scholarly journals Ensemble modelling of nitrogen fluxes: data fusion for a Swedish meso-scale catchment

2010 ◽  
Vol 14 (12) ◽  
pp. 2383-2397 ◽  
Author(s):  
J.-F. Exbrayat ◽  
N. R. Viney ◽  
J. Seibert ◽  
S. Wrede ◽  
H.-G. Frede ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Coefficient Of Determination ◽  
Nitrogen Species ◽  
Linear Regression Models ◽  
Biogeochemical Fluxes ◽  
Model Predictions ◽  
Daily Discharge ◽  
Hydrological Fluxes ◽  
Model Ensembles ◽  
Hydrological Parameter

Abstract. Model predictions of biogeochemical fluxes at the landscape scale are highly uncertain, both with respect to stochastic (parameter) and structural uncertainty. In this study 5 different models (LASCAM, LASCAM-S, a self-developed tool, SWAT and HBV-N-D) designed to simulate hydrological fluxes as well as mobilisation and transport of one or several nitrogen species were applied to the mesoscale River Fyris catchment in mid-eastern Sweden. Hydrological calibration against 5 years of recorded daily discharge at two stations gave highly variable results with Nash-Sutcliffe Efficiency (NSE) ranging between 0.48 and 0.83. Using the calibrated hydrological parameter sets, the parameter uncertainty linked to the nitrogen parameters was explored in order to cover the range of possible predictions of exported loads for 3 nitrogen species: nitrate (NO3), ammonium (NH4) and total nitrogen (Tot-N). For each model and each nitrogen species, predictions were ranked in two different ways according to the performance indicated by two different goodness-of-fit measures: the coefficient of determination R2 and the root mean square error RMSE. A total of 2160 deterministic Single Model Ensembles (SME) was generated using an increasing number of members (from the 2 best to the 10 best single predictions). Finally the best SME for each model, nitrogen species and discharge station were selected and merged into 330 different Multi-Model Ensembles (MME). The evolution of changes in R2 and RMSE was used as a performance descriptor of the ensemble procedure. In each studied case, numerous ensemble merging schemes were identified which outperformed any of their members. Improvement rates were generally higher when worse members were introduced. The highest improvements were achieved for the nitrogen SMEs compiled with multiple linear regression models with R2 selected members, which resulted in the RMSE decreasing by up to 90%.

scholarly journals Ensemble modelling of nitrogen fluxes: data fusion for a Swedish meso-scale catchment

2010 ◽  
Vol 7 (4) ◽  
pp. 5299-5334 ◽  
Author(s):  
J.-F. Exbrayat ◽  
N. R. Viney ◽  
J. Seibert ◽  
S. Wrede ◽  
H.-G. Frede ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Coefficient Of Determination ◽  
Nitrogen Species ◽  
Linear Regression Models ◽  
Biogeochemical Fluxes ◽  
Model Predictions ◽  
Daily Discharge ◽  
Hydrological Fluxes ◽  
Model Ensembles ◽  
Hydrological Parameter

Abstract. Model predictions of biogeochemical fluxes at the landscape scale are highly uncertain, both with respect to stochastic (parameter) and structural uncertainty. In this study 5 different models (LASCAM, LASCAM-S, a self-developed tool, SWAT and HBV-N-D) designed to simulate hydrological fluxes as well as mobilisation and transport of one or several nitrogen species were applied to the mesoscale River Fyris catchment in mid-eastern Sweden. Hydrological calibration against 5 years of recorded daily discharge at two stations gave highly variable results with Nash-Sutcliffe Efficiency (NSE) ranging between 0.48 and 0.83. Using the calibrated hydrological parameter sets, the parameter uncertainty linked to the nitrogen parameters was explored in order to cover the range of possible predictions of exported loads for 3 nitrogen species: nitrate (NO3), ammonium (NH4) and total nitrogen (Tot-N). For each model and each nitrogen species, predictions were ranked in two different ways according to the performance indicated by two different goodness-of-fit measures: the coefficient of determination R2 and the root mean square error RMSE. A total of 2160 deterministic Single Model Ensembles (SME) was generated using an increasing number of members (from the 2 best to the 10 best single predictions). Finally, the best SME for each model, nitrogen species and discharge station were selected and merged into 330 different Multi-Model Ensembles (MME). The evolution of changes in R2 and RMSE was used as a performance descriptor of the ensemble procedure. In each studied case, numerous ensemble merging schemes were identified which outperformed any of their members. Improvement rates were generally higher when worse members were introduced. The highest improvements were achieved for the nitrogen SMEs compiled with multiple linear regression models with R2 selected members, which resulted in the RMSE decreasing by up to 90%.

scholarly journals Grapevine bunch weight estimation using image-based features: comparing the predictive performance of number of visible berries and bunch area

OENO One ◽  
2021 ◽  
Vol 55 (4) ◽  
pp. 209-226
Author(s):  
Carlos Lopes ◽  
Jorge Cadima
Keyword(s):  
Multiple Regression ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Quantitative Estimation ◽  
Explanatory Power ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Predictor Models ◽  
Single Predictor ◽  
2D Images

Recent advances in machine vision technologies have provided a multitude of automatic tools for recognition and quantitative estimation of grapevine bunch features in 2D images. However, converting them into bunch weight (BuW) is still a big challenge. This paper aims to compare the explanatory power of the number of visible berries (#vBe) and the bunch area (BuA) in 2D images, in order to predict BuW. A set of 300 bunches from four grapevine cultivars were picked at harvest and imaged using a digital RGB camera. Then each bunch was manually assessed for several morphological attributes and, from each image, the #vBe was visually assessed while BuA was segmented using manual labelling combined with an image processing software. Single and multiple regression analysis between BuW and the image-based variables were performed and the obtained regression models were subsequently validated with two independent datasets.The high goodness of fit obtained for all the linear regression models indicates that either one of the image-based variables can be used as an accurate proxy of actual bunch weight and that a general model is also suitable. The comparison of the explanatory power of the two image-based attributes for predicting bunch weight showed that the models based on the predictor #vBe had a slightly lower coefficient of determination (R2) than the models based on BuA. The combination of the two image-based explanatory variables in a multiple regression model produced predictor models with similar or noticeably higher R2 than those obtained for single-predictor models. However, adding a second variable produced a higher and more generalised gain in accuracy for the simple regression models based on the predictor #vBe than for the models based on BuA. Our results recommend the use of the models based on the two image-based variables, as they were generally more accurate and robust than the single variable models. When the gains in accuracy produced by adding a second image-based feature are small, the option of using only a single predictor can be chosen; in such a case, our results indicate that BuA would be a more accurate and less cultivar-dependent option than the #vBe.

scholarly journals Isotonic regression analysis of Guzerá cattle growth curves

Revista CERES ◽  
2018 ◽  
Vol 65 (1) ◽  
pp. 24-27 ◽  
Author(s):  
Adriano Rodrigues ◽  
Lucas Monteiro Chaves ◽  
Fabyano Fonseca Silva ◽  
Idalmo Pereira Garcia ◽  
Darlene Ana Souza Duarte ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Age Groups ◽  
Growth Curves ◽  
Generalized Least Squares ◽  
Isotonic Regression ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Generalized Least Squares Method

ABSTRACT The objective of this study was to apply data transformation via isotonic regression in growth curves studies of Guzerá cattle whose data presented disturbances characterized by decreased body weight in certain age groups. Weight-age data were collected on newly weaned Guzerá males according to the methodology of weight gain tests (WGT) defined by the Brazilian Association of Zebu Breeders (ABCZ). The Logistic, Von Bertalanffy and Gompertz models were fitted to weight-age data using the generalized least squares method for non-linear regression models through the Gauss-Newton algorithm. The proposed transformation based on isotonic regression theory proved to be efficient; and the Logistic model was the best to describe the growth of animals, with a high percentage of convergence (100%) and goodness of fit assessed by the mean squared error (MSE) and the coefficient of determination (R2).

scholarly journals Evaluation of NASA POWER Reanalysis Products to Estimate Daily Weather Variables in a Hot Summer Mediterranean Climate

Agronomy ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1207
Author(s):  
Gonçalo C. Rodrigues ◽  
Ricardo P. Braga
Keyword(s):  
Wind Speed ◽  
Bias Correction ◽  
Goodness Of Fit ◽  
Mediterranean Climate ◽  
Weather Data ◽  
Coefficient Of Determination ◽  
Mean Bias Error ◽  
Bias Error ◽  
Weather Variables ◽  
Weather Stations

This study aims to evaluate NASA POWER reanalysis products for daily surface maximum (Tmax) and minimum (Tmin) temperatures, solar radiation (Rs), relative humidity (RH) and wind speed (Ws) when compared with observed data from 14 distributed weather stations across Alentejo Region, Southern Portugal, with a hot summer Mediterranean climate. Results showed that there is good agreement between NASA POWER reanalysis and observed data for all parameters, except for wind speed, with coefficient of determination (R2) higher than 0.82, with normalized root mean square error (NRMSE) varying, from 8 to 20%, and a normalized mean bias error (NMBE) ranging from –9 to 26%, for those variables. Based on these results, and in order to improve the accuracy of the NASA POWER dataset, two bias corrections were performed to all weather variables: one for the Alentejo Region as a whole; another, for each location individually. Results improved significantly, especially when a local bias correction is performed, with Tmax and Tmin presenting an improvement of the mean NRMSE of 6.6 °C (from 8.0 °C) and 16.1 °C (from 20.5 °C), respectively, while a mean NMBE decreased from 10.65 to 0.2%. Rs results also show a very high goodness of fit with a mean NRMSE of 11.2% and mean NMBE equal to 0.1%. Additionally, bias corrected RH data performed acceptably with an NRMSE lower than 12.1% and an NMBE below 2.1%. However, even when a bias correction is performed, Ws lacks the performance showed by the remaining weather variables, with an NRMSE never lower than 19.6%. Results show that NASA POWER can be useful for the generation of weather data sets where ground weather stations data is of missing or unavailable.

Building hydrological single-model ensembles using artificial neural networks and a combinatorial optimization approach

2021 ◽  
Author(s):  
Juan F. Farfán-Durán ◽  
Luis Cea
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Goodness Of Fit ◽  
Hydrological Model ◽  
Hill Climbing ◽  
Single Model ◽  
Pearson Coefficient ◽  
Gradient Based ◽  
Artificial Neural ◽  
Model Ensembles

<p>In recent years, the application of model ensembles has received increasing attention in the hydrological modelling community due to the interesting results reported in several studies carried out in different parts of the world. The main idea of these approaches is to combine the results of the same hydrological model or a number of different hydrological models in order to obtain more robust, better-fitting models, reducing at the same time the uncertainty in the predictions. The techniques for combining models range from simple approaches such as averaging different simulations, to more complex techniques such as least squares, genetic algorithms and more recently artificial intelligence techniques such as Artificial Neural Networks (ANN).</p><p>Despite the good results that model ensembles are able to provide, the models selected to build the ensemble have a direct influence on the results. Contrary to intuition, it has been reported that the best fitting single models do not necessarily produce the best ensemble. Instead, better results can be obtained with ensembles that incorporate models with moderate goodness of fit. This implies that the selection of the single models might have a random component in order to maximize the results that ensemble approaches can provide.</p><p>The present study is carried out using hydrological data on an hourly scale between 2008 and 2015 corresponding to the Mandeo basin, located in the Northwest of Spain. In order to obtain 1000 single models, a hydrological model was run using 1000 sets of parameters sampled randomly in their feasible space. Then, we have classified the models in 3 groups with the following characteristics: 1) The 25 single models with highest Nash-Sutcliffe coefficient, 2) The 25 single models with the highest Pearson coefficient, and 3) The complete group of 1000 single models.</p><p>The ensemble models are built with 5 models as the input of an ANN and the observed series as the output. Then, we applied the Random-Restart Hill-Climbing (RRHC) algorithm choosing 5 random models in each iteration to re-train the ANN in order to identify a better ensemble. The algorithm is applied to build 50 ensembles in each group of models. Finally, the results are compared to those obtained by optimizing the model using a gradient-based method by means of the following goodness-of-fit measures: Nash-Sutcliffe (NSE) coefficient, adapted for high flows Nash-Sutcliffe (HF−NSE), adapted for low flows Nash-Sutcliffe (LF−W NSE) and coefficient of determination (R2).</p><p>The results show that the RRHC algorithm can identify adequate ensembles. The ensembles built using the group of models selected based on the NSE outperformed the model optimized by the gradient method in 64 % of the cases in at least 3 of 4 coefficients, both in the calibration and validation stages. Followed by the ensembles built with the group of models selected based on the Pearson coefficient with 56 %. In the case of the third group, no ensembles were identified that outperformed the gradient-based method. However, the most part of the ensembles outperformed the 1000 individual models.</p><p><strong>Keywords: Multi-model ensemble; Single-model ensemble; Artificial Neural Networks; Hydrological Model; Random-restart Hill-climbing</strong></p><p> </p>

scholarly journals Non-Linear Regression Models with Vibration Amplitude Optimization Algorithms in a Microturbine

Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 130
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
L. A. Montoya-Santiyanes ◽  
José Manuel Álvarez-Alvarado
Keyword(s):  
Linear Regression ◽  
Vibration Amplitude ◽  
Regression Models ◽  
Engineering Problem ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Gray Wolf ◽  
Linear Regression Models ◽  
Machinery Condition Monitoring ◽  
Non Linear

Machinery condition monitoring and failure analysis is an engineering problem to pay attention to among all those being studied. Excessive vibration in a rotating system can damage the system and cannot be ignored. One option to prevent vibrations in a system is through preparation for them with a model. The accuracy of the model depends mainly on the type of model and the fitting that is attained. The non-linear model parameters can be complex to fit. Therefore, artificial intelligence is an option for performing this tuning. Within evolutionary computation, there are many optimization and tuning algorithms, the best known being genetic algorithms, but they contain many specific parameters. That is why algorithms such as the gray wolf optimizer (GWO) are alternatives for this tuning. There is a small number of mechanical applications in which the GWO algorithm has been implemented. Therefore, the GWO algorithm was used to fit non-linear regression models for vibration amplitude measurements in the radial direction in relation to the rotational frequency in a gas microturbine without considering temperature effects. RMSE and R2 were used as evaluation criteria. The results showed good agreement concerning the statistical analysis. The 2nd and 4th-order models, and the Gaussian and sinusoidal models, improved the fit. All models evaluated predicted the data with a high coefficient of determination (85–93%); the RMSE was between 0.19 and 0.22 for the worst proposed model. The proposed methodology can be used to optimize the estimated models with statistical tools.

scholarly journals BIDIRECTIONAL REFLECTANCE MODELING OF THE GEOSTATIONARY SENSOR HIMAWARI-8/AHI USING A KERNEL-DRIVEN BRDF MODEL

2016 ◽  
Vol III-7 ◽  
pp. 3-8 ◽  
Author(s):  
M. Matsuoka ◽  
M. Takagi ◽  
S. Akatsuka ◽  
R. Honda ◽  
A. Nonomura ◽  
...  
Keyword(s):  
Surface Properties ◽  
Land Surface ◽  
Goodness Of Fit ◽  
Near Infrared ◽  
Temporal Frequency ◽  
Atmospheric Correction ◽  
Time Of Day ◽  
Coefficient Of Determination ◽  
Near Infrared Reflectance ◽  
Bidirectional Reflectance

Himawari-8/AHI is a new geostationary sensor that can observe the land surface with high temporal frequency. Bidirectional reflectance derived by the Advanced Himawari Imager (AHI) includes information regarding land surface properties such as albedo, vegetation condition, and forest structure. This information can be extracted by modeling bidirectional reflectance using a bidirectional reflectance distribution function (BRDF). In this study, a kernel-driven BRDF model was applied to the red and near infrared reflectance observed over 8 hours during daytime to express intraday changes in reflectance. We compared the goodness of fit for six combinations of model kernels. The Ross-Thin and Ross-Thick kernels were selected as the best volume kernels for the red and near infrared bands, respectively. For the geometric kernel, the Li-sparse-Reciprocal and Li-Dense kernels displayed similar goodness of fit. The coefficient of determination and regression residuals showed a strong dependency on the azimuth angle of land surface slopes and the time of day that observations were made. Atmospheric correction and model adjustment of the terrain were the main issues encountered. These results will help to improve the BRDF model and to extract surface properties from bidirectional reflectance.

scholarly journals Customer Satisfaction Measurement – Clustering Approach

2018 ◽  
Vol 66 (2) ◽  
pp. 561-569 ◽  
Author(s):  
David Schüller ◽  
Jan Pekárek
Keyword(s):  
Linear Regression ◽  
Customer Satisfaction ◽  
Hierarchical Clustering ◽  
Theory And Practice ◽  
Coefficient Of Determination ◽  
Individual Factors ◽  
Marketing Theory ◽  
Linear Regression Models ◽  
Satisfaction Measurement ◽  
Customer Satisfaction Measurement

The paper deals with the issue of customer satisfaction measurement. The aim of this study is to determine the importance of the individual factors and their impact on total customer satisfaction for multiple segments by using linear regression and hierarchical clustering. This study is focused on the market of café establishment. We applied hierarchical clustering with Ward’s criterion to partition customers into segments and then we developed linear regression models for each segment. Linear models for partitioned data showed higher coefficient of determination than the model for the whole market. The results revealed that there are quite significant differences in rankings of customer satisfaction factors among the segments. This is caused by the different preferences of customers. The clustered data allows to achieve a higher homogeneity of data within the segment, which is crucial both for marketing theory and practice. The approach i.e. partitioning the market into smaller more specific segments could become perspective for marketing use in different economic sectors. This attitude can allow marketers to target better on customer segments according to the importance of individual factors.

scholarly journals Mathematical Models for Tumor Growth and the Reduction of Overtreatment

2018 ◽  
Vol 80 (01) ◽  
pp. 072-078 ◽  
Author(s):  
Berdine Heesterman ◽  
John-Melle Bokhorst ◽  
Lisa de Pont ◽  
Berit Verbist ◽  
Jean-Pierre Bayley ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Age At Onset ◽  
Growth Curves ◽  
Magnetic Resonance Images ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Significant Difference

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation. Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated. Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model. Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

scholarly journals Abdominal subcutaneous fat quantification in obese patients from limited field-of-view MRI data

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Sophia Michel ◽  
Nicolas Linder ◽  
Tobias Eggebrecht ◽  
Alexander Schaudinn ◽  
Matthias Blüher ◽  
...  
Keyword(s):  
Gender Differences ◽  
Adipose Tissue ◽  
Goodness Of Fit ◽  
Imaging Techniques ◽  
Subcutaneous Fat ◽  
Field Of View ◽  
Coefficient Of Determination ◽  
Obese Patients ◽  
Obese Subjects ◽  
Surrogate Measures

Abstract Different types of adipose tissue can be accurately localized and quantified by tomographic imaging techniques (MRI or CT). One common shortcoming for the abdominal subcutaneous adipose tissue (ASAT) of obese subjects is the technically restricted imaging field of view (FOV). This work derives equations for the conversion between six surrogate measures and fully segmented ASAT volume and discusses the predictive power of these image-based quantities. Clinical (gender, age, anthropometry) and MRI data (1.5 T, two-point Dixon sequence) of 193 overweight and obese patients (116 female, 77 male) from a single research center for obesity were analyzed retrospectively. Six surrogate measures of fully segmented ASAT volume (VASAT) were considered: two simple ASAT lengths, two partial areas (Ap-FH, Ap-ASIS) and two partial volumes (Vp-FH, Vp-ASIS) limited by either the femoral heads (FH) or the anterior superior iliac spine (ASIS). Least-squares regression between each measure and VASAT provided slope and intercept for the computation of estimated ASAT volumes (V~ASAT). Goodness of fit was evaluated by coefficient of determination (R2) and standard deviation of percent differences (sd%) between V~ASAT and VASAT. Best agreement was observed for partial volume Vp-FH (sd% = 14.4% and R2 = 0.78), followed by Vp-ASIS (sd% = 18.1% and R2 = 0.69) and AWFASIS (sd% = 23.9% and R2 = 0.54), with minor gender differences only. Other estimates from simple lengths and partial areas were moderate only (sd% > 23.0% and R2 < 0.50). Gender differences in R2 generally ranged between 0.02 (dven) and 0.29 (Ap-FH). The common FOV restriction for MRI volumetry of ASAT in obese subjects can best be overcome by estimating VASAT from Vp-FH using the equation derived here. The very simple AWFASIS can be used with reservation.

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