Carlos E. Puente

Estimation of in situ hydraulic conductivity function from nonlinear filtering theory

Note: 29(4): 1063-1070 Reference EFLUM-ARTICLE-1993-006doi:10.1029/92WR02593 Record created on 2005-09-08, modified on 2017-02-23

Multinomial multifractals, fractal interpolators, and the Gaussian distribution

Abstract Transformations of (multiplicative) multinomial multifractals via deterministic fractal interpolating functions are shown to yield a wide variety of derived distributions. Depending on the fractal dimension of the graph of such a function, three distinct cases may be identified: (a) when the dimension of the graph is low (close to 1), derived multifractal measures are obtained; (b) as the dimension is increased, the multifractal nature of the derived measures steadily disappears, and absolutely continuous distributions are found; and (c) as the fractal dimension is increased towards 2, the derived measure tends to be Gaussian.

Strange attractors in atmospheric boundary-layer turbulence

The possible chaotic nature of the turbulence of the atmospheric boundary layer in and above a decidious forest is investigated. In particular, this work considers high resolution temperature and three-dimensional wind speed measurements, gathered at six alternative elevations at Camp Borden, Ontario, Canada (Shawet al., 1988). The goal is to determine whether these time series may be described (individually) by sets of deterministic nonlinear differential equations, such that: (i) the datas intrinsic (and seemingly random) irregularities are captured by suitable low-dimensional fractal sets (strange attractors), and (ii) the equations lack of knowledge of initial conditions translates into unpredictable behavior (chaos). Analysis indicates that indeed all series exhibit chaotic behavior, with strange attractors whose (correlation) dimensions range from 4 to 7. These results support the existence of a low-dimensional chaotic attractor in the lower atmosphere.

A nonlinear filtering approach for determining hydraulic conductivity functions in field soils

A nonlinear Extended Kalman Filter approach is used to explicitly account for measurement and model uncertainty in field soil hydraulic conductivity function determination. The standard deviation that such a procedure provides for hydraulic conductivity, as a function of water content, is estimated from water content and matric potential measurements. These measurements were obtained following 43 days of water redistribution in a two-layer soil profile previously ponded with water. Except for a brief initial period during redistribution, water content changes can be described with a single exponential conductivity function. Also, reducing the frequency of measurements by 50|X% and 80|X% would change the mean hydraulic conductivity function less than -|Mp1. standard deviation, i.e., half an order of magnitude. The filtering scheme, which accounts for both model and measurement uncertainty, provides an improved description of in situ hydraulic conductivity functions when compared with previous methods, which fail to supply fiducial limits of uncertainty

DETERMINISTIC FRACTAL GEOMETRY AND PROBABILITY

A possible connection between deterministic fractal geometry and the most important probabilistic models (Gaussian distribution and Brownian motion) is exhibited.

Disjunctive kriging, universal kriging, or no kriging: Small sample results with simulated fields

This paper provides a comparison between linear (universal) and nonlinear (disjunctive) kriging estimators when they are computed from small samples chosen randomly on simulated stationary and nonstationary fields. Point estimation results are reported. In all cases considered, kriging estimators were found better than a local mean estimator, with universal kriging either better than or as good as disjunctive kriging. The latter, which is suited to handle stationary fields, did not provide more accurate estimates because the use of small samples led to inconsistencies in the assumed bivariate model. Universal kriging was particularly better with nonstationary fields.

Combined hydrologic sampling criteria for rainfall and streamflow

Abstract This paper considers the joint sampling of the rainfall and streamflow processes. The sampling frequencies in time and space are obtained as a function of basin and rainfall characteristics. The effectiveness of different sampling strategies is measured by the variance of the error of estimated or predicted streamflow. This is related to the rainfall and basin rainfall-discharge properties through parameterizations of these processes. Rainfall is modelled as a stochastic process with covariance structure separable in time and space. Streamflow is parameterized in terms of the fluvial geomorphology of the basin. Linear systems theory is used to link precipitation to flow and to compute the variance of basin discharge. The variance of the error in prediction of streamflow is computed in terms of the following: (1) basin and rainfall model parameters; and (2) measurement strategy consisting of numbers of rain gages plus rainfall and flow measurement intervals. This error variance is used to assess the effectiveness of a measurement strategy. The results should be of use in the formulation of hydrologic sampling strategies.

Hydrologic Sampling: A characterization in terms of Rainfall and basin properties

Abstract This paper considers the sampling of rainfall and discharge processes both in time and in space and links the sampling problem to basin and rainfall characteristics. The effectiveness of different sampling strategies is measured by the variance of the error in estimating either total or peak of streamflow from a single storm event. This is related to the rainfall and basin rainfall-discharge properties through parameterizations of these processes. Rainfall is modeled as a collection of rain cells which occur randomly in space and time and has parameters which define the probability of occurrence of rain cells in space and time and the spread of rainfall due to a cell. Discharge from rainfall is parameterized in terms of the fluvial geomorphology of the basin. Linear filtering techniques are used to compute the variance of the estimation error for different sampling strategies. Sampling strategies are defined by the number of rain gages, rainfall sampling interval and discharge measurement interval. The results can be used in hydrologic network design to assess the effectiveness of different sampling options.

A Fractal-Multifractal Approach to Geostatistics

A new approach for the description of geophysical data in space (either along a line or over the plane) is introduced. The procedure consists of using fractal interpolating functions (either, from the line to the line or from the line to the plane) to transform arbitrary multinomial multifractal measures defined over a closed interval. Specifically, and for the most general case, let Xbe a multinomial multifractal measure on a closed interval I with parameters p 1 P 2,…,PN, and let fΘ: I → R 2be a deterministic continuous fractal interpolating function, as introduced by Barnsley (1988), which interpolates a set of data points, and which has parameters Θ. Then, we show via simulations that measures Y=fΘ (X), provide good models for a variety of geophysical phenomena. A deterministic connection between turbulence-related measures and the Gaussian distribution is shown as a limiting case when the graph of the fractal interpolating function fΘ (X) is spacefilling. It is suggested that the evolution of complex geophysical patterns may be approached via this geometric description.

Error Identification and Decomposition in Large State-Space Stochastic Rainfall-Runoff Models

Abstract The quality of the streamflow predictions is known to be dependent on the accuracy of the rainfall-runoff model. Based on the maximum likelihood method, a simple procedure to Identify the statistics errors of a conceptual hydrologic model is presented. The procedure is Illustrated with data from the Bird Creek River basin in Oklahoma The problem of forecasting river flows in a basin composed of several Interconnected sub-bas1ns is also Investigated. Decomposition procedures are proposed to efficiently filter and forecast states in all sub-basins simultaneously. The procedures decouple soil states in different sub-bas1ns and connects them through the river network. This time a branch of the Potomac River is used as a case study