Rainfall models in small catchments in the context of hydrologic and hydraulic assessment of watercourses

Flood frequency prediction for data limited catchments in the Czech Republic using a stochastic rainfall model and TOPMODEL

Arid and semi-arid regions typically lack high-resolution river gauging data causing difficulties in understanding rainfall-runoff patterns. A common predictive method for discharge estimation within ungauged catchments is regional flood frequency estimation (RFFE), deriving peak discharge estimates from similar, gauged catchments and applying them to the catchment of interest. The majority of RFFE equations are developed for larger catchments where flow events may be larger and of greater interest. We test a series of RFFE methods derived for the Pilbara region, applying them to new ungauged small catchments under 10 km2. Rainfall values are derived from a guideline Australian design rainfall database, Australian Rainfall and Runoff 2019 (ARR2019) which was recently updated with an additional 30 years of rainfall data. RFFE equations are compared to a direct rainfall model to evaluate their performance within small catchments, identifying key limitations and considerations when modelling small headwater catchments.

Every year in the UK, many flood risk assessments are carried out on small catchments, typically draining areas of less than 25 km2 . Standard hydrological practice in all UK catchments is to apply the methods presented in the Flood Estimation Handbook (FEH) and its subsequent updates. FEH methods are practical, relatively easy to apply and based on extensive statistical analyses. However, uncertainties can be large, especially in atypical catchments, and small catchments can present unique challenges in terms of heavy urbanisation and rapid flood responses. Compared to larger catchments, small catchment flood data are limited. In this study, we use a dataset of annual maxima and digital catchment descriptors at 205 small catchments to benchmark the QMED and Q100 estimation performance of current UK flood estimation methods: the FEH statistical method, ReFH2 and MacDonald and Fraser’s method, in rural and urbanised catchments separately. All methods perform similarly in rural catchments overall, although MacDonald and Fraser’s method underestimates QMED in urbanised catchments. The methods show a larger factorial standard error against this small catchment dataset than they do against typical datasets of mixed-size catchments. Further work will evaluate the performance of ReFH2 in combination with the latest FEH13 rainfall model.

Abstract. The prediction of the small-scale spatial-temporal pattern of intense rainfall events is crucial for flood risk assessment in small catchments and urban areas. In the absence of a full deterministic modelling of small-scale rainfall, it is common practice to resort to the use of stochastic downscaling models to generate ensemble rainfall predictions to be used as inputs to rainfall-runoff models. In this work we present an application of a new spatial-temporal downscaling procedure, called RainFARM, to an intense precipitation event predicted by the limited-area meteorological model Lokal Model over north-west Italy. The uncertainty in flood prediction associated with the small unresolved scales of forecasted precipitation fields is evaluated by using an ensemble of downscaled fields to drive a semi-distributed rainfall-runoff model.

An original method for analyzing the influence of the meteorological, as well as physical-geographical conditions on the flooding of stormwater in small urban catchment areas is proposed. A logistical regression model is employed for the identification of the flooding events. The elaborated model enables to simulate the stormwater flooding in a single rainfall event, on the basis of the rainfall depth, duration, imperviousness of the catchment and its spatial distribution within the analyzed area, as well as the density of the stormwater network. The rainfall events are predicted considering the regional convective rainfall model for 32 rain gauges located in Poland, based on 44 years of rainfall data. In the study, empirical models are obtained to calculate the rainfall duration conditioning the flooding of stormwater in a small urban catchment area depending on the characteristics of the examined urban basins. The empirical models enabling to control the urbanization process of catchment areas, accounting for the local rainfall and meteorological characteristics are provided. The paper proposes a methodology for the identification of the areas especially sensitive to stormwater flooding in small urban catchment areas depending to the country scale. By employing the presented methodology, the regions with most sensitive urban catchments are identified. On this basis, a ranking of towns and cities is determined from the most sensitive to flooding in small urban catchment areas to the regions where the risk of flooding is lower. Using the method developed in the paper, maximum impervious catchment area are determined for the selected regions of the country, the exceedance of which determines the occurrence of stormwater flooding.

The French Mediterranean area is subject to intense rainfall events which might cause flash floods, the main natural hazard in the area. Flood-risk rainfall is defined as rainfall with a high spatial average and encompasses rainfall which might lead to flash floods. We aim to compare eight multivariate density models for multi-site flood-risk rainfall. In particular, an accurate characterization of the spatial variability of flood-risk rainfall is crucial to help understand flash flood processes. Daily data from eight rain gauge stations at the Gardon at Anduze, a small Mediterranean catchment, are used in this work. Each multivariate density model is made of a combination of a marginal model and a dependence structure. Two marginal models are considered: the Gamma distribution (parametric) and the Log-Normal mixture (non-parametric). Four dependence structures are included in the comparison: Gaussian, Student t, Skew Normal and Skew t in increasing order of complexity. They possess a representative set of theoretical properties (symmetry/asymmetry and asymptotic dependence/independence). The multivariate models are compared in terms of three types of criteria: (1) separate evaluation of the goodness-of-fit of the margins and of the dependence structures, (2) model selection with a leave-one-out evaluation of the Anderson-Darling and Cramer-Von Mises statistics and (3) comparison in terms of two hydrologically interpretable quantities (return periods of the spatial average and conditional probabilities of exceedances). The key outcome of the comparison is that the Skew Normal with the Log-Normal mixture margins outperform significantly the other models. The asymmetry introduced by the Skew Normal is an added-value with respect to the Gaussian. Therefore, the Gaussian dependence structure, although widely used in the literature, is not recommended for the data in this study. In contrast, the asymptotically dependent models did not provide a significant improvement over the asymptotically independent ones.

Risk assessment for inland flooding in a small urban catchment : Focusing on the temporal distribution of rainfall and dual drainage model

Modelling the effects of spatial variability in rainfall on catchment response. 1. Formulation and calibration of a stochastic rainfall field model

This paper examines methodologies for the simulation of storms for the purpose of design flood generation in the Thames region. Existing methods are reviewed and two new approaches are proposed. One combines point profiles of storms extracted from long rainfall records with depth-duration-frequency statistics. The other uses a stochastic rainfall model based upon the Poisson point process to generate data. Rainfall events simulated by these two methods are compared and the flood statistics obtained by inputting these events into a rainfall-runoff model are examined for a small catchment in Surrey, England. The Poisson based model is recommended as the more reliable.

<p>For derived flood frequency analyses, stochastic rainfall models can be linked with rainfall-runoff models to improve the accuracy of design flood estimations when the length of observed rainfall and runoff data is not sufficient. The stochastic rainfall time series, which are used as input for the rainfall-runoff model, can be generated with different spatial resolution: (a) Point rainfall, which is stochastically generated rainfall at a single site. (b) Areal rainfall, which is catchment rainfall averaged over multiple sites before using the single-site stochastic rainfall model. (c) Multiple point rainfall, which is stochastically generated at multiple sites with spatial correlation before averaging to catchment rainfall. To find the most applicable spatial representation of stochastically generated rainfall for derived flood frequency analysis, simulated and observed runoff time series will be compared based on runoff statistics. The simulated runoff time series are generated utilizing the rainfall-runoff model HBV-IWW with an hourly time step. The rainfall-runoff model is driven with point, areal and multiple point stochastic rainfall time series generated by an Alternating Renewal rainfall model (ARM). In order to take into account the influence of catchment size on the results, catchments of different sizes within Germany are considered in this study.  While point rainfall may be applicable for small catchments, it is expected that above a certain catchment size a more detailed spatial representation of stochastically generated rainfall is necessary. Here, it would be advantageous if the results based on areal rainfall are comparable to those of the multiple point rainfall. The stochastically generation of areal rainfall is less complex compared to the stochastically generation of multiple point rainfall and extremes at the catchment scale may also be better represented by areal rainfall.    </p>

Sensitivity of effective rainfall amount to land use description using GIS tool. Case of a small mediterranean catchment

The classical ‘decoupled’ approach for fluvial flooding makes use of hydrographs as input boundary conditions. The catchment hydrology is determined by empirical semi‐distributed rainfall–runoff models, the flood processes by the use of hydrodynamic models. However, for urban floods, the distributed rainfall is set directly as input (‘direct rainfall modelling’ – DRM) to the elements of the 2D model. This ‘integrated approach’ aims to include hydrological and hydraulic processes in one single model. In this study, both modelling approaches are applied and evaluated for their suitability to determine flood hazards in small, rural catchments. The resulting flood maps and flow hydrographs are compared for selected rainfall–runoff events in a catchment located in Central Germany. In the first approach, the hydrological model (HEC‐HMS) from the Hydrologic Engineering Center (HEC) is used to generate the inflow boundary hydrographs for the 2D model (HEC‐RAS), which is then used to simulate the flow variables for the river network and its floodplains. For the second approach, the DRM is applied over the whole catchment by the use of HEC‐RAS. Special focus is given for the integrated approach to the difficulties occurring during the model optimisation and calibration. The comparison of the results and modelling processes of both approaches give insights into the advantages, disadvantages and difficulties or limitations of each presented approach.

The effects of relative climatic and catchment scales on flood frequency response are studied with the aid of a dimensionless derived flood frequency equation. The dimensionless frequency is developed by applying the method of derived distributions from probability theory to an Instantaneous Unit Hydrograph (IUH) runoff model and a probabilistic areal rainfall model. The derived distribution approach provides a theoretical framework for treating the scale interactions in a systematic way, while the dimensionless formulation makes for a straightforward generalization of the results. The component models in the frequency are characterized by various scales, so that the frequency itself is an implicit function of those scale effects. Catchment/climate interaction works in two notable ways: 1) through the ratio λ* of characteristic storm duration to catchment response time and 2) through the shape of the input areal rainfall intensity distribution as it is affected by the relative correlation and catchment scales, lumped in the dimensionless correlation parameter b *. With regards to catchment scale, these two parameters have opposite effects on frequency skewness. However, in most cases the areal averaging effect is dominant and the net effect shows that flood frequency behavior in small catchments should be flashier and more highly skewed than in large catchments. These same properties are often observed in real data.KeywordsFlood FrequencyFrequency CurveWater Resource ResearchCatchment ScaleSmall CatchmentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The rational-method equation for estimating peak flow rates for storm-water runoff is derived from the balanced-design storm unit hydrograph approach presented in the U.S. Army Corps of Engineers HEC Training Document 15. The new form of the rational-method equation is Q p = (αI−φ) A , instead of the well known Q p = ( I −φ) A ; or Q p =αCIA, instead of the well known Q p =CIA, depending on the respective loss function used in the unit hydrograph effective rainfall model. The preceding fixed constant α is found to depend on the type of unit hydrograph used (i.e., S -Graph) and the log-log slope of the rainfall depth-duration curve, and is easily determined by equating to a known unit hydrograph design storm model peak flow rate result. This new development provides a significant foundation for the use of the well-known rational-method equation in small catchments where rainfall depth-area effects are negligible.

Empirical distribution functions of flood peaks in small catchments sometimes show discontinuities in the slope; that is, the largest flood peaks are significantly larger than the rest of the record. The aim of this paper is to understand whether these discontinuities, or step changes, can be a consistent effect of hydrological processes. We conducted field surveys in two Austrian alpine catchments 73 km2in size to map the spatial patterns of surface runoff generation and hydrogeologic storage. On the basis of this information, we selected the parameters of a distributed continuous runoff model, which is designed to simulate well the point when the storage capacity of the catchment is exhausted. Then we calibrated a stochastic rainfall model and performed Monte Carlo simulations of runoff to generate flood frequency curves for the two catchments. The curves exhibit a step change around a return period of 30 years. An analysis of the storage capacities suggests that this step change is due to a threshold of storage capacity being exceeded, which causes fast surface runoff in large parts of the catchments. The threshold occurs when the storage within the catchment is spatially rather uniform. To identify step changes, reliable estimates of the catchment storage capacity are needed on the basis of detailed hydrogeological information. The occurrence of a step change is of importance for estimating low‐probability floods since the flood estimates with the step change accounted for can be significantly different from those based on commonly used distribution functions. We therefore suggest that step changes in the flood frequency curve of small catchments can be real and their possible presence should be taken into account in design flood estimation.