Exact and heuristic formulae to compute the geodetic height from the ellipse equation

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy.The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates.This research analyzes this influence and how it can contribute to their solutions.The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation.In addition,a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed,which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %.The calculation is stable,and the cost is low.

A Fine-grained Building Height Control Method for Heritage Areas from the Perspective of Visual Integrity

This study proposes a refined methodology for controlling building heights in heritage areas.In order to protect the visual integrity of the heritage area,buildings should not obstruct the view from important site points and viewpoints to the periphery.By calculating the building height thresholds that buildings should not obscure the view from each viewpoint,the results of which are weighted and superimposed,and the values are extracted to each building unit as a refined building height control guideline.This study takes the Zhoukoudian area as a case study,applies the refined building height control criterion to the Zhoukoudian Site,and relies on this refined criterion to assess the visual integrity of the Zhoukoudian area,so as to realize the scientific planning and monitoring of the Zhoukoudian area.The refined building height control method can be applied to building height planning and visual landscape protection in large heritage areas.

The influence of inter-band rock on rib spalling in longwall panel with large mining height

In order to improve rib stability,failure criteria and instability mode of a thick coal seam with inter-band rock layer are analysed in this study.A three-dimensional mechanical model is established for the rib by considering the rock layer.A safety factor is defined foy the rib,and it is observed that the safety factor exhibits a positive correlation with the thickness and strength of the inter-band rock.A calculation method for determining critical parameters of the rock layer is presented to ensure the rib stability.It is revealed that incomplete propagation of the fracture at the hard rock constitutes a fundamental prerequisite for ensuring the rib stability.The influence of the position of the inter-band rock in the coal seam on failure mechanism of the rib was thoroughly investigated by developing a series of physical models for the rib at the face area.The best position for the inter-band rock in the coal seam is at a height of 1.5 m away from the roof line,which tends to provide a good stability state for the rib.For different inter-band rock positions,two ways of controlling rib by increasing supports stiffness and flexible grouting reinforcement are proposed.

An Analysis of Catherine’s Tragedy at Wuthering Heights—from the Contradiction between“Id”and“Social Reality”

There exist discussions about the heroine's love tragedy in Wuthering Heights from time to time.Based on Freud's Id theory as the starting point,it serves as a new viewpoint of review focusing on the conflict between“Social Reality”and“Id”in the novel to analyse the causes of Catherine's love tragedy and criticize the devastation of humanity brought by the concept of“money first”and“family hierarchy”in the 19th century capitalist society.

The effect of topographic density variations on the geoid and orthometric heights in Hong Kong

Utilizing the adopted average topographic density of 2670 kg/m^(3)in the reduction of gravity anomalies introduces errors attributed to topographic density variations,which consequently affect geoid modeling accuracy.Furthermore,the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincar e-Prey gravity reduction where the topographic density variations are disregarded.The Helmert orthometric heights of benchmarks are then affected by errors.These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined.An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits,the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights.The same applies to geoid modeling errors.In this study,we investigate these errors in the Hong Kong territory,where topographic density is about 20%lower than the density of 2670 kg/m^(3).We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights.Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm,respectively.Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models.However,in regions dominated by sedimentary and igneous rocks,the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m^(3),thus introducing large systematic errors in geoid and orthometric heights.

The Kuroshio Transport East of Taiwan and the Sea Surface Height Anomaly from the Interior Ocean

The relationship between the Kuroshio transport to the east of Taiwan and the SSHA (Sea Surface Height Anomaly) field is studied based on the World Ocean Circulation Experiment (WOCE) PCM-1 moored current meter array observation, the satellite altimeter data from the MSLA (Map of Sea Level Anomaly) products merged with the ERS and TOPEX/POSEIDON (T/P) data sets, and the WOCE satellite-tracked drifting buoy data. It is confirmed that the Kuroshio transport across PCM-1 array highly correlates with the SSHA upstream (22°-24°N, 121.75°-124°E). The SSHA is not locally generated by the developed Kuroshio meandering but is from the interior ocean and is propagating westward or northwestward. During the period from October 1992 to January 1998, two events of the northwestward propagating negative SSHA occurred, during which the SSHA merged into the Kuroshio and caused the remarkable low transport events in contrast to the normal westward propagating negative SSHA. It is also shown that the lower Kuroshio transport event would be generated in different ways. The negative anomaly in the upstream of PCM-1 array can reduce the Kuroshio transport by either offshore or onshore Kuroshio meandering. The positive anomaly, which is strong enough to detour the Kuroshio, can cause an offshore meandering and a low transport event at the PCM-1 array.

Influence of pier height on the safety of trains running on high-speed railway bridges during earthquakes

Sudden earthquakes pose a threat to the running safety of trains on high-speed railway bridges,and the stiffness of piers is one of the factors affecting the dynamic response of train-track-bridge system.In this paper,a experiment of a train running on a high-speed railway bridge is performed based on a dynamic experiment system,and the corresponding numerical model is established.The reliability of the numerical model is verified by experiments.Then,the experiment and numerical data are analyzed to reveal the pier height effects on the running safety of trains on bridges.The results show that when the pier height changes,the frequency of the bridge below the 30 m pier height changes greater;the increase of pier height causes the transverse fundamental frequency of the bridge close to that of the train,and the shaking angle and lateral displacement of the train are the largest for bridge with 50 m pier,which increases the risk of derailment;with the pier height increases from 8 m to 50 m,the derailment coefficient obtained by numerical simulations increases by 75% on average,and the spectral intensity obtained by experiments increases by 120% on average,two indicators exhibit logarithmic variation.

BnaC03.BIN2 regulates plant height by affecting the main inflorescence length and first effective branch height in Brassica napus L.

Rapeseed(Brassica napus L.)is one of the main oil crops in the world,and increasing its yield is of great significance for ensuring the safety of edible oil.Presently,improving rapeseed plant architecture is an effective way to increase rapeseed yield with higher planting density.However,the regulatory mechanism of rapeseed plant architecture is poorly understood.In this study,a dwarf rapeseed mutant dwarf08(df08)is obtained by ethyl methane sulfonate(EMS)-mutagenesis.The decrease in plant height of df08 is mainly caused by the reduction in main inflorescence length and first effective branch height and controlled by a single semi-dominant gene.The hybrid plants(F1)show a semi-dwarf phenotype.Through map-based cloning and transgenic assay,we confirm that the nonsynonymous single nucleotide variant(SNV)(C to T)in BnaC03.BIN2,which is homologous with Arabidopsis(Arabidopsis thaliana)BIN2,is responsible for the dwarfism of df08.BnaC03.BIN2 interacts with BnaBZR1/BES1 and involves in brassinosteroids(BRs)signal transduction.Proline to Leucine substitution in 284(P284L)enhances the protein stability of BnaC03.bin2-D,disrupts BRs signal transduction and affects the expression of genes regulating cell division,leading to dwarfism of df08.This study provides a new insight for the mechanism of rapeseed plant height regulation and creates an elite germplasm that can be used for genetic improvement of rapeseed architecture.

A Multi-Baseline PolInSAR Forest Height Inversion Method Taking into Account the Model Ill-posed Problem

Affected by the insufficient information of single baseline observation data,the three-stage method assumes the Ground-to-Volume Ratio(GVR)to be zero so as to invert the vegetation height.However,this assumption introduces much biases into the parameter estimates which greatly limits the accuracy of the vegetation height inversion.Multi-baseline observation can provide redundant information and is helpful for the inversion of GVR.Nevertheless,the similar model parameter values in a multi-baseline model often lead to ill-posed problems and reduce the inversion accuracy of conventional algorithm.To this end,we propose a new step-by-step inversion method applied to the multi-baseline observations.Firstly,an adjustment inversion model is constructed by using multi-baseline volume scattering dominant polarization data,and the regularized estimates of model parameters are obtained by regularization method.Then,the reliable estimates of GVR are determined by the MSE(mean square error)analysis of each regularized parameter estimation.Secondly,the estimated GVR is used to extracts the pure volume coherence,and then the vegetation height parameter is inverted from the pure volume coherence by least squares estimation.The experimental results show that the new method can improve the vegetation height inversion result effectively.The inversion accuracy is improved by 26%with respect to the three-stage method and the conventional solution of multi-baseline.All of these have demonstrated the feasibility and effectiveness of the new method.

Determining Atmospheric Boundary Layer Height with the Numerical Differentiation Method Using Bending Angle Data from COSMIC

This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data(January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops(large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e.,the uncertainties are small; whereas, for non-sharp ABL tops(small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.

Sea surface height anomaly and geostrophic circulation variations in the South China Sea from TOPEX/POSEIDON altimetry

The sea surface height anomaly (SSHA) and geostrophic circulation in the South ChinaSea (SCS) are studied using TOPEX/POSEIDON (T/P) altimetry data. The SSHA, which is obtained after tidal correction based on the tidal results from T/P data, is predominated by seasonal alternating monsoons. The results reveal that the SSHA in the central part of the SCS is positive in spring and summer, but negative in autumn and winter. It is also found that the SSHA in the SCS can be approached with the sum of tidal constituents SA and SSA. The geostrophic circulations in the SCS are calculated according to sea surface dynamic topography, which is the sum of SSHA and mean sea surface height. It is suggested that the circulation in the upper layer of the SCS is generally cyclonic and notably western intensified during autumn and winter, while the western intensification is weak during spring and summer. It is also indicated that the Kuroshio intrudes into the northeastern SCS throuth the Luzon Strait in winter. But there is no indication of Kuroshio intruding into the SCS in summer.

Diurnal variability of the planetary boundary layer height estimated from radiosonde data

Diurnal variations in the planetary boundary layer height(PBLH)at different latitudes over different surface characteristics are described,based on 45 years(1973−2017)of radiosonde observations.The PBLH is determined from the radiosonde data by the bulk Richardson number(BRN)method and verified by the parcel method and the potential temperature gradient method.In general,the BRN method is able to represent the height of the convective boundary layer(BL)and neutral residual layer cases but has relatively large uncertainty in the stable BL cases.The diurnal cycle of the PBLH over land is quite different from the cycle over ocean,as are their seasonal variations.For stations over land,the PBLH shows an apparent diurnal cycle,with a distinct maximum around 15:00 LT,and seasonal variation,with higher values in summer.Compared with the PBLH over land,over oceans the PBLH diurnal cycles are quite mild,the PBLHs are much lower,and the seasonal changes are less pronounced.The seasonal variations in the median PBLH diurnal cycle are positively correlated with the near-surface temperature and negatively correlated with the near-surface relative humidity.Finally,although at most latitudes the daytime PBLH exhibits,over these 45 years,a statistically significant increasing trend at most hours between 12:00 LT and 18:00 LT over both land and ocean,there is no significant trend over either land or ocean in the nighttime PBLH for almost all the studied latitudes.

Factors influencing further vertebral height loss following percutaneous vertebroplasty in osteoporotic vertebral compression fractures:A 1-year follow-up study

BACKGROUND Osteoporotic vertebral compression fractures(OVCFs)contribute to back pain and functional limitations in older individuals,with percutaneous vertebroplasty(PVP)emerging as a minimally invasive treatment.However,further height loss post-PVP prompts investigation into contributing factors.AIM To investigate the factors associated with further height loss following PVP with cement augmentation in OVCF patients.METHODS A total of 200 OVCF patients who underwent successful PVP between January 2021 and December 2022 were included in this study.“Further height loss”during 1 year of follow-up in OVCF patients with bone edema was defined as a vertical height loss of≥4 mm.The study population was divided into two groups for analysis:The“No Further Height Loss group(n=179)”and the“Further Height Loss group(n=21).”RESULTS In comparing two distinct groups of patients,significant differences existed in bone mineral density(BMD),vertebral compression degree,prevalence of intravertebral cleft(IVF),type of bone cement used,and cement distribution patterns.Results from binary univariate regression analysis revealed that lower BMD,the presence of IVF,cleft distribution of bone cement,and higher vertebral compression degree were all significantly associated with further height loss.Notably,the use of mineralized collagen modified-poly(methyl methacrylate)bone cement was associated with a significant reduction in the risk of further height loss.In multivariate regression analysis,lower BMD and the presence of IVF remained significantly associated with further height loss.CONCLUSION Further height loss following PVP in OVCF patients is influenced by a complex interplay of factors,especially lower BMD and the presence of IVF.These findings underscore the importance of assessing and managing these factors when addressing height loss following PVP in OVCF patients.

An approach to estimate tree height using PolInSAR data constructed by the Sentinel-1 dual-pol SAR data and RVoG model

We estimate tree heights using polarimetric interferometric synthetic aperture radar(PolInSAR)data constructed by the dual-polarization(dual-pol)SAR data and random volume over the ground(RVoG)model.Considering the Sentinel-1 SAR dual-pol(SVV,vertically transmitted and vertically received and SVH,vertically transmitted and horizontally received)configuration,one notes that S_(HH),the horizontally transmitted and horizontally received scattering element,is unavailable.The S_(HH)data were constructed using the SVH data,and polarimetric SAR(PolSAR)data were obtained.The proposed approach was first verified in simulation with satisfactory results.It was next applied to construct PolInSAR data by a pair of dual-pol Sentinel-1A data at Duke Forest,North Carolina,USA.According to local observations and forest descriptions,the range of estimated tree heights was overall reasonable.Comparing the heights with the ICESat-2 tree heights at 23 sampling locations,relative errors of 5 points were within±30%.Errors of 8 points ranged from 30%to 40%,but errors of the remaining 10 points were>40%.The results should be encouraged as error reduction is possible.For instance,the construction of PolSAR data should not be limited to using SVH,and a combination of SVH and SVV should be explored.Also,an ensemble of tree heights derived from multiple PolInSAR data can be considered since tree heights do not vary much with time frame in months or one season.

Feasibility of Transferring Drinking Water from the Senegal River in the East (Backel) to the West Center (Fatick) in Senegal

Every year, 24 billion m3 of fresh water are thrown into the sea by the Senegal River, while most of the country’s populations do not have permanent access to drinking water. Also, agricultural land, which extends as far as the eye can see, is only used during winter periods, thus slowing down the development of agriculture. It is in this context that this article studies the feasibility of transferring drinking water from the Senegal River in the east of the country to the center-west through a transfer canal to meet the drinking water needs of the populations. In addition, we intend to flood the fossil valleys from this canal and recharge the aquifers. The watershed resulting from the juxtaposition of the two watersheds which dominate central Senegal has a slightly descending profile from Bakel to Fatick. This promotes gravity flow of water over 542 km. This analysis is carried out by the Glabal Mapper software and SRTM1 images. We report that all water needs have been estimated at approximately 70 m3/s based on the ANDS census in 2023, the distribution of arable land and groundwater recharge areas in the country. The waters flowing in the canal have depths (draft) not reaching 4.6 m. These results are obtained by applying the Manning Strickler equation, on a channel with a straight cross-section in the shape of a trapezoid and lined with sand concrete. The canal thus designed will bring water to populations and arid zones in the central and central-western regions of the country where problems persist. However, it will be necessary to overcome a difference in altitude of 96 m over 30 km to raise the water from the river to the threshold of the canal in order to ensure the flow in the latter. We have retained two calculation variants (Canal + Pumping or Single Pumping) whose pumping stations will be powered by solar fields. Due to the heavy investments, the installations upstream of the canal will be modular over time. Consequently, the central canal project will be constructed in six (6) phases of ten (10) years.

Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

An Experimental and Numerical Thermal Flow Analysis in a Solar Air Collector with Different Delta Wing Height Ratios

This study conducts both numerical and empirical assessments of thermal transfer and fluid flow characteristics in a Solar Air Collector(SAC)using a Delta Wing Vortex Generator(DWVG),and the effects of different height ratios(Rh=0.6,0.8,1,1.2 and 1.4)in delta wing vortex generators,which were not considered in the earlier studies,are investigated.Energy and exergy analyses are performed to gain maximum efficiency.The Reynolds number based on the outlet velocity and hydraulic diameter falls between 4400 and 22000,corresponding to the volume flow rate of 5.21–26.07 m^(3)/h.It is observed that the delta wing vortex generators with a higher height ratio yield maximum heat transfer enhancement and overall enhancement ratio.The empirical and numerical findings demonstrate that the exergy and thermal efficiencies decline in a specific range.TheNusselt number,pressure drop,energy,and exergy efficiencies enhance with rising Reynolds number,although the friction coefficient diminishes.The maximum heat transfer enhancement is 57%.According to the evaluation of exergy efficiency,the greatest efficiency of 31.2%is obtained at Rh=1.4 and Reynolds number 22000.

Comparisons in the global planetary boundary layer height obtained from COSMIC radio occultation,radiosonde,and reanalysis data

The global planetary boundary layer height(PBLH)estimated from 11 years(2007–17)of Integrated Global Radiosonde Archive(IGRA)data,Constellation Observing System for Meteorology,Ionosphere and Climate(COSMIC)soundings,and European Center for Medium-Range Weather Forecasts(ECMWF)interim reanalysis(ERAInterim)data,are compared in this study.In general,the spatial distribution of global PBLH derived from ERAInterim is consistent with the one from IGRA,both at 1200 UTC and 0000 UTC.High PBLH occurs at noon local time,because of strong radiation energy and convective activity.There are larger differences between the results of COSMIC and the other two datasets.PBLHs derived from COSMIC are much higher than those from radiosonde and reanalysis data.However,PBLHs derived from the three datasets all exhibit higher values in the low latitudes and lower ones in the high latitudes.The latitudinal difference between IGRA and COSMIC ranges from−1700 m to−500 m,while it ranges from−500 m to 250 m for IGRA and ERA-Interim.It is found that the differences among the three datasets are larger in winter and smaller in summer for most studied latitudes.

Assessment of reprocessed sea surface height measurements derived from HY-2A radar altimeter and its application to the observation of 2015–2016 El Nino

Haiyang-2A（HY-2A） is China＇s first ocean dynamic environment satellite and the radar altimeter is one of its main payloads. One of the main purposes of the radar altimeter is to measure the sea surface height（SSH）. The SSH determined from the altimeter range measurements includes some range and geophysical corrections. These corrections largely affect the accuracy of the SSH measurements. The range and the geophysical corrections are reprocessed and the altimeter waveforms in HY-2A sensor interim geophysical data set records（S-IGDR） are retracked from June 1, 2014 to June 14, 2014, and the accuracy of the reprocessed SSH measurements is evaluated.The methods of the range and geophysical corrections used to reprocess HY-2A altimeter data are validated by using these methods to reprocess the Jason-2 range and geophysical corrections and comparing the results with the range and geophysical corrections in Jason-2 geophysical dataset records（GDR） product. A crossover analysis is used to evaluate the accuracy of the reprocessed HY-2A SSH measurements. The standard deviation（STD） of the crossover SSH differences for HY-2A is around 4.53 cm while the STD of the SSH differences between HY-2A and Jason-2 is around 5.22 cm. The performance of the reprocessed HY-2A SSH measurements is significantly improved with respect to the SSH measurements derived from HY-2A interim geophysical dataset records（IGDR）product. The 2015–2016 El Ni？o has been the strongest El Ni？o event since 1997–1998. The range and the geophysical corrections in HY-2A IGDR are reprocessed and sea level anomalies are used to monitor the2015–2016 El Ni？o. The results show that the HY-2A altimeter can well observe the 2015–2016 El Ni？o.

Obtaining accurate measurements of the sea surface height from a GPS buoy

A dedicated GPS buoy is designed for calibration and validation(Cal/Val)of satellite altimeters since 2014.In order to evaluate the accuracy of the sea surface height(SSH)measured by the GPS buoy,twelve campaigns have been done within China sea area between 2014 and 2021.In six of these campaigns,two static Global Navigation Satellite System stations were installed at distances of<1 km and 19 km from the buoy to assess how the baseline length influenced the derived SSH from the buoy solutions.The GPS buoy data was processed using the GAMIT/GLOBK software+TRACK module and CSRS-PPP tool to achieve the SSH.The SSH was compared with conventionally tide gauge(TG)data to evaluate the accuracy of the buoy with the standard deviation of the height element.The results showed that the difference in the standard deviation of the SSH from the buoy and the TG was less than 16 mm.The SSHs processed with different ephemeris(Ultra-Rapid,Rapid,Final)were not significantly different.When the baseline length was 19 km,the SSH solution of the GPS buoy performed well,with standard bias of less than 26 mm between the heights measured by the buoy and TG,meaning that the buoy could be used for Cal/Val of altimeters.The bias between the Canadian Spatial Reference System-precise point positioning tool and the TRACK varied a lot,and some of them were over 130 mm.This deemed too high to be useful for Cal/Val of satellite altimeters.Moreover,the GPS buoy solutions processed by GAMIT/GLOBK software+TRACK module were used for in-orbit Cal/Val of HY-2B/C satellites in ten campaigns.The SSH and significant wave height of the altimeters showed good agreements with the GPS buoy solutions.