Development of a Stepped Calibration Approach for XAJ Hydrological Model

This paper discusses the conceptual stepped calibration approach (SCA) which has been developed for the Xinanjiang (XAJ) model. Multi-layer and multi-objective functions which can make optimization work simpler and more effective are introduced in this procedure. In all eight parameters were considered, they were divided into four layers according to the structure of XAJ model, and then calibrated layer by layer. The SCA procedure tends to improve the performance of the traditional method of calibration (thus, using a single objective function, such as root mean square error RMSE). The compared results demonstrate that the SCA yield better model performance than RMSE.

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Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

Computational Intelligence and Neuroscience ◽

10.1155/2020/8594727 ◽

2020 ◽

Vol 2020 ◽

pp. 1-23 ◽

Cited By ~ 2

Author(s):

Jiuyuan Huo ◽

Liqun Liu

Keyword(s):

Objective Function ◽

Parameter Optimization ◽

Optimization Problem ◽

Hydrological Model ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Objective Functions ◽

Hydrological Forecasting ◽

Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

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Robust multi-objective calibration strategies – possibilities for improving flood forecasting

Hydrology and Earth System Sciences ◽

10.5194/hess-16-3579-2012 ◽

2012 ◽

Vol 16 (10) ◽

pp. 3579-3606 ◽

Cited By ~ 11

Author(s):

T. Krauße ◽

J. Cullmann ◽

P. Saile ◽

G. H. Schmitz

Keyword(s):

Parameter Estimation ◽

Objective Function ◽

Model Performance ◽

Data Depth ◽

Automatic Calibration ◽

Multi Objective ◽

Robust Model ◽

Robust Parameter ◽

Robust Parameter Estimation ◽

Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

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Multi-objective calibration of a distributed eco-hydrological model using several remotely sensed information

10.5194/egusphere-egu2020-18880 ◽

2020 ◽

Author(s):

Félix Francés ◽

Carlos Echeverría ◽

Maria Gonzalez-Sanchis ◽

Fernando Rivas

Keyword(s):

Remote Sensing ◽

Model Calibration ◽

Hydrological Model ◽

Model Performance ◽

Temporal Information ◽

Temporal Data ◽

Hydrological Models ◽

Validation Period ◽

Spatio Temporal ◽

Calibration Approach

Calibration of eco-hydrological models is difficult to carry on, even more if observed data sets are scarce. It is known that calibration using traditional trial-and-error approach depends strongly of the knowledge and the subjectivity of the hydrologist, and automatic calibration has a strong dependency of the objective-function and the initial values established to initialize the process.The traditional calibration approach mainly focuses on the temporal variation of the discharge at the catchment outlet point, representing an integrated catchment response and provides thus only limited insight on the lumped behaviour of the catchment. It has been long demonstrated the limited capabilities of such an approach when models are validated at interior points of a river basin. The development of distributed eco-hydrological models and the burst of spatio-temporal data provided by remote sensing appear as key alternative to overcome those limitations. Indeed, remote sensing imagery provides not only temporal information but also valuable information on spatial patterns, which can facilitate a spatial-pattern-oriented model calibration.However, there is still a lack of how to effectively handle spatio-temporal data when included in model calibration and how to evaluate the accuracy of the simulated spatial patterns. Moreover, it is still unclear whether including spatio-temporal data improves model performance in face to an unavoidable more complex and time-demanding calibration procedure. To elucidate in this sense, we performed three different multiobjective calibration configurations: (1) including only temporal information of discharges at the catchment outlet (2) including both temporal and spatio-temporal information and (3) only including spatio-temporal information. In the three approaches, we calibrated the same distributed eco-hydrological model (TETIS) in the same study area: Carraixet Basin, and used the same multi-objective algorithm: MOSCEM-UA. The spatio-temporal information obtained from satellite has been the surface soil moisture (from SMOS-BEC) and the leaf area index (from MODIS).Even though the performance of the first calibration approach (only temporal information included) was slightly better than the others, all calibration approaches provided satisfactory and similar results within the calibration period. To put these results into test, we also validated the model performance by using historical data that was not used to calibrate the model (validation period). Within the validation period, the second calibration approach obtained better performance than the others, pointing out the higher reliability of the obtained parameter values when including spatio-temporal data (in this case, in combination with temporal data) in the model calibration. It is also reliable to mention that the approaches considering only spatio-temporal information provided interesting results in terms of discharges, considering that this variable was not used at all for calibration purposes.

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Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature

Geoscientific Model Development ◽

10.5194/gmd-7-1247-2014 ◽

2014 ◽

Vol 7 (3) ◽

pp. 1247-1250 ◽

Cited By ~ 1200

Author(s):

T. Chai ◽

R. R. Draxler

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Model Evaluation ◽

Mean Absolute Error ◽

Evaluation Studies ◽

Model Performance ◽

Absolute Error ◽

Average Error ◽

Mean Square

Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.

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Characterization of Synthetic Non-Metallic Inclusions Consisting of TiN, Ti2O3, and Oxides of Al2O3 and MgO·Al2O3 Spinel Using Raman Spectroscopy

Metals ◽

10.3390/met11101549 ◽

2021 ◽

Vol 11 (10) ◽

pp. 1549

Author(s):

Francis Gyakwaa ◽

Tuomas Alatarvas ◽

Qifeng Shu ◽

Matti Aula ◽

Timo Fabritius

Keyword(s):

Raman Spectroscopy ◽

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Raman Spectra ◽

Model Performance ◽

Qualitative Evaluation ◽

Quantitative Prediction ◽

Mean Square ◽

Improved Model

Steel quality and properties can be affected by the formation of complex inclusions, including Ti-based inclusions such as TiN and Ti2O3 and oxides like Al2O3 and MgO·Al2O3 (MA). This study assessed the prospective use of Raman spectroscopy to characterize synthetic binary inclusion samples of TiN–Al2O3, TiN–MA, Ti2O3–MA, and Ti2O3–Al2O3 with varying phase fractions. The relative intensities of the Raman peaks were used for qualitative evaluation and linear regression calibration models were used for the quantitative prediction of individual phases. The model performance was evaluated with root mean square error of cross-validation (RMSECV) and root mean square error of prediction (RMSEP). For the raw Raman spectra data, R2 values were between 0.48–0.98, the RMSECV values varied between 3.26–14.60 wt%, and the RMSEP ranged between 2.98–15.01 wt% for estimating the phases. The SNV Raman spectra data had estimated R2 values within 0.94–0.99 and RMSECV and RMSEP values ranged between 2.50–3.26 wt% and 2.80–9.01 wt%, respectively, showing improved model performance. The study shows that the specific phases of TiN, Al2O3, MA, and Ti2O3 in synthetic inclusion mixtures of TiN–(Al2O3 or MA) and Ti2O3–(Al2O3 or MA) could be characterized by the Raman spectroscopy.

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Estimation of coarse dead wood stocks in intact and degraded forests in the Brazilian Amazon using airborne lidar

Biogeosciences ◽

10.5194/bg-16-3457-2019 ◽

2019 ◽

Vol 16 (17) ◽

pp. 3457-3474 ◽

Cited By ~ 1

Author(s):

Marcos A. S. Scaranello ◽

Michael Keller ◽

Marcos Longo ◽

Maiza N. dos-Santos ◽

Veronika Leitold ◽

...

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Dead Wood ◽

Model Performance ◽

Forest Carbon ◽

Airborne Lidar ◽

Mean Square ◽

Improved Model ◽

Relative Root

Abstract. Coarse dead wood is an important component of forest carbon stocks, but it is rarely measured in Amazon forests and is typically excluded from regional forest carbon budgets. Our study is based on line intercept sampling for fallen coarse dead wood conducted along 103 transects with a total length of 48 km matched with forest inventory plots where standing coarse dead wood was measured in the footprints of larger areas of airborne lidar acquisitions. We developed models to relate lidar metrics and Landsat time series variables to coarse dead wood stocks for intact, logged, burned, or logged and burned forests. Canopy characteristics such as gap area produced significant individual relations for logged forests. For total fallen plus standing coarse dead wood (hereafter defined as total coarse dead wood), the relative root mean square error for models with only lidar metrics ranged from 33 % in logged forest to up to 36 % in burned forests. The addition of historical information improved model performance slightly for intact forests (31 % against 35 % relative root mean square error), not justifying the use of a number of disturbance events from historical satellite images (Landsat) with airborne lidar data. Lidar-derived estimates of total coarse dead wood compared favorably with independent ground-based sampling for areas up to several hundred hectares. The relations found between total coarse dead wood and variables quantifying forest structure derived from airborne lidar highlight the opportunity to quantify this important but rarely measured component of forest carbon over large areas in tropical forests.

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Pareto Artificial Life Algorithm for Multi-Objective Optimization

Journal of Information Technology Research ◽

10.4018/jitr.2011040104 ◽

2011 ◽

Vol 4 (2) ◽

pp. 43-60

Author(s):

Jin-Dae Song ◽

Bo-Suk Yang

Keyword(s):

Objective Function ◽

Artificial Life ◽

Pareto Set ◽

Function Optimization ◽

Objective Functions ◽

Multi Objective Optimization ◽

Multi Objective ◽

Single Function ◽

Artificial Life Algorithm ◽

Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

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Pareto Artificial Life Algorithm for Multi-Objective Optimization

Interdisciplinary Advances in Information Technology Research ◽

10.4018/978-1-4666-3625-5.ch008 ◽

2013 ◽

pp. 100-115

Author(s):

Jin-Dae Song ◽

Bo-Suk Yang

Keyword(s):

Objective Function ◽

Artificial Life ◽

Pareto Set ◽

Function Optimization ◽

Objective Functions ◽

Multi Objective Optimization ◽

Multi Objective ◽

Single Function ◽

Artificial Life Algorithm ◽

Single Objective

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Multi-Objective Function for SWIPT System by SADDE

Applied Sciences ◽

10.3390/app10093124 ◽

2020 ◽

Vol 10 (9) ◽

pp. 3124

Author(s):

Wei Chien ◽

Chien-Ching Chiu ◽

Yu-Ting Cheng ◽

Wei-Lin Fang ◽

Eng Hock Lim

Keyword(s):

Objective Function ◽

Path Loss ◽

Wireless Power Transfer ◽

Function Optimization ◽

Multiple Objective ◽

Power Transfer ◽

Objective Functions ◽

Wireless Power ◽

Real Environment ◽

Single Objective

Simultaneous wireless information and power transfer (SWIPT) optimization with multiple objective function optimization is presented in the millimeter band in this paper. Three different objective functions that are used for harvest power (HP), capacity, and bit error rate (BER) were studied. There are three different nodes in real environment for wireless power transfer (WPT) and SWIPT. The channel estimation calculated by shooting and bouncing ray/image techniques includes multi-path, fading effect, and path-loss in the real environment. We applied beamforming techniques at the transmitter to focus the transmitter energy in order to reduce the multi-path effect and adjust the length of the feed line on each array element in order to find the extremum of the objective functions by the self-adaptive dynamic differential evolution (SADDE) method. Numerical results showed that SWIPT node cannot achieve good performance by single objective function, but wireless power transfer (WPT) can. Nevertheless, both WPT and SWIPT nodes can meet the criteria by the multiple objective function. The harvesting power ratio as well as the BER and capacity can be improved by the multiple objective function to an acceptable level by only reducing a little harvesting energy compared to the best harvesting energy for the single objective function. Finally, the multiple optimization function cannot merely provide good information quality for SWIPT node but achieve good total harvesting power for WPT and SWIPT node as well.

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Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

10.5194/hess-2016-88 ◽

2016 ◽

Cited By ~ 1

Author(s):

Fuqiang Tian ◽

Yu Sun ◽

Hongchang Hu ◽

Hongyi Li

Keyword(s):

Objective Function ◽

Power Function ◽

Automatic Calibration ◽

Efficiency Coefficient ◽

Hydrological Models ◽

Objective Functions ◽

Multi Objective ◽

Hydrological Variable ◽

Flow Part ◽

Single Objective

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.

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