Conceptual Rainfall-runoff Model Research Articles

Practical Experience of Sensitivity Analysis: Comparing Six Methods, on Three Hydrological Models, with Three Performance Criteria

Currently, practically no modeling study is expected to be carried out without some form of Sensitivity Analysis (SA). At the same time, there is a large number of various methods and it is not always easy for practitioners to choose one. The aim of this paper is to briefly review main classes of SA methods, and to present the results of the practical comparative analysis of applying them. Six different global SA methods: Sobol, eFAST (extended Fourier Amplitude Sensitivity Test), Morris, LH-OAT, RSA (Regionalized Sensitivity Analysis), and PAWN are tested on three conceptual rainfall-runoff models with varying complexity: (GR4J, Hymod, and HBV) applied to the case study of Bagmati basin (Nepal). The methods are compared with respect to effectiveness, efficiency, and convergence. A practical framework of selecting and using the SA methods is presented. The result shows that, first of all, all the six SA methods are effective. Morris and LH-OAT methods are the most efficient methods in computing SI and ranking. eFAST performs better than Sobol, and thus it can be seen as its viable alternative for Sobol. PAWN and RSA methods have issues of instability, which we think are due to the ways Cumulative Distribution Functions (CDFs) are built, and using Kolmogorov–Smirnov statistics to compute Sensitivity Indices. All the methods require sufficient number of runs to reach convergence. Difference in efficiency of different methods is an inevitable consequence of the differences in the underlying principles. For SA of hydrological models, it is recommended to apply the presented practical framework assuming the use of several methods, and to explicitly take into account the constraints of effectiveness, efficiency (including convergence), ease of use, and availability of software.

Effectiveness of introducing crop coefficient and leaf area index to enhance evapotranspiration simulations in hydrologic models

AbstractEvapotranspiration (ET) is an essential component of the hydrological cycle and plays a critical role in water resource management. However, ET is often overlooked in order to transform rainfall to runoff for better streamflow simulation. Hydrological models are commonly used to estimate areal actual evapotranspiration (AET) after calibration against observed discharge. However, classical approaches are often inadequate to appropriately simulate other hydrologic components. Hence, it is important to introduce natural heterogeneity to enhance hydrological processes and reduce water balance errors. In this study, the effectiveness of introducing a constant crop coefficient (Kc), flux tower‐based Kc, and leaf area index (LAI) to three hydrological models (Three‐Parametric Hydrologic Model [TPHM], Génie Rural à 4 paramètres Journalier [GR4J], and Catchment hydrologic cycle Assessment Tool [CAT]) is assessed for the simulation of daily streamflow and AET in a mountainous mixed forest watershed (8.54 km2) in South Korea. The results show that the streamflow simulations after introduction of Kc and LAI to the original models are quite similar. However, the effectiveness of the AET estimation was significantly enhanced after introduction of the flux tower‐based Kc and LAI. The information criterion computed to compare the models reveals that the flux tower‐based Kc‐simulated AET demonstrated better agreement with the observed AET. The Pearson's correlation coefficients (R2) of the TPHM (8%), GR4J (55%), and CAT (55%) models also showed improvements that were greater than the constant based Kc simulation. Similarly, the limitations of the three models with respect to capturing seasonal variation as well as high and low flows were enhanced after the introduction of the flux tower‐based Kc, which adequately reproduced hydrological processes with minimum water balance errors and bias. A regression analysis revealed the potential of estimating Kc as a linear function of LAI (R2 = 0.84). The results of this study indicate that introduction of Kc and LAI to the conceptual rainfall–runoff models can be considered an effective approach to reduce water balance errors and uncertainties in hydrological models and improve the reliability of climate change studies and water resource management.

A bootstrap-based differential split-sample test to assess the transferability of conceptual rainfall-runoff models under past and future climate variability

This study proposes a general differential split-sample test (GDSST) based on an oriented bootstrap to assess the transferability of conceptual rainfall-runoff models to climatically contrasting periods. Compared to existing benchmark techniques, the GDSST allows a larger number of climatically contrasted discontinuous periods to be sampled, and is computationally more effective than the basic bootstrap to identify the most contrasted periods. When applied to three hydrological models (GR4J, HBV and IHACRES) in five catchments in northern Tunisia, the GDSST provided clear limits of the transferability of the models under changing precipitation (P) and temperature (T) conditions towards drier and hotter conditions. According to the criteria and thresholds retained, approximate limits of model transferability are drawn. The models are roughly transferable for relative changes in precipitation ΔP < (0.08 ΔT − 0.18) with ΔP ∈ [−30%, +80%], and changes in temperature ΔT ∈ [−2 °C, +2 °C]. These transferability limits suggest selecting a past sub-period as close as possible to the future climate to identify calibration parameters, which can be used for hydrological projections. The limits of transferability were then compared to climate projections by eight high-resolution Regional Climate Model (RCM) simulations resulting from the EURO-CORDEX initiative. The RCMs’ precipitation and temperature simulations of the historical period 1970–2000 were first assessed to select the most realistic ones for future projections. A delta-change monthly correction was used to perturb the observed climate series according to climate simulations under two Radiative Concentration Pathway (RCP) scenarios (RCP4.5 and RCP8.5) for one medium-term horizon (2040–2070) and one long-term horizon (2070–2100). The effects of the selected past calibration period on the hydrological projections were then analysed. The RCP 8.5 climate projections fall outside the limits of transferability of all rainfall-runoff models tested. Models calibrated on the whole observed period were found to underestimate the impacts of climate change on runoff by 5%–20% in comparison with models calibrated on sub-periods with mean annual P and T closer to projected climate conditions.

The comprehensive differential split-sample test: A stress-test for hydrological model robustness under climate variability

The choice of data periods for calibrating and evaluating conceptual hydrological models often seems ad-hoc, with no objective guidance on choosing calibration periods that produce the most reliable predictions. We therefore propose to systematically investigate the effects of calibration and validation data choices on parameter identification and predictive performance. We demonstrate our analysis on the Deggendorf/Kollbach catchment in Bavaria, Germany, for its long series of continuous hydrological and meteorological records. After classifying these data into three hydrological conditions (wet, dry and mixed) and combining them into periods of varied data length (2, 4, 8, 15, 20 and 25 years), we repeatedly calibrate a conceptual rainfall runoff hydrological model – Hydrologiska Byråns Vattenbalansavdelning (HBV) to these distinct data sets via Bayesian updating in a Monte Carlo setting. Then, we analyze predictive performance and posterior parameter statistics in various validation periods of distinct hydrological condition and time-series length. We call this the Comprehensive Differential Split-Sample Test (CDSST). Our results suggest that hydrological conditions in calibration tend to have a stronger impact than time-series length, and that calibrating on dry conditions might be a robust choice when aiming at predicting arbitrary future conditions (wet, dry or mixed). Furthermore, we found that posterior parameter estimates converged to a common optimum range with increasing data size under all investigated calibration scenarios, indicating that compensation of model structural errors by parameter fitting is independent of the chosen calibration condition. However, calibrating on time-series 8 years or longer led to overconfident predictions that failed to reliably envelope future data. While these findings are specific to our case study, we recommend using the CDSST to stress-test conceptual hydrological models to identify robust model parameters and/or deficiencies in the model structure. In general, we expect our proposed approach to be a valuable basis for model error diagnosis in any type of dynamic environmental system model, because it answers the following three questions: (1) what is the importance of physical processes not explicitly covered by the model? (2) How much overconfidence is present in the model? And (3), what are case-specific recommendations for appropriate calibration and validation setups?

Coupling Tank Model and Lars-Weather Generator in Assessments of the Impacts of Climate Change on Water Resources

Abstract With the aim of assessing the impact of climate change on surface water resources, a conceptual rainfall-runoff model (the tank model) was coupled with LARS-WG as a weather generator model. The downscaled daily rainfall, temperature, and evaporation from LARS-WG under various IPCC climate change scenarios were used to simulate the runoff through the calibrated Tank model. A catchment (4648 ha) located in the southern basin of the Caspian Sea was chosen for this research study. The results showed that this model has a reasonable predictive capability in simulating minimum and maximum temperatures at a level of 99%, rainfall at a level of 93%, and radiation at a level of 97% under various scenarios in agreement with the observed data. Moreover, the results of the rainfall-runoff model indicated an increase in the flow rate of about 108% under the A1B scenario, 101% under the A2 scenario, and 93% under the B1 scenario over the 30-year time period of the discharge prediction.

A simple topography-driven and calibration-free runoff generation module

Abstract. Reading landscapes and developing calibration-free runoff generation models that adequately reflect land surface heterogeneities remains the focus of much hydrological research. In this study, we report a novel and simple topography-driven runoff generation parameterization – the HAND-based Storage Capacity curve (HSC), which uses a topographic index (HAND, Height Above the Nearest Drainage) to identify hydrological similarity and the extent of saturated areas in catchments. The HSC can be used as a module in any conceptual rainfall–runoff model. Further, coupling the HSC parameterization with the mass curve technique (MCT) to estimate root zone storage capacity (SuMax), we developed a calibration-free runoff generation module, HSC-MCT. The runoff generation modules of HBV and TOPMODEL were used for comparison purposes. The performance of these two modules (HSC and HSC-MCT) was first checked against the data-rich Bruntland Burn (BB) catchment in Scotland, which has a long time series of field-mapped saturation area extent. We found that HSC, HBV and TOPMODEL all perform well to reproduce the hydrograph, but the HSC module performs better in reproducing saturated area variation, in terms of correlation coefficient and spatial pattern. The HSC and HSC-MCT modules were subsequently tested for 323 MOPEX catchments in the US, with diverse climate, soil, vegetation and geological characteristics. In comparison with HBV and TOPMODEL, the HSC performs better in both calibration and validation, particularly in the catchments with gentle topography, less forest cover, and arid climate. Despite having no calibrated parameters, the HSC-MCT module performed comparably well with calibrated modules, highlighting the robustness of the HSC parameterization to describe the spatial distribution of the root zone storage capacity and the efficiency of the MCT method to estimate SuMax. This novel and calibration-free runoff generation module helps to improve the prediction in ungauged basins and has great potential to be generalized at the global scale.

A comparative study of conceptual rainfall-runoff models GR4J, AWBM and Sacramento at catchments in the upper Godavari river basin, India

Accurate catchment level water resource assessment is the base for integrated river basin management. Due to the complexity in model structure and requirement of a large amount of input data for semi-distributed/distributed models, the conceptual models are gaining much attention in catchment modelling these days. The present study compares the performance of three conceptual models, namely GR4J, Australian Water Balance Model (AWBM) and Sacramento for runoff simulation. Four small catchments and one medium catchment in the upper Godavari river basin are selected for this study. Gap-filled daily rainfall data and potential evapotranspiration (PET) measured from the same catchment or adjacent location are the major inputs to these models. These models are calibrated using daily Nash–Sutcliffe efficiency (NSE) with bias penalty as the objective function. GR4J, AWBM and Sacramento models have four, eight and twenty-two parameters, respectively, to optimise during the calibration. Various statistical measures such as NSE, the coefficient of determination, bias and linear correlation coefficient are computed to evaluate the efficacy of model runoff predictions. From the obtained results, it is found that all the models provide satisfactory results at the selected catchments in this study. However, it is found that the performance of GR4J model is more appropriate in terms of prediction and computational efficiency compared to AWBM and Sacramento models.

Evaluation of evolutionary algorithms for the optimization of storm water drainage network for an urbanized area

The studies pertaining to urban storm water drainage system have picked up importance lately in light of pluvial flooding. The flooding is mostly due to urban expansion, reduction in infiltration rate and environmental change. In order to minimize flooding, hydrologists are using conceptual rainfall–runoff models as a tool for predicting surface runoff and flood forecasting. Manual calibration is often a tedious process because of the involved subjectivity, which makes the automatic approach more preferable. In this study, three evolutionary algorithms (EAs), namely SFLA, GA and PSO, were used to calibrate SWMM parameters for the two study areas of the highly urbanized catchments of Delhi, India. The work incorporates auto-tuning of a widely used SWMM, via internal coupling of SWMM with all three EAs in MATLAB environment separately. Results were tested using statistical parameters, i.e., Nash–Sutcliffe efficiency (NSE), Percent Bias (PBIAS) and root-mean-square error–observations standard deviation ratio (RSR). GA results were in good agreement with the observed data in both the study area with NSE and PBIAS values lying between 0.60 and 0.91, and 1.29 and 7.41%, respectively. Also, RSR value was near zero, indicating reasonably good model performance. Subsequently, the model reasonably predicted the flooding hotspots that should be controlled to prevent any possible inundation of the surrounding areas. SFLA results were also promising, but better than PSO. Thus, the approach has demonstrated the potential use and combination of single-objective optimization algorithms and hydrodynamic models for assessing the risk in urban storm water drainage systems, providing valuable information for decision-makers.

Impacts of land use and land cover changes on hydrology of the Gumara catchment, Ethiopia

Land use and land cover (LULC) changes are continuous phenomena, often driven by natural and anthropogenic factors. In Ethiopia, a conversion of forest and grass lands into cultivated and urbanized lands has been reported. While such changes are known to have multidirectional impacts on river flows, erosion and sedimentation, and the socio-economic situation within a catchment, there is a lack of assessment on the scale and rate of these changes, and consequent impacts. This study quantifies the rate of LULC in the Gumara catchment (1413 km2), an important tributary to Lake Tana in northwest Ethiopia. Landsat images of three years (1986, 2001 and 2015) were processed using the supervised classification method. An extensive field survey generated over 150 ground truth points, which were used in the classification and accuracy assessment process. Then, a conceptual rainfall-runoff model (HBV) was calibrated and validated to assess the impacts of LULC changes on water balance components - evapotranspiration, soil moisture, groundwater recharge and runoff. Additionally, the decadal means and trends of precipitation and discharge were analysed to further examine and quantify the observed changes (if any).A reasonably reliable LULC classification was achieved, with an overall accuracy of 90%. The results indicated that the catchment area under forest and grass land was about 11 and 18%, respectively, in 1986, which reduced to 5 and 10%, respectively, in 2015. In contrast, cultivated land increased from 70% in 1986 to 82% in 2015. Contrary to the expected impact of these LULC changes on hydrology, the HBV model, indicated only a slight change in the water balance components (±5%). Runoff and all other water balance components remained more or less stable despite considerable LULC changes. However, the uncertainties encountered in the modelling process (e.g. model structure, LULC representation) could have masked the LULC impacts on hydrology. This was supported by the significant increase in the observed discharge indicated by the statistical analysis, even in view of no substantial changes in precipitation. Therefore, LULC could cause considerable increase in discharge, which needs further testing (e.g. through physically based modelling with detailed inclusion of LULC processes).

Diagnosis of the hydrology of a small Arctic permafrost catchment using HBV conceptual rainfall-runoff model

Abstract Changes in active layer thickness (ALT) over Arctic and permafrost regions have an important impact on rainfall-runoff transformation. General warming is observed across Svalbard Archipelago and corresponds to increases in ground temperatures. Permafrost thaw and changes in ALT due to climate warming alter how water is routed and stored in catchments, and thus impact both surface and subsurface processes. The overall aim of the present study is to examine the relationships between temporal changes of active layer depth and hydrological model parameters, together with variation in the catchment response. The analysis was carried out for the small unglaciated catchment Fuglebekken, located in the vicinity of the Polish Polar Station Hornsund on Spitsbergen. For hydrological modelling, the conceptual rainfall-runoff HBV (Hydrologiska Byråns Vattenbalansavdelning) model was used. The model was calibrated and validated on runoff within subperiods. A moving window approach (3 weeks long) was applied to derive temporal variation of parameters. Model calibration, together with an estimation of parametric uncertainty, was carried out using the Shuffled Complex Evolution Metropolis algorithm. This allowed the dependence of HBV model parameters on ALT to be analysed. Also, we tested the influence of model simplification, correction of precipitation, and initial conditions on the modelling results.

Performance evaluation of conceptual rainfall-runoff models GR4J and AWBM

ABSTRACT Among the different hydrological models used for water resources assessment, conceptual models are gaining popularity due to their simple structure and satisfactory performance. In this study, performance of two conceptual rainfall-runoff models, GR4J (Génie Rural) and AWBM (Australian Water Balance Model), working in Source modelling platform is evaluated at two catchments in the upper Godavari basin, Maharashtra, India. Source is an integrated water resource management tool, developed by eWater Ltd, Australia. GR4J is a four parameter two water store model and AWBM is an eight parameter three water store model. Gap-filled daily rainfall and potential evapotranspiration (PET) data measured from adjacent station is used as input to these models. The models are calibrated for the period 2000–2007 and validated for 2008–2011 using the observed streamflow data. A combination of Shuffle Complex Evolution (SCE) and the Rosenbrock equation is used to calibrate each model in Source framework. Statistical measures such as NSE (Nash–Sutcliffe Efficiency) and correlation coefficient (R2) are computed to evaluate the efficacy of model predictions. From the results obtained, it is found that GR4J model provides better streamflow predictions for the study catchments than AWBM. As GR4J is a simpler model, it is more adaptable for water balance modelling.

Factors controlling alterations in the performance of a runoff model in changing climate conditions

Abstract In many Austrian catchments in recent decades an increase in the mean annual air temperature and precipitation has been observed, but only a small change in the mean annual runoff. The main objective of this paper is (1) to analyze alterations in the performance of a conceptual hydrological model when applied in changing climate conditions and (2) to assess the factors and model parameters that control these changes. A conceptual rainfall-runoff model (the TUW model) was calibrated and validated in 213 Austrian basins from 1981–2010. The changes in the runoff model’s efficiency have been compared with changes in the mean annual precipitation and air temperature and stratified for basins with dominant snowmelt and soil moisture processes. The results indicate that while the model’s efficiency in the calibration period has not changed over the decades, the values of the model’s parameters and hence the model’s performance (i.e., the volume error and the runoff model’s efficiency) in the validation period have changed. The changes in the model’s performance are greater in basins with a dominant soil moisture regime. For these basins, the average volume error which was not used in calibration has increased from 0% (in the calibration periods 1981–1990 or 2001–2010) to 9% (validation period 2001–2010) or –8% (validation period 1981–1990), respectively. In the snow-dominated basins, the model tends to slightly underestimate runoff volumes during its calibration (average volume error = –4%), but the changes in the validation periods are very small (i.e., the changes in the volume error are typically less than 1–2%). The model calibrated in a colder decade (e.g., 1981–1990) tends to overestimate the runoff in a warmer and wetter decade (e.g., 2001–2010), particularly in flatland basins. The opposite case (i.e., the use of parameters calibrated in a warmer decade for a colder, drier decade) indicates a tendency to underestimate runoff. A multidimensional analysis by regression trees showed that the change in the simulated runoff volume is clearly related to the change in precipitation, but the relationship is not linear in flatland basins. The main controlling factor of changes in simulated runoff volumes is the magnitude of the change in precipitation for both groups of basins. For basins with a dominant snowmelt runoff regime, the controlling factors are also the wetness of the basins and the mean annual precipitation. For basins with a soil moisture regime, landcover (forest) plays an important role.

Transferability of regionalization methods under changing climate

Regionalization methods have been extensively discussed as the solution for runoff predictions in ungauged basins (PUB), especially during the PUB decade (2003–2012). At the same time, research topics relevant to climate change appear to be an essential and attractive field for hydrologists in recent decades, because the availability and quality of water resources are strongly affected by climate change. However, it is still unknown whether regionalization methods can be used to predict hydrological impacts of climate change for ungauged catchments or how much uncertainty of future predictions may result from the use of regionalization methods. Therefore, in this study, we investigate the transferability of regionalization methods (i.e. spatial proximity and physical similarity methods, regression method) under changing climate conditions and compare the uncertainty resulting from regionalization methods with that from using climate models. The investigation is based on 108 catchments in Norway, with large variability in climate conditions and geographic characteristics. The study applies a lumped conceptual rainfall-runoff model (WASMOD) with simple structure and six model parameters. Our result shows that (a) the differences in the predictions by the regionalization methods tend to increase in the future, (b) the physical similarity method with parameter option (i.e. the model parameters from the physically-similar donor catchments are first averaged and then used to run the model for the target catchment) shows higher transferability than other methods, (c) the uncertainty contributions from climate models and regionalization methods to future runoff prediction are basin dependent, and (d) the uncertainty of future runoff prediction due to regionalization methods can be higher than that from climate models in low precipitation areas. This study provides insight to the choice of regionalization methods under changing climate conditions and the role of regionalization methods to the uncertainty contributions in future runoff predictions.

Relationship Between Calibration Time and Final Performance of Conceptual Rainfall-Runoff Models

Various methods are used in the literature for calibration of conceptual rainfall-runoff models. However, very rarely the question on the relation between the number of model runs (or function calls) and the quality of solutions found is asked. In this study two lumped conceptual rainfall-runoff models (HBV and GR4J with added snow module) are calibrated for five catchments, located in temperate climate zones of USA and Poland, by means of three modern variants of Evolutionary Computation and Swarm Intelligence optimization algorithms with four different maximum numbers of function calls set to 1000, 3000, 10,000 and 30,000. At the calibration stage, when more than 10,000 function calls is used, only marginal improvement in model performance has been found, irrespective of the catchment or calibration algorithm. For validation data, the relation between the number of function calls and model performance is even weaker, in some cases the longer calibration, the poorer modelling performance. It is also shown that the opinion on the model performance based on different popular hydrological criteria, like the Nash-Sutcliffe coefficient or the Persistence Index, may be misleading. This is because very similar, largely positive values of Nash-Sutcliffe coefficient obtained on different catchments may be accompanied by contradictory values of the Persistence Index.

The temporally varying roles of rainfall, snowmelt and soil moisture for debris flow initiation in a snow-dominated system

Abstract. Debris flows represent frequent hazards in mountain regions. Though significant effort has been made to predict such events, the trigger conditions as well as the hydrologic disposition of a watershed at the time of debris flow occurrence are not well understood. Traditional intensity-duration threshold techniques to establish trigger conditions generally do not account for distinct influences of rainfall, snowmelt, and antecedent moisture. To improve our knowledge on the connection between debris flow initiation and the hydrologic system at a regional scale, this study explores the use of a semi-distributed conceptual rainfall–runoff model, linking different system variables such as soil moisture, snowmelt, or runoff with documented debris flow events in the inner Pitztal watershed, Austria. The model was run on a daily basis between 1953 and 2012. Analysing a range of modelled system state and flux variables at days on which debris flows occurred, three distinct dominant trigger mechanisms could be clearly identified. While the results suggest that for 68 % (17 out of 25) of the observed debris flow events during the study period high-intensity rainfall was the dominant trigger, snowmelt was identified as the dominant trigger for 24 % (6 out of 25) of the observed debris flow events. In addition, 8 % (2 out of 25) of the debris flow events could be attributed to the combined effects of low-intensity, long-lasting rainfall and transient storage of this water, causing elevated antecedent soil moisture conditions. The results also suggest a relatively clear temporal separation between the distinct trigger mechanisms, with high-intensity rainfall as a trigger being limited to mid- and late summer. The dominant trigger in late spring/early summer is snowmelt. Based on the discrimination between different modelled system states and fluxes and, more specifically, their temporally varying importance relative to each other, this exploratory study demonstrates that already the use of a relatively simple hydrological model can prove useful to gain some more insight into the importance of distinct debris flow trigger mechanisms. This highlights in particular the relevance of snowmelt contributions and the switch between mechanisms during early to mid-summer in snow-dominated systems.

Modeling and Combined Application of Orthogonal Chaotic NSGA-II and Improved TOPSIS to Optimize a Conceptual Hydrological Model

Conceptual rainfall-runoff modelling is a widely-used approach for rainfall-runoff simulation in streamflow forecasting. The objective of this paper is to introduce an improved non-dominated sorting genetic algorithm-II (NSGA-II) for multi-objective automatic calibration of a hydrologic model. The orthogonal design based initialization technique is exploited to produce a more uniformly-distributed initial population. At the same time, a chaotic crossover operator as well as a chaotic mutation operator are presented to avoid trapping into local minima and to obtain high quality solutions. Finally, a multi-criteria decision-making (MCDM) approach combing Shannon entropy weighting method and an improved technique for order preference by similarity to ideal solution (ITOPSIS) based on projection is introduced to prioritize the Pareto optimal solutions and select the comprehensive optimal solution as a follow-up step. Hydrological data from two river basins named the Leaf and Muma River basins are exploited to test the ability of the orthogonal chaotic NSGA-II (OCNSGA-II) for solving the multi-objective HYMOD (MO-HYMOD) problem. The results demonstrate that the OCNSGA-II can obtain better-distributed Pareto optimal front and thus can be exploited as an effective alternative approach for the multi-objective automatic calibration of hydrologic model.

Assimilation of near-real time data products into models of an urban basin

The goal of this study was to determine if assimilating a combination of various derived data products can help circumvent some of the difficulties associated with urban watershed modeling. Combinations of the SNODAS (Snow Data Assimilation System) snow water equivalent data, the SMOS (Soil Moisture and Ocean Salinity) L2 soil moisture, and streamflow observations were used for the data assimilation schemes. Combinations of these observation data sets were assimilated into lumped conceptual rainfall-runoff models of the highly-urbanized Don River basin (in southern Ontario) to determine if assimilation of geophysical variables will have a significant impact on simulations and forecasting in an urbanized watershed. The Ensemble Kalman Filter (EnKF) data assimilation method was used for these analyses, with various rainfall-runoff models that include GR4J, HyMod, MAC-HBV, and SAC-SMA models. The best data assimilation scheme for hydrologic modeling involved using a combination of streamflow, soil moisture, and snow water equivalent while performing both state and parameter updating. These results suggest that using a combination of soil moisture and snow water equivalent from the SMOS and SNODAS data products can improve simulations and ensemble forecasts in an urban basin.

An inverse method for watershed change detection using hybrid conceptual and artificial intelligence approaches

Land Use and Land Cover (LULC) changes intrinsically lead to various hydrological impacts especially on the outflow rate of the watersheds. This research investigated LULC changes and its effect on outlet runoff by detecting LULC changes location and severity via an inverse method for the Little River Watershed, USA. For this purpose, the Clark’s conceptual Rainfall-Runoff model was applied to the delineated sub-watersheds of the basin to generate different outflows by altering the Storage Coefficient (SC) of the model for each sub-watershed as the representative of LULC. Then, the relation between SC values and outflow time series was simulated by Artificial Intelligence (AI) based models of artificial neural network and least square support vector machine. In this way, in order to ignore redundant information and reduce the dimension of input vector, Wavelet-Entropy (WE) values of the outflow sub-series were computed and used as the inputs of the AI model to compute SCs of the sub-watersheds as the outputs. The trained multi-output AI model as an inverse method could be then used to predict the SC values (as representative of LULC) of the sub-watersheds using the observed time series of runoff at the outlet. The obtained results showed that the proposed inverse method could reliably detect not only the location but also the severity of LULC changes by prediction of SC values in the coming future years. For validation of the method, a comparison was also performed between the obtained results and recorded changes via normalized difference vegetation index (NDVI) and land use classification, extracted from Landsat images. The comparison approved the ability of the proposed method for LULC change detection in a way that deforestation and cropland increasing of the sub-watersheds from 1990 to 2013 were aligned with the SC reduction e.g., 26% decrease of SC for downstream sub-watershed versus 53% decrease and 21% increase of forest and crop lands, respectively.

Continuous state-space representation of a bucket-type rainfall-runoff model: a case study with the GR4 model using state-space GR4 (version 1.0)

Abstract. In many conceptual rainfall–runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called “operator splitting”. As a result, only the solutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall–runoff model explicit and to solve them continuously. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which makes the structural analysis of the model more complex, could be removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in rainfall–runoff models and make the resolution of the representation difficult, are first replaced by a so-called “Nash cascade” and then solved with a robust numerical integration technique. To illustrate this methodology, the GR4J model is taken as an example. The substitution of the unit hydrographs with a Nash cascade, even if it modifies the model behaviour when solved using operator splitting, does not modify it when the state-space representation is solved using an implicit integration technique. Indeed, the flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The use of a robust numerical technique that approximates a continuous-time model also improves the lag parameter consistency across time steps and provides a more time-consistent model with time-independent parameters.

Integrated modelling of a megacity water system – The application of a transdisciplinary approach to the Lima metropolitan area

The rapidly growing urban centres throughout the world are facing serious problems due to the fast-changing developments in all of their environmental spheres (nature, society, politics, culture and economics). Therefore, strategic planning becomes even more important in order to develop strategies that allow cities to adapt to new challenges and to prevent or to mitigate negative trends. This paper presents a transdisciplinary approach to water management, which combines adaptation and application of methods from hydrology, social sciences, water engineering and modelling; furthermore, this approach also involves stakeholders in this process. This methodology assists cities in addressing risks by elaborating solutions, which are characterised by ownership and acceptance of the stakeholders involved. The presented methodology proposed here has been applied to the water system of the desert megacity of Lima/Peru. As a city of almost 10 million inhabitants and with an annual rainfall of about 10 mm per year, Lima presents a unique case with particular challenges regarding water supply. In order to assess the changes in precipitation and temperature for the next decades, two global circulation models and three scenarios have been used. Changes in discharge was addressed using the conceptual rainfall-runoff model HBV applied in both the Atlantic and Pacific catchments relevant to the capital city Lima in terms of water supply. A scenario methodology, combining qualitative and quantitative elements, based on the Cross-Impact Balance Analysis, has been developed and applied. From the millions of theoretically possible combinations of future developments of “descriptors” (driving forces) of the water system, four have been identified as the (only) consistent potential developments of the future. Local stakeholders, stemming from a wide range of institutions have been actively involved in the definition of these driving forces and the set of scenarios. The evaluation of these scenarios and potential options to adapt the water system to future developments was carried out by modelling and simulation, using a purpose-built, yet general, simulator which represents the entire water and wastewater system and includes the important inherent feedback loops (e.g. water demand by irrigation, reuse of treated and untreated wastewaters). The setup of the simulator and the implemented models was done in a way that the simulator formed an integral element in the design of strategies and measures, derived by this innovative combination of qualitative scenario building, quantitative modelling and stakeholder participation. As a core result of this process, the Action Plan “Lima 2040” has been developed and adopted, in which the signatories (the main institutions and organisations responsible for the water sector of Lima) commit themselves to specific actions to be implemented over the years to come.