Comparative analysis of predictive methods for drought durations: a case of monthly and annual streamflow droughts in Atlantic Canada

Methods based on the recursive probability, the extreme number theorem, and Markov chain (MC) concepts were applied to predict drought lengths (duration) on the standardized (termed as standardized hydrological index, SHI) sequences of monthly and annual river flows from Atlantic Canada. Results of the study indicated that the MC-based method is the most efficient, reliable and versatile method for predicting drought durations followed by the extreme-number-based method. The recursive-probability-based method was found to be computationally intensive and less efficient, although it provided a powerful means for calibrating the empirical plotting position formula needed in the MC-based method. The Weibull plotting position formula turned out to be a suitable measure of the exceedance probability in MC methodology for predicting drought lengths in Atlantic Canada. Based on results, it can be inferred that the MC-based method can be extended to MC2 and higher-order chains for predicting drought lengths on SHI sequences. The predictive capability of the extreme-number-theorem-based method is limited only to independent or weakly first-order persistent SHI sequences.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR Q. Zhang     

Predicting return periods of hydrological droughts using the Pearson 3 distribution: a case from rivers in the Canadian prairies

Abstract

The standardized series of monthly and weekly flow sequences, referred to as standardized hydrological index (SHI) series, from five rivers in the Canadian prairies were subjected to return period (T_r) analysis of drought length (L). The SHI series were truncated at drought probability levels q ranging from 0.5 to 0.05 with the intention of deducing drought events and corresponding drought lengths. The values of L were fitted to the Pearson 3, the gamma (2-parameter), the exponential (1-parameter), the Weibull 3 and the Weibull (2-parameter) probability density functions (pdfs). A priori assignment of one week or one month for the location parameter in the Pearson 3 pdf proved logical and also facilitated the rapid estimation of other parameters using either the method of moments or the method of maximum likelihood. The Pearson 3 turns out to be the most suitable pdf to describe and to estimate return periods of drought lengths. At the monthly and weekly time scales, it was inferred that the sample size (T, months or weeks) of SHI series could be treated equivalent to the return period of the largest recorded drought length. At the annual time scale, however, the sample size (T, years) should be modified using either the Hazen or the Gringorten plotting position formula to reflect the actual return period of the largest recorded drought length in years.

Editor D. Koutsoyiannis; Associate editor E. Gargouri     

A semi-empirical method for predicting hydrological drought magnitudes in the Canadian prairies

Abstract

A hydrological drought magnitude (M _T ) expressed in standardized terms is predicted on annual, monthly and weekly time scales for a sampling period of T years in streamflow data from the Canadian prairies. The drought episodes are considered to follow the Poisson law of probability and, when coupled with the gamma probability distribution function (pdf) of drought magnitude (M) in the extreme number theorem, culminate in a relationship capable of evaluating the expected value, E(M _T ). The parameters of the underlying pdf of M are determined based on the assumption that the drought intensity follows a truncated normal pdf. The E(M _T ) can be evaluated using only standard deviation (σ), lag-1 autocorrelation (ρ) of the standardized hydrological index (SHI) sequence, and a weighting parameter Φ (ranging from 0 to 1) to account for the extreme drought duration (L _T ), as well as the mean drought duration (L_m ), in a characteristic drought length (L_c ). The SHI is treated as standard normal variate, equivalent to the commonly-used standardized precipitation index. A closed-form relationship can be used for the estimation of first-order conditional probabilities, which can also be estimated from historical streamflow records. For all rivers, at the annual time scale, the value of Φ was found equal to 0.5, but it tends to vary (in the range 0 to 1) from river to river at monthly and weekly time scales. However, for a particular river, the Φ value was nearly constant at monthly and weekly time scales. The proposed method estimates E(M _T ) satisfactorily comparable to the observed counterpart. At the annual time scale, the assumption of a normal pdf for drought magnitude tends to yield results in close proximity to that of a gamma pdf. The M _T , when transformed into deficit-volume, can form a basis for designing water storage facilities and for planning water management strategies during drought periods.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Sharma, T.C. and Panu, U.S., 2013. A semi-empirical method for predicting hydrological drought magnitudes in the Canadian prairies. Hydrological Sciences Journal, 58 (3), 549–569.     

Drought analysis of monthly hydrological sequences: a case study of Canadian rivers

Abstract

Two parameters of importance in hydrological droughts viz. the longest duration, L_T and the largest severity, S_T (in standardized form) over a desired return period, T years, have been analysed for monthly flow sequences of Canadian rivers. An important point in the analysis is that monthly sequences are non-stationary (periodic-stochastic) as against annual flows, which fulfil the conditions of stochastic stationarity. The parameters mean, μ, standard deviation, σ (or coefficient of variation), lag1 serial correlation, ρ, and skewness, γ (which is helpful in identifying the probability distribution function) of annual flow sequences, when used in the analytical relationships, are able to predict expected values of the longest duration, E(L_T ) in years and the largest standardized severity, E(S_T ). For monthly flow sequences, there are 12 sets of these parameters and thus the issue is how to involve these parameters to derive the estimates of E(L_T ) and E(S_T ). Moreover, the truncation level (i.e. the monthly mean value) varies from month to month. The analysis in this paper demonstrates that the drought analysis on an annual basis can be extended to monthly droughts simply by standardizing the flows for each month. Thus, the variable truncation levels corresponding to the mean monthly flows were transformed into one unified truncation level equal to zero. The runs of deficits in the standardized sequences are treated as drought episodes and thus the theory of runs forms an essential tool for analysis. Estimates of the above parameters (denoted as μ_av, σ_av, ρ_av, and γ_av) for use in the analytical relationships were obtained by averaging 12 monthly values for each parameter. The product- and L-moment ratio analyses indicated that the monthly flows in the Canadian rivers fit the gamma probability distribution reasonably well, which resulted in the satisfactory prediction of E(L_T ). However, the prediction of E(S_T ) tended to be more satisfactory with the assumption of a Markovian normal model and the relationship E(S_T ) ≈ E(L_T ) was observed to perform better.     

Prediction of hydrological drought durations based on Markov chains: case of the Canadian prairies

Abstract

Hydrological drought durations (lengths) in the Canadian prairies were modelled using the standardized hydrological index (SHI) sequences derived from the streamflow series at annual, monthly and weekly time scales. The rivers chosen for the study present high levels of persistence (as indicated by values exceeding 0.95 for lag-1 autocorrelation in weekly SHI sequences), because they encompass large catchment areas (2210–119 000 km²) and traverse, or originate in, lakes. For such rivers, Markov chain models were found to be simple and efficient tools for predicting the drought duration (year, month, or week) based on annual, monthly and weekly SHI sequences. The prediction of drought durations was accomplished at threshold levels corresponding to median flow (Q50) (drought probability, q?=?0.5) to Q95 (drought probability, q?=?0.05) exceedence levels in the SHI sequences. The first-order Markov chain or the random model was found to be acceptable for the prediction of annual drought lengths, based on the Hazen plotting position formula for exceedence probability, because of the small sample size of annual streamflows. On monthly and weekly time scales, the second-order Markov chain model was found to be satisfactory using the Weibull plotting position formula for exceedence probability. The crucial element in modelling drought lengths is the reliable estimation of parameters (conditional probabilities) of the first- and second-order persistence, which were estimated using the notions implicit in the discrete autoregressive moving average class of models. The variance of drought durations is of particular significance, because it plays a crucial role in the accurate estimation of persistence parameters. Although, the counting method of the estimation of persistence parameters was found to be unsatisfactory, it proved useful in setting the initial values and also in subsequent adjustment of the variance-based estimates of persistence parameters. At low threshold levels corresponding to q < 0.20, even the first-order Markov chain can be construed as a satisfactory model for predicting drought durations based on monthly and weekly SHI sequences.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Sharma, T.C. and Panu, U.S., 2012. Prediction of hydrological drought durations based on Markov chains in the Canadian prairies. Hydrological Sciences Journal, 57 (4), 705–722.     

Effects of the Three Gorges Reservoir on the hydrological droughts at the downstream Yichang station during 2003–2011

Since the Three Gorges Reservoir (TGR) was put into operation in June 2003, the effects of the TGR on downstream hydrology and water resources have become the focus of public attention. This article examines the effects of the TGR on the hydrological droughts at the downstream Yichang hydrological station during 2003–2011. The two‐parameter monthly water balance model was used to generate the monthly discharges at the Yichang station for the period of 2003–2011 to represent the unregulated flow regime and thus to provide a comparison benchmark for the observed flow series at the Yichang station after the operation of the TGR. To provide a reference series for the observed monthly discharge series of the entire study period of 1951–2011, we constructed the naturalized monthly discharge series at the Yichang station by joining the observed monthly discharge at the Yichang station for the period of 1951–2002 and the two‐parameter monthly water balance simulated monthly runoff at the Yichang station for the period of 2003–2011. For both the observed and naturalized monthly discharge series of 1951–2011, the hydrological drought index series were calculated using the standardized streamflow index method. By comparing the drought indices of these two monthly discharge series, we investigated the effects of the TGR on the hydrological droughts at the downstream Yichang station during 2003–2011. The results show that the hydrological droughts at the downstream Yichang station are slightly aggravated by the TGR's initial operation from 2003 to 2011. The river flow reduction at the Yichang station after impoundment of the TGR might account for the downstream drought aggravation. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of four hydrological models for operational flood forecasting in a Canadian Prairie watershed

The complexities of the Prairie watersheds, including potholes, drainage interconnectivities, changing land-use patterns, dynamic watershed boundaries and hydro-meteorological factors, have made hydrological modelling on Prairie watersheds one of the most complex task for hydrologists and operational hydrological forecasters. In this study, four hydrological models (WATFLOOD, HBV-EC, HSPF and HEC-HMS) were developed, calibrated and tested for their efficiency and accuracy to be used as operational flood forecasting tools. The Upper Assiniboine River, which flows into the Shellmouth Reservoir, Canada, was selected for the analysis. The performance of the models was evaluated by the standard statistical methods: the Nash-Sutcliffe efficiency coefficient, correlation coefficient, root mean squared error, mean absolute relative error and deviation of runoff volumes. The models were evaluated on their accuracy in simulating the observed runoff for calibration and verification periods (2005–2015 and 1994–2004, respectively) and also their use in operational forecasting of the 2016 and 2017 runoff.     

Assessment of hydrological droughts for the Yellow River,China, using copulas

Droughts are one of the normal and recurrent climatic phenomena on Earth. However, recurring prolonged droughts have caused far‐reaching and diverse impacts because of water deficits. This study aims to investigate the hydrological droughts of the Yellow River in northern China. Since drought duration and drought severity exhibit significant correlation, a bivariate distribution is used to model the drought duration and severity jointly. However, drought duration and drought severity are often modelled by different distributions; the commonly used bivariate distributions cannot be applied. In this study, a copula is employed to construct the bivariate drought distribution. The copula is a function that links the univariate marginal distributions to form the bivariate distribution. The bivariate return periods are also established to explore the drought characteristics of the historically noticeable droughts. The results show that the return period of the drought that occurred in late 1920s to early 1930s is 105 years. The significant 1997 dry‐up phenomenon that occurred in the downstream Yellow River (resulting from the 1997–1998 drought) only has a return period of 4·4 years and is probably induced by two successive droughts and deteriorated by other factors, such as human activities. Copyright © 2007 John Wiley & Sons, Ltd.     

A framework for quantifying the impacts of climate change and human activities on hydrological drought in a semiarid basin of Northern China

Climate change and human activities are two major driving forces affecting the hydrologic cycle, which further influence the stationarity of the hydrologic regime. Hydrological drought is a substantial negative deviation from the normal hydrologic conditions affected by these two phenomena. In this study, we propose a framework for quantifying the effects of climate change and human activities on hydrological drought. First, trend analysis and change‐point test are performed to determine variations of hydrological variables. After that, the fixed runoff threshold level method (TLM) and the standardized runoff index (SRI) are used to verify whether the traditional assessment methods for hydrological drought are applicable in a changing environment. Finally, two improved drought assessment methods, the variable TLM and the SRI based on parameter transplantation are employed to quantify the impacts of climate change and human activities on hydrological drought based on the reconstructed natural runoff series obtained using the variable infiltration capacity hydrologic model. The results of a case study on the typical semiarid Laohahe basin in North China show that the stationarity of the hydrological processes in the basin is destroyed by human activities (an obvious change‐point for runoff series is identified in 1979). The traditional hydrological drought assessment methods can no longer be applied to the period of 1980–2015. In contrast, the proposed separation framework is able to quantify the contributions of climate change and human activities to hydrological drought during the above period. Their ranges of contributions to hydrological drought calculated by the variable TLM method are 20.6–41.2% and 58.8–79.4%, and the results determined by the SRI based on parameter transplantation method are 15.3–45.3% and 54.7–84.7%, respectively. It is concluded that human activities have a dominant effect on hydrological drought in the study region. The novelty of the study is twofold. First, the proposed method is demonstrated to be efficient in quantifying the effects of climate change and human activities on hydrological drought. Second, the findings of this study can be used for hydrological drought assessment and water resource management in water‐stressed regions under nonstationary conditions.     

The great 1983 floods in South American large rivers: a continental hydrological modelling approach

ABSTRACT

This study provides a spatio-temporal analysis of the great floods that occurred in South America in 1983 using hydrometeorological data and outputs from a continental-scale hydrological-hydrodynamic model. In the extreme year 1983, there were three main flooding periods (February, June and July) in many South American river basins, such as the Araguaia, Tocantins, São Francisco, Uruguay, La Plata and its tributaries, resulting in high discharge of the Paraguay River for many months. Depth–area–duration curves show that 3-day precipitation events in northern regions of South America were among the largest 15 events in the period 1980–2015 but only for specific locations, whereas in southern areas, the most extreme events in the same period were for larger durations (≥7-day precipitation). Modelled total export of water volume to the oceans indicates that rivers draining to the South Atlantic reached an anomaly of 3.7 during 1983, followed by 1998 (1.9) and 1992 (1.1), all of them corresponding to El Niño years.     

Validation of hydrological models for climate scenario simulation: the case of Saguenay watershed in Quebec

This paper presents the results of an investigation into the problems associated with using downscaled meteorological data for hydrological simulations of climate scenarios. The influence of both the hydrological models and the meteorological inputs driving these models on climate scenario simulation studies are investigated. A regression‐based statistical tool (SDSM) is used to downscale the daily precipitation and temperature data based on climate predictors derived from the Canadian global climate model (CGCM1), and two types of hydrological model, namely the physically based watershed model WatFlood and the lumped‐conceptual modelling system HBV‐96, are used to simulate the flow regimes in the major rivers of the Saguenay watershed in Quebec. The models are validated with meteorological inputs from both the historical records and the statistically downscaled outputs. Although the two hydrological models demonstrated satisfactory performances in simulating stream flows in most of the rivers when provided with historic precipitation and temperature records, both performed less well and responded differently when provided with downscaled precipitation and temperature data. By demonstrating the problems in accurately simulating river flows based on downscaled data for the current climate, we discuss the difficulties associated with downscaling and hydrological models used in estimating the possible hydrological impact of climate change scenarios. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of land-use/cover change on hydrological processes using a GIS/RS-based integrated hydrological model: case study of the East River,China

Abstract

An integrated model, combining a surface energy balance system, an LAI-based interception model and a distributed monthly water balance model, was developed to predict hydrological impacts of land-use/land-cover change (LUCC) in the East River basin, China, with the aid of GIS/RS. The integrated model is a distributed model that not only accounts for spatial variations in basin terrain, rainfall and soil moisture, but also considers spatial and temporal variation of vegetation cover and evapotranspiration (ET), in particular, thus providing a powerful tool for investigating the hydrological impact of LUCC. The model was constructed using spatial data on topography, soil types and vegetation characteristics together with time series of precipitation from 170 stations in the basin. The model was calibrated and validated based on river discharge data from three stations in the basin for 21 years. The calibration and validation results suggested that the model is suitable for application in the basin. The results show that ET has a positive relationship with LAI (leaf area index), while runoff has a negative relationship with LAI in the same climatic zone that can be described by the surface energy balance and water balance equation. It was found that deforestation would cause an increase in annual runoff and a decrease in annual ET in southern China. Monthly runoff for different land-cover types was found to be inversely related to ET. Also, for most of the scenarios, and particularly for grassland and cropland, the most significant changes occurred in the rainy season, indicating that deforestation would cause a significant increase in monthly runoff in that season in the East River basin. These results are important for water resources management and environmental change monitoring.

Editor Z.W. Kundzewicz     

Detection of trends in hydrological extremes for Canadian watersheds

The potential impacts of climate change can alter the risk to critical infrastructure resulting from changes to the frequency and magnitude of extreme events. As well, the natural environment is affected by the hydrologic regime, and changes in high flows or low flows can have negative impacts on ecosystems. This article examines the detection of trends in extreme hydrological events, both high and low flow events, for streamflow gauging stations in Canada. The trend analysis involves the application of the Mann–Kendall non‐parametric test. A bootstrap resampling process has been used to determine the field significance of the trend results. A total of 68 gauging stations having a nominal record length of at least 50 years are analysed for two analysis periods of 50 and 40 years. The database of Canadian rivers investigated represents a diversity of hydrological conditions encompassing different extreme flow generating processes and reflects a national scale analysis of trends. The results reveal more trends than would be expected to occur by chance for most of the measures of extreme flow characteristics. Annual and spring maximum flows show decreasing trends in flow magnitude and decreasing trends in event timing (earlier events). Low flow magnitudes exhibit both decreasing and increasing trends. Copyright © 2010 John Wiley & Sons, Ltd.     

The droughts of 1996–1997 and 2004–2005 in Amazonia: hydrological response in the river main‐stem

Severe hydrological droughts in the Amazon have generally been associated with strong El Niño events. More than 100 years of stage record at Manaus harbour confirms that minimum water levels generally coincide with intense warming in the tropical Pacific sea waters. During 2005, however, the Amazon experienced a severe drought which was not associated with an El Niño event. Unless what usually occurs during strong El Niño events, when negative rainfall anomalies usually affect central and eastern Amazon drainage basin; rainfall deficiencies in the drought of 2005 were spatially constrained to the west and southwest of the basin. In spite of this, discharge stations at the main‐stem recorded minimum water levels as low as those observed during the basin‐wide 1996–1997 El Niño‐related drought. The analysis of river discharges along the main‐stem and major tributaries during the drought of 2004–2005 revealed that the recession on major tributaries began almost simultaneously. This was not the case in the 1996–1997 drought, when above‐normal contribution of some tributaries for a short period during high water was crucial to partially counterbalance high discharge deficits of the other tributaries. Since time‐lagged contributions of major tributaries are fundamental to damp the extremes in the main‐stem, an almost coincident recession in almost all tributaries caused a rapid decrease in water discharges during the 2005 event. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical solutions for transport of decaying solutes in rivers with transient storage

Analytical solutions are presented for solute transport in rivers including the effects of transient storage and first order decay. The solute transport model considers an advection–dispersion equation for transport in the main channel linked to a first order mass exchange between the main channel and the transient storage zones. In case of a conservative tracer, it is shown that different analytical solutions presented in the literature are mathematically identical. For non-conservative solutes, first order decay reactions are considered with different reaction rate coefficients in the main river channel and in the dead zones. New analytical solutions are presented for different boundary conditions, i.e. instantaneous injection in an infinite river reach, and variable concentration time series input in a semi-infinite river reach. The correctness and accuracy of the analytical solutions is verified by comparison with the OTIS numerical model. The results of analytical and numerical approaches compare favourably and small differences can be attributed to the influence of boundary conditions. It is concluded that the presented analytical solutions for solute transport in rivers with transient storage and solute decay are accurate and correct, and can be usefully applied for analyses of tracer experiments and transport characteristics in rivers with mass exchange in dead zones.     

Precipitation as a proxy for climate variables: application for hydrological modelling

It has been proposed that linear regression curves can be used to estimate monthly climate variables from observed precipitation. This approach was explored by applying the MGB hydrological model to the Paraná Basin (Brazil). Linear regressions were obtained for 54 climate gauges, and most of them showed at least six months of significant correlation between monthly climate variables (sunlight hours and relative humidity) and precipitation. The regression equations were applied to 5201 raingauges to estimate monthly climate variables and evapotranspiration, and the results were compared with a scenario using long-term climate averages only. The main differences occurred in wetter periods, where negative correlations between monthly precipitation and evapotranspiration were obtained when using precipitation as a proxy. Long-term changes in the hydrological regime were assessed and showed that the effect of precipitation on relative humidity and sunlight hours seems to have a minor effect on the alterations observed in river discharge in the Paraná Basin.     

Development of a distributed hydrological model to facilitate watershed management

To facilitate precise and cost-effective watershed management, a simple yet spatially and temporally distributed hydrological model (DHM-WM) was developed. The DHM-WM is based on the Mishra-Singh version of the curve number method, with several modifications: The spatial distribution of soil moisture was considered in moisture updating; the travel time of surface runoff was calculated on a grid cell basis for routing; a simple tile flow module was included as an option. The DHM-WM was tested on a tile-drained agricultural watershed in Indiana, USA. The model with the tile flow module performed well in the study area, providing a balanced water budget and reasonable flow partitioning. The daily coefficient of determination and Nash-Sutcliffe coefficient were 0.58 and 0.56, for the calibration period, and 0.63 and 0.62 for the validation period. The DHM-WM also provides detailed information about the source areas of flow components, the travel time and pathways of surface runoff.

EDITOR A. Castellarin; ASSOCIATE EDITOR F.-J. Chang     

Distributed hydrological modelling of a heavily glaciated Alpine river basin

Abstract

A glacier submodel was successfully integrated into the distributed hydrological model WaSiM-ETH to simulate the discharge of a heavily glaciated drainage basin. The glacier submodel comprises a distributed temperature index model including solar radiation to simulate the melt rate of glaciated areas. Meltwater and rainfall are transformed into glacier discharge by using a linear reservoir approach. The model was tested on a high-alpine sub-basin of the Rhone basin (central Switzerland) of which 48% is glaciated. Continuous discharge simulations were performed for the period 1990–1996 and compared with hourly discharge observations. The pronounced daily and annual fluctuations in discharge were simulated well. The obtained efficiency criterion, R², exceeds 0.89 for all years. The good performance of the glacier submodel is also demonstrated by integrating it into the hydrological model PREVAH.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.