A BTOP model to extend TOPMODEL for distributed hydrological simulation of large basins

Topography is a dominant factor in hillslope hydrology. TOPMODEL, which uses a topographical index derived from a simplified steady state assumption of mass balance and empirical equations of motion over a hillslope, has many advantages in this respect. Its use has been demonstrated in many small basins (catchment areas of the order of 2–500 km²) but not in large basins (catchment areas of the order of 10 000–100 000 km²). The objective of this paper is to introduce the Block‐wise TOPMODEL (BTOP) as an extension of the TOPMODEL concept in a grid based framework for distributed hydrological simulation of large river basins. This extension was made by redefining the topographical index by using an effective contributing area af(a) (0?f(a)?1) per unit grid cell area instead of the upstream catchment area per unit contour length and introducing a concept of mean groundwater travel distance. Further the transmissivity parameter T₀ was replaced by a groundwater dischargeability D which can provide a link between hill slope hydrology and macro hydrology. The BTOP model uses all the original TOPMODEL equations in their basic form. The BTOP model has been used as the core hydrological module of an integrated distributed hydrological model YHyM with advanced modules of precipitation, evapotranspiration, flow routing etc. Although the model has been successfully applied to many catchments around the world since 1999, there has not been a comprehensive theoretical basis presented in such applications. In this paper, an attempt is made to address this issue highlighted with an example application using the Mekong basin. Copyright © 2007 John Wiley & Sons, Ltd.     

Toward a physical undenstanding of earthquake scaling relations

In seismological literature, there exist two competing theories (the so-calledW model andL model) treating earthquake scaling relations between mean slip and rupture dimension and between seismic moment and rupture dimension. The core of arguments differentiating the two theories is whether the mean slip should scale with the rupture width or with the rupture length for large earthquakes. In this paper, we apply the elastic theory of dislocation to clarify the controversy. Several static dislocation models are used to simulate strike-slip earthquakes. Our results show that the mean slip scales linearly with the rupture width for small earthquakes with a rupture length smaller than the thickness of the seismogenic layer. However, for large earthquakes with a rupture length larger than the thickness of the seismogenic layer, our models show a more complicated scaling relation between mean slip and rupture dimension. When the rupture length is smaller than a cross-over length, the mean slip scales nearly linearly with the rupture length. When the rupture length is larger than a cross-over length, the mean slip approaches asymptotically a constant value and scales approximately with the rupture width. The cross-over length is a function of the rupture width and is about 75 km for earthquakes with a saturated rupture width of 15 km. We compare our theoretical predictions with observed source parameters of some large strike-slip earthquakes, and they match up well. Our results also suggest that when large earthquakes have a fixed aspect ratio of rupture length to rupture width (which seems to be the case for most subduction earthquakes) the mean slip scales with the rupture dimension in the same way as small earthquakes.     

A catchment framework for one‐dimensional models: introducing FLUSH and its application

A new modelling framework capable of incorporating detailed one‐dimensional models in a catchment context is presented which can be used to asses the hydrological implications (recharge, discharge, salt movement) of different land uses on different parts of the catchment. The modelling framework incorporates farming systems models and, thus, simulates crop and pasture production, whilst also accounting for lateral fluxes of water (surface and subsurface) and groundwater recharge and discharge. The framework was applied to Simmons Creek catchment, a subcatchment of the Billabong Creek in southern New South Wales, comprising gentle uplands and substantial low‐relief areas containing swamps. An integrated approach incorporating soil, hydrology, hydrogeology, and terrain analysis resulted in interpretation of landscape function and the necessary parameterization of the modelling framework. Current land use (crop rotation and pasture) and an alternative land use (10% trees on uphill units and pasture in the lower lying lands) were simulated to compare the relative contribution of parts of the catchment with total recharge. Comparison between current and alternative land use over 44 years of simulations indicated a decrease of mean annual drainage from 39 to 29 mm year^?1 and an average reduction of the groundwater level of about 0·4 m. A more substantial decrease in water‐table depth would require targeted tree planting over larger areas. This can be investigated further with the spatial framework. Copyright © 2007 John Wiley & Sons, Ltd.     

Effective impervious area for runoff in urban watersheds

Effective impervious area (EIA), or the portion of total impervious area (TIA) that is hydraulically connected to the storm sewer system, is an important parameter in determining actual urban runoff. EIA has implications in watershed hydrology, water quality, environment, and ecosystem services. The overall goal of this study is to evaluate the application of successive weighted least square (WLS) method to urban catchments with different sizes and various hydrologic conditions to determine EIA fraction. Other objectives are to develop insights on the data selection issues, EIA fraction, EIA/TIA ratio, and runoff source area patterns in urban catchments. The successive WLS method is applied to 50 urban catchments with different sizes from less than 1 ha to more than 2000 ha in Minnesota, Wisconsin, Texas, USA as well as Europe, Canada, and Australia. The average, median, and standard deviation of EIA fractions for the 42 catchments with residential land uses are found to be 0.222, 0.200, and 0.113, respectively. These values for the EIA/TIA ratio in the same 42 catchments are 0.50, 0.48, and 0.21, respectively. While the EIA/TIA results indicate the importance of EIA, 95% prediction interval of the mean EIA/TIA is found to be 0.07 to 0.93, which shows that using an average value for this ratio in each land use to determine EIA from TIA in ungauged urban watersheds can be misleading. The successive WLS method was robust and is recommended for determining EIA in gauged urban catchments. Copyright © 2016 John Wiley & Sons, Ltd.     

Surface stone cover on desert hillslopes; parameterizing characteristics relevant to infiltration and surface runoff

Surface stones are a common feature of desert hillslopes. They influence slope processes ranging from the interception and partitioning of rainwater to the dislodgement and transport of regolith particles. The aspects of a stone mantle which relate to these various influences are diverse, and include surface cover fraction, dimensions of the infiltration annulus, and geometric and packing effects. Analyses of the characteristics of stone cover at two study sites were made using photographic methods and are used to evaluate different means of reporting mean stone sizes. It is found that mean diameter based on weight, as conventionally employed in sieve analysis, is insensitive to important stone cover characteristics and may be influenced greatly by uncommon, large stones. Similarly, mean diameters based on count become inappropriate if large numbers of small stones dominate the calculated mean, concealing other site-to-site differences in stone cover. As a more appropriate parameterization of stone geometry, the use of mean diameters weighted by stone surface area and perimeter length are proposed. These weighting factors have the advantage that they relate closely to stone characteristics relevant to slope hydrology and erosion processes.     

A discrete particle representation of hillslope hydrology: hypothesis testing in reproducing a tracer experiment at Gårdsjön,Sweden

Despite the long history of the continuum equation approach in hydrology, it is not a necessary approach to the formulation of a physically based representation of hillslope hydrology. The Multiple Interacting Pathways (MIPs) model is a discrete realization that allows hillslope response and transport to be simultaneously explored in a way that reflects the potential occurrence of preferential flows and lengths of pathways. The MIPs model uses random particle tracking methods to represent the flow of water within the subsurface alongside velocity distributions that acknowledge preferential flows and transition probability matrices, which control flow pathways. An initial realization of this model is presented here in application to a tracer experiment carried out in Gårdsjön, Sweden. The model is used as an exploratory tool, testing several hypotheses in relation to this experiment. Copyright © 2011 John Wiley & Sons, Ltd.     

On the use of partial probability weighted moments in the analysis of hydrological extremes

The use of partial probability weighted moments (PPWM) for estimating hydrological extremes is compared to that of probability weighted moments (PWM). Firstly, estimates from at‐site data are considered. Two Monte Carlo analyses, conducted using continuous and empirical parent distributions (of peak discharge and daily rainfall annual maxima) and applying four different distributions (Gumbel, Fréchet, GEV and generalized Pareto), show that the estimates obtained from PPWMs are better than those obtained from PWMs if the parent distribution is unknown, as happens in practice. Secondly, the use of partial L‐moments (obtained from PPWMs) as diagnostic tools is considered. The theoretical partial L‐diagrams are compared with the experimental data. Five different distributions (exponential, Pareto, Gumbel, GEV and generalized Pareto) and 297 samples of peak discharge annual maxima are considered. Finally, the use of PPWMs with regional data is investigated. Three different kinds of regional analyses are considered. The first kind is the regression of quantile estimates on basin area. The study is conducted applying the GEV distribution to peak discharge annual maxima. The regressions obtained with PPWMs are slightly better than those obtained with PWMs. The second kind of regional analysis is the parametric one, of which four different models are considered. The congruence between local and regional estimates is examined, using peak discharge annual maxima. The congruence degree is sometimes higher for PPWMs, sometimes for PWMs. The third kind of regional analysis uses the index flood method. The study, conducted applying the GEV distribution to synthetic data from a lognormal joint distribution, shows that better estimates are obtained sometimes from PPWMs, sometimes from PWMs. All the results seem to indicate that using PPWMs can constitute a valid tool, provided that the influence of ouliers, of course higher with censored samples, is kept under control. Copyright © 2007 John Wiley & Sons, Ltd.     

Importance of no‐rain measurements on the comparison of radar and rain gauge rain rate

This study evaluated four possible cases of comparing radar and rain gauge rain rate for the detection of mean‐field bias. These four cases, or detection designs, consider in this study are: (1) design 1‐uses all the data sets available, including zero radar rain rate and zero rain gauge rain rate, (2) design 2—uses the data sets of positive radar rain rate and zero or positive rain gauge rain rate, (3) design 3—uses the data sets of zero or positive radar rain rate and positive rain gauge rain rate and (4) design 4—uses the data sets of positive radar rain rate and positive rain gauge rain rate. A theoretical review of these four detection designs showed that only the design 1 causes no design bias, but designs 2, 3 and 4 can cause positive, negative and negative design biases, respectively. This theoretical result was also verified by applying these four designs to the rain rate field generated by a multi‐dimensional rain rate model, as well as to that of the Mt Gwanak radar in Korea. The results from both applications showed that especially the design 4, which is generally used for the detection of mean‐field bias of radar rain rate, causes a serious design bias; therefore, is inappropriate as a design for detecting the mean‐field bias of radar rain rate. Copyright © 2009 John Wiley & Sons, Ltd.     

Flood frequency analysis of Turkey using L‐moments method

The index flood procedure coupled with the L‐moments method is applied to the annual flood peaks data taken at all stream‐gauging stations in Turkey having at least 15‐year‐long records. First, screening of the data is done based on the discordancy measure (D_i) in terms of the L‐moments. Homogeneity of the total geographical area of Turkey is tested using the L‐moments based heterogeneity measure, H, computed on 500 simulations generated using the four parameter Kappa distribution. The L‐moments analysis of the recorded annual flood peaks data at 543 gauged sites indicates that Turkey as a whole is hydrologically heterogeneous, and 45 of 543 gauged sites are discordant which are discarded from further analyses. The catchment areas of these 543 sites vary from 9·9 to 75121 km² and their mean annual peak floods vary from 1·72 to 3739·5 m³ s^?1. The probability distributions used in the analyses, whose parameters are computed by the L‐moments method are the general extreme values (GEV), generalized logistic (GLO), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA), and five‐parameter Wakeby (WAK). Based on the L‐moment ratio diagrams and the |Z_dist|‐statistic criteria, the GEV distribution is identified as the robust distribution for the study area (498 gauged sites). Hence, for estimation of flood magnitudes of various return periods in Turkey, a regional flood frequency relationship is developed using the GEV distribution. Next, the quantiles computed at all of 543 gauged sites by the GEV and the Wakeby distributions are compared with the observed values of the same probability based on two criteria, mean absolute relative error and determination coefficient. Results of these comparisons indicate that both distributions of GEV and Wakeby, whose parameters are computed by the L‐moments method, are adequate in predicting quantile estimates. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of instantaneous peak flows from maximum mean daily flows using the HBV hydrological model

The record length and quality of instantaneous peak flows (IPFs) have a great influence on flood design, but these high resolution flow data are not always available. The primary aim of this study is to compare different strategies to derive frequency distributions of IPFs using the Hydrologiska Byråns Vattenbalansavdelning (HBV) hydrologic model. The model is operated on a daily and an hourly time step for 18 catchments in the Aller‐Leine basin, Germany. Subsequently, general extreme value (GEV) distributions are fitted to the simulated annual series of daily and hourly extreme flows. The resulting maximum mean daily flow (MDF) quantiles from daily simulations are transferred into IPF quantiles using a multiple regression model, which enables a direct comparison with the simulated hourly quantiles. As long climate records with a high temporal resolution are not available, the hourly simulations require a disaggregation of the daily rainfall. Additionally, two calibrations strategies are applied: (1) a calibration on flow statistics; (2) a calibration on hydrographs. The results show that: (1) the multiple regression model is capable of predicting IPFs with the simulated MDFs; (2) both daily simulations with post‐correction of flows and hourly simulations with pre‐processing of precipitation enable a reasonable estimation of IPFs; (3) the best results are achieved using disaggregated rainfall for hourly modelling with calibration on flow statistics; and (4) if the IPF observations are not sufficient for model calibration on flow statistics, the transfer of MDFs via multiple regressions is a good alternative for estimating IPFs. Copyright © 2015 John Wiley & Sons, Ltd.     

First-order reversal curve (FORC) diagrams for pseudo-single-domain magnetites at high temperature

The recently developed first-order reversal curve (FORC) technique for rapidly examining magnetic domain state has great potential for paleomagnetic and environmental magnetic investigations. However, there are still some gaps in the basic understanding of FORC diagrams, in particular the behavior of pseudo-single-domain (PSD) grains and the contribution of magnetostatic interactions. In this paper we address some of these problems. We report the first FORC diagrams measurements on narrowly sized and well-characterized synthetic PSD through multidomain (MD) magnetite samples. The FORC diagrams evolve with grain size from single-domain (SD)-like to MD-like through the PSD grain size range. Since each sample contains grains of essentially a single size, individual PSD grains evidently contain contributions from both SD-like and MD-like magnetic moments, in proportions that vary with grain size; the evolving FORC diagrams cannot be due to physical mixtures of SD and MD grains of widely different sizes. The FORC diagrams were all asymmetric. Small PSD samples have FORC diagrams with a distinctive closed-contour structure. The distributions of the larger MD grains display no peak, and lie closer to the interaction-field axis. To assess the effect of magnetostatic interactions, we measured FORC diagrams between room temperature and the Curie temperature. On heating the FORC distributions contract without changing shape until ∼500°C. Above this temperature the diagrams become more MD-like, and in addition become more symmetric. The temperature dependence of the interaction-field parameter is proportional to that of the saturation magnetization, in accordance with Néel’s interpretation of the Preisach diagram. The decrease in asymmetry with heating suggests that the origin of the asymmetry lies in magnetostatic interactions. The magnetic hysteresis parameters as a function of temperature were determined from the FORC curves. As the grain size decreased the normalized coercive force was found to decrease more rapidly with temperature.     

Hydrological transit times in nested urban and agricultural watersheds in the Greater Toronto Area,Canada

Watershed mean transit times (MTTs) are used to characterize the hydrology of watersheds. Watershed MTTs could have important implications for water quality, as relatively long MTTs imply lengthier water retention, thereby allowing more time for pollutant transformation and more moderate release of pollutants into streams. Although estimates of MTTs are common for undisturbed watersheds, only a few studies to date have applied MTT models to urbanized watersheds. In the present study, we use δ¹⁸O to compare estimates of MTTs for paired suburban‐industrial and agricultural watersheds in Toronto, Canada. Although differences in precipitation δ¹⁸O between the two watersheds were negligible, there were significant differences in stream δ¹⁸O, suggesting differences in water transport pathways. Less damping between input precipitation δ¹⁸O and output stream δ¹⁸O in the suburban‐industrial watershed indicated a larger streamflow contribution from quick‐flow transport pathways. We applied three transit time models to quantify MTTs. Considering overall model fit, root mean square error, and uncertainty in model parameters, the exponential model performed the best of the three models. Optimized MTTs using this distribution across the suburban‐industrial subwatersheds ranged from 2.1 to 2.9 months, whereas those in the agricultural subwatersheds ranged from 2.7 to 7.5 months. The relatively small difference between urban and agricultural MTTs coincides with observations elsewhere. Model efficiencies could potentially be improved, and MTTs estimated more reliably, with a higher sampling frequency that captures a greater volume of overall discharge. Overall, this work provides a distinct first glimpse into the separation of MTTs between paired watersheds with such a large contrast in their land use.     

Inter‐catchment comparison to assess the influence of topography and soils on catchment transit times in a geomorphic province; the Cairngorm mountains,Scotland

A quantitative, process relevant analysis of ten mesoscale (ca 10–90 km²) catchments in the Cairngorm mountains, Scotland was carried out using 10‐m digital terrain models (DTMs). This analysis produced a range of topographic indices that described differences in the landscape organisation of the catchments in a way that helped explain contrasts in their hydrology. Mean transit time (MTT)—derived from isotopic tracer data—was used as a metric that characterised differences in the hydrological function of the ten catchments. Some topographic indices exhibited significant correlations with MTT. Most notably, the ratio of the median flow path length to the median flow path gradient was negatively correlated with MTT, whilst the median upslope area was positively correlated. However, the relationships exhibited significant scatter which precluded their use as a predictive tool that could be applied to ungauged basins in this region. In contrast, maps of soil hydrological properties could be used to differentiate hydrologically responsive soils (which are dominated by overland flow and shallow sub‐surface storm flow) from free draining soils (that facilitate deeper sub‐surface flows). MTT was negatively correlated with the coverage of responsive soils in catchments. This relationship provided a much better basis for predicting MTT in ungauged catchments in this geomorphic province. In the Cairngorms, the extensive cover of various glacial drift deposits appears to be a first order control on soil distributions and strongly influences the porosity and permeability of the sub‐surface. These catchment characteristics result in soil cover being a much more discerning indicator of hydrological function than topography alone. The study highlights the potential of quantitative landscape analysis in catchment comparison and the need for caution in extrapolating relationships between landscape controls and metrics of hydrological function beyond specific geomorphic provinces. Copyright © 2009 John Wiley & Sons, Ltd.     

Pay the PIED Piper: Guidelines to Visualize Large Geochemical Datasets on Piper Diagrams

The Piper diagram has increased in popularity since its 1944 introduction and is now one of the most familiar and effective tools in the hydrogeologist's toolbox. Within the Piper diagram, three points on three related plots fully display the major ionic species of a water sample. Recently the size and availability of datasets have increased as additional field measurements and modeling results are shared more effectively in online databases. This growth presents opportunities and challenges for data analysis and conveyance—larger and longer datasets increase the potential to identify trends and patterns, but traditional Piper diagrams are quickly overwhelmed by large datasets as dense points overlap and become obscured. We present guidelines for effectively displaying large geochemical datasets on traditional Piper diagrams and new code that adds novel functionality for following these generic guidelines. This code, plotting interesting environmental data with Piper diagrams (PIED Piper), can be run within the Matlab environment or through a stand-alone graphical user interface, and is the first Matlab code to generate Piper diagrams. The illustrative examples herein demonstrate (1) how limitations in displays of large datasets may be overcome with translucent symbology, contours, and heatmaps to identify trends and patterns, (2) how clusters of similar points can be identified and differentiated with convex hulls, and (3) how temporal-and-spatial patterns may be visually diagnosed with image groups and movies. The guidelines discussed in these examples will aid PIED Piper users to achieve the two goals of effective big data visualization: analysis and communication.     

Limitations on linear elastic procedures in performance assessment of regular frames

Linear elastic analysis procedures are employed exclusively in the traditional seismic design of new structures and widely employed in the seismic assessment of existing structures. It is also a convenient tool for the initial checking of deformations in displacement‐based design. The limitations that should be imposed on linear elastic procedures have been evaluated in this study by comparing the deformation‐based response quantities obtained from response spectrum analysis with those from the nonlinear time history analysis. Both procedures were applied to different design variants of 5, 8, and 12 story moment frames, subjected to 20 strong motion components exhibiting a variety of intensities. Member plastic rotations and interstory drift ratios were employed as the basic response parameter in performance assessment. It has been found that average column demand to capacity ratio (DCR) (the ratio of flexural demand from linear elastic analysis to flexural capacity) and average beam DCR at the critical story are the most effective parameters in determining the validity range of linear elastic procedures in regular moment frames. Limiting values for these response parameters are proposed. Furthermore, amplification factors for member rotation demands predicted by the linear procedures are suggested for moment frames when these limiting values are exceeded. These factors ensure that the amplified linear elastic rotations are not smaller than 84 percentile (mean – 1sigma) of the rotations obtained from nonlinear time history analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Determination of horizontal and vertical design spectra based on ground motion records at Lali tunnel,Iran

Most acceleration diagrams show high levels of unpredictability, as a result, it is the best to avoid using diagrams of earthquake acceleration spectra, even if the diagrams recorded at the site in question. In order to design earthquake resistant structures, we, instead, suggest constructing a design spectrum using a set of spectra that have common characteristics to the recorded acceleration diagrams at a particular site and smoothing the associated data. In this study, we conducted a time history analysis and determined a design spectrum for the region near the Lali tunnel in Southwestern Iran. We selected 13 specific ground motion records from the rock site to construct the design spectrum. To process the data, we first applied a base-line correction and then calculated the signal-to-noise ratio (R_SN) for each record. Next, we calculated the Fourier amplitude spectra of the acceleration pertaining to the signal window (1), and the Fourier amplitude spectra of the associated noise (2). After dividing each spectra by the square root of the selected window interval, they were divided by each other (1 divided by 2), in order to obtain the R_SN ratio (filtering was also applied). In addition, all data were normalized to the peak ground acceleration (PGA). Next, the normalized vertical and horizontal responses and mean response spectrum (50%) and the mean plus-one standard deviation (84%) were calculated for all the selected ground motion records at 5% damping. Finally, the mean design spectrum and the mean plus-one standard deviation were plotted for the spectrums. The equation of the mean and the above-mean design spectrum at the Lali tunnel site are also provided, along with our observed conclusions.     

A sensitivity analysis of lake water level response to changes in climate and river regimes

Lake water level regimes are influenced by climate, hydrology and land use. Intensive land use has led to a decline in lake levels in many regions, with direct impacts on lake hydrology, ecology and ecosystem services. This study examined the role of climate and river flow regime in controlling lake regimes using three different lakes with different hydraulic characteristics (volume-inflow ratio, CIR). The regime changes in the lakes were determined for five different river inflows and five different climate patterns (hot-arid, tropical, moderate, cold-arid, cold-wet), giving 75 different combinations of governing factors in lake hydrology. The input data were scaled to unify them for lake comparisons. By considering the historical lake volume fluctuations, the duration (number of months) of lake volume in different ‘wetness’ regimes from ‘dry’ to ‘wet’ was used to develop a new index for lake regime characterisation, ‘Degree of Lake Wetness’ (DLW). DLW is presented as two indices: DLW₁, providing a measure of lake filling percentage based on observed values and lake geometry, and DLW₂, providing an index for lake regimes based on historical fluctuation patterns. These indices were used to classify lake types based on their historical time series for variable climate and river inflow. The lake response time to changes in hydrology or climate was evaluated. Both DLW₁ and DLW₂ were sensitive to climate and hydrological changes. The results showed that lake level in high CIR systems depends on climate, whereas in systems with low CIR it depends more on river regime.     

Self-reversal of magnetization in titanomagnetite: Effective field theory

In this paper, we analyze the self-reversal of magnetization in titanomagnetites as a function of the Ti content and the distribution of Fe³⁺ to Fe²⁺ ion transitions in sublattices (which is associated with the law of charge conservation). The dependence of the Curie point on the Ti concentration and the temperature dependence of the mean magnetic moment per iron atom at different Ti concentrations and different cation distributions in sublattices are calculated.     

Grain yield reliability analysis with crop water demand uncertainty

A new method of reliability analysis for crop water production function is presented considering crop water demand uncertainty. The procedure uses an advanced first-order second moment (AFOSM) method in evaluating the crop yield failure probability. To determine the variance and the mean of actual evapotranspiration as the component of interest for AFOSM analysis, an explicit stochastic optimization model for optimal irrigation scheduling is developed based on the first and second-order moment analysis of the soil moisture state variables. As a result of the study, the violation probabilities of crop yield at different levels were computed from AFOSM method. Also using the optimization results and the double bounded density function estimation methodology, the weekly soil moisture density function is derived which can be used as a short term reliability index. The proposed approach does not involve any discretization of system variables. The results of reliability analysis and optimization model compare favorably with those obtained from simulation.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.