Advection Errors Research Articles

High-Resolution Simulation of Hurricane Bonnie (1998). Part II: Water Budget

Abstract The fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) is used to simulate Hurricane Bonnie at high resolution (2-km spacing) in order to examine budgets of water vapor, cloud condensate, and precipitation. Virtually all budget terms are derived directly from the model (except for the effects of storm motion). The water vapor budget reveals that a majority of the condensation in the eyewall occurs in convective hot towers, while outside of the eyewall most of the condensation occurs in weaker updrafts, indicative of a larger role of stratiform precipitation processes. The ocean source of water vapor in the eyewall region is only a very small fraction of that transported inward in the boundary layer inflow or that condensed in the updrafts. In contrast, in the outer regions, the ocean vapor source is larger owing to the larger area, counters the drying effect of low-level subsidence, and enhances the moisture transported in toward the eyewall. In this mature storm, cloud condensate is consumed as rapidly as it is produced. Cloud water peaks at the top of the boundary layer and within the melting layer, where cooling from melting enhances condensation. Unlike in squall lines, in the hurricane, very little condensate produced in the eyewall convection is transported outward into the surrounding precipitation area. Most of the mass ejected outward is likely in the form of small snow particles that seed the outer regions and enhance in situ stratiform precipitation development through additional growth by vapor deposition and aggregation. This study also examines artificial source terms for cloud and precipitation mass associated with setting to zero negative mixing ratios that arise from numerical advection errors. Although small at any given point and time, the cumulative effect of these terms contributes an amount of mass equivalent to 13% of the total condensation and 15%–20% of the precipitation. Thus, these terms must be accounted for to balance the model budgets, and the results suggest the need for improved model numerics.

Gap-filling measurements of carbon dioxide storage in tropical rainforest canopy airspace

For the determination of biotic fluxes of carbon dioxide (CO 2) or other trace gases to or from a forest canopy, it is important to measure the storage of the trace gas within the forest canopy in addition to the net vertical flux above the forest canopy. However, the data continuity of within-canopy storage measurements can be poor because these measurements are subject to frequent equipment breakdowns. We here explore methods for gap-filling within-canopy CO 2 storage, using the data derived from an Amazonian rainforest (Caxiuanã). Our first approach was to estimate hourly storage from hourly CO 2 concentration measured above the canopy at the tower top. This proved unreliable, since at this hourly time scale the variations in above-canopy CO 2 are often decoupled from local changes in within-canopy storage. We then explored a second approach based on determination of the total CO 2 accumulation over a night. This was found to be adequately correlated with a time-weighted friction velocity ( u *w) averaged over a night ( R 2 = 0.42). The total night-time storage was then used to model daytime depletion of CO 2 within the canopy. The gap-filling model was validated against independent data from the same site, and also applied to another tropical forest (Jarú) with similar results. The modelled storage is in good agreement with the measured storage, and by reducing susceptibility to advection error it is in some ways superior to the direct storage measurements. This suggests at the possibility of a general method for estimating storage in forest canopies, with re-calibration for each site.

Derivation of Large Igneous Provinces of the past 200 million years from long-term heterogeneities in the deep mantle

Large Igneous Provinces (LIPs) result from local catastrophically rapid dissipation of great quantities of internal heat. LIPs are overwhelmingly of basaltic affinity representing partial melting of the mantle at shallow depths but whether any of the heat or material involved in the generation of LIP rocks comes from great depth has remained controversial. To address this fundamental issue we restored 25 LIPs of the past 200 My to their eruption sites using a new global palaeomagnetic reference model. Ninety percent of the LIPs, when erupted, lay above low-velocity seismic-shear-wave regions of the Dʺ zone just above the core–mantle boundary (CMB) and ∼50% overlay CMB low-velocity regions with δ V s≤−1%. Considering the modifying effects of plume advection, palaeolongitudinal uncertainty and plate circuit errors, the majority of the restored LIPs may in fact overlie regions with δ V s≤−1%. Because those low velocity regions occupy only 27% of the Dʺ zone, the concentration of LIPs above them indicates that the low velocity (hotter?) regions are the sources of the mantle plumes that generated the LIPs. We demonstrate that most LIPs of the past 200 My owe their origin to plumes that rose from low-velocity regions of the lower mantle, and that this long-term association indicates that the low-velocity regions have been relatively stationary with respect to the Earth's spin-axis and the core since the Early Jurassic, and perhaps since the Permo-Triassic boundary.

Fluxes of NH3 and CO2 over upland moorland in the vicinity of agricultural land

Intensive field measurements of NH3 and CO2 exchange were made over a wet heathland in the vicinity (<500 m) of sheep pastures in the Cairngorm mountains of Scotland for a two‐week period in the summer. Fluxes of NH3 were determined using the aerodynamic gradient method with a 3‐height continuous denuder system; fluxes of CO2 were determined using eddy correlation, while sensible and latent heat fluxes were determined by both methods. Few studies have measured NH3 and CO2 fluxes simultaneously, making these measurements relevant to compare exchange dynamics. Both NH3 and CO2 exchanged bidirectionally, in response to a combination of biological (foliar, soil) and physico‐chemical controls (solubility). NH3 was deposited rapidly to leaf surfaces, although during warm, dry daytime conditions periods of emission occurred, explained by the existence of a compensation point concentration for NH3. By contrast, CO2 followed a characteristic pattern of absorption during the day associated with net photosynthesis and emission at night. Both gases showed net uptake from the atmosphere, at 30 μmol NH3 m−2 d−1 and 74 mmol CO2 m−2 d−1. In southeast winds, NH3 emissions from the sheep pasture caused a significant advection error to the measured fluxes (>10%). Corrections were applied using a local‐scale dispersion‐exchange model. The analysis highlights how advection modifies the classical one‐dimensional inferential resistance approach. It is concluded that ecosystems in the vicinity of agricultural land receive more dry deposition than would be estimated using NH3 concentration monitoring and standard inferential models. In the present study, this effect represented an overall increase in total NH3 deposition of 32%.

A Semi-Lagrangian High-Order Method for Navier–Stokes Equations

We present a semi-Lagrangian method for advection–diffusion and incompressible Navier–Stokes equations. The focus is on constructing stable schemes of second-order temporal accuracy, as this is a crucial element for the successful application of semi-Lagrangian methods to turbulence simulations. We implement the method in the context of unstructured spectral/hp element discretization, which allows for efficient search-interpolation procedures as well as for illumination of the nonmonotonic behavior of the temporal (advection) error of the form: O(Δtk+Δxp+1Δt). We present numerical results that validate this error estimate for the advection–diffusion equation, and we document that such estimate is also valid for the Navier–Stokes equations at moderate or high Reynolds number. Two- and three-dimensional laminar and transitional flow simulations suggest that semi-Lagrangian schemes are more efficient than their Eulerian counterparts for high-order discretizations on nonuniform grids.

Physical evolution of the IronEx-I open ocean tracer patch

An 8×8 km tracer-enriched patch was successfully formed in an open-ocean mixed layer in the equatorial Pacific during the first uncontained test of the iron hypothesis. To minimize the effects of horizontal advection, the patch formation and subsequent rapid underway sampling of the patch properties were performed in a Lagrangian reference frame centered on a navigated, drogued buoy that tracked the mixed layer movements on O(1 d) timescales. Daily maps of the evolving patch shape, and corrections for the buoy drift relative to the patch center, were based on objectively analyzed surface concentration maps of an inert tracer, SF 6, which had been injected into the ocean surface with trace quantities of iron during the patch formation. The Lagrangian reference frame significantly reduced large scale circular and lateral advection errors in maps of the surface patch shape. A strong pycnocline at approximately 35 m depth and very constant 6 m s -1 wind forcing greatly limited turbulent diffusion below the mixed layer. Rapid small scale mixing over the first 24 h was followed by a four day period of slow spreading, primarily in the along-wind direction. Estimates of along wind horizontal diffusivity using a Fickian model were 600±100 m 2 s -1, with a mean cross wind value of 200±30 m 2 s -1 over a 4 d period. On the fifth day an intruding low salinity surface front effectively capped the patch between a 10–20 m thick fresh surface layer and the pycnocline. This experiment demonstrated that an O(100 km 2) open ocean mixed layer tracer tagged patch could be formed, and its evolution mapped the presence of advection over 5–10 d periods.

A particle‐in‐cell sea‐ice model

Abstract Fronts or discontinuities in geophysical flows are often smoothed in numerical models owing to artificial diffusion and dispersion introduced by the advection algorithm. This is a particular problem in operational sea‐ice forecasting where the position of the ice edge must be accurately predicted. The particle‐in‐cell (PIC) scheme avoids artificial smoothing by partitioning the ice volume into individual particles whose motion is integrated in a Lagrangian sense. The velocity field is obtained by solving the momentum equation on an underlying fixed Eulerian grid. Comparisons between the PIC scheme and more conventional advection algorithms are presented using both idealized and observed forcing fields. An advantage of the PIC model is that the resolution of the underlying Eulerian grid (on which the computationally expensive momentum equation is solved) can be chosen to represent the spatial variability of the forcing fields (winds and currents) rather than to minimize advection errors. A large number of particles per unit area can be used to resolve features of interest while maintaining only a sparse particle distribution elsewhere. The model is readily extended to include additional particles representing, for example, an oil spill.