scholarly journals Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multifractal approach

2021 ◽  
Author(s):  
Arun Ramanathan ◽  
Pierre-Antoine Versini ◽  
Daniel Schertzer ◽  
Remi Perrin ◽  
Lionel Sindt ◽  
...  
Keyword(s):  
Exceedance Probability ◽  
Specific Reference ◽  
Rainfall Time Series ◽  
Spatial Dimensions ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
T Values ◽  
Renormalization Constants ◽  
Meteorological Models ◽  
Hydrological Applications

Abstract. Hydrological applications such as storm-water management or flood design usually deal with and are driven by region-specific reference rainfall regulations or guidelines based on Intensity-Duration-Frequency (IDF) curves. IDF curves are usually obtained via frequency analysis of rainfall data using which the exceedance probability of rain intensity for different durations are determined. It is also rather common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D (related to rainfall intensity ), with a return period T (inverse of exceedance probability). Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes (non-homogeneity or intermittency, scale invariance and extremal statistics) seems to suit this purpose. Here we propose a discrete-in-scale universal multifractal (UM) cascade based approach. Daily, Hourly and six-minute rainfall time series datasets (with lengths ranging from 100 to 15 years) over three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates are analyzed to identify scaling regimes and estimate corresponding UM parameters (α, C1) required by the UM cascade model. Suitable renormalization constants that correspond to the P, D, T values of reference rainfall are used to simulate an ensemble of reference rainfall scenarios, and the simulations are finally compared with datasets. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.

Simulating reference rainfall scenarios for hydrological applications using a multifractal approach

2021 ◽  
Author(s):  
Arun Ramanathan ◽  
Pierre-Antoine Versini ◽  
Daniel Schertzer ◽  
Ioulia Tchiguirinskaia ◽  
Remi Perrin ◽  
...  
Keyword(s):  
Time Series ◽  
Moment Analysis ◽  
Specific Reference ◽  
Rainfall Time Series ◽  
Time Series Dataset ◽  
Hourly Rainfall ◽  
Spatial Dimensions ◽  
Multifractal Theory ◽  
Intensity Duration Frequency ◽  
Hydrological Applications

<p><strong>Abstract</strong></p><p>Hydrological applications such as flood design usually deal with and are driven by region-specific reference rainfall regulations, generally expressed as Intensity-Duration-Frequency (IDF) values. The meteorological module of hydro-meteorological models used in such applications should therefore be capable of simulating these reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes such as non-homogeneity (intermittency), scale invariance, and extremal statistics, seems to be an appropriate choice for this purpose. Here we suggest a rather simple discrete-in-scale multifractal cascade based approach. Hourly rainfall time-series datasets (with lengths ranging from around 28 to 35 years) over six cities (Paris, Marseille, Strasbourg, Nantes, Lyon, and Lille) in France that are characterized by different climates and a six-minute rainfall time series dataset (with a length of around 15  years) over Paris were analyzed via spectral analysis and Trace Moment analysis to understand the scaling range over which the universal multifractal theory can be considered valid. Then the Double Trace Moment analysis was performed to estimate the universal multifractal parameters α,C<sub>1</sub> that are required by the multifractal cascade model for simulating rainfall. A renormalization technique that estimates suitable renormalization constants based on the IDF values of reference rainfall is used to simulate the reference rainfall scenarios. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.</p><p><strong>Keywords</strong></p><p>Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Stochastic rainfall simulations.</p>

An Extended Model in Estimating Consistent Quantiles for Intensity-Duration-Frequency Curves

2021 ◽  
Author(s):  
Felix Fauer ◽  
Jana Ulrich ◽  
Oscar E. Jurado ◽  
Uwe Ulbrich ◽  
Henning W. Rust
Keyword(s):  
Extreme Value ◽  
Data Availability ◽  
Extreme Value Statistics ◽  
Statistical Characteristics ◽  
Exceedance Probability ◽  
Extended Model ◽  
Adequate Model ◽  
Extreme Precipitation Events ◽  
Idf Curves ◽  
Intensity Duration Frequency

<p>Intensity-Duration-Frequency (IDF) curves describe the main statistical characteristics of extreme precipitation events. Providing information on the exceedance probability or return period of certain precipitation intensities for a range of durations, IDF curves are an important tool for the design of hydrological structures.</p><p>Although the Generalized-Extreme-Value (GEV) distribution is an adequate model for annual precipitation maxima of a certain duration, the core problem of extreme value statistics remains: the limited data availability. Hence, it is reasonable to use a model that can describe all durations simultaneously. This reduces the total number of parameters and a more efficient usage of data is achieved. The idea of implementing a duration dependence directly into the parameters of the extreme value distribution and therefore obtaining a single distribution for a range of durations was proposed by Koutsoyiannis et al. (1998). However, while the use of the GEV is justified by a strong theoretical basis, only empirical models exist for the dependence of the parameters on duration.</p><p>In this study, we compare different models regarding the dependence of the GEV parameters on duration with the aim of finding a model for a wide duration range (1 min - 5 days). We use a combination of existing model features, especially curvature for small durations and multi-scaling for all durations, and extend them by a new feature that allows flattening of the IDF curves for long durations. Using the quantile score in a cross-validation setting, we provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features lead to improved modeling skill.</p><p>Our results show that allowing curvature or multi-scaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening of the IDF curves leads to an improvement for medium durations between 1 hour and 1 day without affecting other duration regimes.</p>

Estimating IDF-Relations consistently using a duration-dependent GEV with spatial covariates

2020 ◽  
Author(s):  
Jana Ulrich ◽  
Madlen Peter ◽  
Oscar E. Jurado ◽  
Henning W. Rust
Keyword(s):  
Extreme Precipitation ◽  
Probability Distributions ◽  
Skill Score ◽  
Exceedance Probability ◽  
Ungauged Sites ◽  
Extreme Precipitation Events ◽  
One Step ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
A Site

<p>Intensity-Duration-Frequency (IDF) Curves are a popular tool in Hydrology for estimating the properties of extreme precipitation events. They describe the relationship between rainfall intensity and duration for a given non-exceedance probability (or frequency). For a site where precipitation measurements are available, these curves can be estimated consistently over durations using a duration-dependent GEV (d-GEV, after Koutsoyiannis et al. 1998). In this approach, the probability distributions are modeled simultaneously for all durations.</p><p>Additionally, we integrate covariates to describe the spatial variability of the d-GEV parameters so that we can model the distribution of extreme precipitation for a range of durations and locations in one step. Thus IDF Curves can be estimated even at ungauged sites. Further advantages are parameter reduction and more efficient use of the available data. We use the Quantile Skill Score to investigate under which conditions this method leads to an improved estimate compared to the single-site approach and to evaluate the performance at ungauged sites.</p>

Development of space-time rainfall intensity duration frequency curves based on a multifractal approach

2021 ◽  
Author(s):  
David Serrano ◽  
Mahesh Lal Maskey ◽  
Adrian Rizo ◽  
Victor Peñaranda
Keyword(s):  
Rainfall Intensity ◽  
Geometrical Structure ◽  
Multifractal Spectrum ◽  
Space Time ◽  
Time Structure ◽  
Rainfall Time Series ◽  
Time And Space ◽  
Space Time Structure ◽  
Idf Curves ◽  
Intensity Duration Frequency

<p>Changing climate signals and urban populations' growth requires proper hydrologic risk analysis to create and operate water resource infrastructures in a sustainable way. Although modernized computational facilities are becoming popular to understand different complex systems, the scientific community is still behind in proper analysis of extreme rainfall events as they are erratic in time and space. To fill the existing knowledge gap, it becomes obvious to incorporate spatiotemporal rainfall variability in designing rainfall Intensity Duration Frequency (IDF) curves.  Many statistical approaches have been suggested to describe the space-time structure of rainfall; nevertheless, none of them is enough to represent, for all observational scales, the geometrical structure observed in either rainfall time series or rainfall-derived spatial fields. This research presents a more holistic approach to derive the IDF curves without losing information and (or) statistical assumptions.  This study uses such a promising notion to understand the rainfall field's space-time geometrical structure via codimension functions. The results show us the space-time structure of rainfall exhibits a dynamical scaling, and it suggests the idea of a double multifractal spectrum for representing time and space. Based on the idea of a double multifractal spectrum, IDF curves can be shifted to Intensity – Area – Frequency – Duration (IADF) curves to get a better approach for engineering and scientific purposes. Furthermore, this research suggests that changes of parameters for this approach could reflect climate-change signals and would be useful to generate non-stationary IADF curves and improve engineering design practices.</p>

scholarly journals Temporal change of extreme precipitation intensity–duration–frequency relationships in Thailand

2021 ◽  
Author(s):  
N. Yamoat ◽  
R. Hanchoowong ◽  
S. Sriboonlue ◽  
A. Kangrang
Keyword(s):  
Time Series ◽  
Extreme Precipitation ◽  
Extreme Rainfall ◽  
Precipitation Intensity ◽  
Rainfall Time Series ◽  
The Past ◽  
The North ◽  
Hourly Rainfall ◽  
Idf Curves ◽  
Intensity Duration Frequency

Abstract Due to climate change, many research studies have derived the updated extreme precipitation intensity–duration–frequency relationship (IDF curve) from forecasted sub-hourly rainfall intensity time series, which is one of the most important tools for the planning and designing of hydraulic infrastructures. In this study, the IDF curves (1990–2016) of the six regions and procedures are used in accordance with those of the Royal Irrigation Department (RID)’s study (1950–1988). Each set of IDF relationships consists of 81 intensity values which are the combination of nine durations and nine return periods. The intensity ratios of this study and RID are compared. A greater-than-1 ratio indicates extreme intensity increment from the past to the present. Considering 81 ratios for each region, the number of greater-than-1 ratios for the North, Northeast, Central, East, West, and South regions are 8, 2, 31, 34, 6, and 7, respectively. These ratio numbers are far below 81 which means that the majority of extreme rainfall intensities do not increase from the past to the present. The study found that using accurate historical sub-hourly rainfall time series to create a set of IDF curves would be more reliable than using forecasted rainfall modeling.

scholarly journals Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1296 ◽  
Author(s):  
Huiying Ren ◽  
Z. Jason Hou ◽  
Mark Wigmosta ◽  
Ying Liu ◽  
L. Ruby Leung
Keyword(s):  
High Resolution ◽  
Spatial Heterogeneity ◽  
Time Windows ◽  
Exceedance Probability ◽  
Extreme Precipitation Events ◽  
Climate Simulations ◽  
Engineering Standards ◽  
Intensity Duration Frequency ◽  
Using Data

Changes in extreme precipitation events may require revisions of civil engineering standards to prevent water infrastructures from performing below the designated guidelines. Climate change may invalidate the intensity-duration-frequency (IDF) computation that is based on the assumption of data stationarity. Efforts in evaluating non-stationarity in the annual maxima series are inadequate, mostly due to the lack of long data records and convenient methods for detecting trends in the higher moments. In this study, using downscaled high resolution climate simulations of the historical and future periods under different carbon emission scenarios, we tested two solutions to obtain reliable IDFs under non-stationarity: (1) identify quasi-stationary time windows from the time series of interest to compute the IDF curves using data for the corresponding time windows; (2) introduce a parameter representing the trend in the means of the extreme value distributions. Focusing on a mountainous site, the Walker Watershed, the spatial heterogeneity and variability of IDFs or extremes are evaluated, particularly in terms of the terrain and elevation impacts. We compared observations-based IDFs that use the stationarity assumption with the two approaches that consider non-stationarity. The IDFs directly estimated based on the traditional stationarity assumption may underestimate the 100-year 24-h events by 10% to 60% towards the end of the century at most grids, resulting in significant under-designing of the engineering infrastructure at the study site. Strong spatial heterogeneity and variability in the IDF estimates suggest a preference for using high resolution simulation data for the reliable estimation of exceedance probability over data from sparsely distributed weather stations. Discrepancies among the three IDFs analyses due to non-stationarity are comparable to the spatial variability of the IDFs, underscoring a need to use an ensemble of non-stationary approaches to achieve unbiased and comprehensive IDF estimates.

Interpolation of Regionalized Intensity Duration Frequency (IDF) Estimates based on the observed precipitation data of Baden Wurttemberg (BW), Germany

2021 ◽  
Author(s):  
Bushra Amin ◽  
András Bárdossy
Keyword(s):  
Mean Square Error ◽  
Hydrological Cycle ◽  
Information Criteria ◽  
Regional Frequency Analysis ◽  
Mean Square ◽  
Time Duration ◽  
Ungauged Sites ◽  
Marquardt Algorithm ◽  
Idf Curves ◽  
Intensity Duration Frequency

<p>This study is intended to carry out the spatial mapping with ordinary Kriging (OK) of regional point Intensity Duration Frequency (IDF) estimates for the sake of approximation and visualization at ungauged location. Precipitation IDF estimates that offer us valuable information about the frequency of occurrence of extreme events corresponding to different durations and intensities are derived through the application of robust and efficient regional frequency analysis (RFA) based on L-moment algorithm. IDF curves for Baden Wrttemberg (BW) are obtained from the long historical record of daily and hourly annual maximum precipitation series (AMS) provided by German Weather Service from 1960-2020 and 1949-2020 respectively under the assumption of stationarity. One of the widely used Gumbel (type 1)  distribution is applied for IDF analysis because of its suitability for modeling maxima. The uncertainty in IDF curves is determined by the bootstrap method and are revealed in the form of the prediction and confidence interval for each specific time duration on graph. Five metrics such as root mean square error (RMSE), coefficient of determination (R²), mean square error (MSE), Akaike information criteria (AIC) and Bayesian information criteria (BIC) are used to assess the performance of the employed IDF equation. The coefficients of 3-parameteric non-linear IDF equation is determined for various recurrence interval by means of Levenberg–Marquardt algorithm (LMA), also referred to as damped least square (DLS) method. The estimated coefficients vary from location to location but are insensitive to duration. After successfully determining the IDF parameters for the same return period, parametric contour or isopluvial maps can be generated using OK as an interpolation tool with the intention to provide estimates at ungauged locations. These estimated regional coefficients of IDF curve are then fed to the empirical intensity frequency equation that may serve to estimate rainfall intensity for design purposes for all ungauged sites. The outcomes of this research contribute to the construction of IDF-based design criteria for water projects in ungauged sites located anywhere in the state of BW.</p><p>In conclusion, we conducted IDF analysis for the entire state of BW as it is considered to be more demanding due to the increased impact of climate change on the intensification of hydrological cycle as well as the expansion of urban areas rendering watershed less penetrable to rainfall and run-off, the better understanding of spatial heterogeneity of intense rainfall patterns for the proposed domain.</p>

scholarly journals Establishment of IDF-curves for precipitation in the tropical area of Central Africa - comparison of techniques and results

2004 ◽  
Vol 4 (3) ◽  
pp. 375-387 ◽  
Author(s):  
B. Mohymont ◽  
G. R. Demarée ◽  
D. N. Faka
Keyword(s):  
Return Period ◽  
Central Africa ◽  
Tropical Region ◽  
Data Sets ◽  
Physically Based ◽  
Physically Based Models ◽  
Comparison Of Techniques ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Technique Comparison

Abstract. The establishment of Intensity-Duration-Frequency (IDF) curves for precipitation remains a powerful tool in the risk analysis of natural hazards. Indeed the IDF-curves allow for the estimation of the return period of an observed rainfall event or conversely of the rainfall amount corresponding to a given return period for different aggregation times. There is a high need for IDF-curves in the tropical region of Central Africa but unfortunately the adequate long-term data sets are frequently not available. The present paper assesses IDF-curves for precipitation for three stations in Central Africa. More physically based models for the IDF-curves are proposed. The methodology used here has been advanced by Koutsoyiannis et al. (1998) and an inter-station and inter-technique comparison is being carried out. The IDF-curves for tropical Central Africa are an interesting tool to be used in sewer system design to combat the frequently occurring inundations in semi-urbanized and urbanized areas of the Kinshasa megapolis.

scholarly journals Deriving intensity–duration–frequency (IDF) curves using downscaled in situ rainfall assimilated with remote sensing data

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Yabin Sun ◽  
Dadiyorto Wendi ◽  
Dong Eon Kim ◽  
Shie-Yui Liong
Keyword(s):  
Remote Sensing ◽  
Daily Rainfall ◽  
Remote Sensing Data ◽  
Rainfall Events ◽  
Hourly Rainfall ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Improved Accuracy

AbstractThe rainfall intensity–duration–frequency (IDF) curves play an important role in water resources engineering and management. The applications of IDF curves range from assessing rainfall events, classifying climatic regimes, to deriving design storms and assisting in designing urban drainage systems, etc. The deriving procedure of IDF curves, however, requires long-term historical rainfall observations, whereas lack of fine-timescale rainfall records (e.g. sub-daily) often results in less reliable IDF curves. This paper presents the utilization of remote sensing sub-daily rainfall, i.e. Global Satellite Mapping of Precipitation (GSMaP), integrated with the Bartlett-Lewis rectangular pulses (BLRP) model, to disaggregate the daily in situ rainfall, which is then further used to derive more reliable IDF curves. Application of the proposed method in Singapore indicates that the disaggregated hourly rainfall, preserving both the hourly and daily statistic characteristics, produces IDF curves with significantly improved accuracy; on average over 70% of RMSE is reduced as compared to the IDF curves derived from daily rainfall observations.

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