scholarly journals The use of B-splines to represent the topography of river networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Eva Boergens ◽  
Michael Schmidt ◽  
Florian Seitz
Keyword(s):  
Standard Deviation ◽  
Water Level ◽  
River Networks ◽  
Distributed Data ◽  
Outlier Removal ◽  
Directed Tree ◽  
B Splines ◽  
Tree Graphs ◽  
Main Challenge ◽  
Mean Square Errors

AbstractThis work presents a new extension to B-Splines that enables them to model functions on directed tree graphs such as non-braided river networks. The main challenge of the application of B-splines to graphs is their definition in the neighbourhood of nodes with more than two incident edges. Achieving that the B-splines are continuous at these points is non-trivial. For both, simplification reasons and in view of our application, we limit the graphs to directed tree graphs. To fulfil the requirement of continuity, the knots defining the B-Splines need to be located symmetrically along the edges with the same direction. With such defined B-Splines, we approximate the topography of the Mekong River system from scattered height data along the river. To this end, we first test and validate successfully the method with synthetic water level data, with and without added annual signal. The quality of the resulting heights is assessed besides others by means of root mean square errors (RMSE) and mean absolute differences (MAD). The RMSE values are 0.26 m and 1.05 m without and with added annual variation respectively and the MAD values are even lower with 0.11 m and 0.60 m. For the second test, we use real water level observations measured by satellite altimetry. Again, we successfully estimate the river topography, but also discuss the short comings and problems with unevenly distributed data. The unevenly distributed data leads to some very large outliers close to the upstream ends of the rivers tributaries and in regions with rapidly changing topography such as the Mekong Falls. Without the outlier removal the standard deviation of the resulting heights can be as large as 50 m with a mean value of 15.73 m. After the outlier removal the mean standard deviation drops to 8.34 m.

scholarly journals Outlier Detection and Smoothing Process for Water Level Data Measured by Ultrasonic Sensor in Stream Flows

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 951 ◽  
Author(s):  
Inhyeok Bae ◽  
Un Ji
Keyword(s):  
Water Level ◽  
Outlier Detection ◽  
Measurement Range ◽  
Ultrasonic Sensor ◽  
Sensitivity Analyses ◽  
Data Sets ◽  
Ultrasonic Sensors ◽  
Outlier Removal ◽  
Level Data ◽  
Water Level Data

Water level data sets acquired by ultrasonic sensors in stream-scale channels exhibit relatively large numbers of outliers that are off the measurement range between the ultrasonic sensor and water surface, as well as data dispersion of approximately 2 cm due to random errors such as water waves. Therefore, this study develops a data processing algorithm for outlier removal and smoothing for water level data measured by ultrasonic sensors to consider these characteristics. The outlier removal process includes an initial cutoff process to remove outliers out of the measurement range and an outlier detection process using modified Z-scores based on the median absolute deviation (MAD) of a robust estimator. In addition, an exponentially weighted moving average (EWMA) method is applied to smooth the processed data. Sensitivity analyses are performed for factors that are subjectively set by the user, including the window size for the MAD outlier detection stage, the rejection criterion for the modified Z-score outlier removal stage, and the smoothing constant for the EWMA smoothing stage, based on four different water level data sets acquired by ultrasonic sensors in stream-scale experiments.

The 2D Spring Splines Procedure Application With Prescribed Accuracy for Determination of the Global (Pipe Centerline) as Well as the Local (Dent) Curvatures

2012 ◽  
Author(s):  
I. V. Orynyak ◽  
A. V. Bohdan ◽  
I. V. Lokhman
Keyword(s):  
Standard Deviation ◽  
Wave Length ◽  
Elastic Beam ◽  
Local Geometry ◽  
Bending Stress ◽  
Position Measurement ◽  
Mean Square Errors ◽  
Local Dent ◽  
Derivatives Of

The problem of smoothing the spatial line based on position measurements of discrete points exists in cases where a) the positions of points are determined with some errors, b) the goal of smoothing is not a continuous position itself but the higher derivatives of it. It is a very common problem in many engineering applications. With respect to the pipeline industry this problem is very prominent at least in two cases but regretfully many researchers do not pay due attention to it at all. First, the Geopigs are widely used for the determination of spatial position of the pipe centerline points. This information inter alia may be (and in fact are widely) used for the calculation of the global centerline curvatures which are proportional to the global bending strains. Second, the maximum strain levels of the dents are calculated based on the local geometry of the dent as determined by radial sensor measurements from the in line inspection survey. Note, that in both cases mathematically the curvatures are the second derivatives of the function of global (pipeline) or local (dent) positions. The input information about the global X–Y–Z position of each consecutive point of axis line as well as the local radial position of the dent points are given with some error. This leads to a huge noise in predicted curvatures which can overrun the useful information. The amplitude of errors of calculation is inversely proportional to the squared distance between the points of measurement. The application of any smoothing procedure may lead to the loss of the useful information about real curvatures. Thus tradeoff between the smoothing of the noise and the loss of accuracy presents a big problem in the pipeline industry. Two quantitative parameters are introduced here to allow performing such a tradeoff. First parameter characterizes the standard deviation (also referred to as standard in the following) of the random value of the position measurement accuracy by the devices, ρ. Second parameter is the requested accuracy of the curvature determination and is defined in terms of the standard deviation of the bending stress, σ or strain, ε. The spatial beam on elastic foundation model is used to fit the measured point positions to the spatial curve. Its main characteristic is the specific compliance of the foundation α which is determined based on two above root-mean-square errors ρ and σ. The corresponding formulas and tables based on the solution for the elastic beam are obtained. The bigger the allowed error in bending stress σ the lesser is required compliance of the foundation, α. In turn this leads to the smaller value of characteristic wave length of solution and the possibility to retain more useful information about the actual short length stresses in the pipeline. Some practical examples of applications of the procedure are given.

Pendugaan Standar Deviasi untuk Sampel Kecil dalam Penelitian Pertanian

2019 ◽  
Author(s):  
Weksi Budiaji
Keyword(s):  
Standard Deviation ◽  
Small Sample ◽  
Range Data ◽  
Distributed Data ◽  
Square Root ◽  
Rule Of Thumb ◽  
Standard Normal

There is a rule of thumb formula to estimate a standard deviation for a small sample (2 to 15 samples). This formula is based on a ratio between the range data (maximum minus minimum) and the square root of the number of the samples. Although this formula has a small bias, a Mantel formula used some constants instead of the square root of the number of the samples that produced even a smaller bias to a normal and a uniform distributed data. In this manuscript, we modify three constants that Mantel formula is proposed when the number of objects is equal to 2 and 3. We also add a rule that the data must be assumed to be a standard normal (N (0,1)) or a standard uniform (U (0,1)) distribution. (citation: Budiaji W., Suherna, S., Salampessy, YLA. 2012. Pendugaan Standar Deviasi untuk Sampel Kecil dalam Penelitian Pertanian. Jurnal Ilmu Pertanian dan Perikanan Vol. 1 No. 1 Hal: 37-42)

scholarly journals On variability in the density of corticocortical and thalamocortical connections

2000 ◽  
Vol 355 (1393) ◽  
pp. 21-35 ◽  
Author(s):  
Jack W. Scannell ◽  
Simon Grant ◽  
Bertram R. Payne ◽  
Roland Baddeley
Keyword(s):  
Standard Deviation ◽  
Frequency Distribution ◽  
Negative Binomial ◽  
Distributed Data ◽  
Corticocortical Connections ◽  
Quantitative Measurements ◽  
Quantitative Studies ◽  
Thalamocortical Connections ◽  
The Mean ◽  
Connection Density

Variability is an important but neglected aspect of connectional neuroanatomy. The quantitative density of the ‘same’ corticocortical or thalamocortical connection may vary by over two orders of magnitude between different injections of the same tracer. At present, however, the frequency distribution of connection densities is unknown. Therefore, it is unclear what kind of sampling strategies or statistical methods are appropriate for quantitative studies of connectivity. Nor is it clear if the measured variability represents differences between subjects, or if it is simply a consequence of intra–individual differences resulting from experimental technique and the exact placement of tracers relative to local spatial and laminar variation in connectivity. W e used quantitative measurements of the density of a large number of corticocortical and thalamocortical connections from our own laboratories and from the literature. V ariability in the density of given corticocortical and thalamocortical connections is high, with the standard deviation of density proportional to the mean. The frequency distribution is close to exponential. Therefore, analysis methods relying on the normal distribution are not appropriate. W e provide an appendix that gives simple statistical guidance for samples drawn from exponentially distributed data. For a given corticocortical or thalamocortical connection density, between–individual standard deviation is 0.85 to 1.25 times the within–individual standard deviation. Therefore, much of the variability reported in conventional neuroanatomical studies (with one tracer deposited per animal) is due to within–individual factors. W e also find that strong, but not weak, corticocortical connections are substantially more variable than thalamocortical connections. We propose that the near exponential distribution of connection densities is a simple consequence of ‘patchy’ connectivity. W e anticipate that connection data will be well described by the negative binomial, a class of distribution that applies to events occurring in clumped or patchy substrates. Local patchiness may be a feature of all corticocortical connections and could explain why strong corticocortical connections are more variable than strong thalamocortical connections. This idea is supported by the columnar patterns of many corticocortical but few thalamocortical connections in the literature.

scholarly journals WATER LEVEL MONITORING ON TIBETAN LAKES BASED ON ICESAT AND ENVISAT DATA SERIES

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 1529-1533 ◽  
Author(s):  
H. W. Li ◽  
G. Qiao ◽  
Y. J. Wu ◽  
Y. J. Cao ◽  
H. Mi
Keyword(s):  
Standard Deviation ◽  
Water Level ◽  
Lake Water ◽  
Water Footprint ◽  
Scientific Data ◽  
Quality Data ◽  
Tibet Plateau ◽  
Data Series ◽  
Data Set ◽  
Wide Range

Satellite altimetry technique is an effective method to monitor the water level of lakes in a wide range, especially in sparsely populated areas, such as the Tibet Plateau (TP). To provide high quality data for time-series change detection of lake water level, an automatic and efficient algorithm for lake water footprint (LWF) detection in a wide range is used. Based on ICESat GLA14 Release634 data and ENVISat GDR 1Hz data, water level of 167 lakes were obtained from ICESat data series, and water level of 120 lakes were obtained from ENVISat data series. Among them, 67 lakes contained two data series. Mean standard deviation of all lakes is 0.088 meters (ICESat), 0.339 meters (ENVISat). Combination of multi-source altimetry data is helpful for us to get longer and more dense periods cover water level, study the lake level changes, manage water resources and understand the impacts of climate change better. In addition, the standard deviation of LWF elevation used to calculate the water level were analyzed by month. Based on lake data set for the TP from the 1960s, 2005, and 2014 in Scientific Data, it is found that the water level changes in the TP have a strong spatial correlation with the area changes.

scholarly journals MEASURING OF SQUAT IN THE FAIRWAY TO THE PORT OF LULEA, NORTH SWEDEN

1968 ◽  
Vol 1 (11) ◽  
pp. 97
Author(s):  
Carl G. Carlstrom
Keyword(s):  
Standard Deviation ◽  
Turbulent Flow ◽  
Water Level ◽  
Measuring Method ◽  
Field Work ◽  
Accuracy Of Measurements ◽  
Solid Foundation ◽  
Sheltered Water ◽  
North Sweden

The importance of knowledge of squat and expected underkeel clearance for ships passing a fairway is essential to the navigational safety and the economy of a harbour. In order to check the squat of ships in the fairway to the port of Lulea a photographic measuring method has been evolved and used in measurements on three different ships. Determining of squat is made by levelling the position of vessels in relation to water level at the berth before sailing and en route at measuring points along the fairway. The accuracy of measurements was determined by observations on reference staffs. The order of standard deviation is 1/2 inch, at 2,400 feet distance. Observations indicate squat ranging from 1 foot 5 inches at speeds of 9 knots to 2 inches at 3>7 knots. The measured squat corresponds rather good to tneoretically calculated values according to Woltiger and Shell/Sogreah. The measuring method used has reduced the field work. The greatest advantage is that adequate values of squat will be directly recorded with only a few corrections including irregular factors such as turbulent flow, hull deformations and variable channel sections. A condition is however sheltered water and possioilities of solid foundation for instrument arrangement. 1499

Predictive Simulation of Concurrent Debris Flow: How Slope Failure Locations Affect Predicted Damage

2020 ◽  
Author(s):  
Kazuki Yamanoi ◽  
Satoru Oishi ◽  
Kenji Kawaike ◽  
Hajime Nakagawa
Keyword(s):  
Standard Deviation ◽  
Debris Flow ◽  
Water Level ◽  
Slope Failure ◽  
Predictive Simulation ◽  
Relative Standard ◽  
Case Simulation ◽  
Failure Location ◽  
Downstream Area ◽  
Debris Flow Initiation

Predictive simulation of concurrent debris flow using only pre-disaster information has proven to be difficult as a result of problems in predicting the location of debris-flow initiation (i.e., slope failure). However, because catchment topography has concave characteristics, with all channels in a catchment joining each other as they flow downstream, it is possible to predict damage to downstream area using relatively inaccurate initiation points. Based on this, this paper presents methodologies employing debris-flow initiation points generated randomly using statistical slope failure prediction. A many-case simulation across numerous initiation points was performed to quantify the effect of slope-failure location in terms of deviations in the predicted water level and terrain deformation. It was found that the relative standard deviation diminished as the points approached the downstream area, indicating a location-based predictability effect.

The rapid glacial-proglacial landscape modification at Pasterze Glacier in a one-year period as revealed by multiple aerial flight and field campaigns

2020 ◽  
Author(s):  
Gernot Seier ◽  
Andreas Kellerer-Pirklbauer ◽  
Wolfgang Sulzer ◽  
Christian Ziesler ◽  
Philipp Krisch ◽  
...  
Keyword(s):  
Water Level ◽  
Transition Zone ◽  
Diurnal Cycle ◽  
Horizontal Displacement ◽  
Aerial Imagery ◽  
Visual Interpretation ◽  
Landscape Modification ◽  
Glacier Tongue ◽  
Ground Truthing ◽  
Mean Square Errors

<p>The Pasterze Glacier is an approx. 16 km² large and rapidly receding glacier in the Austrian Alps. The aim of this study was to detect and quantify the rapid landscape modification of its glacial-proglacial transition zone between September 2018 and September 2019. The study is primarily based on the analysis of aerial imagery of five different acquisition dates, two in 2018 (11 September and 15 November) and three in 2019 (17 June, 13 and 21 September). The platforms used for data acquisition comprised unmanned and manned aircrafts that led to ground sampling distances (GSDs) of the aerial imagery of approx. 10 cm. These data were photogrammetrically processed to orthophotos and digital elevation models (DEMs), which are the main input for the subsequent analysis. The flight campaigns were complemented mainly with geodetic measurements for ground-truthing purposes, water level measurements and field observations in order to facilitate a better geomorphological and glaciological interpretation.</p><p>Thickness changes and horizontal displacement of the Pasterze Glacier tongue and its adjacent proglacial transition zone were detected applying DEM differencing and normalized cross-calculation (orthophotos). These analyses also included a quality assessment, which allowed to discriminate changes from unchanged subareas. By visual interpretation of the orthophotos and our in-situ measurements, we detected substantial geomorphic changes, the further evolution of the proglacial lake’s extent and water level changes.</p><p>Results show that the thickness of the investigated subarea at the glacier tongue (0.2 km²) decreased up to approx. 18 m from June 2019 to September 2019 with a mean ice thickness decrease of approx. 4.2 m. In contrast, a subarea of the studied proglacial area (0.14 km²) remained rather unchanged (mean thickness decrease of only 0.7 m). Taking into account the comparison of DEM elevation values with geodetically and thus independent elevation measurements, the vertical quality of the DEMs is described by a standard deviation of 0.14-0.16 m and a mean of 0.07 m. The Root Mean Square Errors of the GCPs are 0.08-0.13 m in planimetry and 0.10-0.16 m in heights.</p><p>Comparing the orthophotos of June 2019 and September 2019 shows a distinct expansion of the glacier lake towards the eastern part of the debris-covered glacier tongue by several meters in one summer only. The lake level shows a clear diurnal cycle of typically around 20 cm during sunny days (high irradiation) and changes in the order of half a meter over the entire summer season. Water temperatures of the lake follow a clear diurnal cycle, too with typical values between 1°C and 3°C.</p><p>We conclude that the Pasterze Glacier tongue and its adjacent proglacial area changed rapidly in terms of glacier surfaces modification and in terms of proglacial changes on an annual (September 2018 to September 2019) and sub-annual (June to September 2019) time-scale.</p>

Sign in / Sign up

Export Citation Format

Share Document