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>

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.

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 Cascade-based disaggregation of continuous rainfall time series: the influence of climate

2001 ◽  
Vol 5 (2) ◽  
pp. 145-164 ◽  
Author(s):  
A. Güntner ◽  
J. Olsson ◽  
A. Calver ◽  
B. Gannon
Keyword(s):  
Time Series ◽  
Extreme Rainfall ◽  
High Accuracy ◽  
Lower Percentage ◽  
Temperate Climate ◽  
Model Parameters ◽  
Hourly Rainfall ◽  
The Uk ◽  
Semi Arid ◽  
Hydrological Applications

Abstract. Rainfall data of high temporal resolution are required in a multitude of hydrological applications. In the present paper, a temporal rainfall disaggregation model is applied to convert daily time series into an hourly resolution. The model is based on the principles of random multiplicative cascade processes. Its parameters are dependent on (1) the volume and (2) the position in the rainfall sequence of the time interval with rainfall to be disaggregated. The aim is to compare parameters and performance of the model between two contrasting climates with different rainfall generating mechanisms, a semi-arid tropical (Brazil) and a temperate (United Kingdom) climate. In the range of time scales studied, the scale-invariant assumptions of the model are approximately equally well fulfilled for both climates. The model parameters differ distinctly between climates, reflecting the dominance of convective processes in the Brazilian rainfall and of advective processes associated with frontal passages in the British rainfall. In the British case, the parameters exhibit a slight seasonal variation consistent with the higher frequency of convection during summer. When applied for disaggregation, the model reproduces a range of hourly rainfall characteristics with a high accuracy in both climates. However, the overall model performance is somewhat better for the semi-arid tropical rainfall. In particular, extreme rainfall in the UK is overestimated whereas extreme rainfall in Brazil is well reproduced. Transferability of parameters in time is associated with larger uncertainty in the semi-arid climate due to its higher interannual variability and lower percentage of rainy intervals. For parameter transferability in space, no restrictions are found between the Brazilian stations whereas in the UK regional differences are more pronounced. The overall high accuracy of disaggregated data supports the potential usefulness of the model in hydrological applications. Keywords: Rainfall, temporal disaggregation, random cascade, scaling, semi-arid, temperate climate.

Reversing hydrology: Estimation of sub-hourly rainfall time-series from streamflow

2014 ◽  
Vol 60 ◽  
pp. 290-301 ◽  
Author(s):  
Ann Kretzschmar ◽  
Wlodek Tych ◽  
Nick A. Chappell
Keyword(s):  
Time Series ◽  
Rainfall Time Series ◽  
Hourly Rainfall

scholarly journals Model Selection For Forecasting Rainfall Dataset

2021 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
Amri Muhaimin ◽  
Hendri Prabowo ◽  
Suhartono
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Time Series ◽  
Statistical Methods ◽  
Seasonal Pattern ◽  
Information Criteria ◽  
Rainfall Time Series ◽  
Machine Learning Method ◽  
Learning Method ◽  
Hourly Rainfall

The objective of this research is to obtain the best method for forecasting rainfall in the Wonorejo reservoir in Surabaya. Time series and causal approaches using statistical methods and machine learning will be compared to forecast rainfall. Time series regression (TSR), autoregressive integrated moving average (ARIMA), linear regression (LR), and transfer function (TF) are used as a statistical method. Feedforward neural network (FFNN) and deep feed-forward neural network (DFFNN) is used as a machine learning method. Statistical methods are used to capture linear patterns, whereas the machine learning method is used to capture nonlinear patterns. Data about hourly rainfall in the Wonorejo reservoir is used as a case study. The data has a seasonal pattern, i.e. monthly seasonality. Based on the cross-validation and information criteria, the results showed that DFFNN using the time series approach has a more accurate forecast than other methods. In general, machine learning methods have better accuracy than statistical methods. Furthermore, additional information is obtained, through this research the parameter that best to make a neural network model is known. Moreover, these results are also not in line with the results of M3 and M4 competition, i.e. more complex methods do not necessarily produce better forecasts than simpler methods.

scholarly journals Circulation pattern based parameterization of a multiplicative random cascade for disaggregation of observed and projected daily rainfall time series

2013 ◽  
Vol 17 (7) ◽  
pp. 2487-2500 ◽  
Author(s):  
D. Lisniak ◽  
J. Franke ◽  
C. Bernhofer
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Global Climate ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Time Slice ◽  
Model Parameters ◽  
Rainfall Time Series ◽  
Rainfall Characteristics ◽  
Hourly Rainfall

Abstract. The use of multiplicative random cascades (MRCs) for temporal rainfall disaggregation has been extensively studied in the past. MRCs are appealing for rainfall disaggregation due to their formal simplicity and the possibility to extract the model parameters directly from observed high resolution rainfall data. These parameters, however, represent the rainfall characteristics of the observation period. Since rainfall characteristics of different time slices are changing due to climate variability, we propose a parameterization approach for MRCs to adjust the parameters according to past (observed) or future (projected) time series. This is done on the basis of circulation patterns (CPs) by extracting a distinct MRC parameterization from high resolution rainfall data, as observed on days governed by each individual CP. The parameterization approach is tested by comparing the statistical properties of disaggregated rainfall time series of two time slices, 1969–1979 and 1989–1999, to the results obtained by two other disaggregation methods (a conceptually similar MRC without CP-based parameterization and a recombination approach) and to the statistical properties of observed hourly rainfall data. In this context, all three approaches use rainfall data of the time slice 1989–1999 for parameterization. We found that the inclusion of CPs into the parameterization of a MRC yields hourly time series that better reproduce the properties of observed rainfall in time slice 1989–1999, as compared to the simple MRC. Despite similar results of both MRCs in the validation period of 1969–1979, we can conclude that the CP-based parameterization approach is applicable for temporal rainfall disaggregation in time slices distinct from the parameterization period. This approach accounts for changes in rainfall characteristics due to changes in the frequency of occurrence of the CPs and allows generating hourly rainfall from daily data, as often provided by a statistical downscaling of global climate change.

scholarly journals Circulation pattern based parameterization of a multiplicative random cascade for disaggregation of daily rainfall under nonstationary climatic conditions

2012 ◽  
Vol 9 (9) ◽  
pp. 10115-10149 ◽  
Author(s):  
D. Lisniak ◽  
J. Franke ◽  
C. Bernhofer
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Climatic Conditions ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Time Slice ◽  
Model Parameters ◽  
Rainfall Time Series ◽  
Rainfall Characteristics ◽  
Hourly Rainfall

Abstract. The use of multiplicative random cascades (MRCs) for temporal rainfall disaggregation has been extensively studied in the past. MRCs are appealing for rainfall disaggregation due to their formal simplicity and the possibility to extract the model parameters directly from observed high resolution rainfall data. These parameters, however, represent the rainfall characteristics of the observation period. Since rainfall characteristics of different time slices are changing due to climate variability, we propose a parameterization approach for MRCs to adjust the parameters according to past (observed) or future (projected) time series. This is done on the basis of circulation patterns (CPs) by extracting a distinct MRC parameterization from high resolution rainfall data, as observed on days governed by each individual CP. The parameterization approach is tested by comparing the statistical properties of disaggregated rainfall time series of two time slices, 1969–1979 and 1989–1999, to the results obtained by two other disaggregation methods (a conceptually similar MRC without CP-based parameterization and a recombination approach) and to the statistical properties of observed hourly rainfall data. In this context, all three approaches use rainfall data of the time slice 1989–1999 for parameterization. We found that the inclusion of CPs into the parameterization of a MRC yields hourly time series that better reproduce the properties of observed rainfall in time slice 1989–1999, as compared to the simple MRC. Despite similar properties of both MRCs for the time slice 1969–1979, we can conclude that the CP-based parameterization approach is applicable for temporal rainfall disaggregation in time slices distinct from the parameterization period. This approach accounts for changes in rainfall characteristics due to changes in the frequency of occurrence of the CPs and allows generating hourly rainfall from daily data, as often provided by a statistical downscaling of global climate change.

scholarly journals Cascade Rainfall Disaggregation Application in U.S. Central Plains

2017 ◽  
Vol 7 (4) ◽  
pp. 30 ◽  
Author(s):  
Jurgen D. Garbrecht ◽  
Rabi Gyawali ◽  
Robert W. Malone ◽  
John C. Zhang
Keyword(s):  
Time Series ◽  
Model Performance ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Rainfall Time Series ◽  
Random Component ◽  
Rainfall Characteristics ◽  
Hourly Rainfall ◽  
Replicated Observations

Long-term observations of daily rainfall are common and routinely available for a variety of hydrologic applications. In contrast, observations of 10 or more years of continuous hourly rainfall are rare. Yet, sub-daily rainfall data are required in rainfall-runoff models. Rainfall disaggregation can generate sub-daily time-series from available long term daily observations. Herein, the performance of Multiplicative Random Cascade (MRC) model at disaggregating daily-to-hourly rainfall was investigated. The MRC model was parameterized and validated with 15 years of continuous observed daily and hourly rainfall data at three weather stations in Oklahoma. Model performance, or degree to which the disaggregated rainfall time series replicated observations, was assessed using 46 variables of hourly rainfall characteristics, such as longest wet spell duration, average number of rainfall hours per year, and largest hourly rainfall. Findings include: a) average-type hourly rainfall characteristics were better replicated than single value characteristics such as longest, maximum, or peak hourly rainfall; b) the large number of sub-trace hourly rainfall values (<0.254 mm h-1) generated by the MRC model were not supported by observations; c) the random component of the MRC model led to a variation under 15% of the average value for most rainfall characteristics with the exceptions of the “longest wet spell duration” and “maximum hourly rainfall”; and d) the MRC model produced fewer persistent rainfall events compared to those in the observed rainfall record. The large number of generated trace rainfall values and difficulties to replicate reliably extreme rainfall characteristics, reduces the number of potential hydrologic applications that could take advantage of the MRC disaggregated hourly rainfall. Nevertheless, in most cases, the disaggregated rainfall generated by the MRC model replicated observed average-type rainfall characteristics well.

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