W.E. Bardsley

Note on the use of the inverse Gaussian distribution for wind energy applications

Abstract The inverse Gaussian distribution is suggested as an alternative to the three-parameter Weibull distribution for the description of wind speed data with low frequencies of low speeds. A comparison of the two distributions indicates a region of strong similarity, corresponding reasonably well to three-parameter Weibull distributions which have been fitted to wind data. Maximum likelihood estimation of the inverse Gaussian parameters is much simpler than the iterative technique required for the three-parameter Weibull distribution. In addition, the inverse Gaussian distribution features the mean wind speed as a parameter, a desirable property for wind energy investigations. A summation-reproductive property of the distribution permits estimation of the mean wind energy flux from a sequence of speed averages.

A new method for measuring near-surface moisture budgets in hydrological systems

Abstract Preliminary results from a groundwater experiment set up near Matamata (New Zealand) reveal that confined aquifers can act as giant weighing lysimeters, with pore water pressures giving real-time measures of changes in amounts of surface and near-surface water. This opens the possibility of water balance studies at the scale of hectares using measurements from a single site. Given suitable confined aquifers, the technique has application in various environments for hydrological measurements as diverse as quantification of evapotranspiration loss, areal precipitation measurement, monitoring the water content of an accumulating snowpack, and net lateral groundwater transfers in unconfined aquifers.

Using historical data in nonparametric flood estimation

Abstract In recent years, a nonparametric approach to design flood analysis has emerged which is based on estimating the whole distribution of annual flood maxima from standard hydrological records. A simple modification is suggested here for incorporating historical or paleoflood data as well. The resulting analysis is somewhat different from the parametric alternative in that it may not prove possible to estimate within a “data gap” which may appear between the magnitudes of the largest modern floods and historical/paleoflood events. It is a matter of personal philosophy whether such gaps represent a true indication of the state of knowledge or are simply a disadvantage not experienced by parametric methods. An illustrative example is given using recent and historical flood data from the Yangtze River.

An improved method of least-squares parameter estimation with pumping-test data

Abstract Least-squares estimation of storativity and transmissivity from pumping-test data has been concerned with finding the lowest point on a mathematical surface. Since there is no guarantee that such surfaces do not contain local minima, the accuracy of the estimate may be dependent upon the selection of “good” initial values. An improved estimation procedure can be obtained by converting the two-dimensional minimisation problem into an equivalent form in one dimension. The resulting line function can then be easily evaluated through any given feasible interval. This approach avoids the requirement of initial estimates and always returns the true estimates after a single computation sequence. Examples are given of the application of the method to both drawdown and recovery data, together with a simple model for the determination of estimation error.

Natural Geological Weighing Lysimeters: Calibration Tools for Satellite and Ground Surface Gravity Monitoring of Subsurface Water-Mass Change

Increased accuracy in measuring temporal variations in the Earths gravity field allow inprinciple the use of gravity observations to deduce subsurface water-mass changes. This canbe with respect to a small area, or as a larger spatial average of water mass change usinggravity observations from low-altitude satellites, such as the forthcoming GRACE mission.At both scales, there is a need to validate gravity-based estimates against field recordings ofactual subsurface water-mass variations. In practice, this could prove difficult because thespatial integral of all water-storage change components can be subject to considerable fieldmeasurement error. An alternative approach to the validation process is proposed by whichsuitable geological formations are utilized as giant weighing devices to directly measure area-integratedwater-mass changes. The existence of such “natural geological weighing lysimeters”is demonstrated using observations from a replicated experimental site in New Zealand. Sitesof this type could be used to verify water-storage change estimates derived from sensitiveground surface gravity instrumentation. In addition, geological lysimeters could be used tomake local checks on the accuracy of any estimated regional water-mass time series, whichis proposed for satellite calibration. The land area “weighed” by a geological lysimeter increaseswith formation depth and it is speculated that recordings made at oil well depth may allowdirect monitoring of subsurface water mass changes at the regional scale.

Temporal moments of a tracer pulse in a perfectly parallel flow system

Abstract Perfectly parallel groundwater transport models partition water flow into isolated one-dimensional stream tubes which maintain total spatial correlation of all properties in the direction of flow. The case is considered of the temporal moments of a conservative tracer pulse released simultaneously into N stream tubes with arbitrarily different advective–dispersive transport and steady flow speeds in each of the stream tubes. No assumptions are made about the form of the individual stream tube arrival-time distributions or about the nature of the between-stream tube variation of hydraulic conductivity and flow speeds. The tracer arrival-time distribution g ( t , x ) is an N -component finite-mixture distribution, with the mean and variance of each component distribution increasing in proportion to tracer travel distance x . By utilising moment relations of finite mixture distributions, it is shown (to r =4) that the r th central moment of g ( t , x ) is an r th order polynomial function of x or φ , where φ is mean arrival time. In particular, the variance of g ( t , x ) is a positive quadratic function of x or φ . This generalises the well-known quadratic variance increase for purely advective flow in parallel flow systems and allows a simple means of regression estimation of the large-distance coefficient of variation of g ( t , x ). The polynomial central moment relation extends to the purely advective transport case which arises as a large-distance limit of advective–dispersive transport in parallel flow models. The associated limit g ( t , x ) distributions are of N -modal form and maintain constant shapes independent of travel distance. The finite-mixture framework for moment evaluation is also a potentially useful device for forecasting g ( t , x ) distributions, which may include multimodal forms. A synthetic example illustrates g ( t , x ) forecasting using a mixture of normal distributions.

On the Maximum Observed Hailstone Size

Abstract The largest hailstone to strike a hailpad is often smaller than the largest hailstone observed in the immediate vicinity. This has given rise to some comment in the literature, but the apparent anomaly is only a trivial consequence of the observation process. However, relationships between these two types of maxima can be utilized via extreme value theory to make inferences concerning the largest hailstones beyond the immediate observation area.

Graphical estimation of extreme value prediction functions

Abstract Graphical application of the Type 1 (Gumbel) extreme value distribution is very simple since the distribution inverse gives a linear x-y plot. In contrast, the Type 2 and Type 3 extreme value distributions have nonlinear functions with respect to the same axes. A simple three-point graphical estimation procedure is described for these two distributions. This approach allows the nonlinear flood magnitude prediction functions to be located in any desirable position relative to the plotted annual maxima, subject to the constraint of having an extreme value form. The computation is very simple and requires only the location of a unique zero of a one-parameter function within a defined interval.

A test for distinguishing between extreme value distributions

Abstract Asymptotic distributions of largest extremes are frequently used to estimate flood probabilities. The correct choice of distribution is of some importance as the three asymptotic types may differ considerably in their right tails. This paper gives a test where the null hypothesis is the type-I distribution and the alternative is one of the other extreme value distributions. Power curves are given for sample sizes of 50 and 100.

A simple parameter-free flood magnitude estimator

Abstract Some simulation results are presented with respect to the parameter-free flood magnitude estimator: where p is the estimated probability of a smaller annual maximum flood, and the ri are the ranked annual flood maxima. The design magnitude estimates are obtained by solving for x with p specified. Root-mean-square values and probabilities of an underestimate are tabulated with respect to samples of size 20, 30 and 50 from a selection of “floodlike” distributions. As well as indicating the region of applicability of the estimator, the tabulated results provide a useful basis for measuring the improvement of future parameter-free estimators.