Note on the pumped storage potential of the Onslow-Manorburn depression, New Zealand

The Onslow-Manorburn depression in the South Island of New Zealand has possibility for development as the upper reservoir of the world's largest pumped storage scheme, as measured by an energy storage capacity of 10,200 GWh of realisable potential energy. This would more than triple the total national hydro-power energy storage capacity. It is envisaged that the scheme could either operate on a seasonal cycle or act as a passive energy reserve to buffer existing hydro-power capacity against the effect of dry years

The sustainable global energy economy: Hydrogen or silicon?

A sustainable global silicon energy economy is proposed as a potential alternative to the hydrogen economy. This first visualisation of a silicon energy economy is based on largescale and carbon-neutral metallic silicon production from major smelters in North Africa and elsewhere, supplied by desert silica sand and electricity from extensive solar generating systems. The resulting “fuel silicon” is shipped around the world to emission-free silicon power stations for either immediate electricity generation or stockpiling. The high energy density of silicon and its stable storage make it an ideal material for maintaining national economic functioning through security of base load power supply from a renewable source. This contrasts with the present situation of fossil fuel usage with its associated global warming and geopolitical supply uncertainties. Critical technological requirements for the silicon economy are carbon-neutral silicon production and the development of efficient silicon-fired power stations capable of high-temperature rapid oxidation of fuel silicon. A call is made for the development of research effort into these specific engineering issues, and also with respect to large-scale economical solar power generation

A goodness of fit measure related to r² for model performance assessment

Checking the predictive worth of an environmental model inevitably includes a goodness of fit metric to quantify the degree of matching to recorded data, thereby giving a measure of model performance. Considerable analysis and discussion have taken place over fit indices in hydrology, but a neglected aspect is the degree of communicability to other disciplines. It is suggested that a fit index is best communicated to colleagues via reference to models giving unbiased predictions, because unbiased environmental models are a desirable goal across disciplines. That is, broad recognition of a fit index is aided if it simplifies in the unbiased case to a familiar and logical expression. This does not hold for the Nash–Sutcliffe Efficiency E which reduces to the somewhat awkward unbiased expression E = 2 – 1/r², where r² is the coefficient of determination. A new goodness of fit index V is proposed for model validation as V =  r²/(2-E), which simplifies to the easily communicated V = r4 in the unbiased case. The index is defined over the range 0 ≤ V ≤ 1, and it happens that V < E for larger values of E. Some synthetic and recorded data sets are used to illustrate characteristics of V in comparison to

Note on y-truncation: a simple approach to generating bounded distributions for environmental applications

It may sometimes be desirable to introduce bounds into probability distributions to formalise the presence of upper or lower physical limits to data to which the distribution has been applied. For example, an upper bound in raindrop sizes might be represented by introducing an upper bound to an exponential drop-size distribution. However, the standard method of truncating unbounded probability distributions yields distributions with non-zero probability density at the resulting bounds. In reality it is likely that physical bounding processes in nature increase in intensity as the bound is approached, causing a progressive decline in observation relative frequency to zero at the bound. Truncation below a y-axis point is proposed as a simple alternative means of creating more natural truncated probability distributions for application to data of this type. The resulting “y-truncated” distributions have similarities with the traditional truncated distributions but probability densities have the desirable feature of always declining to zero at the bounds. In addition, the y-truncation approach can also serve in its own right as a mean

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

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 rth central moment of g(t,x) is an rth 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

A simple graphical technique for conditional long range forecasting of below-average rainfall periods in the Tuvalu Islands, Western Pacific

For the Tuvalu Island group in the western Pacific, a simple graphical method is proposed as a means of forecasting whether rainfall totals for the next 1, 2,…,6 months will be below average. The method is based on scatter plots where the points are color-coded as above- or below-average rainfall, with the plot axes being lag-1 and lag-2 NINO4 sea surface temperatures. Within the scatter plots there are reasonably clear data fields with higher frequencies of below-average rainfalls associated with cooler precursor NINO4 temperatures. These data fields are defined by subjectively emplaced separation lines which bifurcate the scatter plots into “predictable” and “unpredictable” fields. If two precursor NINO4 temperature values define a point located in a predictable field then a warning would be issued for below-average rainfall over the next n-month period, depending on the time scale of the scatter plot. A long rainfall record at Funafuti in Tuvalu indicates that success in predictable-field forecasting of below-average rainfalls would range between 68% for 1-month rainfall totals and 89% for 6-month totals. The forecasting success derives from persistence of cooler NINO4 sea surface temperatures which are associated with lower rainfalls in Tuvalu. However, many dry periods are also located in the unpredictable field and cannot be forecast by this method

An expression for land surface water storage monitoring using a two-formation geological weighing lysimeter

Field studies have demonstrated that ground surface rainfall accumulation can be detected at depth by synchronous increases in static confined groundwater pore pressures. This opens the way for “geological weighing lysimeters” providing disturbance-free water storage monitoring of the surface environment, in effect by weighing a significant land area in real time. Such systems require specific hydrogeological conditions, which are not easily verified by field observations and replicated observations from multiple geological formations are a prerequisite for quality control. Given replication over two monitored formations, we introduce an expression which utilises the respective formation piezometric water levels to give an improved combined estimate of the ground surface water budget. The expression utilises raw piezometric levels and has the advantage of direct correction for Earth tide noise, which may sometimes be influenced by local effects in addition to the pure solar/lunar tidal potential. The expression is particularly simple, if the two formations have similar (but possibly unknown) undrained Poisson ratios and porosities. Surface water budgets can then be estimated using only the respective formation barometric coefficients and piezometric levels. An example application to two vertically separated confined aquifers at a New Zealand site indicate an improved accuracy over single-formation observations. The two-formation expression for surface storage could find use as an accurate water budget tool with particular application to monitoring diffuse hydrological systems such as wetlands, arid regions, and heavily forested localities

Technical note: A significance test for data-sparse zones in scatter plots

Data-sparse zones in scatter plots of hydrological variables can be of interest in various contexts. For example, a well-defined data-sparse zone may indicate inhibition of one variable by another. It is of interest therefore to determine whether data-sparse regions in scatter plots are of sufficient extent to be beyond random chance. We consider the specific situation of data-sparse regions defined by a linear internal boundary within a scatter plot defined over a rectangular region. An Excel VBA macro is provided for carrying out a randomisation-based significance test of the data-sparse region, taking into account both the within-region number of data points and the extent of the region. Example applications are given with respect to a rainfall time series from Israel and also to validation scatter plots from a seasonal forecasting model for lake inflows in New Zealand

Seasonal prediction of lake inflows and rainfall in a hydro-electricity catchment, Waitaki river, New Zealand

The Waitaki River is located in the centre of the South Island of New Zealand, and hydro-electricity generated on the river accounts for 35-40% of New Zealand's electricity. Low inflows in 1992 and 2001 resulted in the threat of power blackouts. Improved seasonal rainfall and inflow forecasts will result in the better management of the water used in hydro-generation on a seasonal basis. Researchers have stated that two key directions in the fields of seasonal rainfall and streamflow forecasting are to a) decrease the spatial scale of forecast products, and b) tailor forecast products to end-user needs, so as to provide more relevant and targeted forecasts. Several season-ahead lake inflow and rainfall forecast models were calibrated for the Waitaki river catchment using statistical techniques to quantify relationships between land-ocean-atmosphere state variables and seasonally lagged inflows and rainfall. Techniques included principal components analysis and multiple linear regression, with cross-validation techniques applied to estimate model error and randomization techniques used to establish the significance of the skill of the models. Many of the models calibrated predict rainfall and inflows better than random chance and better than the long-term mean as a predictor. When compared to the range of all probable inflow seasonal totals (based on the 80-year recorded history in the catchment), 95% confidence limits around most model predictions offer significant skill. These models explain up to 19% of the variance in season-ahead rainfall and inflows in this catchment. Seasonal rainfall and inflow forecasting on a single catchment scale and focussed to end-user needs is possible with some skill in the South Island of New Zealand

An invalidation test for predictive models

The standard means of establishing predictive ability in hydrological models is by finding how well predictions match independent validation data. This matching may not be particularly good in some situations such as seasonal flow forecasting and the question arises as to whether a given model has any predictive capacity. A model-independent significance test of the presence of predictive ability is proposed through random permutations of the predicted values. The null hypothesis of no model predictive ability is accepted if there is a sufficiently high probability that a random reordering of the predicted values will yield a better fit to the validation data. The test can achieve significance even with poor model predictions and its value is for invalidating bad models rather than verifying good models as suitable for application. Some preliminary applications suggest that test outcomes will often be similar at the 0.05 level for standard fit measures using absolute or squared residuals. In addition to hydrological application, the test may also find use as a base quality control measure for predictive models generally