Nonlinear response of stratospheric ozone column to chlorine injections

We have developed a fast two-dimensional residual circulation stratospheric model. In order to calculate possible effects of long-term changes for trace gases for a large number of scenarios and to examine the model sensitivities to dynamical and photochemical assumptions and inputs, the model is designed to minimize computer requirements. The species continuity equations are solved using process splitting, that is, by successively applying the operators associated with advective changes with photochemical and diffusive forcing. The first study undertaken with this model concerns family chemistry approximations, in which groups of species are related by photochemical equilibrium assumptions and transported as one species.

Section: Introductionsupporting

confidence: 67%

Comparison of model results transporting the odd nitrogen family with results transporting separate odd nitrogen species

Douglass¹,

Jackman²,

Stolarski³

1989

“…The model results are displayed for different values of the aerosol surface area density (from 1 to 100 μm 2 cm −3 ) and for the background level of NO y = 9 ppbv (or S N = 60 cm −3 s −1 ). Again, even though no catastrophic transition is noticeable, the state of the system responds in a highly nonlinear way [ Cicerone et al , 1983; Prather et al , 1984] to the value of parameter S Cl , in particular for high values of the aerosol surface area density A . For an increase of a factor of 10 in S Cl (corresponding to a change in the Cl y mixing ratio from 2.3 to 22.5 ppbv) the ozone concentration decreases by factors of 4, 30, 500, and 1000 when A is equal to 1, 10, 50, and 100 μm 2 cm −3 , respectively.…”

Section: Response Of the Photochemical Systemmentioning

confidence: 99%

“…Chemical reactions in the atmosphere are nonlinear processes. Over the last decades, various mathematical analyses of chemical systems [ Prather et al , 1979; Fox et al , 1982; Cicerone et al , 1983; White and Dietz , 1984; Kasting and Ackerman , 1985; Stewart , 1993; Yang and Brasseur , 1994, 2001; Hess and Madronich , 1997; Montecinos and Felmer , 1999] have revealed that the chemical composition of the troposphere and stratosphere could exhibit unexpected behavior and abrupt changes in response to external forcing. Prather et al [1979], for example, showed that the equations describing chemical partitioning between the nitrogen, chlorine, and hydrogen species may admit multiple, physically reasonable solutions with abrupt changes to be expected at high latitudes during wintertime.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of the stratospheric photochemical system

Yang

Brasseur

2004

[1] The impact of odd chlorine (Cl y ) and odd nitrogen (NO y ) perturbations (resulting from human activities) and of enhanced H 2 O-H 2 SO 4 aerosol load (associated with volcanic activity) on stratospheric ozone (25 km altitude, midlatitudes) is assessed by using a chemical box model in which key heterogeneous reactions on the surface of sulfate aerosol particles are taken into account. The model shows that if transport is ignored, the response of the photochemical system to increased abundances of odd chlorine and odd nitrogen and to enhanced aerosol surface area density is characterized by a multiequilibrium regime. Catastrophic transitions may occur and may produce dramatic reductions in the stratospheric ozone concentration. When the dissipative effects associated with transport are taken into account, the system still exhibits a nonlinear response to external nitrogen and chlorine sources but without multiequilibrium solutions or catastrophic transitions. Over a sensitive interval, small external disturbances applied to model parameters can lead to large changes in the state of the system. For example, the large drop in ozone derived by the model when dissipative transport effects are taken into account corresponds to a degeneracy of the multiequilibrium regime found when dissipative terms are omitted.

“…In one approach, researchers have sought to reduce the effective size of the JacobJan system matrix, thus reducing the number of computations needed to carry out the required matrix inversions. Elliott et al [1993Elliott et al [ , 1995Elliott et al [ , 1996 developed an approach employing "minimatrices" that represent submatrices of the Jacobian corresponding to specific families or groups of related species [e.g., Crutzen, 1971;Turco and Whitten, 1974;Cicerone et al, 1983;Brasseur and Solomon, 1984;Austin, 1991]. Families are selected so that their equivalent chemical rate equations, which are derived by summing the member species' rate equations [see Turco and Whitten, 1974], are much less stiff than those of the individual species.…”

Section: Introductionmentioning

confidence: 99%

A new family Jacobian solver for global three‐dimensional modeling of atmospheric chemistry

Zhao¹,

Turco²,

Shen³

1999

Abstract. We present a new technique to solve complex sets of photochemical rate equations that is applicable to global modeling of the troposphere and stratosphere. The approach is based on the concept of "families" of species, whose chemical rate equations are tightly coupled. Variations of species concentrations within a family can be determined by inverting a linearized Jacobian matrix representing the family group. Since this group consists of a relatively small number of species the corresponding Jacobian has a low order (a minimatrix) compared to the Jacobian of the entire system. However, we go further and define a super-family that is the set of all families. The super-family is also solved by linearization and matrix inversion. The resulting Super-Family Matrix Inversion (SFMI) scheme is more stable and accurate than common family approaches. We discuss the numerical structure of the SFMI scheme and apply our algorithms to a comprehensive set of photochemical reactions. To evaluate performance, the SFMI scheme is compared with an optimized Gear solver. We find that the SFMI technique can be at least an order of magnitude more efficient than existing chemical solvers while maintaining relative errors in the calculations of 15% or less over a diurnal cycle. The largest SFMI errors arise at sunrise and sunset and during the evening when species concentrations may be very low. We show that sunrise/sunset errors can be minimized through a careful treatment of photodissociation during these periods; the nighttime deviations are negligible from the point of view of acceptable computational accuracy. The stability and flexibility of the SFMI algorithm should be sufficient for most modeling applications until major improvements in other modeling factors are achieved. In addition, because of its balanced computational design, SFMI can easily be adapted to parallel computing architectures. SFMI thus should allow practical long-term integrations of global chemistry coupled to general circulation and climate models, studies of interannual and interdecadal variability in atmospheric composition, simulations of past multidecadal trends owing to anthropogenic emissions, long-term forecasting associated with projected emissions, and sensitivity analyses for a wide range of physical and chemical parameters. To carry out practical calculations, the earliest and most straightforward explicit approaches for solving atmospheric chemical rate equations were quickly abandoned in favor of numerical implicitness (or semi-implicitness), with or without iterative procedures to stabilize the solutions [e.g., see Shimazaki and Laird, 1970; Turco and Whirten, 1974]. At a given time step, species concentrations could be repeatedly calculated using a simple semi implicit form of (1) by updating the chemical production and loss rates using species concentrations calculated at the previous iteration. While this gener-1767