Application of distributed hydrological models for predictions in ungauged basins: a method to quantify predictive uncertainty

Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd.     

Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins

Approaches to modeling the continuous hydrologic response of ungauged basins use observable physical characteristics of watersheds to either directly infer values for the parameters of hydrologic models, or to establish regression relationships between watershed structure and model parameters. Both these approaches still have widely discussed limitations, including impacts of model structural uncertainty. In this paper we introduce an alternative, model independent, approach to streamflow prediction in ungauged basins based on empirical evidence of relationships between watershed structure, climate and watershed response behavior. Instead of directly estimating values for model parameters, different hydrologic response behaviors of the watershed, quantified through model independent streamflow indices, are estimated and subsequently regionalized in an uncertainty framework. This results in expected ranges of streamflow indices in ungauged watersheds. A pilot study using 30 UK watersheds shows how this regionalized information can be used to constrain ensemble predictions of any model at ungauged sites. Dominant controlling characteristics were found to be climate (wetness index), watershed topography (slope), and hydrogeology. Main streamflow indices were high pulse count, runoff ratio, and the slope of the flow duration curve. This new approach provided sharp and reliable predictions of continuous streamflow at the ungauged sites tested.     

Improving streamflow estimation in ungauged basins using a multi-modelling approach

ABSTRACT

In this study, a multi-modelling approach is proposed for improved continuous daily streamflow estimation in ungauged basins using regionalization—the process of transferring hydrological data from gauged to ungauged watersheds. Four regionalization models, two data-driven and two hydrological, were used for continuous daily streamflow estimation. Comparison of the individual models reveals that each of the four models performed well on a limited number of ungauged basins while none of them performed well for the entire 90 selected watersheds. The results obtained from the four models are evaluated and reported in a deterministic way by a model combination approach along with its uncertainty range consisting of 16 ensemble members. It is shown that a combined model of the four individual models performed well on all 90 watersheds and the ensemble range can account for the uncertainty of models. The combined model was more efficient and appeared more robust compared to the individual models. Furthermore, continuous ranked probability scores (CRPS) calculated for the ensemble model outputs indicate better performance compared to individual models and competitive with the combined model.

EDITOR A. Castellarin ASSOCIATE EDITOR G. Di Baldassarre     

Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa

Abstract

The increasing demand for water in southern Africa necessitates adequate quantification of current freshwater resources. Watershed models are the standard tool used to generate continuous estimates of streamflow and other hydrological variables. However, the accuracy of the results is often not quantified, and model assessment is hindered by a scarcity of historical observations. Quantifying the uncertainty in hydrological estimates would increase the value and credibility of predictions. A model-independent framework aimed at achieving consistency in incorporating and analysing uncertainty within water resources estimation tools in gauged and ungauged basins is presented. Uncertainty estimation in ungauged basins is achieved via two strategies: a local approach for a priori model parameter estimation from physical catchment characteristics, and a regional approach to regionalize signatures of catchment behaviour that can be used to constrain model outputs. We compare these two sources of information in the data-scarce region of South Africa. The results show that both approaches are capable of uncertainty reduction, but that their relative values vary.

Editor D. Koutsoyiannis

Citation Kapangaziwiri, E., Hughes, D.A., and Wagener, T., 2012. Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa. Hydrological Sciences Journal, 57 (5), 1000–1019.     

Can climate variability information constrain a hydrological model for an ungauged Costa Rican catchment?

Long‐term hydrological data are key to understanding catchment behaviour and for decision making within water management and planning. Given the lack of observed data in many regions worldwide, such as Central America, hydrological models are an alternative for reproducing historical streamflow series. Additional types of information—to locally observed discharge—can be used to constrain model parameter uncertainty for ungauged catchments. Given the strong influence that climatic large‐scale processes exert on streamflow variability in the Central American region, we explored the use of climate variability knowledge as process constraints to constrain the simulated discharge uncertainty for a Costa Rican catchment, assumed to be ungauged. To reduce model uncertainty, we first rejected parameter relationships that disagreed with our understanding of the system. Then, based on this reduced parameter space, we applied the climate‐based process constraints at long‐term, inter‐annual, and intra‐annual timescales. In the first step, we reduced the initial number of parameters by 52%, and then, we further reduced the number of parameters by 3% with the climate constraints. Finally, we compared the climate‐based constraints with a constraint based on global maps of low‐flow statistics. This latter constraint proved to be more restrictive than those based on climate variability (further reducing the number of parameters by 66% compared with 3%). Even so, the climate‐based constraints rejected inconsistent model simulations that were not rejected by the low‐flow statistics constraint. When taken all together, the constraints produced constrained simulation uncertainty bands, and the median simulated discharge followed the observed time series to a similar level as an optimized model. All the constraints were found useful in constraining model uncertainty for an—assumed to be—ungauged basin. This shows that our method is promising for modelling long‐term flow data for ungauged catchments on the Pacific side of Central America and that similar methods can be developed for ungauged basins in other regions where climate variability exerts a strong control on streamflow variability.     

基于卫星遥感的太湖蓝藻水华时空分布规律认识

由于大尺度水文模型和无资料区水文研究是当前国际水文研究的重点和难点,通过参数区域化方法来估计大尺度区域和无资料区的模型参数值成为了研究的热点之一将HBV模型应用于东江流域及其子流域,采用代理流域法和全局乎均法来估计该区域内无资料流域的模型参数研究表明：HBV模型能较好得用于东江流域径流模拟;交叉检验中,较小的序和ME值对应的参数,其转移效果不一定比较大的R^2和ME值对应的参数转移效果差;全局平均法中,面积权重平均值和泰森多边形插值后平均并不能明显改进子流域算术平均值估计无资料流域的模型参数的模拟结果;两者都能有效用于东江流域无资料流域的参数估计,且效果相差不大。     

How informative are stream level observations in different geographic regions?

Simple runoff models with a low number of model parameters are generally able to simulate catchment runoff reasonably well, but they rely on model calibration, which makes their use in ungauged basins challenging. In a previous study it has been shown that a limited number of streamflow measurements can be quite informative for constraining runoff models. In practice, however, instead of performing such repeated flow measurements, it might be easier to install a stream level logger. Here, a dataset of 600+ gauged basins in the USA was used to study how well models perform when only stream level data, rather than streamflow data, are available. A runoff model (the HBV model) was calibrated assuming that only stream level observations were available, and the simulations were evaluated on the full observed streamflow record. The results indicate that stream level data alone can already provide surprisingly good model simulation results in humid catchments, whereas in arid catchments some form of quantitative information (e.g. a streamflow observation or a regional average value) is needed to obtain good results. These results are encouraging for hydrological observations in data scarce regions as level observations are much easier to obtain than streamflow measurements. Based on runoff modelling, it might even be possible to derive streamflow time series from the level data obtained from loggers, satellites or community‐based approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel approach to infer streamflow signals for ungauged basins

In this paper, we present a novel paradigm for inference of streamflow for ungauged basins. Our innovative procedure fuses concepts from both kernel methods and data assimilation. Based on the modularity and flexibility of kernel techniques and the strengths of the variational Bayesian Kalman filter and smoother, we can infer streamflow for ungauged basins whose hydrological and system properties and/or behavior are non-linear and non-Gaussian. We apply the proposed approach to two watersheds, one in California and one in West Virginia. The inferred streamflow signals for the two watersheds appear promising. These preliminary and encouraging validations demonstrate that our new paradigm is capable of providing accurate conditional estimates of streamflow for ungauged basins with unknown and non-linear dynamics.     

新安江模型在资料匮乏的长江中下游山区中小流域洪水预报应用

水文资料匮乏流域的洪水预报(PUBs)是水文科学与工程中一个尚未解决的重大挑战.中国湿润山区中小流域大多是水文资料匮乏的流域,在此地区进行洪水预报的重要手段之一就是水文模型参数的估计.对基于参数物理意义的估算方法(以下简称物理估算法)及两种区域化方法进行了研究,将其用于新安江模型参数的估算及移植.皖南山区的29个中小流域被选作水文资料丰富的测量流域,鄂西山区的3个中小流域被视为水文资料匮乏的目标流域,目的是研究目标流域与测量流域空间位置较远但物理条件相似时,区域化等方法是否可以有效估计模型参数.结果表明,即使目标流域与测量流域空间距离较远,区域化及物理估算法也能一定程度上减少参数估计导致的模型效率损失,且在研究区的最优参数估计方案为单流域物理相似法结合回归法及物理估算法.为长江中下游资料匮乏的山区中小流域提出了可行的新安江模型参数估计方案,为该地区的洪水预报提供指导.     

Use of a parsimonious rainfall–run‐off model for predicting hydrological response in ungauged basins

A new parameter parsimonious rainfall–run‐off model, the Distance Distribution Dynamics (DDD) model, is used to simulate hydrological time series at ungauged sites in the Lygne basin in Norway. The model parameters were estimated as functions of catchment characteristics determined by geographical information system. The multiple regression equations relating catchment characteristics and model parameters were trained from 84 calibrated catchments located all over Norway, and all model parameters showed significant correlations with catchment characteristics. The significant correlation coefficients (with p‐value < 0.05) ranged from 0.22 to 0.55. The suitability of DDD for predictions in ungauged basins was tested for 17 catchments not used to estimate the multiple regression equations. For ten of the 17 catchments, deviations in Nash–Sutcliffe efficiency (NSE) criteria between the calibrated and regionalised model were less than 0.1, and for two calibrated catchments within the Lygne basin, the deviations were less than 0.08. The median NSE for the regionalized DDD for the 17 catchments for two time series was 0.66 and 0.72. Deviations in NSE between calibrated and regionalised models are well explained by the deviations between calibrated and regressed parameters describing spatial snow distribution and snowmelt respectively. The quality of the simulated run‐off series for the ungauged sites in the Lygne basin was assessed by comparing flow indices describing high, medium and low flow estimated from observed run‐off at the 17 catchments and for the simulated run‐off series. The indices estimated for the simulated series were generally well within the ranges defined by the 17 observed series. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling daily streamflow at ungauged catchments: what information is necessary?

Rainfall–runoff modelling at ungauged catchments often involves the transfer of calibrated model parameters from ‘donor’ gauged catchments. However, in any rainfall–runoff model, some parameters tend to be more sensitive to the objective function, whereas others are insensitive over their entire feasible range. In this paper, we analyse the effect of selectively transferring sensitive versus insensitive parameters on streamflow predictability at ungauged catchments. We develop a simple daily time‐step rainfall–runoff model [exponential bucket hydrologic model (EXP‐HYDRO)] and calibrate it at 756 catchments within the continental USA. Nash–Sutcliffe efficiency of (NS) is used as the objective function. The model simulates satisfactorily at 323 catchments (NS > 0.6), most of which are located in the eastern part of the USA, along the Rocky Mountain Range, and near the western Pacific coast. Of the six calibration parameters, only three parameters are found to be sensitive to NS. Two of these parameters control the hydrograph recession behaviour of a catchment, and the third parameter controls the snowmelt rate. We find that when only sensitive parameters are transferred, model performance at ungauged catchments is almost at par with that of transferring all six parameters. Conversely, the transfer of only insensitive parameters results in a significant deterioration in model performance. Results suggest that streamflow predictability at ungauged catchments using rainfall–runoff models is largely dependent on the transfer of a small subset of parameters. We recommend that, in any modelling framework, such parameters should be identified and further characterized to better understand the information controlling streamflow predictability at ungauged catchments. Copyright © 2012 John Wiley & Sons, Ltd.     

Observed hydrographs: on their ability to infer a time‐invariant hydrological transfer function for flow prediction in ungauged basins

Streamflow measurements provide information about the flow generation characteristics of land surfaces as well as the flow transferring nature of the channel network. In this study, such flow transferring properties of the channel network that were obtained from downstream flow observations were used for predicting flow in ungauged basins. A temporally averaged transfer function (ATF) of the channel segments of Kentucky River Basin (KRB) in Kentucky, USA, was extracted from observed hydrographs in a time‐invariant system as a function of drainage area. The ATF was regionalized through multiple regression analysis for 194 combinations of drainage areas that differ in topography, terrain, and geology. The application of ATF for flow prediction in ungauged basins was performed for Goose Creek, a subbasin of KRB by integrating ATF with the TOPMODEL. In addition, the ATF was shown to be capable of providing calibration and validation data for ungauged basins in a backward technique from a measured stream gauge downstream, with minimal data requirement of drainage area. The applicability of ATF was illustrated across a range of streamflow conditions from watersheds that varied greatly in their terrain and geology. Nash–Sutcliffe efficiency of the proposed method, as a function of drainage areas of the corresponding basins, to predict daily streamflow from ungauged basins ranged from 0.83 to 0.92. The results of the study concluded that the ATF obtained from measured streamflow thus proved to be a quick and simple tool for assessment of streamflow in both operational and modeling hydrology. Copyright © 2012 John Wiley & Sons, Ltd.     

Regional calibration of a watershed model

Abstract

As watershed models become increasingly sophisticated and useful, there is a need to extend their applicability to locations where they cannot be calibrated or validated. A new methodology for the regionalization of a watershed model is introduced and evaluated. The approach involves calibration of a watershed model to many sites in a region, concurrently. Previous research that has sought to relate the parameters of monthly water balance models to physical drainage basin characteristics in a region has met with limited success. Previous studies have taken the two-step approach: (a) estimation of watershed model parameters at each site, followed by (b) attempts to relate model parameters to drainage basin characteristics. Instead of treating these two steps as independent, both steps are implemented concurrently. All watershed models in a region are calibrated simultaneously, with the dual objective of reproducing the behaviour of observed monthly streamflows and, additionally, to obtain good relationships between watershed model parameters and basin characteristics. The approach is evaluated using 33 basins in the southeastern region of the United States by comparing simulations using the regional models for three catchments which were not used to develop the regional regression equations. Although the regional calibration approach led to nearly perfect regional relationships between watershed model parameters and basin characteristics, these “improved” regional relationships did not result in improvements in the ability to model streamflow at ungauged sites. This experiment reveals that improvements in regional relationships between watershed model parameters and basin characteristics will not necessarily lead to improvements in the ability to calibrate a watershed model at an ungauged site.     

IAHS Decade on Predictions in Ungauged Basins (PUB), 2003–2012: Shaping an exciting future for the hydrological sciences

Abstract

Drainage basins in many parts of the world are ungauged or poorly gauged, and in some cases existing measurement networks are declining. The problem is compounded by the impacts of human-induced changes to the land surface and climate, occurring at the local, regional and global scales. Predictions of ungauged or poorly gauged basins under these conditions are highly uncertain. The IAHS Decade on Predictions in Ungauged Basins, or PUB, is a new initiative launched by the International Association of Hydrological Sciences (IAHS), aimed at formulating and implementing appropriate science programmes to engage and energize the scientific community, in a coordinated manner, towards achieving major advances in the capacity to make predictions in ungauged basins. The PUB scientific programme focuses on the estimation of predictive uncertainty, and its subsequent reduction, as its central theme. A general hydrological prediction system contains three components: (a) a model that describes the key processes of interest, (b) a set of parameters that represent those landscape properties that govern critical processes, and (c) appropriate meteorological inputs (where needed) that drive the basin response. Each of these three components of the prediction system, is either not known at all, or at best known imperfectly, due to the inherent multi-scale space—time heterogeneity of the hydrological system, especially in ungauged basins. PUB will therefore include a set of targeted scientific programmes that attempt to make inferences about climatic inputs, parameters and model structures from available but inadequate data and process knowledge, at the basin of interest and/or from other similar basins, with robust measures of the uncertainties involved, and their impacts on predictive uncertainty. Through generation of improved understanding, and methods for the efficient quantification of the underlying multi-scale heterogeneity of the basin and its response, PUB will inexorably lead to new, innovative methods for hydrological predictions in ungauged basins in different parts of the world, combined with significant reductions of predictive uncertainty. In this way, PUB will demonstrate the value of data, as well as provide the information needed to make predictions in ungauged basins, and assist in capacity building in the use of new technologies. This paper presents a summary of the science and implementation plan of PUB, with a call to the hydrological community to participate actively in the realization of these goals.     

Scaling and physiographic controls on streamflow behaviour on the Precambrian Shield, south-central Ontario

Relationships explaining streamflow behaviour in terms of drainage basin physiography greatly assist efforts to extrapolate streamflow metrics from gauged to ungauged basins in the same landscape. The Dorset Environmental Science Centre (DESC) has monitored streamflow from 22 small basins (3.4–190.5 ha) on the Precambrian Shield in south-central Ontario, in some cases since 1976. The basins exhibit regional coherence in their interannual response to precipitation; however, there is often a poor correlation between streamflow metrics from basins separated by as little as 1 km. This study assesses whether inter-basin variations in such metrics can be explained in terms of basin scale and physiography. Several characteristics (annual maximum, minimum and average flow) exhibited simple scaling with basin area, while magnitude, range and timing of annual maximum daily runoff showed scaling behaviour consistent with the Representative Elementary Area (REA) concept. This REA behaviour is partly attributed to convergence of fractional coverage of the two dominant and hydrologically-contrasting land cover types in the DESC region with increasing basin size. Three Principal Components (PCs) explained 82.4% of the variation among basin physiographic properties, and several runoff metrics (magnitude and timing of annual minimum daily runoff, mean number of days per year with 0 streamflow) exhibited significant relationships with one or more PC. Significant relationships were obtained between basin quickflow (QF) production and the PCs on a seasonal and annual basis, almost all of which were superior to simple area-based relationships. Basin physiography influenced QF generation via its control on slope runoff, water storage and hydrologic connectivity; however, this role was minimized during Spring when QF production in response to large rain-on-snow events was relatively uniform across the DESC basins. The PC-based relationships and inter-seasonal changes in their form were consistent with previous research conducted at point, slope and basin scales in the DESC region, and perceptions of key hydrological processes in these small basins may not have been as readily obtained from scaling studies using streamflow from larger basins. This process understanding provides insights into scaling behaviour beyond those derived from simple scaling and REA analyses. The physiography of the study area is representative of large portions of the Precambrian Shield, such that basin streamflow behaviour could potentially be extended across much of south-central Ontario. This would assist predictions of streamflow conditions at ungauged locations, development and testing of hydrological models for this landscape, and interpretation of inter-basin and intra-annual differences in hydrochemical behaviour on the southern Precambrian Shield.     

Modeling Monthly Mean Flow in a Poorly Gauged Basin by Fuzzy Logic

The estimation of the monthly mean flow is a critical issue in many water resource development projects. However, in practice the mean flow is not easily determined in ungauged and poorly gauged basins. Therefore, in the literature, various flow estimation methods have been developed recently for mountainous regions which are generally ungauged or poorly gauged basins. In this study a fuzzy logic model based on the Mamdani approach was developed to estimate the flow for poorly gauged mountainous basins. This model was applied to the Solakli Basin which is located in the Eastern Black Sea Region of Turkey. Limited rainfall and flow data are available for this basin. In addition to these variables, the stream and time coefficients were introduced and used as variables for modeling. The data was divided into training and testing phases. The model results were compared with the measured data. The comparison depends on seven statistical characteristics, four different error modes and the contour map method. It was observed that the fuzzy model developed in this study yielded reliable results.     

A canonical correlation approach to the determination of homogeneous regions for regional flood estimation of ungauged basins

Abstract

A canonical correlation method for determining the homogeneous regions used for estimating flood characteristics of ungauged basins is described. The method emphasizes graphical and quantitative analysis of relationships between the basin and flood variables before the data of the gauged basins are used for estimating the flood variables of the ungauged basin. The method can be used for both homogeneous regions, determined a priori by clustering algorithms in the space of the flood-related canonical variables, as well as for “regions of influence” or “neighbourhoods” centred on the point representing the estimated location of the ungauged basin in that space.     

On a PUB methodology from Chinese lessons

Abstract

Based on a Chinese saying: “Even a clever housewife cannot cook a meal without rice”, a simple categorization of the methods for Predictions in Ungauged Basins (PUB) is proposed, including: Borrowing, obtaining hydrological information by transplanting measurements from a similar basin, or extrapolating/interpolating the data from neighbouring catchments; Substituting, finding substitutes either from the ungauged basin or from donating area(s); and Generating, obtaining data via field or laboratory observations. The Substituting category is classified further into: S1, substitution only from within the ungauged basin using fully process-based models without calibration; S2-1, from similar gauged basins using established index/distribution; S2-2, from various gauged basins using regression and/or process-based relationships between the climate/catchment features and hydrological signatures (CCH), and S3, from the information beyond the CCH relationship. Based on a review, the Darwinian S2-2 and Newtonian S1 were found to be the two most popular methods, both for China and worldwide PUB.

Editor Z.W. Kundzewicz