Green‐Ampt Curve‐Number mixed procedure as an empirical tool for rainfall–runoff modelling in small and ungauged basins

The Soil Conservation Service Curve Number (SCS‐CN) method is a popular rainfall–runoff model that is widely used to estimate direct runoff from small and ungauged basins. The SCS‐CN is a simple and valuable approach to quantify the total streamflow volume generated by storm rainfall, but its use is not appropriate for estimating the sub‐daily incremental rainfall excess. To overcome this drawback, we propose to include the Green‐Ampt (GA) infiltration model into a mixed procedure, which is referred to as Curve Number for Green‐Ampt (CN4GA), aiming to distribute in time the information provided by the SCS‐CN method. For a given storm, the computed SCS‐CN total net rainfall amount is employed to calibrate the soil hydraulic conductivity parameter of the GA model. The proposed procedure is evaluated by analysing 100 rainfall–runoff events that were observed in four small catchments of varying size. CN4GA appears to provide encouraging results for predicting the net rainfall peak and duration values and has shown, at least for the test cases considered in this study, better agreement with the observed hydrographs than the classic SCS‐CN method. Copyright © 2012 John Wiley & Sons, Ltd.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Direct estimation of catchment response time parameters in medium to large catchments using observed streamflow data

In single‐event deterministic design flood estimation methods, estimates of the peak discharge are based on a single and representative catchment response time parameter. In small catchments, a simplified convolution process between a single‐observed hyetograph and hydrograph is generally used to estimate time parameters such as the time to peak (T_P), time of concentration (T_C), and lag time (T_L) to reflect the “observed” catchment response time. However, such simplification is neither practical nor applicable in medium to large heterogeneous catchments, where antecedent moisture from previous rainfall events and spatially non‐uniform rainfall hyetographs can result in multi‐peaked hydrographs. In addition, the paucity of rainfall data at sub‐daily timescales further limits the reliable estimation of catchment responses using observed hyetographs and hydrographs at these catchment scales. This paper presents the development of a new and consistent approach to estimate catchment response times, expressed as the time to peak (T_Px) obtained directly from observed streamflow data. The relationships between catchment response time parameters and conceptualised triangular‐shaped hydrograph approximations and linear catchment response functions are investigated in four climatologically regions of South Africa. Flood event characteristics using primary streamflow data from 74 flow‐gauging stations were extracted and analysed to derive unique relationships between peak discharge, baseflow, direct runoff, and catchment response time in terms of T_Px. The T_Px parameters are estimated from observed streamflow data using three different methods: (a) duration of total net rise of a multipeaked hydrograph, (b) triangular‐shaped direct runoff hydrograph approximations, and (c) linear catchment response functions. The results show that for design hydrology and for the derivation of empirical equations to estimate catchment response times in ungauged catchments, the catchment T_Px should be estimated from both the use of an average catchment T_Px value computed using either Methods (a) or (b) and a linear catchment response function as used in Method (c). The use of the different methods in combination is not only practical but is also objective and has consistent results.     

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

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

Spatial and temporal variability of the hydrological response in a small Mediterranean research catchment (Vallcebre,Eastern Pyrenees)

This paper analyses the spatial and temporal variability of the hydrological response in a small Mediterranean catchment (Cal Rodó). The first part of the analysis focuses on the rainfall–runoff relationship at seasonal and monthly scale, using an 8‐year data set. Then, using storm‐flow volume and coefficient, the temporal variability of the rainfall–runoff relationship and its relationship with several hydrological variables are analysed at the event scale from hydrographs observed over a 3‐year period. Finally, the spatial non‐linearity of the hydrological response is examined by comparing the Cal Rodó hydrological response with the Can Vila sub‐catchment response at the event scale. Results show that, on a seasonal and monthly scale, there is no simple relationship between rainfall and runoff depths, and that evapotranspiration is a factor that introduced some non‐linearity in the rainfall–runoff relationship. The analysis of monthly values also reveals the existence of a threshold in the relationship between rainfall and runoff depths, denoting a more contrasted hydrological response than the one usually observed in humid catchments. At the event scale, the storm‐flow coefficient has a clear seasonal pattern with an alternance between a wet period, when the catchment is hydrologically responsive, and a dry summer period, when the catchment is much less reactive to any rainfall. The relationship between the storm‐flow coefficient and rainfall depth, rainfall maximum intensity and base‐flow shows that observed correlations are the same as those observed for humid conditions, even if correlation coefficients are notably lower. Comparison with the Can Vila sub‐catchment highlights the spatial heterogeneity of the rainfall‐runoff relationship at the small catchment scale. Although interpretation in terms of runoff processes remains delicate, heterogeneities between the two catchments seem to be related to changes in the ratio between infiltration excess and saturation processes in runoff formation. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessing urban rainfall-runoff response to stormwater management extent

We report an empirical analysis of the hydrologic response of three small, highly impervious urban watersheds to pulse rainfall events, to assess how traditional stormwater management (SWM) alters urban hydrographs. The watersheds vary in SWM coverage from 3% to 61% and in impervious cover from 45% to 67%. By selecting a set of storm events that involved a single rainfall pulse with >96% of total precipitation delivered in 60 min, we reduced the effect of differences between storms on hydrograph response to isolate characteristic responses attributable to watershed properties. Watershed-average radar rainfall data were used to generate local storm hyetographs for each event in each watershed, thus compensating for the extreme spatial and temporal heterogeneity of short-duration, intense rainfall events. By normalizing discharge values to the discharge peak and centring each hydrograph on the time of peak we were able to visualize the envelope of hydrographs for each group and to generate representative composite hydrographs for comparison across the three watersheds. Despite dramatic differences in the fraction of watershed area draining to SWM features across these three headwater tributaries, we did not find strong evidence that SWM causes significant attenuation of the hydrograph peak. Hydrograph response for the three watersheds is remarkably uniform despite contrasts in SWM, impervious cover and spatial patterns of land cover type. The primary difference in hydrograph response is observed on the recession limb of the hydrograph, and that change appears to be associated with higher storm-total runoff in the watersheds with more area draining to SWM. Our findings contribute more evidence to the work of previous authors suggesting that SWM is less effective at attenuating urban hydrographs than is commonly assumed. Our findings also are consistent with previous work concluding that percent impervious cover may have greater influence on runoff volume than percent SWM coverage.     

Using synthetic flow duration curves for rainfall–runoff model calibration at ungauged sites

The primary objective of the study is to propose a strategy for rainfall–runoff model calibration at ungauged sites. This strategy comprises two main components: (1) development of the regional analysis method to synthesize the flow duration curves at ungauged sites; and (2) utilization of the synthetic flow duration curves for model calibration. Since the regional analysis method can synthesize the flow duration curves at ungauged sites, the continuous rainfall–runoff model coupled with a global optimization method were applied in southern Taiwan using the synthetic flow duration curve as an objective for model calibration. The results reveal that the regional flow duration curve and the strategy for model calibration at ungauged sites have good performances in the study area. Copyright © 2000 John Wiley & Sons, Ltd.     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

Propagation of uncertainties in interpolated rainfields to runoff errors

Conditional daily rainfields were generated using collocated raingauge radar data by a kriging interpolation method, and disaggregated into hourly rainfields using variants of the method of fragments. A geographic information system (GIS)-based distributed rainfall–runoff model was used to convert the hourly rainfields into hydrographs. Using the complete radar rainfall as input, the rainfall–runoff model was calibrated based on storm events taken from nested catchments. Performance statistics were estimated by comparing the observed and the complete radar rainfall simulated hydrographs. Degradation in the hydrograph performance statistics by the simulated hourly rainfields was used to identify runoff error propagation. Uncertainty in daily rainfall amounts alone caused higher errors in runoff (depth, peak, and time to peak) than those caused by uncertainties in the hourly proportions alone. However, the degradation, which reduced with runoff depth, caused by the combined uncertainties was not significantly different from that caused by the uncertainty of amounts alone.     

A regional model of low flow for southern Taiwan

The primary purpose of this study is to develop regional models of the lower part of flow duration curves (LPFDCs) to synthesize low‐flow characteristics at ungauged sites in southern Taiwan. Because of the close relationship between low streamflow regimes and hydrogeological features, the model development first involved delimiting homogeneous hydrogeological regions by using two‐step cluster analysis. Each homogeneous region was then discriminated by an equation developed on the basis of its hydrogeological features, which was then used to determine which of three sets of regional LPFDC models would be appropriate for a particular ungauged site. Each of the three sets of regional LPFDC models were developed using both conventional multivariate statistical regression and fuzzy regression. Thirty‐four stream‐gauged watersheds located in southern Taiwan provide the data set. The study results reveal that the regional LPFDC models developed in this study could be applied reasonably at ungauged sites. Copyright © 2002 John Wiley & Sons, Ltd.     

A technique for deriving an average event unit hydrograph from streamflow—only data for ephemeral quick-flow-dominant catchments

A technique is presented for empirical and parametric estimation of an average event unit hydrograph response curve solely from measured streamflow data for use in rainfall-runoff models with a focus on modelling flow for natural resource management. As the technique does not require rainfall data, the unit hydrograph can be derived solely from streamflow data at a temporal resolution appropriate for the response of the catchment. The response curves derived for a number of stations show a power law relationship of decay in flow after peak that can be described using a three-parameter function. The approach is best suited to ephemeral streamflow regimes dominated by surface and near-surface runoff (quick-flow component) where flow events are well-separated and largely independent of each other. Analysis of the derived unit hydrograph for 28 quick-flow-dominated catchments illustrates the range of parameter values obtained in fitting the power law.     

Energy considerations in groundwater‐ridging mechanism of streamflow generation

Groundwater ridging is the rapid rise of a shallow water table during a rainfall event, in an environment where, in the pre‐event period, the capillary fringe extends to the ground surface. Groundwater ridging is widely cited to account for the observed significant appearance of pre‐event water in a stream stormflow hydrograph. Various hypotheses have been advanced to explain the groundwater‐ridging mechanism; and most recently, from a field study site in South Africa, an energy hypothesis was proposed, which explains that groundwater‐ridging water‐table rise is a result of rapid introduction and transmission of additional pressure head into the capillary fringe from an intense rainfall at the ground surface. However, there is a need for further analysis and evidence from other field study sites to confirm and support this newly proposed energy hypothesis. The objectives of this paper are, therefore, as follows: to review previous observations on groundwater ridging, from other study sites, in order to deduce evidence of the newly proposed energy hypothesis; to present and evaluate a one‐dimensional diffusion mathematical model that can simulate groundwater‐ridging water‐table rise, based on the newly proposed energy hypothesis; and to evaluate the importance of a capillary fringe in streamflow generation. Analysis of previous observations from other study sites generally indicated that the rate of groundwater‐ridging water‐table rise is directly related to the rainfall intensity, hence confirming and agreeing with the newly proposed energy hypothesis. Additionally, theoretical results by the mathematical model agreed fairly well with the field results observed under natural rainfall, confirming that the rapidly rainfall‐induced energy is diffusively transmitted downwards through pore water, elevating the pressure head at every depth. The results in this study also support the concept of a three‐end‐member stream stormflow hydrograph and contribute to the explanation of how catchments can store water for long periods but then release it rapidly during storm events. Copyright © 2015 John Wiley & Sons, Ltd.     

Climate variability,snow, and physiographic controls on storm hydrographs in small forested basins,western Cascades,Oregon

Large floods are often attributed to the melting of snow during a rain event. This study tested how climate variability, snowpack presence, and basin physiography were related to storm hydrograph shape in three small (<1 km²) basins with old‐growth forest in western Oregon. Relationships between hydrograph characteristics and precipitation were tested for approximately 800 storms over a nearly 30‐year period. Analyses controlled for (1) snowpack presence/absence, (2) antecedent soil moisture, and (3) hillslope length and gradient. For small storms (<150 mm precipitation), controlling for precipitation, the presence of a snowpack on near‐saturated soil increased the threshold of precipitation before hydrograph rise, extended the start lag, centroid lag, and duration of storm hydrographs, and increased the peak discharge. The presence of a snowpack on near‐saturated soil sped up and steepened storm hydrographs in a basin with short steep slopes, but delayed storm hydrographs in basins with longer or more gentle slopes. Hydrographs of the largest events, which were extreme regional rain and rain‐on‐snow floods, were not sensitive to landform characteristics or snowpack presence/absence. Although the presence of a snowpack did not increase peak discharge in small, forested basins during large storms, it had contrasting effects on storm timing in small basins, potentially synchronizing small basin contributions to the larger basin hydrograph during large rain‐on‐snow events. By altering the relative timing of hydrographs, snowpack melting could produce extreme floods from precipitation events whose size is not extreme. Further work is needed to examine effects of canopy openings, snowpack, and climate warming on extreme rain‐on‐snow floods at the large basin scale. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of conditional parameterization on performance of rainfall‐runoff model regarding hydrologic non‐stationarity

Better parameterization of a hydrological model can lead to improved streamflow prediction. This is particularly important for seasonal streamflow forecasting with the use of hydrological modelling. Considering the possible effects of hydrologic non‐stationarity, this paper examined ten parameterization schemes at 12 catchments located in three different climatic zones in east Australia. These schemes are grouped into four categories according to the period when the data are used for model calibration, i.e. calibration using data: (1) from a fixed period in the historical records; (2) from different lengths of historical records prior to prediction year; (3) from different climatic analogue years in the past; and (4) data from the individual months. Parameterization schemes were evaluated according to model efficiency in both the calibration and verification period. The results show that the calibration skill changes with the different historic periods when data are used at all catchments. Comparison of model performance between the calibration schemes indicates that it is worth calibrating the model with the use of data from each individual month for the purpose of seasonal streamflow forecasting. For the catchments in the winter‐dominant rainfall region of south‐east Australia, a more significant shift in rainfall‐runoff relationships at different periods was found. For those catchments, model calibration with the use of 20 years of data prior to the prediction year leads to a more consistent performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthetic design hydrographs for ungauged catchments: a comparison of regionalization methods

Design flood estimates for a given return period are required in both gauged and ungauged catchments for hydraulic design and risk assessments. Contrary to classical design estimates, synthetic design hydrographs provide not only information on the peak magnitude of events but also on the corresponding hydrograph volumes together with the hydrograph shapes. In this study, we tested different regionalization approaches to transfer parameters of synthetic design hydrographs from gauged to ungauged catchments. These approaches include classical regionalization methods such as linear regression techniques, spatial methods, and methods based on the formation of homogeneous regions. In addition to these classical approaches, we tested nonlinear regression models not commonly used in hydrological regionalization studies, such as random forest, bagging, and boosting. We found that parameters related to the magnitude of the design event can be regionalized well using both linear and nonlinear regression techniques using catchment area, length of the main channel, maximum precipitation intensity, and relief energy as explanatory variables. The hydrograph shape, however, was found to be more difficult to regionalize due to its high variability within a catchment. Such variability might be better represented by looking at flood-type specific synthetic design hydrographs.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Remotely sensed ET for streamflow modelling in catchments with contrasting flow characteristics: an attempt to improve efficiency

An efficient calibration with remotely sensed (RS) data is important for accurate predictions at ungauged catchments. This study investigates the advantages of streamflow-sensitive regionalization on calibration with RS evapotranspiration (ET). Regionalization experiments are performed at 28 catchments in Australia. The catchments are classified into three groups based on annual rainfall and runoff coefficients. Streamflow, RS ET, and a multi-objective RS ET-streamflow calibration are performed using the DiffeRential Evolution Adaptive Metropolis algorithm in each catchment. Simplified Australian Water Resource Assessment-Landscape model is calibrated for a selection of five parameters. Posterior probability distributions of parameters from three calibrations performed at donor catchments in each group are inspected to find the parameter for regionalization in the individual group. In group 1 of wetter catchments, regionalization of parameter FsoilEmax (soil evaporation scaling factor) helps to simplify the calibration without any deterioration in ET, soil moisture (SM) and streamflow predictions. Regionalization of parameter Beta (coefficient describing rate of hydraulic conductivity increase with water content) in group 2 assists to improve the streamflow predictions with no decrement in ET and SM predictions. However, regionalization is not able to provide satisfactory results in group 3. Group 3 includes low-yielding catchments, with average annual rainfall below 1000 mm/year and runoff coefficient less than 0.1, where traditional streamflow calibration also fails to produce accurate results. This study concludes that streamflow-sensitive regionalization is effective for improving the efficacy of RS ET calibration in wetter catchments.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Isotopic investigation of runoff generation in a glacierized catchment in northern Sweden

In this study, summer rainfall contributions to streamflow were quantified in the sub‐arctic, 30% glacierized Tarfala (21.7 km²) catchment in northern Sweden for two non‐consecutive summer sampling seasons (2004 and 2011). We used two‐component hydrograph separation along with isotope ratios (δ¹⁸O and δD) of rainwater and daily streamwater samplings to estimate relative fraction and uncertainties (because of laboratory instrumentation, temporal variability and spatial gradients) of source water contributions. We hypothesized that the glacier influence on how rainfall becomes runoff is temporally variable and largely dependent on a combination of the timing of decreasing snow cover on glaciers and the relative moisture storage condition within the catchment. The results indicate that the majority of storm runoff was dominated by pre‐event water. However, the average event water contribution during storm events differed slightly between both years with 11% reached in 2004 and 22% in 2011. Event water contributions to runoff generally increased over 2011 the sampling season in both the main stream of Tarfala catchment and in the two pro‐glacial streams that drain Storglaciären (the largest glacier in Tarfala catchment covering 2.9 km²). We credit both the inter‐annual and intra‐annual differences in event water contributions to large rainfall events late in the summer melt season, low glacier snow cover and elevated soil moisture due to large antecedent precipitation. Together amplification of these two mechanisms under a warming climate might influence the timing and magnitude of floods, the sediment budget and nutrient cycling in glacierized catchments. Copyright © 2012 John Wiley & Sons, Ltd.