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The probability distribution of daily streamflow in perennial rivers of Angola
Abstract
Hydrological observations in Angola are quite scarce and, as such, the water allocation process, one of the main components of water resources management, is commonly undertaken with a high degree of uncertainty. It is, therefore, vital to increase our understanding of the hydrological processes, namely the frequency distribution of daily streamflow, in this part of southern Africa and validate efficient methods that facilitate the extrapolation of information from gauged to ungauged catchments. All the components of this study were carefully designed to address all the above-mentioned goals. This was achieved with the modelling of 121 flow-duration curve samples observed in different parts of the country, including large datasets (e.g., 1954/55 to 1968/69) but mainly focused on the hydrological years of 1967/1968 and 1973/1974 and the implementation of regional frequency analysis based on the L-moments approach. The frequency distribution of daily streamflow was approximated with nine different probability distribution functions considering different subsets of the daily streamflow time series: (i) daily streamflow (ii) different subsets of daily streamflow divided into two ‘flows seasons’, wet and dry, (iii) and the previous subsets transformed with the definition of a thirty-day time lag, thereby reducing the serial dependency of daily streamflow and enabling the use of the L-moments approach. Overall, the results enabled two probability distribution functions to be identified able to provide a remarkable approximation to all the above-mentioned daily streamflow datasets (the four-parameter Kappa and three-parameter Generalized Pareto distributions). Furthermore, the regional frequency analysis supported the prediction of daily streamflow quantiles for eight test catchments with impressive accuracy (Nash-Sutcliffe efficiency coefficient: μ = 0.86; σ = 0.10; Pearson correlation coefficient: μ = 0.97; σ = 0.02), clearly showing that this approach represents a sound alternative for the prediction of daily streamflow in ungauged catchments located in this region.
... The graphic method is based on exploring the relationship between the shape characteristics of FDC and the climate and geomorphologic characteristics of the catchment, such as the steepness or quantile of the curve, to estimate the shape of the FDC, which represents the flow condition of unmeasured catchments (Mohamoud, 2008). The statistical method aims to fit the empirical FDC through appropriate distribution functions (such as gamma distribution, lognormal distribution, generalized Pareto distribution, kappa distribution, etc.) (Almeida et al., 2021;Burgan & Aksoy, 2022;Cheng et al., 2012;Ghotbi, Wang, Singh, Blöschl, & Sivapalan, 2020;Ghotbi, Wang, Singh, Mayo, & Sivapalan, 2020;Shin & Park, 2022), and then find the quantitative and qualitative relationship between the estimated parameters of the fitting function and the characteristics of the local climate and geographical environment of the measured catchment. Villalobos and Neelin explained why the gamma distribution can well fit the daily precipitation distribution. ...
The flow duration curve (FDC) is the cumulative distribution function, which represents the relationship between the frequency and magnitude of streamflow, and the precipitation duration curves (PDC) follows the same principle. Nowadays, the correlation between the shape of PDC and FDCs, their respective physical control factors including human activities, and their fitting conditions in unmeasured catchments across China have not been fully understood. In this paper, daily precipitation and streamflow data with 30 years records from 224 hydrological stations in the middle and lower Yangtze River basin were chosen to fit PDC and FDCs through gamma distribution. Framework was proposed for modelling FDCs to analyse the relationship, similarity, regional patterns and response mechanism of fitting parameters between PDC and FDCs, dividing the streamflow time series into fast and base flow and stations into three categories in consideration of human activities to attribute the shapes of PDC and FDCs to catchment meteorological and geographical characteristics and physical processes under natural conditions. Results indicate that the parameters of PDC and certain FDCs (TFDC, FFDC, SFDC) share similar spatial patterns but vary for the different duration and interactions of the processes. The climate and catchment characteristics such as extreme properties of precipitation, base flow index ( BFI ), P max *α p and concentration ratio index ( CIM ) will influence the shape of PDC and FDCs. The relationship between BFI and SFDC/TFDC can be better reflected in “Regulated watersheds”, while CIM/ P max * α p and PDC/FFDC in “watersheds in the mainstream” are more related. This paper provides a deeper understanding and more accurate way of the application of these parameters in describing and predicting hydrological processes and estimation of PDC and FDCs in unmeasured catchments, and can be applied to more future research about processes based on catchment rainfall‐runoff responses and physical controls.
... The applicability of these common PDFs to the statistical FFD from the measured data was evaluated. Due to the complexity and nonindependence of continuous daily flow data series, there is a current lack of a standard theoretical function and a rigorous fitting method for daily FFDs (Segura and Pitlick, 2010;Almeida et al., 2021). To emphasise the behaviours of different magnitudes of discharge, the logarithmic Nash-Sutcliffe efficiency coefficient (LNSE, Eq. (1)) was used as the goodness-of-fit criterion (WöHling et al., 2013). ...
In natural quasi-equilibrium rivers or anthropogenically-influenced nonequilibrium rivers, the occurrence frequency and sediment transport capacity of different flow levels are greatly important to understanding the linkage between forms and processes. However, our knowledge of the controlling factors on flow frequency and sediment-transport magnitude in large river systems remains limited. In this paper, the hydrological and sediment-transport characteristics of the middle and lower Yangtze River (MLYR) were systematically examined before and after impoundment of the Three Georges Reservoir (TGR). More than 30 years of daily discharge and suspended sediment concentration data were collected from six hydrological stations. The results showed that in the pre-TGR period, the flow frequency distributions (FFDs) and sediment-transport rating curves had segmen-tation characteristics. Generally, the FFDs of medium-high flow agreed well with the broken power law, and the sediment-transport rating curves deviated from the power law at high flow. This was because the floodplains, especially the Dongting Lake, had significant effects on flood attenuation and sediment storage. Compared the inflection points of the FFD and the sediment-transport rating curve, as well as the effective discharge and bankfull discharge, these four values were of the same order of magnitude. This suggested that the local river system had a dominant effect on the hydrological and sediment-transport characteristics. In the post-TGR period, the overall characteristics of the FFDs were preserved, but the segmental characteristics of the sediment-transport rating curves at higher discharges disappeared. Through analysis, the effective discharge was largely determined by the inflection value (a 1) of the FFD. The reduced a 1 induced a 10%-20% decrease in effective discharge, which indicated flood channel shrinkage in the long run. These findings not only further the understanding of water-sediment regimes in a large alluvial river with an extensive floodplain system but also offer guidance for improving dam operation schemes for river restoration.
... The graphic method is based on exploring the relationship between the shape characteristics of FDC and the climate and geomorphologic characteristics of the catchment, such as the steepness or quantile of the curve, to estimate the shape of the FDC, which represents the flow condition of unmeasured catchments (Mohamoud, 2008). The statistical method aims to fit the empirical FDC through appropriate distribution functions (such as gamma distribution, lognormal distribution, generalized Pareto distribution, kappa distribution, etc.) (Almeida et al., 2021;Burgan & Aksoy, 2022;Cheng et al., 2012;Ghotbi, Wang, Singh, Blöschl, & Sivapalan, 2020;Ghotbi, Wang, Singh, Mayo, & Sivapalan, 2020;Shin & Park, 2022), and then find the quantitative and qualitative relationship between the estimated parameters of the fitting function and the characteristics of the local climate and geographical environment of the measured catchment. Villalobos and Neelin explained why the gamma distribution can well fit the daily precipitation distribution. ...
The flow duration curve (FDC) is the cumulative distribution function, which represents the relationship between the frequency and magnitude of streamflow，and the precipitation duration curves (PDC) follows the same principle. Nowadays, the correlation between the shape of PDC and FDC curves, their respective physical control factors, and their fitting conditions in unmeasured catchments across China have not been fully understood. In this paper, daily precipitation from 698 weather stations across China and streamflow from more than 200 hydrological stations in the middle and lower Yangtze River basin were chosen to analyze the relationship, similarity, regional pattern and response mechanism of fitting parameters between PDC and FDCs. Framework was proposed for modeling FDC, decomposing the Streamflow time series into fast flow and slow flow time series and attributing the shapes of PDC and FDCs to catchment meteorological and geographical characteristics and physical processes. Results indicate that the parameters of PDC and certain FDCs (TFDC, FFDC, SFDC) share similar spatial patterns but the value of parameters and shape of curves varies for the different duration and interactions of the processes. The climate and catchment characteristics such as extreme properties of precipitation, base flow index ( BFI ), Pmax*αp and concentration ratio index based on monthly precipitation ( CIM ) will influence the shape of normalized PDC and FDCs, which provides a way to predict unmeasured catchments for PDC and FDCs, diagnose catchment rainfall-runoff responses, including similarity and differences between catchments, and can be applied to more future research about processes based on physical controls.
... Blum et al. (2017) tried to identify the probability distribution of daily streamflows across the conterminous United States (US) at nearly 400 unregulated, perennial streams and found KAP to be a good alternative along with three-parameter generalized Pareto (GPA) and lognormal distributions (LN) which can also be applied in some US regions. Almeida et al. (2021) concluded that four-parameter Kappa and three-parameter Generalized Pareto distributions are sufficient for characterizing the daily streamflow frequency distribution in Angola, Southern Africa. The correct identification of the distribution describing the daily streamflow dataset considering the right tail enables the estimation of return periods corresponding to any flood amount (i.e., the average time interval for an event of a given magnitude to be exceeded). ...
The adequate choice of a distribution that can fit a dataset, especially to its right tail (large extreme events), is a major problem in flood frequency analysis. Decision support systems (DSS) have been used in the past to define the appropriate class of distribution based on the tail behaviour of the data before its model selection. This paper investigates the tail behaviour of probability distribution of the daily streamflow data in south Indian rivers and also assesses the information related to tail risk, as it has many practical and societal consequences. In this paper, we apply and compare two DSS, (i) given by Martel et al. (J Hydrol Eng 18(1):1–9, 2013) and (ii) concentration profile–concentration adjusted expected shortfall (CP–CAES) based DSS, along with some newly developed graphical diagnostic tools, such as CP, CAES, discriminant moment ratio plot, maximum-to-sum plot, and Zenga plot to characterize the tails of probability distributions into an appropriate class. Further, the tail risk is analyzed using a novel risk management approach known as a concentration map (CM), which makes use of the concentration profiles of daily streamflow datasets. Results indicate that the proposed DSS is a potential tool for tail characterization. The study suggests the use of heavy-tailed distributions to model daily streamflow data over south Indian catchments. Neglecting heavy-tailed distributions, when found appropriate, can lead to an underestimation of the likelihood of floods and has catastrophic consequences for risk. CM is found suitable for assessing the tail risk associated with the daily streamflow dataset, which inherently represents the frequency and magnitude of extreme floods.
... The annual mean flow on the Tana river was found to fit the lognormal and generalized extreme value probability distributions best (Langat et al. 2019). Both the four-parameter Kappa and three-parameter Generalized Pareto distributions were found to approximate daily streamflow dataset in Angola (Almeida et al. 2021). The Weibull probability distribution gave the best parameters when fitted to the monthly discharge in Strymon river, Greece (Antonopoulos et al. 2001). ...
Rivers are important for domestic, industrial, agricultural, and geopolitical purposes. Within the tropics, rivers are fed by rainfall and underground recharge. Understanding the contribution of rainfall to the dynamics of river is necessary for several reasons. In this study, the best fit marginal probability distribution function for rainfall and river discharge from among Gamma, Beta, Gaussian, Student T, and Uniform were considered. Furthermore, the dependence between rainfall and river discharge was investigated using three copula functions: Gumbel, Clayton and Frank. Results obtained suggests that the Student T’s distribution was best suited for rainfall and river discharge at Lokoja. It was also found that using the Akaike Information Criteria, that the Frank copula provides the best model for dependence between rainfall and river discharge. These results are important for an effective integrated water resources planning and management.
This paper aims to solve the problem of accurately estimating flow duration curves (FDC) in catchments lacking diachronic flow data. Based on 645 sets of observed data in the middle and lower reaches of the Yangtze River (YZR), which include 22 basin characteristic variables, eight machine learning (ML) models (SVM, RF, BPNN, ELM, XGB, RBF, PSO-BP, GWO-BP) were integrated to predict the FDC (quantiles of flow rate corresponding to 15 exceedance probabilities were studied), after which the model most suitable for predicting was determined. Finally, the SHapley Additive exPlanation (SHAP) method was used to determine and quantify the impact of various input variables on different quantiles and the degree of that influence. Results indicate that: (1) The GWO-BP model is the best ML model for predicting FDC among the eight, having good prediction performances throughout the entire duration with determination coefficients (R2) on the testing set of 0.86 to 0.94 and Nash-Sutcliff criterion (NSE) of 0.78 to 0.94. (2) The ML model (BPNN) optimized using swarm intelligence can effectively predict FDC. (3) The predictive impact of variables on different quantiles varies, with and BFI_mean contributes significantly to predicting FDC. The former has a negative effect on the prediction result and has better contribution to predicting higher flow rate (i.e., having higher accuracy in predicting the upper tail of FDC), whereas the latter is the opposite. SHAP’s explanations are consistent with the physical model, revealing local interactions between predictive factors. The results demonstrate that the method proposed in this paper can greatly improve the prediction accuracy and is innovative and valuable in model interpretation and factor selection.
This report presents the results of Phase 1 Hydrogeological survey, aiming at identifying 5 potential areas for groundwater prospection for meeting the future water supply demand of Lubango city.
A hydrogeological inventory is carried out in the Humpata plateau and surroundings - the main output is the identification of 7 areas where further geotechnical survey will be carried out.
Satellite precipitation products have been largely improved in the recent years particularly with the launch of the global precipitation measurement (GPM) core satellite. Moreover, the development of techniques for exploiting the information provided by satellite soil moisture to complement/enhance precipitation products have improved the accuracy of accumulated rainfall estimates over land. Such satellite enhanced precipitation products, available with a short latency (< 1 day), represent an important and new source of information for river flow prediction and water resources management, particularly in developing countries in which ground observations are scarcely available and the access to such data is not always ensured. In this study, three recently developed rainfall products obtained from the integration of GPM rainfall and satellite soil moisture products have been used; namely GPM+SM2RAIN, PRISM-SMOS, and PRISM-SMAP. The prediction of observed daily river discharge at 10 basins located in Europe (4), West Africa (3) and South Africa (3) is carried out. For comparison, we have also considered three rainfall products based on: (1) GPM only, i.e., the Early Run version of the Integrated Multi-Satellite Retrievals for GPM (GPM-ER), (2) rain gauges, i.e., the Global Precipitation Climatology Centre, and (3) the latest European Centre for Medium-Range Weather Forecasts reanalysis, ERA5. Three different conceptual and lumped rainfall-runoff models are employed to obtain robust and reliable results over the 3-year data period 2015–2017. Results indicate that, particularly over scarcely gauged areas (West Africa), the integrated products outperform both ground- and reanalysis-based rainfall estimates. For all basins, the GPM+SM2RAIN product is performing the best among the short latency products with mean Kling–Gupta Efficiency (KGE) equal to 0.87, and significantly better than GPM-ER (mean KGE = 0.77). The integrated products are found to reproduce particularly well the high flows. These results highlight the strong need to disseminate such integrated satellite rainfall products for hydrological (and agricultural) applications in poorly gauged areas such as Africa and South America.
In this study, a comparative evaluation of the statistical methods for daily streamflow estimation at ungauged basins is presented. The single donor station drainage area ratio (DAR) method, the multiple-donor stations drainage area ratio (MDAR) method, the inverse similarity weighted (ISW) method, and its variations with three different power parameters (1, 2, and 3) are applied to the two main subbasins of the Euphrates Basin in Turkey to estimate daily streamflow data. Each station in each basin is considered in turn as the target station where there are no streamflow data. The donor stations are selected based on the physical similarities between the donor and target stations. Then, streamflow data from the most physically similar donor station(s) is transferred to the target station using the statistical methods. In addition, the effect of data preprocessing on the estimation performance of the statistical methods is investigated. The preprocessing discussed in this study is streamflow data smoothing using the two-sided moving average (MA). Three statistical methods using the smoothed data by the MA, named as DAR-MA, MDAR-MA, and ISW-MA, are proposed. The estimation performance of the statistical methods is compared by using daily streamflow data with preprocessing and without preprocessing. The Nash–Sutcliffe efficiency (NSE), the ratio of the root mean square error (RMSE) to the standard deviation of the observed data (RSR), the percent bias (PBIAS), and the coefficient of determination (R2) are used to evaluate the performance of the statistical methods. The results show that MDAR and ISW give improved performances compared to DAR to estimate daily streamflow for 7 out of 8 target stations in the Middle Euphrates Basin and for 4 out of 7 target stations in the Upper Euphrates Basin. Higher NSE values for both MDAR and ISW are mostly obtained with the three most physically similar donor stations in the Middle Euphrates Basin and with the two most physically similar donor stations in the Upper Euphrates Basin. The best statistical method for each target station exhibits slightly greater NSE when the smoothed data by the MA is used for all target stations in the Middle Euphrates Basin and for 6 out of 7 target stations in the Upper Euphrates Basin.
Rapid advancements in technologies open up possibilities for water resource authorities to increase their ability to accurately, safely and efficiently establish river flow observation through remote and non-intrusive observation methods. Low-cost Unmanned Aerial Vehicles (UAVS) in combination with Global Navigation Satellite Systems (GNSS) can be used to collect geometrical information of the riverbed and floodplain. Such information, in combination with hydraulic modelling tools, can be used to establish physically based relationships between river flows and permanent proxy. This study proposes a framework for monitoring volatile, dangerous and difficult to access rivers using only affordable and easy to maintain new technologies. The framework consists of four main components: i) establishment of geometry using airborne photogrammetry and bathymetry; ii) physically based rating curve development through hydraulic modelling of surveyed river sections; iii) determination of non-intrusive observations with for instance simple cameras or satellite observations; and iv) evaluating the institutional and societal impacts of using new technology. To establish this framework, a number of research questions require addressing. First, the factors impacting on accuracy of geometrical information of the floodplain terrain and bathymetry need to be investigated. Second the accuracy of a physically based rating curve compared to a traditional rating curve needs to be established. Third, for rapidly changing river segments, it should be investigated if the collection of occasional snapshots of multiple proxies for flow can be used to assess the uncertainty of river flows. The study finally explores the social and institutional impact of using new technologies for remote river monitoring. If these research gaps are addressed, this may strengthen water manager's ability to observe flows and extend observation networks.
The design of hydraulic structures and the assessment of flood control measures require the estimation of flood quantiles. Since observed flood data are rarely available at the specific location, flood estimation in un-gauged or poorly gauged basins is a common problem in engineering hydrology. We investigated the flood estimation method in a poorly gauged basin. The flood estimation method applied the combination of rainfall-runoff model simulation and regional flood frequency analysis (RFFA). The L-moment based index flood method was performed using the annual maximum flood (AMF) data simulated by the rainfall-runoff model. The regional flood frequency distribution with 90% error bounds was derived in the Chungju dam basin of Korea, which has a drainage area of 6648 km2. The flood quantile estimates based on the simulated AMF data were consistent with the flood quantile estimates based on the observed AMF data. The widths of error bounds of regional flood frequency distribution increased sharply as the return period increased. The results suggest that the flood estimation approach applied in this study has the potential to estimate flood quantiles when the hourly rainfall measurements during major storms are widely available and the observed flood data are limited.
The Angola Low is a summertime low-pressure system that affects the convergence of low-level moisture fluxes into southern Africa. Interannual variations of the Angola Low reduce the seasonal prediction skills for this region that arise from coupled atmosphere-ocean variability. Despite its importance, the interannual dynamics of the Angola Low, and its relationship with El Niño-Southern Oscillation (ENSO) and other coupled modes of variability, are still poorly understood, mostly because of the scarcity of atmospheric data and short-term duration of atmospheric reanalyses in the region. To bypass this issue, we use a long-term(3500 years) run from a 50-km-resolution global coupled model capable of simulating the summertime southern African large-scale circulation and teleconnections. We find that the meridional displacement and strength of the Angola Loware moderately modulated by local sea surface temperature anomalies, especially those in proximity of the southeastern African coast, and to a lesser extent by ENSO and other coupled atmosphere-ocean modes like the Subtropical Indian Ocean Dipole. Comparison of the coupled run with a 1000-year run driven by climatological sea surface temperatures reveals that the interannual excursions of the Angola Low are in both cases associated with geopotential height anomalies over the southern Atlantic and Indian Ocean related to extratropical atmospheric variability. Midlatitude atmospheric variability explains almost 60% of the variance of the Angola Low variability in the uncoupled run, but only 20% in the coupled run. Therefore, while the Angola Low appears to be intrinsically controlled by atmospheric extratropical variability, the interference of the atmospheric response forced by tropical sea surface temperature anomalies weakens this influence.
This open access multi-authored book presents a 'state of the science' synthesis of knowledge on the biodiversity of Angola, based on sources in peer-reviewed journals, in books and where appropriate, unpublished official reports. The book identifies Angola as one of the most biologically diverse countries in Africa, but notes that its fauna, flora, habitats and the processes that drive the dynamics of its ecosystems are still very poorly researched and documented.
This 'state of the science' synthesis is for the use of all students of Angola's biodiversity, and for those responsible for the planning, development and sustainable management of the country's living resources. The volume brings together the results of expeditions and research undertaken in Angola since the late eighteenth century, with emphasis on work conducted in the four decades since Angola's independence in 1975. The individual chapters have been written by leaders in their fields, and reviewed by peers familiar with the region.
Regional flood frequency analysis has been carried out for estimating peak discharge at regional level over the Kerala State, India, along with at-site flood frequency analysis. For the study, the annual peak discharges of 43 gauging stations having length of data from 14 to 47 years spread over the Kerala State were used. Using L moments and L moment ratio, best fit distribution was identified among the five distributions; Generalised Extreme Value (GEV), Generalised Pareto Distribution (GPA), Generalised Logistic (GLO), Generalised Normal (LN3) and Pearson Type III (PE3) distribution for both at-site and regional flood frequency analysis. Chi-square test, ranking method using statistical indicators and L moment ratio diagram were used for identifying the best fit distribution for at-site flood frequency analysis. It was found that GPA was the best fit distribution for 27 stations, GLO for 14, LN3 for 1 station and GEV for 2 station. After discordancy test, five different homogeneous regions were identified through heterogeneity test to carry out the regional flood frequency analysis (RFFA). After identifying best-fit distributions for each zone, flood growth curves were derived by incorporating the catchment characteristics of the basins. The distribution that was best fit in case of at-site analysis for a gauging site is found to be entirely different than the best fit distribution resulted from RFFA. In RFFA, growth curves that provide the flood magnitude for various return periods can be used to estimate the flood magnitude and frequency at ungauged sites in each region of the Kerala State in India.
The devastating effects of floods, combined with scarce datasets, have stimulated the development of hydrological regionalisation techniques. The present study proposed an evaluation of the L‐moments based index‐flood procedure, coupled with watershed grouping based on geographical convenience for regionalization of maximum streamflows. A pioneer analysis for South America, addressing the geographical classification method adopted by National Water Agency of Brazil (ANA), was conducted considering over 100 watersheds in southern Brazil. Non‐stationary and discordant maximum annual streamflow series were removed with the aid of the Mann‐Kendall test and Discordancy Measure, whereas the Heterogeneity Measure was used to check regional homogeneity. The best regional distribution was identified by the ZDIST goodness‐of‐fit measure. Finally, multiple non‐linear regressions, considering morphological and meteorological watershed characteristics, were performed to obtain better index‐flood estimates. It was concluded that: i) the proposed methodological strategy provided satisfactory estimation of design floods; ii) area, mean slope, stream gradient, and flow length, were the most satisfactory explanatory variables; iii) the fitted equations stand out as a state‐of‐art alternative for the scarce hydrological monitoring in southern Brazil; iv) the hydrological boundaries defined by ANA might not be the most adequate approach from a regional point of view.
Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.
Drought indicators are used as triggers for action and so are the foundation of drought monitoring and early warning. The computation of drought indicators like the standardized precipitation index (SPI) and standardized streamflow index (SSI) require a statistical probability distribution to be fitted to the observed data. Both precipitation and streamflow have a lower bound at zero, and their empirical distributions tend to have positive skewness. For deriving the SPI, the Gamma distribution has therefore often been a natural choice. The concept of the SSI is newer and there is no consensus regarding distribution. In the present study, twelve different probability distributions are fitted to streamflow and catchment average precipitation for four durations (1, 3, 6, and 12 months), for 121 catchments throughout the UK. The more flexible three- and four-parameter distributions generally do not have a lower bound at zero, and hence may attach some probability to values below zero. As a result, there is a censoring of the possible values of the calculated SPIs and SSIs. This can be avoided by using one of the bounded distributions, such as the reasonably flexible three-parameter Tweedie distribution, which has a lower bound (and potentially mass) at zero. The Tweedie distribution has only recently been applied to precipitation data, and only for a few sites. We find it fits both precipitation and streamflow data nearly as well as the best of the traditionally used three-parameter distributions, and should improve the accuracy of drought indices used for monitoring and early warning.
This paper examines the performance of three climate re-analysis datasets in Angola, namely the ERA-40, NCEP-r1 and JRA-55, by comparing annual and seasonal estimates of precipitation, surface air temperature and evaporation with ground observation measurements. The observational dataset describes a region poorly covered by international climate databases and it is believed that most of its data have not been used in the data assimilation procedures of the climate models. This paper therefore provides a fresh look at the performance of these climate re-analysis datasets in a vast area where distance and civil war have hindered ground monitoring efforts. The re-analysis exercises offer better temperature estimates than precipitation estimates. When offered, the evaporation estimates from all three products are very poor. The three products are able to describe the main features of the spatial distribution of average annual precipitation and temperature, but struggle to reproduce the temporal changes of these variables. The results from a set of performance criteria show that the correlation between the observed ground measurements and re-analysis estimates is poor overall and the NSE values indicate that the average measured value at each location is usually a better estimate than the re-analysis estimate.
EDITOR A. Castellarin
ASSOCIATE EDITOR S. Kanae
The assessment of collective risk for flood risk management requires a better understanding of the space-time characteristics of flood magnitude and occurrence. In particular, classic formulation of collective risk implies hypotheses concerning the independence of intensity and number of events over fixed time windows that are unlikely to be tenable in real-world hydroclimatic processes exhibiting persistence. In this study, we investigate the links between the serial correlation properties of 473 daily stream flow time series across the major river basins in Europe, and the characteristics of over-threshold events which are used as proxies for the estimation of collective risk. The aim is to understand if some key features of the daily stream flow data can be used to infer properties of extreme events making a more efficient and effective use of the available data. Using benchmark theoretical processes such as Hurst-Kolmogorov (HK), generalized HK (gHK), autoregressive fractionally integrated moving average (ARFIMA) models, and Fourier surrogate data preserving second order linear moments, our findings confirm and expand some results previously reported in the literature, namely: (1) the interplay between short range dependence (SRD) and long range dependence (LRD) can explain the majority of the serial dependence structure of deseasonalized data, but losing information on nonlinear dynamics; (2) the standardized return intervals between over-threshold values exhibit a sub-exponential Weibull-like distribution, implying a higher frequency of return intervals longer than expected under independence, and expected return intervals depending on the previous return intervals; this results in a tendency to observe short (long) inter-arrival times after short (long) inter-arrival times; (3) as the average intensity and the number of events over one-year time windows are not independent, years with larger events are also the more active in terms of number of events; and (4) persistence influences the distribution of the collective risk producing a spike of probability at zero, which describes the probability of years with no events, and a heavier upper tail, suggesting a probability of more extreme annual losses higher than expected under independence. These results provide new insights into the clustering of stream flow extremes, paving the way for more reliable simulation procedures of flood event sets to be used in flood risk management strategies.
We study the ability of 24 Ocean Atmosphere global coupled models from the Coupled Model Intercomparison Project 5 (CMIP5) to reproduce the teleconnections between El Niño Southern Oscillation (ENSO) and Southern African rainfall in austral summer using historical forced simulations, with a focus on the atmospheric dynamic associated with El Niño. Overestimations of summer rainfall occur over Southern Africa in all CMIP5 models. Abnormal westward extensions of ENSO patterns are a common feature of all CMIP5 models, while the warming of the Indian Ocean that happens during El Niño is not correctly reproduced. This could impact the teleconnection between ENSO and Southern African rainfall which is represented with mixed success in CMIP5 models. Large-scale anomalies of suppressed deep-convection over the tropical maritime continent and enhanced convection from the central to eastern Pacific are correctly simulated. However, regional biases occur above Africa and the Indian Ocean, particularly in the position of the deep convection anomalies associated with El Niño, which can lead to the wrong sign in rainfall anomalies in the northwest part of South Africa. From the near-surface to mid-troposphere, CMIP5 models underestimate the observed anomalous pattern of pressure occurring over Southern Africa that leads to dry conditions during El Niño years.
Estimation of peak flow quantiles in ungauged catchments is a challenge
often faced by water professionals in many parts of the world.
Approaches to address such problem exist but widely used technique such
as flood frequency regionalization is often not subjected to performance
evaluation. In this study we used the jack-knifing principle to assess
the performance of the flood frequency regionalization in the complex
and data scarce River Nile basin by examining the error (regionalization
error) between locally and regionally estimated peak flow quantiles for
different return periods (QT). Agglomerative hierarchical
clustering based algorithms were used to search for regions with similar
hydrological characteristics taking into account the huge catchment area
and strong climatic differences across the area. Hydrological data sets
employed were from 180 gauged catchments and several physical
characteristics in order to regionalize 365 identified catchments. The
GEV distribution, selected using L-moment based approach, was used to
construct regional growth curves from which peak flow growth factors
(QT/MAF) could be derived and mapped through interpolation.
Inside each region, variations in at-site flood frequency distribution
were modeled by regression of the mean annual maximum peak flow (MAF)
versus catchment area. The results show that the performance of the
regionalization is heavily dependent on the historical flow record
length and the similarity of the hydrological characteristics inside the
regions. The flood frequency regionalization of the River Nile basin can
be improved if sufficient flow data of longer record length × 40
become available.
Estimation of peak flow quantiles in ungauged catchments is a challenge
often faced by water professionals in many parts of the world.
Approaches to address such problem exist, but widely used techniques
such as flood frequency regionalisation is often not subjected to
performance evaluation. In this study, the jack-knifing principle is
used to assess the performance of the flood frequency regionalisation in
the complex and data-scarce River Nile basin by examining the error
(regionalisation error) between locally and regionally estimated peak
flow quantiles for different return periods (QT).
Agglomerative hierarchical clustering based algorithms were used to
search for regions with similar hydrological characteristics.
Hydrological data employed were from 180 gauged catchments and several
physical characteristics in order to regionalise 365 identified
catchments. The Generalised Extreme Value (GEV) distribution, selected
using L-moment based approach, was used to construct regional growth
curves from which peak flow growth factors could be derived and mapped
through interpolation. Inside each region, variations in at-site flood
frequency distribution were modelled by regression of the mean annual
maximum peak flow (MAF) versus catchment area. The results showed that
the performance of the regionalisation is heavily dependent on the
historical flow record length and the similarity of the hydrological
characteristics inside the regions. The flood frequency regionalisation
of the River Nile basin can be improved if sufficient flow data of
longer record length of at least 40 yr become available.
Predictions of hydrological responses in ungauged catchments can benefit
from a classification scheme that can organize and pool together
catchments that exhibit a level of hydrologic similarity, especially
similarity in some key variable or signature of interest. Since
catchments are complex systems with a level of self-organization arising
from co-evolution of climate and landscape properties, including
vegetation, there is much to be gained from developing a classification
system based on a comparative study of a population of catchments across
climatic and landscape gradients. The focus of this paper is on climate
seasonality and seasonal runoff regime, as characterized by the ensemble
mean of within-year variation of climate and runoff. The work on regime
behavior is part of an overall study of the physical controls on
regional patterns of flow duration curves (FDCs), motivated by the fact
that regime behavior leaves a major imprint upon the shape of FDCs,
especially the slope of the FDCs. As an exercise in comparative
hydrology, the paper seeks to assess the regime behavior of 428
catchments from the MOPEX database simultaneously, classifying and
regionalizing them into homogeneous or hydrologically similar groups. A
decision tree is developed on the basis of a metric chosen to
characterize similarity of regime behavior, using a variant of the
Iterative Dichotomiser 3 (ID3) algorithm to form a classification tree
and associated catchment classes. In this way, several classes of
catchments are distinguished, in which the connection between the five
catchments' regime behavior and climate and catchment properties becomes
clearer. Only four similarity indices are entered into the algorithm,
all of which are obtained from smoothed daily regime curves of climatic
variables and runoff. Results demonstrate that climate seasonality plays
the most significant role in the classification of US catchments, with
rainfall timing and climatic aridity index playing somewhat secondary
roles in the organization of the catchments. In spite of the tremendous
heterogeneity of climate, topography, and runoff behavior across the
continental United States, 331 of the 428 catchments studied are seen to
fall into only six dominant classes.
In this paper we investigate the climatic and landscape controls on the flow duration curve (FDC) with the use of a physically-based rainfall-runoff model. The FDC is a stochastic representation of the variability of runoff, which arises from the transformation, by the catchment, of within-year variability of precipitation that can itself be characterized by a corresponding duration curve for precipitation (PDC). Numerical simulations are carried out with the rainfall-runoff model under a variety of combinations of climatic inputs (i.e. precipitation, potential evaporation, including their within-year variability) and landscape properties (i.e. soil type and depth). The simulations indicated that the FDC can be disaggregated into two components, with sharply differing characteristics and origins: the FDC for surface (fast) runoff (SFDC) and the FDC for subsurface (slow) runoff (SSFDC), which included base flow in our analysis. SFDC closely tracked PDC and can be approximated with the use of a simple, nonlinear (threshold) filter model. On the other hand, SSFDC tracked the FDC that is constructed from the regime curve (i.e. mean monthly runoff), which can be closely approximated by a linear filter model. Sensitivity analyses were carried out to understand the climate and landscape controls on each component, gaining useful physical insights into their respective shapes. In particular the results suggested that evaporation from dynamic saturated areas, especially in the dry season, can contribute to a sharp dip at the lower tail of the FDCs. Based on these results, we develop a conceptual framework for the reconstruction of FDCs in ungauged basins. This framework partitions the FDC into: (1) a fast flow component, governed by a filtered version of PDC, (2) a slow flow component governed by the regime curve, and (3) a correction to SSFDC to capture the effects of high evapotranspiration (ET) at low flows.
Given the contradictory results from recent studies, this paper compares classical regionalization schemes of catchment model parameters over the wide range of hydroclimates found in France. To ensure the generality of the conclusions, we used two lumped rainfall-runoff models applied to daily data over a large set of 913 French catchments. Three types of approaches were considered: regionalization using regression, regionalization based on spatial proximity and regionalization based on physical similarity. This comparison shows that in France, where a dense network of gauging stations is available, spatial proximity provides the best regionalization solution. The regression approach is the least satisfactory, with results very close to those obtained using one median parameter set for the whole country. The physical similarity approach is intermediary. However, the results obtained with these three methods lag far behind those obtained by full model calibration. Our results also show that some improvement could be made by combining spatial proximity and physical similarity, and that there is still considerable room for progress in the field of ungaged catchment modeling.
A regionalization scheme by which parameters of a continuous rainfall-runoff model are estimated from physiographic and climatic watershed descriptors is presented. The approach makes use of the spatial structures displayed by the parameters within a physiographic-climatic space defined on the basis of a canonical correlation analysis between model parameters and watershed descriptors. Traditionally, regionalization has been performed using a two-step procedure of first estimating the model parameters in a set of subwatersheds independently and then establishing a relationship between the parameters thus estimated and a set of watershed descriptors. The approach presented in this paper follows a procedure by which the two steps are combined into one. The model is calibrated for the training subwatersheds with a dual objective of maximizing the model performance and achieving well-defined spatial structures of the parameters within the physiographic-climatic space. The model parameters in the subwatersheds that are not used for training are estimated from the optimum parameters obtained in the training set of subwatersheds using ordinary kriging within the physiographic-climatic space. The performance of the model in these subwatersheds is comparable to the performance in the training set obtained using the optimum parameters estimated through model calibration. The results also indicate the possibility of extrapolation of the model parameters under a situation where some of the watershed descriptors lie slightly outside the range within which the training was done.
Since Hurst [1951] detected the presence of long-term persistence in hydrologic data, new estimation methods and long-memory models have been developed. The lack of flexibility in representing the combined effect of short and long memory has been the major limitation of stochastic models used to analyze hydrologic time series. In the present paper a fractionally differenced autoregressive integrated moving average (FARIMA) model is considered. In contrast to using traditional ARIMA models, this approach allows the modeling of both short- and long-term persistence in a time series. A framework for identification and estimation is presented. The data do not have to be Gaussian. The resulting model, which replicates the sample probability density of the data, can be used for the generation of long synthetic series. An application to the monthly and daily inflows of Lake Maggiore, Italy, is presented.
River flows have been known to be scaling for over 40 years and scaling notions have developed rapidly since the 1980s. Using the framework of universal multifractals and time series of rainfall and river runoff for 30 French catchments (basin sizes of 40 km2 to 200 km2) from 1 day to 30 years, we quantify types and extent of the scaling regimes. For both flow and rain series, we observed a scale break at roughly 16 days, which we associate with the ``synoptic maximum'' the time scale of structures of planetary spatial extent. For the two scaling regimes in both series, we estimate the universal multifractal parameters as well as the critical exponents associated with multifractal phase transitions. Using these exponents, we perform (causal) multifractal time series simulations and show how a simple (linear) scaling transfer function can be used to relate the low-frequency rainfall series to the corresponding river flow series. The high-frequency regime requires nonlinear transforms.
This study presents the results of a detailed river flow fluctuation analysis on daily records from 14 stations in the Flint River Basin in Georgia in the southeastern United States with special focus on the effect of watershed area on long memory of river flow fluctuations. The areas of the watersheds draining to the stations range from 23 to 19,606 km2. The climatic and seasonal trends are removed using the detrended fluctuation analysis technique. Results show that (1) river flow fluctuations have two distinct scaling regimes, and the scaling break is delayed for large watershed areas; (2) large watersheds have more persistent river flow fluctuations and stronger long memory (i.e., for lag times beyond the scale break) than small watersheds do; (3) the long memory of river flow fluctuations does not come from the long memory of precipitation; (4) a linear reservoir unit hydrograph transfer function approach does not capture correctly the basin processes that convert short-memory precipitation to long-memory streamflow; and (5) the degree of multifractality of river flow fluctuations decreases with increasing watershed area. The results clearly indicate that watershed area is an important factor in the long-memory studies of streamflow such as streamflow prediction.
Land use and land management changes usually occur at relatively localised scales (e.g. fields), and therefore to model the catchment scale hydrological implications a distributed model is generally used. A physics based distributed model needs a large number of parameters to be specified and this may result in non-identifiability and insufficient prediction accuracy. Moreover, the land use change effects on physical properties are not generally well understood. Alternatively, a conceptual model has more parsimonious structure, but it is harder to parameterize, since the parameters correspond less directly to physical properties, and so regionalisation must be relied upon. In our research, we use readily available indices that summarize hydrological system behavior depending on catchment geology, soils, land use and management, and therefore can be used to constrain a hydrological model for application to ungauged catchments or scenarios of change. We integrate information on Base Flow Index and Curve Number using a novel Bayesian conditioning scheme so that the overall response of the conditioned model is consistent with the information in the aforementioned indices. The approach is assessed on British catchments and used to predict effects of different land use scenarios on flood flow responses.
Flow duration curves (FDCs) are a useful tool for characterising hydrological regimes and flow variability. FDCs observed at 379 gauging stations located across New Zealand were analysed with the aim of investigate how parameterisation and generalisation combine to influence the accuracy of empirically predicted FDCs at ungauged sites. The appropriateness of four strategies for estimating FDCs was compared: (a) parameterise then generalise; (b) parameterise then regionalise then generalise; (c) parameterise and generalise together; and (d) FDC substitution. These strategies were deployed using various combinations of methods for calculating parameters that describe the shape of FDCs (polynomial expressions and probability distribution functions) and then methods for estimating these parameters at ungauged sites using available catchment characteristics (stepwise linear regression and random forests). A parameterise and generalise together strategy was devised by applying a mixed-effects approach. A jack-knife cross-validation procedure was used to provide an independent test of each method for estimating the FDC at ungauged sites. For parameterise then regionalise strategies, it was found that the combination of parameterisation method and generalisation method together, rather than either in isolation, was important in determining overall performance. Results indicated that predictive capability varied between methods and across exceedence percentiles. The mixed-effects approach provided the most parsimonious method for estimating FDC at ungauged sites. A method using the generalised extreme value probability distribution that was generalised using random forests was the most accurate method of estimating flow duration curves at ungauged sites across New Zealand.
Correlation and correlation-based measures (e.g., the coefficient of determination) have been widely used to evaluate the "goodness-of-fit" of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values (outliers) and are insensitive to additive and proportional differences between model predictions and observations. Because of these limitations, correlation-based measures can indicate that a model is a good predictor, even when it is not. In this paper, useful alternative goodness-of-fit or relative error measures (including the coefficient of efficiency and the index of agreement) that overcome many of the limitations of correlation-based measures are discussed. Modifications to these statistics to aid in interpretation are presented. It is concluded that correlation and correlation-based measures should not be used to assess the goodness-of-fit of a hydrologic or hydroclimatic model and that additional evaluation measures (such as summary statistics and absolute error measures) should supplement model evaluation tools.
A method is described that allows long-term 1-day annual and seasonal flow duration curves at any ungauged location in one of the drainage regions of South Africa to be established. The method is based on normalization of observed flow duration curves by a long-term mean daily flow and subsequent averaging of normalized ordinates of the curves. The estimate of mean daily discharge for an ungauged site is obtained using the information from the existing national data base of flow characteristics. The established set of flow duration curves at a site is further translated into actual daily streamflow time series using a simple nonlinear spatial interpolation technique. Régionalisation des caractéristiques des débits journaliers dans une région du Cap Oriental (Afrique du Sud) Résumé La méthode décrite permet d'établir pour n'importe quel site non jaugé de l'une des régions de drainage d'Afrique du Sud, les courbes des débits journaliers classés annuelles et saisonnières. La méthode est basée sur la normalisation , par le débit journalier moyen, des courbes de débits journaliers classés observées, dont on moyenne ensuite les ordonnées. L'estimation du débit journalier moyen pour un site non jaugé est obtenue à partir de l'information contenue dans la base de données nationale des caractéristiques d'écoulement. Les courbes des débits classés ainsi calculées sont converties en séries temporelles d'écoulement journalier, en utilisant une simple technique d'interpolation spatiale non linéaire.
A review of the interannual to interdecadal variability of the southern African region and its links with the Atlantic is given. Emphasis is placed on modes such as the Benguela Niño that develop within the Atlantic and may have some predictability. Seasonal forecasting and climate prediction efforts within the region are discussed. Most southern African countries rely on a combination of products obtained overseas and simple statistical methods. GCM-based forecasts and statistical downscaling of their outputs are used operationally in South Africa and also applied to some neighboring countries. A review of these downscaling efforts and their various applications is given. Research is also taking place into the predictability of quantities such as the onset of the rainy season (which appears to be associated with anomalous South Atlantic anticyclonic ridging) and dry spell frequencies within it. These parameters are often more useful to farmers in the region than forecasting above- or below-average seasonal rainful totals. A strong link between dry spells and Niño-3.4 SST is evident for certain regions of southern Africa, suggesting that some predictability exists. This link is weaker for countries like Namibia and Angola that border the Atlantic than for southeastern Africa. It is concluded that some aspects of southern Africa climate variability may have predictability but considerably more research is needed to better understand the influence of variablity over the Atlantic. An added concern is the ongoing reduction in data collection in many parts of southern Africa. This reduction has serious implications for model development and validation, and for the accuracy of reanalysis products.
Classifying watersheds prior to regionalization improves streamflow predictions in ungauged basin. Present study aims to assess the ability of combining watershed classification using dimensionality reduction techniques with regionalization methods for reliable streamflow prediction using soil and water assessment tool (SWAT). Isomap and principal component analysis (PCA) are applied to watershed attributes of 30 watersheds from Godavari river basin in India to classify them. The best classification technique is determined by calculating similarity index (SI). The results showed that Isomap is better at classifying hydrologically similar watersheds than PCA with an average SI value of 0.448. The regionalization methods such as global mean, inverse distance weighted (IDW) and physical similarity were applied to transfer the parameters from watersheds of best watershed classification group to the pseudo-ungauged watersheds, using SWAT model. The present study suggests that classifying watersheds with Isomap and regionalization using physical similarity improves the efficiency of streamflow estimation in ungauged basins.
L‐moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis described in Section 2, and new methods of parameter estimation for several distributions. The theory of L‐moments parallels the theory of (conventional) moments, as this list of applications might suggest. The main advantage of L‐moments over conventional moments is that L‐moments, being linear functions of the data, suffer less from the effects of sampling variability: L‐moments are more robust than conventional moments to outliers in the data and enable more secure inferences to be made from small samples about an underlying probability distribution. L‐moments sometimes yield more efficient parameter estimates than the maximum likelihood estimates.
A flow-duration curve represents the annual flow-frequency characteristics of rivers by depicting the cumulative frequencies for average ranked flows in a river. Generally the process requires the empirical estimation of the mean flow at each of 365 ranks. A model requiring only five parameters is developed by combining the principles of order statistics and traditional flow-frequency analyses and is applied to flow-duration curves for rivers in the province of British Columbia, Canada. Results from the Model may be interpreted both statistically and physically and allow the identification of hydrologically similar regions. The model presented incorporates the physical generating processes of streamflow in both the statistical representation of flow-duration curves and their interpretation. Similarly, the spatial model presents hydrologic regions that correspond to the known physical environment. -from Authors
Predicting water runoff in ungauged water catchment areas is vital to practical applications such as the design of drainage infrastructure and flooding defences, runoff forecasting, and for catchment management tasks such as water allocation and climate impact analysis. This important new book synthesises decades of international research, forming a holistic approach to catchment hydrology and providing a one-stop resource for hydrologists in both developed and developing countries. Topics include data for runoff regionalisation, the prediction of runoff hydrographs, flow duration curves, flow paths and residence times, annual and seasonal runoff, and floods. Illustrated with many case studies and including a final chapter on recommendations for researchers and practitioners, this book is written by expert authors involved in the prestigious IAHS PUB initiative. It is a key resource for academic researchers and professionals in the fields of hydrology, hydrogeology, ecology, geography, soil science, and environmental and civil engineering.
This paper and its companion critique the common frequency analysis techniques for hydrological extremes-in particular, the claims that their increasingly refined mathematical structures have increased the accuracy and credibility of the extrapolated upper tails of the fitted distribution models over and above that achieved by the 50-year-old empirical methods. Part 1 compares the common-sense engineering origins of frequency analysis with its present ostensibly "rigorous theory''; some myths advanced under the banner of the latter are analyzed in greater detail in Part 2.
A flow-duration curve (FDC) is simply the complement of the cu-mulative distribution function of daily, weekly, monthly (or some other time interval of) streamflow. Applications of FDCs include, but are not limmited to, hydropower planning, water-quality management, river and reservoir sedimentation studies, habitat suitability, and low-flow augmentation. Although FDCs have a long and rich history in the field of hydrology, they are sometimes criticized because, tra-ditionally, their interpretation depends on the particular period of record on which they are based. If one considers n individual FDCs, each corresponding to one of the individual n years of record, then one may treat those n annual FDCs in much the same way one treats a sequence of annual maximum or annual minimum streamflows. This new annual-based interpretation enables confidence intervals and recurrence intervals to be associated with FDCs in a nonparametric framework.
It is well known that product moment ratio estimators of the coefficient of variation Cν, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (n ≤ 100) samples normally encountered in hydrologic applications. Consequently, L moment ratio estimators, termed L coefficient of variation τ2, L skewness τ3, and L kurtosis τ4 are now advocated because they are nearly unbiased for all underlying distributions. The advantages of L moment ratio estimators over product moment ratio estimators are not limited to small samples. Monte Carlo experiments reveal that product moment estimators of Cν and γ are also remarkably biased for extremely large samples (n ≥ 1000) from highly skewed distributions. A case study using large samples (n ≥ 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments Cν, γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of τ2, τ3, and τ4 enabled us to discriminate among alternate distributional hypotheses.
In situ ground observation measurement of precipitation is difficult in sparsely populated areas with trying access conditions, as is the case in many countries in Africa. The use of remote sensors installed in satellites can be very useful in overcoming this challenge, enabling the improvement of the spatial variability description of this variable and the extension of data series.A number of standard products offering precipitation estimates on a regular basis is now available and may be used for water planning and management purposes. The present study examines the performance of four of these products in Angola, namely the Tropical Rainfall Measuring Mission (TRMM) 3B43 (version 6), Global Precipitation Climatology Project (GPCP) Combined Precipitation Data Set (version 2.2), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) and the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Centre (CPC) Morphing Technique (CMORPH), by comparing annual and monthly precipitation estimates with ground observation measurements. The data set of precipitation ground observation measurements was collected by the authors from different sources in Angola and Portugal, and is the result of an intense effort to gather hydrological records from Angola. It is believed to be one of the most complete data sets of monthly precipitation data from Angola.The four remote-sensing products are able to describe the main features of the spatial and temporal variability of annual and monthly precipitation in Angola. The results also show that the estimates from the TRMM are more accurate than the estimates offered by the other products, a conclusion which is in line with previous studies and which may be explained by the fact that this is the first product to incorporate measurements from precipitation radar. The estimation bias of TRMM is also more consistent which means that the results presented in the present study can be used in an operational environment to reduce the precipitation estimation error.
Distributional analysis of river discharge time series is an important
task in many areas of hydrological engineering, including optimal design
of water storage and drainage networks, management of extreme events,
risk assessment for water supply, and environmental flow management,
among many others. Having diverging moments, heavy-tailed power law
distributions have attracted widespread attention, especially for the
modeling of the likelihood of extreme events such as floods and
droughts. However, straightforward distributional analysis does not
connect well with the complicated dynamics of river flows, including
fractal and multifractal behavior, chaos-like dynamics, and seasonality.
To better reflect river flow dynamics, we propose to carry out
distributional analysis of river flow time series according to three
"flow seasons": dry, wet, and transitional. We present a concrete
statistical procedure to partition river flow data into three such
seasons and fit data in these seasons using two types of distributions,
power law and lognormal. The latter distribution is a salient property
of the cascade multiplicative multifractal model, which is among the
best models for turbulence and rainfall. We show that while both power
law and lognormal distributions are relevant to dry seasons, river flow
data in wet seasons are typically better fitted by lognormal
distributions than by power law distributions.
Flow duration curves (FDCs) are the most popular tools to estimate the amount of water available in a basin. They show the link between streamflows and the respective exceedance frequencies, but their use and reliability depends on the availability of observed data. With the aim of overcoming the lack of information about observed streamflow in many basins, several procedures for the regionalization of the estimate have been developed. In this paper the performances of seven models (five parametric and two statistical), two of these original, were analyzed. These models are able to describe the behavior of intermittent regimes, and were used for regional estimates of the FDCs of a southern Italian region (Calabria). The non-regionalized models applied to 19 gauged basins present throughout the region showed good performance. For the definition of the regional models a multivariate stepwise regression analysis was used, while a jack-knife procedure in the validation phase was performed. The comparison between cross-validated and observed FDCs allowed several synthetic performance indexes (some of which were used in a combined Taylor diagram) to be calculated, showing a good reliability of the models, especially in the case of the statistical approaches, thereby allowing compensation, at least in part, for the limited availability of long observed streamflow series in the region analyzed.
[1] One approach to predicting streamflow in an ungauged catchment is to select an ensemble of hydrological models previously identified for similar gauged catchments, where the similarity is based on some combination of important physical catchment attributes. The focus of this paper is the identification of catchment attributes and optimization of a similarity measure to produce the best possible ungauged streamflow predictions given a data set and a conceptual model structure. As a case study, the SimHyd rainfall-runoff model is applied to simulate monthly streamflow in 184 Australian catchments. Initial results show that none of 27 catchment attributes can be safely said to consistently give a better ensemble of models than random selection when used independently of other attributes. This is contrary to prior expectations and indicates the sparseness of information within our database of catchments, the importance in this case of prior knowledge for defining important attributes, and the potential importance of combining multiple attributes in order to usefully gauge similarity. Seven relatively independent attributes are then selected on the basis of prior knowledge. The weight with which each of these attributes contributes to the similarity measure is optimized to maximize streamflow prediction performance across a set of 95 catchments. The other 89 catchments are used to independently test the accuracy of streamflow predictions. Using the optimal set of weights led to marked improvement in the accuracy of predictions, showing that the method, while inferior to local calibration, is superior to alternative methods of model regionalization based on regression and spatial proximity. However, there is evidence of nonuniqueness in the optimal solution and the possibility that the attribute weights are somewhat dependent on the catchments used.
The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely-specified continuous distribution. If one or more parameters must be estimated from the sample then the tables are no longer valid.A table is given in this note for use with the Kolmogorov-Smirnov statistic for testing whether a set of observations is from a normal population when the mean and variance are not specified but must be estimated from the sample. The table is obtained from a Monte Carlo calculation.A brief Monte Carlo investigation is made of the power of the test.
Dr. Gulliver feels a text has been needed for 20 years to cover all engineering aspects of hydropower. He feels this book fills the void and provides a valuable service - despite some notable shortcomings, which he points out. He notes the book is organized in a logical manner and emphasizes water-flow aspects, with sections on hydraulics, hydrologic analysis, pressure surges, and turbine similarity, selection, and setting. Dr. Gulliver agrees that water-flow aspects are the most unique to hydropower development, but feels the wide range of subjects is covered too briefly. He feels that the primary value of the book is as a readable, complete introduction to hydropower engineering for engineers and planners unfamiliar with the field - and fully recommends the book for this purpose. However, for practicing hydropower engineers, he lists 15 references at the end of the review, which he feels should be used to supplement.
Daily streamflow time series are critical to a very broad range of hydrologic problems. Whereas daily streamflow time series are readily obtained from gaged catchments, streamflow information is commonly needed at catchments for which no measured streamflow information exists. At ungaged catchments, methods to estimate daily streamflow time series typically require the use of a reference streamgage, which transfers properties of the streamflow time series at a reference streamgage to the ungaged catchment. Therefore, the selection of a reference streamgage is one of the central challenges associated with estimation of daily streamflow at ungaged basins. The reference streamgage is typically selected by choosing the nearest streamgage; however, this paper shows that selection of the nearest streamgage does not provide a consistent selection criterion. We introduce a new method, termed the map-correlation method, which selects the reference streamgage whose daily streamflows are most correlated with an ungaged catchment. When applied to the estimation of daily streamflow at 28 streamgages across southern New England, daily streamflows estimated by a reference streamgage selected using the map-correlation method generally provides improved estimates of daily streamflow time series over streamflows estimated by the selection and use of the nearest streamgage. The map correlation method could have potential for many other applications including identifying redundancy and uniqueness in a streamgage network, calibration of rainfall runoff models at ungaged sites, as well as for use in catchment classification.
For univariate or one-dimensional distributions the standard tables used
for the Kolmogorov-Smirnov test are valid when testing whether a set of
observations are from a completely specified distribution. If one or
more parameters must be estimated from the sample, then the standard
tables are no longer valid. Other tables must be used.Lilliefors
indicates the conservative extent of the tests when parameters are
estimated for the sample and used with the standard tables. He provides
valid tables for the univariate normal, exponential, gamma, and extreme
value distributions when one or more parameters must be estimated from
the sample. For the multivariate normal distributions the only tables
known to the author are those of Malkovich and Afifi.This note brings
the problem to the attention of scientists who rely on the tools
developed by statisticians to help them to use the appropriate tools
correctly.
Meso-scale catchments are often of great interest for water resources development and for development interventions aimed at uplifting rural livelihoods. However, in Sub-Saharan Africa IWRM planning in such catchments, and the basins they form part of, are often ungauged or constrained by poor data availability. Regionalisation of a hydrological model presents opportunities for prediction in ungauged basins and catchments. This study regionalises HBVx, derived from the conceptual hydrological model HBV, in the semi-arid Mzingwane Catchment, Limpopo Basin, Zimbabwe. Fifteen meso-catchments were studied, including three that were instrumented during the study. Discriminant analysis showed that the characteristics of catchments in the arid agro-ecological Region V were significantly different from those in semi-arid Region IV. Analysis of flow duration curves statistically separated sub-perennial catchments from (sub-)ephemeral catchments. Regionalised parameter sets for HBVx were derived from means of parameters from the sub-perennial catchments, the (sub-)ephemeral catchments and all catchments. The parameter sets that performed best in the regionalisation are characterised by slow infiltration with moderate/fast “overland flow”. These processes appear more extreme in more degraded catchments. This is points to benefits to be derived from conservation techniques that increase infiltration rate and from runoff farming. Faster, and possibly greater, sub-surface contribution to streamflow is expected from catchments underlain by granitic rocks. Calibration and regionalisation were more successful at the dekad (10 days) time step than when using daily or monthly data, and for the sub-perennial catchments than the (sub-)ephemeral catchments. However, none of the regionalised parameter sets yielded CNS ⩾ 0.3 for half of the catchments. The HBVx model thus does offer some assistance to river basin planning in semi-arid basins, particularly for predicting flows in ungauged catchments at longer time steps, such as for water allocation purposes. However, the model is unreliable for more ephemeral and drier catchments. Without more reliable and longer rainfall and runoff data, regionalisation in semi-arid ephemeral catchments will remain highly challenging.Highlights► This study regionalises HBVx in the semi-arid and variable Mzingwane Catchment, Limpopo Basin. ► Calibration and regionalisation were more successful at the dekad time step. ► The model offers some assistance to river basin planning for predicting flows in ungauged catchments. ► The model offers planning support for water allocation. ► However, the model is unreliable for more ephemeral and drier catchments.
Intensities and amounts of water infiltration and runoff on sloping land are governed by the rainfall pattern and soil hydraulic conductivity, as well as by the microtopography and soil surface conditions. These components are closely interrelated and occur simultaneously, and their particular contribution may change during a rainfall event, or their effects may vary at different field scales. The scale effect on the process of infiltration/runoff was studied under natural field and rainfall conditions for two plot sizes: small plots of 0·25 m2 and large plots of 50 m2. The measurements were carried out in the central region of Chile in a piedmont most recently used as natural pastureland. Three blocks, each having one large plot and five small plots, were established. Cumulative rainfall and runoff quantities were sampled every 5 min. Significant variations in runoff responses to rainfall rates were found for the two plot sizes. On average, large plots yielded only 40% of runoff quantities produced on small plots per unit area. This difference between plot sizes was observed even during periods of continuous runoff. Copyright © 2002 John Wiley & Sons, Ltd.
Prediction in ungauged basins is an important task for water resources planning and management and remains a fundamental challenge for the hydrological community. Regionalization is typically used to estimate parameter values of hydrological predictive tools for catchments without observed streamflow. This study proposes a new regionalization method, called the index model. The index model establishes a nonparametric relationship between each parameter of predictive tools and a linear combination of predicators. This method is able to describe a wide range of functions, linear or nonlinear, and avoids the potential misspecification which usually occurs as a result of using the ordinary linear regression. We illustrate the method by predicting flow duration curves at 227 unimpaired catchments in southeast Australia. This study also compares results from regional models based on the linear regression, nearest neighbour and hydrological similarity. The results show that the index model produces the most accurate prediction with highest coefficients of efficiency, followed by the linear regression. In particular, the index model improves the model performance substantially at catchments where the linear regression is a fair to poor fit. The index model was also interpretable and showed that potential evapotranspiration and summary statistics of rainfall are predominant in prediction.