Improving rainfall–runoff modelling through the control of uncertainties under increasing climate variability in the Ouémé River basin (Benin,West Africa)

ABSTRACT

The objective of this paper is to understand how the natural dynamics of a time-varying catchment, i.e. the rainfall pattern, transforms the random component of rainfall and how this transformation influences the river discharge. To this end, this paper develops a rainfall–runoff modelling approach that aims to capture the multiple sources and types of uncertainty in a single framework. The main assumption is that hydrological systems are nonlinear dynamical systems which can be described by stochastic differential equations (SDE). The dynamics of the system is based on the least action principle (LAP) as derived from Noether’s theorem. The inflow process is considered as a sum of deterministic and random components. Using data from the Ouémé River basin (Benin, West Africa), the basic properties for the random component are considered and the triple relationship between the structure of the inflowing rainfall, the corresponding SDE that describes the river basin and the associated Fokker-Planck equations (FPE) is analysed.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR D. Gerten     

Assessment of deterministic PMF modelling approaches

Probable maximum flood (PMF) event estimation has challenged the scientific community for many years. Although the concept of the PMF is often applied, there is no consensus on the methods that should be applied to estimate it. In PMF estimation, the spatio-temporal representation of the probable maximum precipitation (PMP) as well as the choice of modelling approach is often not theoretically founded. Moreover, it is not clear how these choices influence PMF estimation itself. In this study, combinations of three different spatio-temporal PMP representations and three different modelling approaches are applied to determine the PMF of a mesoscale basin keeping the antecedent catchment conditions and the total precipitation amount constant. The nine resulting PMF estimations are used to evaluate each combination of methods. The results show that basic methods allow for a rough estimation of the PMF. In cases where a physically plausible and reliable estimation is required, sophisticated PMP and PMF estimation approaches are recommended.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Viglione     

Weather noise impact on the uncertainty of simulated water balance components of river basins

Assessments of hydrological response to climatic changes are characterized by different types of uncertainties. Here, the uncertainty caused by weather noise associated with the chaotic character of atmospheric processes is considered. A technique for estimating such uncertainty in simulated water balance components based on application of the land surface model SWAP and the climate model ECHAM5 is described. The technique is applied for estimating the uncertainties in the simulated water balance components (precipitation, river runoff and evapotranspiration) of some northern river basins of Russia. It is shown that the larger the area of a basin the less the uncertainty. This dependency is smoothed by differences in natural conditions of the basins. Analysis of the spectral densities of water balance components shows that a river basin filters out high-frequency harmonics of spectral density of precipitation (corresponding to synoptic or sub-seasonal scale) during its transformation into evapotranspiration and especially into runoff.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR H. Kreibich     

Uncertainty in levee heights and its effect on the spatial pattern of flood hazard in a floodplain

Levees are not usually built to a uniform height due to the varying priority of protecting urban and agricultural lands and they are often maintained in segments. Ad hoc alteration of the heights of these segments may aggravate flood conditions. Alterations lead to complex feedback loops in velocity and depth of water that are difficult to predict. A large number of possible configurations of the levee segments renders a deterministic modelling approach ineffective. The current analysis, based on a two-dimensional hydrodynamic model involving 1000 Monte Carlo realizations of randomly varying levee heights in segments, presents a methodology of dealing with the effect of uncertainty in levee heights on the inundation pattern in a probabilistic framework. Spatially distributed model outcomes include the likelihood of inundation, range and standard deviation of flood depths and maximum speed of water. The results indicate the necessity of adopting a probabilistic approach for robust flood hazard assessment when dealing with levee segments with uncertain heights.

EDITOR M.C. Acreman; ASSOCIATE EDITOR H. Kreibich     

Investigation of the groundwater modelling component of the Integrated Water Flow Model (IWFM)

ABSTRACT

The Integrated Water Flow Model (IWFM), developed by the California Department of Water Resources, is an integrated hydrological model that simulates key flow processes including groundwater flows, streamflow, stream–aquifer interactions, rainfall–runoff and infiltration. It also simulates the agricultural water demand as a function of soil, crop and climatic characteristics, as well as irrigation practices, and allows the user to meet these demands through pumping and stream diversions. This study investigates the modelling performance of the groundwater module of IWFM using several hypothetical test problems that cover a wide range of settings and boundary conditions, by comparing the simulation results with analytical solutions, field and laboratory observations, or with results from MODFLOW outputs. The comparisons demonstrate that IWFM is capable of simulating various hydrological processes reliably.

EDITOR M.C. Acreman; ASSOCIATE EDITOR A. Efstratiadis     

A revisit of NRCS-CN inspired models coupled with RS and GIS for runoff estimation

The Natural Resource Conservation Service – Curve Number (NRCS-CN) methodology is a widely used tool for estimating surface runoff, which is of prime importance in hydrological engineering, agricultural planning and management, environmental impact assessment, flood forecasting, and others fields. This article reviews the methodology and associated hydrological models used for runoff estimation along with their advantages and limitations. Furthermore, discussion focuses on the potential applications of Remote Sensing (RS) and Geographical Information System (GIS) techniques for estimating hydrological variables, such as rainfall, soil moisture and CN required for the NRCS-CN methodology, as well as future research and opportunities for improved runoff estimation at the macro scale.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR A. Efstratiadis     

An adaptive multilevel correlation analysis: a new algorithm and case study

ABSTRACT

An adaptive multilevel correlation analysis, a kind of data-driven methodology, is proposed. The analysis is done by subdividing the time series into segments such that adjacent segments have significantly different mean values. It is shown that the proposed methodology can provide multilevel information about the correlation between two variables. An integrated coefficient with its significance testing is also proposed to summarize the correlation at each level. Using the adaptive multilevel correlation analysis methodology, the correlation between streamflow and water level is investigated for a case study, and the results indicate that real correlation might be far more complicated than the empirically constructed picture.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR E. Volpi     

Analysis of recharge conceptualization in inverse groundwater modelling

ABSTRACT

This study presents a systematic illustration quantifying how misleading the calibration results of a groundwater simulation model can be when recharge rates are considered as the model parameters to be estimated by inverse modelling. Three approaches to recharge estimation are compared: autocalibration (Model 1), the empirical return coefficient method (Model 2), and distributed hydrological modelling using the Soil and Water Assessment Tool, SWAT (Model 3). The methodology was applied in the Dehloran Plain, western Iran, using the MODFLOW modular flow simulator and the PEST method for autocalibration. The results indicate that, although Model 1 performed the best in simulating water levels at observation wells in the calibration stage, it did not perform satisfactorily in real future scenarios. Model 3, with SWAT-based recharge rates, performed better than the other models in the validation stage. By not evaluating the model performance solely on calibration results, we demonstrate the relative significance of using more accurate recharge estimates when calibrating groundwater simulation models.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR M. Besbes     

Model structure and uncertainty for stochastic non-point source modelling applications

Abstract

The uncertainty associated with a rainfall–runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions.

Citation Parker, G. T. Rennie, C. D. & Droste, R. L. (2011) Model structure and uncertainty for stochastic non-point source modelling applications. Hydrol. Sci. J. 56(5), 870–882.     

Integrative stochastic model standardization with genetic algorithm for rainfall pattern forecasting in tropical and semi-arid environments

ABSTRACT

Climate patterns, including rainfall prediction, is one of the most complex problems for hydrologist. It is inherited by its natural and stochastic phenomena. In this study, a new approach for rainfall time series forecasting is introduced based on the integration of three stochastic modelling methods, including the seasonal differencing, seasonal standardization and spectral analysis, associated with the genetic algorithm (GA). This approach is specially tailored to eradicate the periodic pattern effects notable on the rainfall time series stationarity behaviour. Two different climates are selected to evaluate the proposed methodology, in tropical and semi-arid regions (Malaysia and Iraq). The results show that the predictive model registered an acceptable result for the forecasting of rainfall for both the investigated regions. The attained determination coefficient (R²) for the investigated stations was approx. 0.91, 0.90 and 0.089 for Mosul, Baghdad and Basrah (Iraq), and 0.80, 0.87 and 0.94 for Selangor, Negeri Sembilan and Johor (Malaysia).     

Simple stochastic simulation of time irreversible and reversible processes

ABSTRACT

As time irreversibility of streamflow is marked for time scales up to several days, while common stochastic generation methods are good only for time-symmetric processes, the need for new methods to handle irreversibility, particularly in flood simulations, has been recently highlighted. From an investigation of the historical evolution of existing stochastic generation methods, which is a useful step before proposing new methods, the strengths and weaknesses of current approaches are located. Following this investigation, a generic solution to the stochastic generation problem is proposed. This is an analytical exact method based on an asymmetric moving-average scheme, capable of handling time irreversibility in addition to preserving the second-order stochastic structure, as well as higher-order marginal statistics, of a process. The method is studied theoretically in its general setting, as well as in its most interesting special cases, and is successfully applied to streamflow generation at an hourly scale.     

Improvement and comparative assessment of a hydrological modelling approach on 20 catchments of various sizes under different climate conditions

Assessing water resources is an important issue, especially in the context of climatic changes. Although numerous hydrological models exist, new approaches are still under investigation. In this context, we propose a modelling approach based on the physical principle of least action. We present new hypotheses to develop the model further, to widen its application. The improved version of the model MODHYPMA was applied on 20 sub-catchments in Africa and the USA. Its performance was compared with two well-known lumped conceptual models, GR4J and HBV. The model could be successfully calibrated and validated. In calibration, GR4J performed better, while other models had similar performance. In validation, MODHYPMA and GR4J performed similarly and better than HBV. The parameter λ has medium sensitivity while parameters λ and TX have low sensitivity. The parameter uncertainty for MODHYPMA, analysed using the GLUE methodology, was higher during high flows but with good p and r factors.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR not assigned     

Data-driven modelling approaches for socio-hydrology: opportunities and challenges within the Panta Rhei Science Plan

ABSTRACT

“Panta Rhei – Everything Flows” is the science plan for the International Association of Hydrological Sciences scientific decade 2013–2023. It is founded on the need for improved understanding of the mutual, two-way interactions occurring at the interface of hydrology and society, and their role in influencing future hydrologic system change. It calls for strategic research effort focused on the delivery of coupled, socio-hydrologic models. In this paper we explore and synthesize opportunities and challenges that socio-hydrology presents for data-driven modelling. We highlight the potential for a new era of collaboration between data-driven and more physically-based modellers that should improve our ability to model and manage socio-hydrologic systems. Crucially, we approach data-driven, conceptual and physical modelling paradigms as being complementary rather than competing, positioning them along a continuum of modelling approaches that reflects the relative extent to which hypotheses and/or data are available to inform the model development process.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR not assigned     

Data-driven modelling approaches for socio-hydrology: opportunities and challenges within the Panta Rhei Science Plan

ABSTRACT

“Panta Rhei – Everything Flows” is the science plan for the International Association of Hydrological Sciences scientific decade 2013–2023. It is founded on the need for improved understanding of the mutual, two-way interactions occurring at the interface of hydrology and society, and their role in influencing future hydrologic system change. It calls for strategic research effort focused on the delivery of coupled, socio-hydrologic models. In this paper we explore and synthesize opportunities and challenges that socio-hydrology presents for data-driven modelling. We highlight the potential for a new era of collaboration between data-driven and more physically-based modellers that should improve our ability to model and manage socio-hydrologic systems. Crucially, we approach data-driven, conceptual and physical modelling paradigms as being complementary rather than competing, positioning them along a continuum of modelling approaches that reflects the relative extent to which hypotheses and/or data are available to inform the model development process.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR not assigned     

Hydrological modelling of temporally-varying catchments: facets of change and the value of information

Abstract

River basins are by definition temporally-varying systems: changes are apparent at every temporal scale, in terms of changing meteorological inputs and catchment characteristics due to inherently uncertain natural processes and anthropogenic interventions. In an operational context, the ultimate goal of hydrological modelling is predicting responses of the basin under conditions that are similar or different to those observed in the past. Since water management studies require that anthropogenic effects are considered known and a long hypothetical period is simulated, the combined use of stochastic models, for generating the inputs, and deterministic models that also represent the human interventions in modified basins, is found to be a powerful approach for providing realistic and statistically consistent simulations (in terms of product moments and correlations, at multiple time scales, and long-term persistence). The proposed framework is investigated on the Ferson Creek basin (USA) that exhibits significantly growing urbanization during the last 30 years. Alternative deterministic modelling options include a lumped water balance model with one time-varying parameter and a semi-distributed scheme based on the concept of hydrological response units. Model inputs and errors are respectively represented through linear and nonlinear stochastic models. The resulting nonlinear stochastic framework maximizes the exploitation of the existing information by taking advantage of the calibration protocol used in this issue.     

Dairy of forthcoming events

Abstract

Due to its great importance, the availability of long flow records, contemporary as well as older, and the additional historical information of its behaviour, the Nile is an ideal test case for identifying and understanding hydrological behaviours, and for model development. Such behaviours include the long-term persistence, which historically has motivated the discovery of the Hurst phenomenon and has put into question classical statistical results and typical stochastic models. Based on the empirical evidence from the exploration of the Nile flows and on the theoretical insights provided by the principle of maximum entropy, a concept newly employed in hydrological stochastic modelling, an advanced yet simple stochastic methodology is developed. The approach is focused on the prediction of the Nile flow a month ahead, but the methodology is general and can be applied to any type of stochastic prediction. The stochastic methodology is also compared with deterministic approaches, specifically an analogue (local nonlinear chaotic) model and a connectionist (artificial neural network) model based on the same flow record. All models have good performance with the stochastic model outperforming in prediction skills and the analogue model in simplicity. In addition, the stochastic model has other elements of superiority such as the ability to provide long-term simulations and to improve understanding of natural behaviours.     

A hybrid factorial stepwise-cluster analysis method for streamflow simulation – a case study in northwestern China

ABSTRACT

In this study, a hybrid factorial stepwise-cluster analysis (HFSA) method is developed for modelling hydrological processes. The HFSA method employs a cluster tree to represent the complex nonlinear relationship between inputs (predictors) and outputs (predictands) in hydrological processes. A real case of streamflow simulation for the Kaidu River basin is applied to demonstrate the efficiency of the HFSA method. After training a total of 24?108 calibration samples, the cluster tree for daily streamflow is generated based on a stepwise-cluster analysis (SCA) approach and is then used to reproduce the daily streamflows for calibration (1995–2005) and validation (2008–2010) periods. The Nash-Sutcliffe coefficients for calibration and validation are 0.68 and 0.65, respectively, and the deviations of volume are 1.68% and 4.11%, respectively. Results show that: (i) the HFSA method can formulate a SCA-based hydrological modelling system for streamflow simulation with a satisfactory fitting; (ii) the variability and peak value of streamflow in the Kaidu River basin can be effectively captured by the SCA-based hydrological modelling system; (iii) results from 2⁶ factorial experiments indicate that not only are minimum temperature and precipitation key drivers of system performance, but also the interaction between precipitation and minimum temperature significantly impacts on the streamflow. The findings are useful in indicating that the streamflow of the study basin is a mixture of snowmelt and rainfall water.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR G. Thirel     

Projections of future deterioration in UK river quality are hampered by climatic uncertainty under extreme conditions

ABSTRACT

A modelling study was undertaken to quantify effects that the climate likely to prevail in the 2050s might have on water quality in two contrasting UK rivers. In so doing, it pinpointed the extent to which time series of climate model output, for some variables derived following bias correction, are fit for purpose when used as a basis for projecting future water quality. Working at daily time step, the method involved linking regional climate model (HadRM3-PPE) projections, Future Flows Hydrology (rainfall–runoff modelling) and the QUESTOR river network water quality model. In the River Thames, the number of days when temperature, dissolved oxygen, biochemical oxygen demand and phytoplankton exceeded undesirable values (>25°C, <6 mg L^?1, >4 mg L^?1 and >0.03 mg L^?1, respectively) was estimated to increase by 4.1–26.7 days per year. The changes do not reflect impacts of any possible change in land use or land management. In the River Ure, smaller increases in occurrence of undesirable water quality are likely to occur in the future (by 1.0–11.5 days per year) and some scenarios suggested no change. Results from 11 scenarios of the hydroclimatic inputs revealed considerable uncertainty around the levels of change, which prompted analysis of the sensitivity of the QUESTOR model to simulations of current climate and hydrology. Hydrological model errors were deemed of less significance than those associated with the derivation and downscaling of driving climatic variables (rainfall, air temperature and solar radiation). Errors associated with incomplete understanding of river water quality interactions with the aquatic ecosystem were found likely to be more substantial than those associated with hydrology, but less than those related to climate model inputs. These errors are largely a manifestation of uncertainty concerning the extent to which phytoplankton biomass is controlled by invertebrate grazers, particularly in mid-summer; and the degree to which this varies from year to year. The quality of data from climate models for generating flows and defining driving variables at the extremes of their distributions has been highlighted as the major source of uncertainty in water quality model outputs.

EDITOR A. Castellarin; ASSOCIATE EDITOR X. Fang     

A comparative study on a simple two-parameter monthly water balance model and the Kajiyama formula for monthly runoff estimation

ABSTRACT

A two-parameter monthly water balance model to simulate runoff can be used for a water resources planning programme and climate impact studies. However, the model estimates two parameters of transformation of time scale (c) and of the field capacity (SC) by a trial-and-error method. This study suggests a modified methodology to estimate the parameters c and SC using the meteorological and geological conditions. The modified model is compared with the Kajiyama formula to simulate the runoff in the Han River and International Hydrological Programme representative basins in South Korea. We show that the estimated c and SC can be used as the initial or optimal values for the monthly runoff simulation study in the model.

EDITOR M.C. Acreman; ASSOCIATE EDITOR S. Kanae