Dissecting the effect of rainfall variability on the statistical structure of peak flows

This study examines the role of rainfall variability on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas as an illustration. Specifically, we investigate the effect of rainfall on the scatter, the scale break and the power law (peak flows vs. upstream areas) regression exponent. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations and subsequently investigate the role of storm advection velocity, storm variability characterized by variance, spatial correlation and intermittency. Finally, we use a realistic space–time rainfall field obtained from a popular rainfall model that combines the aforementioned features. For each of these scenarios, we employ a recent formulation of flow velocity for a network of channels, assume idealized conditions of runoff generation and flow dynamics and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the width function maxima. Our results show that the peak flow scaling exponent is always larger than the width function scaling exponent. The simulation scenarios are used to identify the smaller scale basins, whose response is dominated by the rainfall variability and the larger scale basins, which are driven by rainfall volume, river network aggregation and flow dynamics. The rainfall variability has a greater impact on peak flows at smaller scales. The effect of rainfall variability is reduced for larger scale basins as the river network aggregates and smoothes out the storm variability. The results obtained from simple scenarios are used to make rigorous interpretations of the peak flow scaling structure that is obtained from rainfall generated with the space–time rainfall model and realistic rainfall fields derived from NEXRAD radar data.     

A physically based distributed subsurface–surface flow dynamics model for forested mountainous catchments

This study was designed to develop a physically based hydrological model to describe the hydrological processes within forested mountainous river basins. The model describes the relationships between hydrological fluxes and catchment characteristics that are influenced by topography and land cover. Hydrological processes representative of temperate basins in steep terrain that are incorporated in the model include intercepted rainfall, evaporation, transpiration, infiltration into macropores, partitioning between preferential flow and soil matrix flow, percolation, capillary rise, surface flow (saturation‐excess and return flow), subsurface flow (preferential subsurface flow and baseflow) and spatial water‐table dynamics. The soil–vegetation–atmosphere transfer scheme used was the single‐layer Penman–Monteith model, although a two‐layer model was also provided. The catchment characteristics include topography (elevation, topographic indices), slope and contributing area, where a digital elevation model provided flow direction on the steepest gradient flow path. The hydrological fluxes and catchment characteristics are modelled based on the variable source‐area concept, which defines the dynamics of the watershed response. Flow generated on land for each sub‐basin is routed to the river channel by a kinematic wave model. In the river channel, the combined flows from sub‐basins are routed by the Muskingum–Cunge model to the river outlet; these comprise inputs to the river downstream. The model was applied to the Hikimi river basin in Japan. Spatial decadal values of the normalized difference vegetation index and leaf area index were used for the yearly simulations. Results were satisfactory, as indicated by model efficiency criteria, and analysis showed that the rainfall input is not representative of the orographic lifting induced rainfall in the mountainous Hikimi river basin. Also, a simple representation of the effects of preferential flow within the soil matrix flow has a slight significance for soil moisture status, but is insignificant for river flow estimations. Copyright © 2005 John Wiley & Sons, Ltd.     

Linking space–time variability of river runoff and rainfall fields: a dynamic approach

Statistical self-similarity in the spatial and temporal variability of rainfall, river networks, and runoff processes has been observed in many empirical studies. To theoretically investigate the relationships between the various time and space scales of variability in rainfall and runoff process we propose a simplified, yet physically based model of a catchment–rainfall interaction. The channel network is presented as a random binary tree, having topological and hydraulic geometry properties typically observed in real river networks. The continuous rainfall model consists of individual storms separated by dry periods. Each given storm is disaggregated in space and time using the random cascade model. The flow routing is modelled by the network of topologically connected nonlinear reservoirs, each representing a link in the channel network. Running the model for many years of synthetic rainfall time series and a continuous water balance model we generate an output, in the form of continuous time series of water discharge in all links in the channel network. The main subject of study is the annual peak flow as a function of catchment area and various characteristics of rainfall. The model enables us to identify different physical processes responsible for the empirically observed scaling properties of peak flows.     

Regionalizing mean annual flow and daily flow variability for basin‐scale sediment and nutrient modelling

River discharges vary strongly through time and space, and quantifying this variability is fundamental to understanding and modelling river processes. The river basin is increasingly being used as the unit for natural resource planning and management; to facilitate this, basin‐scale models of material supply and transport are being developed. For many basin‐scale planning activities, detailed rainfall‐runoff modelling is neither necessary nor tractable, and models that capture spatial patterns of material supply and transport averaged over decades are sufficient. Nevertheless, the data to describe the spatial variability of river discharge across large basins for use in such models are often limited, and hence models to predict river discharge at the basin scale are required. We describe models for predicting mean annual flow and a non‐dimensional measure of daily flow variability for every river reach within a drainage network. The models use sparse river gauging data, modelled grid surfaces of mean annual rainfall and mean annual potential evapotranspiration, and a network accumulation algorithm. We demonstrate the parameterization and application of the models using data for the Murrumbidgee basin, in southeast Australia, and describe the use of these predictions in modelling sediment transport through the river network. The regionalizations described contain less uncertainty, and are more sensitive to observed spatial variations in runoff, than regionalizations based on catchment area and rainfall alone. Copyright © 2006 John Wiley & Sons, Ltd.     

Net rainfall estimation by the inversion of a geomorphology-based transfer function and discharge deconvolution

The assessment of net rainfall, defined as the intermediate hydrological variable linked in between the hillslope and the river network, is a challenge. This paper presents a method for net rainfall estimation, using inverse modelling associated to a geomorphology-based transfer function. The analysis is carried out in semi-arid Tunisia, with a dataset from event discharges in a mesoscale dryland basin. A complete sensitivity analysis is developed, along with a discussion of validity limits for simplifying assumptions and the identification of paths for improvement. This work could be relevant for data-scarce areas, thanks to the use of simple dynamic conceptualization and being based on observable geomorphological features, adjusted to the available data and knowledge.     

Model study of the relationship between sediment yield and river basin area

The SHETRAN physically based, spatially distributed model is used to investigate the scaling relationship linking specific sediment yield to river basin area, for two contrasting topographies of upland and more homogeneous terrain and as a function of sediment source, land use and rainfall distribution. Modelling enables the effects of the controls to be examined on a systematic basis, while avoiding the difficulties associated with the use of field data (which include limited data, lack of measurements for nested basins and inability to isolate the effects of individual controls). Conventionally sediment yield is held to decrease as basin area increases, as the river network becomes more remote from the headwater sediment sources (an inverse relationship). However, recent studies have reported the opposite variation, depending on the river basin characteristics. The simulation results are consistent with these studies. If the sediment is supplied solely from hillslope erosion (no channel bank erosion) then, with uniform land use, sediment yield either decreases or is constant as area increases. The downstream decrease is accentuated if rainfall (and thence erosion) is higher in the headwaters than at lower elevations. Introducing a non‐uniform land use (e.g. forest at higher elevations, wheat at lower elevations) can reverse the trend, so that sediment yield increases downstream. If the sediment is supplied solely from bank erosion (no hillslope erosion), the sediment yield increases downstream for all conditions. The sediment yield/basin area relationship can thus be inverse or direct, depending on basin characteristics. There still remains, therefore, considerable scope for defining a universal scaling law for sediment yield. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation of suspended sediment rating curves in western and northern Greece

ABSTRACT

The suspended sediment rating curves for six stations on four rivers in western and northern Greece are investigated. For each station the suspended sediment load is a power function of the water discharge, which may be distinguished according to wet and dry seasons; the latter yields higher sediment loads for a given discharge than the former. This is due to the higher erosivity of dry season rainfall compared to wet season rainfall producing the same runoff. All rating curve exponents b lie in the range 2.5–3.5 for the wet and 2.0–3.0 for the dry season and are related to the constants a of the curves by empirical equations. The variation in a and b is explained in terms of the annual precipitation and area of the basin, the hypsometric fall, the main channel length, and the average bedslope of the river from the basin divide to the station, through empirical relationships, which also permit the prediction of rating curves for ungauged basins.     

A methodological approach for estimating turbidity in a river

During the operations of purging and disposal of sediments of a reservoir it is necessary to know the values of turbidity in the river downstream in natural condition,in the absence of dams or river training works.The paper shows that under these conditions the ratio of the average values of sediment discharge to the annual maximum value of water discharge is a function of the average annual turbidity.Turbidity can be considered as representative synthetic index of the climatic conditions,the lithological features and the land cover of the basin,and the geometric characteristics of the river network.The proposed relationship of sediment discharge as a function of water discharge were validated on the basis of data collected from different Italian regions that have very different morphological,geo-lithological and rainfall features and that are characterised by a basin area changing between a few dozen and thousands of square kilometres.The results can be considered satisfying.     

Daily hydrological modeling in the Amazon basin using TRMM rainfall estimates

Rainfall measurements by conventional raingauges provide relatively accurate estimates at a few points of a region. The actual rainfield can be approximated by interpolating the available raingauge data to the remaining of the area of interest. In places with relatively low gauge density such interpolated rainfields will be very rough estimates of the actual events. This is especially true for tropical regions where most rainfall has a convective origin with high spatial variability at the daily level. Estimates of rainfall by remote sensing can be very useful in regions such as the Amazon basin, where raingauge density is very low and rainfall highly variable. This paper evaluates the rainfall estimates of the Tropical Rainfall Measuring Mission (TRMM) satellite over the Tapajós river basin, a major tributary of the Amazon. Three-hour TRMM rainfall estimates were aggregated to daily values and were compared with catch of ground-level precipitation gauges on a daily basis after interpolating both data to a regular grid. Both daily TRMM and raingauge-interpolated rainfields were then used as input to a large-scale hydrological model for the whole basin; the calculated hydrographs were then compared to observations at several streamgauges along the river Tapajos and its main tributaries. Results of the rainfield comparisons showed that satellite estimates can be a practical tool for identifying damaged or aberrant raingauges at a basin-wide scale. Results of the hydrological modeling showed that TRMM-based calculated hydrographs are comparable with those obtained using raingauge data.     

Effects of hillslope dynamics and network geometry on the scaling properties of the hydrologic response

This paper investigates the specific contributions of river network geomorphology, hillslope flow dynamics and channel routing to the scaling behavior of the hydrologic response as function of drainage area. Scaling relationships emerged from the observations of geomorphological and hydrological data and were reproduced in previous works through mathematical models, for both idealized self-similar networks and natural basins. Recent literature highlighted that scale invariance of hydrological quantities depends not only on the metrics of the drainage catchment but also on effective flow routing. In this study we employ a geomorphological width function scheme to test the simple scaling hypothesis adopting more realistic dynamic conditions than in previous approaches, specifically taking into account the role of hillslopes. The analysis is based on the derivation of the characteristic distributions of path lengths and travel times, inferred from DEM processing and measurements of rainfall and runoff data. The study area is located in the Tiber River region (central Italy).Results indicate that, while scaling properties clearly emerge when the hydrologic response is defined on the basis of the sole geomorphology, scale invariance is broken when less idealized flow dynamics are taken into account. Lack of scaling appears in particular as a consequence of the catchment to catchment variability of hillslope velocities.     

A Power Function Method for Estimating Base Flow

Analytical base flow separation techniques are often used to determine the base flow contribution to total stream flow. Most analytical methods derive base flow from discharge records alone without using basin‐specific variables other than basin area. This paper derives a power function for estimating base flow, the form being aQ^b + cQ, an analytical method calibrated against an integrated basin variable, specific conductance, relating base flow to total discharge, and is consistent with observed mathematical behavior of dissolved solids in stream flow with varying discharge. Advantages of the method are being uncomplicated, reproducible, and applicable to hydrograph separation in basins with limited specific conductance data. The power function relationship between base flow and discharge holds over a wide range of basin areas. It better replicates base flow determined by mass balance methods than analytical methods such as filters or smoothing routines that are not calibrated to natural tracers or empirical basin and gauge‐specific variables. Also, it can be used with discharge during periods without specific conductance values, including separating base flow from quick flow for single events. However, it may overestimate base flow during very high flow events. Application of geochemical mass balance and power function base flow separation methods to stream flow and specific conductance records from multiple gauges in the same basin suggests that analytical base flow separation methods must be calibrated at each gauge. Using average values of coefficients introduces a potentially significant and unknown error in base flow as compared with mass balance methods.     

Influence of rainfall and soil properties spatial aggregation on extreme flash flood response modelling: An evaluation based on the Sesia river basin,North Western Italy

High resolution radar rainfall fields and a distributed hydrologic model are used to evaluate the sensitivity of flood and flash flood simulations to spatial aggregation of rainfall and soil properties at catchment scales ranging from 75 to 983 km². Hydrologic modeling is based on a Hortonian infiltration model and a network-based representation of hillslope and channel flow. The investigation focuses on three extreme flood and flash flood events occurred on the Sesia river basin, North Western Italy, which are analysed by using four aggregation lengths ranging from 1 to 16 km. The influence of rainfall spatial aggregation is examined by using the flow distance as a spatial coordinate, hence emphasising the role of river network in the averaging of space–time rainfall. The effects of reduced and distorted rainfall spatial variability on peak discharge have been found particularly severe for the flash flood events, with peak errors up to 35% for rainfall aggregation of 16 km and at 983 km² catchment size. Effects are particularly remarkable when significant structured rainfall variability combines with relatively important infiltration volumes due to dry initial conditions, as this emphasises the non-linear character of the rainfall–runoff relationship. In general, these results confirm that the correct estimate of rainfall volume is not enough for the accurate reproduction of flash flood events characterised by large and structured rainfall spatial variability, even at catchment scales around 250 km². However, accurate rainfall volume estimation may suffice for less spatially variable flood events. Increasing the soil properties aggregation length exerts similar effects on peak discharge errors as increasing the rainfall aggregation length, for the cases considered here and after rescaling to preserve the rainfall volume. Moreover, peak discharge errors are roughly proportional to runoff volume errors, which indicates that the shape of the flood wave is influenced in a limited way by modifying the detail of the soil property spatial representation. Conversely, rainfall aggregation may exert a pronounced influence on the discharge peak by reshaping the spatial organisation of the runoff volumes and without a comparable impact on the runoff volumes.     

Implementing Integrated Catchment Management in the upper Limpopo River basin: A situational assessment

A three-phase study was initiated as a way to promote Integrated Catchment Management approaches in the Limpopo River basin. This paper presents the situational assessment, which should enable De Beers to understand how their Venetia Mine operations are located within a broader and highly dynamic socio-economic and ecohydrological landscape as it pertains to water risks. The second phase, Risk assessment, aims to develop conservation interventions in the identified areas; the third phase will develop mechanisms for implementing water stewardship schemes to mitigate the shared water risks.Analysis of the social-ecological system (hydrological, climatic, ecological, socio-economic and governance systems) of the Limpopo River basin indicates that the institutional arrangement of the Limpopo River basin is neither simple nor effective. The basin is rapidly approaching closure in the sense that almost all of the available supplies of water have already been allocated to existing water users. If the proposed ecological flow requirements were to be met for all of the tributaries, the basin would be ‘closed’. On-going and projected land use changes and water resources developments in the upper reaches of the basin, coupled with projected rainfall reductions and temperature increases, and allocation of the flows for the ecological reserve, are likely to further reduce downstream river flows. The coupled increase in temperature and decrease in rainfall is of great concern for everyone in the basin, especially the poorer communities, who rely on rain-fed agriculture for their livelihoods. Increased temperatures also lead to increased evaporation from reservoirs and therefore result in a decrease in water availability. This will lead to increased abstraction of groundwater, especially from alluvial aquifers, and consequently an increase in river transmission losses and a decrease in river flows.     

THE 1998 FLOOD OF THE YANGTZE RIVER

1INTRODUCTIONDuringthefloodseasonof1998,anothercatastrophicfloodoccurredinthemiddleandlowerYangtzeRiverfollowingthecatastrophicfloodin1954.Ascomparedwiththe54flood,the1998floodwascharacterizedbythefactsthatthedurationofthehighwaterstagewasmuchlonger,thefloodcontrolwasmuchmoredifficult,andthetotalmanpowerandmaterialresourcesexpelldedintilefloodfightingweremuchmoreenormous.TOsummarizetheexperienceandlessonsfromthefloodissignificanttotilehydraulicengineeringandfloodcontroloftheYangtzeRiver.…     

Analytical model for a geomorphological instantaneous unit hydrograph

The rainfall‐runoff modelling of a river basin can be divided into two processes: the production function and the transfer function. The production function determines the proportion of gross rainfall actually involved in the runoff. The transfer function spreads the net rainfall over time and space in the river basin. Such a transfer function can be modelled using the approach of the geomorphological instantaneous unit hydrograph (GIUH). The effectiveness of geomorphological models is actually revealed in rainfall‐runoff modelling, where hydrologic data are desperately lacking, just as in ungauged basins. These models make it possible to forecast the hydrograph shape and runoff variation versus time at the basin outlet. This article is an introduction to a new GIUH model that proves to be simple and analytical. Its geomorphological parameters are easily available on a map or from a digital elevation model. This model is based on general hypotheses on symmetry that provide it with multiscale versatile characteristics. After having validated the model in river basins of very different nature and size, we present an application of this model for rainfall‐runoff modelling. Since parameters are determined relying on real geomorphological data, no calibration is necessary, and it is then possible to carry out rainfall‐runoff simulations in ungauged river basins. Copyright © 2006 John Wiley & Sons, Ltd.     

The design storm concept in flood control design and planning

The design storm approach, where the subject criterion variable is evaluated by using a synthetic storm pattern composed of identical return frequencies of storm pattern input, is shown to be an effective approximation to a considerably more complex probabilistic model. The single area unit hydrograph technique is shown to be an accurate mathematical model of a highly discretized catchment with linear routing for channel flow approximation, and effective rainfalls in subareas which are linear with respect to effective rainfall output for a selected “loss” function. The use of a simple “loss” function which directly equates to the distribution of rainfall depth-duration statistics (such as a constant fraction of rainfall, or a ?-index model) is shown to allow the pooling of data and thereby provide a higher level of statistical significance (in estimating T-year outputs for a hydrologic criterion variable) than use of an arbitrary “loss” function. The above design storm unit hydrograph approach is shown to provide the T-year estimate of a criterion variable when using rainfall data to estimate runoff.     

Exploring the effects of hillslope-channel link dynamics and excess rainfall properties on the scaling structure of peak-discharge

Several studies revealed that peak discharges (Q) observed in a nested drainage network following a runoff-generating rainfall event exhibit power law scaling with respect to drainage area (A) as Q(A) = αA^θ. However, multiple aspects of how rainfall-runoff process controls the value of the intercept (α) and the scaling exponent (θ) are not fully understood. We use the rainfall-runoff model CUENCAS and apply it to three different river basins in Iowa to investigate how the interplay among rainfall intensity, duration, hillslope overland flow velocity, channel flow velocity, and the drainage network structure affects these parameters. We show that, for a given catchment: (1) rainfall duration and hillslope overland flow velocity play a dominant role in controlling θ, followed by channel flow velocity and rainfall intensity; (2) α is systematically controlled by the interplay among rainfall intensity, duration, hillslope overland flow velocity, and channel flow velocity, which highlights that it is the combined effect of these factors that controls the exact values of α and θ; and (3) a scale break occurs when runoff generated on hillslopes runs off into the drainage network very rapidly and the scale at which the break happens is determined by the interplay among rainfall duration, hillslope overland flow velocity, and channel flow velocity.     

Assessment of flooding in urbanized ungauged basins: a case study in the Upper Tiber area,Italy

The reliability of a procedure for investigation of flooding into an ungauged river reach close to an urban area is investigated. The approach is based on the application of a semi‐distributed rainfall–runoff model for a gauged basin, including the flood‐prone area, and that furnishes the inlet flow conditions for a two‐dimensional hydraulic model, whose computational domain is the urban area. The flood event, which occurred in October 1998 in the Upper Tiber river basin and caused significant damage in the town of Pieve S. Stefano, was used to test the approach. The built‐up area, often inundated, is included in the gauged basin of the Montedoglio dam (275 km²), for which the rainfall–runoff model was adapted and calibrated through three flood events without over‐bank flow. With the selected set of parameters, the hydrological model was found reasonably accurate in simulating the discharge hydrograph of the three events, whereas the flood event of October 1998 was simulated poorly, with an error in peak discharge and time to peak of −58% and 20%, respectively. This discrepancy was ascribed to the combined effect of the rainfall spatial variability and a partial obstruction of the bridge located in Pieve S. Stefano. In fact, taking account of the last hypothesis, the hydraulic model reproduced with a fair accuracy the observed flooded urban area. Moreover, incorporating into the hydrological model the flow resulting from a sudden cleaning of the obstruction, which was simulated by a ‘shock‐capturing’ one‐dimensional hydraulic model, the discharge hydrograph at the basin outlet was well represented if the rainfall was supposed to have occurred in the region near the main channel. This was simulated by reducing considerably the dynamic parameter, the lag time, of the instantaneous unit hydrograph for each homogeneous element into which the basin is divided. The error in peak discharge and time to peak decreased by a few percent. A sensitivity analysis of both the flooding volume involved in the shock wave and the lag time showed that this latter parameter requires a careful evaluation. Moreover, the analysis of the hydrograph peak prediction due to error in rainfall input showed that the error in peak discharge was lower than that of the same input error quantity. Therefore, the obtained results allowed us to support the hypothesis on the causes which triggered the complex event occurring in October 1998, and pointed out that the proposed procedure can be conveniently adopted for flood risk evaluation in ungauged river basins where a built‐up area is located. The need for a more detailed analysis regarding the processes of runoff generation and flood routing is also highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

Drainage density changes during rainfall

Observations of stream behaviour during rainfall indicate that previous notions of a simple expanding and contracting network need review and refinement. In a small rural catchment near Armidale, N.S.W. changes in flowing stream length during rainfall have been depicted on flow length graphs which indicate a varied network response to similar rainfall amounts. Channel flow phenomena include discontinuous flow, the generation of flow points within the channel and movement of water downslope from saturated depression sources. Localized physical controls have a significant effect on stream growth which is a sensitive indicator of the catchment response to rainfall. During rapid changes in stream length total flowing length and discharge are highly correlated. A model of the pattern of network expansion and contraction involves several phases of flow contraction.