Cyclic extrusion of a lava dome based on a stick-slip mechanism

Lava dome eruptions are sometimes characterised by large periodic fluctuations in extrusion rate over periods of hours that may be accompanied by Vulcanian explosions and pyroclastic flows. We consider a simple system of nonlinear equations describing a 1D flow of lava extrusion through a deep elastic dyke feeding a shallower cylindrical conduit in order to simulate this short-period cyclicity. Stick-slip conditions depending on a critical shear stress are assumed at the wall boundary of the cylindrical conduit. By analogy with the behaviour of industrial polymers in a plastic extruder, the elastic dyke acts like a barrel and the shallower cylindrical portion of the conduit as a die for the flow of magma acting as a polymer. When we applied the model to the Soufrière Hills Volcano, Montserrat, for which the key parameters have been evaluated from previous studies, cyclic extrusions with periods from 3 to 30 h were readily simulated, matching observations. The model also reproduces the reduced period of cycles observed when a major unloading event occurs due to lava dome collapse.

On the momentum fluxes associated with mountain waves in directionally sheared flows

The direct impact of mountain waves on the atmospheric circulation is due to the deposition of wave momentum at critical levels, or levels where the waves break. The first process is treated analytically in this study within the framework of linear theory. The variation of the momentum flux with height is investigated for relatively large shears, extending the authors’ previous calculations of the surface gravity wave drag to the whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation is used to treat inviscid, steady, nonrotating, hydrostatic flow with directional shear over a circular mesoscale mountain, for generic wind profiles. This approximation must be extended to third order to obtain momentum flux expressions that are accurate to second order. Since the momentum flux only varies because of wave filtering by critical levels, the application of contour integration techniques enables it to be expressed in terms of simple 1D integrals. On the other hand, the momentum flux divergence (which corresponds to the force on the atmosphere that must be represented in gravity wave drag parameterizations) is given in closed analytical form. The momentum flux expressions are tested for idealized wind profiles, where they become a function of the Richardson number (Ri). These expressions tend, for high Ri, to results by previous authors, where wind profile effects on the surface drag were neglected and critical levels acted as perfect absorbers. The linear results are compared with linear and nonlinear numerical simulations, showing a considerable improvement upon corresponding results derived for higher Ri.

Mountain waves in two-layer sheared flows: Critical-level effects, wave reflection, and drag enhancement

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.

The influence of the QBO on the propagation of equatorial waves into the stratosphere

The variation of stratospheric equatorial wave characteristics with the phase of the quasi-biennial oscillation (QBO) is investigated using ECMWF Re-Analysis and NOAA outgoing longwave radiation (OLR) data. The impact of the QBO phases on the upward propagation of equatorial waves is found to be consistent and significant. In the easterly phase, there is larger Kelvin wave amplitude but smaller westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave amplitude due to reduced propagation from the upper troposphere into the lower stratosphere, compared with the westerly phase. Differences in the wave amplitude exist in a deeper layer in summer than in winter, consistent with the seasonality of ambient zonal winds. There is a strong evidence of Kelvin wave amplitude peaking just below the descending westerly phase, suggesting that Kelvin waves act to bring the westerly phase downward. However, the corresponding evidence for WMRG and R1 waves is less clear. In the lower stratosphere there is zonal variation in equatorial waves. This reflects the zonal asymmetry of wave amplitudes in the upper troposphere, the source for the lower-stratospheric waves. In easterly winters the upper-tropospheric WMRG and R1 waves over the eastern Pacific region appear to be somewhat stronger compared to climatology, perhaps because of the accumulation of waves that are unable to propagate upward into the lower stratosphere. Vertical propagation features of these waves are generally consistent with theory and suggest a mixture of Doppler shifting by ambient flows and filtering. Some lower-stratosphere equatorial waves have a connection with preceding tropical convection, especially for Kelvin and R1 waves in winter.

The determination of total nitrogen and total phosphorus concentrations in freshwaters from land use, stock headage and population data: testing of a model for use in conservation and water quality management

1. Nutrient concentrations (particularly N and P) determine the extent to which water bodies are or may become eutrophic. Direct determination of nutrient content on a wide scale is labour intensive but the main sources of N and P are well known. This paper describes and tests an export coefficient model for prediction of total N and total P from: (i) land use, stock headage and human population; (ii) the export rates of N and P from these sources; and (iii) the river discharge. Such a model might be used to forecast the effects of changes in land use in the future and to hindcast past water quality to establish comparative or baseline states for the monitoring of change. 2. The model has been calibrated against observed data for 1988 and validated against sets of observed data for a sequence of earlier years in ten British catchments varying from uplands through rolling, fertile lowlands to the flat topography of East Anglia. 3. The model predicted total N and total P concentrations with high precision (95% of the variance in observed data explained). It has been used in two forms: the first on a specific catchment basis; the second for a larger natural region which contains the catchment with the assumption that all catchments within that region will be similar. Both models gave similar results with little loss of precision in the latter case. This implies that it will be possible to describe the overall pattern of nutrient export in the UK with only a fraction of the effort needed to carry out the calculations for each individual water body. 4. Comparison between land use, stock headage, population numbers and nutrient export for the ten catchments in the pre-war year of 1931, and for 1970 and 1988 show that there has been a substantial loss of rough grazing to fertilized temporary and permanent grasslands, an increase in the hectarage devoted to arable, consistent increases in the stocking of cattle and sheep and a marked movement of humans to these rural catchments. 5. All of these trends have increased the flows of nutrients with more than a doubling of both total N and total P loads during the period. On average in these rural catchments, stock wastes have been the greatest contributors to both N and P exports, with cultivation the next most important source of N and people of P. Ratios of N to P were high in 1931 and remain little changed so that, in these catchments, phosphorus continues to be the nutrient most likely to control algal crops in standing waters supplied by the rivers studied.

The prediction of nutrients into estuaries and their subsequent behaviour: application to the Tamar and comparison with the Tweed, U.K.

Some of the techniques used to model nitrogen (N) and phosphorus (P) discharges from a terrestrial catchment to an estuary are discussed and applied to the River Tamar and Tamar Estuary system in Southwest England, U.K. Data are presented for dissolved inorganic nutrient concentrations in the Tamar Estuary and compared with those from the contrasting, low turbidity and rapidly flushed Tweed Estuary in Northeast England. In the Tamar catchment, simulations showed that effluent nitrate loads for typical freshwater flows contributed less than 1% of the total N load. The effect of effluent inputs on ammonium loads was more significant (∼10%). Cattle, sheep and permanent grassland dominated the N catchment export, with diffuse-source N export greatly dominating that due to point sources. Cattle, sheep, permanent grassland and cereal crops generated the greatest rates of diffuse-source P export. This reflected the higher rates of P fertiliser applications to arable land and the susceptibility of bare, arable land to P export in wetter winter months. N and P export to the Tamar Estuary from human sewage was insignificant. Non-conservative behaviour of phosphate was particularly marked in the Tamar Estuary. Silicate concentrations were slightly less than conservative levels, whereas nitrate was essentially conservative. The coastal sea acted as a sink for these terrestrially derived nutrients. A pronounced sag in dissolved oxygen that was associated with strong nitrite and ammonium peaks occurred in the turbidity maximum region of the Tamar Estuary. Nutrient behaviour within the Tweed was very different. The low turbidity and rapid flushing ensured that nutrients there were essentially conservative, so that flushing of nutrients to the coastal zone from the river occurred with little estuarine modification.

Deriving global flood hazard maps of fluvial floods through a physical model cascade

Global flood hazard maps can be used in the assessment of flood risk in a number of different applications, including (re)insurance and large scale flood preparedness. Such global hazard maps can be generated using large scale physically based models of rainfall-runoff and river routing, when used in conjunction with a number of post-processing methods. In this study, the European Centre for Medium Range Weather Forecasts (ECMWF) land surface model is coupled to ERA-Interim reanalysis meteorological forcing data, and resultant runoff is passed to a river routing algorithm which simulates floodplains and flood flow across the global land area. The global hazard map is based on a 30 yr (1979–2010) simulation period. A Gumbel distribution is fitted to the annual maxima flows to derive a number of flood return periods. The return periods are calculated initially for a 25×25 km grid, which is then reprojected onto a 1×1 km grid to derive maps of higher resolution and estimate flooded fractional area for the individual 25×25 km cells. Several global and regional maps of flood return periods ranging from 2 to 500 yr are presented. The results compare reasonably to a benchmark data set of global flood hazard. The developed methodology can be applied to other datasets on a global or regional scale.

Numerical simulation of the Filchner overflow

The plume of Ice Shelf Water (ISW) flowing into the Weddell Sea over the Filchner sill contributes to the formation of Antarctic Bottom Water. The Filchner overflow is simulated using a hydrostatic, primitive equation three-dimensional ocean model with a 0.5–2 Sv ISW influx above the Filchner sill. The best fit to mooring temperature observations is found with influxes of 0.5 and 1 Sv, below a previous estimate of 1.6 ± 0.5 Sv based on sparse mooring velocities. The plume first moves north over the continental shelf, and then turns west, along slope of the continental shelf break where it breaks up into subplumes and domes, some of which then move downslope. Other subplumes run into the eastern submarine ridge and propagate along the ridge downslope in a chaotic manner. The next, western ridge is crossed by the plume through several paths. Despite a number of discrepancies with observational data, the model reproduces many attributes of the flow. In particular, we argue that the temporal variability shown by the observations can largely be attributed to the unstable structure of the flow, where the temperature fluctuations are determined by the motion of the domes past the moorings. Our sensitivity studies show that while thermobaricity plays a role, its effect is small for the flows considered. Smoothing the ridges out demonstrate that their presence strongly affects the plume shape around the ridges. An increase in the bottom drag or viscosity leads to slowing down, and hence thickening and widening of the plume

Foreword: International Space Science Institute (ISSI) workshop on observing and predicting Earth’s energy flows

The Earth’s climate, as well as planetary climates in general, is broadly regulated by three fundamental parameters: the total solar irradiance, the planetary albedo and the planetary emissivity. Observations from series of different satellites during the last three decades indicate that these three quantities are generally very stable. The total solar irradiation of some 1,361 W/m2 at 1 A.U. varies within 1 W/m2 during the 11-year solar cycle (Fröhlich 2012). The albedo is close to 29 % with minute changes from year to year but with marked zonal differences (Stevens and Schwartz 2012). The only exception to the overall stability is a minor decrease in the planetary emissivity (the ratio between the radiation to space and the radiation from the surface of the Earth). This is a consequence of the increase in atmospheric greenhouse gas amounts making the atmosphere gradually more opaque to long-wave terrestrial radiation. As a consequence, radiation processes are slightly out of balance as less heat is leaving the Earth in the form of thermal radiation than the amount of heat from the incoming solar radiation. Present space-based systems cannot yet measure this imbalance, but the effect can be inferred from the increase in heat in the oceans where most of the heat accumulates. Minor amounts of heat are used to melt ice and to warm the atmosphere and the surface of the Earth.

Near-Earth initiation of a terrestrial substorm

Despite the characterization of the auroral substorm more than 40 years ago, controversy still surrounds the processes triggering substorm onset initiation. That stretching of the Earth's magnetotail following the addition of new nightside magnetic flux from dayside reconnection powers the substorm is well understood; the trigger for explosive energy release at substorm expansion phase onset is not. Using ground-based data sets with unprecedented combined spatial and temporal coverage, we report the discovery of new localized and contemporaneous magnetic wave and small azimuthal scale auroral signature of substorm onset. These local auroral arc undulations and magnetic field signatures rapidly evolve on second time scales for several minutes in advance of the release of the auroral surge. We also present evidence from a conjugate geosynchronous satellite of the concurrent magnetic onset in space as the onset of magnetic pulsations in the ionosphere, to within technique error. Throughout this time period, the more poleward arcs that correspond to the auroral oval which maps to the central plasma sheet remain undisturbed. There is good evidence that flows from the midtail crossing the plasma sheet can generate north-south auroral structures, yet no such auroral forms are seen in this event. Our observations present a severe challenge to the standard hypothesis that magnetic reconnection in stretched magnetotail fields triggers onset, indicating substorm expansion phase initiation occurs on field lines that are close to the Earth, as bounded by observations at geosynchronous orbit and in the conjugate ionosphere.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.