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Thomas McMahon

University of Melbourne, Infrastructure Engineering, Emeritus

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Papers by Thomas McMahon

Single and Multi-Site Operational Hydrology

Hydrology Research, 1972

This paper reviews several different single- and multi-site generation models to complement those... more This paper reviews several different single- and multi-site generation models to complement those papers in which the models are developed but not applied. Initially the historical time series is looked at using various time series techniques, including correlograms and spectral analyses, to determine whether a lag one Markov model will satisfactorily represent the historical data. The single site models which are examined include an empirical model using the historical probability distribution of the random component, the Thomas and Fiering model using both logarithms of the data and Matalas' log-normal transformation equations, and finally Moran's Gamma distribution. Matalas' Residual method with several probability distributions and Moran's Multivariate Gamma technique are used in the multi-site analysis. All models are applied to the streams of the Melbourne metropolitan water supply system.

Global streamfl performance

a nviron b nviron c me, U R receiv Global hydrology; of continuous data. Capacity estimates of hy... more a nviron b nviron c me, U R receiv Global hydrology; of continuous data. Capacity estimates of hypothetical reservoirs are computed for each theoretical Gould–Dincer Gamma procedure was also shown to be a suitable technique vulnerability – are computed and their continental variations described. As a result of and South America, lower still in northern Africa, followed by Australia and the lowest value in southern Africa. This distribution follows inversely with the coefficient of varia-tion of annual streamflow between continents.

Floodflow frequency model selection in Australia

Journal of Hydrology, 1993

Uniform flood frequency guidelines in Australia and the United States recommend the use of the lo... more Uniform flood frequency guidelines in Australia and the United States recommend the use of the log Pearson type 3 (LP3) distribution in flood frequency investigations. Many investigators have suggested alternate models such as the Generalized Extreme Value (GEV) distribution as an improvement over the LP3 distribution. Using floodflow data at 61 sites across Australia, we explore the suitability of various flood frequency models using L-moment diagrams. We also repeat the experiment performed in the original US Water Resource Council report (Bulletin 17B) which led to the LP3 mandate in the United States. Our evaluations reveal that among the models tested, the GEV and Wakeby distributions provide the best approximation 1o floodflow data in the regions of Australia that are dominated by rainfall during the winter months, such as southwest Western Australia and Tasmania. For the remainder of the continent, the Generalized Pareto (GPA) and Wakeby distributions provide the best approximation to floodflow data. The two-and three-parameter log-normal models and the LP3 distribution performed satisfactorily, yet not as well as either the GEV or GPA distributions. Other models such as the Gumbel, log-normal, normal, Pearson, exponential, and uniform distributions are shown to perform poorly. Recent research indicates that regional index-flood type procedures should be more accurate and more robust than the type of at-site procedures evaluated here. Nevertheless, this study reveals that index-flood procedures should not be restricted to a single distribution such as the GEV distribution because other distributions such as the GPA distribution perform significantly better in the most densely populated regions of Australia. INTRODUCTION Many innovations in the field of flood frequency analysis have occurred since the decision of the Institution of Engineers (Pilgrim, 1987) and the US Water Resources Council (1967) to recommend the use of the log Pearson type 3 (LP3) distribution for floodflow investigations in Australia and the United States, respectively. The state of the art of selecting a regional flood

Prediction of annual runoff in ungauged basins

Runoff Prediction in Ungauged Basins

Runof f Predic tion in Unga uged Basins A1 nnual precipit at on .S 10 firrure 5.2. Daily precipit... more

Stochastic Generation of Monthly Rainfall Data

Advances in Geosciences

Effects of rainfall seasonality and soil moisture capacity on mean annual water balance for Australian catchments

Water Resources Research, 2005

An important factor controlling catchment-scale water balance is the seasonal variation of climat... more An important factor controlling catchment-scale water balance is the seasonal variation of climate. The aim of this study is to investigate the effect of the seasonal distributions of water and energy, and their interactions with the soil moisture store, on mean annual water balance in Australia at catchment scales using a stochastic model of soil moisture balance with seasonally varying forcing. The rainfall regime at 262 catchments around Australia was modeled as a Poisson process with the mean storm arrival rate and the mean storm depth varying throughout the year as cosine curves with annual periods. The soil moisture dynamics were represented by use of a single, finite water store having infinite infiltration capacity, and the potential evapotranspiration rate was modeled as an annual cosine curve. The mean annual water budget was calculated numerically using a Monte Carlo simulation. The model predicted that for a given level of climatic aridity the ratio of mean annual evapotranspiration to rainfall was larger where the potential evapotranspiration and rainfall were in phase, that is, in summer-dominant rainfall catchments, than where they were out of phase. The observed mean annual evapotranspiration ratios have opposite results. As a result, estimates of mean annual evapotranspiration from the model compared poorly with observational data. Because the inclusion of seasonally varying forcing alone was not sufficient to explain variability in the mean annual water balance, other catchment properties may play a role. Further analysis showed that the water balance was highly sensitive to the catchment-scale soil moisture capacity. Calibrations of this parameter indicated that infiltration-excess runoff might be an important process, especially for the summer-dominant rainfall catchments; most similar studies have shown that modeling of infiltration-excess runoff is not required at the mean annual timescale.

Observed spatial organization of soil moisture and its relation to terrain indices

Water Resources Research, 1999

We analyze the degree of spatial organization of soil moisture and the ability of terrain attribu... more We analyze the degree of spatial organization of soil moisture and the ability of terrain attributes to predict that organization. By organization we mean systematic spatial variation or consistent spatial patterns. We use 13 observed spatial patterns of soil moisture, each based on over 500 point measurements, from the 10.5 ha Tarrawarra experimental catchment in Australia. The measured soil moisture patterns exhibit a high degree of organization during wet periods owing to surface and subsurface lateral redistribution of water. During dry periods there is little spatial organization. The shape of the distribution function of soil moisture changes seasonally and is influenced by the presence of spatial organization. Generally, it is quite different from the shape of the distribution functions of various topographic indices. A correlation analysis found that ln(a), where a is the specific upslope area, was the best univariate spatial predictor of soil moisture for wet conditions and...

The (mis)behavior of behavior analysis storage estimates

Water Resources Research, 1997

This paper investigates the dependence of estimates of reservoir storage capacity derived using b... more This paper investigates the dependence of estimates of reservoir storage capacity derived using behavior analysis on the length of inflow sequence used for overyear reservoir simulation. It has generally been assumed that simulation using behavior analysis, which incorporates a given probability of failure, will always give steady state estimates of the storage capacity (apart from the effects of the initial reservoir condition). The results reported here show that it may take sequence lengths as much as 1000 years or more for the mean of the distribution of storage capacity estimates to approach a stationary value. For some cases with high draft and high inflow variability, we show that a significant swing of the mean storage estimates from an initial downward bias into an upward bias occurs before their convergence to a stationary level. However, the median storage estimates always showed downward bias which sometimes decreased very slowly with increasing sequence length. We provi...

Comparison of two approaches for generation of daily rainfall data

Stochastic Environmental Research and Risk Assessment, 2005

Models for generating daily rainfall are in great demand for various needs and have seen much dev... more Models for generating daily rainfall are in great demand for various needs and have seen much development. Srikanthan and McMahon (1985) showed that the transition probability matrix (TPM) model performed better than alternative models available then. However a noted shortcoming is the underestimation of the variances of the simulated monthly and annual rainfall. Boughton (1999) proposed an empirical adjustment to match the observed annual standard deviation, which although improves the variability in the annual rainfall, still underestimates the variability in the annual number of wet days. Recently, Harrold et al. (2002) proposed nonparametric models for the generation of daily rainfall occurrences and rainfall amounts on wet days. The rainfall occurrence model was conditioned on a combination of daily, seasonal, annual, and multi-year predictors. By conditioning on short, medium and long-term characteristics, this model was able to preserve the variability in the annual number of wet days. The model to generate the rainfall depth also used a combination of short and long term predictors which consisted of the rainfall depth on the previous day and an indicator of the annual rainfall total. This model also differed from the TPM model in the representation of seasonality in the rainfall simulations by a seasonal moving window. The above two approaches were compared by generating daily rainfall data for Melbourne and Sydney. Both approaches preserved most of the daily, monthly and annual characteristics but failed to preserve the correlations in monthly and annual rainfall. However, the nonparametric approach was able to preserve the variability and persistence in the annual number of wet days.

A review of paired catchment studies for determining changes in water yield resulting from alterations in vegetation

Journal of Hydrology, 2005

Paired catchment studies have been widely used as a means of determining the magnitude of water y... more Paired catchment studies have been widely used as a means of determining the magnitude of water yield changes resulting from changes in vegetation. This review focuses on the use of paired catchment studies for determining the changes in water yield at various time scales resulting from permanent changes in vegetation. The review considers long term annual changes, adjustment time scales, the seasonal pattern of flows and changes in both annual and seasonal flow duration curves. The paired catchment studies reported in the literature have been divided into four broad categories: afforestation experiments, deforestation experiments, regrowth experiments and forest conversion experiments. Comparisons between paired catchment results and a mean annual water balance model are presented and show good agreement between the two methodologies. The results highlight the potential underestimation of water yield changes if regrowth experiments are used to predict the likely impact of permanent alterations to a catchment's vegetation. An analysis of annual water yield changes from afforestation, deforestation and regrowth experiments demonstrates that the time taken to reach a new equilibrium under permanent land use change varies considerably. Deforestation experiments reach a new equilibrium more quickly than afforestation experiments. The review of papers reporting seasonal changes in water yield highlights the proportionally larger impact on low flows. Flow duration curve comparison provides a potential means of gaining a greater understanding of the impact of vegetation on the distribution of daily flows.

Global streamflows – Part 1: Characteristics of annual streamflows

Journal of Hydrology, 2007

... which, in the context of our global data set of streamflows, involves learning how surfacestr... more

Global streamflows – Part 2: Reservoir storage–yield performance

Journal of Hydrology, 2007

This is the second of three papers describing hydrologic analyses of monthly and annual streamflo... more This is the second of three papers describing hydrologic analyses of monthly and annual streamflow data for a global set of 729 unregulated rivers with at least 25 years of continuous data. Capacity estimates of hypothetical reservoirs are computed for each river using the Sequent Peak Algorithm (SPA), Behaviour analysis and the Gould-Dincer Gamma procedure. Based on SPA and Behaviour procedures, empirical relationships relating reservoir capacity and yield were developed which accounted for 87-96% of the variance in capacity estimates across the global data set of monthly streamflows. The theoretical Gould-Dincer Gamma procedure was also shown to be a suitable technique to estimate reservoir capacity-yield relationships. It is noted that the three procedures are based on different definitions of supply reliability. Continental variations of the estimated capacities under equivalent conditions are examined. Reservoir performance measures-reliability, resilience and dimensionless vulnerability-are computed and their continental variations described. As a result of these analyses a number of differences are noted about the performance of reservoirs across continental regions. For example, the median continental reservoir capacity as a ratio of the mean annual flow varied by a factor of 9 across the continental regions. Furthermore, based on the reliability metric as an example of reservoir performance, high reliabilities occur in the South Pacific and Europe, slightly less reliable systems in North and South America, lower still in northern Africa, followed by Australia and the lowest value in southern Africa. This distribution follows inversely with the coefficient of variation of annual streamflow between continents.

Global streamflows – Part 3: Country and climate zone characteristics

Journal of Hydrology, 2007

This is the final paper in a series of three dealing with global hydrology based on a worldwide h... more This is the final paper in a series of three dealing with global hydrology based on a worldwide historical data set of monthly and annual streamflow records. In this paper hypothetical reservoir capacity estimates and reservoir-yield performance characteristics are compared between countries and between climate zones. The comparison for each characteristic is based mainly on its median value. For the comparison based on countries, the median value for 17 countries was based on at least 10 rivers, and for a further 19 countries on at least three rivers within the country. For the 30 Köppen climate zones, 13 zones had at least 10 rivers and a further seven zones were represented by at least three rivers. Some conclusions include: rivers in the Sahel region of Africa exhibit larger inter-decadal variances compared with those for other global rivers; the observation that western Canadian rivers display longer run lengths than expected from an AR(1) model may be due to the influence of the Pacific Decadal Oscillation; between countries, storage resilience is strongly positively related to reliability, and dimensionless vulnerability is strongly negatively related to reliability; and, finally, rivers in countries that exhibit low resilience tend to show high dimensionless vulnerability. It was also observed for several rivers in Finland and Sudan, that large natural lakes, not unexpectedly, increase streamflow auto-correlation and thereby reduce a reservoir's ability to recover quickly following a major deficit.

Reply to comment by Tromp van Meerveld and McDonnell on Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes

Journal of Hydrology, 2005

Modelling streamflow in a large anastomosing river of the arid zone, Diamantina River, Australia

Journal of Hydrology, 2006

Anastomosing rivers form a subset of the anabranching family of river types and provide considera... more Anastomosing rivers form a subset of the anabranching family of river types and provide considerable challenges to modelling of their streamflow because of complex flow patterns across greatly varying floodplain widths. Estimates of distributed flow data are required for catchment management purposes and ecological studies of these rivers but are hindered by a paucity of measured discharge data. A grid-based, semi-distributed, conceptual model structure is applied to a 330 km reach of the arid zone Diamantina River of central Australia. Model complexity is constrained by data availability with only a single gauging station located at the downstream end of the reach to provide discharge data for model calibration. The model uses a simple conceptual bucket structure and accounts for exceptionally high transmission losses as well as flow patterns and wave speeds that vary with discharge within the reach. The intricate flow patterns across the floodplains widths of up to 50 km are simulated using a grid-based structure that required the following features: (i) cell connections that are explicitly defined using a code that allows for multi-directional flow from a cell; and (ii) each cell having a binary flow pattern, with the second connection pattern being triggered when the surface storage of the cell exceeds a calibrated level for a given land-type. Satellite images were used to define the flow paths, and hence cell connection patterns, utilised by various sized floods. The model was able to provide acceptable simulation of large floods but with decreasing model performance in the simulation of small to medium sized floods. Simulation suggested that incorrectly defined flow paths for the smaller floods were a major factor in this decreased performance. The capability of the model would be improved by further detailed mapping, using satellite imagery, of spatial patterns of inundation as discharge varies.

Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes

Journal of Hydrology, 2004

The geostatistical properties of soil moisture patterns from five different sites in Australia (T... more The geostatistical properties of soil moisture patterns from five different sites in Australia (Tarrawarra and Point Nepean) and New Zealand (three sites from the Mahurangi River Basin-Carran's, Clayden's and Satellite Station) are analysed here. The soil moisture data were collected using time domain reflectometry and consistent methods for all sites, thereby allowing comparisons to be drawn between sites without the complication of methodological differences. The sites have contrasting climatic and soils characteristics. Soil moisture in the top 30 cm of the soil profile was measured using time domain reflectometry on 6-8 occasions at each site. The variance and correlation structure of the patterns was analysed. Typical correlation scales lie between 30 and 60 m. We found that there was a seasonal evolution in the spatial soil moisture variance that was related to changes in the spatial mean moisture content at all sites. At the Australian sites there was also a seasonal evolution in the correlation length related to changes in the spatial mean moisture, but not at the New Zealand sites. The seasonal evolution of the correlation length in the Australian catchments is likely to be associated with a seasonal change in the processes controlling the soil moisture pattern. The more humid climate at the New Zealand sites leads to more consistent spatial controls over the year. Similarities between the correlation structure of the moisture and topographic indices representing lateral flow and topographically modulated evaporative forcing were found at Tarrawarra, Carran's and Clayden's. At Point Nepean the correlation structure of the soil moisture pattern is controlled by a larger (than the topography) scale variation in soils, properties and at Satellite Station a smaller scale source of variability is apparent in the data (although there were also topographical effects apparent, associated with valley features). The results demonstrate that the processes controlling spatial patterns can change between places and over time with catchment moisture status; however, when similar general conditions reoccur in a catchment, similar spatial patterns result. Soil characteristics and climate do provide a general pointer to what we might expect but the results also show subtleties specific to place.

Spatial distribution of soil moisture over 6 and 30cm depth, Mahurangi river catchment, New Zealand

Journal of Hydrology, 2003

Ground-based measurement of the spatial distribution of soil moisture can be difficult because sa... more Ground-based measurement of the spatial distribution of soil moisture can be difficult because sampling is essentially made at a point and the choice of both sample depth and sample spacing affects the interpretation of the measurements. Hydrological interest has generally been in soil moisture of the root zone. Microwave Remote Sensing methods are now available that allow the interpretation of spatial distributions of soil moisture, however, their signals respond to moisture in the upper few centimetres of soil. These instruments are still being developed, but one of the questions surrounding their application is how to interpret the surface moisture in a hydrological context. In this study we compare measurements of soil moisture in 0-30 cm of soil with those in 0-6 cm to examine how representative this surface measure is with regard to the root zone. Detailed spatial measurements of soil moisture were conducted at three pasture sites in the 50 km 2 Mahurangi River catchment of northern New Zealand as part of a comprehensive hydrology project; MARVEX (MAhurangi River Variability EXperiment). In three field sites, on each of three occasions, field measurements were made using both 30 and 6 cm dielectric-based instruments. Spatial grids of several hundred moisture measurements were collected over 0-30 cm and compared with those collected simultaneously over 0-6 cm. Results indicate that temporal and spatial issues interfere with correlation of the two sets of series. Rapid wetting of 0-6 cm compared with 0-30 cm is seen following storm activity. Some evidence of the decoupling of moisture content response is also evident when sites are measured on days following a storm. Rapid, but not unrealistic, response to intense rainfall was also observed. Implications are that detailed and accurate knowledge of local soil conditions and a sound model of soil water redistribution are required before surface soil moisture measurements can be used to infer root zone behaviour. Such knowledge was not available in this study, from either published data or field observation. In this study, without suitable a priori knowledge, soil property information was found via calibration.

Development of Exceedance Probability Streamflow Forecast

Journal of Hydrologic Engineering, 2001

This paper presents a methodology for forecasting seasonal streamflow and is an extension of a pr... more This paper presents a methodology for forecasting seasonal streamflow and is an extension of a previously developed categorical streamflow forecast model that used persistence (i.e., the previous season's streamflow) and El-Southern Oscillation (ENSO) indicators. This newly developed methodology takes Nino persistence, an ENSO indicator, and several Pacific/Indian Ocean sea surface temperature (SST) series as the main predictor variables. Using linear discriminant analysis, the forecast is expressed as probability of exceedance of continuous streamflow amounts. An exceedance probability forecast is continuous and is useful for the design and operation of water resource systems, which require a high degree of system reliability. Application of the forecast model to five Australian catchments shows that persistence is the most important predictor of streamflow for the next season. The other predictors, SSTs and the Southern Oscillation Index, may be more useful for forecasts with longer lead times when the degree of persistence is less noticeable. Finally, it is noteworthy that this generic approach to making an exceedance probability forecast can be used on any predictors and predictands.

Stochastic generation of climate data: a review

This is the fi rst of a series of reports expected from CRC for Catchment Hydrology Program 5, Cl... more This is the fi rst of a series of reports expected from CRC for Catchment Hydrology Program 5, Climate Variability. This program aims to reduce management uncertainty by developing space-time models for Australia, improving the representativeness of surface hydrology in numerical weather prediction models, developing methods to forecast rainfall and streamfl ow several hours to several months ahead, and establishing a robust set of stochastic models for the generation of climate and streamfl ow. Summary iii Notations/Abbreviations vi 2 Annual and monthly rainfall data 2.1 Annual rainfall data at a site 2.2 Annual rainfall data at a number of sites 2.3 Monthly rainfall data at a site 2.4 Monthly rainfall data at a number of sites 2.5 Summary 3 Daily rainfall data 3.1 Daily rainfall data at a site 3.1.1 Two-part models 3.1.2 Transition probability matrix models 3.1.3 Resampling models 3.1.4 Time series models 3.1.5 Conditional daily rainfall models 3.1.6 Uncertainty in model parameters 3.1.7 Regionalisation of daily rainfall model parameters 3.1.8 Summary 3.2 Daily rainfall data at a number of sites 3.2.1 Conditional models 3.2.2 Extension of single site Markov chain models 3.2.3 Random cascade models 3.3 Summary 4 Climate data 4.1 Annual climate data 4.2 Monthly climate data 4.3 Daily climate data 4.3.1 Daily climate data at a site 4.3.2 Daily climate data at multiple sites 4.4 Summary 5 Rainfall and climate data under climate change scenario 5.1 Adjustment of historical data 5.2

Stochastic generation of annual, monthly and daily climate data: A review

Hydrology and Earth System Sciences, 2001

The generation of rainfall and other climate data needs a range of models depending on the time a... more The generation of rainfall and other climate data needs a range of models depending on the time and spatial scales involved. Most of the models used previously do not take into account year to year variations in the model parameters. Long periods of wet and dry years were observed in the past but were not taken into account. Recently, Thyer and Kuczera (1999) developed a hidden state Markov model to account for the wet and dry spells explicitly in annual rainfall. This review looks firstly at traditional time series models and then at the more complex models which take account of the pseudo-cycles in the data. Monthly rainfall data have been generated successfully by using the method of fragments. The main criticism of this approach is the repetitions of the same yearly pattern when only a limited number of years of historical data are available. This deficiency has been overcome by using synthetic fragments but this brings an additional problem of generating the right number of months with zero rainfall. Disaggregation schemes are effective in obtaining monthly data but the main problem is the large number of parameters to be estimated when dealing with many sites. Several simplifications have been proposed to overcome this problem. Models for generating daily rainfall are well developed. The transition probability matrix method preserves most of the characteristics of daily, monthly and annual characteristics and is shown to be the best performing model. The two-part model has been shown by many researchers to perform well across a range of climates at the daily level but has not been tested adequately at monthly or annual levels. A shortcoming of the existing models is the consistent underestimation of the variances of the simulated monthly and annual totals. As an alternative, conditioning model parameters on monthly amounts or perturbing the model parameters with the Southern Oscillation Index (SOI) result in better agreement between the variance of the simulated and observed annual rainfall and these approaches should be investigated further. As climate data are less variable than rainfall, but are correlated among themselves and with rainfall, multisite-type models have been used successfully to generate annual data. The monthly climate data can be obtained by disaggregating these annual data. On a daily time step at a site, climate data have been generated using a multisite type model conditional on the state of the present and previous days. The generation of daily climate data at a number of sites remains a challenging problem. If daily rainfall can be modelled successfully by a censored power of normal distribution then the model can be extended easily to generate daily climate data at several sites simultaneously. Most of the early work on the impacts of climate change used historical data adjusted for the climate change. In recent studies, stochastic daily weather generation models are used to compute climate data by adjusting the parameters appropriately for the future climates assumed.