Effect of the IMF B y component on the ionospheric flow overhead at EISCAT: observations and theory

We have analysed a database of 300 h of tristatic ionospheric velocity measurements obtained overhead at Tromsø (66.3° magnetic latitude) by the EISCAT UHF radar system, for the presence of flow effects associated with the y-component of the IMF. Since it is already known that the flow depends upon IMF B_z, a least-squares multivariate analysis has been used to determine the flow dependence on both IMF B_y and B_z simultaneously. It is found that significant flow variations with IMF B_y occur, predominantly in the midnight sector (2100/0300 MLT), but also pre-dusk (1600/1700 MLT), which are directed eastward for IMF B_y positive and westward for IMF B_y negative. The flows are of magnitude 20/30 m s^–1 nT^–1 in the midnight sector, and smaller, 10/20 m s^–1 nT^–1, pre-dusk, and are thus associated with significant changes of flow of order a few hundred m s^–1 over the usual range of IMF B_y of about ±5 nT. At other local times the IMF B_y-related perturbation flows are much smaller, less than 5 m s^–1 nT^–1, and consistent with zero within the uncertainty estimates. We have investigated whether these IMF B_y-dependent flows can be accounted for quantitatively by a theoretical model in which the equatorial flow in the inner magnetosphere is independent of IMF B_y, but where distortions of the magnetospheric magnetic field associated with a penetrating component of the IMF B_y field changes the mapping of the field to the ionosphere, and hence the ionospheric flow. We find that the principal flow perturbation produced by this effect is an east-west flow whose sense is determined by the north-south component of the unperturbed flow. Perturbations in the north-south flow are typically smaller by more than an order of magnitude, and generally negligible in terms of observations. Using equatorial flows which are determined from EISCAT data for zero IMF B_y, to which the corotation flow has been added, the theory predicts the presence of zonal perturbation flows which are generally directed eastward in the Northern Hemisphere for IMF B_y positive and westward for IMF B_y negative at all local times. However, although the day and night effects are therefore similar in principle, the model perturbation flows are much larger on the nightside than on the dayside, as observed, due to the day-night asymmetry in the unperturbed magnetospheric magnetic field. Overall, the model results are found to account well for the observed IMF B_y-related flow perturbations in the midnight sector, in terms of the sense and direction of the flow, the local time of their occurrence, as well as the magnitude of the flows (provided the magnetic model employed is not too distorted from dipolar form). At other local times the model predicts much smaller IMF B_y-related flow perturbations, and thus does not account for the effects observed in the pre-dusk sector.     

Hydromagnetic waves in a differentially rotating Annulus I. A test of local stability analysis

Abstract

A cylindrical annulus containing a conducting fluid and rapidly rotating about its axis is a useful model for the Earth's core. With a shear flow U ₀(s)∮, magnetic field B ₀(s)∮, and temperature distribution T _o(s) (where (s, ∮, z) are cylindrical polar coordinates), many important properties of the core can be modelled while a certain degree of mathematical simplicity is maintained. In the limit of rapid rotation and at geophysically interesting field strengths, the effects of viscous diffusion and fluid inertia are neglected. In this paper, the linear stability of the above basic state to instabilities driven by gradients of B ₀ and U ₀ is investigated. The global numerical results show both instabilities predicted by a local analysis due to Acheson (1972, 1973, 1984) as well as a new resistive magnetic instability. For the non-diffusive field gradient instability we looked at both monotonic fields [for which the local stability parameter Δ, defined in (1.4), is a constant] and non-monotonic fields (for which Δ is a function of s). For both cases we found excellent qualitative agreement between the numerical and local results but found the local criterion (1.6) for instability to be slightly too stringent. For the non-monotonic fields, instability is confined approximately to the region which is locally unstable. We also investigated the diffusive buoyancy catalysed instability for monotonic fields and found good quantitative agreement between the numerical results and the local condition (1.9). The new resistive instability was found for fields vanishing (or small) at the outer boundary and it is concentrated in the region of that boundary. The resistive boundary layer plays an important part in this instability so it is not of a type which could be predicted using a local stability analysis (which takes no account of the presence of boundaries).     

A steady state of the disc dynamo

Abstract

We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD ₀, and the other for |D| ? 1. Asymptotic solutions for |D—D ₀| ? |D ₀| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|^?s) for |B| → ∞, we demonstrate that |B| = O(|D|^1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.     

Tangential discontinuities and the optical analogy for stationary fields. v. formal integration of the force-free field equations

Abstract

This paper demonstrates the appearance of tangential discontinuities in deformed force-free fields by direct integration of the field equation ? x B = αB. To keep the mathematics tractable the initial field is chosen to be a layer of linear force-free field B_x = + B ₀cosqz, B_y = — B ₀sinqz, B_z = 0, anchored at the distant cylindrical surface ? = (x ² + y ²)^1/2 = R and deformed by application of a local pressure maximum of scale l centered on the origin x = y = 0. In the limit of large R/l the deformed field remains linear, with α = q[1 + O(l ²/R ²)]. The field equations can be integrated over ? = R showing a discontinuity extending along the lines of force crossing the pessure maximum. On the other hand, examination of the continuous solutions to the field equations shows that specification of the normal component on the enclosing boundary ? = R completely determines the connectivity throughout the region, in a form unlike the straight across connections of the initial field. The field can escape this restriction only by developing internal discontinuities.

Casting the field equation in a form that the connectivity can be specified explicitly, reduces the field equation to the eikonal equation, describing the optical analogy, treated in papers II and III of this series. This demonstrates the ubiquitous nature of the tangential discontinuity in a force-free field subject to any local deformation.     

Dayside convection and auroral morphology during an interval of northward interplanetary magnetic field

We investigate the dayside auroral dynamics and ionospheric convection during an interval when the interplanetary magnetic field (IMF) had predominantly a positive B_z component (northward IMF) but varying B_y. Polar UVI observations of the Northern Hemisphere auroral emission indicate the existence of a region of luminosity near local noon at latitudes poleward of the dayside auroral oval, which we interpret as the ionospheric footprint of a high-latitude reconnection site. The large field-of-view afforded by the satellite-borne imager allows an unprecedented determination of the dynamics of this region, which has not previously been possible with ground-based observations. The location of the emission in latitude and magnetic local time varies in response to changes in the orientation of the IMF; the cusp MLT and the IMF B_y component are especially well correlated, the emission being located in the pre- or post-noon sectors for B_y < 0 nT or B_y > 0 nT, respectively. Simultaneous ground-based observations of the ionospheric plasma drift are provided by the CUTLASS Finland HF coherent radar. For an interval of IMF B_y 0 nT, these convection flow measurements suggest the presence of a clockwise-rotating lobe cell contained within the pre-noon dayside polar cap, with a flow reversal closely co-located with the high-latitude luminosity region. This pattern is largely consistent with recent theoretical predictions of the convection flow during northward IMF. We believe that this represents the first direct measurement of the convection flow at the imaged location of the footprint of the high-latitude reconnection site.     

THE PROBLEM OF LONG-TERM STORAGE IN RESERVOIRS

Abstract

The geometry of a meandering stream depends strongly on the relative stream size (Q ^2/5 / g ^1/5)/D, on the valley slope, Sv, and on the charge, Q _s/Q, where Q and Q _s are the fluid and sediment discharges respectively, g is acceleration due to gravity and D is the mean sediment size. The geometry depends less strongly on the relative settling size of sediment, D/(v ^2/3 / g ^1/3), where v is the kinematic viscosity. For constant values of Q, S _v and D, the effect of increase of charge reduces the meander length, M _L, and the mean channel surface width, B, whereas meander width, M _B, bend radius, R _M, and mean channel depth, H, increase, For a constant value of (Q ^2/5 / g^1/5)/D the values of M _L, M _B, R _M and B increase with the increase of valley slope but the value of H tends to decrease.     

The Carbonate Radical (HCO3·/CO3–·) as a Reactive Intermediate in Water Chemistry: Kinetics and Modelling

Results from kinetic laboratory studies of reactions of the carbonate radical anion (CO₃^–·) with aromatic compounds in aqueous solution at T = 298 K are presented. Data were obtained in using a laser photolysis laser long-path absorption (LP-LPLA) apparatus which was designed for direct time-resolved studies of radical reactions. For the reactions of CO₃^–· with hydroquinone dimethyl ether (2), methyl anisole (3), benzene (4), p-xylene (5), toluene (6), chlorobenzene (7), nitrobenzene (8), and benzonitrile (9), rate coefficients of k₂ = (3.0 ± 0.6)·10⁷ M^–1 s^–1, k₃ = (9.7 ± 1.7)·10⁵ M^–1 s^–1, k₄ = (3.2 ± 0.7)·10⁵ M^–1 s^–1, k₅ = (3.8 ± 0.9)·10⁴ M^–1 s^–1, k₆ = (6.8 ± 2.3)·10⁴ M^–1 s^–1, k₇ = (2.7 ± 0.6)·10⁵ M^–1 s^–1, k₈ = (1.4 ± 0.5)·10⁴ M^–1 s^–1, and k₉ < 1.3·10² M^–1 s^–1 were obtained. In further studies the effect of temperature on the reactions (2), (4), and (5) has been studied. The kinetic data obtained for the reaction of the carbonate radical anion with aromatic compounds were compared to the corresponding reactions of the hydroxyl radical. Finally, these kinetic data were used within a simple model system to investigate the implications of carbonate radical anion kinetics within water treatment processes. It is shown that the degradation of organic pollutants in ^·OH-radical based water treatment may proceed via the CO₃^–·/HCO_3· radical under certain conditions.     

Fault dimensions,displacements and growth

Maximum total displacement (D) is plotted against fault or thrust width(W) for 65 faults, thrusts, and groups of faults from a variety of geological environments. Displacements range from 0.4 m to 40 km and widths from 150 m to 630 km, and there is a near linear relationship betweenD andW ². The required compatibility strains (e _s) in rocks adjacent to these faults increases linearly withW and with and ranges frome _s=2×10^–4 toe _s=3×10^–1. These are permanent ductile strains, which compare with values ofe _s=2×10^–5 for the elastic strains imposed during single slip earthquake events, which are characterised by a linear relationship between slip (u) andW.The data are consisten with a simple growth model for faults and thrusts, in which the slip in successive events increases by increments of constant size, and which predicts a relationship between displacement and width of the formD=cW ². Incorporation of constant ductile strain rate into the model shows that the repreat time for slip events remains constant throughout the life of a fault, while the displacement rate increases with time. An internally consistent model withe _s=2×10^–5, giving repeat times of 160 years and instantaneous displacement rates of 0.02 cm/yr, 0.2 cm/yr, and 2.0 cm/yr when total displacement is 1 m, 100 m, and 10 km, and slip increasing by 0.5 mm with each event, gives a good approximation of the data. The model is also applicable to stable sliding, the slip rate varying with ductile strain rate and withW ².     

A theoretical study of correlation between scaled energy and earthquake magnitude based on two source displacement models

The correlation of the scaled energy, ê = E_s/M₀, versus earthquake magnitude, M_s, is studied based on two models: (1) Model 1 based on the use of the time function of the average displacements, with a ω^-2 source spectrum, across a fault plane; and (2) Model 2 based on the use of the time function of the average displacements, with a ω^-3 source spectrum, across a fault plane. For the second model, there are two cases: (a) As τ ≒ T, where τ is the rise time and T the rupture time, lg(ê) ~ -M_s; and (b) As τ ≪ T, lg(ê) ~ -(1/2)M_s. The second model leads to a negative value of ê. This means that Model 2 cannot work for studying the present problem. The results obtained from Model 1 suggest that the source model is a factor, yet not a unique one, in controlling the correlation of ê versus M_s.     

Properties of electric turbulence in the polar cap ionosphere

Small-scale (scales of ∼0.5–256 km) electric fields in the polar cap ionosphere are studied on the basis of measurements of the Dynamics Explorer 2 (DE-2) low-altitude satellite with a polar orbit. Nineteen DE-2 passes through the high-latitude ionosphere from the morning side to the evening side are considered when the IMF z component was southward. A rather extensive polar cap, which could be identified using the ɛ-t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is shown that the logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields in the polar cap, are power law (μ ∼ s ^α). Here, μ is the variance of the detail coefficients of the signal discrete wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non-Gaussian and have intensified wings. When the probability density functions are renormalized, that is constructed of δE/s ^γ, where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statistically self-similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much smaller than in the auroral zone, the quantitative characteristics of field scaling in the two regions are similar. Two possible causes of the observed turbulent structure of the electric field in the polar cap are considered: (1) the structure is transferred from the solar wind, which is known to have turbulent properties, and (2) the structure is generated by convection velocity shears in the region of open magnetic field lines. The detected dependence of the characteristic distribution of turbulent electric fields over the polar cap region on IMF B _y and the correlation of the rms amplitudes of δE fluctuations with IMF B _z and the solar wind transfer function (B _y ² + B _z ²)^1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the dayside magnetopause when IMF B _z < 0, together with the absence of dependence on the IMF variability are arguments for the second mechanism.     

A modified multiple tension upward infiltration method to estimate the soil hydraulic properties

Determination of saturated hydraulic conductivity, K_s, and the shape parameters α and n of the water retention curve, θ(h), is of paramount importance to characterize the water flow in the vadose zone. This work presents a modified upward infiltration method to estimate K_s, α and n from numerical inverse analysis of the measured cumulative upward infiltration (CUI) at multiple constant tension lower boundary conditions. Using the HYDRUS‐2D software, a theoretical analysis on a synthetic loam soil under different soil tensions (0, 0–10, 0–50 and 0–100 cm), with and without an overpressure step of 10 cm high from the top boundary condition at the end of the upward infiltration process, was performed to check the uniqueness and the accuracy of the solutions. Using a tension sorptivimeter device, the method was validated in a laboratory experiment on five different soils: a coarse and a fine sand, and a 1‐mm sieved loam, clay loam and silt‐gypseous soils. The estimated α and n parameters were compared to the corresponding values measured with the TDR‐pressure cell method. The theoretical analysis demonstrates that K_s and θ(h) can be simultaneously estimated from measured upward cumulative infiltration when high (>50 cm) soil tensions are initially applied at the lower boundary. Alternatively, satisfactory results can be also obtained when medium tensions (<50 cm) and the K_s calculated from the overpressure step at the end of the experiment are considered. A consistent relationship was found between the α (R² = 0.86, p < 0.02) and n (R² = 0.97, p < 0.001) values measured with the TDR‐pressure cell and the corresponding values estimated with the tension sorptivimeter. The error between the α (in logarithm scale) and n values estimated with the inverse analysis and the corresponding values measured with pressure chamber were 3.1 and 6.1%, respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

Cusp Modeling and Observations at Low Altitude

Cusp properties have been investigated with an open-field line particle precipitation model and Defense Meteorological Satellite Program (DMSP) satellite observations. Particular emphasis is placed on the effects of IMF B_y, since previous studies focus mostly on IMF B_z. The model-data comparisons for various IMF configurations show that the model captures the large-scale features of the particle precipitation very well, not only in the cusp region, but also in other open-field line regions such as the mantle, polar rain, and open-field line low-altitude boundary layer (LLBL). When the IMF is strongly duskward/dawnward and weakly southward, the model predicts the occurrence of double cusp near noon: one cusp at lower latitude and one at higher latitude. The lower latitude cusp ions originate from the low-latitude magnetosheath whereas the higher latitude ions originate from the high-latitude magnetosheath. The lower latitude cusp is located in the region of weak azimuthal E × B drift, resulting in a dispersionless cusp. The higher latitude cusp is located in the region of strong azimuthal and poleward E × B drift. Because of a significant poleward drift, the higher latitude cusp dispersion has some resemblance to that of the typical southward IMF cusp. Occasionally, the two parts of the double cusp have such narrow latitudinal separation that they give the appearance of just one cusp with extended latitudinal width. From the 40 DMSP passes selected during periods of large (positive or negative) IMF B_y and small negative IMF B_z, 30 (75%) of the passes exhibit double cusps or cusps with extended latitudinal width. The double cusp result is consistent with the following statistical results: (1) the cusp’s latitudinal width increases with |IMF B_y| and (2) the cusp’s equatorward boundary moves to lower latitude with increasing |IMF B_y|.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.     

Source parameters of the Gonghe,Qinghai Province,China,earthquake from inversion of digital broadband waveform data

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Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

Geoidal Geopotential and World Height System

The geoidal geopotential value of W ₀ = 62 636 856.0 ± 0.5m ² s ^–2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W ₀ -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W ₀ -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W ₀ ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W ₀ ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: –55.1 cm, –11.0 cm, +42.4 cm, –11.1 cm and +1.8 cm, respectively.     

Response of ionospheric electric fields to variations in the interplanetary magnetic field

The STARE system (Scandinavian Twin Auroral Radar Experiment) provides estimates of electron drift velocities, and hence also of the electric field in the high-latitude E-region ionosphere between 65 and 70 degrees latitude. The occurrence of drift velocities larger than about 400 m/s (equivalent to an electric field of 20 mV/m) have been correlated with the magnitude of the Interplanetary Magnetic Field (IMF) components B_z and B_y at all local times. Observation days have been considered during which both southward (B_z<0) and northward (B_z>0) IMF occurred. The occurrence of electric fields larger than 20 mV/m increases with increases in B_z magnitudes when B_z<0. It is found that the effects of southward IMF continue for some time following the northward turnings of the IMF. In order to eliminate such residual effects for B_z<0, we have, in the second part of the study, considered those days which were characterized by a pure northward IMF. The occurrence is considerably lower during times when B_z>0, than during those when B_z is negative. These results are related to the expansion and contraction of the auroral oval. The different percentage occurrences of large electric field for B_y>0 and B_y<0 components of the IMF during times when B_z>0, clearly display a dawn-dusk asymmetry of plasma flow in the ionosphere. The effects of the time-varying solar-wind speed, density, IMF fluctuations, and magnetospheric substorms on the occurrence of auroral-backscatter observations are also discussed.     

A statistical study of the interplanetary magnetic field control of sporadic E-layer occurrence in the southern polar cap ionosphere

The influence of the interplanetary magnetic field (IMF) on the occurrence of sporadic E (Es)-layers in the southern polar cap ionosphere has been investigated. We statistically analysed ionogram and Doppler velocity observations made using a HF digital ionosonde located at Casey, Antarctica (66.3°S, 110.5°E; 81°S magnetic latitude) during the two summer campaign intervals 1 January to 18 February, and 1 November to 31 December 1997. The ionogram and Doppler velocity measurements were used to determine the Es-occurrence and electric field vectors (assuming E×B/B² drift), respectively. Concurrent IMF data were obtained from measurements made on board the Wind spacecraft. First, the gross properties of the IMF dependence of Es-formation were obtained: the occurrence rate was higher for negative B_y and/or positive B_z, and lower for positive B_y and/or negative B_z. To reconcile these gross properties with the electric field theory of Es-layer formation, the detailed diurnal variation of both Es-occurrence and the ionospheric electric field were obtained for different orientations of the IMF. The main statistical results are that: (1) the B_y component mainly controls the occurrence of the midnight Es-layers through its influence on the corresponding South West electric field; and (2) the B_z component mainly controls the occurrence of the evening Es-layers. However, the change in the occurrence rate for evening Es-layers was not related to the strength of the associated North West and North East electric fields. The total occurrence of Es-layers depended more on B_y than on B_z, owing to the dominance of B_y-controlled midnight Es-layers in the occurrence distribution. Nevertheless, the dependence of Es-occurrence on B_z was important. We suggest that the increase in Es-occurrence for positive B_z might be explained by the intermittent production of lower F-region ionisation by polar showers and squalls, which also increase in frequency and intensity for positive B_z. The importance of metallic ion transport within the ionosphere is also considered.     

Surface energy balance at a tropical station

Summary Studies of various fluxes, namely net radiation, soil heat, sensible heat and latent heat observed at a tropical station are presented in this paper. The time variation of these fluxes are examined in relation to various meteorological parameters and atmospheric conditions. The turbulent transfer coefficients have been evaluated to examine the applicability of the classical theory or the non-equivalence theory for eddy transport in the lower layers of the atmosphere. The energy balance at a tropical station is evaluated. It is found over year there is a net surplus of 94,000 ly. A detailed discussion of the disposal of this energy by various consuming processes is given.Symbols and notation All the quantities represented by symbols in the text of the paper are defined below C _p specific heat at constant pressure in cal. g^–1 °K - E evaporation in g cm^–2 hr^–1 - E ^* evaporative heat flux cal. cm^–2 sec^–1 (in Eq. 10) - e vapour pressure in millibars - e _z ,e _2z vapour pressure at heightsz and 2z - g acceleration due to gravity - H sensible heat flux cal cm^–2 sec^–1 (in Eq. 12) - K _M ,K _H ,K _W coefficients of eddy diffusivities of momentum, heat, and water vapour respectively in cm² sec^–1 - k von Karman' constant=0.4 - L Monin-Obukhov length (according to Monin and Obukhov [53] the structure of the turbulent boundary layer is determined by the non-dimensional variableZ/L whereL is defined byL=–(u _* ³ C _p T)/(kgH) - ly langleys - Q _c Q—sensible heat flux in langleys (in Eqs. 3 and 4) - Q _e E—latent heat flux in langleys (in Eqs. 3 and 4) - Q _s S—soil heat flux in langleys (in Eqs. 3 and 4) - Q _i Q _c +Q _e +Q _s whenK _M K _H K _W , (in Eq. 6) - Q' _i Q' _c +Q' _e +Q _s whenK _M =K _H =K _W (in Eq. 7) - qq mean specific humidity g kg^–1     

River flux uncertainties predicted by hydrological variability and riverine material behaviour

Data on riverine fluxes are essential for calculating element cycles (carbon, nutrients, pollutants) and erosion rates from regional to global scales. At most water‐quality stations throughout the world, riverine fluxes are calculated from continuous flow data (q) and discrete concentration data (C), the latter being the main cause of sometimes large uncertainties. This article offers a comprehensive approach for predicting the magnitude of these uncertainties for water‐quality stations in medium to large basins (drainage basin area > 1000 km²) based on the commonly used discharge‐weighted method. Uncertainty levels – biases and imprecisions – for sampling intervals of 3 to 60 days are correlated first through a nomograph with a flux variability indicator, the quantity of riverine material discharged in 2% of time (M_2%). In turn, M_2% is estimated from the combination of a hydrological reactivity index, W_2% (the cumulative flow volume discharged during the upper 2% of highest daily flow) and the truncated b_50sup exponent, quantifying the concentration versus discharge relationship for the upper half of flow values (C = a q ^b50sup, for q > q₅₀, where q₅₀ is the median flow): M_2% = W_2% + 27.6b_50sup. W_2% can be calculated from continuous flow measurements, and the b_50sup indicator can be calculated from infrequent sampling, which makes it possible to predict a priori the level of uncertainty at any station, for any type of riverine material either concentrated (b_50sup > 0) or diluted (b_50sup > 0) with flow. A large data base of daily surveys, 125 station variables of suspended particulate matter (SPM), total dissolved solids (TDS) and dissolved and particulate nutrients, was used to determine uncertainties from simulated discrete surveys and to establish relationships between indicators. Results show, for example, that for the same relatively reactive basin (W_2% > 25%), calculated fluxes from monthly sampling would yield uncertainties approaching ±100% for SPM (b_50sup > 1.4) fluxes and ±10% for TDS (b_50sup = ?0.2). The application to the nitrate survey of the river Seine shows significant trends for the 1972–2009 records. Copyright © 2012 John Wiley & Sons, Ltd.