact, that the budget equations for the moments in the parameterized models are of the form of quasi-linear advection equations, with the decisive nonlinearity arising from the parameterization relation for the sedimentation flux, whereas the reference solution follows from a linear partial differential equation. Hence, the quasi-linear shock effects have to be interpreted as a mathematical artifact of the parameterization assumptions. The differing evolution of the liquid water profiles finds expression in remarkable differences in the time series of surface precipitation rate for the spectral and parameterized models.

Background effects on Faraday collectors in gas‐source mass spectrometry and implications for clumped isotope measurements

RATIONALE The measurement of the abundances of minor isotopologues by mass spectrometry requires correction of subtle non-linearities in the mass spectrometer that cause deviations in the relationship between actual and measured isotope ratios. Here we show that negative backgrounds on the Faraday cups recording the minor ion beams are the cause of the observed non-linearities in the measurement of CO(2) isotopologues, and propose a new correction procedure for clumped isotope measurements. METHODS We carefully investigated the cause of non-linearity effects in the measurement of the abundance of (13)C(18)O(16)O, a minor isotopologue of CO(2) with m/z 47, on two different mass spectrometers. By using gases of different composition with close to stochastic and with non-random distribution of isotopes we demonstrate that the apparent dependence of the excess abundance of the isotopologue of m/z 47 on the bulk isotopic composition of CO(2) is due to a background interference that is linearly dependent on the partial pressure of the gas in the source of the mass spectrometer. CONCLUSIONS Background determination with gas flowing into the source of the mass spectrometer is necessary for accurate clumped isotope measurements of CO(2). Background corrections can be performed accurately if the slit width of the m/z 44 Faraday cup significantly exceeds that of the one for m/z 47, using a correlation between m/z 44 signal intensity and the corresponding minimum in m/z 47 background. We propose two new correction schemes that reduce the time-consuming measurement of gases of different bulk isotopic compositions. These findings may also be relevant for the measurement of other rare isotopologues by mass spectrometry.

On the selection of prognostic moments in parametrization schemes for drop sedimentation

Abstract Common parametrizationmodels for cloud microphysical processes use condensate mass density and/or particle number density as prognostic properties. However, other moments of the particle size distribution can likewise be chosen for prediction. This study deals with parametrization models with one and two, respectively, prognostic moments for the sedimentation of drop ensembles. The spectral resolving model defines the reference solution. The evolution of the vertical profiles of liquid water content, drop number density and rain rate strongly depend on the choice of the prognostic moments in the parametrizationmodels. Inmodels with a single prognostic moment, its vertical profile is copied by all other moments. The moment of most physical pertinence is recommended for prediction. In models with two prognostic moments, the vertical profiles of all moments differ. The orders of the prognostic moments should be chosen close to the order of moments of highest relevance. Otherwise large errors occur. For example, comparison of modelled versus observed radar reflectivity (6th moment with respect to diameter) does not tell much about the quality of other properties if reflectivity is diagnosed from for example, number density and mass density. Furthermore, mass conservation is fulfilled only if mass density is forecasted.

Slight pressure imbalances can affect accuracy and precision of dual inlet-based clumped isotope analysis.

It is well known that a subtle nonlinearity can occur during clumped isotope analysis of CO2 that – if remaining unaddressed – limits accuracy. The nonlinearity is induced by a negative background on the m/z 47 ion Faraday cup, whose magnitude is correlated with the intensity of the m/z 44 ion beam. The origin of the negative background remains unclear, but is possibly due to secondary electrons. Usually, CO2 gases of distinct bulk isotopic compositions are equilibrated at 1000 °C and measured along with the samples in order to be able to correct for this effect. Alternatively, measured m/z 47 beam intensities can be corrected for the contribution of secondary electrons after monitoring how the negative background on m/z 47 evolves with the intensity of the m/z 44 ion beam. The latter correction procedure seems to work well if the m/z 44 cup exhibits a wider slit width than the m/z 47 cup. Here we show that the negative m/z 47 background affects precision of dual inlet-based clumped isotope measurements of CO2 unless raw m/z 47 intensities are directly corrected for the contribution of secondary electrons. Moreover, inaccurate results can be obtained even if the heated gas approach is used to correct for the observed nonlinearity. The impact of the negative background on accuracy and precision arises from small imbalances in m/z 44 ion beam intensities between reference and sample CO2 measurements. It becomes the more significant the larger the relative contribution of secondary electrons to the m/z 47 signal is and the higher the flux rate of CO2 into the ion source is set. These problems can be overcome by correcting the measured m/z 47 ion beam intensities of sample and reference gas for the contributions deriving from secondary electrons after scaling these contributions to the intensities of the corresponding m/z 49 ion beams. Accuracy and precision of this correction are demonstrated by clumped isotope analysis of three internal carbonate standards. The proposed correction scheme can be easily applied if the slit width of the m/z 49 Faraday cup is bigger than that of the m/z 47 cup.

Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air

Abstract The local mass balance equations of cloudy air are formulated for a model system composed of dry air, water vapor, and four categories of water condensate particles, as typically adopted for numerical weather prediction and climate models. The choice of the barycentric velocity as reference motion provides the most convenient form of the total mass continuity equation. Mass transfer across the earth’s surface due to precipitation and evaporation causes a nonvanishing barycentric vertical velocity ws and is proportional to the local difference between evaporation rate and rain plus snow rate. Hence ws vanishes only in the special situation that evaporation and precipitation balance exactly. Alternative concepts related to different reference motions are reviewed. However, the choice of the barycentric velocity turns out to be advantageous for several reasons. The implication of the nonvanishing total mass transport across the earth’s surface is estimated from model simulations for two extreme weat...

Continuity equations as expressions for local balances of masses in cloudy air

The mathematical representation of the mass continuity equation and a boundary condition for thevertical velocity at the earth’s surface is re-examined in terms of its dependence on the frame ofreference velocity. Three of the most prominent meteorological examples are treated here: (a) thebarycentric velocity of a full cloudy air system, (b) the barycentric velocity of a mixture consisting ofdry air andwater vapour and (c) the velocity of dry air. Although evidently the physical foundation holdsindependently of the choice of a particular frame, the resulting equations differ in their mathematicalstructure: In examples (b) and (c) the diffusion flux divergence that appears in the corresponding massequation of continuity should not be omitted a priori. As to the lower boundary condition for the normalcomponent of velocity, special emphasis is placed on the net mass transfer across the earth’s surfaceresulting from precipitation and evaporation. It is shown that for a flat surface, the reference verticalvelocity vanishes only in case (c). Regarding cases (a) and (b), the vertical reference velocities aredetermined as functions of the precipitation and evaporation rates. They are nonzero, and it is shownthat they cannot generally be neglected.

Competition of Precipitation Particles in a Model with Parameterized Cloud Microphysics

Abstract The nonlinear open system cloud is analyzed in this basic study in the context of the theory of self-organization. Emphasis is placed on the microphysical processes of riming, accretion, and sedimentation in a supercooled cloud containing several types of precipitation particles. These processes are mathematically described using a parameterization scheme of the Kessler type. This model of the competition of precipitation particle types for cloud water is analogous to the famous predator-prey model in population dynamics. The models differ, however, in the role of the exponents in the transformation rates, which can be interpreted as control parameters for the cloud physics model. The number as well as the type of attractors depend on a set of parameters including, for example, the attributes of the chosen type of precipitation particles and the prescribed external source rates. If only spherically shaped precipitation particles are considered, the system is characterized by a single point attrac...

Mesoscale modelling of the Arctic atmospheric boundary layer and its interaction with sea ice

This chapter summarises mesoscale modelling studies, which were carried out during the ACSYS decade until 2005. They were aiming at the parameterisation and improved understanding of processes in the Arctic boundary layer over the open ocean and marginal sea ice zones and over the Greenland ice sheet. It is shown that progress has been achieved with the parameterization of fluxes in strong convective situations such as cold-air outbreaks and convection over leads. A first step was made towards the parameterization of the lead-induced turbulence for high-resolution, but non-eddy resolving models. Progress has also been made with the parameterization of the near-surface atmospheric fluxes of energy and momentum modified by sea ice pressure ridges and by ice floe edges. Other studies brought new insight into the complex processes influencing sea ice transport and atmospheric stability over sea ice. Improved understanding was obtained on the cloud effects on the snow/ice surface temperature and further on the near-surface turbulent fluxes. Finally, open questions are addressed, which remained after the ACSYS decade for future programmes having been started in the years after 2005.

Parameterization of the Sedimentation of Raindrops with Finite Maximum Diameter

In common cloud microphysics parameterization models, the prognostic variables are one to three moments of the drop size distribution function. They are defined as integrals of the distribution function over a drop diameter ranging from zero to infinity. Recent works (by several authors) on a one-dimensional sedimentation problem have pointed out that there are problems with those parameterization models caused by the differing average propagation speeds of the prognostic moments. In this study, the authors propose to define the moments over a finite drop diameter range of [0, Dmax], corresponding to the limitation of drop size in nature. The ratios of the average propagation speeds are thereby also reduced. In the new model, mean particle masses above a certain threshold depending on Dmax lead to mathematical problems, which are solved by a mirroring technique. An identical, one-dimensional sedimentation problem for two moments is used to analyze the sensitivity of the results to the maximum drop diameter and to compare the proposed method with recent works. It turns out that Dmax has a systematic influence on the model’s results. A small, finite maximum drop diameter leads to a better representation of the moments and the mean drop mass when compared to the detailed microphysical model.