ANALYSIS OF SOME CRITERIA FOR DESIGN AND OPERATION SURFACE WATER GAUGING NETWORKS/ J.W. Dr. VAN DER MADE

1 Introduction 1.1 Motivation for measurement 1.2 Aspects of measurement 1.3 Definition of a measurement network 1.4 Requirements and criteria for network design 1.5 Interpolation methods 1.6 The design process 1.7 A glance into history 1.8 The role of the World Meteorological Organization in hydrological net-work design 1.9 Plan of this study 2 Background for the determination of station distance 2.1 The need for information 2.2 Economical implications of a reduction of the standard error of estimate 2.3 The standard error as a design criterion 2.4 Determination of the desirable station distance in a special case 2.5 Application of corrections 2.6 Example 3 Accuracy of measurements 3.1 General 3.2 Order of magnitude of the errors of measurement 3.2.1 Errors due to the location of the gauging station at the river and the hydraulic conditions of the adjacent area 3.2.2 Errors due to the construction of the station house, the stilling well and the inlet tube 3.2.3 Errors due to differences in density between the open water and the water in the stilling well 3.2.4 Instrument errors 3.2.5 Levelling errors in the gauge reference datum and the zero of the gauge 3.2.6 Oberservation and processing errors 3.3 Random errors and systematic errors 3.4 Determination of the error of measurement 3.4.1 Comparison of measurements at the same station at different times 3.4.2 Comparison with measurements at a station close to the station under examination Example. 3.4.3 Comparison with measurements at stations at different distances from the station under examination Examples 1) River IJssel stations 2) Rio Magdalena stations 3) River Rhine stations General discussion of Section 3.4.3 3.5 Summary 4. Mathematical interpolation methods . 4.1 Interpolation methods in general 4.2 Exact interpolation using a single polynomial or separated polynomials of degree n Examples of error propagation 1. Linear interpolation 2. Square interpolation 3. Cubic interpolation Example of interpolation 4.3 Approximate interpolation using a single polynomial of degree n . Examples 4.4 Interpolation with spline functions 4.4.1 Exact interpolation Example Lagrange functions Example 4.4.2 Approximate interpolation using spline functions Example Lagrange and propagation functions 4.4.3 Extensions 4.4.3.1 Dummy points 4.4.3.2 Measured values between two transition points Example 4.4.3.3 Fixation of slope Example 4.5 Summary of mathematical interpolation methods 5 Interpolation bij linear regression to sites with earlier measurements 5.1 General 5.2 Determination of the values at the site under examination 5.3 The variance of the errors of estimate 5.4 Effect of measurement error on the estimate y and on the variance of estimate 5.4.1 The expected value of a measured level and its variance of estimate 5.4.2 The expected value of a calculated level (in the two-dimensional case) 5.4.3 The variance of estimate of a calculated level (in the two-dimen-sional case) 5.4.4 The expected value of a calculated level and its variance of estimate (in the generalized case). 5.5 Estimation of values of y and their confidence interval Example 5.6 Lagrange functions 5.6.1 Application to linear regression interpolation 5.6.2 Consideration of a series of examined stations and network stations Example 5.7 Extension of the method to include measurements at different points in time Examples 1 The river Rhine in Germany 2 The Rio Magdalena in Columbia 3 Tidal waters in the Netherlands - The western part of the Wadden Sea - The Western Scheldt estuary 6 Regression interpolation along the intermediate reaches between net-work stations 6.1 General 6.2 Calculation of the standard error 6.3 Calculation of the regression coefficients 6.4 Some hypothetical cases of networks 6.4.1 Interpolation between two stations at variable distance 6.4.2 Interpolation between four stations a Symmetrical network configuration; middle reach of constant length b Symmetrical network configuration; total constant length of the three reaches together 6.4.3 Interpolation between five stations at equal distances 6.5 The river IJssel network 6.6 The Western Scheldt estuary network 6.7 Application to an areal network 6.8 The Lake Grevelingen network 7. Calculation of intermediate water levels using physically-based mathe-matical methods 7.1 Physically-based methods 7.2 A physically-based mathematical model 7.3 The numerical finite difference equations 7.4 Boundary conditions 7.5 Initial conditions 7.6 Calculation procedure 7.7 Further evaluation of the model. 7.8 Assessment of model parameters 7.9 Testing of the model: a hypothetical case 7.10 The starting period 7.11 Example of the Western Scheldt tidal estuary 7.12 Comparison of the mathematical model with the linear regression method 8. Combination of a physically-based mathematical approach and a statisti-cal approach 8.1 Application of linear regression to the deviations Ay 8.2 Explanation in the light of a linear model 8.3 Principles of the Kalman filter 8.4 Application to semi constant parameters 8.5 Non linear relations 8.6 The use of matrix notation 8.7 Application to time series 8.8 Determination of the matrix elements 8.9 Application to a hypothetical case 8.10 Application to the Western Scheldt estuary 8.10.1 Determination of parameters and dimensions 8.10.2 Calculations without Kalman filter, using revised parameters.. 8.10.3 Determination of water levels at non gauged sites 8.11 Use in network design.

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