Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.     

Detrital Amino Acids and the Growth of Sarotherodon mossambicus — a Reply to DABROWSKI

It depends on the trophic position of a species whether its growth is limited by the quantity or quality of diet: predators are frequently limited by the quantity of diet, primary consumers frequently by the quality of diet. The protein deficiency is of decisive importance for the growth of primary consumers. The digestible protein/digestible energy ratio is most important: 4 mg/kJ are sufficient for maintenance, 20… 30 mg/kJ are necessary for maximum growth. These values can be confirmed by feeding tests with Carassius auratus. According to measurements by different methods, the organic nitrogen is present in the detritus in the form of amino acids as bonded to organis matter. Thus, Sarotherodon mossambicus assimilates 25.6 mg amino acids/kJ from detritus, whereas only 25% of these amino acids can be identified as protein. Due to the utilization of this source of diet, detrivorous fish occupy a special position in the chain of diet, thus gaining a great importance for the aquatic culture.     

Development of a fuzzy logic-based rainfall-runoff model

Abstract

Rainfall-runoff models are used to describe the hydrological behaviour of a river catchment. Many different models exist to simulate the physical processes of the relationship between precipitation and runoff. Some of them are based on simple and easy-to-handle concepts, others on highly sophisticated physical and mathematical approaches that require extreme effort in data input and handling. Recently, mathematical methods using linguistic variables, rather than conventional numerical variables applied extensively in other disciplines, are encroaching in hydrological studies. Among these is the application of a fuzzy rule-based modelling. In this paper an attempt was made to develop fuzzy rule-based routines to simulate the different processes involved in the generation of runoff from precipitation. These routines were implemented within a conceptual, modular, and semi-distributed model-the HBV model. The investigation involved determining which modules of this model could be replaced by the new approach and the necessary input data were identified. A fuzzy rule-based routine was then developed for each of the modules selected, and application and validation of the model was done on a rainfall-runoff analysis of the Neckar River catchment, in southwest Germany.     

A formal approach to hydrological model conceptualization

Abstract

A two-stage formal approach to hydrological model conceptualization is described. The approach requires the definition of hydrological variables in terms of states and rates, the construction of state-rate diagrams and the definition of equations for the rates based on an indepth understanding of the related hydrological processes. It is inferred that the approach can help modellers arrive at models which are conceptually more feasible for operational use and for theoretical studies. STELLA, a programme specifically designed to facilitate model conceptualization using this approach, is also briefly described. The use of the two stage formal approach with STELLA will be an excellent teaching tool for hydrological modelling.     

A simplified model for estimating field‐scale surface runoff hydrographs

The problem of obtaining field‐scale surface response to rainfall events is complicated by the spatial variability of infiltration characteristics of the soil and rainfall. In this paper, we develop and test a simplified model for generating surface runoff over fields with spatial variation in both rainfall rate and saturated hydraulic conductivities. The model is able to represent the effects of local variation in infiltration, as well as the run‐on effect that controls infiltration of excess water from saturated upstream areas. The effective rainfall excess is routed to the slope outlet using a simplified solution of the kinematic wave approximation. Model results are compared to averaged hydrographs from numerically‐intensive Monte–Carlo simulations for observed and design rainfall events and soil patterns that are typical of Central Italy. The simplified model is found to yield satisfactory results at a relatively small computational expense. A proposal to include a simple channel routing scheme is also presented as a prelude to extend this conceptualization to watershed scales. Copyright © 2006 John Wiley & Sons, Ltd.     

Toxicity of Interactions of Zinc —Nickel,Copper —Nickel and Zinc —Nickel —Copper to a Freshwater Teleost,Lebistes reticulatus (PETERS)1

The lethal toxicity of mixtures of Zn²⁺ —Ni²⁺, Cu²⁺ —Ni²⁺ and Zn²⁺ —Cu²⁺ —Ni²⁺ to common guppy at 21£C in hard water (total hardness = 260 mg/l as CaCO₃) was studied under static bioassays test conditions with renewal of the test solutions every 24 h. The heavy metals were tested separately and in mixtures. The 48 h median lethal concentrations (LC₅₀) for individual salts were 75 mg/l Zn²⁺, 37 mg/l for Ni²⁺ and 2.5 mg/l for Cu²⁺. Concentrations were expressed in “toxic units” by taking them as proportions of LC₅₀ values. Experiments showed that in the Zn²⁺-Ni²⁺ mixture, when Ni²⁺ was more in proportion, the toxicity was more than additive. The 48 h LC₅₀ value and 95% confidence limits in the Ni²⁺-Cu²⁺ mixture were 0.684 (0.484 … 0.807) toxic units and the mixture produced more than the additive toxicity (synergism.). The LC₅₀ value and its 95% confidence limits in a Zn²⁺?Cu²⁺?Ni²⁺ mixture also suggested that the mixture was again strictly additive. The results indicate that heavy metallic mixtures would pose a greater toxicological danger to fish than the respective individual metals.     

Holocene depletion and active recharge of the Kalahari groundwaters — A review and an indicative model

A paramount question in the evaluation of groundwater resources in the Kalahari semi-desert is whether there is any active infiltration of present-day rainfall to the deep aquifers. Previous investigations with isotope analyses gave evidence of recent recharge but no unanimity about the distribution of this process has been reached until now. The present study investigates whether the regional hydraulic gradient means a modern replenishment, or whether the slope of the piezometric surface should be explained as a residual feature resulting from head decay since the last pluvial period. It is concluded that the hydraulic gradient is most probably of a residual nature, and the replenishment has been less than 0.5 mm yr.⁻¹ during at least the last 4000 yr. or so.     

A hydrological record extension model for reconstructing streamflows from tree‐ring chronologies

Characterizing drought events is an important factor in designing and operating water resource projects, but instrumental hydrologic records are generally short (<100 years). Because estimates of drought statistics can improve when longer records are available, we developed a stochastic model to extend instrumental streamflows based on tree‐ring chronologies. This Record Extension plus Noise (or REXTN) model consists of an autoregressive term to account for the temporal persistence of streamflows, predictor variables with longer records, and a noise term. The noise term was included to avoid underestimating the variability of the flows and to generate multiple extensions, which offer the possibility of quantifying the uncertainty of drought statistics such as the critical drought. For cases where having multiple extensions is not desirable, a statistically based algorithm was developed to select a single extended record. Using a simulation experiment, model REXTN was found to perform better than other existing reconstruction methods. The model was then applied to extend streamflows of the Poudre River, CO, USA, based on tree ring‐chronologies back to the year 1600, and the reconstructions were used to determine drought statistics such as duration and magnitude. When results based on the classical linear regression model were compared with those calculated by model REXTN, the latter was found to better match flow and drought statistics from the instrumental records, as well as to give a broader range of drought duration and magnitude. The REXTN model provides a useful addition to the range of tools available to hydrologists for coping with the uncertainty associated with water resource management under future climate scenarios. Copyright © 2014 John Wiley & Sons, Ltd.     

A simplified climate model with combined atmospheric-hydrological processes

Abstract

Global climate change can be reproduced in detail by using three-dimensional general circulation models (GCMs). However, such complex models require super-computers and extensive hours of computational time for a single attempt at reproducing long term climate change. An alternative approach is to make simplifying assumptions that retain the essential physics for the desired simulation. Energy balance and Radiative-convective models are examples of such models. The model in this study follows the simplified approach using physics-based climate processes as well as interactions between atmospheric and hydrological processes. The vertically and latitudinally averaged mean temperature and mean water vapour content between 30°N-50°N latitudes are considered as atmospheric state variables while soil and sea temperatures and water storage amount are considered for describing the behaviour of the hydrological system. Temperatures in both the atmosphere and ground are calculated by a thermal energy equation that considers the physically-based processes of shortwave radiation, longwave radiation, sensible heat flux, and latent heat flux. Precipitation and evaporation processes transport moisture between the atmosphere and ground. In this study, the radiation parameterization of the simplified climate model is tested in the investigation of the various effects of global warming due to doubling and quadrupling of CO₂. Changes of temperature, soil water content, evaporation rate and precipitation rate are investigated by numerical experiments. The simplified climate model provides acceptable simulation of climate change and holds promise for practical investigations such as the interactions of physical processes in the evolution of drought phenomena.     

A contour-based topographic model for hydrological and ecological applications

A digital model for discretizing three-dimensional terrain into small irregularly shaped polygons or elements based on contour lines and their orthogonals is described. From this subdivision the model estimates a number of topographic attributes for each element including the total upslope contributing area, element area, slope, and aspect. This form of discretization of a catchment produces natural units for problems involving water flow as either a surface or subsurface flow phenomenon. The model therefore has wide potential application for representing the three-dimensionality of natural terrain and water flow processes in the fields of hydrology, sedimentology, and geomorphology. Three example applications are presented and discussed. They are the prediction of zones of surface saturation, the prediction of the distribution of potential daily solar radiation, and the prediction of zones of erosion and deposition in a catchment.     

A data-based regional scale autoregressive rainfall-runoff model: a study from the Odra River

This paper aims to compare the performances of multivariate autoregressive (MAR) techniques and univariate autoregressive (AR) methods applied to regional scale rainfall-runoff modelling. We focus on the case study from the upper and middle reaches of the Odra River with its main tributaries in SW Poland. The rivers drain both the mountains (the Sudetes) and the lowland (Nizina Śląska). The region is exposed to extreme hydrologic and meteorological events, especially rain-induced and snow-melt floods. For the analysis, four hydrologic and meteorological variables are chosen, i.e., discharge (17 locations), precipitation (7 locations), thickness of snow cover (7 locations) and groundwater level (1 location). The time period is November 1971–December 1981 and the temporal resolution of the time series is of 1 day. Both MAR and AR models of the same orders are fitted to various subsets of the data and subsequently forecasts of discharge are derived. In order to evaluate the predictions the stepwise procedure is applied to make the validation independent of the specific sample path of the stochastic process. It is shown that the model forecasts peak discharges even 2–4 days in advance in the case of both rain-induced and snow-melt peak flows. Furthermore, the accuracy of discharge predictions increases if one analyses the combined data on discharge, precipitation, snow cover, and groundwater level instead of the pure discharge multivariate time series. MAR-based discharge forecasts based on multivariate data on discharges are more accurate than AR-based univariate predictions for a year with a flood, however, this relation is reverse in the case of the free-of-flooding year. In contrast, independently of the occurrence of floods within a year, MAR-based discharge forecasts based on discharges, precipitation, snow cover, and groundwater level are more precise than AR-based predictions.