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.     

QANAT SYSTEMS IN IRAN

Abstract

A fuzzy rule-based technique is used for modelling the relationship between climatic forcing and droughts in a Central/Eastern European country, Hungary. Two types of climatic forcing'called premises'are considered: atmospheric circulation patterns (CP) and El Niño Southern Oscillation (ENSO). Both the Hess-Brezowsky CP types and ENSO events influence the occurrence of droughts, but the ENSO signal is relatively weak in a statistical sense. The fuzzy rule-based approach is able to learn the high space—time variability of monthly Palmer Drought Severity Index (PDSI) and results in a proper reproduction of the empirical frequency distributions. The “engine” of the approach, the fuzzy rules, are ascertained from a subset called the learning set of the observed time series of premises (monthly CP frequencies and Southern Oscillation Index) and PDSI response. Then an independent subset, the validation set, is used to check how the application of fuzzy rules reproduces the observed PDSI.     

Regional precipitation and temperature scenarios for climate change

Abstract

To investigate the consequences of climate change on the water budget in small catchments, it is necessary to know the change of local precipitation and temperature. General Circulation Models (GCM) cannot provide regional climate parameters yet, because of their coarse resolution and imprecise modelling of precipitation. Therefore downscaling of precipitation and temperature has to be carried out from the GCM grids to a small scale of a few square kilometres. Daily rainfall and temperature are modelled as processes conditioned on atmospheric circulation. Rainfall is linked to the circulation patterns (CPs) using conditional probabilities and conditional rainfall amount distribution. Both temperature and precipitation are downscaled to several locations simultaneously taking into account the CP dependent spatial correlation. Temperature is modelled using a simple autoregressive approach, conditioned on atmospheric circulation and local areal precipitation. The model uses the classification scheme of the German Weather Service and a fuzzy rule-based classification. It was applied in the Aller catchment for validation using observed rainfall and temperature, and observed classified geopotential pressure heights. GCM scenarios of the ECHAM model were used to make climate change predictions (using classified GCM geopotential heights); simulated values agree fairly well with historical data. Results for different GCM scenarios are shown.     

Delineation of precipitation regions in two Canadian study areas: the role of the temporal resolution of the precipitation data

The identification of homogeneous precipitation regions has value in many water resources engineering applications (infrastructure planning, design, operations; climate forecasting, modelling). The objective of this paper is to assess the sensitivity of precipitation regions to the temporal resolution (monthly, seasonal, annual and the annual maximum series) of the data. The presented method uses the fuzzy c-means clustering algorithm to partition climate sites into statistically homogeneous precipitation regions. The regions are validated using an approach based on L-moment statistics. The method is conducted in two climatically different study areas in western and eastern Canada. There does not appear to be a relationship between the spatial distributions of the regions formed using different temporal resolutions of the precipitation data. It is recommended to delineate precipitation regions that are specific to the task at hand, and to select a temporal resolution that is consistent with the final application of the regional precipitation dataset.

EDITOR A. Castellarin; ASSOCIATE EDITOR T. Kjeldsen     

Updating Real-Time Flood Forecasting Using a Fuzzy Rule-Based Model/Mise à Jour de Prévision de Crue en Temps Réel Grâce à un Modèle à Base de Règles Floues

Abstract

An updating technique is a tool to update the forecasts of mathematical flood forecasting model based on data observed in real time, and is an important element in a flood forecasting model. An error prediction model based on a fuzzy rule-based method was proposed as the updating technique in this work to improve one- to four-hour-ahead flood forecasts by a model that is composed of the grey rainfall model, the grey rainfall—runoff model and the modified Muskingum flow routing model. The coefficient of efficiency with respect to a benchmark is applied to test the applicability of the proposed fuzzy rule-based method. The analysis reveals that the fuzzy rule-based method can improve flood forecasts one to four hours ahead. The proposed updating technique can mitigate the problem of the phase lag in forecast hydrographs, and especially in forecast hydrographs with longer lead times.     

A simple method to combine snow height and meteorological observations to estimate winter precipitation at sub-daily resolution

ABSTRACT

Measuring winter solid and liquid precipitation with high temporal resolution in remote or higher elevation regions is a challenging task because of undercatch and power supply issues. However, the number of micro-meteorological stations and ultrasonic height sensors in mountain regions is steadily increasing. To gain more benefit from such stations, a new simple approach for EStimating SOlid and LIquid Precipitation (ESOLIP) is presented. The method consists of three main steps: (1) definition of precipitation events using micro-meteorological data, (2) quantification of solid and liquid precipitation using wet-bulb temperature and filtered snow height and (3) calculation of fresh snow density. ESOLIP performance was validated using data from a heated rain gauge, snow pillow and daily manual observations both for single precipitation events and over three winter seasons. Results proved ESOLIP as an effective approach for precipitation quantification, where snow height observations and basic meteorological measurements (air temperature, solar radiation, wind speed, relative humidity), but no reliable rain gauges are available.     

A hybrid multi-model approach to river level forecasting

Abstract

This paper presents four different approaches for integrating conventional and AI-based forecasting models to provide a hybridized solution to the continuous river level and flood prediction problem. Individual forecasting models were developed on a stand alone basis using historical time series data from the River Ouse in northern England. These include a hybrid neural network, a simple rule-based fuzzy logic model, an ARMA model and naive predictions (which use the current value as the forecast). The individual models were then integrated via four different approaches: calculation of an average, a Bayesian approach, and two fuzzy logic models, the first based purely on current and past river flow conditions and the second, a fuzzification of the crisp Bayesian method. Model performance was assessed using global statistics and a more specific flood related evaluation measure. The addition of fuzzy logic to the crisp Bayesian model yielded overall results that were superior to the other individual and integrated approaches.     

A comparison of local and aggregated climate model outputs with observed data

Abstract

We compare the output of various climate models to temperature and precipitation observations at 55 points around the globe. We also spatially aggregate model output and observations over the contiguous USA using data from 70 stations, and we perform comparison at several temporal scales, including a climatic (30-year) scale. Besides confirming the findings of a previous assessment study that model projections at point scale are poor, results show that the spatially integrated projections are also poor.

Citation Anagnostopoulos, G. G., Koutsoyiannis, D., Christofides, A., Efstratiadis, A. & Mamassis, N. (2010) A comparison of local and aggregated climate model outputs with observed data. Hydrol. Sci. J. 55(7), 1094–1110.     

Simulated precipitation fields with variance-consistent interpolation

Abstract

Gridded meteorological data are available for all of Norway as time series dating from 1961. A new way of interpolating precipitation in space from observed values is proposed. Based on the criteria that interpolated precipitation fields in space should be consistent with observed spatial statistics, such as spatial mean, variance and intermittency, spatial fields of precipitation are simulated from a gamma distribution with parameters determined from observed data, adjusted for intermittency. The simulated data are distributed in space, using the spatial pattern derived from kriging. The proposed method is compared to indicator kriging and to the current methodology used for producing gridded precipitation data. Cross-validation gave similar results for the three methods with respect to RMSE, temporal mean and standard deviation, whereas a comparison on estimated spatial variance showed that the new method has a near perfect agreement with observations. Indicator kriging underestimated the spatial variance by 60–80% and the current method produced a significant scatter in its estimates.

Citation Skaugen, T. & Andersen, J. (2010) Simulated precipitation fields with variance-consistent interpolation. Hydrol. Sci. J. 55(5), 676–686.     

Evaluation of satellite-based rainfall products for hydrological modelling in Morocco

ABSTRACT

Several satellite-based precipitation estimates are becoming available at a global scale, providing new possibilities for water resources modelling, particularly in data-sparse regions and developing countries. This work provides a first validation of five different satellite-based precipitation products (TRMM-3B42 v6 and v7, RFE 2.0, PERSIANN-CDR, CMORPH1.0 version 0.x) in the 1785 km² Makhazine catchment (Morocco). Precipitation products are first compared against ground observations. Ten raingauges and four different interpolation methods (inverse distance, nearest neighbour, ordinary kriging and residual kriging with altitude) were used to compute a set of interpolated precipitation reference fields. Second, a parsimonious conceptual hydrological model is considered, with a simulation approach based on the random generation of model parameters drawn from existing parameter set libraries, to compare the different precipitation inputs. The results indicate that (1) all four interpolation methods, except the nearest neighbour approach, give similar and valid precipitation estimates at the catchment scale; (2) among the different satellite-based precipitation estimates verified, the TRMM-3B42 v7 product is the closest to observed precipitation, and (3) despite poor performance at the daily time step when used in the hydrological model, TRMM-3B42 v7 estimates are found adequate to reproduce monthly dynamics of discharge in the catchment. The results provide valuable perspectives for water resources modelling of data-scarce catchments with satellite-based rainfall data in this region.

Editor M.C. Acreman; Associate editor N. Verhoest     

Evaluation of the North American Regional Reanalysis (NARR) precipitation fields in a topographically complex domain

ABSTRACT

The North American Regional Reanalysis (NARR) precipitation product was evaluated using station observations and catchment water yield in British Columbia (BC), Canada, at inter-annual, monthly, and daily time scales. A structural break occurred in 2003, associated with exclusion of Canadian precipitation gauge data from NARR’s data assimilation process beginning in that year. The NARR product under-predicted precipitation in mountainous regions, over-predicted in the northern region of BC’s Interior Plateau, and catchment-averaged NARR precipitation was less than observed water yield in coastal BC. The product was unable to reproduce even the seasonal pattern at three stations. This study highlights uncertainties associated with the NARR precipitation product, and presents a cautionary tale that is likely relevant not only to the application of NARR in BC, but may be relevant for other re-analysis products and other regions with complex topography and sparse station networks.     

MAPPING MEAN AREAL PRECIPITATION

Abstract

A method is presented for using point mean precipitation data to estimate areal values in regions of high relief. Variation of precipitation with altitude is determined. Local anomalies from this relationship are mapped, and lines of equal anomaly are drawn. By use of the mean relation corrected for the local anomaly, the mean precipitation at any point can be determined and an isohyetal map drawn. A similar approach can be used to determine mean temperature for studies of snowmelt or of potential evapotranspiration.     

The spatially heterogeneous distribution of precipitation of the Anduo area,Tibetan Plateau,in summer 1998

Abstract

Examination of precipitation in the Tibetan Plateau is important to understanding the regional water cycle processes and the plateau-scale energy budget. Based on hourly precipitation data obtained during the GAME-Tibet intensive observation period at four sites, the spatial distribution of precipitation in summer 1998 within the Anduo area was examined. The results show that, between 1 July and 11 September 1998, the precipitation that occurred simultaneously (at the same hours) at the sites accounted for 6.9–15.3% of the total precipitation at each site during the study period. Even at the two observation sites that are only 20 km apart, the percentage of precipitation that occurred simultaneously was quite small. This indicates that precipitation occurred not only frequently but also very locally, except on several days with very strong monsoon precipitation. The limited observations highlight that the precipitation distribution is quite complex, and large-scale intensive precipitation observations are needed in the future to clarify the heterogeneity of precipitation on the Tibetan Plateau.     

Fuzzy logic model approaches to daily pan evaporation estimation in western Turkey / Estimation de l’évaporation journalière du bac dans l’Ouest de la Turquie par des modèles à base de logique floue

Abstract

Abstract Evaporation is one of the fundamental elements in the hydrological cycle, which affects the yield of river basins, the capacity of reservoirs, the consumptive use of water by crops and the yield of underground supplies. In general, there are two approaches in the evaporation estimation, namely, direct and indirect. The indirect methods such as the Penman and Priestley-Taylor methods are based on meteorological variables, whereas the direct methods include the class A pan evaporation measurement as well as others such as class GGI-3000 pan and class U pan. The major difficulty in using a class A pan for the direct measurements arises because of the subsequent application of coefficients based on the measurements from a small tank to large bodies of open water. Such difficulties can be accommodated by fuzzy logic reasoning and models as alternative approaches to classical evaporation estimation formulations were applied to Lake Egirdir in the western part of Turkey. This study has three objectives: to develop fuzzy models for daily pan evaporation estimation from measured meteorological data, to compare the fuzzy models with the widely-used Penman method, and finally to evaluate the potential of fuzzy models in such applications. Among the measured meteorological variables used to implement the models of daily pan evaporation prediction are the daily observations of air and water temperatures, sunshine hours, solar radiation, air pressure, relative humidity and wind speed. Comparison of the classical and fuzzy logic models shows a better agreement between the fuzzy model estimations and measurements of daily pan evaporation than the Penman method.     

Suspended load estimation using L1-fuzzy regression,L2-fuzzy regression and MARS-fuzzy regression models

ABSTRACT

The problem of estimation of suspended load carried by a river is an important topic for many water resources projects. Conventional estimation methods are based on the assumption of exact observations. In practice, however, a major source of natural uncertainty is due to imprecise measurements and/or imprecise relationships between variables. In this paper, using the Multivariate Adaptive Regression Splines (MARS) technique, a novel fuzzy regression model for imprecise response and crisp explanatory variables is presented. The investigated fuzzy regression model is applied to forecast suspended load by discharge based on two real-world datasets. The accuracy of the proposed method is compared with two well-known parametric fuzzy regression models, namely, the fuzzy least-absolutes model and the fuzzy least-squares model. The comparison results reveal that the MARS-fuzzy regression model performs better than the other models in suspended load estimation for the particular datasets. This comparison is done based on four goodness-of-fit criteria: the criterion based on similarity measure, the criterion based on absolute errors and the two objective functions of the fuzzy least-absolutes model and the fuzzy least-squares model. The proposed model is general and can be used for modelling natural phenomena whose available observations are reported as imprecise rather than crisp.

Editor D. Koutsoyiannis; Associate editor H. Aksoy     

Spatial variability of precipitation regimes over Turkey

Abstract

This study aims to predict the daily precipitation from meteorological data from Turkey using the wavelet—neural network method, which combines two methods: discrete wavelet transform (DWT) and artificial neural networks (ANN). The wavelet—ANN model provides a good fit with the observed data, in particular for zero precipitation in the summer months, and for the peaks in the testing period. The results indicate that wavelet—ANN model estimations are significantly superior to those obtained by either a conventional ANN model or a multi linear regression model. In particular, the improvement provided by the new approach in estimating the peak values had a noticeably high positive effect on the performance evaluation criteria. Inclusion of the summed sub-series in the ANN input layer brings a new perspective to the discussions related to the physics involved in the ANN structure.     

Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.     

A new fuzzy linear regression approach for dissolved oxygen prediction

Abstract

A new method for fuzzy linear regression is proposed to predict dissolved oxygen using abiotic factors in a riverine environment, in Calgary, Canada. The proposed method is designed to accommodate fuzzy regressors, regressand and coefficients, i.e. representing full system uncertainty. The regression equation is built to minimize the distance between fuzzy numbers, and generalizes to crisp regression when crisp parameters are used. The method is compared to two existing fuzzy linear regression techniques: the Tanaka method and the Diamond method. The proposed new method outperforms the existing methods with higher Nash-Sutcliffe efficiency, and lower RMSE, AIC and total fuzzy distance. The new method demonstrates that nonlinear membership functions are more suitable for representing uncertain environmental data than the typical triangular representations. A result of this research is that low DO prediction is improved and consequently the approach can be used for risk analysis by water resource managers.

Editor D. Koutsoyiannis; Associate editor T. Okruszko     

An evaluation of numerical weather prediction based rainfall forecasts

ABSTRACT

Assessment of forecast precipitation is required before it can be used as input to hydrological models. Using radar observations in southeastern Australia, forecast rainfall from the Australian Community Climate Earth-System Simulator (ACCESS) was evaluated for 2010 and 2011. Radar rain intensities were first calibrated to gauge rainfall data from four research rainfall stations at hourly time steps. It is shown that the Australian ACCESS model (ACCESS-A) overestimated rainfall in low precipitation areas and underestimated elevated accumulations in high rainfall areas. The forecast errors were found to be dependent on the rainfall magnitude. Since the cumulative rainfall observations varied across the area and through the year, the relative error (RE) in the forecasts varied considerably with space and time, such that there was no consistent bias across the study area. Moreover, further analysis indicated that both location and magnitude errors were the main sources of forecast uncertainties on hourly accumulations, while magnitude was the dominant error on the daily time scale. Consequently, the precipitation output from ACCESS-A may not be useful for direct application in hydrological modelling, and pre-processing approaches such as bias correction or exceedance probability correction will likely be necessary for application of the numerical weather prediction (NWP) outputs.

EDITOR M.C. Acreman ASSOCIATE EDITOR A. Viglione     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi