Trend In Amplitude Research Articles

TH-CD-304-06: Amplitude and Frequency Characteristics of Acoustic Waves Induced Following Radiotherapy Linear Accelerator Irradiation

Purpose: To enhance understanding of the characteristics of acoustic waves induced following irradiation by a linac photon beam through experiments and simulations. Such waves have potential applications in in vivo dosimetry since their properties are related to the dose distribution following a single pulse of irradiation. Methods: The acoustic waves induced following linac photon beam irradiation of different metal blocks suspended in a water tank were investigated. Experimentally, these waves were detected with an ultrasound transducer and amplification electronics. Computationally, the acoustic waves were modeled by combining Monte Carlo dose calculations and acoustic wave transport techniques. The effect of varying metal block size, material, depth, and linac photon beam energy on the amplitude and frequency of the induced acoustic signal was investigated. Results: Experimental and simulated acoustic waveforms indicated that increasing photon beam energy and decreasing metal block depth along the central axis increases signal amplitude by an amount proportional to the increased dose deposited in the block. Decreasing in-plane lead block width increased the frequency of acoustic waves due to the smaller dimension of the lead-induced perturbation in the global dose distribution. Varying the metal block material from lead to aluminum resulted in smaller amplitude acoustic waves due to aluminum’s lower electron density, while aluminum’s higher speed of sound resulted in higher frequency waves. Both simulated and experimental waveforms showed similar trends in signal amplitude and frequency when set-up variables were altered. Conclusion: This study revealed factors that affect the amplitude and frequency of radiation-induced acoustic waves and their relation to the deposited dose characteristics. The agreement between simulated and experimental waveforms verifies the simulation workflow’s ability to model such acoustic waves, and indicates that it could be utilized to explore more complex irradiation scenarios and potentially aid in the development of experimental detection systems for in vivo dosimetry. This work was supported by NSERC and CIHR grants. S.H. acknowledges support by the NSERC CREATE Medical Physics Research Training Network grant 432290.

Interdecadal variations and trends of the Urban Heat Island in Athens (Greece) and its response to heat waves

The study explores the interdecadal and seasonal variability of the urban heat island (UHI) intensity in the city of Athens. Daily air temperature data from a set of urban and surrounding non urban stations over the period 1970–2004 were used. Nighttime and daytime heat island revealed different characteristics as regards the mean amplitude, seasonal variability and temporal variation and trends. The difference of the annual mean air temperature between urban and rural stations exhibited a progressive statistically significant increase over the studied period, with rates equal to+0.2°C/decade. A gradual and constant increase of the daytime UHI intensity was detected, in contrast to the nighttime UHI intensity which increases only in summer, after the mid 1980s. UHI phenomenon was found to be related to higher increasing rates of hot days frequency at the urban stations. It was found that the interaction between heat waves and heat island in Athens, results to pronounced amplification of nocturnal UHI intensity under exceptionally hot weather.

Medication effects on periurethral sensation and urethral sphincter activity.

The aim of this study was to characterize urethral neuromuscular function before and 2 weeks after medication therapy. Premenopausal women without lower urinary tract symptoms were randomly allocated to 1 of the 6 medications for 2 weeks (pseudoephedrine ER of 120 mg, imipramine of 25 mg, cyclobenzaprine of 10 mg, tamsulosin of 0.4 mg, solifenacin of 5 mg, or placebo). At baseline and after medication, participants underwent testing: quantitative concentric needle electromyography (CNE) of the urethral sphincter using automated multimotor unit action potential software, current perception threshold (CPT) testing to measure periurethral sensation, and standard urodynamic pressure flow studies (PFS). Nonparametric tests were used to compare pre-post differences. Fifty-six women had baseline testing, 48 (85.7%) completed follow-up CNE, and 49 (87.5%) completed follow-up CPT and PFS testing. Demographics showed no significant differences among medication groups with respect to age (mean, 34.3; SD, 10.1), body mass index (mean, 31.8; SD, 7.5), parity (median, 1; range, 0-7), or race (14% Caucasian, 80% African American). The PFS parameters were not significantly different within medication groups. No significant pre-post changes in CNE values were noted; however, trends in amplitudes were in a direction consistent with the expected physiologic effect of the medications. With CPT testing, a trend toward increased urethral sensation at the 5-Hz stimulation level was observed after treatment with pseudoephedrine (0.15-0.09 mA at 5 Hz, P = 0.03). In women without lower urinary tract symptoms, pseudoephedrine improved urethral sensation but not urethral neuromuscular function on CNE or PFS. Imipramine, cyclobenzaprine, tamsulosin, solifenacin, and placebo did not change urethral sensation or neuromuscular function.

Multidecadal variability of the continental precipitation annual amplitude driven by AMO and ENSO

AbstractAs the water vapor content in the atmosphere scales with temperature, a warmer world is expected to feature an intensification of the hydrological cycle. Work to date has mainly focused on mean precipitation changes, whose connection to climatic modes is elusive at a global scale. Here we show that continental precipitation annual amplitude, which represents the annual range between minimum and maximum (monthly) rainfall, covaries with a linear combination of the Atlantic Multidecadal Oscillation and low‐frequency variations in the El Niño–Southern Oscillation on a decadal to multidecadal scale with a correlation coefficient of 0.92 (P < 0.01). The teleconnection is a result of changes in moisture transport in key regions. Reported trends in the annual amplitude of global precipitation in recent decades need to be assessed in light of this substantial low‐frequency variability, which could mask or enhance an anthropogenic signal in hydrological cycle changes.

Effect of aspect ratio on wing rock at low Reynolds number

Wing rock phenomenon has been studied extensively on slender delta wings but a little is understood about wing rock occurring on rectangular wing planforms, which is the focus of this paper. Specifically, a systematic procedure is discussed for experimental studies of single degree-of-freedom wing rock on rectangular wings. The characterization of limit cycle oscillations in terms of amplitude and frequency is based on the free-to-roll tests in wind tunnel. Rectangular wings with aspect ratio from 2 to 4.5 (with increment of 0.25) are studied at low Reynolds numbers (less than 0.1 million) and low Strouhal numbers (10−2) that are typical for the flight of micro air vehicles in urban environment. The changing trend in oscillation amplitude and frequency of the resulting sustained limit cycle oscillations is analyzed. The results indicate that wing rock occurs in post-stall regime (14–16° of angle of attack) and its amplitude tends to increase from aspect ratio 2 to 3.25 and decrease thereafter. The wing-rock frequency shows a decrease from aspect ratio of 2 to 3.75 and increase thereafter.

Long-term variation in the upper atmosphere as seen in the geomagnetic solar quiet daily variation

Characteristics of long-term variation in the amplitude of solar quiet (Sq) geomagnetic field daily variation have been investigated using 1-h geomagnetic field data obtained from 69 geomagnetic observation stations within the period of 1947 to 2013. The Sq amplitude observed at these geomagnetic stations showed a clear dependence on the 10- to 12-year solar activity cycle and tended to be enhanced during each solar maximum phase. The Sq amplitude was the smallest around the minimum of solar cycle 23/24 in 2008 to 2009. The relationship between the solar F10.7 index and Sq amplitude was approximately linear but about 53% of geomagnetic stations showed a weak nonlinear relation to the solar F10.7 index. In order to remove the effect of solar activity seen in the long-term variation of the Sq amplitude, we calculated a linear or second-order fitting curve between the solar F10.7 index and Sq amplitude during 1947 to 2013 and examined the residual Sq amplitude, which is defined as the deviation from the fitting curve. As a result, the majority of trends in the residual Sq amplitude that passed through a trend test showed negative values over a wide region. This tendency was relatively strong in Europe, India, the eastern part of Canada, and New Zealand. The relationship between the magnetic field intensity at 100-km altitude and residual Sq amplitude showed an anti-correlation for about 71% of the geomagnetic stations. Furthermore, the residual Sq amplitude at the equatorial station (Addis Ababa) was anti-correlated with the absolute value of the magnetic field inclination. This implies movement of the equatorial electrojet due to the secular variation of the ambient magnetic field.

The Climatology and Characteristics of Rossby Wave Packets Using a Feature-Based Tracking Technique

Abstract This paper describes an objective, track-based climatology of Rossby wave packets (RWPs). NCEP–NCAR reanalysis wind and geopotential height data at 300 hPa every 6 h were spectrally filtered using a Hilbert transform technique under the assumption that RWPs propagate along a waveguide defined by the 14-day running average of the 300-hPa wind. Track data and feature-based descriptive statistics, including area, average intensity, intensity volume (intensity multiplied by area), intensity-weighted centroid position, and velocity, were gathered to describe the interannual, annual, seasonal, and regime-based climatology of RWPs. RWPs have a more pronounced seasonal cycle in the Northern Hemisphere (NH) than the Southern Hemisphere (SH). RWPs are nearly nonexistent in the summer months (June–August; JJA) in the NH, while there is nearly continuous RWP activity downstream of South Africa during austral summer (December–February; DJF). Interannual variability in RWP frequency and intensity in the Northern Hemisphere is found to be strongly connected with the large-scale flow regimes such as El Niño–Southern Oscillation and the Arctic Oscillation. Enhanced RWP activity is also found to coherently propagate from the Pacific into the Atlantic on average when the Arctic Oscillation switches from a positive to a negative phase. No significant long-term (~30 yr) trend in RWP frequency, activity, or amplitude is found.

An Analysis of Secular Change in Tides at Open-Ocean Sites in the Pacific

Abstract Hourly sea level is examined at 25 open-ocean stations in the Pacific Ocean with records longer than 30 yr. A search for trends finds that the amplitude of the dominant semidiurnal tide M2 is increasing at 12 of the 13 sites where a statistically significant trend can be identified. It is also found that nontidal variance in the neighborhood of M2 is decreasing at all 12 of the sites where a significant increase in M2 tide is occurring. The trend in amplitude of the dominant diurnal tide K1 is significant at six stations, and it is both increasing (four stations) and decreasing (two stations). The trend in semidiurnal-band variance suggests the hypothesis that increases in M2 could be caused by improvements in time keeping or data processing that would reduce the apparent phase variability of the tide. This possibility is examined and found to be the likely explanation for tidal trends at four stations. Local changes are found to explain the trend at two stations, Johnston Island and Mokuoloe, as diagnosed from correlated changes in nonlinear overtides and site history. Changes in M2 at the equatorial station of Kanton are significant and unexplained by either timing errors or local morphodynamics; although, strong nonlinear overtides are present. Changing tides at five stations in the western Pacific, Malakal, Yap, Saipan, Kapingamarangi, and Pohnpei cannot be explained by the above and suggest a region where a connection between climate and tides may yet be identified.

Regional Hypothermia Inhibits Spinal Cord Somatosensory-Evoked Potentials without Neural Damage in Uninjured Rats

Both the therapeutic effects of regional hypothermia (RH) and somatosensory-evoked potentials (SSEP) have been intensively studied; however, the in vivo relationship between the two remains unknown. The primary focus of the current study was to investigate the impact of RH on SSEP in uninjured rats, as well as the neural safety of RH on neuronal health. An epidural perfusion model was used to keep local temperature steady by adjusting perfusion speed at 30°C, 26°C, 22°C, and 18°C for 30 min, respectively. Total hypothermic duration lasted up to 3 h. Neural signals were recorded at the end of each hypothermic period, as well as before cooling and after spontaneous rewarming. In addition, the Basso, Beattie, and Bresnahan (BBB) Locomotor Rating Scale was used to evaluate the effects of RH pre- and post-operative, combined with hematoxylin and eosin (H&E) and Fluoro-Jade C (FJC) staining. The results showed a marked declining trend in SSEP amplitude, as well as a significant prolongation in latency only during profound hypothermia (18°C). The BBB scale remained consistent at 21 throughout the entire process, signifying that no motor function injury was caused by RH. In addition, H&E and FJC staining did not show obvious histological injury. These findings firmly support the conclusion that RH, specifically profound RH, inhibits spinal cord SSEP in both amplitude and latency without neural damage in uninjured rats.

The impact of global warming on seasonality of ocean primary production

Abstract. The seasonal cycle (i.e. phenology) of oceanic primary production (PP) is expected to change in response to climate warming. Here, we use output from 6 global biogeochemical models to examine the response in the seasonal amplitude of PP and timing of peak PP to the IPCC AR5 warming scenario. We also investigate whether trends in PP phenology may be more rapidly detectable than trends in annual mean PP. The seasonal amplitude of PP decreases by an average of 1–2% per year by 2100 in most biomes, with the exception of the Arctic which sees an increase of ~1% per year. This is accompanied by an advance in the timing of peak PP by ~0.5–1 months by 2100 over much of the globe, and particularly pronounced in the Arctic. These changes are driven by an increase in seasonal amplitude of sea surface temperature (where the maxima get hotter faster than the minima) and a decrease in the seasonal amplitude of the mixed layer depth and surface nitrate concentration. Our results indicate a transformation of currently strongly seasonal (bloom forming) regions, typically found at high latitudes, into weakly seasonal (non-bloom) regions, characteristic of contemporary subtropical conditions. On average, 36 yr of data are needed to detect a climate-change-driven trend in the seasonal amplitude of PP, compared to 32 yr for mean annual PP. Monthly resolution model output is found to be inadequate for resolving phenological changes. We conclude that analysis of phytoplankton seasonality is not necessarily a shortcut to detecting climate change impacts on ocean productivity.

Weakened stratospheric quasibiennial oscillation driven by increased tropical mean upwelling

The zonal wind in the tropical stratosphere switches between prevailing easterlies and westerlies with a period of about 28 months. In the lowermost stratosphere, the vertical structure of this quasibiennial oscillation (QBO) is linked to the mean upwelling, which itself is a key factor in determining stratospheric composition. Evidence for changes in the QBO have until now been equivocal, raising questions as to the extent of stratospheric circulation changes in a global warming context. Here we report an analysis of near-equatorial radiosonde observations for 1953-2012, and reveal a long-term trend of weakening amplitude in the zonal wind QBO in the tropical lower stratosphere. The trend is particularly notable at the 70-hectopascal pressure level (an altitude of about 19 kilometres), where the QBO amplitudes dropped by roughly one-third over the period. This trend is also apparent in the global warming simulations of the four models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) that realistically simulate the QBO. The weakening is most reasonably explained as resulting from a trend of increased mean tropical upwelling in the lower stratosphere. Almost all comprehensive climate models have projected an intensifying tropical upwelling in global warming scenarios, but attempts to estimate changes in the upwelling by using observational data have yielded ambiguous, inconclusive or contradictory results. Our discovery of a weakening trend in the lower-stratosphere QBO amplitude provides strong support for the existence of a long-term trend of enhanced upwelling near the tropical tropopause.

Reply to Screen and Simmonds: From means to mechanisms

Our recent article on quasiresonant amplification of planetary waves (1) has been addressed in a letter by Screen and Simmonds (2). They report, in particular, that they do not find statistically significant trends in the mean amplitudes of m = 6–8 waves in the 1979–2012 period. This observation does not contradict the statements made in our paper–it actually complements our work and helps to clarify several important issues:

Exploring links between Arctic amplification and mid‐latitude weather

AbstractThis study examines observed changes (1979–2011) in atmospheric planetary‐wave amplitude over northern mid‐latitudes, which have been proposed as a possible mechanism linking Arctic amplification and mid‐latitude weather extremes. We use two distinct but equally‐valid definitions of planetary‐wave amplitude, termed meridional amplitude, a measure of north‐south meandering, and zonal amplitude, a measure of the intensity of atmospheric ridges and troughs at 45°N. Statistically significant changes in either metric are limited to few seasons, wavelengths, and longitudinal sectors. However in summer, we identify significant increases in meridional amplitude over Europe, but significant decreases in zonal amplitude hemispherically, and also individually over Europe and Asia. Therefore, we argue that possible connections between Arctic amplification and planetary waves, and implications of these, are sensitive to how waves are conceptualized. The contrasting meridional and zonal amplitude trends have different and complex possible implications for midlatitude weather, and we encourage further work to better understand these.

Changes in the Seasonal Cycle of Temperature and Atmospheric Circulation

The vast majority of variability in the instrumental surface temperature record is at annual frequencies. Systematic changes in the yearly Fourier component of surface temperature have been observed since the midtwentieth century, including a shift toward earlier seasonal transitions over land. Here it is shown that the variability in the amplitude and phase of the annual cycle of surface temperature in the northern extratropics is related to Northern Hemisphere atmospheric circulation as represented by the northern annular mode (NAM) and the Pacific–North America mode (PNA). The phase of the seasonal cycle is most strongly influenced by changes in spring atmospheric circulation, whereas amplitude is most strongly influenced by winter circulation. A statistical model is developed based on the NAM and PNA values in these seasons and it successfully predicts the interdecadal trends in the seasonal cycle using parameters diagnosed only at interannual time scales. In particular, 70% of the observed amplitude trends and 68% of the observed phase trends are predicted over land, and the residual trends are consistent with internal variability. The strong relationship between atmospheric circulation and the structure of the seasonal cycle indicates that physical explanations for changes in atmospheric circulation also extend to explaining changes in the structure of the seasonal cycle.

On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments

AbstractIn the present study, shock tube experiments are used to study the very late-time development of the Richtmyer–Meshkov instability from a diffuse, nearly sinusoidal, initial perturbation into a fully turbulent flow. The interface is generated by two opposing gas flows and a perturbation is formed on the interface by transversely oscillating the shock tube to create a standing wave. The puncturing of a diaphragm generates a Mach $1. 2$ shock wave that then impacts a density gradient composed of air and SF6, causing the Richtmyer–Meshkov instability to develop in the 2.0 m long test section. The instability is visualized with planar Mie scattering in which smoke particles in the air are illuminated by a Nd:YLF laser sheet, and images are recorded using four high-speed video cameras operating at 6 kHz that allow the recording of the time history of the instability. In addition, particle image velocimetry (PIV) is implemented using a double-pulsed Nd:YAG laser with images recorded using a single CCD camera. Initial modal content, amplitude, and growth rates are reported from the Mie scattering experiments while vorticity and circulation measurements are made using PIV. Amplitude measurements show good early-time agreement but relatively poor late-time agreement with existing nonlinear models. The model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502) agrees with growth rate measurements at intermediate times but fails at late experimental times. Measured background acceleration present in the experiment suggests that the late-time growth rate may be influenced by Rayleigh–Taylor instability induced by the interfacial acceleration. Numerical simulations conducted using the LLNL codes Ares and Miranda show that this acceleration may be caused by the growth of boundary layers, and must be accounted for to produce good agreement with models and simulations. Adding acceleration to the Richtmyer–Meshkov buoyancy–drag model produces improved agreement. It is found that the growth rate and amplitude trends are also modelled well by the Likhachev–Jacobs vortex model (Likhachev & Jacobs, Phys. Fluids, vol. 17, 2005, 031704). Circulation measurements also show good agreement with the circulation value extracted by fitting the vortex model to the experimental data.

Motif Discovery on Seismic Amplitude Time Series: The Case Study of Mt Etna 2011 Eruptive Activity

Algorithms searching for similar patterns are widely used in seismology both when the waveforms of the events of interest are known and when there is no a priori-knowledge. Such methods usually make use of the cross-correlation coefficient as a measure of similarity; if there is no a-priori knowledge, they behave as brute-force searching algorithms. The disadvantage of these methods, preventing or limiting their application to very large datasets, is computational complexity. The Mueen–Keogh (MK) algorithm overcomes this limitation by means of two optimization techniques—the early abandoning concept and space indexing. Here, we apply the MK algorithm to amplitude time series retrieved from seismic signals recorded during episodic eruptive activity of Mt Etna in 2011. By adequately tuning the input to the MK algorithm we found eight motif groups characterized by distinct seismic amplitude trends, each related to a different phenomenon. In particular, we observed that earthquakes are accompanied by sharp increases and decreases in seismic amplitude whereas lava fountains are accompanied by slower changes. These results demonstrate that the MK algorithm, because of its particular features, may have wide applicability in seismology.

Systematic trends in Sloan Digital Sky Survey photometric data

We investigate the Sloan Digital Sky Survey (SDSS) photometry from Data Release 8 (DR8) in the search for systematic trends that still exist after the calibration effort of Padmanabhan et al. We consider both the aperture and point-spread function (PSF) magnitudes in DR8. Using the objects with repeat observations, we find that a large proportion of the aperture magnitudes suffer a ~0.2-2% systematic trend as a function of PSF full-width half-maximum (FWHM), the amplitude of which increases for fainter objects. Analysis of the PSF magnitudes reveals more complicated systematic trends of similar amplitude as a function of PSF FWHM and object brightness. We suspect that sky over-subtraction is the cause of the largest amplitude trends as a function of PSF FWHM. We also detect systematic trends as a function of subpixel coordinates for the PSF magnitudes with peak-to-peak amplitudes of ~1.6 mmag and ~4-7 mmag for the over- and under-sampled images, respectively. We note that the systematic trends are similar in amplitude to the reported ~1% and ~2% precision of the SDSS photometry in the griz and u wavebands, respectively, and therefore their correction has the potential to substantially improve the SDSS photometric precision. We provide an {\tt IDL} program specifically for this purpose. Finally, we note that the SDSS aperture and PSF magnitude scales are related by a non-linear transformation that departs from linearity by ~1-4%, which, without correction, invalidates the application of a photometric calibration model derived from the aperture magnitudes to the PSF magnitudes, as has been done for SDSS DR8.

Computerised lung sound monitoring to assess effectiveness of chest physiotherapy and secretion removal: a feasibility study

ObjectivesTo explore the feasibility of computerised lung sound monitoring to evaluate secretion removal in intubated and mechanically ventilated adult patients. DesignBefore and after observational investigation. SettingIntensive care unit. ParticipantsFifteen intubated and mechanically ventilated adult patients receiving chest physiotherapy. InterventionsChest physiotherapy included combinations of standard closed airway suctioning, saline lavage, postural drainage, chest wall vibrations, manual-assisted cough and/or lung hyperinflation, dependent upon clinical indications. Main outcome measuresLung sound amplitude at peak inspiration was assessed using computerised lung sound monitoring. Measurements were performed immediately before and after chest physiotherapy. Data are reported as mean [standard deviation (SD)], mean difference and 95% confidence intervals (CI). Significance testing was not performed due to the small sample size and the exploratory nature of the study. ResultsFifteen patients were included in the study [11 males, four females, mean age 65 (SD 14) years]. The mean total lung sound amplitude at peak inspiration decreased two-fold from 38 (SD 59) units before treatment to 17 (SD 19) units after treatment (mean difference 22, 95% CI of difference −3 to 46). The mean total lung sound amplitude from the lungs of patients with a large amount of secretions (n=9) was over four times ‘louder’ than the lungs of patients with a moderate or small amount of secretions (n=6) [56 (SD 72) units vs 12 (13) units, respectively; mean difference −44, 95% CI of difference −100 to 11]. The mean total lung sound amplitude decreased in the group of ‘loud’ right and left lungs (n=15) from 37 (SD 36) units before treatment to 15 (SD 13) units after treatment (mean difference 22, 95% CI of difference 6 to 38). ConclusionComputerised lung sound monitoring in this small group of patients demonstrated a two-fold decrease in lung sound amplitude following chest physiotherapy. Subgroup analysis also demonstrated decreasing trends in lung sound amplitude in the group of ‘loud’ lungs following chest physiotherapy. Due to the small sample size and large SDs with high variability in the lung sound amplitude measurements, significance testing was not reported. Further investigation is needed in a larger sample of patients with more accurate measurement of sputum wet weight in order to distinguish between secretion-related effects and changes due to other factors such as airflow rate and pattern.

A benthic δ13C‐based proxy for atmospheric pCO2 over the last 1.5 Myr

A high‐resolution marine proxy for atmospheric pCO2 is needed to clarify the phase lag between pCO2 and marine climate proxies and to provide a record of orbital‐scale pCO2 variations before the oldest ice core measurement at 800 ka. Benthic δ13C data should record deep ocean carbon storage and, thus, atmospheric pCO2. This study finds that a modified δ13C gradient between the deep Pacific and intermediate North Atlantic (Δδ13CP−) correlates well with pCO2. Δδ13CP− reproduces characteristic differences between pCO2 and ice volume during Late Pleistocene glaciations and indicates that pCO2 usually leads terminations by 0.2–3.7 kyr but lags by 3–10 kyr during two “failed” terminations at 535 and 745 ka. Δδ13CP− gradually transitions from 41‐ to 100‐kyr cyclicity from 1.3–0.7 Ma but has no secular trend in mean or amplitude since 1.5 Ma. The minimum pCO2 of the last 1.5 Myr is estimated to be 155 ppm at ∼920 ka.

Analysis of ground temperature trends in Alpine permafrost using generalized least squares

Warming air temperatures induce ground warming and can therefore lead to permafrost degradation, which in turn may produce rock fall, debris flows, or cause serious problems for infrastructure stability. In the last two decades, many boreholes for thermal permafrost monitoring have been drilled in Alpine regions. Factors such as snow or scree cover, hydrology, or topography strongly affect the ground thermal regime and make trend estimation very difficult. Furthermore, ground temperature series exhibit a pronounced annual cycle and are strongly temporally correlated. For the sake of simplicity, often only annual values are analyzed for trend estimation, which is usually not robust for short measurement periods. This study intends to model time series with annual cycles and a daily database. A family of nine different models for trend estimation is proposed. The models are able to fit both overall trends and trends in the annual cycle amplitudes and therefore allow more robust and accurate trend estimation than when annual values only are used. Evaluation and comparison of the models is demonstrated using short‐range (less than two decades, 1996–2008) permafrost temperature series from two adjacent boreholes in the Muot da Barba Peider ridge (Eastern Swiss Alps). The results suggest an increase in cycle amplitudes for near‐surface coarse‐blocky ground layers and an overall warming trend for deeper bedrock layers where the annual cycles are less pronounced.