Time-Series Heston Model Calibration Using a Trinomial Tree

2020 ◽  
Author(s):  
Michael A. Clayton
Keyword(s):  
Time Series ◽  
Model Calibration ◽  
Heston Model ◽  
Trinomial Tree

scholarly journals Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows

2014 ◽  
Vol 18 (1) ◽  
pp. 353-365 ◽  
Author(s):  
U. Haberlandt ◽  
I. Radtke
Keyword(s):  
Time Series ◽  
Frequency Analysis ◽  
Model Calibration ◽  
Hydrological Model ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Rainfall Data ◽  
Flood Frequency Analysis ◽  
Peak Flows ◽  
Hourly Rainfall

Abstract. Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the application for derived flood frequency analysis.

scholarly journals Information content of stream level class data for hydrological model calibration

2017 ◽  
Vol 21 (9) ◽  
pp. 4895-4905 ◽  
Author(s):  
H. J. Ilja van Meerveld ◽  
Marc J. P. Vis ◽  
Jan Seibert
Keyword(s):  
Time Series ◽  
Citizen Science ◽  
Model Calibration ◽  
Hydrological Model ◽  
Model Performance ◽  
Added Value ◽  
Distributed Data ◽  
Vertical Resolution ◽  
Level Data ◽  
Spatially Distributed

Abstract. Citizen science can provide spatially distributed data over large areas, including hydrological data. Stream levels are easier to measure than streamflow and are likely also observed more easily by citizen scientists than streamflow. However, the challenge with crowd based stream level data is that observations are taken at irregular time intervals and with a limited vertical resolution. The latter is especially the case at sites where no staff gauge is available and relative stream levels are observed based on (in)visible features in the stream, such as rocks. In order to assess the potential value of crowd based stream level observations for model calibration, we pretended that stream level observations were available at a limited vertical resolution by transferring streamflow data to stream level classes. A bucket-type hydrological model was calibrated with these hypothetical stream level class data and subsequently evaluated on the observed streamflow records. Our results indicate that stream level data can result in good streamflow simulations, even with a reduced vertical resolution of the observations. Time series of only two stream level classes, e.g. above or below a rock in the stream, were already informative, especially when the class boundary was chosen towards the highest stream levels. There was some added value in using up to five stream level classes, but there was hardly any improvement in model performance when using more level classes. These results are encouraging for citizen science projects and provide a basis for designing observation systems that collect data that are as informative as possible for deriving model based streamflow time series for previously ungauged basins.

scholarly journals Streamflow characteristics from modeled runoff time series – importance of calibration criteria selection

2017 ◽  
Vol 21 (11) ◽  
pp. 5443-5457 ◽  
Author(s):  
Sandra Pool ◽  
Marc J. P. Vis ◽  
Rodney R. Knight ◽  
Jan Seibert
Keyword(s):  
Time Series ◽  
Model Calibration ◽  
Performance Metrics ◽  
Low Flow ◽  
Flow Conditions ◽  
Ungauged Catchments ◽  
Calibration Process ◽  
Model Efficiency ◽  
Runoff Model ◽  
Calibration Approach

Abstract. Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash–Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash–Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV – Hydrologiska Byråns Vattenavdelning – model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

scholarly journals Objective functions used as performance metrics for hydrological models: state-of-the-art and critical analysis

RBRH ◽  
2020 ◽  
Vol 25 ◽  
Author(s):  
Paloma Mara de Lima Ferreira ◽  
Adriano Rolim da Paz ◽  
Juan Martín Bravo
Keyword(s):  
Time Series ◽  
Model Calibration ◽  
Hydrological Model ◽  
Performance Metrics ◽  
Low Flow ◽  
Hydrological Models ◽  
Objective Functions ◽  
Flow Rates ◽  
Daily Streamflow ◽  
Synthetic Time Series

ABSTRACT Hydrological models (HMs) can be applied for different purposes, and a key step is model calibration using objective functions (OF) to quantify the agreement between observed and calculated discharges. Fully understanding the OF is important to properly take advantage of model calibration and interpret the results. This study evaluates 36 OF proposed in the literature, considering two watersheds of different hydrological regimes. Daily simulated streamflow time-series, using a distributed hydrological model (MGB-IPH), and ten daily streamflow synthetic time-series, generated from the observed and calculated streamflows, were used in the analysis of each watershed. These synthetic data were used to evaluate how does each metric evaluate hypothetical cases that present isolated very well known error behaviors. Despite of all NSE-derived (Nash-Sutcliffe efficiency) metrics that use the square of the residuals in their formulation have shown higher sensitivity to errors in high flows, the ones that use daily and monthly averages of flow rates in absolute terms were more stringent than the others to assess HMs performance. Low flow errors were better evaluated by metrics that use the flow logarithm. The constant presence of zero flow rates deteriorate them significantly, with the exception of the metrics TRMSE (Transformed root mean square error) did not demonstrate this problem. An observed limitation of the formulations of some metrics was that the errors of overestimation or underestimation are compensated. Our results reassert that each metric should be interpreted specifically thinking about the aspects it has been proposed for, and simultaneously taking into account a set of metrics would lead to a broader evaluation of HM ability (e.g. multiobjective model evaluation). We recommend that the use of synthetic time series as those proposed in this work could be useful as an auxiliary step towards better understanding the evaluation of a calibrated hydrological model for each study case, taking into account model capabilities and observed hydrologic regime characteristics.

scholarly journals Information content of stream level class data for hydrological model calibration

2017 ◽  
Author(s):  
Ilja van Meerveld ◽  
Marc Vis ◽  
Jan Seibert
Keyword(s):  
Time Series ◽  
Citizen Science ◽  
Model Calibration ◽  
Hydrological Model ◽  
Model Performance ◽  
Added Value ◽  
Data Sets ◽  
Distributed Data ◽  
Vertical Resolution ◽  
Level Data

Abstract. Citizen science can provide spatially distributed data over large areas, including hydrological data. Stream levels are easier to measure than streamflow and can be observed more easily by citizen scientists. However, the challenge with crowd-based stream level data is that observations are taken at irregular time intervals and with a limited vertical resolution. The latter is especially the case at sites where no staff gauge is available and relative stream levels are observed based on (in)visible features in the stream, such as rocks. In order to assess the potential value of crowd-based stream level observations for model calibration, we pretended that stream level observations were available at a limited vertical resolution by transferring streamflow data into stream level classes. A bucket-type hydrological model was calibrated with these hypothetical data sets and subsequently evaluated on the observed streamflow records. Our results indicate that stream level data can result in good streamflow simulations, even with a reduced vertical resolution of the observations. Time series of only two stream level classes, e.g. above or below a rock in the stream, were already informative, especially when the class boundary was chosen towards the highest stream levels. There was some added value in using up to five stream level classes but there was hardly any improvement in model performance when using more level classes. These results are encouraging for citizen science projects and provide a basis for designing observation systems that collect data that are as informative as possible for deriving model-based streamflow time series for previously ungauged basins.

Integration of Hidden Markov States in a hydrological model calibration/validation protocol

2021 ◽  
Author(s):  
Étienne Guilpart ◽  
Vahid Espanmanesh ◽  
Amaury Tilmant ◽  
François Anctil
Keyword(s):  
Time Series ◽  
Hidden Markov Models ◽  
Model Calibration ◽  
Hydrological Model ◽  
Markov Models ◽  
Hidden Markov ◽  
Change Points ◽  
Climate Trend ◽  
Split Sample ◽  
Sample Test

<p>Due to climate changes, the stationary assumption in hydrology has become obsolete. Moreover, the uncertainty regarding the future evolution of the Earth's climate and its impact on flow regimes is still large. Over the last decade, new risk management approaches have been proposed to support water resources planning under deep uncertainty. Those approaches rely at some point on a hydrological model to derive time series of streamflows for various hydro-climatic scenarios. One of the key issue is to make sure that the hydrological model is robust, i.e. that it performs well over contrasted hydro-climatic conditions. The differential split-sample test principle proposed by Klemes in 1986 recommends partitioning the time series into numerous and independent subperiods with different stationary climate features. Then, the hydrological model calibration is achieved on a specific climate period, and the validation on other(s). Classical detection methods commonly used to partition the times series, such as Mann-Kendall test or Pettitt test, can only detect a single change point, and thus are unable to handle complex climate sequences with multiple change points. We propose a calibration/validation protocol of hydrological models which rely on both the differential split-sample test and on an Hidden Markov Model to identify a succession of subsequences in a time series based on the state of the underlying process. We applied the proposed protocol on the Senegal River (West Africa). The hydrological model used is the conceptual GR2M model. Results show that (i) when the river discharges time series does not display a clear climate trend, and have multiple change points, classical rupture tests are not suitable. Hidden Markov Models are a good alternative as long as the climate sub-sequences are long enough (typically around 30 years or more); (ii) including a Hidden Markov Models in such protocol open up the range of possibilities for calibrate/validate, which can lead to an enhancement of the criterion function (but not necessarily).</p><p>Klemes, V.: Operational testing of hydrological simulation models, Hydrological Sciences Journal, 31, 13-24, 415 https://doi.org/10.1080/02626668609491024, 1986.</p>

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