Advection Distance Research Articles

Synchronization of turbulence in channel flow

Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds numbers up to one thousand, wall-attached horizontal layers can synchronize as long as their thickness is less than approximately thirty wall units. When the horizontal layer is detached from the wall, the critical thickness increases with height and is proportional to the local wall-normal Taylor microscale. A flow-parallel, vertical layer that spans the height of the channel synchronizes when its spanwise width is of the order of the near-wall Taylor microscale, while the criterion for a crossflow vertical layer is set by the advection distance within a Lyapunov time scale. Finally, we demonstrate that synchronization is possible when only planar velocity data are available, rather than the full outer state, as long as the unknown region satisfies the condition for synchronization in one direction. These numerical experiments demonstrate the capacity of accurately reconstructing, or synchronizing, the missing scales of turbulence from observations, using continuous data assimilation.

Shift in the larval phenology of a marine ectotherm due to ocean warming with consequences for larval transport

AbstractBecause environmental temperature has an important influence on developmental rate and physiology, marine ectotherms are vulnerable to phenology changes due to ocean warming. Identifying changes to phenology, the timing of biological events, and understanding their effect on recruitment and abundance is of critical importance to establish potential population effects. We examined the larval phenology of the commercially important Norway lobster (Nephrops norvegicus) and used a larval transport model to examine its effect on simulated transport patterns. Using a model to estimate annual larval release dates based on temperature‐dependent embryo incubation, an earlier shift of 17.2 d occurred between 1982–1995 and 2000–2010 in the Irish Sea, similar to an observed empirical shift in phenology of 19.1 d using historical zooplankton data sets. Despite this earlier phenology, temperature‐dependent pelagic larval durations were unchanged because the water column to which larvae were released earlier had also warmed. Larval transport simulations in the western Irish Sea indicated that the phenology shift had minimal effects on larval retention and advection distance overall, because major variations were observed only at very early or late stages of the larval season, that is, times when lower proportions of larvae were present. As the western Irish Sea grounds exports small but consistent quantities of larvae to nearby populations, especially off Scotland, it may act as an important source of larvae, especially when retention of native larvae is low. Overall, larval transport tools may indicate grounds that are periodically vulnerable to recruitment failures and offer potentially valuable information in fishery management.

Veins in clay-rich aquitards as records of deformation and fluid-flow events in northern Switzerland

The Jurassic clay-rich aquitard sequence underlying the Swiss Molasse Basin is locally penetrated by unusually frequent veins consisting of calcite ± celestite, in particular in the Schlattingen-1 and Oftringen drill cores. The veins are linked to extensional brittle structures, with shear senses ranging between dip-slip and strike-slip. Deformation triggered transient and localised events of fluid flow within the aquitard followed by sealing of the structures by the vein minerals. Vein calcite was dated by LA-ICP-MS analysis using the U/Pb method. While this was a demanding undertaking, given the low U and high common Pb contents of calcite, 9 significant ages could be obtained. Two groups of ages can be distinguished, namely 31–39 and 11–18 Ma. Both age groups are consistent with the known regional tectonic evolution. The older age group corresponds to the main phase of rifting in the Upper Rhine Graben, a major crustal discontinuity, whose effects were not limited to the graben proper but affected large parts of the Molasse Basin. The younger age group is linked to crustal tilting and related extensional deformation.Isotopic compositions of O and C in vein calcite from the Schlattingen-1 core show substantial variability but do not discriminate between veins of the two age groups. In contrast, 87Sr/86Sr ratios in veins show different signatures. The depth trend of 87Sr/86Sr ratios in veins fits well with that in pore water obtained by rock squeezing. The two data sets define a trend of values increasing with depth, connecting the current values in the embedding Malm and Keuper aquifer waters. This trend is best explained as a near-steady-state diffusion profile. While advective mixing of waters originating from the embedding aquifers to produce the veins, implying structures that cross cut the whole low-permeability sequence, cannot be discarded on the basis of existing data, it is considered more likely that the veins have local fluid sources. These are mixtures of local pore water with a possible contribution of water from the nearest aquifer, implying maximum vertical advection distances in the order of 50–100 m.

Aerodynamic influences on a tethered high-altitude lighter-than-air platform system to its behavior

The goal of this study was to investigate the influence of aerodynamic factors on the static behavior of a tethered high-altitude lighter-than-air platform. The system design comprised a lighter-than-air vehicle and a tether cable, and the conceptual platform configuration of such a system is studied herein. Governing equations were derived to model the static behavior of the system, and the effects of aerodynamic lift and buoyancy were parametrically analyzed based on the advection distance of the platform under storm conditions. The aerodynamic lift and buoyancy of the hull were shown to have nonlinear effects. We further analyzed the influence of the aerodynamic drag created by the tether. Since this was shown to have a significant influence, we concluded that the cable should ideally have a cross-sectional shape resembling the airfoil of a heavier-than-air aircraft. However, it is sufficient to ensure that the drag coefficient is of the order of 10−1.

The stratigraphic record and processes of turbidity current transformation across deep‐marine lobes

AbstractSedimentary facies in the distal parts of deep‐marine lobes can diverge significantly from those predicted by classical turbidite models, and sedimentological processes in these environments are poorly understood. This gap may be bridged using outcrop studies and theoretical models. In the Skoorsteenberg Formation (South Africa), a downstream transition from thickly bedded turbidite sandstones to argillaceous, internally layered hybrid beds, is observed. The hybrid beds have a characteristic stratigraphic and spatial distribution, being associated with bed successions which generally coarsen and thicken‐upward reflecting deposition on the fringes of lobes in a dominantly progradational system. Using a detailed characterization of bed types, including grain size, grain‐fabric and mineralogical analyses, a process‐model for flow evolution is developed. This is explored using a numerical suspension capacity model for radially spreading and decelerating turbidity currents. The new model shows how decelerating sediment suspensions can reach a critical suspension capacity threshold beyond which grains are not supported by fluid turbulence. Sand and silt particles, settling together with flocculated clay, may form low yield strength cohesive flows; development of these higher concentration lower boundary layer flows inhibits transfer of turbulent kinetic energy into the upper parts of the flow ultimately resulting in catastrophic loss of turbulence and collapse of the upper part of the flow. Advection distances of the now transitional to laminar flow are relatively long (several kilometres) suggesting relatively slow dewatering (several hours) of the low yield strength flows. The catastrophic loss of turbulence accounts for the presence of such beds in other fine‐grained systems without invoking external controls or large‐scale flow partitioning and also explains the abrupt pinch‐out of all divisions of these sandstones. Estimation of the point of flow transformation is a useful tool in the prediction of heterogeneity distribution in subsurface systems.

Modeling sorting dynamics of cohesive and non-cohesive sediments on intertidal flats under the effect of tides and wind waves

We extend a numerical model to explore the morphodynamics of intertidal flats, with a specific focus on the sorting dynamics of sand and mud. We investigate the effect of tidal currents, wind waves, sediment properties, external sediment supply, flocculation and initial bed composition on the cross-shore profile shape and sediment sorting of intertidal flats. Consistent with existing analytical theories and benchmark simplified numerical solutions, the equilibrium cross-shore profile of intertidal flats simulated by the extended model is convex-up when tidal currents dominate and it progressively becomes concave-up when the strength of wind waves increases. The equilibrium profile is influenced by the external sediment supply which can lead to the seaward advance of intertidal flats. In line with field observations, mud tends to deposit on the upper intertidal flats when wind waves are relatively weak, while sand is mainly distributed on the middle and lower tidal flats. When wind waves are strong, both sand and mud are more easily resuspended and eroded, resulting in a noticeably concave-up profile near the high water mark. The initial bed composition (e.g., percentage of mud and sand fractions) is also found to play an important role: the intertidal flat is more convex-up in a muddier environment. Numerical modeling demonstrates that sediment properties (e.g., critical shear stress for erosion, settling velocity) and flocculation can pronouncedly influence the sediment sorting dynamics by modifying the initiation threshold and the advection distance of entrained sediments. Application of the extended model to a natural study site indicates a qualitative agreement with field observations.

Behavior of Tether for Captive Stratosphere Platform Using Airship

The existence of a platform at the stratosphere is expected to be the role to gain a foothold in space. When the platform is employed airship in, it is transported by advection due to its light-weight body. Thereupon, a mooring of platform is reasonable in order to incarnate fixed-point platform. Conception of a captive platform system is similar to the Rockoon one which rendered remarkable services for the space observation of the early days. Therefore, the application of captive platform system to the launch site is highly expected in order to realize the space transportation system with a large quantity and high frequency. In this study, the motion of a captive platform system constructed from an airship and a tether is analyzed in order to ensure that the motion of a captive platform system is practically incarnated. Moreover, the sensitivity of aerodynamic performance of the airship is observed. Consequently, the practically incarnated motion of a captive platform system has been identified under the condition of the storm environment. Furthermore, the reduction of the advection distance driven away by the storm has been quantitatively indicated under the different condition of aerodynamic performance of the airship.

The effects of physical and geochemical heterogeneities on hydro-geochemical transport and effective reaction rates

The role of coupled physical and geochemical heterogeneities in hydro-geochemical transport is investigated by simulating three-dimensional transport in a heterogeneous system with kinetic mineral reactions. Ensembles of 100 physically heterogeneous realizations were simulated for three geochemical conditions: 1) spatially homogeneous reactive mineral surface area, 2) reactive surface area positively correlated to hydraulic heterogeneity, and 3) reactive surface area negatively correlated to hydraulic heterogeneity. Groundwater chemistry and the corresponding effective reaction rates were calculated at three transverse planes to quantify differences in plume evolution due to heterogeneity in mineral reaction rates and solute residence time (τ). The model is based on a hypothetical CO2 intrusion into groundwater from a carbon capture utilization and storage (CCUS) operation where CO2 dissolution and formation of carbonic acid created geochemical dis-equilibrium between fluids and the mineral galena that resulted in increased aqueous lead (Pb2+) concentrations. Calcite dissolution buffered the pH change and created conditions of galena oversaturation, which then reduced lead concentrations along the flow path. Near the leak kinetic geochemical reactions control the release of solutes into the fluid, but further along the flow path mineral solubility controls solute concentrations. Simulation results demonstrate the impact of heterogeneous distribution of geochemical reactive surface area in coordination with physical heterogeneity on the effective reaction rate (Krxn,eff) and Pb2+ concentrations within the plume. Dissimilarities between ensemble Pb2+ concentration and Krxn,eff are attributed to how geochemical heterogeneity affects the time (τeq) and therefore advection distance (Leq) required for the system to re-establish geochemical equilibrium. Only after geochemical equilibrium is re-established, Krxn,eff and Pb2+ concentrations are the same for all three geochemical conditions. Correlation between reactive surface area and hydraulic conductivity, either positive or negative, results in variation in τeq and Leq.

Advection shapes Southern Ocean microbial assemblages independent of distance and environment effects

Although environmental selection and spatial separation have been shown to shape the distribution and abundance of marine microorganisms, the effects of advection (physical transport) have not been directly tested. Here we examine 25 samples covering all major water masses of the Southern Ocean to determine the effects of advection on microbial biogeography. Even when environmental factors and spatial separation are controlled for, there is a positive correlation between advection distance and taxonomic dissimilarity, indicating that an 'advection effect' has a role in shaping marine microbial community composition. This effect is likely due to the advection of cells increasing the probability that upstream microorganisms will colonize downstream sites. Our study shows that in addition to distance and environmental selection, advection shapes the composition of marine microbial communities.

Advection-Based Adjustment of Radar Measurements

When making radar-based precipitation products, a radar measurement is commonly taken to represent the geographical location vertically below the contributing volume of the measurement sample. However, when wind is present during the fall of the hydrometeors, precipitation will be displaced horizontally from the geographical location of the radar measurement. Horizontal advection will introduce discrepancies between the radar-measured and ground level precipitation fields. The significance of the adjustment depends on a variety of factors related to the characteristics of the observed precipitation as well as those of the desired end product. In this paper the authors present an advection adjustment scheme for radar precipitation observations using estimated hydrometeor trajectories obtained from the High-Resolution Limited-Area Model (HIRLAM) MB71 NWP model data. They use the method to correct the operational Finnish radar composite and evaluate the significance of precipitation advection in typical Finnish conditions. The results show that advection distances on the order of tens of kilometers are consistently observed near the edge of the composite at ranges of 100–250 km from the nearest radar, even when using a low elevation angle of 0.3°. The Finnish wind climatology suggests that approximately 15% of single radar measurement areas are lost on average when estimating ground level rainfall if no advection adjustment is applied. For the Finnish composite, area reductions of approximately 10% have been observed, while the measuring area is extended downstream by a similar amount. Advection becomes increasingly important at all ranges in snowfall with maximum distances exceeding 100 km.

Physical processes impacting passive particle dispersal in the Upper Florida Keys

Physical processes affecting the dispersion of passive particles (e.g., coral larvae, pollutants) in the Upper Florida Keys are investigated through in situ observations (acoustic Doppler current profilers and surface drifters) and numerical ocean circulation modeling (horizontal resolution: 800 m, vertical resolution: 0.1–1 m). During the study period in August 2006 (set to coincide with an annual coral spawning event), Lagrangian trajectories in the vicinity of the reef tract indicate that alongshelf advection was mainly poleward and due to the subtidal flow of the Florida Current, while cross-shelf advection was mainly onshore and due to wind-driven currents. Tidal currents resulted in predominantly alongshelf displacements, but did not contribute significantly to net passive particle transport on a weekly timescale. Typical advection distances were of the order of 10 to 50 km for pelagic durations of 1 week, with significant variability linked to geographical location. In contrast, the direction of transport from the offshore reefs remained essentially constant (i.e., potential dispersion pathways were limited). In addition, Lagrangian trajectories and progressive vector diagrams in the vicinity of the reef tract indicate that alongshelf variations in the cross-shelf velocity gradient associated with the FC are relatively weak on an alongshore scale of ca. 50 km. For August 2006, the highest particle concentrations typically occur inshore of the reef tract, thereby suggesting that onshore transport associated with wind-driven currents contributes significantly to the local retention of passive organisms (and other tracers) in the Upper Florida Keys. Overall, the results illustrate the necessity of conducting targeted in situ observations and numerical model predictions to quantify the physical processes affecting reef-scale advection, especially in an effort to understand local retention and dispersion mechanisms for larval marine organisms.

Alongshore advection and marine reserves: consequences for modeling and management

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 309:11-24 (2006) - doi:10.3354/meps309011 Alongshore advection and marine reserves: consequences for modeling and management David M. Kaplan* Department of Wildlife, Fish, & Conservation Biology, University of California, Davis, California 95616, USA *Email: dmkaplan@ucdavis.edu ABSTRACT: The appropriate configuration of marine reserves for maximizing harvests or ensuring species persistence when there is uncertainty or variability in larval dispersal patterns is not completely understood. This is particularly true in environments with large alongshore advection rates, as the success of a system of marine reserves depends on connectivity through larval and/or adult dispersal between adjacent marine reserves. In this paper, the consequences of alongshore advection in the presence of marine reserves for a fish species with sedentary adults and widely dispersing larvae are examined. First, a uniform configuration of reserves with constant alongshore advection rate is considered. The highest overall catch and recruitment rates occur when the spacing between reserves is precisely tuned to the advection distance. When the alongshore advection distance is allowed to vary in time, catch and recruitment are considerably less sensitive to alongshore advection. At small diffusion distances, catch values differ from what would be predicted from the time-averaged larval dispersal pattern due to density-dependent post-settlement effects. It is important to include short time scale settlement variability in marine reserve models under these conditions. When the spacing between reserves is allowed to vary, the tuning of the system to particular advection distances is less precise. Configurations of marine reserves with a variety of spacings between reserves exhibited more uniform catch levels as a function of advection distance. This suggests that variability in the spacing between reserves is desirable for protecting a diverse group of species with different dispersal patterns. KEY WORDS: Marine protected areas · Fisheries management · Population dynamics · Variable reserve-spacing · Advection variability Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 309. Online publication date: March 15, 2006 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2006 Inter-Research.

A Linear Theory of Orographic Precipitation

A linear theory of orographic precipitation is developed, including airflow dynamics, condensed water advection, and downslope evaporation. The formulation extends the widely used ‘‘upslope’’ model. Vertically integrated steady-state governing equations for condensed water are solved using Fourier transform techniques. Closed form expressions are derived for special cases. For more general cases, the precipitation field is computed quickly by multiplying the terrain transform by a wavenumber-dependent transfer function. Five length scales are included in the model: mountain width, a buoyancy wave scale, the moist layer depth, and two condensed water advection distances. The efficiency of precipitation in the model is sensitive to the decay of the forced ascent through the moist layer and to the advection of condensed water downwind into the region of descent. The strong influence of horizontal scale on precipitation pattern and amount predicted by the model is discussed. The model is illustrated by applying it to the Olympic Mountains in Washington State.

A simple but accurate mass conservative, peak-preserving, mixing ratio bounded advection algorithm with FORTRAN code

A simplified but very accurate method for calculating advection of mixing ratios in a mass conservative and monotonic manner is presented. This scheme replaces the polynomial approximations of other advection algorithms with dual-linear segments, and employs a special treatment near local maxima and minima to preserve extremes very well. Before updating mixing ratios, fluxes at grid-cell faces are bounded to yield conservative, monotonic, maximum-bounded and minimum-bounded solutions to the advection equation with very little numerical diffusion, even in locally deformational flows. “Bounded” here means that updated mixing ratios never exceed local maxima or fall below local minima. If an initial tracer distribution is everywhere positive, the solution is positive-definite, but negative values can be advected. With a “sharpening” option fully enabled, local maxima or minima are usually perfectly preserved, and features as small as 2–3Δ x in width are advected with virtually no numerical diffusion for many Courant numbers and advection distances. Algorithms are presented for advecting mixing ratios through variable-spaced grids in any flow, including strongly deformational flows. One- and two-dimensional tests of the scheme are presented. Relative to other advection algorithms, this scheme yields significantly lower peak, distribution and rms errors, especially when advecting poorly resolved features with sizes 1–3Δ x. Therefore this scheme may be useful in applications where peak and minima preservation of small features is desirable. A 41-line FORTRAN advection subroutine which can be readily applied for general advection problems is provided in the appendix.

Advection Distance of Water Droplets in Strong Winds

As part of a study on wind effects on runup and overtopping of coastal structures, advection distances for water droplets of various sizes were measured in a wind/wave flume. The study found that advection distances were considerably greater than would be expected from wind forces acting on spherical droplets. Flattening of the windward face of water droplets from splash and spray in the presence of strong wind was found to increase the drag of droplets in this study and possibly add a lifting force, thereby increasing the distances droplets were carried. Results of this study indicate that splash and spray may be carried over a coastal structure considerably farther than may be expected, which in turn may contribute to higher overtopping rates.

Controls on the mechanisms of fluid infiltration and front advection during regional metamorphism: a stable isotope and textural study of retrograde Dalradian rocks of the SW Scottish Highlands

ABSTRACTVein‐controlled retrograde infiltration of H2O‐CO2 fluids into Dalradian epidote amphibolite facies rocks of the SW Scottish Highlands under greenschist facies conditions resulted in alteration of calcite‐rich marble bands to dolomite and spatially associated 18O enrichment of about 10%. on a scale of metres. Fluid inclusion data indicate that the retrograde fluid was an H2O‐salt mixture with a low CO2 content, and that the temperature of the fluid was about 400d̀ C. Detailed petrographic and textural (backscattered electron imaging) studies at one garnet‐grade locality show that advection of fluid into marbles proceeded by a calcite‐calcite grain edge flow mechanism, while alteration of non‐carbonate wall‐rock is associated with veinlets and microcracks.Stable isotopic analysis of carbonates from marble bands provides evidence for advection of isotopic fronts through carbonate wall‐rocks perpendicular to dolomite veins, and fluid fluxes in the range 2.4–28.6 m3/m2 have been computed from measured advection distances. Coincidence of isotope and reaction fronts is considered to result from reaction‐enhanced kinetics of isotope exchange at the reaction front. Front advection distances are related to the proportion of calcite to quartz in each marble band, with the largest advection distance occurring in nearly pure calcite matrix. This relationship indicates that fluid flow in carbonates is only possible along fluid‐calcite‐calcite grain edges. However, experimental constraints on dihedral angles in calcite‐fluid systems require that pervasive infiltration occurred in response to calcite dissolution initiated at calcite‐calcite grain junctions rather than to an open calcite pore geometry.The regional extent of the retrograde infiltration event has been documented from the high δ18O of dolomite‐ankerite carbonates from veins and host‐rocks over an area of least 50 × 50 km in the SW Scottish Highlands. Isotopically exotic 18O‐rich retrograde fluids have moved rapidly upwards through the crust, inducing isotopic exchange and mineral reaction in wall‐rocks only where lithology, pore geometry or mineral solubilities, pressure and temperature have been appropriate for pervasive infiltration to occur.

Turbulence Length Scales in Stably Stratified Free Shear Flow Analyzed from Slant Aircraft Profiles

The vertical turbulence structure in the marine atmosphere close to a coastline is investigated using airborne measurements. The measurements are from a field experiment close to the coast in the southeast of Sweden, in the Baltic Sea. The Baltic Sea has two main properties that make it particularly interesting to study: significant annual lag in sea surface temperature compared to inland surface temperatures and the fact that it is surrounded by land in all directions within advection distances of from a few hours up to 10–15 hours in normal meteorological conditions. The present results are mostly from spring or early summer with mainly cool water that is, with a stable or neutral marine boundary layer but with substantial heating of the land area during daytime, thus considerable thermal contrasts. When the daytime inland convective boundary layer is advected out over the cool sea, there is a frictional decoupling in space analogous to the same nocturnal process in time. This sometimes creates a residual layer, a remnant of the inland convective boundary layer, that can be advected for considerable distances over the sea. At the top of this layer, wind shear gives rise to a local increase in turbulent kinetic energy. These layers are used for an analysis of turbulent scales for free shear flow in stable stratification. The analysis is based on different length scales used in numerical model closures for turbulence processes and reveals the asymptotic behavior of different scales in the neutral limit and their functional form, and also illustrates the nonlinear relationship between scales for different properties. The applicability of some often used formulations is also discussed. The profiles from the aircraft are taken from 25 slant soundings performed in connection to low-level boundary-layer flights. The results are calculated from turbulence data extracted through filtering techniques on instantaneous time (space) series (individual profiles). The calculated turbulence parameters from all profiles are lumped together and finally averaged compositely over all profiles.

The vertical turbulence structure of the coastal marine atmospheric boundary layer

The vertical turbulence structure in the marine atmosphere along a shoreline has been investigated using data from tower and aircraft measurements performed along the Baltic coast in the southeast of Sweden. Two properties make the Baltic Sea particularly interesting. It is surrounded by land in all directions within moderate advection distances, and it features a significant annual lag in sea surface temperature as compared with inland surface temperature. The present data were collected mostly during spring or early summer, when the water is cool, i.e., with a stably or neutrally stratified marine boundary layer usually capped by an inversion. Substantial daytime heating over the land area results in a considerable horizontal thermal contrast. Measurements were made on a small island, on a tower with a good sea fetch, and with an airborne instrument package. The profile data from the aircraft is from 25 slant soundings performed in connection to low level boundary layer flights. The results from the profiles are extracted through filtering techniques on individual time (space) series (individual profiles), applying different normalization and finally averaging over all or over groups of profiles. The land‐based data are from a low tower situated on the shoreline of a small island with a wide sector of unobstructed sea fetch. Several factors are found that add to the apparent complexity of the coastal marine environment: the state of the sea appears to have a major impact on the turbulence structure of the surface layer, jet‐shaped wind speed profiles were very common at the top of the boundary layer (in about 50% of the cases) and distinct layers with increased turbulence were frequently found well above the boundary layer (in about 80% of the cases). The present paper will concentrate on a description of the experiment, the analysis methods, and a general description of the boundary layer turbulence structure over the Baltic Sea.

WITAN: A Wind-Time Analyzer*

Airline meteorology requires procedures that offer both simplicity and speed of flight weather problems. Many of these problems have their basis in wind-time analysis. A WInd-Time-ANalyzer called WITAN can be developed from the simple geostrophic wind equation for constant pressure surfaces. This instrument speedily and with simplicity solves problems of geostrophic winds, wind components, advection components, advection distance, cross and on route components, ground speed, and flying time between check points. In addition with the polar parameters, (Rφ) given WITAN is an aid in the procedures of finding tracks better than the great circle under certain wind conditions.