Factors influencing long range dependence in streamflow of European rivers

Investigating long range dependence of river flows, especially in connection with various climate and storage related factors, is important in order to improve stochastic models for long range dependence and in order to understand deterministic and stochastic variability in long‐term behaviour of streamflow. Long range dependence expressed by the Hurst coefficient H is estimated for 39 (deseasonalized) mean daily runoff time series in Europe of at least 59 years using five estimators (rescaled range, regression on periodogram, Whittle, aggregated variances, and least squares based on variance). All methods yield estimates of H > 0.5 for all data sets. The results from the different estimators are significantly positively correlated for all pairs of methods indicating consistency of the methods used. Correlations between H and various catchment attributes are also analysed. H is strongly positively correlated with catchment area. Apparently, increasing storage with catchment area translates into increasing long range dependence. H is also positively correlated with mean discharge and air temperature and negatively correlated with the mean specific discharge and the seasonality index (maximum Pardé coefficient). No significant correlation is found between the Hurst coefficient and the length of the analyzed time series. The correlations are interpreted in terms of snow processes and catchment wetness. Copyright © 2012 John Wiley & Sons, Ltd.     

Regional assimilation of in situ observed soil moisture into the VIC model considering spatial variability

ABSTRACT

In order to improve the soil moisture (SM) modelling capacity, a regional SM assimilation scheme based on an empirical approach considering spatial variability was constructed to assimilate in situ observed SM data into a hydrological model. The daily variable infiltration capacity (VIC) model was built to simulate SM in the Upper Huai River Basin, China, with a resolution of 5 km × 5 km. Through synthetic assimilation experiments and validations, the assimilated SM was evaluated, and the assimilation feedback on evapotranspiration (ET) and streamflow are analysed and discussed. The results show that the assimilation scheme improved the SM modelling capacity, both spatially and temporally. Moreover, the simulated ET was continually affected by changes in SM simulation, and the streamflow predictions were improved after applying the SM assimilation scheme. This study demonstrates the potential value of in situ observations in SM assimilation, and provides valuable ways for improving hydrological simulations.     

Derivation of streamflow statistics based on a filtered point process

This work presents the derivation of general streamflow cumulants from daily rainfall time series. The general streamflow cumulants can be used to compute basic streamflow statistics such as mean, variance, coefficient of skewness, and correlation coefficient. Streamflow is considered as a filtered point process where the input is a daily rainfall time series assumed to be a marked point process. The marks of the process are the daily rainfall amounts which are assumed independent and identically distributed. The number of rainfall occurrences is a counting process represented by either the binomial, the Poisson, or the negative binomial probability distribution depending on its ratio of mean to variance. The first three cumulants and the covariance function of J-day averaged streamflows are deduced based on the characteristic function of a filtered point process. These cumulants are functions of the stochastic properties of the daily rainfall process and the basin-response function representing the causal relationship between rainfall and runoff.     

Addressing uncertainty in reflectivity‐rainfall relations in mountain watersheds during summer convection

The use of precipitation estimates from weather radar reflectivity has become widespread in hydrologic predictions. However, uncertainty remains in the use of the nonlinear reflectivity–rainfall (Z‐R) relation, in particular for mountainous regions where ground validation stations are often lacking, land surface data sets are inaccurate and the spatial variability in many features is high. In this study, we assess the propagation of rainfall errors introduced by different Z‐R relations on distributed hydrologic model performance for four mountain basins in the Colorado Front Range. To do so, we compare spatially integrated and distributed rainfall and runoff metrics at seasonal and event time scales during the warm season when convective storms dominate. Results reveal that the basin simulations are quite sensitive to the uncertainties introduced by the Z‐R relation in terms of streamflow, runoff mechanisms and the water balance components. The propagation of rainfall errors into basin responses follows power law relationships that link streamflow uncertainty to the precipitation errors and streamflow magnitude. Overall, different Z‐R relations preserve the spatial distribution of rainfall relative to a reference case, but not the precipitation magnitude, thus leading to large changes in streamflow amounts and runoff spatial patterns at seasonal and event scales. Furthermore, streamflow errors from the Z‐R relation follow a typical pattern that varies with catchment scale where higher uncertainties exist for intermediate‐sized basins. The relatively high error values introduced by two operational Z‐R relations (WSR‐57 and NEXRAD) in terms of the streamflow response indicate that site‐specific Z‐R relations are desirable in the complex terrain region, particularly in light of other uncertainties in the modelling process, such as model parameter values and initial conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi‐temporal scale changes of streamflow and sediment load in a loess hilly watershed of China

Global climate change and diverse human activities have resulted in distinct temporal–spatial variability of watershed hydrological regimes, especially in water‐limited areas. This study presented a comprehensive investigation of streamflow and sediment load changes on multi‐temporal scales (annual, flood season, monthly and daily scales) during 1952–2011 in the Yanhe watershed, Loess Plateau. The results indicated that the decreasing trend of precipitation and increasing trend of potential evapotranspiration and aridity index were not significant. Significant decreasing trends (p < 0.01) were detected for both the annual and flood season streamflow, sediment load, sediment concentration and sediment coefficient. The runoff coefficient exhibited a significantly negative trend (p < 0.01) on the flood season scale, whereas the decreasing trend on the annual scale was not significant. The streamflow and sediment load during July–August contributed 46.7% and 86.2% to the annual total, respectively. The maximum daily streamflow and sediment load had the median occurrence date of July 31, and they accounted for 9.7% and 29.2% of the annual total, respectively. All of these monthly and daily hydrological characteristics exhibited remarkable decreasing trends (p < 0.01). However, the contribution of the maximum daily streamflow to the annual total progressively decreased (?0.07% year^?1), while that of maximum daily sediment load increased over the last 60 years (0.08% year^?1). The transfer of sloping cropland for afforestation and construction of check‐dams represented the dominant causes of streamflow and sediment load reductions, which also made the sediment grain finer. Copyright © 2015 John Wiley & Sons, Ltd.     

Continental Scale Hydrostratigraphy: Comparing Geologically Informed Data Products to Analytical Solutions

This study synthesizes two different methods for estimating hydraulic conductivity (K) at large scales. We derive analytical approaches that estimate K and apply them to the contiguous United States. We then compare these analytical approaches to three-dimensional, national gridded K data products and three transmissivity (T) data products developed from publicly available sources. We evaluate these data products using multiple approaches: comparing their statistics qualitatively and quantitatively and with hydrologic model simulations. Some of these datasets were used as inputs for an integrated hydrologic model of the Upper Colorado River Basin and the comparison of the results with observations was used to further evaluate the K data products. Simulated average daily streamflow was compared to daily flow data from 10 USGS stream gages in the domain, and annually averaged simulated groundwater depths are compared to observations from nearly 2000 monitoring wells. We find streamflow predictions from analytically informed simulations to be similar in relative bias and Spearman's rho to the geologically informed simulations. R-squared values for groundwater depth predictions are close between the best performing analytically and geologically informed simulations at 0.68 and 0.70 respectively, with RMSE values under 10 m. We also show that the analytical approach derived by this study produces estimates of K that are similar in spatial distribution, standard deviation, mean value, and modeling performance to geologically-informed estimates. The results of this work are used to inform a follow-on study that tests additional data-driven approaches in multiple basins within the contiguous United States.     

A spatially distributed Clark’s unit hydrograph based hybrid hydrologic model (Distributed-Clark)

ABSTRACT

A hybrid hydrologic model (Distributed-Clark), which is a lumped conceptual and distributed feature model, was developed based on the combined concept of Clark’s unit hydrograph and its spatial decomposition methods, incorporating refined spatially variable flow dynamics to implement hydrological simulation for spatially distributed rainfall–runoff flow. In Distributed-Clark, the Soil Conservation Service (SCS) curve number method is utilized to estimate spatially distributed runoff depth and a set of separated unit hydrographs is used for runoff routing to obtain a direct runoff flow hydrograph. Case studies (four watersheds in the central part of the USA) using spatially distributed (Thiessen polygon-based) rainfall data of storm events were used to evaluate the model performance. Results demonstrate relatively good fit to observed streamflow, with a Nash-Sutcliffe efficiency (E_NS) of 0.84 and coefficient of determination (R²) of 0.86, as well as a better fit in comparison with outputs of spatially averaged rainfall data simulations for two models including HEC-HMS.     

Spatially distributed long‐term hydrologic simulation using a continuous SCS CN method‐based hybrid hydrologic model

A continuous Soil Conservation Service (SCS) curve number (CN) method that considers time‐varied SCS CN values was developed based on the original SCS CN method with a revised soil moisture accounting approach to estimate run‐off depth for long‐term discontinuous storm events. The method was applied to spatially distributed long‐term hydrologic simulation of rainfall‐run‐off flow with an underlying assumption for its spatial variability using a geographic information systems‐based spatially distributed Clark's unit hydrograph method (Distributed‐Clark; hybrid hydrologic model), which is a simple few parameter run‐off routing method for input of spatiotemporally varied run‐off depth, incorporating conditional unit hydrograph adoption for different run‐off precipitation depth‐based direct run‐off flow convolution. Case studies of spatially distributed long‐term (total of 6 years) hydrologic simulation for four river basins using daily NEXRAD quantitative precipitation estimations demonstrate overall performances of Nash–Sutcliffe efficiency (E_NS) 0.62, coefficient of determination (R²) 0.64, and percent bias 0.33% in direct run‐off and E_NS 0.71, R² 0.72, and percent bias 0.15% in total streamflow for model result comparison against observed streamflow. These results show better fit (improvement in E_NS of 42.0% and R² of 33.3% for total streamflow) than the same model using spatially averaged gauged rainfall. Incorporation of logic for conditional initial abstraction in a continuous SCS CN method, which can accommodate initial run‐off loss amounts based on previous rainfall, slightly enhances model simulation performance; both E_NS and R² increased by 1.4% for total streamflow in a 4‐year calibration period. A continuous SCS CN method‐based hybrid hydrologic model presented in this study is, therefore, potentially significant to improved implementation of long‐term hydrologic applications for spatially distributed rainfall‐run‐off generation and routing, as a relatively simple hydrologic modelling approach for the use of more reliable gridded types of quantitative precipitation estimations.     

Simulated response of an intermittent stream to rainfall frequency patterns

The response of intermittent catchments to rainfall is complex and difficult to model. This study uses the spatially distributed CATchment HYdrology (CATHY) model to explore how the frequency of daily rainfall (λ) can affect the hydrologic regime of intermittent catchments. After a multi-objective calibration and validation of CATHY against experimental measurements of streamflow and groundwater levels in a catchment used as a pasture, the role of λ in affecting streamflow characteristics was explored using different scenarios. With different values of λ for the dry and wet periods of the year, CATHY showed that a series of frequent rainfall events was often associated with incipient streamflow, independent of the season. Activation of streamflow during the wet season was related to multiple factors and was not often associated with the shallow groundwater levels near the outlet of the catchment. The interplay between rainfall depth and intensity acted as the most important factor for the generation of streamflow. Using the difference between accumulated rainfall and evapotranspiration as a measure of wetness, saturated subsurface flow mechanism generated streamflow in simulations with wetness at least three times larger than mean wetness of other simulations. Although groundwater uprise near the outlet did not effectively contribute to streamflow in the initial days of flow, it strongly correlated with the magnitude of the runoff coefficient. Values of λ close or equal to the maximum value in the wet season can sustain the connectivity between groundwater and streamflow in the riparian zone. This connectivity increases the catchment wetness, which consequently results in an increase of the generated streamflow. Our study showed that rainfall regimes characterized by different λ were able to identify distinct flow regimes typical of either intermittent, ephemeral, or nonflowing catchments. Decrease of λ in the wet season is likely associated with a reduction of streamflow, with a shift of flow regime from intermittent to ephemeral or no-flow.     

Simulating precipitation in the Northeast United States using a climate-informed K-nearest neighbour algorithm

Decadal prediction using climate models faces long-standing challenges. While global climate models may reproduce long-term shifts in climate due to external forcing, in the near term, they often fail to accurately simulate interannual climate variability, as well as seasonal variability, wet and dry spells, and persistence, which are essential for water resources management. We developed a new climate-informed K-nearest neighbour (K-NN)-based stochastic modelling approach to capture the long-term trend and variability while replicating intra-annual statistics. The climate-informed K-NN stochastic model utilizes historical data along with climate state information to provide improved simulations of weather for near-term regional projections. Daily precipitation and temperature simulations are based on analogue weather days that belong to years similar to the current year's climate state. The climate-informed K-NN stochastic model is tested using 53 weather stations in the Northeast United States with an evident monotonic trend in annual precipitation. The model is also compared to the original K-NN weather generator and ISIMIP-2b GFDL general circulation model bias-corrected output in a cross-validation mode. Results indicate that the climate-informed K-NN model provides improved simulations for dry and wet regimes, and better uncertainty bounds for annual average precipitation. The model also replicates the within-year rainfall statistics. For the 1961–1970 dry regime, the model captures annual average precipitation and the intra-annual coefficient of variation. For the 2005–2014 wet regime, the model replicates the monotonic trend and daily persistence in precipitation. These improved modelled precipitation time series can be used for accurately simulating near-term streamflow, which in turn can be used for short-term water resources planning and management.     

Stochastic simulation of bivariate gamma distribution: a frequency-factor based approach

A frequency-factor based approach for stochastic simulation of bivariate gamma distribution is proposed. The approach involves generation of bivariate normal samples with a correlation coefficient consistent with the correlation coefficient of the corresponding bivariate gamma samples. Then the bivariate normal samples are transformed to bivariate gamma samples using the well-known general equation of hydrological frequency analysis. We demonstrate that the proposed bivariate gamma simulation approach is capable of generating random sample pairs which not only have the desired marginal densities of component random variables but also their correlation coefficient. Scatter plots of simulated bivariate sample pairs also exhibit appropriate linear patterns (dependence structure) that are commonly observed in environmental and hydrological applications. Caution should also be exercised when specifying combinations of coefficients of skewness and the correlation coefficient for bivariate gamma simulation.     

赣江流域多种数据同化方案的径流模拟比较

为了探讨水文模型在不同水文数据同化方案下的径流模拟差异,本文采用集合卡尔曼滤波算法,以遥感蒸散发产品、实测径流为观测数据,构建了基于新安江模型的数据同化框架。基于此框架设计了4种不同同化方案(DA-ET、DAET(K)、DA-ET-Q、DA-ET-Q(K))以及1种对照方案OL,以赣江流域开展实例研究,评估了水文数据同化中遥感蒸散发产品的时间分辨率、模型蒸散发相关参数时变与否以及多源数据同化对径流模拟的影响。结果表明:在DA-ET方案下,同化两种不同时间分辨率的蒸散发产品均能提高模型整体的径流模拟精度,且时间分辨率更高的产品的同化效果更好;在DA-ET方案的基础上,考虑加入实测径流进行同化能够提升模型径流模拟精度,且DA-ET(K)与DA-ET-Q(K)方案所得径流相对误差的减幅均超过了20%,说明在蒸散发同化过程中同时考虑蒸散发参数动态变化的结果更优;相较于OL方案,4种同化方案均能不同程度地提高模型对径流高水部分的模拟能力,但DA-ET-Q(K)方案表现最差,而其余方案差异并不显著。本研究有助于进一步了解不同数据同化方案在径流模拟中的差异,从而为水资源高效利用与科学管理提供科学依据...     

Estimation of phosphorus loads with sparse data for agricultural watersheds in the Czech Republic

Abstract

Agricultural watersheds in the Czech Republic are one of the primary sources of non-point-source phosphorus (P) loads in receiving waters. Since such non-point sources are generally located in headwater catchments, streamflow and P concentration data are sparse. We show how very short daily streamflow and P concentration records can be combined with nearby longer existing daily streamflow records to result in reliable estimates of daily and annual P concentrations and loads. Maintenance of variance streamflow record extension methods (MOVE) can be employed to extend short streamflow records. Constituent load regressions are used to predict daily P constituent loads from streamflow and other time varying characteristics. Annual P loads are then estimated for individual watersheds. Resulting annual P load estimates ranged from 0.21 to 95.4 kg year^-1 with a mean value of 11.77 kg year^-1. Similarly annual P yield estimates ranged from 0.01 to 0.3 kg ha^-1 year^-1 with an average yield of 0.07 kg ha^-1 year^-1. We document how short records of daily streamflow and P concentrations can be combined with a national network of daily streamflow records in the Czech Republic to arrive at meaningful and reliable estimates of annual P loads for small agricultural watersheds.

Citation Beránková, T., Vogel, R. M., Fiala, D. & Rosendorf, P. (2010) Estimation of phosphorus loads with sparse data for agricultural watersheds in the Czech Republic. Hydrol. Sci. J. 55(8), 1417–1426.     

Modelling streamflow trends for a watershed with limited data: case of the Litani basin,Lebanon

Abstract

Streamflow variability in the Upper and Lower Litani basin, Lebanon was modelled as there is a lack of long-term measured runoff data. To simulate runoff and streamflow, daily rainfall was derived using a stochastic rainfall generation model and monthly rainfall data. Two distinct synthetic rainfall models were developed based on a two-part probabilistic distribution approach. The rainfall occurrence was described by a Markov chain process, while the rainfall distribution on wet days was represented by two different distributions (i.e. gamma and mixed exponential distributions). Both distributions yielded similar results. The rainfall data were then processed using water balance and routing models to generate daily and monthly streamflow. Compared with measured data, the model results were generally reasonable (mean errors ranging from 0.1 to 0.8?m³/s at select locations). Finally, the simulated monthly streamflow data were used to investigate discharge trends in the Litani basin during the 20th century using the Mann-Kendall and Sen slope nonparametric trend detection methods. A significant drying trend of the basin was detected, reaching a streamflow reduction of 0.8 and 0.7 m³/s per decade in January for the Upper and Lower basin, respectively.

Editor D. Koutsoyiannis; Associate editor Sheng Yue

Citation Ramadan, H.H., Beighley, R.E., and Ramamurthy, A.S., 2012. Modelling streamflow trends for a watershed with limited data: case of the Litani basin, Lebanon. Hydrological Sciences Journal, 57 (8), 1516–1529.     

Parameter identification and uncertainty analysis for simulating streamflow in a river basin of Eastern India

Uncertainty is inherent in modelling studies. However, the quantification of uncertainties associated with a model is a challenging task, and hence, such studies are somewhat limited. As distributed or semi‐distributed hydrological models are being increasingly used these days to simulate hydrological processes, it is vital that these models should be equipped with robust calibration and uncertainty analysis techniques. The goal of the present study was to calibrate and validate the Soil and Water Assessment Tool (SWAT) model for simulating streamflow in a river basin of Eastern India, and to evaluate the performance of salient optimization techniques in quantifying uncertainties. The SWAT model for the study basin was developed and calibrated using Parameter Solution (ParaSol), Sequential Uncertainty Fitting Algorithm (SUFI‐2) and Generalized Likelihood Uncertainty Estimation (GLUE) optimization techniques. The daily observed streamflow data from 1998 to 2003 were used for model calibration, and those for 2004–2005 were used for model validation. Modelling results indicated that all the three techniques invariably yield better results for the monthly time step than for the daily time step during both calibration and validation. The model performances for the daily streamflow simulation using ParaSol and SUFI‐2 during calibration are reasonably good with a Nash–Sutcliffe efficiency and mean absolute error (MAE) of 0.88 and 9.70 m³/s for ParaSol, and 0.86 and 10.07 m³/s for SUFI‐2, respectively. The simulation results of GLUE revealed that the model simulates daily streamflow during calibration with the highest accuracy in the case of GLUE (R² = 0.88, MAE = 9.56 m³/s and root mean square error = 19.70 m³/s). The results of uncertainty analyses by SUFI‐2 and GLUE were compared in terms of parameter uncertainty. It was found that SUFI‐2 is capable of estimating uncertainties in complex hydrological models like SWAT, but it warrants sound knowledge of the parameters and their effects on the model output. On the other hand, GLUE predicts more reliable uncertainty ranges (R‐factor = 0.52 for daily calibration and 0.48 for validation) compared to SUFI‐2 (R‐factor = 0.59 for daily calibration and 0.55 for validation), though it is computationally demanding. Although both SUFI‐2 and GLUE appear to be promising techniques for the uncertainty analysis of modelling results, more and more studies in this direction are required under varying agro‐climatic conditions for assessing their generic capability. Copyright © 2015 John Wiley & Sons, Ltd.     

Spatial scaling properties of annual streamflow in the United States

Abstract

The spatial scaling properties of annual average streamflow is examined using records from 1 433 river basins across the continental United States. The log-linear relationship ln(E[Q^r _i]) = a + b_r ln(A_i) is representative throughout the United States, where E[Q^r _i] represents the expectation of the rth moment of annual streamflow at site i, and A_i represents drainage area. The scaling model parameters a_r and b_r follow nearly perfect linear relationships a_r = rα and b_r = rβ throughout the continental United States. We conclude that the probability distribution of annual streamflow follows simple scaling relationships in all regions of the United States. In temperate regions where climate is relatively homogeneous, scale alone describes most of the variability in the moments of annual streamflow. In the more climatically heterogeneous regions, such as in the Upper Colorado and Missouri river basins, scale alone is a poor predictor of the moments of annual flow.     

Streamflow trends in Nepal

Abstract

This study presents the first comprehensive nationwide trend detection of streamflow in Nepal, a country that has been historically understudied despite its critical location as the southern pathway for most of the Himalayan snowpack melt and torrential seasonal monsoon rains. We applied Mann-Kendall and Sen's trend tests using trend-free pre-whitening and bootstrap approaches to two streamflow data sets to deal with serial and cross-correlation. The two data sets comprised 23–33 hydrometric stations with 31 years and more than 20 years of published data, respectively. The test on the 33 stations data set showed that 23% of the streamflow variables studied had statistically significant trends, evenly divided between upward and downward trends. Similarly, in the second, relatively smaller data set, 24% of variables exhibited trends, of which 41% were downward and 59% upward. The higher percentage of observed upward trends in pre-monsoon and winter seasonal average flow is noteworthy given the potential snowmelt contribution in many of the studied sites. Trends were mostly absent in stations draining the larger basins. However, some spatial patterns were seen in the observed trend directions, specifically, a downward trend in the Karnali-Mahakali River basin and an upward trend in the West Rapti River basin, as well as a nationwide absence of trend in the post-monsoon season.

Editor Z.W. Kundzewicz

Citation Gautam, M.R. and Acharya, K., 2011. Streamflow trends in Nepal. Hydrological Sciences Journal, 57 (2), 344–357.     

Minimum relative entropy theory for streamflow forecasting with frequency as a random variable

This paper develops a minimum relative entropy theory with frequency as a random variable, called MREF henceforth, for streamflow forecasting. The MREF theory consists of three main components: (1) determination of spectral density (2) determination of parameters by cepstrum analysis, and (3) extension of autocorrelation function. MREF is robust at determining the main periodicity, and provides higher resolution spectral density. The theory is evaluated using monthly streamflow observed at 20 stations in the Mississippi River basin, where forecasted monthly streamflows show the coefficient of determination (r ²) of 0.876, which is slightly higher in the Upper Mississippi (r ² = 0.932) than in the Lower Mississippi (r ² = 0.806). Comparison of different priors shows that the prior with the background spectral density with a peak at 1/12 frequency provides satisfactory accuracy, and can be used to forecast monthly streamflow with limited information. Four different entropy theories are compared, and it is found that the minimum relative entropy theory has an advantage over maximum entropy (ME) for both spectral estimation and streamflow forecasting, if additional information as a prior is given. Besides, MREF is found to be more convenient to estimate parameters with cepstrum analysis than minimum relative entropy with spectral power as random variable (MRES), and less information is needed to assume the prior. In general, the reliability of monthly streamflow forecasting from the highest to the lowest is for MREF, MRES, configuration entropy (CE), Burg entropy (BE), and then autoregressive method (AR), respectively.