Annual Streamflow Series Research Articles

CEREF: A hybrid data-driven model for forecasting annual streamflow from a socio-hydrological system

Hydrological forecasting is complicated by flow regime alterations in a coupled socio-hydrologic system, encountering increasingly non-stationary, nonlinear and irregular changes, which make decision support difficult for future water resources management. Currently, many hybrid data-driven models, based on the decomposition–prediction-reconstruction principle, have been developed to improve the ability to make predictions of annual streamflow. However, there exist many problems that require further investigation, the chief among which is the direction of trend components decomposed from annual streamflow series and is always difficult to ascertain. In this paper, a hybrid data-driven model was proposed to capture this issue, which combined empirical mode decomposition (EMD), radial basis function neural networks (RBFNN), and external forces (EF) variable, also called the CEREF model. The hybrid model employed EMD for decomposition and RBFNN for intrinsic mode function (IMF) forecasting, and determined future trend component directions by regression with EF as basin water demand representing the social component in the socio-hydrologic system. The Wuding River basin was considered for the case study, and two standard statistical measures, root mean squared error (RMSE) and mean absolute error (MAE), were used to evaluate the performance of CEREF model and compare with other models: the autoregressive (AR), RBFNN and EMD–RBFNN. Results indicated that the CEREF model had lower RMSE and MAE statistics, 42.8% and 7.6%, respectively, than did other models, and provided a superior alternative for forecasting annual runoff in the Wuding River basin. Moreover, the CEREF model can enlarge the effective intervals of streamflow forecasting compared to the EMD–RBFNN model by introducing the water demand planned by the government department to improve long-term prediction accuracy. In addition, we considered the high-frequency component, a frequent subject of concern in EMD-based forecasting, and results showed that removing high-frequency component is an effective measure to improve forecasting precision and is suggested for use with the CEREF model for better performance. Finally, the study concluded that the CEREF model can be used to forecast non-stationary annual streamflow change as a co-evolution of hydrologic and social systems with better accuracy. Also, the modification about removing high-frequency can further improve the performance of the CEREF model. It should be noted that the CEREF model is beneficial for data-driven hydrologic forecasting in complex socio-hydrologic systems, and as a simple data-driven socio-hydrologic forecasting model, deserves more attention.

Wavelet‐based time series bootstrap model for multidecadal streamflow simulation using climate indicators

AbstractA model to generate stochastic streamflow projections conditioned on quasi‐oscillatory climate indices such as Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO) is presented. Recognizing that each climate index has underlying band‐limited components that contribute most of the energy of the signals, we first pursue a wavelet decomposition of the signals to identify and reconstruct these features from annually resolved historical data and proxy based paleoreconstructions of each climate index covering the period from 1650 to 2012. A K‐Nearest Neighbor block bootstrap approach is then developed to simulate the total signal of each of these climate index series while preserving its time‐frequency structure and marginal distributions. Finally, given the simulated climate signal time series, a K‐Nearest Neighbor bootstrap is used to simulate annual streamflow series conditional on the joint state space defined by the simulated climate index for each year. We demonstrate this method by applying it to simulation of streamflow at Lees Ferry gauge on the Colorado River using indices of two large scale climate forcings: Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO), which are known to modulate the Colorado River Basin (CRB) hydrology at multidecadal time scales. Skill in stochastic simulation of multidecadal projections of flow using this approach is demonstrated.

Estimating distribution parameters of annual maximum streamflows in Johor, Malaysia using TL-moments approach

TL-moments approach has been used in an analysis to identify the best-fitting distributions to represent the annual series of maximum streamflow data over seven stations in Johor, Malaysia. The TL-moments with different trimming values are used to estimate the parameter of the selected distributions namely: Three-parameter lognormal (LN3) and Pearson Type III (P3) distribution. The main objective of this study is to derive the TL-moments (t1,0), t1 = 1,2,3,4 methods for LN3 and P3 distributions. The performance of TL-moments (t1,0), t1 = 1,2,3,4 was compared with L-moments through Monte Carlo simulation and streamflow data over a station in Johor, Malaysia. The absolute error is used to test the influence of TL-moments methods on estimated probability distribution functions. From the cases in this study, the results show that TL-moments with four trimmed smallest values from the conceptual sample (TL-moments [4, 0]) of LN3 distribution was the most appropriate in most of the stations of the annual maximum streamflow series in Johor, Malaysia.

Return period and risk analysis of nonstationary low-flow series under climate change

Summary Return period and risk of extreme hydrological events are critical considerations in water resources management. The stationarity assumption of extreme events for conducting hydrological frequency analysis to estimate return period and risk is now problematic due to climate change. Two different interpretations of return period, i.e. the expected waiting time (EWT) and expected number of exceedances (ENE), have already been proposed in literature to consider nonstationarity in return period and risk analysis by introducing the time-varying moment method into frequency analysis, under the assumption that the statistical parameters are functions only of time. This paper aimed at improving the characterization of nonstationary return period and risk under the ENE interpretation by employing meteorological covariates in the nonstationary frequency analysis. The advantage of the method is that the downscaled meteorological variables from the General Circulation Models (GCMs) can be used to calculate the nonstationary statistical parameters and exceedance probabilities for future years and thus the corresponding return period and risk. The traditional approach using time as the only covariate under both the EWT and ENE interpretations was also applied for comparison. Both approaches were applied to annual minimum monthly streamflow series of two stations in the Wei River, China, and gave estimates of nonstationary return period and risk that were significantly different from the stationary case. The nonstationary return period and risk under the ENE interpretation using meteorological covariates were found more reasonable and advisable than those of the EWT and ENE cases using time alone as covariate. It is concluded that return period and risk analysis of nonstationary low-flow series can be helpful to water resources management during dry seasons exacerbated by climate change.

Linkages between hydrological drought, climate indices and human activities: a case study in the Columbia River basin

It is of great importance to investigate links between hydrological drought and climate indices, which helps to further reveal the cause of hydrological drought from a perspective of climate change, thus helping guiding future drought prediction and control. For a case study in the Columbia River basin, the Standardized Streamflow Index (SSI) was employed to characterize hydrological drought. The heuristic segmentation method was applied to identify change points of annual streamflow series spanning 1960–2012 in the Columbia River basin, and the cross-wavelet analysis was utilized to reveal the correlations between monthly climate indices and SSI. The primary results are as following: (1) monthly SSI has a statistically significantly increasing trend in November and December and a noticeably decreasing trend in June and July in the main stream of the basin; (2) generally, hydrological drought risk in this basin is high, and that in the Snake River is higher than the main stream of the Columbia River; (3) El Niño Southern Oscillation (ENSO) and Arctic Oscillation (AO) play a major role in affecting hydrological drought in the Columbia River basin, and ENSO index mainly affects SSI at a relatively short time scale (2–7 years), while AO primarily impacts SSI at a relatively long time scale (more than 10 years); (4) anthropogenic activities intensify hydrological drought in the Columbia River basin, and they primarily influence the linkages between climate indices and hydrological drought at intra-annual scale (less than 12 months), however, which do not change the basic pattern of their correlations.

Multi-scale analysis of streamflow using the Hilbert-Huang Transform

Purpose– The purpose of this paper is to simulate and analyze accurately the multi-scale characteristics, variation periods and trends of the annual streamflow series in the Haihe River Basin (HRB) using the Hilbert-Huang Transform (HHT).Design/methodology/approach– The Empirical Mode Decomposition (EMD) approach is adopted to decompose the original signal into intrinsic mode functions (IMFs) in multi-scales. The Hilbert spectrum is applied to each IMF component and the localized time-frequency-energy distribution. The monotonic residues obtained by EMD can be treated as the trend of the original sequence.Findings– The authors apply HHT to 14 hydrological stations in the HRB. The annual streamflow series are decomposed into four IMFs and a residual component, which exhibits the multi-scale characteristics. After the Hilbert transform, the instantaneous frequency, center frequency and mean period of the IMFs are obtained. Common multi-scale periods of the 14 series exist, e.g. 3.3a, 4∼7a, 8∼10a, 11-14a, 24∼25a and 43∼45a. The residues indicate that the annual streamflow series has exhibited a decreasing trend over the past 50 years.Research limitations/implications– The HHT method is still in its early stages of application in hydrology and needs to be further tested.Practical implications– It is helpful for the study of the complex features of streamflow.Social implications– This paper will contribute to the sustainable utilization of water resources.Originality/value– This study represents the first use of the HHT method to analyze the multi-scale characteristics of the streamflow series in the HRB. This paper provides an important theoretical support for water resources management.

Sample entropy‐based adaptive wavelet de‐noising approach for meteorologic and hydrologic time series

AbstractDe‐noising meteorologic and hydrologic time series is important to improve the accuracy and reliability of extraction, analysis, simulation, and forecasting. A hybrid approach, combining sample entropy and wavelet de‐noising method, is developed to separate noise from original series and is named as AWDA‐SE (adaptive wavelet de‐noising approach using sample entropy). The AWDA‐SE approach adaptively determines the threshold for wavelet analysis. Two kinds of meteorologic and hydrologic data sets, synthetic data set and 3 representative field measured data sets (one is the annual rainfall data of Jinan station and the other two are annual streamflow series from two typical stations in China, Yingluoxia station on the Heihe River, which is little affected by human activities, and Lijin station on the Yellow River, which is greatly affected by human activities), are used to illustrate the approach. The AWDA‐SE approach is compared with three conventional de‐noising methods, including fixed‐form threshold algorithm, Stein unbiased risk estimation algorithm, and minimax algorithm. Results show that the AWDA‐SE approach separates effectively the signal and noise of the data sets and is found to be better than the conventional methods. Measures of assessment standards show that the developed approach can be employed to investigate noisy and short time series and can also be applied to other areas.

Quantitative assessment of climate and human impacts on surface water resources in a typical semi‐arid watershed in the middle reaches of the Yellow River from 1985 to 2006

ABSTRACTThe surface water resources of a typical semi‐arid watershed (Huangfuchuan) in the middle reaches of the Yellow River have drastically decreased over the past decade, which has affected the governance strategies of the entire Yellow River. The causes of the decrease in surface water are generally attributed to climate fluctuations and human activities. In this study, a distributed biosphere hydrological model the Water and Energy Budget‐based Distributed Hydrological Model (WEB‐DHM) and a Contribution Assessment method were jointly applied to diagnose and quantify climate and human impacts on the streamflow change. Long‐term hydrometeorological trends were analysed first and one major change‐point (in 1998) in the annual streamflow series was identified through the nonparametric Mann–Kendall test and the annual precipitation‐streamflow double cumulative curve method. The WEB‐DHM model was calibrated and validated over the baseline period of 1985–1998; the natural streamflow was reconstructed for the impacted period of 1999–2006. Then, the contributions of climate fluctuations and human activities to streamflow change were determined quantitatively by comparing the natural streamflow with the observed value. The mean annual streamflow significantly decreased from 34.05 mm year−1 to 13.72 mm year−1 in the baseline and impacted periods, respectively, showing a reduction of 60%. Climate fluctuations accounted for a decrease in mean annual streamflow of approximately 10.38 mm year−1 (51.03%), whereas human activities (including soil–water conservation measures, artificial water intakes and man‐made water storage infrastructure) caused a decrease of approximately 9.96 mm year−1 (48.97%). These findings are potentially helpful to support the water resources planning and management in the middle reaches of the Yellow River.

Effects of Climate Variations and Human Activities on Runoff in the Zoige Alpine Wetland in the Eastern Edge of the Tibetan Plateau

The Zoige alpine wetland on the eastern edge of the Tibetan Plateau is an important headwater area for the Yellow River Basin. The White and Black Rivers are two major tributaries in the Zoige Basin. However, the alpine wetland has experienced a rapid degradation due to human and other recent environmental changes in the region. The effects of climate variations and human activities on runoff in this region are still unclear. In this study, those changes in runoff were quantified and categorized using the hydrologic sensitivity analysis method and a monthly water balance model. The temperature index-based snow melting submodel was integrated into a monthly water balance model to account for the considerable snow meltwater from the wetland in the summer season. The nonparametric Mann-Kendall test was used to analyze the annual and seasonal climatic trends in the Zoige Basin. Results suggest that during the past 55 years (1957–2011), annual precipitation was significantly decreasing at a rate of −0.978 mm/year while the air temperature and potential evapotranspiration (PET) have increasing trends at the rates of 0.029°C/year and 0.755 mm/year, respectively. Using three change-point detection methods, one change point was detected at 1989 in the annual streamflow series (1960–2011) and was adopted to divide the data set into two study periods—the baseline period (1960–1989) and the human-induced period (1990–2011). The mean annual runoff depth from the White (Black) River in the baseline period was 448.9 mm (151.5 mm), while the mean of the human-induced period decreased by 28% (35%). It was determined that decreases in runoff between the two periods can be attributed to 55% (64%) from climate variations and 45% (36%) from human activities in the White River (Black River). Thus, climatic impact exerted more important influence on runoff decline in the Zoige wetland basin as compared to human activities. This study enhances our understanding of the changes caused by climate variations and runoff (and their contributing factors) in the alpine wetland.

Analysis of changes in the relationship between precipitation and streamflow in the Yiluo River, China

The Yiluo River is the largest tributary of the middle and lower Yellow River below the Sanmenxia Dam. Hydro-climatic variables have changed in the Yiluo River during the last half century. In this study, the trends in the annual precipitation and streamflow were analyzed in the Yiluo River during 1960–2006. The results indicated that both the annual precipitation and streamflow decreased significantly (P < 0.05) from 1960 to 2006. Pettitt’s test shows that there was a change point for annual streamflow series around the year 1986 (P < 0.05), while there was no change point identified for the annual precipitation series from 1960 to 2006. Annual streamflow decreased more significantly than annual precipitation since 1986. The relationship between the annual precipitation and streamflow presented a non-stationary state since 1986. This non-stationary relationship was mainly influenced by human activities. The average annual amount of water diversion from the Yiluo River increased significantly since the mid-1980s, accounting for 31.3 % of the total streamflow decrease from 1986 to 2006. In addition, land use/cover change (LUCC) contributed to 27.1–29.8 % of the decrease in streamflow. Human activities, including water diversion and LUCC, together contributed to 58.4–61.1 % of the decrease in streamflow and led to the non-stationary relationship between the annual precipitation and streamflow from 1986 to 2006. This study detected the changes in the precipitation–streamflow relationship and investigated the possible causes in the Yiluo River, which will be helpful for the understanding of the changes in streamflow in the Yellow River Basin.

Hydrological Design of Nonstationary Flood Extremes and Durations in Wujiang River, South China: Changing Properties, Causes, and Impacts

The flood-duration-frequency (QDF) analysis is performed using annual maximum streamflow series of 1–10 day durations observed at Pingshi and Lishi stations in southern China. The trends and change point of annual maximum flood flow and flood duration are also investigated by statistical tests. The results indicate that (1) the annual maximum flood flow only has a marginally increasing trend, whereas the flood duration exhibits a significant decreasing trend at the 0.10 significant level. The change point for the annual maximum flood flow series was found in 1991 and after which the mean maximum flood flow increased by 45.26%. (2) The period after 1991 is characterized by frequent and shorter duration floods due to increased rainstorm. However, land use change in the basin was found intensifying the increased tendency of annual maximum flow after 1991. And (3) under nonstationary environmental conditions, alternative definitions of return period should be adapted. The impacts on curve fitting of flood series showed an overall change of upper tail from “gentle” to “steep,” and the design flood magnitude became larger. Therefore, a nonstationary frequency analysis taking account of change point in the data series is highly recommended for future studies.

Trend and change-point detection for the annual stream-flow series of the Karun River at the Ahvaz hydrometric station

Karun River watershed located in southwest of Iran experiences great changes in the last decade due to hydro climatic changes, large-scale land use and land cover changes, construction of dams and agricultural and industrial development. Stream-flow series of the annual maximum, annual minimum and annual mean in Ahvaz hydrometric station as representative of the watershed have been considered. In order to determine the change points, we use the Pettitt test while the trend in the annual stream-flow series of this station is evaluated by the Mann-Kendall test. However, the Pettitt test cannot detect any change point in these series, but the Mann-Kendall test shows that there is an increasing trend. This increasing trend has no fitness with observed data in recent decade. Therefore, the potential change points were determined and consequently, these series converted to two sub-series based on the results obtained from the Pettitt test, wide variation from human activities and variation of hydro climatic conditions. We then applied the Mann-Kendall test in these two sub-series which showed significant decreasing trend in both of them. From this method, it can be concluded that the averages of the second sub-series are larger than the first one in the three annual stream-flow series. This increasing ratio is equal to 1.34, 1.16 and 1.2 for stream-flow series of annual maximum, annual minimum and annual mean respectively. These changes are similar to changes in annual rainfall time series. We can say that the sudden increase of precipitation in recent decades makes the averages of the second sub-series larger. Results showed that inspite of wide range human induced changes, stream-flow series is more affected from the watershed rainfall time series variations. In addition, significant decreasing trend in the two sub-series can be due to the following causes: the growth of population, temperature rise, construction of three dams on the Karun River, implementing the different projects for developing agricultural, and conservation from soil and water resources. Key words: Pettit test, Mann-kendall test, annual stream-flow series, Ahvaz hydrometric station.

An analysis of annual maximum streamflows in Terengganu, Malaysia using TL-moments approach

TL-moments approach has been used in an analysis to determine the best-fitting distributions to represent the annual series of maximum streamflow data over 12 stations in Terengganu, Malaysia. The TL-moments with different trimming values are used to estimate the parameter of the selected distributions namely: generalized pareto (GPA), generalized logistic, and generalized extreme value distribution. The influence of TL-moments on estimated probability distribution functions are examined by evaluating the relative root mean square error and relative bias of quantile estimates through Monte Carlo simulations. The boxplot is used to show the location of the median and the dispersion of the data, which helps in reaching the decisive conclusions. For most of the cases, the results show that TL-moments with one smallest value was trimmed from the conceptual sample (TL-moments (1,0)), of GPA distribution was the most appropriate in majority of the stations for describing the annual maximum streamflow series in Terengganu, Malaysia.

Disaggregation modelling of monthly streamflows using a new approach of the method of fragments

The method of fragments is applied to the generation of synthetic monthly streamflow series using streamflow data from 34 gauging stations in mainland Portugal. A generation model based on the random sampling of the log-Pearson Type III distribution was applied to each sample to generate 1200 synthetic series of annual streamflow with an equal length to that of the sample. The synthetic annual streamflow series were then disaggregated into monthly streamflows using the method of fragments, by three approaches that differed in terms of the establishment of classes and the selection of fragments. The results of the application of such approaches were compared in terms of the capacity of the method to preserve the main monthly statistical parameters of the historical samples. Editor D. Koutsoyiannis; Associate editor C. Onof Citation Silva, A.T. and Portela, M.M., 2012. Disaggregation modelling of monthly streamflows using a new approach of the method of fragments. Hydrological Sciences Journal, 57 (5), 942–955.

Markov Chain Models for Hydrological Drought Characteristics

Abstract Estimation of drought characteristics such as probabilities and return periods of droughts of various lengths is of major importance in drought forecast and management and in solving water resources problems related to water quality and navigation. This study aims at applying first- and second-order Markov chain models to dry and wet periods of annual streamflow series to reproduce the stochastic structure of hydrological droughts. Statistical evaluation of drought duration and intensity is usually carried out using runs analysis. First-order Markov chain model (MC1) for dry and wet periods is not adequate when autocorrelation of the original hydrological series is high. A second-order Markov chain model (MC2) is proposed to estimate the probabilities and return periods of droughts. Results of these models are compared with those of a simulation study assuming a lag-1 autoregressive [AR(1)] process widely used to model annual streamflows. Probability distribution and return periods of droughts of various lengths are estimated and compared with the results of MC1 and MC2 models using efficacy evaluation statistics. It is found that the MC2 model in general gives results that are in better agreement with simulation results as compared with the MC1 model. Skewness is found to have little effect on return periods except when autocorrelation is very high. MC1 and MC2 models are applied to droughts observed in some annual streamflow series, with the result that the MC2 model has a relatively good agreement considering the limited duration of the records.

Block bootstrap for Mann–Kendall trend test of serially dependent data

AbstractMann–Kendall (MK) test for trend detection must be modified when the data are serially correlated, to prevent the detection of false trends. Various approaches are developed for this purpose, such as prewhitening, trend‐free prewhitening, variance correction and block bootstrap. Each method has its own Type I and Type II errors. In this study, the errors of block bootstrapping MK test are estimated by a simulation study and compared with other methods. Optimal block length that minimizes the Type I error is determined as function of sample size and autocorrelation coefficient. It is shown that the power of block bootstrapping MK test is comparable with those of other modified MK tests. These tests are applied to some annual streamflow series with trend recorded in Turkish rivers, and their powers are compared. A modified form of the trend‐free prewhitening procedure is proposed that has a smaller Type I error. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Homogeneity and Trend Analysis of Hydrometeorological Data of the Eastern Black Sea Region, Turkey

Eastern Black Sea Region in northeastern part of Turkey has the highest precipitation total in the country, approaching 2500 mm per a year. It is therefore an important region as it frequently encounters with flash floods due to heavy rains. For future planning of water resources, environment and urbanization, it is important to know the expected behavior of hydrometeorological processes, mainly precipitation and flow. Due to these facts, in this study, homogeneity of long-term annual precipitation and streamflow series of the Eastern Black Sea Region, Turkey is checked using double mass curve method and trends are determined by means of the Mann-Kendall test. The data network consists of 38 precipitation gauging stations and 40 flow gauging stations across the Eastern Black Sea Region. It is found that 27 precipitation stations out of 38 are homogeneous and no trend is available. Out of the remaining stations, nine are found non-homogeneous and four with trend. For annual flow data, it is found that 22 stations out of 40 are homogeneous and no trend is available. The remaining 18 stations are found non-homogeneous, among which 5 stations have trend at the same time.

Wavelet transform‐based analysis of periodicities and trends of Sakarya basin (Turkey) streamflow data

AbstractIn this study, the wavelet transform and the Mann–Kendall test are used to determine possible trends in annual streamflow series. The wavelet analysis provides detailed information about the time‐frequency contents of the data. Using wavelet components of the original data, it was aimed to find which periodicities are mainly responsible for a trend in the original data. Also, the global wavelet spectra and the continuous wavelet transform (CWT) were used for the analysis of the streamflow data, in order to explain its time‐frequency characteristics. Annual streamflow series across Turkey were used for the detection of trends for the original data and the periodic wavelet components (obtained by discrete wavelet transform). It was found that some periodic events clearly affect the trend in the streamflow series. The DW4 component (16‐yearly periodic component) at the stations of the Sakarya basin is the effective periodic component and is responsible for producing a real trend in the data. The effects of regional differences on the wavelet‐trend analysis are studied using records of the stations located in different climate areas. DW2 (4‐yearly component) and DW3 (8‐yearly component) are the dominant periodic components of this data. This study aims to explain the trend structure in the data. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Streamflow Trends and Climate Variability Impacts in Poyang Lake Basin, China

Under the background of global warming, does the effect of the rising global surface temperature accelerate the hydrological cycle? To address this issue, we use the hydro-climatic data from five sub-basins in Poyang Lake basin in the southeast China over the past 50 years, to investigate the annual and seasonal trends of streamflow and the correlations between streamflow and climatic variables. The Theil–Sen Approach and the non-parametric Mann–Kendall test are applied to identify the trends in the annual and seasonal streamflow, precipitation and evapotranspiration series. It was found that annual and seasonal streamflow of all the stations had increasing trends except Lijiadu station in wet season. Only 37.5% hydro-stations in annual streamflow increased significantly, while most stations increased at 95% significance level in dry season. Trends in annual and seasonal precipitation during the whole period were generally not as significant as those in evapotranspiration. The correlations between streamflow and climate variables (precipitation and evapotranspiration) were detected by the Pearson’s test. The results showed that streamflow in the Poyang Lake basin are more sensitive to changes in precipitation than potential evapotranspiration.

A Bayesian method for multi-site stochastic data generation: Dealing with non-concurrent and missing data, variable transformation and parameter uncertainty

Stochastically generated stream flow and climatic data may be used as input to water resources simulation models for planning purposes. Dealing with non-concurrent and missing data, variable transformation and parameter uncertainty presents a significant challenge in the development of methods for stochastic data generation. In this paper, a Bayesian method is introduced for multi-site stochastic generation of annual stream flow and climatic data. A contemporaneous autoregressive lag-one model CAR(1) with the Box–Cox transformation is used to capture key statistical structure of multiple annual stream flow and climatic time series while keeping the number of model parameters to a minimum. The posterior joint distribution of the model parameters is formulated, allowing for inputs of historical data series that are not continuous or concurrent, thus avoiding the need to infill or truncate data records and maximising the value of available data. Parameter and uncertainty inference are solved numerically by using Markov Chain Monte Carlo simulations. Subsequent stochastic generation of data fully accounts for parameter uncertainty. In addition, a re-parameterization scheme is used to handle the problem of strong inter-parameter dependence from the Box–Cox transformation. The method was applied to the Melbourne Water supply system to demonstrate its computational feasibility.