The joint probability problem inherent in flood estimation is complex Although the design storm approach has a long tradition it lacks the fundamental rigour of joint probability analysis The use of average values for random inputs other than rainfall intensity and duration can be justified from a joint probability perspective provided variations in the input affect the peak flow density in a linear fashion However, the assignment of the average value for initial conditions is problematic A case study involving a detention basin demonstrates large biases arising from mis-specification of initial conditions in volume-sensitive systems It is suggested that the current revision of ARR needs to articulate the shortcomings of the design storm approach, identify calibration strategies that ensure closure and give guidance about its reliability in different applications Looking to the future, ARR needs to move towards event and total joint probability approaches that are underpinned by a rigorous joint probability framework Continuous simulation is emerging as a practical tool and remains the most rigorous tool available Event joint probability methods based on Monte Carlo simulation are computationally less demanding but require specification of the probability distribution of initial conditions Stochastic rainfall models are on the verge of practical application to service Monte Carlo methods

Joint Probability and Design Storms at the Crossroads

Flood frequency approaches vary from statistical methods, directly applied on the observed annual maximum flood series, to adopting rainfall–runoff simulation models that transform design rainfalls to flood discharges. Reliance on statistical flood frequency analysis depends on several factors such as the selected probability distribution function, estimation of the function parameters, possible outliers, and length of the observed flood series. Through adopting the simulation approach in this paper, watershed-average rainfalls of various occurrence probabilities were transformed into the corresponding peak discharges using a calibrated hydrological model. A Monte Carlo scheme was employed to consider the uncertainties involved in rainfall spatial patterns and antecedent soil moisture condition (AMC). For any given rainfall depth, realizations of rainfall spatial distribution and AMC conditions were entered as inputs to the model. Then, floods of different return periods were simulated by transforming rainfall to runoff. The approach was applied to Tangrah watershed in northeastern Iran. It was deduced that the spatial rainfall distribution and the AMCs exerted a varying influence on the peak discharge of different return periods. Comparing the results of the simulation approach with those of the statistical frequency analysis revealed that, for a given return period, flood quantiles based on the observed series were greater than the corresponding simulated discharges. It is also worthy to note that existence of outliers and the selection of the statistical distribution function has a major effect in increasing the differences between the results of the two approaches.

Flood frequency analysis based on simulated peak discharges

The traditional rainfall-runoff modelling based on the Design Event Approach has some serious limitations as this ignores the probabilistic nature of the key flood producing variables in the modelling except for rainfall depth. A more holistic approach of design flood estimation such as the Joint Probability Approach/Monte Carlo simulation can overcome some of the limitations associated with the Design Event Approach. The Monte Carlo simulation technique is based on the principle that flood producing variables are random variables instead of fixed values. This allows accounting for the inherent variability in the flood producing variables in the rainfall-runoff modelling. This paper applies the Monte Carlo simulation technique and hydrologic model URBS to a large catchment with multiple pluviograph and stream gauging stations. It has been found that it is quite feasible to apply the Monte Carlo simulation technique to large catchments. The Monte Carlo simulation technique has much greater flexibility than the Design Event approach and can provide more realistic design flood estimates with multiple scenarios, which is likely to replace the Design Event Approach. The method developed here can be applied to other catchments in Australia and other countries.

Application of Monte Carlo simulation technique to design flood estimation : a case study for North Johnstone River in Queensland, Australia

The magnitude of the flood generated from a storm depends to a significant degree on how much of the rainfall is converted into surface runoff and how much of it is 'lost'. For design flood estimation, lumped conceptual loss models such as the 'initial loss - continuing loss model' are frequently adopted in Australia. This paper examines the role played by initial loss modelling in flood estimation for selected Victorian catchments. The large variability of initial loss for different flood events in a catchment is represented by a four-parameter Beta distribution fitted to the observed initial loss data. These stochastic losses are used in a Monte Carlo simulation technique with stochastically generated design rainfall events to determine derived flood frequency curves. It has been found that, in the range of relatively frequent floods, the derived flood frequency curves are quite sensitive to details of the adopted loss modelling approach. The paper shows the potential of adopting stochastic losses in design flood estimation.

The use of probability-distributed initial losses in design flood estimation

Rainfall-based design flood estimation methods in Australia traditionally follow the design event approach. However, the basic assumption of a probability neutral transformation in the design event approach has been widely criticised. For this reason, joint probability approaches (like Monte Carlo simulation) were proposed in the 1970s to account for the probabilistic nature of key inputs in rainfall–runoff modelling. However, these techniques were not seriously tested until the 1990s, when a simple Monte Carlo simulation technique was developed that used existing design data and models, for Australian hydrologic practice. This paper summarises the evolution of Monte Carlo simulation techniques for design flood estimation with a particular emphasis on Australian practice. It has been found that significant advancements have been made in the development and testing of Monte Carlo simulation in Australia; but, there is still a lack of commercial software hindering the routine application of holistic...

Monte Carlo simulation for design flood estimation: a review of Australian practice

This paper summarises the results of a 3-year research project by the CRC for Catchment Hydrology (CRCCH). It identifies significant shortcomings in the current Design Event Approach to rainfall-based design flood estimation, and argues that substantial improvements in the accuracy and reliability of flood estimates can be obtained from a more rigorous treatment of probability aspects in the generation of design floods. Application of the proposed Monte Carlo Simulation approach to three test catchments in Victoria has produced promising results, and has demonstrated the feasibility and in-principle advantages of the approach. The paper discusses how far the CRCCH work has advanced towards resolving the main research issues, and outlines desirable future development work to allow the new method to be routinely applied as a design tool.

Monte Carlo Simulation of Flood Frequency Curves from Rainfall - the Way Ahead

This paper summarises the results of a 3-year research project by the CRC for Catchment Hydrology (CRCCH) on the joint probability approach (Monte Carlo simulation technique) to design flood estimation and the subsequent research activities to further the CRCCH method towards industrial applications. It identifies significant shortcomings in the current design event approach to rainfall-based design flood estimation, and argues that substantial improvements in the accuracy and reliability of flood estimates can be obtained from a more rigorous treatment of probability aspects in the generation of design floods. Applications of the proposed Monte Carlo simulation approach to test catchments in Victoria and Queensland have produced promising results, and demonstrated the feasibility and in-principle advantages of the approach. More recently, the Monte Carlo simulation approach has been integrated with the industry-based flood estimation model URBS thus significantly broadening its range of application. The paper discusses how far the recent research on the joint probability approach has advanced towards resolving the main research issues, and outlines desirable future development work to allow the new method to be routinely applied as a design tool.

Monte Carlo simulation of flood frequency curves from rainfall : the way ahead

In the currently applied rainfall-based flood estimation methods, design storms for pre-defined durations are represented by probabilistic design rainfall intensities and fixed temporal patterns. This does not adequately reflect the great degree of variability of real storm events and, in catchments with strongly non-linear runoff response, may lead to significantly biased flood estimates. The paper proposes a new definition for storm events of random duration. It demonstrates that a joint probability description of design rainfall using these new storm events is quite feasible, and explores their potential for practical design flood estimation applications.

EM Laurenson

Papers

Monte Carlo Simulation of Flood Frequency Curves from Rainfall - the Way Ahead

Monte Carlo simulation of flood frequency curves from rainfall : the way ahead

Joint Probability Description of Design Rainfalls