"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

The Fractal Geometry of Nature

Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

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The design and analysis of computer experiments

The objective of this paper is to review the state-of-the-art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are presented.

Reservoir Management and Operations Models: A State‐of‐the‐Art Review

Preface Readership Acknowledgements Introduction Part I. The Context for Spatial Data Analysis: 1. Spatial data analysis: scientific and policy context 2. The nature of spatial data Part II. Spatial Data: Obtaining Data And Quality Issues: 3. Obtaining spatial data through sampling 4. Data quality: implications for spatial data analysis Part III. The Exploratory Analysis of Spatial Data: 5. Exploratory analysis of spatial data 6. Exploratory spatial data analysis: visualisation methods 7. Exploratory spatial data analysis: numerical methods Part IV. Hypothesis Testing in the Presence of Spatial Autocorrelation: 8. Hypothesis testing in the presence of spatial dependence Part V. Modeling Spatial Data: 9. Models for the statistical analysis of spatial data 10. Statistical modeling of spatial variation: descriptive modeling 11. Statistical modeling of spatial variation: explanatory modeling Appendices References Index.

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Spatial Data Analysis: Theory and Practice

A methodology for the design of precipitation networks is formulated. The network problem is discussed in its general conception, and then focus is made on networks to provide background information for the design of more specific gaging systems. The rainfall process is described in terms of its correlation structure in time and space. A general framework is developed to estimate the variance of the sample long-term mean areal precipitation and mean areal rainfall of a storm event. The variance is expressed as a function of correlation in time, correlation in space, length of operation of the network, and geometry of the gaging array. The trade of time versus space is quantitatively developed, and realistic examples are worked out showing the influence of the network design scheme on the variance of the estimated values.

The design of rainfall networks in time and space

A general methodology is developed for the transformation of point rainfall to areal rainfall. The reduction factor is shown to depend solely on the expected correlation coefficient between the point rainfall at two randomly chosen points in the area in consideration. The methodology can be used to characterize the input to rainfall-runoff models, and it includes the case in which multiple inputs are used in the model in the form of a subdivision in modules of the whole catchment. An example is worked out discussing the different methodologies for the estimation of total mean volume of rainfall over an area.

On the transformation of point rainfall to areal rainfall

A procedure for the synthesis of processes exhibiting temporal and spatial variability is presented The method involves the addition of harmonics of random frequencies that are sampled from the spectral density function or the radial spectral density function The process obtained is asymptotically Gaussian and ergodic An estimate of the error in time or space averages due to the nonergodicity of the process as a function of the number of harmonics is also included

On the synthesis of random field sampling from the spectrum: An application to the generation of hydrologic spatial processes

The disaggregation model proposed by Schaake et al. (1972) is revised to include linkages with the past at the different levels of aggregation. This modification produces a more realistic hydrologic model.

Disaggregation models in hydrology revisited

This paper deals with the theory of the broken line process and its applications in the simulation of stochastic sequences.

Jose M. Mejia

Papers

The design of rainfall networks in time and space

On the transformation of point rainfall to areal rainfall

On the synthesis of random field sampling from the spectrum: An application to the generation of hydrologic spatial processes

Disaggregation models in hydrology revisited

Streamflow simulation: 2. The broken line process as a potential model for hydrologic simulation