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     

Observations of the response time of high-latitude ionospheric convection to variations in the interplanetary magnetic field using EISCAT and IMP-8 data

We have combined ∼300 h of tristatic measurements of the field-perpendicular F region ionospheric flow measured overhead at Tromsø by the EISCAT UHF radar, with simultaneous IMP-8 measurements of the solar wind and interplanetary magnetic field (IMF) upstream of the Earth’s magnetosphere, in order to examine the response time of the ionospheric flow to changes in the north-south component of the IMF (B_z). In calculating the flow response delay, the time taken by field changes observed by the spacecraft to first effect the ionosphere has been carefully estimated and subtracted from the response time. Two analysis methods have been employed. In the first, the flow data were divided into 2 h-intervals of magnetic local time (MLT) and cross-correlated with the “half-wave rectifier” function V²B_s, where V is the solar wind speed, and B_s is equal to IMF B_z if the latter is negative, and is zero otherwise. Response delays, determined from the time lag of the peak value of the cross-correlation coefficient, were computed versus MLT for both the east-west and north-south components of flow. The combined data set suggests minimum delays at ∼1400 MLT, with increased response times on the nightside. For the 12-h sector centred on 1400 MLT, the weighted average response delay was found to be 1.3 ± 0.8 min, while for the 12-h sector centred on 0200 MLT the weighted average delay was found to increase to 8.8 ± 1.7 min. In the second method we first inspected the IMF data for sharp and enduring (at least ∼5 min) changes in polarity of the north-south component, and then examined concurrent EISCAT flow data to determine the onset time of the corresponding enhancement or decay of the flow. For the case in which the flow response was timed from whichever of the flow components responded first, minimum response delays were again found at ∼1400 MLT, with average delays of 4.8 ± 0.5 min for the 12-h sector centred on 1400 MLT, increasing to 9.2 ± 0.8 min on the nightside. The response delay is thus found to be reasonably small at all local times, but typically ∼6 min longer on the nightside compared with the dayside. In order to make an estimate of the ionospheric information propagation speed implied by these results, we have fitted a simple theoretical curve to the delay data which assumes that information concerning the excitation and decay of flow propagates with constant speed away from some point on the equatorward edge of the dayside open-closed field line boundary, taken to lie at 77° magnetic latitude. For the combined cross-correlation results the best-fit epicentre of information propagation was found to be at 1400 MLT, with an information propagation phase speed of 9.0 km s⁻¹. For the combined event analysis, the best-fit epicentre was also found to be located at 1400 MLT, with a phase speed of 6.8 km s⁻¹.     

Letter to the editor Electric field fluctuations (25–35 min) in the midnight dip equatorial ionosphere

Measurements with a HF Doppler sounder at Kodaikanal (10.2°N, 77.5°E, geomagnetic latitude 0.8°N) showed conspicuous quasi-periodic fluctuations (period 25/35 min) in F region vertical plasma drift, V_z in the interval 0047/0210 IST on the night of 23/24 December, 1991 (A_p = 14, K_p < 4^–). The fluctuations in F region vertical drift are found to be coherent with variations in B_z (north-south) component of interplanetary magnetic field (IMF), in geomagnetic H/X components at high-mid latitude locations both in the sunlit and dark hemispheres and near the dayside dip equator, suggestive of DP2 origin. But the polarity of the electric field fluctuations at the midnight dip equator (eastward) is the same as the dayside equator inferred from magnetic variations, contrary to what is expected of equatorial DP2. The origin of the coherent occurrence of equatorial electric field fluctuations in the DP2 range of the same sign in the day and night hemispheres is unclear and merits further investigations.     

Ion composition measurements and modelling at altitudes from 140 to 350 km using EISCAT measurements

This work aims at processing the data of CP1 and CP2 programs of EISCAT ionospheric radar from 1987 to 1994 using the –full profile method which allows to solve the –temperature-composition ambiguity problem in the lower F region. The program of data analysis was developed in the CEPHAG in 1995–1996. To improve this program, we implemented another analytical function to model the ion composition profile. This new function better reflects the real profile of the composition. Secondly, we chose the best method to select the initial conditions for the –full profile procedure. A statistical analysis of the results was made to obtain the averages of various parameters: electron concentration and temperature, ion temperature, composition and bulk velocity. The aim is to obtain models of the parameter behaviour defining the ion composition profiles: z₅₀ (transition altitude between atomic and molecular ions) and dz (width of the profile), for various seasons and for high and low solar activities. These models are then compared to other models. To explain the principal features of parameters z₅₀ and dz, we made an analysis of the processes leading to composition changes and related them to production and electron density profile. A new experimental model of ion composition is now available.     

Combined geothermal-geophysical models of the earth's crust and upper mantle for the European continent

An attempt is made to obtain a combined geophysical model along two regional profiles: Black Sea— White Sea and Russian Platform—French Central Massif. The process of the model construction had the following stages: 1. The relation between seismic velocity (V_p, km/s) and density (σ, g/cm³) in crustal rocks was determined from seismic profiles and observed gravity fields employing the trial and error method. 2. Relations between heat production HP (μW/m³), velocity and density were established from heat flow data and crustal models of old platforms where the mantle heat flow HF_M is supposed to be constant. The HF_M value was also determined to 11 ± 5 mW/m². 3. A petrological model of the old platform crust is proposed from the velocity-density models and the observed heat flow. It includes 10–12 km of acid rocks, 15–20 km of basic/metamorphic rocks and 7–10 km of basic ones. 4. Calculation of the crustal gravity effects; its substraction from the observed field gave the mantle gravity anomalies. Extensively negative anomalies have been found in the southern part of Eastern Europe (50–70 mgal) and in Western Europe (up to 200 mgal). They correlate with high heat flow and lower velocity in the uppermost mantle. 5. A polymorphic advection mechanism for deep tectonic processes was proposed as a thermal model of the upper mantle. Deep matter in active regions is assumed to be transported (advected) upwards under the crust and in its place the relatively cold material of the uppermost mantle descends. The resulting temperature distribution depends on the type of endogeneous regime, on the age and size of geostructure. Polymorphic transitions were also taken into account.     

Vertical mixing in Überlinger See,western part of Lake Constance

Depth variable vertical eddy diffusion coefficients for heat (K _z) were calculated from continuously measured temperature profiles in Überlinger See (western part of Lake Constance). The temperatures were averaged over vertical intervals of 10 m yielding 14 discrete values (maximum depth of Überlinger See: 147 m). A linear fit from 10 June to 29 September 1987 was used to smooth the significant temperature fluctuations caused by internal seiches of Lake Constance.Assuming horizontal homogeneity for the smoothed data the Gradient-Flux-Method was applied to compute vertical diffusion coefficientsK _z at different depths using the depth variable volumes and surfaces of the 14 layers. The resulting mean diffusion coefficients for the period from June to September are 0.04 cm²/s near the thermocline and up to 0.8 cm²/s in deeper strata (accuracy: ± 50%). It is shown that horizontal mixing between Überlinger See and Obersee (main lake) alters the computation ofK _z by less than 50%.A relationship betweenK _z and stability (Brunt-Väisälä) frequencyN is found which corresponds well to the theory of internal wave induced turbulence.Combining the diffusion coefficients with measured phosphorus profiles, a phosphorus flux from the hypolimnion to the epilimnion of (0.7 ± 0.4) mg P m^–2 d^–1 was calculated, corresponding to about 20% of the average external loading per area of Lake Constance in 1986.     

Wave propagation in a seven-story reinforced concrete building: I. Theoretical models

For transient, high frequency, and pulse like excitation of structures in the near field of strong earthquakes, the classical design approach based on relative response spectrum and mode superposition may not be conservative. For such excitations, it is more natural to use wave propagation methods. In this paper (Part I), we review several two-dimensional wave propagation models of buildings and show results for theoretical dispersion curves computed for these models. We also estimate the parameters of these models that would correspond to a seven-story reinforced concrete building in Van Nuys, California. Ambient vibration tests data for this building imply vertical shear wave velocity β_z=112 m/s and anisotropy factor β_x/β_z=0.55 for NS vibrations, and β_z=88 m/s and β_x/β_z=1 for EW vibrations. The velocity of shear waves propagating through the slabs is estimated to be about 2000 m/s. In the companion paper (Part II), we estimate phase velocities of vertically and horizontally propagating waves between seven pairs of recording points in the building using recorded response to four earthquakes.     

The Entropy Score and its Uses in Earthquake Forecasting

Suppose a forecasting scheme associates a probability p^* with some observed outcome. The entropy score given to this forecast is then –logp^*. This article provides a review of the background to this scoring method, its main properties, and its relationships to concepts such as likelihood, probability gain, and Molchans - diagram. It is shown that, in terms of this score, an intrinsic characterization can be given for the predictability of a given statistical forecasting model. Uses of the score are illustrated by applications to the stress release and ETAS models, electrical signals, and M8.     

Properties and origin of energetic particles at the duskside of the Earth’s magnetosheath throughout a great storm

We study an interval of 56 h on January 16 to 18, 1995, during which the GEOTAIL spacecraft traversed the duskside magnetosheath from X ≅ −15 to −40 R_E and the EPIC/ICS and EPIC/STICS sensors sporadically detected tens of energetic particle bursts. This interval coincides with the expansion and growth of a great geomagnetic storm. The flux bursts are strongly dependent on the magnetic field orientation. They switch on whenever the B_z component approaches zero (B_z ≅ 0 nT). We strongly suggest a magnetospheric origin for the energetic ions and electrons streaming along these “exodus channels”. The time profiles for energetic protons and “tracer” O⁺ ions are nearly identical, which suggests a common source. We suggest that the particles leak out of the magnetosphere all the time and that when the magnetosheath magnetic field connects the spacecraft to the magnetotail, they stream away to be observed by the GEOTAIL sensors. The energetic electron fluxes are not observed as commonly as the ions, indicating that their source is more limited in extent. In one case study the magnetosheath magnetic field lines are draped around the magnetopause within the YZ plane and a dispersed structure for peak fluxes of different species is detected and interpreted as evidence for energetic electrons leaking out from the dawn LLBL and then being channelled along the draped magnetic field lines over the magnetopause. Protons leak from the equatorial dusk LLBL and this spatial differentiation between electron and proton sources results in the observed dispersion. A gradient of energetic proton intensities toward the Z_GSM= 0 plane is inferred. There is a permanent layer of energetic particles adjacent to the magnetosheath during this interval in which the dominant component of the magnetic field was B_z.     

Pulsating of the generalized ion and neutral polar winds

A three-dimensional, time-dependent model of the ion and neutral polar winds was used to study their dynamic evolution during the May 4, 1998 magnetic storm. The simulation tracked the dynamics of five species (O⁺, H⁺, H_s, O_s, and electrons) and covered a 9-h period. During the storm, D_st decreased to −210 nT, Ap reached 300, and K_p was elevated. The IMF B_z component was southward at the start of the storm and for several hours thereafter and then turned northward. However, the magnetospheric energy input to the ionosphere exhibited a 50-min oscillation, with the plasma convection and particle precipitation patterns expanding and contracting in a periodic manner. As a consequence, the ion and neutral polar winds pulsated with an approximate 50-min period. The H⁺ and O⁺ ions displayed cyclic upflows and downflows in the topside ionosphere as well as a highly structured spatial distribution that varied with time. The vertical flux of the neutral H_s atoms was upward at the top of the ionosphere, but the magnitude varied in a cyclic manner in response to the oscillating stormtime energy input. The vertical flux of neutral O_s atoms was downward at the top of the ionosphere and varied significantly with the stormtime energy input. For H⁺, O⁺, and H_s, the maximum total (integrated) vertical flux during the storm was upward at the top of the ionosphere, with values of 8–9×10²⁵ particles/s for H⁺, 2–4×10²⁶ particles/s for O⁺, and 2–3×10²⁷ particles/s for H_s. The corresponding total vertical O_s flux was predominately downward, with only localized areas with positive fluxes.     

Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology

Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology (n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A  10⁻³⁵ Pa⁻³ s⁻¹ for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.     

A fracture mechanics study of subcritical tensile cracking of quartz in wet environments

Load relaxation and cross-head displacement rate-change experiments have been used to establish log₁₀ stress intensity factor (K) versus log₁₀ crack velocity (v) diagrams for double torsion specimens, of synthetic quartz cracked on thea plane in liquid water and moist air.For crack propagation normal toz and normal tor at 20°C,K _Ic (the critical stress intensity factor) was found to be 0.852±0.045 MN·m^–3/2 and 1.002±0.048 MN·m^–3/2, respectively.Subcritical crack growth at velocities from 10^–3 m·s^–1 to 10^–9 m·s^–1 at temperatures from 20°C to 80°C is believed to be facilitated by chemical reaction between the siloxane bonds of the quartz and the water or water vapour of the environment (stress corrosion). The slopes, of isotherms in theK-v diagrams are dependent upon crystallographic orientation. The isotherms have a slope of 12±0.6 for cracking normal tor and 19.9±1.7 for cracking normal toz. The activation enthalpy for crack propagation in the former orientation in liquid water at temperatures from 20°C to 80°C is 52.5±3.8 kJ·mole^–1.A discussion is presented of the characteristics of theK-v diagrams for quartz.     

Sulla turbolenza delle correnti marine nello stretto di messina

Riassunto Gli Autori espongono i risultati di un tentativo di valutazione del grado di turbolenza verticale delle correnti marine davanti alle imboccature Nord e Sud dello Stretto di Messina. I valori massimi ottenuti per il coefficiente di diffusione verticale della salinitàK _z sono dell'ordine di 10³–10⁴ cm²/sec.

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Summary The Authors present the results of some calculations carried out to obtain values of the vertical turbulence (by means of the coefficient of eddy-diffusion of salinityK _z ) of the currents in the Strait of Messina. The maximum values ofK _z are of the order of 10³–10⁴ cm²/sec.

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Comunicazione presentata il 24 Aprile 1957 alla Quinta Assemblea Generale della «Società Italiana di Geofisica e Meteorologia» (Genova: 23–25 Aprile 1957).     

Unified modeling of flow liquefaction and cyclic mobility

Flow liquefaction and cyclic mobility are two different phenomena that are encountered during strong earthquakes. Flow liquefaction is associated with the contractive behavior of loose granular materials and cyclic mobility is associated with the dilative response of both loose and dense granular materials at low confining stresses. These two types of response pertain to the same material and therefore should be modeled in a consistent manner. Whether a soil in a given state exhibits contractive or dilative behavior is dependent on its dilatancy, d=d_v^p/d_q^p. A form of the dilatancy d=d(η,ψ,C) is proposed, where η=q/p is the stress ratio, and ψ and C denote the internal state variables and the intrinsic properties, respectively. It has been shown that such a state-dependent dilatancy is effective in describing both the contractive and dilative behavior. This allows the soil behavior associated with flow liquefaction and cyclic mobility during earthquakes to be modeled in a unified way.     

Anelasticity of the crust and upper mantle beneath north and central India from the inversion of observed Love and Rayleigh wave attenuation data

The fundamental mode Love and Rayleigh waves generated by earthquakes occurring in Kashmir, Nepal Himalaya, northeast India and Burma and recorded at Hyderabad, New Delhi and Kodaikanal seismic stations are analysed. Love and Rayleigh wave attenuation coefficients are obtained at time periods of 15–100 seconds, using the spectral amplitude of these waves for 23 different paths along northern (across Burma to New Delhi) and central (across Kashmir, Nepal Himalaya and northeast India to Hyderabad and Kodaikanal) India. Love wave attenuation coefficients are found to vary from 0.0003 to 0.0022 km^–1 for northern India and 0.00003 km^–1 to 0.00016 km^–1 for central India. Similarly, Rayleigh wave attenuation coefficients vary from 0.0002 km^–1 to 0.0016 km^–1 for northern India and 0.00001 km^–1 to 0.0009 km^–1 for central India. Backus and Gilbert inversion theory is applied to these surface wave attenuation data to obtainQ ^–1 models for the crust and uppermost mantle beneath northern and central India. Inversion of Love and Rayleigh wave attenuation data shows a highly attenuating zone centred at a depth of 20–80 km with lowQ for northern India. Similarly, inversion of Love and Rayleigh wave attenuation data shows a high attenuation zone below a depth of 100 km. The inferred lowQ value at mid-crustal depth (high attenuating zone) in the model for northern India can be by underthrusting of the Indian plate beneath the Eurasian plate which has caused a low velocity zone at this shallow depth. The gradual increase ofQ ^–1 from shallow to deeper depth shows that the lithosphere-asthenosphere boundary is not sharply defined beneath central India, but rather it represents a gradual transformation, which starts beneath the uppermost mantle. The lithospheric thickness is 100 km beneath central India and below that the asthenosphere shows higher attenuation, a factor of about two greater than that in the lithosphere. The very lowQ can be explained by changes in the chemical constitution taking place in the uppermost mantle.     

Graphical analysis of enthalpy-composition relationships in mixed magmas

Enthalpy-composition diagrams (H^*-X) calculated from existing temperature-composition (T-X) phase diagrams and thermodynamic data provide a simple and effective means for evaluating the enthalpy-temperature effects of magma mixing. If athermal mixing is assumed, adiabatic mixing lines on H^*-X diagrams are straight lines because enthalpy, unlike temperature, is an extensive property of a system. Comparison of binary T-X diagrams with their derivative H^*-X diagrams shows that incorrect predictions can be obtained when T-X diagrams are used to analyze mixing problems.An H^*-X diagram calculated using experimentally determined phase equilibria for anhydrous basalt-rhyolite mixtures predicts that adiabatic mixing of basalt and rhyolite at their respective liquidus temperatures will result in small amounts of crystallization ( < 2 wt.% ). Because the phase equilibria of hydrous basalt-rhyolite mixtures have not yet been determined, an H^*-X diagram for such mixtures cannot be constructed. However, existing hydrous phase equilibria can be used to predict whether adiabatic mixtures of anhydrous basalt and hydrous rhyolite will be super- or subliquidus. Calculations at P_total = 200 MPa show that on an H^*-X diagram a mixing chord drawn between anhydrous basalt and water-saturated rhyolite at their respective liquidus temperatures lies below the enthalpy values calculated for a Paricutin andesite and Mt. St. Helens dacite at their estimated liquidus temperatures. This indicates that the liquidus for mixtures of anhydrous basalt and water-saturated rhyolite is noticeably convex upward, suggesting that larger amounts of crystallization will occur than in the anhydrous case.     

Über einige Methoden der «sekundären» gravimetrischen Auswertung

Summary After definitions is given an interpolation-like residual method. —It is pointed out the usual disjoining in two parts of the Bouguer-map to be unsatisfactory; in general is the whole «spectrum» to disjoin in several parts from the «noise» to the «regional». — There are someg _zz (andg _z) methods represented; in this way of representation are the methods without examples direct comparable.     

Dispersion Measurements of <Emphasis Type="Italic">P</Emphasis> Waves and their Implications for Mantle <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We analyze the anelasticity of the earth using group delays of P-body waves of deep (>200 km) events in the period range 4–32 s for epicentral distances of 5–85 degrees. We show that Time Frequency Analysis (TFA), which is usually applied to very dispersive surface waves, can be applied to the much less dispersive P-body waves to measure frequency-dependent group delays with respect to arrival times predicted from the CMT centroid location and PREM reference model. We find that the measured dispersion is due to: (1) anelasticity (described by the P-wave quality factor Q _p ), (2) ambient noise, which results in randomly distributed noise in the dispersion measurements, (3) interference with other phases (triplications, crustal reverberations, conversions at deep mantle boundaries), for which the total dispersion depends on the amplitude and time separation between the different phases, and (4) the source time function, which is dispersive when the wavelet is asymmetrical or contains subevents. These mechanisms yield dispersion ranging in the order of one to 10 seconds with anelasticity responsible for the more modest dispersion. We select 150 seismograms which all have small coda amplitudes extending to ten percent of the main arrival, minimizing the effect of interference. The main P waves have short durations, minimizing effects of the source. We construct a two-layer model of Q _p with an interface at 660 km depth and take Q _p constant with period. Our data set is too small to solve for a possible frequency dependence of Q _p . The upper mantle Q ₁ is 476 [299–1176] and the lower mantle Q ₂ is 794 [633–1064] (the bracketed numbers indicate the 68 percent confidence range of Q _p ^–1). These values are in-between the AK135 model (Kennett et al., 1995) and the PREM model (Dziewonski and Anderson, 1981) for the lower mantle and confirm results of Warren and Shearer (2000) that the upper mantle is less attenuating than PREM and AK135.     

The criterion of dynamic stability of zonal motion including the vertical shear

Summary Many writers treated on the problem of dynamic instability of westerly flow due to the excessive horizontal shear, and the present author discusses the corresponding dynamic instability due to the vertical shear. The critical vertical shear in indifferent stratification is given by the condition — the meridional component of absolute vorticity vanishes, — and is an approximate negative valueof 10^–4 sec ^–1 in middle latitude. However the critical vertical shear in normal stable stratification is a fairly large negative value of 2 sec^–1. It might be emphasized that the problem of this study differs fromRichardson's criterion of turbulence, for the present author discusses the condition under which the zonal flow is dynamically stable, whileRichardson expressed the condition under which the turbulence will decrease.     

Response of fixed offshore platforms to wave and current loading including soil–structure interaction

Fixed offshore platforms supported by pile foundations are required to resist dynamic lateral loading due to wave forces. The response of a jacket offshore tower is affected by the flexibility and nonlinear behaviour of the supporting piles. For offshore towers supported by clusters of piles, the response to environmental loads is strongly affected by the pile–soil–pile interaction. In the present study, the response of fixed offshore platforms supported by clusters of piles is investigated. The soil resistance to the pile movement is modelled using dynamic p–y curves and t–z curves to account for soil nonlinearity and energy dissipation through radiation damping. The load transfer curves for a single pile have been modified to account for the group effect. The wave forces on the tower members and the tower response are calculated in the time domain using a finite element package (ASAS). Several parameters affecting the dynamic characteristics of the platform and the platform response have been investigated.