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- Author or Editor: David G. Andrews x
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Abstract
Isentropic coordinates are used to generalize to finite amplitude the celebrated theorem (1.1) of Eliassen and Palm(1961),under non-acceleration conditions. This primitive-equation result also generalizes the finite-amplitude quasi-geostrophic result of Edmon et at. (1980). A simple physical interpretation is provided, and a set of transformed Eulerian-mean equations arises naturally in the course of the analysis. Isentropes which intersect the lower boundary need special attention; the technique developed to handle them is a generalization of an idea due to Lorenz (1955), and may be of use in other contexts. Mention is also made of a version of the theorem valid for small-amplitude, transient, non-conservative disturbances.
Abstract
Isentropic coordinates are used to generalize to finite amplitude the celebrated theorem (1.1) of Eliassen and Palm(1961),under non-acceleration conditions. This primitive-equation result also generalizes the finite-amplitude quasi-geostrophic result of Edmon et at. (1980). A simple physical interpretation is provided, and a set of transformed Eulerian-mean equations arises naturally in the course of the analysis. Isentropes which intersect the lower boundary need special attention; the technique developed to handle them is a generalization of an idea due to Lorenz (1955), and may be of use in other contexts. Mention is also made of a version of the theorem valid for small-amplitude, transient, non-conservative disturbances.
Abstract
A quadratic conservation law is derived for small-amplitude quasi-geostrophic disturbances on a wavy basic state. The law may be useful for describing the three-dimensional propagation of disturbances on time-averaged flows. This parallels the use of the generalized Eliassen-Palm theorem in the description of waves propagating on zonally-averaged flows.
Abstract
A quadratic conservation law is derived for small-amplitude quasi-geostrophic disturbances on a wavy basic state. The law may be useful for describing the three-dimensional propagation of disturbances on time-averaged flows. This parallels the use of the generalized Eliassen-Palm theorem in the description of waves propagating on zonally-averaged flows.
Abstract
Small-amplitude, transient disturbances to a steady, zonally asymmetric basic state are considered, for barotropic (or baroclinic, quasi-geostrophic) flow on a beta-plane. An explicit expression is derived for the eddy vorticity (or potential vorticity) flux in terms of the basic velocity and basic vorticity (or potential vorticity), and transient and nonconservative eddy effects, plus an identically nondivergent term. The divergence of the time mean of this flux provides the forcing of the time-mean flow. The theory generalizes a “nonacceleration” result due to Plumb. In the case of conservative flow, the relevant expressions can be obtained in Eulerian form; however, for nonconservative flow it appears to be necessary to introduce the Lagrangian fluid particle displacements. Possible applications of the theory to the interpretation of atmospheric and model data are mentioned.
Abstract
Small-amplitude, transient disturbances to a steady, zonally asymmetric basic state are considered, for barotropic (or baroclinic, quasi-geostrophic) flow on a beta-plane. An explicit expression is derived for the eddy vorticity (or potential vorticity) flux in terms of the basic velocity and basic vorticity (or potential vorticity), and transient and nonconservative eddy effects, plus an identically nondivergent term. The divergence of the time mean of this flux provides the forcing of the time-mean flow. The theory generalizes a “nonacceleration” result due to Plumb. In the case of conservative flow, the relevant expressions can be obtained in Eulerian form; however, for nonconservative flow it appears to be necessary to introduce the Lagrangian fluid particle displacements. Possible applications of the theory to the interpretation of atmospheric and model data are mentioned.
Abstract
The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However. some exceptions to this general rule exist.
Abstract
The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However. some exceptions to this general rule exist.
Abstract
Transformed Eulerian mean (TEM) equations and Eliassen–Palm (EP) flux diagnostics are presented for the general nonhydrostatic, fully compressible, deep atmosphere formulation of the primitive equations in spherical geometric coordinates. The TEM equations are applied to a general circulation model (GCM) based on these general primitive equations. It is demonstrated that a naive application in this model of the widely used approximations to the EP diagnostics, valid for the hydrostatic primitive equations using log-pressure as a vertical coordinate and presented, for example, by Andrews et al. in 1987 can lead to misleading features in these diagnostics. These features can be of the same order of magnitude as the diagnostics themselves throughout the winter stratosphere. Similar conclusions are found to hold for “downward control” calculations. The reasons are traced to the change of vertical coordinate from geometric height to log-pressure. Implications for the modeling community, including comparison of model output with that from reanalysis products available only on pressure surfaces, are discussed.
Abstract
Transformed Eulerian mean (TEM) equations and Eliassen–Palm (EP) flux diagnostics are presented for the general nonhydrostatic, fully compressible, deep atmosphere formulation of the primitive equations in spherical geometric coordinates. The TEM equations are applied to a general circulation model (GCM) based on these general primitive equations. It is demonstrated that a naive application in this model of the widely used approximations to the EP diagnostics, valid for the hydrostatic primitive equations using log-pressure as a vertical coordinate and presented, for example, by Andrews et al. in 1987 can lead to misleading features in these diagnostics. These features can be of the same order of magnitude as the diagnostics themselves throughout the winter stratosphere. Similar conclusions are found to hold for “downward control” calculations. The reasons are traced to the change of vertical coordinate from geometric height to log-pressure. Implications for the modeling community, including comparison of model output with that from reanalysis products available only on pressure surfaces, are discussed.
Abstract
Data from the California Land-Falling Jets Experiment (CALJET) are used to explore the causes of variations in flood severity in adjacent coastal watersheds within the Santa Cruz Mountains on 2–3 February 1998. While Pescadero Creek (rural) experienced its flood of record, the adjacent San Lorenzo Creek (heavily populated), attained only its fourth-highest flow. This difference resulted from conditions present while the warm sector of the storm, with its associated low-level jet, high moisture content, and weak static stability, was overhead. Rainfall in the warm sector was dominated by orographic forcing. While the wind speed strongly modulated rain rates on windward slopes, the wind direction positioned the edge of a rain shadow cast by the Santa Lucia Mountains partially over the San Lorenzo basin, thus protecting the city of Santa Cruz from a more severe flood. Roughly 26% ± 9% of the streamflow at flood peak on Pescadero Creek resulted from the warm-sector rainfall. Without this rainfall, the peak flow on Pescadero Creek would likely not have attained record status.
These results are complemented by a climatological analysis based on ∼50-yr-duration streamflow records for these and two other nearby windward watersheds situated ∼20 to 40 km farther to the east, and a comparison of this climatological analysis with composites of NCEP–NCAR reanalysis fields. The westernmost watersheds were found to have their greatest floods during El Niño winters, while the easternmost watersheds peaked during non–El Niño episodes. These results are consistent with the case study, that showed that the composite 925-mb, meridionally oriented wind direction during El Niños favors a rain shadow over the eastern watersheds. During non–El Niño periods, the composite, zonally oriented wind direction indicates that the sheltering effect of the rain shadow on the eastern watersheds is reduced, while weaker winds, less water vapor, and stronger stratification reduce the peak runoff in the western watersheds relative to El Niño periods.
These case study and climatological results illustrate the importance of conditions in the moisture-rich warm sector of landfalling Pacific winter storms. Although many other variables can influence flooding, this study shows that variations of ±10° in wind direction can modulate the location of orographically enhanced floods. While terrain can increase predictability (e.g., rainfall typically increases with altitude), the predictability is reduced when conditions are near a threshold separating different regimes (e.g., in or out of a rain shadow).
Abstract
Data from the California Land-Falling Jets Experiment (CALJET) are used to explore the causes of variations in flood severity in adjacent coastal watersheds within the Santa Cruz Mountains on 2–3 February 1998. While Pescadero Creek (rural) experienced its flood of record, the adjacent San Lorenzo Creek (heavily populated), attained only its fourth-highest flow. This difference resulted from conditions present while the warm sector of the storm, with its associated low-level jet, high moisture content, and weak static stability, was overhead. Rainfall in the warm sector was dominated by orographic forcing. While the wind speed strongly modulated rain rates on windward slopes, the wind direction positioned the edge of a rain shadow cast by the Santa Lucia Mountains partially over the San Lorenzo basin, thus protecting the city of Santa Cruz from a more severe flood. Roughly 26% ± 9% of the streamflow at flood peak on Pescadero Creek resulted from the warm-sector rainfall. Without this rainfall, the peak flow on Pescadero Creek would likely not have attained record status.
These results are complemented by a climatological analysis based on ∼50-yr-duration streamflow records for these and two other nearby windward watersheds situated ∼20 to 40 km farther to the east, and a comparison of this climatological analysis with composites of NCEP–NCAR reanalysis fields. The westernmost watersheds were found to have their greatest floods during El Niño winters, while the easternmost watersheds peaked during non–El Niño episodes. These results are consistent with the case study, that showed that the composite 925-mb, meridionally oriented wind direction during El Niños favors a rain shadow over the eastern watersheds. During non–El Niño periods, the composite, zonally oriented wind direction indicates that the sheltering effect of the rain shadow on the eastern watersheds is reduced, while weaker winds, less water vapor, and stronger stratification reduce the peak runoff in the western watersheds relative to El Niño periods.
These case study and climatological results illustrate the importance of conditions in the moisture-rich warm sector of landfalling Pacific winter storms. Although many other variables can influence flooding, this study shows that variations of ±10° in wind direction can modulate the location of orographically enhanced floods. While terrain can increase predictability (e.g., rainfall typically increases with altitude), the predictability is reduced when conditions are near a threshold separating different regimes (e.g., in or out of a rain shadow).
