Tidal Variations Research Articles

Total phosphorus speciation and transport flux dynamics driven by tidal variations in the Shuidong Bay coastal water during summer, China

Phosphorus (P) is a vital nutrient for the growth of marine organisms. Tidal cycle had major influence on various biogeochemical parameters of the bay and changed nutrients input with the ebb and flow of the tide. Seawater was collected by synchronous continuous observation during summer in 2021, to investigate tide drives total phosphorus (TP) variation on the concentration, speciation and exchange flux between Shuidong Bay (SDB) and South China Sea (SCS). Results indicated that there was significant tidal variation in exchange flux of TP between SDB and SCS. DIP and DOP were the main speciation of TDP in different tidal periods, accounting for 53.9 % and 46.1 %TP flowed from SCS to SDB, and monthly exchange flux was about 21.26 t. This study provides new insights in P tidal cycling across the semi-enclosed bay-coastal water continuum, which was implications for understanding P biogeochemical process and primary production dynamics in coastal water.

Optimizing coastal protection: Nature-based engineering for longitudinal drift reversal and erosion reduction

Traditional hard engineering solutions have shown weaknesses in mitigating erosion processes in vulnerable coastal areas, contributing in some cases to their aggravation, which makes it necessary to study innovative nature-based engineering solutions. This research deals with an in-depth analysis of hydro-morphodynamic modelling results for optimizing the geometry of maritime structures under longitudinal drift reversal conditions by mimicking and manipulating natural processes to promote wave energy dissipation and sediment retention through wave deformation due to obstacle interposition. The solutions draw inspiration from the full-scale observation data of two examples of longitudinal drift reversal. Additionally, numerical simulations were developed for predicting wave climate near the Iberian Peninsula shoreline under different scenarios. Hydrodynamics and morphodynamics modelling results are discussed based on the impact of a specific storm, considering different characteristics of protection structures, followed by parametric sensitivity analysis and comparative studies performed with an optimized solution. Results indicated this solution contributed to sediment accumulation downdrift near the shoreline, as there is no interruption of the longitudinal drift compared to traditional protection structures. At the alignment, the structure also improved nearshore sediment accretion, reduced areas of erosion relative to a no-structure scenario and exhibited behaviour akin to an emerged structure with its crest level. Compared to wholly submerged structures, it becomes a relevant coastal protection alternative, as it guarantees excellent protection on the adjacent coastal zone by safeguarding against tidal variations induced by storm surges and mean sea level rise due to climate change. Furthermore, there is a positive effect to help promote biodiversity whenever the structure is located in an intertidal zone. Despite the enormous computational effort required in the hydro-morphodynamic modelling process, this study shows that it is possible to create innovative engineering coastal solutions to induce longitudinal drift reversal and reduce erosion near the shoreline.

Effect of fortnightly and seasonal changes in estuarine physical variables on phytoplankton distribution in a macrotidal monsoon estuary

Seasonal and neap-spring tidal changes in estuarine physical variables and their effect on the phytoplankton distribution in the macrotidal Tanintharyi River estuary (TRE), Myanmar were studied in 2019. During the dry season, the saltwater intrudes upstream while only until the mid-estuary during the wet season due to the hindering of saltwater by the strong river flow. The turbidity variations driven by enhanced mixing and neap-spring transition influenced the light required for phytoplankton growth during both seasons. The diversity index was higher (2.57–3.07) in the dry season with low evenness (0.64–0.79) compared to the low diversity index (2.16–2.73) with high evenness (0.75–0.90) in the wet season. The peak diatom density was observed under low turbidity (6 FTU) and a salinity of 25, and their distribution were correlated positively with salinity, mean light intensity in the mixed layer (Im) and euphotic depth (Ze) while negatively with light attenuation (K) and turbidity. Among diatoms species, Thalassionema frauenfeldii, Thalassionema nitzschioides and Pseudonitzschia seriata were found as dominant species (positively correlated with salinity and Im whereas negatively with turbidity and K) during the dry season whereas Thalassiosira eccentrica and Coscinodiscus granii were dominant with low salinity in the wet season. The dinoflagellates were more sensitive to strong mixing condition than diatoms and their distribution were positively influenced by Im and Ze. Therefore, the neap-spring tidal and seasonal variations in saltwater intrusion, mixing, turbidity, and light availability are the major factors that maintained the phytoplankton diversity in the tropical TRE.

Seasonal dynamics of mangrove outwelling and its impact on estuarine productivity: insights from multi-parameter analysis across tidal variations

Seasonal dynamics of mangrove outwelling and its impact on estuarine productivity: insights from multi-parameter analysis across tidal variations

A Statistical Study of the Day‐To‐Day Variability of Diurnal and Semidiurnal Tides in the Ionospheric Dynamo Region From MIGHTI/ICON Observations

AbstractThe statistics of day‐to‐day tidal variability within 35‐day running mean windows is obtained from Michelson Interferometer for Global High‐Resolution Thermospheric Imaging (MIGHTI)/Ionospheric Connection Explorer (ICON) observations in the 90–107 km height region for the year 2020. Temperature standard deviations for 18 diurnal and semidiurnal tidal components, and for four quasi‐stationary planetary waves are presented, as function of latitude, altitude, and day‐of‐year. Our results show that the day‐to‐day variability (DTDV) can be as large as 70% of the monthly mean amplitudes, thus providing a significant source of variability for the ionospheric E‐region dynamo and hence for the F‐region plasma. We further validate our results with COSMIC‐2 ionospheric observations and present an approach to extend the MIGHTI/ICON results to all latitudes using Hough Mode Extension fitting, to produce global tidal fields and their statistical DTDV that are suitable as lower boundary conditions for nudging and ensemble modeling of TIE‐GCM. In the future, this will likely help to establish a data‐driven perspective of space weather variability caused by the tidal weather of the lower atmosphere.

Sex differences in chest electrical impedance tomography findings

Objective. Electrical impedance tomography (EIT) has been used to determine regional lung ventilation distribution in humans for decades, however, the effect of biological sex on the findings has hardly ever been examined. The aim of our study was to determine if the spatial distribution of ventilation assessed by EIT during quiet breathing was influenced by biological sex. Approach. 219 adults with no known acute or chronic lung disease were examined in sitting position with the EIT electrodes placed around the lower chest (6th intercostal space). EIT data were recorded at 33 images/s during quiet breathing for 60 s. Regional tidal impedance variation was calculated in all EIT image pixels and the spatial distribution of the values was determined using the established EIT measures of centre of ventilation in ventrodorsal (CoVvd) and right-to-left direction (CoVrl), the dorsal and right fraction of ventilation, and ventilation defect score. Main results. After exclusion of one subject due to insufficient electrode contact, 218 data sets were analysed (120 men, 98 women) (age: 53 ± 18 vs 50 ± 16 yr (p = 0.2607), body mass index: 26.4 ± 4.0 vs 26.4 ± 6.6 kg m−2 (p = 0.9158), mean ± SD). Highly significant differences in ventilation distribution were identified between men and women between the right and left chest sides (CoVrl: 47.0 ± 2.9 vs 48.8 ± 3.3% of chest diameter (p < 0.0001), right fraction of ventilation: 0.573 ± 0.067 vs 0.539 ± 0.071 (p = 0.0004)) and less significant in the ventrodorsal direction (CoVvd: 55.6 ± 4.2 vs 54.5 ± 3.6% of chest diameter (p = 0.0364), dorsal fraction of ventilation: 0.650 ± 0.121 vs 0.625 ± 0.104 (p = 0.1155)). Ventilation defect score higher than one was found in 42.5% of men but only in 16.6% of women. Significance. Biological sex needs to be considered when EIT findings acquired in upright subjects in a rather caudal examination plane are interpreted. Sex differences in chest anatomy and thoracoabdominal mechanics may explain the results.

The combination of detection and simulation for the distribution and sourcing of microplastics in Shing Mun River estuary, Hong Kong

For the first time, combined detection and simulation was performed on microplastic (MP) debris in surface water, sediment, and oyster samples at ten coastal sites of Shing Mun River estuary, Hong Kong at different tidal conditions. The MP debris were extracted and detected using Fourier transform infrared (FT-IR) spectroscopy, and the simulation was conducted using Weather Research & Forecasting Model (WRF) / Regional Ocean Modelling System (ROMS) coupled hydro-dynamic modelling and the subsequent Lagrangian particle tracking.The results demonstrated the majority of polyethylene (with partial chlorine substitution) debris among all the MPs found, and great spatial and tidal variabilities of MP concentrations were observed. The combination of MP observation and simulations referred to the interpretation that a considerable percentage of MPs found in this study originated from South China Sea. Those MPs were probably transported to Tolo Harbour through sea currents and drifted inshore and offshore with tides. This study provided baseline measures of MP concentrations in Shing Mun River estuary and comprehensive understanding for how MPs transport and distribute within a dynamic estuarine system.

Occurrence of pendelluft during ventilator weaning with T piece correlated with increased mortality in difficult-to-wean patients

BackgroundDifficult-to-wean patients, typically identified as those failing the initial spontaneous breathing trial (SBT), face elevated mortality rates. Pendelluft, frequently observed in patients experiencing SBT failure, can be conveniently detected through bedside monitoring with electrical impedance tomography (EIT). This study aimed to explore the impact of pendelluft during SBT on difficult-to-wean patients.MethodsThis retrospective observational study included difficult-to-wean patients undergoing spontaneous T piece breathing, during which EIT data were collected. Pendelluft occurrence was defined when its amplitude exceeded 2.5% of global tidal impedance variation. Physiological parameters during SBT were retrospectively retrieved from the EIT Examination Report Form. Other clinical data including mechanical ventilation duration, length of ICU stay, length of hospital stay, and 28-day mortality were retrieved from patient records in the hospital information system for each subject.ResultsPendelluft was observed in 72 (70.4%) of the 108 included patients, with 16 (14.8%) experiencing mortality by day 28. The pendelluft group exhibited significantly higher mortality (19.7% vs. 3.1%, p = 0.035), longer median mechanical ventilation duration [9 (5–15) vs. 7 (5–11) days, p = 0.041] and shorter ventilator-free days at day 28 [18 (4–22) vs. 20 (16–23) days, p = 0.043]. The presence of pendellfut was independently associated with increased mortality at day 28 (OR = 10.50, 95% confidence interval 1.21–90.99, p = 0.033).ConclusionsPendelluft occurred in 70.4% of difficult-to-wean patients undergoing T piece spontaneous breathing. Pendelluft was associated with worse clinical outcomes, including prolonged mechanical ventilation and increased mortality in this population. Our findings underscore the significance of monitoring pendelluft using EIT during SBT for difficult-to-wean patients.

Hydrodynamics of focused waves acting on netting that extends above the mean sea level

Extreme ocean waves are typically strongly nonlinear, with extreme wave energy concentrated above the static water surface, which has a complex impact on the hydrodynamics of structures extending above the mean sea level. In this study, we designed netting with three different heights above the water surface and two different solidities, and tested the hydrodynamics of these netting under a series of focused waves through physical model tests. The three heights (h) were designed to account for possible nearshore tidal and wave variations. The results indicate that the wave forces of the netting having sharper and steeper crest than those of the wave surface in the time domain, while it is opposite in frequency domain. Moreover, the wave forces changed significantly with increasing height of the netting above the water surface. Wave forces on netting above water were up to 0.8 and 2.0 times greater than those below water for h = 7.25 cm and h = 14.5 cm, respectively. Regardless of solidity, the rate of increase in netting wave forces gradually decreased with growing wave amplitude when h = 0 cm or h = 7.25 cm, but gradually increased when h = 14.5 cm. The force ratios of the two netting solidities were relatively stable and did not change with wave amplitude. The force ratios were always greater than the solidity ratio, mainly because of the drag coefficient in Morison's equation. Furthermore, steep waves acting on netting wound cause obvious vibration of the wave force because of water jet phenomenon, while the jet have little effect on wave surface elevation in 0.5 m behind the netting. Therefore, for aquaculture facilities such as fixed marine aquaculture cages, the netting design is not only limited by the solidity, but should also consider the hydrodynamic influence of the height that the netting extends above the water.

Tidal variation and flow dynamics in Indian Sundarban based on field observation and numerical models

Sundarban is made up of a mesh of macrotidal estuarine systems that contain the world's largest mangroves, the eco-geomorphic environment of which is heavily influenced by tidal behaviour and flow characteristics. The present study aimed to identify the tidal attributes and document the flow character of Indian Sundarban throughout a fortnightly tidal cycle. As such, seven tide monitoring stations were installed across the Saptamukhi-Hariabhanga and connected river system to monitor tidal water levels. Based on this data, the Institute of Ocean Sciences' (IOS) method was used to extract 17-major tidal harmonic components to study the links between various oceanic and shallow-water tidal constituents that may contribute to tidal asymmetry. A Mike-21-flow model was also run to simulate the tidal flow of the regime. Result shows that the progression and convergence of tidal waves in the funnel-shaped estuarine system causes notable lag between the southern and northern limits (avg. 45 min over a 52 km-long stretch of Thakuran estuary). The harmonic components indicate that semi-diurnal M2, S2; over tide 2MS6; and diurnal O1, K1 are the major forces, shaping the tidal amplitude in this region. The third, fourth, and sixth diurnal constituents represent additional tidal components, although with relatively minor amplitudes. The transition from coastal to headward stations sees a shift in the relative phase from 93.73° to 96.17°, suggesting a flood dominance and minimal dissipation of energy within the system. Mike-21FM found that the spring flood-current speed with an average value of 0.42–0.56 m/s is significantly higher than the ebb current of averaging 0.25–0.32 m/s. The nature of neap tidal current speed in the Sundarban region generally mirrors that of the spring condition, although with much less intensity. We assume that since any bi-weekly hydraulic analysis has not yet been conducted in Sundarban, it may be highly valuable for future studies.

Study on the tidal variability related to flooding and hydroelectric operations in the Qiantang river estuary

The Qiantang River estuary, located in southeastern China, displays abnormally large tidal ranges due to its funnel shape. Although numerous studies have discussed river-tide interplay in the Qiantang River estuary, these studies usually treat tidal waves with dramatically different periods as a whole and use ZhaKou as the upstream boundary. To date, the area upstream from ZhaKou to the Fuchun River Power Station (FRPS) remains unexplored, which motives the current study. This research systematically explores the spatiotemporal variations of major tidal constituents in the Qiantang River estuary using classical harmonic analysis (T_TIDE), non-stationary harmonic analysis (NS_TIDE), and variational mode decomposition (VMD). The hindcast of NS_TIDE explains 72.9%–93.9% of original signal variances, better than the T_TIDE. However, the improvement is less from ZhaKou to CangQian, with the hindcast explaining less than 80% of the original signal variance, possibly due to the assumption of a static riverbed topography in NS_TIDE misaligned with the Qiantang River's conditions. Long-period constituents such as MSf, Mf, and Mm have large amplitudes near FRPS. Furthermore, diurnal S1 and P1 tides show notable amplitude increases at TongLu due to hydroelectric operations. The VMD method successfully captured the seasonal changes of tidal parameters caused by nonlinear tide-river-morphology interplay. The amplitudes of semi-diurnal and quarter-diurnal tides increase significantly between July and September due to decreased bottom friction caused by runoff erosion; thereafter, they gradually decrease due to increased bottom friction induced by sediment accumulation. This study has implications for similar fluvial estuaries worldwide with significant variations in water depth.

Investigation of Tidal and Subtidal Variations in Sea Level Close to the Southeastern Coast of Sakhalin Island Using Two-Year Time Series

Investigation of Tidal and Subtidal Variations in Sea Level Close to the Southeastern Coast of Sakhalin Island Using Two-Year Time Series

Subsurface tidal gravity variation and gravimetric factor

SUMMARY Taking advantage of the simultaneous recording during 471 d between 2019 and 2021 by two superconducting gravimeters installed at the surface and 520 m under the surface at the Low Noise Underground Laboratory (LSBB) in Rustrel, France, we investigate whether a difference between the tidal gravity signals at the two locations can be detected. First, we model the periodical variations of the Earth’s gravity owing to the tidal influence from the Sun and Moon, at the Earth’s surface and at shallow depths. We provide analytical formulae for the Love numbers, gravimetric factor and gravity variation of simple spherical planetary models. We also numerically compute those parameters and function for a realistic spherical Earth model. We find that the fractional difference between the semi-diurnal tidal gravity variations at the surface and 520 m below is as small as 8.5 × 10$^{-5}$. We next evaluate the effect on the amplitude of the recorded gravity signal due to the calibration factors of the two superconducting gravimeters at LSBB. Finally, we compute the spectra of the difference between the gravity variations measured on and under the surface in the semi-diurnal band of the M$_2$ tidal wave. We find that the uncertainties associated to the calibration factors are larger than the theoretical or observational difference between the tidal gravity variations on the surface and at a 520-m depth.

Quantification of breathing irregularity for the diagnosis of dysfunctional breathing using proportional tidal volume variation: a cross-sectional, retrospective real-world study

ObjectivesTo develop a statistical approach that provides a quantitative index measuring the magnitude of the irregularity of the breathing response to exercise for the diagnosis of dysfunctional breathing.DesignCross-sectional, retrospective, real-world...

A New Trajectory Clustering Method for Mining Multiple Periodic Patterns from Complex Oceanic Trajectories

Oceanic trajectories frequently exhibit multiple periodic patterns across various time intervals, e.g., tidal variations, mesoscale eddies, and El Niño events correspond to diurnal, seasonal, and interannual fluctuations in environmental factors. To explore hidden spatiotemporal multiple periodic behaviors in noisy ocean data, we propose a novel trajectory clustering method, namely DTID-STFC. It first identifies dense time intervals (DTIs) in which trajectories occur frequently. Subsequently, within each DTI, it utilizes spectral embedding to project trajectories onto a latent subspace and proposes three-way fuzzy clustering to obtain results. We evaluate the proposed method on simulated datasets and compare it with traditional and state-of-the-art trajectory clustering approaches. Experimental results indicate that it outperforms other methods across all five metrics. Moreover, when applying the DTID-STFC method to the analysis of mesoscale cyclonic eddies in the South China Sea and vessel data, it demonstrates more discernible results than traditional methods, and it aligns well with physical oceanographic processes. This proposed method offers valuable insights into identifying periodic behaviors from complex and noisy spatiotemporal oceanic trajectory data.

Improved tide level prediction model combined GA-BP neural networks and GNSS SNR data

High-precision tidal forecasting plays a crucial role in providing reliable tidal information to coastal communities, ship operators, fishermen, and government agencies. Existing tidal prediction models, such as backpropagation neural networks (BPNN) and genetic algorithm-optimized BPNN (GA-BPNN), frequently difficulty in in achieving high precision because they rely solely on past tidal variations for real-time predictions. Signal-to-Noise Ratio (SNR) data have emerged as a valuable indicator closely related to real-time sea level changes due to the widespread adoption of Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology. In this paper, we propose a nowcasting tide level prediction method by adding SNR data to BPNN, i.e., Improved BPNN and Improved GA-BPNN, which predicts the next momentary tide level value by using the previous 15 tidal values and real-time SNR as input factors to BPNN. The results of 100-day, 200-day and 1-year tide prediction based on Astoria and Friday Harbor tide gauge stations show that the improved model prediction accuracies are better than the traditional model. Meanwhile, among the two improved models, Improved GA-BPNN has the higher prediction accuracy and can adapt to different time lengths of tide level prediction.

Assessing Short-range Shore-to-Shore (S2S) and Shore-to-Vessel (S2V) WiFi Communications

Wireless communications increasingly enable ubiquitous connectivity for a large number of nodes, applications and scenarios. One of the less explored scenarios are aquatic ecosystems, specially when enabled by near-shore and short-range communications. Overwater communications are impaired by a number of distinguishing dynamic factors, such as tides, waves or node mobility, that lead to a widely fluctuating and unpredictable channel. In this work, we empirically characterize near-shore, overwater channels at 2.4 GHz under realistic conditions, including tidal variations, and relatively short TX-RX separations. To this end, we conducted experiments in a coastal estuarine region and on a harbor to characterize Shore-to-Shore (S2S) and Shore-to-Vessel (S2V) communication channels, respectively, and to identify major factors impairing communication in such scenarios. The empirical results show that constructive/destructive interference patterns, varying reflecting surface, and node mobility (i.e. travel direction and particular maneuvers) have a relevant and noticeable impact on the received signal strength. Thus, a set of parameters should be simultaneously considered for improving the performance of communication systems supporting S2S and S2V links, namely tidal variations, reflection surface changes, antenna height, TX-RX alignment and TX-RX separation. The results useful provide insights into realistic S2S and S2V link design and operation.

Lung Volume and Ventilation Distribution After Bariatric Surgery: High-Flow Nasal Cannula Versus CPAP.

Patients with obesity are at increased risk of postoperative pulmonary complications. CPAP has been used successfully to prevent and treat acute respiratory failure, but in many clinical scenarios, high-flow nasal cannula (HFNC) therapy is emerging as a possible alternative. We aimed to compare HFNC and CPAP in a sequential study measuring their effects on gas exchange, lung volumes, and gas distribution within the lungs measured through electrical impedance tomography (EIT). We enrolled 15 subjects undergoing laparoscopic bariatric surgery. Postoperatively they underwent the following oxygen therapy protocol (10 min/step): baseline air-entrainment mask, HFNC at increasing (40, 60, 80, and 100 L/min) and decreasing flows (80, 60, and 40 L/min), washout air-entrainment mask and CPAP (10 cm H2O). Primary outcome was the change in end-expiratory lung impedance (ΔEELI) measured by EIT data processing. Secondary outcomes were changes of global inhomogeneity (GI) index and tidal impedance variation (TIV) measured by EIT, arterial oxygenation, carbon dioxide content, pH, respiratory frequency, and subject's comfort. Thirteen subjects completed the study. Compared to baseline, ΔEELI was higher during 10 cm H2O CPAP (P = .001) and HFNC 100 L/min (P = .02), as well as during decreasing flows HFNC 80, 60, and 40 L/min (P = .008, .004, and .02, respectively). GI index was lower during HFNC 100 compared to HFNC 60increasing (P = .044), HFNC 60decreasing (P = .02) HFNC 40decreasing (P = .01), and during 10 cm H2O CPAP compared to washout period (P = .01) and HFNC 40decreasing (P = .03). TIV was higher during 10 cm H2O CPAP compared to baseline (P = .008). Compared to baseline, breathing frequency was lower at HFNC 60increasing, HFNC 100, and HFNC 80decreasing (P = .01, .02, and .03, respectively). No differences were detected regarding arterial oxygenation, carbon dioxide content, pH, and subject's comfort. HFNC at a flow of 100 L/min induced postoperative pulmonary recruitment in bariatric subjects, with no significant differences compared to 10 cm H2O CPAP in terms of lung recruitment and ventilation distribution.

Semidiurnal Internal Tide Interference in the Northern South China Sea

Multiwave interference plays a crucial role in shaping the spatial variations of internal tides. Based on a combination of in situ mooring and altimeter data, interference of semidiurnal internal tides was investigated in the northern South China Sea. Mooring observations indicate the observed kinetic-to-potential energy ratio and group speed are both relatively lower than the theoretical values of mode-1 semidiurnal internal tides, indicating the presence of partly-standing waves. This is consistent with the altimeter result that the mooring was located at the antinode within the interference pattern formed by the superposition of the westward and southward semidiurnal internal tides from the Luzon Strait and the continental slope of the southern Taiwan Strait. However, the kinetic-to-potential energy ratio and group velocity were notably changed when an anticyclonic eddy passed by the mooring. By employing the ray-tracing method, we identified that mesoscale processes may induce a phase difference in the semidiurnal internal tides between the Luzon Strait and the continental slope of the southern Taiwan Strait. This alteration further leads to changes in the positions of nodes and antinodes within the interference pattern of the semidiurnal internal tides.

Comparing sensitivities of groundwater head to variations in hydraulic parameters under boundary conditions of river stage rise and tidal variation

The sensitivity of hydraulic head responses to spatially distributed hydraulic parameters is essential for uncertainty analysis, inverse modeling, and parameter estimation and interpretation. This study formulates the Fréchet sensitivity kernel of hydraulic head responses to a suddenly rising boundary and a sinusoidal head fluctuation boundary to variation of spatially distributed hydraulic parameters in a semi-infinite, one-dimensional (1-D), confined aquifer, and it then derives analytical solutions. Different from previous studies that derived expressions for Fréchet kernels in the time domain for a 2-D pumping test, this study is the first to derive the closed-form Fréchet kernels in time and frequency domains for a semi-infinite, 1-D, confined aquifer. This study uses the Fréchet kernels to investigate the nature of singularities in the spatial sensitivity functions around the observation location and boundary. The information content revealed by observation of head change or head fluctuation amplitude at a given specified location and time (or frequency) under the above two boundary conditions is different. When comparing Fréchet sensitivity kernels across various times or periods, multi-frequency information, much like multi-time information, can be instrumental for hydrogeological parameter inversion. The explicit-form Fréchet sensitivity kernels also identify the optimal time or period for obtaining measurements.