Standard Root Mean Square Error Research Articles

Variability analysis of soil properties, mapping, and crop test responses in Southern Ethiopia

Agricultural productivity is significantly impacted by soil properties, which vary spatially from a small to a larger area. This variation may be caused by a combination of intrinsic and extrinsic factors, including human activities like soil management practices. The aim of the current study was to analyze soil spatial variability, create a Digital Soil Map (DSM), and test map information with crop in Southern Ethiopia. A total of 18 geo-referenced surface soil samples at depth of 20 cm were collected. Selected soil Physico-chemical properties such as soil texture, pH, organic carbon (OC), total nitrogen (TN), available phosphorus (av. P), sulfur (S), exchangeable bases [calcium (Ca), magnesium (Mg), and potassium (K)], soil micronutrients [boron (B), copper (Cu), iron (Fe), manganese (Mn) and zinc (Zn)] and cation exchange capacity (CEC) were analyzed. The results revealed clay texture with a mean pH value of 4.6 (strong acidity). About 50% of essential nutrients [N, P, S, Ca, Mg, B & Fe] were deficient. The geostatistical analysis has shown that the best-fitted models were exponential for (OC, TN, available P, S, Mg, CEC, B, Fe, and Zn), spherical for (pH, Ca, Cu and Mn), and Gaussian for (C:N, K, K:Mg, and PBS). The range of all soil properties varied from 50 m to 84 m which was above the actual distance between soil samples (i.e., 46 m). The result showed that the spatial dependence values for soil properties of [OC, TN, CEC, PBS, ESP, and Cu]; [pH, C: N ratio, available P, S, Ca, Mg, K, Na, K: Mg ratio and Zn] and [B, Fe, M n] were strong (<25%]; weak (>75%) and moderate (25%–75%), respectively. Model performance using indicators such as prediction mean error (PME), root mean square standardized error (RMSSE), mean standard error (MSE), and root-mean-square error (RMSE) also confirmed the acceptable prediction. The DSM demonstrated the limitation of N, P, S, and B nutrients for intervention. The DSM information was tested under field conditions using haricot bean (Phaseolus vulgaris) with lime and organic fertilizers as treatments. The experiment consists of lime rates (0, 3, 6 t/ha), rhizobium inoculation (inoculated and non-inoculated), and fertilizer types (0, 150 kg ha−1 NPSB, 5 t/ha vermi compost, 10t/ha farmyard manure (FYM)) in Randomized Complete Block Design with three replications. The result exhibited interaction effects of lime, inoculation, and fertilizer types significantly influenced (p < 0.05) biomass and grain yield of haricot beans. Rhizobium inoculation x 6t/ha lime x 150 kg ha−1 NPSB recorded the maximum grain yield (3186.1 kg/ha) which was 26.3 fold over the non-treated soil (117 kg ha−1). In conclusion, the DSM classified the area into distinct management zones which were tested with a crop trial. The results of the trial confirm the importance of site-specific nutrients/amendment application for sustainable soil management.

Body Composition in Youths Aged 10‒17 Years by Deuterium Oxide Dilution, Air Displacement Plethysmography, and DXA: Validation of the Medical Body Composition Analyzer Bioimpedance Device by a 4-Compartment Model

BackgroundThe medical body composition analyzer (mBCA) incorporates advances in multifrequency technology and has been validated using a 4-compartment (4C) model in adults but not in youths aged <18 y. ObjectivesThis study aimed to formulate a 4C model based on 3 reference methods and develop and validate a body composition prediction equation for the mBCA in youths aged 10‒17 y. MethodsThe body density of 60 female and male youths was measured by air displacement plethysmography, total body water by deuterium oxide dilution, and BMC by DXA. Data from the equation group (n = 30) were used to formulate a 4C model. The all-possible-regressions method was used to select variables. The model was validated in a second cohort (n = 30) in a random split design. The accuracy, precision, and potential bias were evaluated by the Bland and Altman procedure. ResultsMean age, weight (W), height (H), waist circumference, and z-score of BMI were 13.6 ± 2.3 y, 54.5 ± 15.5 kg, 156 ± 11.9 cm, 75.5 ± 10.9 cm, and 0.70 ± 1.32 z, respectively. The prediction equation was as follows: FFM in kg (FFMkg) = ([0.2081] ∗ [W] + [0.8814] ∗ [H2cm/RΩ] + [0.2055 ∗ XcΩ])–15.343; R2 = 0.96; standardized root-mean-square error (SRMSE) = 2.18 kg. FFM did not differ between the 4C method (38.9 ± 12.0 kg) and the mBCA (38.4 ± 11.4 kg) (P > 0.05). The relationship between these 2 variables did not deviate from the identity line, was not significantly different from 0, and the slope was not significantly different from 1.0. In the precision prediction model of mBCA, the R2 value was 0.98 and SRMSE was 2.1. No significant bias was found when regressing differences between methods and their means (P = 0.08). ConclusionsThe equation for the mBCA was accurate, precise, had no significant bias, had substantial strength of agreement and could be used in this age group when subjects were preferentially within the constraints of a specified body size.

Comparison between Different Mustard Yield Prediction Models Developed using Various Techniques for Udaipur Region of Rajasthan

The present research was conducted to develop and compare mustard yield prediction models using SPSS regression, Artificial Neural Network (ANN) and Autoregressive Moving Average (ARIMA) model. Mustard crop is one of the major rabi crops of India with Rajasthan as the leading mustard producing state. In this study, eight different weather parameters were used to develop mustard yield prediction model, with different yield prediction techniques. Weather and yield data from year 1999 to 2015 were utilised for calibration and year 2016 to 2018 for validation. Three different algorithms were used in ANN to predict mustard yield. Time series model (ARIMA) is another technique used in this study to forecast mustard yield for Udaipur district. In order to analyse and compare error(s) in the developed models and to compare simulated and actual/observed yield, different error indices like root mean square error (RMSE), standardized root mean square error (SRMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and D Index were considered. The validated results showed that, regression model spss performed better than other two models as the RMSE value using SPSS model was very less (0.12 to 0.14), also the D index value using regression model was close to 1.

Near Infrared Spectroscopy: A useful technique for inline monitoring of the enzyme catalyzed biosynthesis of third-generation biodiesel from waste cooking oil

Near Infrared (NIR) spectroscopy was used for inline monitoring the enzymatic production of third-generation biodiesel from waste cooking oil (WCO) —with fatty acid profile similar to olive oil— under the principles of Continued Process Verification (CPV) and Process Analytical Technology (PAT). For this purpose, covalently immobilized mature Rhizopus oryzae lipase (rROL) was used to transesterify WCO with methanol and ethanol, firstly in 10 mL vials under orbital stirring and then it was successfully scaled up to a mechanically stirred 50 mL laboratory reactor specially designed for use of a NIR probe. Biocatalyst half-life and productivity after ten reaction cycles with methanol and ethanol were assessed. Slightly higher operational stability with methanol (337.5 h, 54 batches) vs with ethanol (146.7 h, 44 batches) was observed, but decreased productivity as a result of the increased reaction times used with the former (219 vs 327 µmol min−1). The NIR spectroscopy results were highly correlated with those of gas chromatography (GC) used as reference. Thus, the root mean-square standard error of prediction (RMSEP) was 2.0% for methanol and 2.1% for ethanol. Therefore, NIR spectroscopy, which allows data acquisition in real time, is suitable for inline monitoring of enzymatic production of biodiesel.

Soil respiration and CH4 consumption covary on the plot scale

Assessing the greenhouse gas (GHG) balance of a landscape or land use can be challenging since greenhouse gas fluxes change over time and can be very different locally. While the spatial variability of carbon dioxide (CO2) fluxes and nitrous oxide (N2O) on the plot scale can hardly be explained, there is first evidence that methane (CH4) consumption covaries with CO2 fluxes in upland forest soils. Yet, if this spatial correlation is persistent over time is unclear. We studied the spatial variability in soil respiration (CO2 fluxes) and soil CH4 consumption in a homogenous, planted forest on an 800 m2 plot. The study was repeated after two weeks at sampling points next to those of the first study. Both studies showed that CH4 consumption was higher at locations with higher soil respiration, and that the correlation between CH4 consumption and soil respiration was persistent between the studies. This result agrees with the interpretation of the rhizosphere as most important source of soil CO2 and potentially preferred habitat for methanotrophic bacteria. The correlation found in the first study allowed predicting CH4 consumption rates of the second study based on the observed CO2 fluxes at the new measurement locations with a standardized root-mean-square error (SRMSE) of 26%. Since soil respiration measurements are much easier to conduct, they would be a good means to complement the more laborious and cost-intensive measurements of CH4 consumption in order to get a more comprehensive estimate of the representative CH4 consumption of a site.

Predictive mapping of soil organic carbon in Northeast Algeria

Soils of semi-arid climates undergo organic carbon loss, which in turn affects their agricultural potential. Geostatistics is often used as an interpolation tool to thoroughly describe SOC spatial distribution. To focus on soil organic carbon (SOC) depletion, the Tiffech watershed (Northeast of Algeria), an economically important agricultural area, was chosen due to intensive agricultural practices, decline of forests and occurrence of erosion.The present study aimed to predict the spatial variation of SOC in Tiffech watershed using geostatistics and a Geographical Information System (GIS) software, comparing the performance of two geostatistical methods—Ordinary Kriging (OK) and Regression Kriging (RK)—also assessing the role of auxiliary variables in improving the prediction accuracy and highlighting the role of land cover in SOC storage.The SOC content in Tiffech soils was determined on 42 soil samples from the surface layer (0–10 cm) collected all over the study area and the results were used to estimate SOC density in non-sampled locations.The prediction efficiency of the two methods was evaluated by calculating the Mean Error (ME), the Root Mean Square Error (RMSE) and the Root Mean Square Standardized Error (RMSSE).The interpolation results showed that SOC distribution in the study area was correlated to the topography, the clay index, and general landscape features. SOC content increased northwards in the area, ranging from 0.53 to 6.9 kg·m−2 in relation to land use. As expected, maps figured a good conservation status of SOC stocks in areas with dense vegetation; conversely poor SOC contents were estimated where land degradation factors take place.Cross-validation results showed an outperformance in the interpolation accuracy of RK on OK after the introduction of environmental variables, with an RMSE value of 0.02 versus 0.81. This suggests a higher efficiency of RK in predicting SOC content across the Tiffech area in comparison with OK, confirming that introducing some auxiliary data correlated to the target variable in SOC estimation, considerably improved the interpolation accuracy.

Spatial variability in the distribution of trace metals in groundwater around the Rooppur nuclear power plant in Ishwardi, Bangladesh

Evaluation of groundwater quality is a significant concept for water resources monitoring and management. In this study, we examined the quality of groundwater of Ishwardi Upazila in Pabna District of Bangladesh. This paper has evaluated the spatial pattern and prediction of trace metals in groundwater in the study area with the using of geostatistical model. The best fitted geostatistical model has been used to identify the spatial distribution and prediction that are shown on maps. It was selected on the basis of experimental semivariogram values of twelve water quality trace metal parameters. The bestfitted model's semivariogram values have been verified by using different parameters used to evaluate the quality of geostatistical models (i.e., mean square error (MSE), root mean square error (RMSE), average standard error (ASE) and root mean square standardized error (RMSSE). The values of Barium (maximum 420.30 µg/L), Iron (maximum 0.4967 mg/L) and Arsenic (maximum 0.4983 mg/L) found in this study exceed the safe limit of Bangladesh and World Health Organization for drinking water. The results of this study demonstrate that the groundwater of the study area is no longer suitable for drinking purpose due to the high concentration of trace metals.

SELECTION OF VARIOGRAM MODEL FOR SPATIAL RAINFALL MAPPING USING ANALYTICAL HIERARCHY PROCEDURE (AHP)

In geostatistical analysis, spatial interpolation at any unmeasured point is done using the parameters of a variogram model that matches the experimental data. Several variogram models can be used and the accuracy of the spatial map produced depends on the selection of the most appropriate variogram model that fits the spatial distribution of the experimental data. Therefore, in this study, a multiple-criteria decision-making method, Analytical Hierarchy Procedure (AHP), is used to evaluate and select the best variogram model for mapping spatial rainfall in the upper reaches of the Kelang River basin in Malaysia. Using daily rainfall data from 71 rain gauge stations, geostatistical analysis was done with the Ordinary Kriging interpolation method and 5 alternatives of variogram models, namely Spherical, Tetraspherical, Pentaspherical, Exponential and Gaussian for spatial rainfall mapping. The accuracy of the spatial rainfall map was evaluated using four criteria of spatial interpolation error indicators, which are Root-Mean-Square Error (RMSE), Average Standard Error (ASE), Mean Standardized Error (MSE) and Root-Mean-Square Standardized Error (RMSSE). The results showed that the Spherical model was ranked at the top for producing the best spatial rainfall map of the study area.

Mid-infrared spectroscopy to support regional-scale digital soil mapping on selected croplands of South-West Germany

Digital soil mapping (DSM) relies on statistical relationships between soil properties and covariates (e.g. terrain attributes, land use class, geology) which may not explain a large proportion of measured soil properties variability. This uncertainty combined with low spatial resolution of existing maps makes it difficult to monitor soils. Diffuse reflectance infrared Fourier transform mid-infrared spectroscopy (midDRIFTS) with partial least square regression (PLSR) may offer an alternative source of high quality data for improved DSM. Previously validated midDRIFTS-PLSR models were used to predict soil total carbon (TC), total inorganic carbon (TIC), total organic carbon (TOC) and texture of 1170 samples from contrasting agroecological regions (~3600km2), Kraichgau (K) and Swabian Alb (SA), Southwest Germany. MidDRIFTS-PLSR predictions were integrated with geostatistics for soil property maps (200m resolution). An average of 93% of the total soil samples were predicted within the confidence intervals of the midDRIFTS-PLSR models for the respective properties. Ordinary kriging (OK) resulted in maps for TC, TIC, TOC and texture with a root mean square standardized error (RMSSE) ~1. Soil organic matter (SOM) (DRIFTS_SOM) and texture (DRIFTS_texture) maps developed in the current study were of higher spatial resolution than previously existing maps. The DRIFTS_SOM and DRIFTS_texture in the both regions showed considerable differences when compared to existing maps. The DRIFTS_SOM in K and SA regions had overlaps of 45 and 69% with the 1:200,000 existing map. While the DRIFTS_texture in K had an overlap of 92% with the 1:1,000,000 existing map, the overlap in SA region was only 11%. We conclude that traditional DSM with covariates can be improved via higher sampling density which is made possible using midDRIFTS-PLSR. Incorporation of mid-infrared spectral data with both remote sensing and other environmental data would be a further application to cope with uncertainty associated to both spectroscopic and spatial modeling.

Lessening the adverse effect of the semivariogram model selection on an interpolative survey using kriging technique.

Objective Many parameters in environmental, scientific and human sciences investigations need to be interpolated. Geostatistics, with its structural analysis step, is widely used for this purpose. This precious step that evaluates data correlation and dependency is performed thanks to semivariogram. However, an incorrect choice of a semivariogram model can skew all the prediction results. The main objectives of this paper are (1) to simply illustrate the influence of the choice of an inappropriate semivariogram model and (2) to show how a best-fitted model can be selected. This may lessen the adverse effect of the semivariogram model selection on an interpolation survey using kriging technique.MethodsThe influence of the semivariogram model selection is highlighted and illustrated by thematic maps drawn using four different models (Gaussian, magnetic, spherical and exponential). Then, a guideline to select the most suitable model, using mean error (ME), mean square error (MSE), root mean square error (RMSE), average standard error (ASE), and root mean square standardized error (RMSSE), is proposed.ResultsThe choice of a semivariogram model seriously influences the results of a kriging survey at both endpoints and amplitude of the range of the estimated values. However, the direction of variation of the interpolated values is independent of the semivariogram model: different semivariogram models (with the same characteristics) produce different thematic maps but, the areas of minimum and maximum values remain unchanged. Yet, the suitable model can be selected by means of ME, MSE, RMSE, ASE and RMSSE.ConclusionThe present article illustrates how the use of an inappropriate semivariogram model can seriously distort the results of an evaluation, assessment or prediction survey. To avoid such an inconveniency, a methodical approach based on the computation and analysis of ME, RMSE, ASE, RMSSE and MSE is proposed.

Groundwater Quality Evaluation Using GIS Based Geostatistical Algorithms

Groundwater quality is a major environmental aspect which needs to be analyzed and managed depending on its spatial distribution. Utilization of insufficient management of groundwater resources in Gaza Strip, Palestine, produces not only a reduction in quantity but also deterioration in quality of groundwater. The aim of this study is to provide an overview for evaluation of groundwater quality in the Gaza Strip area as a case study for applying spatially distributed by using Geographic Information System (GIS) and geostatistical algorithms. The groundwater quality parameters, pH, total dissolved solids, total hardness, alkalinity, chloride, nitrate, sulfate, calcium, magnesium, and fluoride, were sampled and analyzed from the existing municipal and agricultural wells in Gaza Strip; maps of each parameter were created using geostatistical (Kriging) approach. Experimental semivariogram values were tested for different ordinary Kriging models to identify the best fitted for the ten water quality parameters and the best models were selected on the basis of mean square error (MSE), root mean square error (RMSE), average standard error (ASE), and root mean square standardized error (RMSSE). Maps of 10 groundwater quality parameters were used to calculate the groundwater quality index (GWQI) map using the index method. In general, the results showed that this integrated method is a sufficient assessment tool for environmental spatially distributed parameters.

The Determination of Reference Evapotranspiration for Spatial Distribution Mapping Using Geostatistics

The reference evapotranspiration (ET0) is an essential variable in the agrohydrological systems and its estimation on a regional scale is limited to its spatial variability. This study compares two approaches for preparation of spatial distribution maps of ET0 in Mazandaran province of Iran. In the first approach, ET0 was calculated using climatic data and Hargreaves-Samani equation in weather stations locations and then were interpolated. In the second approach, the components of the Hargreaves-Samani equation were interpolated and then ET0 maps were prepared by applying the Hargreaves-Samani equation and suitable commands in GIS. The 10-year climatic data for 51 weather stations (46 stations for preparing ET0 maps and 5 stations as validation station) were gathered over Mazandaran province. Semivariograms were calculated and the best semivariogram model was selected on the basis of the least value of Residual Sums of Squares (RSS). The spatial correlation of the data was compared on the basis of Nugget to Sill ratio. The data were interpolated using Ordinary Kriging method and the interpolation error was computed by cross validation technique based on Root Mean Square Standardized Error (RMSSE). The predicted ET0 values were compared to the computed ET0 in validation stations and sensitivity analysis was conducted. Results show the second approach had better spatial correlation and lower interpolation error and the difference between these two approaches were not significant. Therefore, the accuracy of the ET0 maps is more related to the method of computing ET0 than the type of climatic data is being interpolated.

Influence of the Variogram Model on an Interpolative Survey Using Kriging Technique

Geostatistics is an efficient and effective method to continuously assess the content, the spatio-temporal distribution and the correlation of a discretely sampled deposit. It begins with an exploratory analysis that evaluates the consistency and distribution of data through histograms and QQ plots, and then a structural analysis that evaluates data correlation and dependency through variogram and finally a predictive analysis using kriging. This predicting method is used in various geographical investigations: meteorology, demography, hydrology, orography, economy, and pollution, etc. Even when using related software, it is generally of the duty of the user to manually select the suitable variogram model. The main objectives of this paper were to highlight how the choice of a variogram model can affect the results of an interpolating predictive analysis and to show how a best-fitted model can be selected. The results, illustrated with an example, show that the choice of the variogram model inevitably influences the results of a kriging at both endpoints and amplitude of the range of the estimated values. However, the direction of variation of the interpolated values is independent of the variogram model: different variogram models (with the same characteristics) produce different thematic maps but, the areas of minimum and maximum values remain unchanged. Fortunately, the computation of some cross validation tests such as mean error (ME), mean square error (MSE), root mean square error (RMSE), average standard error (ASE) and root mean square standardized error (RMSSE) can help to ascertain the performance of the developed models.

Multiobjective sensitivity analysis and optimization of distributed hydrologic model MOBIDIC

Abstract. Calibration of distributed hydrologic models usually involves how to deal with the large number of distributed parameters and optimization problems with multiple but often conflicting objectives that arise in a natural fashion. This study presents a multiobjective sensitivity and optimization approach to handle these problems for the MOBIDIC (MOdello di Bilancio Idrologico DIstribuito e Continuo) distributed hydrologic model, which combines two sensitivity analysis techniques (the Morris method and the state-dependent parameter (SDP) method) with multiobjective optimization (MOO) approach ε-NSGAII (Non-dominated Sorting Genetic Algorithm-II). This approach was implemented to calibrate MOBIDIC with its application to the Davidson watershed, North Carolina, with three objective functions, i.e., the standardized root mean square error (SRMSE) of logarithmic transformed discharge, the water balance index, and the mean absolute error of the logarithmic transformed flow duration curve, and its results were compared with those of a single objective optimization (SOO) with the traditional Nelder–Mead simplex algorithm used in MOBIDIC by taking the objective function as the Euclidean norm of these three objectives. Results show that (1) the two sensitivity analysis techniques are effective and efficient for determining the sensitive processes and insensitive parameters: surface runoff and evaporation are very sensitive processes to all three objective functions, while groundwater recession and soil hydraulic conductivity are not sensitive and were excluded in the optimization. (2) Both MOO and SOO lead to acceptable simulations; e.g., for MOO, the average Nash–Sutcliffe value is 0.75 in the calibration period and 0.70 in the validation period. (3) Evaporation and surface runoff show similar importance for watershed water balance, while the contribution of baseflow can be ignored. (4) Compared to SOO, which was dependent on the initial starting location, MOO provides more insight into parameter sensitivity and the conflicting characteristics of these objective functions. Multiobjective sensitivity analysis and optimization provide an alternative way for future MOBIDIC modeling.

Modeling the relationship between wrist angle and muscle thickness during wrist flexion–extension based on the bone–muscle lever system: A comparison study

A structural model of skeletal muscle based on the bone–muscle lever system is proposed to describe the relationship between wrist angle and thickness of the extensor carpi radialis muscle during the process of wrist flexion–extension. This model applied the cosine theorem to the expression for muscle length, in order to relate wrist angle to muscle thickness by the invariance of muscle volume, which was used to calculate the length of the extensor carpi radialis muscle from the muscle thickness. To validate the proposed model, wrist angles were also computed by other models based on regression, such as linear regressions, an artificial neural network, and a support vector machine. The results show that wrist angles are predicted well at different extension rates by our proposed model, with correlation coefficient ( R 2) greater than 0.94, standard root mean square error (SRMSE) less than 8.0 and relative root mean square error (RRMSE) less than 13%. These parameters show that the proposed model is better than the other regression-based models ( p < 0.05). More importantly, this model can be clearly related to physiology. Thus, it can potentially be used to investigate the relationship between internal structural changes of skeletal muscle and external limb behaviors, and to develop prosthetic hands and functional electrical stimulation systems.

Towards Standardization of Dual X-ray Absorptiometry (DXA) at the Forearm

Manufacturer-implemented regions of interest (ROIs) to determine the bone mineral density (BMD) at the forearm are currently not standardized across dual X-ray absorptiometry (DXA) devices. We hypothesized that their differences introduce considerable variation in measurement results for forearm BMD when taken on different devices, and that a ROIs common to all devices with standardized placement and size significantly improve device comparability. The common ROI was defined to have a fixed length of 2 cm and to extend proximally from the location where the ulna and radius bones superimpose on the DXA image. The effects of universal standardization of forearm BMD were combined with and compared to those of the common ROI. They were drawn on 91 female study participants (ages 20-80 years, 10 per decade) who were scanned on Hologic QDR-4500, Aloka DCS-600EX, GE Lunar PIXI and Norland pDEXA DXA scanners. For all device combinations, manufacturer-implemented ROI root mean-square errors were significantly higher than for the common ROI, suggesting that implementing an ROI with common design on all scanners is a good way to reduce interdevice variability. When manufacturer-implemented ROIs were universally standardized root mean-square error (RMSE) values were less different from that of the nonstandardized Common ROI, suggesting that universal standardization can further improve interdevice comparability even when a common ROI such as the one implemented here is used. ROI standardization dramatically improves interdevice comparability.

CONSIDERATIONS IN SELECTING A WATER QUALITY SAMPLING STRATEGY

Water quality monitoring programs have expanded in an effort to quantify loadings to streams and lakes fromvarious watershed activities and managements. At the core of monitoring programs are strategies or schemes that determinewhen and how samples are taken for estimating stream loadings. Quantification of the differences between these schemes hasnot been adequately documented. An analytic approach was used to evaluate 45 commonly used sampling strategies thatincluded timebased (5, 10, 15, 30, 60, 120, 180, 300, and 360 min) and flowstratified (2.5, 5.0, 7.5, 10.0, 12.5, and 15.0 mm)schemes using discrete and composite sampling procedures. A total of 300 storm hydrographs from 87 different watershedsin the U.S. were coupled with two concentration graphs (a 100% positive correlation of concentration to flow, and a 100%negative correlation to flow) to estimate average bias values for each sampling strategy. The mean bias and absolute errorfor timebased sampling, as determined by the standardized root mean square error (SRMSE), always increased with a greatersampling time interval. For timebased sampling, a positive correlated concentration graph generally resulted inunderprediction (positive bias) from the true load, while a negative correlated concentration always resulted inoverprediction (negative bias). For flowstratified sampling, the direction of bias was generally reversed from thetimebased case, but the SRMSE increased with a greater flow interval. Even at the lowest flow interval used in this study(2.5 mm), the median residual values were significantly different from zero (. = 0.05). Time discrete sampling schemes<15min provided the only bias and mean residual values not significantly different from zero (. = 0.05). When an equalnumber of samples was obtained, the flowstratified approach had less absolute error than did the timebased approach. Theresults indicate that, prior to water quality monitoring, careful consideration should be given to the sampling strategy andits overall impact on load estimates.

Estimating distribution parameters using optimization techniques

Abstract An improved parameter estimation procedure has been developed by using optimization techniques and applied to estimate the parameters of the log-Pearson type 3 (LP3) distribution. As a result, an improved estimation method was found. The new methods estimates the mean and the standard deviation of the log-transformed data by the method of moments and estimates the coefficient of skewness by minimizing both the relative root average square error (RRASE) and the relative average bias (RAB). Monte Carlo simulation was conducted for four selected LP3 populations. As compared with the method of moments, larger reductions in standard root mean square error (SRMSE) and standard bias (SBIAS) for quantile prediction can be achieved by the new method for small sample sizes and large return periods of quantiles. In addition, the new method can always fit the observed data better than the method of moments.