scholarly journals Effects of intersite dependence of nested catchment structures on probabilistic regional envelope curves

2009 ◽  
Vol 13 (9) ◽  
pp. 1699-1712 ◽  
Author(s):  
B. Guse ◽  
A. Castellarin ◽  
A. H. Thieken ◽  
B. Merz
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Equivalent Number ◽  
Realistic Representation ◽  
Cross Correlations ◽  
Nested Structure ◽  
Recurrence Intervals ◽  
Flood Flows ◽  
Flood Quantiles

Abstract. This study analyses the intersite dependence of nested catchment structures by modelling cross-correlations for pairs of nested and unnested catchments separately. Probabilistic regional envelope curves are utilised to derive regional flood quantiles for 89 catchments located in Saxony, in the Southeast of Germany. The study area has a nested structure and the intersite correlation is much stronger for nested pairs of catchments than for unnested ones. Pooling groups of sites (regions) are constructed based on several candidate sets of catchment descriptors using the Region of Influence method. Probabilistic regional envelope curves are derived on the basis of flood flows observed within the pooling groups. Their estimated recurrence intervals are based on the number of effective sample years of data (i.e. equivalent number of uncorrelated data). The evaluation of the effective sample years of data requires the modelling of intersite dependence. We perform this globally, using a cross-correlation function for the whole study area as well as by using two different cross-correlation functions, one for nested pairs and another for unnested pairs. In the majority of the cases, these two modelling approaches yield significantly different estimates for the effective sample years of data, and therefore also for the recurrence intervals. The reduction of the recurrence interval when using two different cross-correlation functions is larger for larger pooling groups and for pooling groups with a higher fraction of nested catchments. A separation into nested and unnested pairs of catchments gives a more realistic representation of the characteristic river network structure and improves the estimation of regional information content. Hence, applying two different cross-correlation functions is recommended.

scholarly journals Effects of intersite dependence of nested catchment structures on probabilistic regional envelope curves

2009 ◽  
Vol 6 (2) ◽  
pp. 2845-2892
Author(s):  
B. Guse ◽  
A. Castellarin ◽  
A. H. Thieken ◽  
B. Merz
Keyword(s):  
Correlation Functions ◽  
Cross Correlation ◽  
Equivalent Number ◽  
Realistic Representation ◽  
Group A ◽  
Cross Correlations ◽  
Nested Structure ◽  
Recurrence Intervals ◽  
Flood Quantiles ◽  
Quantile Estimates

Abstract. Regional flood quantile estimates are affected by intersite correlation between flood sequences observed at different discharge gauges. This study analyses the intersite dependence of nested catchment structures and investigates the possibility of improving the accuracy of regional flood quantiles, by modelling cross-correlations for pairs of nested and unnested catchments separately. Probabilistic Regional Envelope Curves are utilised to derive regional flood quantiles for 89 catchments belonging to Saxony, in the Southeast of Germany. The study area has a nested structure and a definitely stronger intersite correlation for nested pairs of catchments than for unnested ones. Probabilistic Regional Envelope Curves are constructed on the basis of flood flows observed within pooling groups of sites (regions). Their recurrence intervals are based on the number of effective sample-years of data (i.e., equivalent number of uncorrelated data). The evaluation of the effective sample-years of data required the modelling of intersite dependence, which we performed globally, using a cross-correlation formula identified for the whole study area, and by using two different cross-correlation formulas, one for nested pairs and another for unnested pairs. These two modelling approaches returned significantly different effective sample-years of data estimates, and therefore also recurrence intervals, in the majority of the cases. The differences result from various assumptions of the size and homogeneity degree of the pooling group. The reduction of the recurrence interval, when using two different cross-correlation functions, is larger for higher recurrence intervals and for a higher fraction of nested catchment within the pooling group. A separation into nested and unnested pairs of catchments gives a more realistic representation of the characteristic river network structure and improves the accuracy of the estimation of regional information content. Hence, applying two different cross-correlation functions is recommended.

scholarly journals The Discrete Correlation Function: A New Method for Analyzing Unevenly Sampled Variability Data

1989 ◽  
Vol 134 ◽  
pp. 96-96
Author(s):  
R. A. Edelson ◽  
J. H. Krolik
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Optical Data ◽  
Published Data ◽  
Correlated Errors ◽  
Ngc 4151 ◽  
Temporal Domain ◽  
Intrinsic Scale ◽  
Good Agreement

A method of measuring correlation functions without interpolating in the temporal domain, the Discrete Correlation Function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of the cross-correlation function of two series believed to be related by a convolution requires knowledge of the input function's fluctuation power spectrum. In the case of AGN line-continuum cross-correlation functions, the interpretation also involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. Application to published data for Akn 120 and NGC 4151 illustrates this method's capabilities. No correlation was found for the optical data for Akn 120, but the ultraviolet NGC 4151 data show a strong correlation, indicating that the broad C IV feature emanates from a region whose size is greater than 1.2 and less than 20 light days. These bounds on the size of the line-emitting region in NGC 4151 are in good agreement with the predictions of photoionization models.

scholarly journals The role of galaxies and AGN in reionizing the IGM – III. IGM–galaxy cross-correlations at z ∼ 6 from eight quasar fields with DEIMOS and MUSE

2020 ◽  
Vol 494 (2) ◽  
pp. 1560-1578
Author(s):  
Romain A Meyer ◽  
Koki Kakiichi ◽  
Sarah E I Bosman ◽  
Richard S Ellis ◽  
Nicolas Laporte ◽  
...  
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Mean Free Path ◽  
Lyman Break Galaxies ◽  
The Galaxy ◽  
Cross Correlations ◽  
The Mean ◽  
Improved Model ◽  
First Time

ABSTRACT We present improved results of the measurement of the correlation between galaxies and the intergalactic medium transmission at the end of reionization. We have gathered a sample of 13 spectroscopically confirmed Lyman-break galaxies (LBGs) and 21 Lyman-α emitters (LAEs) at angular separations 20 arcsec ≲ θ ≲ 10 arcmin (∼0.1–4 pMpc at z ∼ 6) from the sightlines to eight background z ≳ 6 quasars. We report for the first time the detection of an excess of Lyman-α transmission spikes at ∼10–60 cMpc from LAEs (3.2σ) and LBGs (1.9σ). We interpret the data with an improved model of the galaxy–Lyman-α transmission and two-point cross-correlations, which includes the enhanced photoionization due to clustered faint sources, enhanced gas densities around the central bright objects and spatial variations of the mean free path. The observed LAE(LBG)–Lyman-α transmission spike two-point cross-correlation function (2PCCF) constrains the luminosity-averaged escape fraction of all galaxies contributing to reionization to $\langle f_{\rm esc} \rangle _{M_{\rm UV}\lt -12} = 0.14_{-0.05}^{+0.28}\, (0.23_{-0.12}^{+0.46})$. We investigate if the 2PCCF measurement can determine whether bright or faint galaxies are the dominant contributors to reionization. Our results show that a contribution from faint galaxies ($M_{\rm UV} \gt -20 \, (2\sigma)$) is necessary to reproduce the observed 2PCCF and that reionization might be driven by different sub-populations around LBGs and LAEs at z ∼ 6.

scholarly journals X-ray cross-correlation analysis of the low-mass X-ray binary 4U 1636-53

2014 ◽  
Vol 10 (S306) ◽  
pp. 397-399
Author(s):  
Ya-Juan Lei
Keyword(s):  
Correlation Function ◽  
Correlation Analysis ◽  
Cross Correlation ◽  
X Rays ◽  
X Ray ◽  
Cross Correlation Analysis ◽  
Low Mass ◽  
Cross Correlations ◽  
The Cross ◽  
Positive Correlations

AbstractWe analyze the cross-correlation function of the soft and hard X-rays of the atoll source 4U 1636-53 with RXTE data. The results show that the cross-correlations evolve along the different branches of the color-color diagram. At the lower left banana states, we have both positive and ambiguous correlations, and positive correlations are dominant for the lower banana and the upper banana states. The anti-correlation is detected at the top of the upper banana states. The cross-correlations of two atoll sources 4U 1735-44 and 4U 1608-52 have been studied in previous work, and the anti-correlations are detected at the lower left banana or the top of the upper banana states. Our results show that, in the 4U 1636-53, the distribution of the cross-correlations in the color-color diagram is similar to those of 4U 1735-44 and 4U 1608-52, and confirm further that the distribution of cross-correlations in color-color diagram could be correlated with the luminosity of the source.

scholarly journals The Cross-Correlation of Abell Clusters with the Lick Galaxy Counts

1988 ◽  
Vol 130 ◽  
pp. 550-550
Author(s):  
Per B. Lilje ◽  
G. Efstathiou
Keyword(s):  
Correlation Function ◽  
Luminosity Function ◽  
Cold Dark Matter ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Galactic Latitude ◽  
Abell Clusters ◽  
Theoretical Predictions ◽  
Cross Correlations ◽  
The Cross

We have analysed the cross-correlations between Abell clusters and the 10′ × 10′ Lick galaxy counts. The main new features of our analysis are as follows: (a) we correct for gradients in the Lick counts that depend only on galactic latitude; (b) we check the effects of applying a filter to remove (likely artificial) gradients on scales >20°; (c) redshifts for Abell clusters are used to compute a cross-correlation function wcg(σ), where σ = vϑ/Ho is the projected separation between a cluster with recession speed v and a galaxy at angular distance ν from the cluster centre; (d) the amplitude of the spatial cross-correlation function ξcg(r) is estimated using modern determinations of the galaxy luminosity function. Our results show that the shape of ξcg is reasonably well determined on scales r ≲20h−1 Mpc. On larger scales, the results depend sensitively on the corrections for large-scale gradients in the Lick counts. The results based on wcg(σ) are well described by a power-law model ξcg(r)≃(r/8.8h−1 Mpc)−2.2, while the angular cross-correlations for Abell clusters in distance class D=5 are better described by the model ξcg(r)=(r/6h−1 Mpc)−2.3 + (r/7h−1 Mpc)−1.7. Seldner and Peebles (1977) derived a larger amplitude for ξcg because they assumed a different luminosity function. We compare these results with theoretical predictions of ξcg in the Ω=1 biased cold dark matter (CDM) model. On scales 1 h−1 Mpc ≲ r ≲ 10 h−1 Mpc, the theoretical predictions for ξcg are in surprisingly good agreement with our observational estimates. On smaller scales, the CDM model gives too high an amplitude whereas on larger scales the predicted amplitude is too low. Neither of these discrepancies is particularly serious.

scholarly journals Statistical Reliability of Neighboring Range Bin Estimates of Coherent Fractional Contributions to Radar Backscattered Power

2011 ◽  
Vol 50 (3) ◽  
pp. 745-749 ◽  
Author(s):  
A. R. Jameson
Keyword(s):  
Correlation Function ◽  
Standard Deviation ◽  
Angular Velocity ◽  
Cross Correlation ◽  
Constant Angular Velocity ◽  
The Other ◽  
Incoherent Scatter ◽  
Statistical Reliability ◽  
Cross Correlations ◽  
Coherent Backscatter

Abstract It was recently demonstrated that magnitudes of the power-normalized cross-correlation functions of complex amplitudes in neighboring range bins are identical to the fractional contributions made by radar coherent backscatter in the direction of propagation to the total backscattered power in rain and snow. Here, a theoretical framework is presented for calculating the noise associated with estimates of these normalized cross correlations. This noise is identical to the statistical uncertainties in . Radar signals consist of two components: the usual incoherent backscatter often modeled by a Gaussian process and a coherent component modeled for the purposes of these calculations by a phasor C of fixed magnitude that rotates at a constant angular velocity ωC. Using the representation of the cross-correlation function as the average over the real part of the phasor dot products, it is found that the noise in this function comes from the dot products of C with the incoherent-scatter phasors in each range bin as well as the dot product between the two incoherent phasors. Furthermore, as long as ωC ≠ 0 and the number of statistically independent realizations (samples) k is sufficiently large, the noise is represented well by a normal distribution with mean 0 and with a variance that goes as 1/(2k). It is then shown that as the magnitude of C increases it acts to suppress the variance of . A formula is derived that gives the standard deviation of as a function of the number of statistically independent samples in the observation and the observed value of . Two examples, one in rain and the other in snow, are also presented.

scholarly journals Tabular algorithm for evaluating the discrete cross-correlation function of the flowmeter acoustic signals

2021 ◽  
pp. 155-161
Author(s):  
С.И. Герасимов ◽  
В.Д. Глушнев
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Acoustic Signals ◽  
Digital Data ◽  
Cross Correlation Function ◽  
Term Operation ◽  
Useful Signal ◽  
Correlation Processing ◽  
The Cross

Корреляционная обработка сигналов как частный случай использования цифровой обработки данных, получаемых с акустических датчиков, находит широкое применение в современных ультразвуковых расходомерах жидкости и газа. К ним можно отнести как непосредственно корреляционные меточные расходомеры, так и расходомеры преимущественно время-импульсного или время-пролетного типов, где корреляционная обработка акустических сигналов является дополнением к общему методу измерения объемного расхода жидкости и газа. Применение корреляционной обработки позволяет повысить разрешающую способность расходомера в целом и обеспечить выделение полезного сигнала на фоне присутствия шумов с высокой степенью достоверности. В статье описан способ вычисления дискретных корреляционных функций на основе обобщенного определения дискретной корреляционной функции через свертку дискретизированных сигналов с выходов датчиков потока. Суть данного метода сводится к вычислению набора значений кумулятивных произведений отсчетов зондирующих сигналов, взятых с разным шагом в зависимости от общего количества отсчетов сигналов и предполагаемого числа значений корреляционной функции. Полученный набор значений оформляется в виде двумерного массива или матрицы, однако для большего понимания его можно представить как таблицу. Результаты суммы отдельных элементов этой таблицы или матрицы, выбранных согласно установленному правилу, и будут являться конечными значениями взаимной корреляционной функции акустических сигналов. В рамках работы составлены непосредственно алгоритм вычисления дискретной корреляционной функции в соответствии с рассмотренным методом расчета корреляционной функции, приведены примеры вычисления программным способом взаимной и автокорреляционной функций акустических сигналов, приближенных по своим свойствам к сигналам реальных ультразвуковых расходомеров. Предложенный вариант расчета дискретных корреляционных функций может быть применен в энергоэффективных вычислительных модулях расходомеров, предназначенных для длительной эксплуатации от источника автономного питания, обладающих низкой производительностью. Correlation signal processing as a particular case of using a digital data processing obtained from acoustic sensors is widely used in modern ultrasonic liquid and gas flowmeters. These include both direct correlation flowmeters and predominantly a time-pulse or time-of-flight type’s flowmeters, where the correlation processing of acoustic signals is an addition to the general method for measuring the volumetric flow rate of liquid and gas. The use of correlation processing makes it possible to increase the resolution of the flowmeter as a whole and to ensure the useful signal extraction against the background of the noise presence with a high degree of reliability. The article describes a method for calculating discrete correlation functions based on the generalized definition of a discrete correlation function through the convolution of sampled signals from the flow sensors outputs. The essence of this method comes down to calculating a values set ​​of the cumulative products of the probing signal’s samples taken with different steps depending on the total number of signal samples and the assumed number of the correlation function samples. The resulting values sequence ​​is formatted as a two-dimensional array or matrix, but for better understanding it can be represented as a table. The results of the sum of the individual elements of this table or matrix, selected according to the established rule, will be the final values ​​of the cross-correlation function of acoustic signals. Within the framework, an algorithm for calculating the discrete correlation function is directly compiled in accordance with the considered method for calculating the correlation function, examples of software calculation of the cross- and autocorrelation functions of acoustic signals, which are close in their properties to the real signals of ultrasonic flowmeters, are given. The proposed option for calculating discrete correlation functions can be applied in energy-efficient computational modules of flowmeters designed for long-term operation from an autonomous power source with low performance.

CROSS-CORRELATION FUNCTIONS OF THE FIELD EMISSION FLUCTUATIONS WITH SLIT PROBED REGIONS

1989 ◽  
Vol 50 (C8) ◽  
pp. C8-97-C8-102 ◽  
Author(s):  
J. BEBEN ◽  
CH. KLEINT ◽  
R. MECLEWSKI
Keyword(s):  
Field Emission ◽  
Correlation Functions ◽  
Cross Correlation

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

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