Identification of trends in Malaysian monthly runoff under the scaling hypothesis

Abstract

Statistical tests have been widely used for several decades to identify and test the significance of trends in runoff and other hydrological data. The Mann-Kendall (M-K) trend test is commonly used in trend analysis. The M-K test was originally proposed for random data. Several variations of the M-K test, as well as pre-processing of data for use with it, have been developed and used. The M-K test under the scaling hypothesis has been developed recently. The basic objective of the research presented in this paper is to investigate the trends in Malaysian monthly runoff data. Identification of trends in runoff data is useful for planning water resources projects. Existence of statistically significant trends would also lead to identification of possible effects of climate change. Monthly runoff data for Malaysian rivers from the past three decades are analysed, in both five-year segments and entire data sequences. The five-year segments are analysed to investigate the variability in trends from one segment to another in three steps: (1) the M-K tests are conducted under random and correlation assumptions; (2) the Hurst scaling parameter is estimated and tested for significance; and (3) the M-K test under the scaling hypothesis is conducted. Thus the tests cover both correlation and scaling. The results show that the number of significant segments in Malaysian runoff data would be the same as those found under the assumption that the river flow sequences are random. The results are also the same for entire sequences. Thus, monthly Malaysian runoff data do not have statistically significant trends. Hence there are no indications of climate change in Malaysian runoff data.

Citation Rao, A. R., Azli, M. & Pae, L. J. (2011) Identification of trends in Malaysian monthly runoff under the scaling hypothesis. Hydrol. Sci. J. 56(6), 917–929.     

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA, where P is the propagation vector, and A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0), homogeneous plane waves (A ≠ 0, P and A parallel), and inhomogeneous plane waves (A ≠ 0, P and A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail. vcerveny@seis.karlov.mff.cuni.cz     

Estimating ground motions using recorded accelerograms

A procedure for estimating ground motions using recorded accelerograms is described. The premise of the study is the assumption that future ground motions will be similar to those observed for similar site and tectonic situations in the past. Direct techniques for scaling existing accelerograms have been developed, based on relative estimates of local magnitude,M _L . Design events are described deterministically in terms of fault dimension, tectonic setting (stress drop), fault distance, and site conditions. A combination of empirical and theoretical arguments is used to develop relationships betweenM _L and other earthquake magnitude scales. In order to minimize scaling errors due to lack of understanding of the physics of strong ground motion, the procedure employs as few intermediate scaling laws as possible. The procedure conserves a meaningful measure of the uncertainty inherent when predicting ground motions from simple parameterizations of earthquake sources and site conditions.     

Evaluating the transferability of monthly water balance models under changing climate conditions

ABSTRACT

Monthly water balance models (MWBMs) are often used for making flow projections under climate change. As such, these models should provide accurate flow simulations; however, they are seldom evaluated in this regard. This paper presents a comprehensive framework intended for the evaluation of the applicability of MWBMs under changing climatic conditions. The framework consists of analyses of consistency in model performance, parameter estimates and simulated water balance components, and a subjective assessment of model transferability. Four MWBMs – abcd, Budyko, GR2M and WASMOD – are used to simulate runoff in the Wimmera catchment affected by the Millennium drought. Although abcd and Budyko slightly outperformed GR2M and WASMOD, none of the models performed well in transfer to the driest period. The greatest variability is detected in simulated groundwater storage and baseflow; thus, these model components should be improved and/or enhanced calibration strategies should be employed to advance the transferability of MWBMs under changing climate.     

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

Abstract

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

Editor D. Koutsoyiannis

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

Asymptotic aspects of the Boussinesq approximation for gases and liquids

Abstract

The asymptotic formulation of the Boussinesq approximation relates the pressure of the fluid to a thermodynamical quantity involving the heat capacity c_Po . In this paper we examine the implications of such a scaling, in particular: (i) the singular degeneracy of the equation of state ρ = ρ* (1 ?α* (T?;T*)) of a liquid: this equation of state is valid only for small values of the coefficient α T*; (ii) in which manner the scaling introduces the Mach number of the flow as a small parameter e for a compressible fluid. The equations at order zero with respect to ? are the same equations for gases and for liquids only if the thermodynamics of the medium is described by using the Brunt-Väisälä frequency instead of the temperature.     

BIBLIOGRAPHIE—BIBLIOGRAPHY

ABSTRACT

With the increasing use of telemetry in the control of water resource systems, a considerable amount of effort is being devoted to the development of models and parameter estimation techniques for on-line use. A variety of models and parameter estimation algorithms have been considered, ranging from complex conceptual models of the soil moisture accounting type, which are traditionally calibrated off-line, to state-space/Kalman filter models which, perhaps, have enjoyed undue popularity in the recent literature due to their mathematical elegance. The fundamental assumptions underlying the various approaches are reviewed, and the validity of these assumptions in the hydrological forecasting context is assessed. The paper draws on some results obtained during a recent workshop at the Institute of Hydrology in making assessments of the relative merits of different models and parameter estimation algorithms; these results have been derived from an intercomparison of a number of real time forecasting models.     

Hydromagnetic waves in rapidly rotating spherical shells generated by poloidal decay modes

Abstract

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number T_m ? 10⁵. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.     

A method of estimating the stress exponent in the flow law for rocks using fold shape

On the basis of experiment and theory, we expect rocks to deform in a linear fashion when diffusive processes control deformation, and nonlinearly in most other situations. The geometric characteristics of buckle folds in layered materials are dependent on rheological parameters, and in particular depend strongly on the stress exponent,n _L , of the stiff layers involved. Thus, information about the deformation rocks have undergone and their rheological state during deformation can be obtained by studying fold shapes and strain distributions. This is important because there is uncertainty in extrapolating laboratory-derived flow laws to the very slow natural strain rates and large strains found in nature.We have studied the development of buckle folds in linear and nonlinear materials using finite-element modeling, and interpolated the numerical results to construct plots relating several geometric parameters to variations in power-law exponent,n _L , and viscosity ratio,m, of layer to matrix. Such plots allow for a comparison of the results of numerical models with data for many natural and experimentally-produced folds, and there is consistency among the data for folds produced in physical models, using both linear and nonlinear materials and the numerical simulations. data for folds from the Appalachian Mountains, the Alps and elsewhere, however, suggest high values ofn _L in the flow laws for a number of rock types. The unexpectedly high estimates ofn _L suggest that other factors, such as strain softening or anisotropy, may influence fold shape, and thus complicate the estimation of the rheological properties of rocks.     

Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

Hydraulic model calibration for extreme floods in bedrock‐confined channels: case study from northern Thailand

Palaeoflood reconstructions based on stage evidence are typically conducted in data‐poor field settings. Few opportunities exist to calibrate the hydraulic models used to estimate discharge from this evidence. Consequently, an important hydraulic model parameter, the roughness coefficient (e.g. Manning's n), is typically estimated by a range of approximate techniques, such as ‘visual estimation’ and semi‐empirical equations. These techniques contribute uncertainty to resulting discharge estimates, especially where the study reach exhibits sensitivity in the discharge–Manning's n relation. We study this uncertainty within a hydraulic model for a large flood of known discharge on the Mae Chaem River, northern Thailand. Comparison of the ‘calibrated’ Manning's n with that obtained from semi‐empirical equations indicates that these underestimate roughness. Substantial roughness elements in the extra‐channel zone, inundated during large events, contribute significant additional sources of flow resistance that are captured neither by the semi‐empirical equations, nor by existing models predicting stage–roughness variations. This bedrock channel exhibits a complex discharge–Manning's n relation, and reliable estimates of the former are dependent upon realistic assignment of the latter. Our study demonstrates that a large recent flood can provide a valuable opportunity to constrain this parameter, and this is illustrated when we model a palaeoflood event in the same reach, and subsequently examine the magnitude–return period consequences of discharge uncertainty within a flood frequency analysis, which contributes its own source of uncertainty. Copyright © 2005 John Wiley & Sons, Ltd.     

A study on the impact of climate change on streamflow at the watershed scale in the humid tropics

Abstract

Climate change is recognized to be one of the most serious challenges facing mankind today. Driven by anthropogenic activities, it is known to be a direct threat to our food and water supplies and an indirect threat to world security. Increase in the concentration of carbon dioxide and other greenhouse gases in the atmosphere will certainly affect hydrological regimes. The consequent global warming is expected to have major implications on water resources management. The objective of this research is to present a general approach for evaluating the impacts of potential climate change on streamflow in a river basin in the humid tropical zone of India. Large-scale global climate models (GCMs) are the best available tools to provide estimates of the effect of rising greenhouse gases on rainfall and temperature. However the spatial resolution of these models (250 km?×?250 km) is not compatible with that of watershed hydrological models. Hence the outputs from GCMs have to be downscaled using regional climate models (RCMs), so as to project the output of a GCM to a finer resolution (50 km?×?50 km). In the present work, the projections of a GCM for two scenarios, A2 and B2 are downscaled by a RCM to project future climate in a watershed. Projections for two important climate variables, viz. rainfall and temperature are made. These are then used as inputs for a physically-based hydrological model, SWAT, in order to evaluate the effect of climate change on streamflow and vegetative growth in a humid tropical watershed.

Citation Raneesh, K. Y. & Santosh, G. T. (2011) A study on the impact of climate change on streamflow at the watershed scale in the humid tropics. Hydrol. Sci. J. 56(6), 946–965.     

Estimation of water cloud model vegetation parameters using a genetic algorithm

Abstract

The water cloud model is used to account for the effect of vegetation water content on radar backscatter data. The model generally comprises two parameters that characterize the vegetated terrain, A and B, and two bare soil parameters, C and D. In the present study, parameters A and B were estimated using a genetic algorithm (GA) optimization technique and compared with estimates obtained by the sequential unconstrained minimization technique (SUMT) from measured backscatter data. The parameter estimation was formulated as a least squares optimization problem by minimizing the deviations between the backscatter coefficients retrieved from the ENVISAT ASAR image and those predicted by the water cloud model. The bias induced by three different objective functions was statistically analysed by generating synthetic backscatter data. It was observed that, when the backscatter coefficient data contain no errors, the objective functions do not induce any bias in the parameter estimation and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the cases considered, the objective function based on the sum of squares of normalized deviations with respect to the computed backscatter coefficient resulted in the best possible estimates. A comparison of the GA technique with the SUMT was undertaken in estimating the water cloud model parameters. For the case considered, the GA technique performed better than the SUMT in parameter estimation, where the root mean squared error obtained from the GA was about half of that obtained by the SUMT.

Editor D. Koutsoyiannis; Associate editor L. See

Citation Kumar, K., Hari Prasad, K.S. and Arora, M.K., 2012. Estimation of water cloud model vegetation parameters using a genetic algorithm. Hydrological Sciences Journal, 57 (4), 776–789.     

Empirical statistical characterization and regionalization of amplitude–duration–frequency curves for extreme peak flows in the Lake Victoria Basin,East Africa

Abstract

This paper focuses on a regionalization attempt to partly solve data limitation problems in statistical analysis of high flows to derive discharge–duration–frequency (QDF) relationships. The analysis is based on 24 selected catchments in the Lake Victoria Basin (LVB) in East Africa. Characteristics of the theoretical QDF relationships were parameterized to capture their slopes of extreme value distributions (evd), tail behaviour and scaling measures. To enable QDF estimates to be obtained for ungauged catchments, interdependence relationships between the QDF parameters were identified, and regional regression models were developed to explain the regional difference in these parameters from physiographic characteristics. In validation of the regression models, from the lowest (5 years) to the highest (25 years) return periods considered, the percentage bias in the QDF estimates ranged from –2% for the 5-year return period to 27% for 25-year return period.

Editor D. Koutsoyiannis     

Changes in concentration–discharge regression parameters due to coal mining and reclamation activities / Changements dans les paramètres de régression entre concentration et débit,causés par l’exploitation minière de charbon et des activités de reconversion

Abstract

Abstract Assessment of the impacts of mining and reclamation, and design of management practices to reduce chemical loads in stream channels, require knowledge of changing hydrological conditions and of changing sources and rates of release of chemicals into stream waters. One simple method for evaluating these impacts is to combine flow duration curves with regression relations between surface-water chemical concentrations (C) and instantaneous discharge (Q). However, little is known regarding the drainage basin-scale effects of mining and reclaiming drainage basins on regression relations. These effects were assessed on three small experimental drainage basins in Ohio subjected to surface mining for coal. Comparisons were made between regression parameter changes for natural/undisturbed conditions, land disturbances caused by mining and reclamation, incomplete reclamation, and the final condition of the reclaimed drainage basins. Regression analysis used a total of 5047 laboratory analyses of 36 constituents. Of 429 regressions, 153 (36%) were statistically significant. Knowledge of changes in regression parameters is important because regressions supply information on the rate of release and supply of chemical constituents in mined and reclaimed drainage basins. Duration curves of concentration and loads can be constructed using these regressions with flow–duration curves to give estimates of the percentage of time that concentrations and loads are exceeded during different phases of disturbance. This study assessed the changes in regression relations due to mining coal seams and reclamation activities for 36 chemical constituents, two mining methods, three reclamation practices and three distinct geologic settings.     

Seasonal climate patterns and their influence on calibration of the Hargreaves-Samani equation

Abstract

Annual patterns in climate parameters were studied to evaluate how these influence the quality of reference evapotranspiration (ETo) estimates obtained from the Hargreaves-Samani (HS) equation, since the method only uses the measured temperature directly. The work evaluates how these patterns can be used to improve the HS ETo estimates. Ten-year moving averages from a set of California Irrigation Management Information System (CIMIS) stations were used to evaluate the relationships between solar radiation (R_s), temperature (T) and ETo. The results indicate that T treads behind solar radiation and its value peaks some 25 days later. Thus, the main irrigation season in the Mediterranean climate (1 May–30 September) can be divided into three phases: increasing R_s and T; decreasing R_s with increasing T; and decreasing R_s and T. Non-univocal annual cycles were observed between R_s and T, ETo and R_s, and ETo and T. These annual patterns result in important seasonal changes in the ratio between the HS and Penman-Monteith (FAO PM) ETo estimates. The changes are particularly important during the irrigation season, where the FAO PM initially calculates greater ETo values than the HS methodology, and from the end of May to early September, where the HS equation overestimates the ETo values (by 17 mm, or 3%). These patterns obtained from 2000–2009 data were used to calibrate and improve HS ETo estimates at new sites for the 2010–2011 period. Calibration based on the proposed seasonal region-wide FAO PM/HS ETo ratios improved both the bias (decreased from 0.40 to 0.36 mm d^-1) and r² (increased from 0.67 to 0.87) of the ETo estimates for the irrigation season. The proposed methodology can be easily applied to other regions, even when the existing weather stations are sparse.

Editor Z.W. Kundzewicz     

Pressure and shear stress caused by raindrop impact at the soil surface: Scaling laws depending on the water depth

Raindrop impact is an important process in soil erosion. Through its pressure and shear stress, raindrop impact causes a significant detachment of the soil material, making this material available for transport by sheet flow. Thanks to the accurate Navier–Stokes equations solver Gerris, we simulate the impact of a single raindrop of diameter D, at terminal velocity, on water layers of different thickness h: , , D, 2D, in order to study pressures and shear stresses involved in raindrop erosion. These complex numerical simulations help in understanding precisely the dynamics of the raindrop impact, quantifying in particular the pressure and the shear stress fields. A detailed analysis of these fields is performed and self‐similar structures are identified for the pressure and the shear stress on the soil surface. The evolution of these self‐similar structures are investigated as the aspect ratio h/D varies. We find that the pressure and the shear stress have a specific dependence on the ratio between the drop diameter and the water layer thickness, and that the scaling laws recently proposed in fluid mechanics are also applicable to raindrops, paving the road to obtain effective models of soil erosion by raindrops. In particular, we obtain a scaling law formula for the dependence of the maximum shear stress on the soil on the water depth, a quantity that is crucial for quantifying erosion materials. Copyright © 2016 John Wiley & Sons, Ltd.     

Upscaling geochemical reaction rates using pore-scale network modeling

Geochemical reaction rate laws are often measured using crushed minerals in well-mixed laboratory systems that are designed to eliminate mass transport limitations. Such rate laws are often used directly in reactive transport models to predict the reaction and transport of chemical species in consolidated porous media found in subsurface environments. Due to the inherent heterogeneities of porous media, such use of lab-measured rate laws may introduce errors, leading to a need to develop methods for upscaling reaction rates. In this work, we present a methodology for using pore-scale network modeling to investigate scaling effects in geochemical reaction rates. The reactive transport processes are simulated at the pore scale, accounting for heterogeneities of both physical and mineral properties. Mass balance principles are then used to calculate reaction rates at the continuum scale. To examine the scaling behavior of reaction kinetics, these continuum-scale rates from the network model are compared to the rates calculated by directly using laboratory-measured reaction rate laws and ignoring pore-scale heterogeneities. In this work, this methodology is demonstrated by upscaling anorthite and kaolinite reaction rates under simulation conditions relevant to geological CO₂ sequestration. Simulation results show that under conditions with CO₂ present at high concentrations, pore-scale concentrations of reactive species and reaction rates vary spatially by orders of magnitude, and the scaling effect is significant. With a much smaller CO₂ concentration, the scaling effect is relatively small. These results indicate that the increased acidity associated with geological sequestration can generate conditions for which proper scaling tools are yet to be developed. This work demonstrates the use of pore-scale network modeling as a valuable research tool for examining upscaling of geochemical kinetics. The pore-scale model allows the effects of pore-scale heterogeneities to be integrated into system behavior at multiple scales, thereby identifying important factors that contribute to the scaling effect.     

Scaling of strength reduction factors for degrading elasto‐plastic oscillators

The inelastic (design) spectra characterizing a seismic hazard are generally obtained by the scaling‐down of the elastic (design) spectra via a set of response modification factors. The component of these factors, which accounts for the ductility demand ratio, is known as the strength reduction factor (SRF), and the variation of this factor with initial period of the oscillator is called an SRF spectrum. This study considers scaling of the SRF spectrum in the case of an elasto‐plastic oscillator with strength and stiffness degradation characteristics. Two models are considered: one depending directly on the characterization of source and site parameters and the other depending on the normalized design spectrum characterization of the seismic hazard. The first model is the same as that proposed earlier by the second author, and is given in terms of earthquake magnitude, strong‐motion duration, predominant period, geological site conditions, ductility demand ratio, and ductility supply‐related parameter. The second model is a new model proposed here in terms of the normalized pseudo‐spectral acceleration values (to unit peak ground acceleration), ductility demand ratio and ductility supply‐related parameter. For each of these models, least‐square estimates of the coefficients are obtained through regression analyses of the data for 956 recorded accelerograms in western U.S.A. Parametric studies carried out with the help of these models confirm the dependence of SRFs on strong‐motion duration and earthquake magnitude besides predominant period and site conditions. It is also seen that degradation characteristics make a slight difference for high ductility demands and may lead to lower values of SRFs, unless the oscillators are very flexible. Copyright © 2004 John Wiley & Sons, Ltd.