The effects of bandwidth, dispersion, and correlation length scale on shallow‐water reverberation

1998 ◽  
Vol 103 (5) ◽  
pp. 2899-2899
Author(s):  
Kevin D. LePage
Keyword(s):  
Shallow Water ◽  
Correlation Length ◽  
Length Scale

The phase lead of shear stress in shallow-water flow over a perturbed bottom

2010 ◽  
Vol 665 ◽  
pp. 516-539 ◽  
Author(s):  
PAOLO LUCHINI ◽  
FRANÇOIS CHARRU
Keyword(s):  
Shear Stress ◽  
Shallow Water ◽  
Wall Stress ◽  
Wall Friction ◽  
Channel Height ◽  
Length Scale ◽  
Mean Velocity ◽  
Phase Lead ◽  
Friction Term ◽  
Large Length Scale

The analysis of flow over a slowly perturbed bottom (when perturbations have a typical length scale much larger than channel height) is often based on the shallow-water (or Saint-Venant) equations with the addition of a wall-friction term which is a local function of the mean velocity. By this choice, small sinusoidal disturbances of wall stress and mean velocity are bound to be in phase with each other. In contrast, studies of shorter-scale disturbances have long established that a phase lead develops between wall stress and mean velocity, with a crucial destabilizing effect on sediment transport along an erodible bed. The purpose of this paper is to calculate the wall-shear stress under large length-scale conditions and provide corrections to the Saint-Venant model.

scholarly journals Hybrid ensemble 4DVar assimilation of stratospheric ozone using a global shallow water model

2016 ◽  
Author(s):  
Douglas R. Allen ◽  
Karl W. Hoppel ◽  
David D. Kuhl
Keyword(s):  
Shallow Water ◽  
Hybrid System ◽  
Stratospheric Ozone ◽  
Water Model ◽  
Advection Equation ◽  
Length Scale ◽  
Shallow Water Model ◽  
Optimal Length ◽  
Large Ensembles ◽  
Optimal Blending

Abstract. Wind extraction from stratospheric ozone (O3) assimilation is examined using a hybrid ensemble 4DVar shallow water model (SWM) system coupled to the tracer advection equation. Stratospheric radiance observations are simulated using global observations of the SWM fluid height (Z), while O3 observations represent sampling by a typical polar-orbiting satellite. Four ensemble sizes were examined (25, 50, 100, and 1518 members), with the largest ensemble equal to the number of dynamical state variables. The optimal length scale for ensemble localization was found by tuning an ensemble Kalman filter (EnKF). This scale was then used for localizing the ensemble covariances that were blended with conventional covariances in the hybrid 4DVar experiments. Both optimal length scale and optimal blending coefficient increase with ensemble size, with optimal blending coefficients varying from 0.2 to 0.5 for small ensembles to 0.5 to 1.0 for large ensembles. The hybrid system outperforms conventional 4DVar for all ensemble sizes, while for large ensembles the hybrid produces similar results to the offline EnKF. Assimilating O3 in addition to Z benefits the winds in the hybrid system, with the fractional improvement in global vector wind increasing from ~35 % with 25 and 50 members to ~50 % with 1518 members. For the smallest ensembles (25 and 50 members), the hybrid 4DVar assimilation improves the zonal wind analysis over conventional 4DVar in the Northern Hemisphere (winter-like) region and also at the equator, where Z observations alone have difficulty constraining winds due to lack of geostrophy. For larger ensembles (100 and 1518 members), the hybrid system results in both zonal and meridional wind error reductions, relative to 4DVar, across the globe.

scholarly journals Forecast Divergences of a Global Wave Model

2005 ◽  
Vol 133 (8) ◽  
pp. 2148-2162 ◽  
Author(s):  
Diana J. M. Greenslade ◽  
Ian R. Young
Keyword(s):  
Correlation Length ◽  
Surface Wind ◽  
Wave Model ◽  
Surface Wind Speed ◽  
Length Scale ◽  
Similar Distribution ◽  
Background Error ◽  
Latitudinal Dependence ◽  
Wave Models ◽  
Seasonal Signal

Abstract One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the “NMC method.” This method examines the forecast divergence component of the background error growth by considering differences between forecasts of different ranges valid at the same time. In this paper, the NMC method is applied to global forecasts of significant wave height (SWH) and surface wind speed (U10). It is found that the isotropic correlation length scale of the SWH forecast divergence (LSWH) has considerable geographical variability, with the longest scales just to the south of the equator in the eastern Pacific Ocean, and the shortest scales at high latitudes. The isotropic correlation length scale of the U10 forecast divergence (LU10) has a similar distribution with a stronger latitudinal dependence. It is found that both LSWH and LU10 increase as the forecast period increases. The increase in LSWH is partly due to LU10 also increasing. Another explanation is that errors in the analysis or the short-range SWH forecast propagate forward in time and disperse and their scale becomes larger. It is shown that the forecast divergence component of the background error is strongly anisotropic with the longest scales perpendicular to the likely direction of propagation of swell. In addition, in regions where the swell propagation is seasonal, the forecast divergence component of the background error shows a similar strong seasonal signal. It is suggested that the results of this study provide a lower bound to the description of the total background error in global wave models.

scholarly journals A new exponentially-decaying error correlation model for assimilating OCO-2 column-average CO<sub>2</sub> data, using a length scale computed from airborne lidar measurements

2021 ◽  
Author(s):  
David F. Baker ◽  
Emily Bell ◽  
Kenneth J. Davis ◽  
Joel F. Campbell ◽  
Bing Lin ◽  
...  
Keyword(s):  
Correlation Length ◽  
Error Model ◽  
Airborne Lidar ◽  
Length Scale ◽  
Correlation Model ◽  
Correlation Lengths ◽  
New Model ◽  
The Mean ◽  
Error Correlation ◽  
Along Track

Abstract. To check the accuracy of column-average dry air CO2 mole fractions (XCO2) retrieved from Orbiting Carbon Overvatory (OCO-2) data, a similar quantity has been measured from the Multi-functional Fiber Laser Lidar (MFLL) aboard aircraft flying underneath OCO-2 as part of the Atmospheric Carbon and Transport (ACT)-America flight campaigns. Here we do a lagged correlation analysis of these MFLL-OCO-2 column CO2 differences and find that their correlation spectrum falls off rapidly at along-track separation distances of under 10 km, with a correlation length scale of about 10 km, and less rapidly at longer separation distances, with a correlation length scale of about 20 km. The OCO-2 satellite takes many CO2 measurements with small (~3 km2) fields of view (FOVs) in a thin (<10 km wide) swath running parallel to its orbit: up to 24 separate FOVs may be obtained per second (across a ~6.75 km distance on the ground), though clouds, aerosols, and other factors cause considerable data dropout. Errors in the CO2 retrieval method have long been thought to be correlated at these fine scales, and methods to account for these when assimilating these data into top-down atmospheric CO2 flux inversions have been developed. A common approach has been to average the data at coarser scales (e.g., in 10-second-long bins) along-track, then assign an uncertainty to the averaged value that accounts for the error correlations. Here we outline the methods used up to now for computing these 10-second averages and their uncertainties, including the constant-correlation-with-distance error model currently being used to summarize the OCO-2 version 9 XCO2 retrievals as part of the OCO-2 flux inversion model intercomparison project. We then derive a new one-dimensional error model using correlations that decay exponentially with separation distance, apply this model to the OCO-2 data using the correlation length scales derived from the MFLL-OCO-2 differences, and compare the results (for both the average and its uncertainty) to those given by the current constant-correlation error model. To implement this new model, the data are averaged first across 2-second spans, to collapse the cross-track distribution of the real data onto the 1-D path assumed by the new model. A small percentage of the data that cause nonphysical negative averaging weights in the model are thrown out. The correlation lengths over the ocean, which the land-based MFLL data do not clarify, are assumed to be twice those over the land. The new correlation model gives 10-second XCO2 averages that are only a few tenths of a ppm different from the constant-correlation model. Over land, the uncertainties in the mean are also similar, suggesting that the +0.3 constant correlation coefficient currently used in the model there is accurate. Over the oceans, the twice-the-land correlation lengths that we assume here result in a significantly lower uncertainty on the mean than the +0.6 constant correlation currently gives – measurements similar to the MFLL ones are needed over the oceans to do better. Finally, we show how our 1-D exponential error correlation model may be used to account for correlations in those inversion methods that choose to assimilate each XCO2 retrieval individually, and to account for correlations between separate 10-second averages when these are assimilated instead.

scholarly journals Hybrid ensemble 4DVar assimilation of stratospheric ozone using a global shallow water model

2016 ◽  
Vol 16 (13) ◽  
pp. 8193-8204 ◽  
Author(s):  
Douglas R. Allen ◽  
Karl W. Hoppel ◽  
David D. Kuhl
Keyword(s):  
Shallow Water ◽  
Hybrid System ◽  
Stratospheric Ozone ◽  
Water Model ◽  
Advection Equation ◽  
Length Scale ◽  
Shallow Water Model ◽  
Optimal Length ◽  
Large Ensembles ◽  
Optimal Blending

Abstract. Wind extraction from stratospheric ozone (O3) assimilation is examined using a hybrid ensemble 4-D variational assimilation (4DVar) shallow water model (SWM) system coupled to the tracer advection equation. Stratospheric radiance observations are simulated using global observations of the SWM fluid height (Z), while O3 observations represent sampling by a typical polar-orbiting satellite. Four ensemble sizes were examined (25, 50, 100, and 1518 members), with the largest ensemble equal to the number of dynamical state variables. The optimal length scale for ensemble localization was found by tuning an ensemble Kalman filter (EnKF). This scale was then used for localizing the ensemble covariances that were blended with conventional covariances in the hybrid 4DVar experiments. Both optimal length scale and optimal blending coefficient increase with ensemble size, with optimal blending coefficients varying from 0.2–0.5 for small ensembles to 0.5–1.0 for large ensembles. The hybrid system outperforms conventional 4DVar for all ensemble sizes, while for large ensembles the hybrid produces similar results to the offline EnKF. Assimilating O3 in addition to Z benefits the winds in the hybrid system, with the fractional improvement in global vector wind increasing from  ∼  35 % with 25 and 50 members to  ∼  50 % with 1518 members. For the smallest ensembles (25 and 50 members), the hybrid 4DVar assimilation improves the zonal wind analysis over conventional 4DVar in the Northern Hemisphere (winter-like) region and also at the Equator, where Z observations alone have difficulty constraining winds due to lack of geostrophy. For larger ensembles (100 and 1518 members), the hybrid system results in both zonal and meridional wind error reductions, relative to 4DVar, across the globe.

scholarly journals Calculating an error correlation length scale from MFLL-OCO-2 column-average CO2 differences and using it to average OCO-2 data

2021 ◽  
Author(s):  
David F Baker ◽  
Emily Bell ◽  
Kenneth J Davis ◽  
Joel F Campbell ◽  
Bing Lin ◽  
...  
Keyword(s):  
Correlation Length ◽  
Length Scale ◽  
Error Correlation

Molecular mass dependence of point-to-set correlation length scale in polymers

2012 ◽  
Vol 137 (8) ◽  
pp. 084904 ◽  
Author(s):  
Ben Hanson ◽  
Victor Pryamitsyn ◽  
Venkat Ganesan
Keyword(s):  
Molecular Mass ◽  
Correlation Length ◽  
Length Scale ◽  
Mass Dependence ◽  
Set Correlation

scholarly journals Emulation of an ensemble Kalman filter algorithm on a flood wave propagation model

2013 ◽  
Vol 10 (6) ◽  
pp. 6963-7001
Author(s):  
S. Barthélémy ◽  
S. Ricci ◽  
O. Pannekoucke ◽  
O. Thual ◽  
P. O. Malaterre
Keyword(s):  
Correlation Length ◽  
Computational Cost ◽  
Error Variance ◽  
Observation Point ◽  
Propagation Model ◽  
Length Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Covariance Functions ◽  
Error Covariance

Abstract. This study describes the emulation of an Ensemble Kalman Filter (EnKF) algorithm on a 1-D flood wave propagation model. This model is forced at the upstream boundary with a random variable with gaussian statistics and a correlation function in time with gaussian shape. This allows for, in the case without assimilation, the analytical study of the covariance functions of the propagated signal anomaly. This study is validated numerically with an ensemble method. In the case with assimilation with one observation point, where synthetical observations are generated by adding an error to a true state, the dynamic of the background error covariance functions is not straightforward and a numerical approach using an EnKF algorithm is prefered. First, those numerical experiments show that both background error variance and correlation length scale are reduced at the observation point. This reduction of variance and correlation length scale is propagated downstream by the dynamics of the model. Then, it is shown that the application of a Best Linear Unbiased Estimator (BLUE) algorithm using the background error covariance matrix converged from the EnKF algorithm, provides the same results as the EnKF but with a cheaper computational cost, thus allowing for the use of data assimilation in the context of real time flood forecasting. Moreover it was demonstrated that the reduction of background error correlation length scale and variance at the observation point depends on the error observation statistics. This feature is quantified by abacus built from linear regressions over a limited set of EnKF experiments. These abacus that describe the background error variance and the correlation length scale in the neighboring of the observation point combined with analytical expressions that describe the background error variance and the correlation length scale away from the observation point provide parametrized models for the variance and the correlation length scale. Using this parametrized variance and correlation length scale with a diffusion operator makes it possible to model the converged background error covariance matrix from the EnKF without actually integrating the EnKF algorithm. This method was finally applied to a case with two different observation point with different error statistics. It was shown that the results of this emulated EnKF (EEnKF) in terms of background error variance, correlation length scale and analyzed water level is close to those of the EnKF but with a significantly reduced computational cost.

Sign in / Sign up

Export Citation Format

Share Document