Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Earth’s free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth’s principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate ω ₃ fluctuates with the semi-Euler/Chandler period, although its amplitude (about 10⁻¹⁹ rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), θ, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth’s triaxial nature has little impact on ω ₃, but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency–amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m ₁, m ₂) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.     

Singlet oxygen O2(b1Σ g + ) production at altitudes of the polar ionosphere

The relative rate constants of O₂(b¹Σ _g ⁺ , v= 1–4) production at an inelastic interaction between electronically excited N(²D) atoms and O₂(X³Σ _g ^? , v = 0) oxygen molecules have been calculated. It was shown that an increase in equilibrium distances between oxygen atoms in NO₂ quasi-molecule, produced during the interaction, substantially increases the calculated relative production rates of O₂(b¹Σ _g ⁺ , v > 1). The obtained coefficients are used to calculate the O₂(b¹Σ _g ⁺ , v= 1–4) relative populations at 110 km (T = 250 K) and 150 km (T = 500 K) altitudes of the polar ionosphere. The calculated populations have been compared with the results of the published measurements of the Atmospheric system band luminosity intensities, and satisfactory agreement has been obtained for low altitudes.     

Study on the property of apparent resistivity changes of rock samples byin situ shear and friction test

In the strip limestone mine in Guiding county, Guizhou Province the shear and frictionin situ tests of rock body were made for the three typical inclined weak bands C ₃ ¹ /C ₃ ¹ , C ₃ ¹ /C ₂ ² and C ₂ ² /C ₂ ¹ . The tests were made according to the second scheme of cuneate sample of the standards on rock mechanics test of Water Conservancy and Electricity Ministry. The changes of the resistivity in the weak band and the acoustic speed across the weak band were measured in the same time. The apparent resistivity data, obtained for 8 samples on 27 measure lines in 38 cycle tests, show that the apparent resistivity changes have rather obvious characters as follows: 1. At shear and friction stage, the change of the apparent resistivity accelerates after the yield point, and reaches the maximum of change rate and change amplitude near fracture point (except the lines with resistivity invariant); 2. On the same sample, the resistivity changes are different on the various lines and related to the location settled the lines, there are some “sensitive” location; 3. At the stage of preloading normal stress before shearing, the resistivity decreases on most lines, but on a few lines the resistivity does not changes; 4. After unloading shear stress, the resistivity could not recover completely and the hysteresis of resistiviity takes place on a few lines.     

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T ₁ (maximal tension in the deviatoric sense) and T ₃ (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and ?, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain ? to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T ₁ and T ₃ should be analyzed simultaneously. For each side, + and ?, the projections of the T ₁ and T ₃ axes on the generally oriented plane n form the shear sectors S ⁺ and S ^?, which are determined unambiguously and to whose angular domains the possible directions p ⁺ and p ^? of the shear stress vectors belong. In order for the extreme stress axes T ₁ ⁺ ,T ₃ ⁺ and T ₁ ^? , T ₃ ^? to be statically compatible on the generally oriented plane n, it is required that sectors S ⁺ and S ^? had a nonempty intersection. The direction vectors p ⁺ and p ^? are determined uniquely if, besides axes T ₁ ^? , T ₃ ^? and T ₁ ⁺ , T ₃ ⁺ , also the ratios of differential stresses R ⁺ and R ^? (0 ≤ R ^± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors T _R ⁺ and T _R ^? The necessary condition for tensors T _R ⁺ and T _R ^? being statically compatible on plane n is the equality p ⁺ = p ^?. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T ₁ ⁺ , T ₃ ⁺ are determined if the projections of axes T ₁ ^? , T ₃ ^? axes on side — are given. The angle between the projections of axes T ₁ ⁺ , T ₁ ^? and/or T ₃ ⁺ , T ₃ ^? on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T ₁ ⁺ , T ₃ ⁺ for a given sector S ^?. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T ₃ ⁺ and T ₁ ⁺ axes, respectively. The compression-extension zones can contain the poles of either T ₁ ⁺ or T ₃ ⁺ axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p ^? on side ?, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T ₁ ^? , T ₃ ^? and T ₁ ⁺ , T ₃ ⁺ is specified, then, the stress values on side + are uniquely determined from the known stress values on side ?. From the value of differential stress ratio R ^?, one can calculate the value of R ⁺, and using the values of the principal stresses on side ?, determine the total stress tensor T ⁺ on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.     

Oscillations of the Earth with periods of 9–57 min in the background seismic process and the energy flux direction in the range of the free oscillation 0 S 2

Retrospective data of monitoring under conditions of low seismic activity are used to identify free oscillations of the Earth, including the fundamental mode, the oscillation with a central period of 54 min (₀ S ₂ ^m multiplet), split into five lines with azimuthal numbers m = ?2, ?1, 0, 1, 2. It is shown that some lines of this oscillation are also recorded in atmospheric pressure variation spectra and group in ensembles of observations around frequencies predicted by the ₀ S ₂ ^m splitting theory. This phenomenon is discovered in data recorded both synchronously and in different time intervals. A causal relationship involved in the oscillation under study is determined on the basis of the examination of the direction of the acoustic energy flux. The energy flux in the region of the ₀ S ₂ ^m multiplet is shown to be directed from the Earth toward the atmosphere. This suggests that deep processes in the Earth are capable of exciting its upper shells.     

The role of the SO2 oxidation for the background stratospheric sulfate layer in the light of new reaction rate data

Presently available data on the reaction of SO₂ with OH radicals (OH + SO₂ + \(M\xrightarrow[{k_1 }]{}\) HSO₃ +M) are critically reviewed in light of recent stratospheric sulfur budget calculations. These calculations impose that the net oxidation ratek of SO₂ within the stratosphere should fall within the range 10^?7≤k≤10^?9, if the SO₂ oxidation model for the stratospheric sulfate layer is assumed to be correct. The effective reaction rate constantk ₁ ^* =k ₁[M] at the stratospheric temperature is estimated as $$k_1^* = \frac{{(8.2 \pm 2.2) \times 10^{ - 13} \times [M]}}{{(0.79 \mp 0.34) \times 10^{ - 13} + [M]}}cm^3 /molecules sec$$ where [M] refers to the total number density (molecules/cm³). Using the above limiting values ofk ₁ ^* , and the estimated OH density concentrations, the net oxidation rate is calculated as 3.6×10^?7≤k≤1.3×10^?8 at 17 km altitude. This indicates that the upper limit of thesek values exceeds the tolerable range imposed by the model by a factor of about four. Obviously the uncertainty of thek ₁ ^* values and of the OH concentrations in the stratosphere is still too large to make definite conclusions on the validity of the SO₂ model.     

On the determination of the energy and depth of volcanic explosions (paper dedicated to G. S. Gorshkov)

The determination of the energy and depth of powerful volcanic explosions using direct geophysical and geological methods is rarely successful. In most of cases investigators have to solve the problem of estimating the energy of an explosion, its depth, the mass and the amount of thrown-out materials from the dimensions of the funnel (crater, maar) and from geological data. Experiments with big throw-out blasts have allowed us to determine the energy and depth of explosions by giving us relations which determine the radius of the explosion funnel as a function of the energy of explosion and of the depth of its center (1) $$R_o = F(E,W)$$ whereR _o is the radius of the funnel,E is the energy,W is the depth of the explosion center. The inverse problem — to determineE andW from a knownR _o — has an ambiguous solution and it is solved parametrically relative toE andW. In order to obtain an unambiguous solution, some more or less arbitrary conditions must be assumed. When the problem of volcanic explosions is examined from the outer ballistic point of view the following equation is obtained whereR _t is the throw-out distance of explosion fragments. (2) $$R_1 = F(E,W)$$ Equations (1) and (2) give us an unambiguous determination of the energy of explosionE and of the depth of the centerW. There is a good correlation between these results and the data from direct geophysical observations.     

Polar motion influences in the gravity data recorded by superconducting gravimeters

Gravity data stored in the GGP database (GGP-ISDC) are used to study the small gravity variations caused by polar motion. In a first step the dominant tidal signal and the instrumental drift have to be eliminated from the gravity data. In most cases it is sufficient to model the instrumental drift by polynomials of low degree. The resulting non-tidal gravity variations are split up into their main constituents by fitting two sinusoidal waves with periods of 365.25 days (annual wobble) and 432 days (Chandler wobble). In a similar way the gravity effect of the observed polar motion (IERS-Data) is processed. The ratio between the correspondent amplitudes gives the amplitude factors δ of both wobbles.In a more sophisticated model an additional annual wave was included, destined to absorb disturbing influences with annual period (e.g. environmental influences of different origin). The amount of these influences and the success of their elimination are very different at the individual stations.Besides the comparison of the amplitude factors it also was tried to compare the gravity residuals itself. For that purpose the data series recorded at the different stations were transferred to a common reference point (0°E, 45°N). The graph of the stacked data series gives a first impression of the accordance of the data series recorded at the different stations. Since randomly distributed disturbing influences are reduced by the averaging the amplitude factors derived from the mean of the stacked data series are more reliable than the values derived from the data at the individual stations.In the end 12 data series were included in a common processing. Amplitude factors of 1.183 for the annual and 1.168 for the Chandler wobble result with mean errors less than ±0.010 (roughly estimated). Although corrections for environmental influences were not included directly, the additionally fitted annual wave reduced the scatter of the amplitude factors in the annual range considerably. In contrast to that the amplitude factor of the Chandler wobble remains nearly unaffected, confirming the assumption that the disturbing environmental influences do not extend into the period range of the Chandler wobble.     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

Dependence of the chemical composition of thermal waters upon seismic activity

Changes in the chemical composition of the hot springs of Mendeleev Volcano (Kunashir Island) as for Cl^?, SO ₄ ^2? , CO₂, NH ₄ ⁺ and Cl^?/SO ₄ ^2? are given in function of the 1965–66 and 1973 (in part) seismic activity in the South Kurile islands.     

Influence of advection on the characteristics of turbulence over uneven surface in the oasis and the Gobi Desert

Utilizing experimental data of the atmospheric surface layer in the Gobi Oasis of Jinta in a comparative study, we demonstrate that under the condition of unstable stratification, the normalization variances of temperature in the oasis and Gobi Desert meet 1/3(z/Λ)(z/Λ)while normalization variances of both humidity and CO2 in the oasis meet(z)sz\Λ-1/3;s s z Λ the normalization variance of temperature in the oasis is large due to disturbance by advection, whereas variance of CO2 in the Gobi Desert has certain degree of deviation relative to Monin-Obukhov(M-O) scaling, and humidity variance completely deviates from variance M-O scaling. The above result indicates that under the condition of advection, humidity variance meets the relationsm sA sB D and it is determined by relative magnitude of scalar variance of advection transport. Our study reveals that, if the scalar variance of humidity or CO2 transported by advection is much larger than local scalar variance, observation value of scalar variance will deviate from M-O scaling; when scalar variance of advection transport is close to or less than local scalar variance, the observation value of scalar variance approximately meets M-O scaling.     

Chemical Composition of Dew Resulting from Radiative Cooling at a Semi-arid Site in Agra, India

Dew samples were collected between October 2007 and February 2008 from a suburban site in Agra. pH, conductivity, major inorganic ions (F^?, Cl^?, NO ₃ ^? , SO ₄ ^2? , Na⁺, K⁺, Ca²⁺, Mg²⁺, and NH ₄ ⁺ ), and some trace metals (Cr, Sn, Zn, Pb, Cd, Ni, Mn, Fe, Si, Al, V, and Cu) were determined to study the chemistry of dew water. The mean pH was 7.3, and the samples exhibited high ionic concentrations. Dew chemistry suggested both natural and anthropogenic influences, with acidity being neutralized by atmospheric ammonia and soil constituents. Ion deposition flux varied from 0.25 to 3.0?neq?m^?2?s^?1, with maximum values for Ca²⁺ followed by NH ₄ ⁺ , Mg²⁺, SO ₄ ^2? , Cl^?, NO ₃ ^? , Na⁺, K⁺, and F^?. Concentrations of trace metals varied from 0.13 to 48?μg?l^?1 with maximum concentrations of Si and minimum concentration of Cd. Correlation analysis suggested their contributions from both crustal and anthropogenic sources.     

Tsunami Early Warning Within Five Minutes

Tsunamis are most destructive at near to regional distances, arriving within 20–30 min after a causative earthquake; effective early warning at these distances requires notification within 15 min or less. The size and impact of a tsunami also depend on sea floor displacement, which is related to the length, L, width, W, mean slip, D, and depth, z, of the earthquake rupture. Currently, the primary seismic discriminant for tsunami potential is the centroid-moment tensor magnitude, M _w ^CMT , representing the product LWD and estimated via an indirect inversion procedure. However, the obtained M _w ^CMT and the implied LWD value vary with rupture depth, earth model, and other factors, and are only available 20–30 min or more after an earthquake. The use of more direct discriminants for tsunami potential could avoid these problems and aid in effective early warning, especially for near to regional distances. Previously, we presented a direct procedure for rapid assessment of earthquake tsunami potential using two, simple measurements on P-wave seismograms—the predominant period on velocity records, T _d , and the likelihood, T ₅₀ ^Ex , that the high-frequency, apparent rupture-duration, T ₀, exceeds 50–55 s. We have shown that T _d and T ₀ are related to the critical rupture parameters L, W, D, and z, and that either of the period–duration products T _d T ₀ or T _d T ₅₀ ^Ex gives more information on tsunami impact and size than M _w ^CMT , M _wp, and other currently used discriminants. These results imply that tsunami potential is not directly related to the product LWD from the “seismic” faulting model, as is assumed with the use of the M _w ^CMT discriminant. Instead, information on rupture length, L, and depth, z, as provided by T _d T ₀ or T _d T ₅₀ ^Ex , can constrain well the tsunami potential of an earthquake. We introduce here special treatment of the signal around the S arrival at close stations, a modified, real-time, M _wpd(RT) magnitude, and other procedures to enable early estimation of event parameters and tsunami discriminants. We show that with real-time data currently available in most regions of tsunami hazard, event locations, m _b and M _wp magnitudes, and the direct, period–duration discriminant, T _d T ₅₀ ^Ex can be determined within 5 min after an earthquake occurs, and T ₀, T _d T ₀, and M _wpd(RT) within approximately 10 min. This processing is implemented and running continuously in real-time within the Early-est earthquake monitor at INGV-Rome (http://early-est.rm.ingv.it). We also show that the difference m _b  ? log₁₀(T _d T ₀) forms a rapid discriminant for slow, tsunami earthquakes. The rapid availability of these measurements can aid in faster and more reliable tsunami early warning for near to regional distances.     

New Progress in LURR-Integrating with the Dimensional Method

The evolution laws of LURR (Loading–Unloading Response Ratio) before strong earthquakes, especially the peak point of LURR, are described in this paper. The results of four methods (experimental, numerical simulation, seismic data analysis and with damage mechanics analysis) lead to a consistent conclusion—the evolution laws of LURR before strong earthquakes are that, at the early stage of the seismic cycle, LURR will fluctuate around 1 and in the late stage, it rises swiftly and to its peak point. At some time after this peak point, a catastrophic event or events occur. These do not occur at the peak point, but lag behind. The lag time which is denoted by T ₂ depends on the magnitude M of the upcoming earthquake among other factors. In order to consider the influence of geophysical parameters in a specific region such as $ \dot{\gamma }, $ E _a and J _(t), where $ \dot{\gamma } $ is the shear strain rate of tectonic loading in situ, E _a is the sum of radiated energy of all earthquake occurring in a specific region measured during a long time duration (110 years in this paper) divided by the area of the region and the time duration, and J _(t) is a parameter denoting the LURR anomaly area weighted with Y (the value of LURR) and represents the expanse and degree of the seismogenic zone. The dimensional analysis method has been used to reveal the relation between M, T ₂ and other parameters in situ for more reliable earthquake prediction.     

Planetary distribution of the intensity of Auroral luminosity obtained using a model of Aurora precipitation

A model of auroral precipitation (AP) developed on the basis of statistical processing of DMSP F6 and F7 satellite data (Vorobjev and Yagodkina, 2005, 2007) was used for the calculation of the global distribution of the auroral luminosity in different spectral ranges. The algorithm for the calculation of the integral intensity in bands N₂ LBH (170.0 nm), ING N ₂ ⁺ (391.4 nm), 1PG N₂ (669.0 nm), and (OI) 557.7-nm emission is shown in detail. The processes of formation of electronically excited atoms O(¹S) as a result of the transport of excitation energy from metastable state N₂(A³Σ _u ⁺ ), excitation of O(³P) by primary and secondary electrons, and dissociative recombination were taken into account to calculate the intensity of emission at 557.7 nm. A high correlation between the model distribution of the auroral luminosity in the UV spectral range and the observations of the Polar satellite is demonstrated.     

Equilibrium approaches to natural water systems—Part 2

The apparent equilibrium constant, K ₁ ^′ , for the first acidity constant of carbonic acid has been determined in a lake water of 1.6 mM ionic strength in the temperature interval 4–18°C. The experimental method used comprises pH measurements in situ (NBS scale) with a probe and an IR-method for the selective determination of [H₂CO₃] and [HCO ₃ ^? ] in water samples. In the temperature interval studied the results can be described by the equation logK ₁ ^′ =126.39?6320.81/T?19.5682 ln T and are in agreement with the values of K ₁ ^′ obtained by the empirical equation presented by Millero [15]. This experimental agreement justifies thermodynamic calculations in the carbonate system based on field data. Also the experimental method described can be used to evaluate the acid-base balance of organic rich natural waters.     

Examining the fate of WWTP effluent nitrogen using δ 15N–NH4 +, δ 15N–NO 3 − and δ 15N of submersed macrophytes

The use of submersed macrophyte tissue δ ¹⁵N to quantify the level of WWTP effluent use in a highly urbanized and agricultural river was evaluated using several methods. Macrophytes, NH₄ ⁺ and NO₃ ^? were collected by canoe along two 10 km reaches of river, upstream and downstream of two major municipal WWTPs over 3 years. NH₄ ⁺ decreased in concentration while δ ¹⁵N–NH₄ ⁺ increased as a function of distance downstream of both WWTPs, changing in one survey from 13 to 31 ‰ over 1 km. This increase is attributed to the combined effects of volatilization, nitrification and uptake. While NO ₃ ^? concentrations increased downstream of the WWTP over one of the survey reaches, δ ¹⁵N–NO ₃ ^? showed no prominent trend with distance at either. Macrophyte tissue δ ¹⁵N increased with distance downstream of both WWTPs, with a slope not significantly different from that of δ ¹⁵N–NH₄ ⁺ suggesting that macrophytes incorporate effluent NH₄ ⁺ as their main N source in those areas. However, mixing models suggest that towards the end of the reach, where source separation is distinct, macrophytes may utilize background NO ₃ ^? . Our study indicates the difficulty of deriving precise estimates of effluent use by macrophytes in a system where the δ ¹⁵N of the effluent changes rapidly. It also illustrates the utility of macrophytes in describing those changes where the effluent is too attenuated to allow for direct isotopic analysis.