Estimation of wind speed using regional frequency analysis based on linear‐moments

In the first part of this study, five homogeneous regions in view of topographical and geographically homogeneous aspects except Jeju and Ulreung islands in Korea were accomplished by K-means clustering method. A total of 57 rain gauges were used for the regional frequency analysis with minimum rainfall series for the consecutive durations. Generalized Extreme Value distribution was confirmed as an optimal one among applied distributions. Drought rainfalls following the return periods were estimated by at-site and regional frequency analysis using L-moments method. It was confirmed that the design drought rainfalls estimated by the regional frequency analysis were shown to be more appropriate than those by the at-site frequency analysis. In the second part of this study, LH-moment ratio diagram and the Kolmogorov-Smirnov test on the Gumbel (GUM), Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distributions were accomplished to get optimal probability distribution. Design drought rainfalls were estimated by both at-site and regional frequency analysis using LH-moments and GEV distribution, which was confirmed as an optimal one among applied distributions. Design rainfalls were estimated by at-site and regional frequency analysis using LH-moments, the observed and simulated data resulted from Monte Carlotechniques. Design drought rainfalls derived by regional frequency analysis using L1, L2, L3 and L4-moments (LH-moments) method have shown higher reliability than those of at-site frequency analysis in view of RRMSE (Relative Root-Mean-Square Error), RBIAS (Relative Bias) and RR (Relative Reduction) for the estimated design drought rainfalls. Relative efficiency were calculated for the judgment of relative merits and demerits for the design drought rainfalls derived by regional frequency analysis using L-moments and L1, L2, L3 and L4-moments applied in the first report and second report of this study, respectively. Consequently, design drought rainfalls derived by regional frequency analysis using L-moments were shown as more reliable than those using LH-moments. Finally, design drought rainfalls for the classified five homogeneous regions following the various consecutive durations were derived by regional frequency analysis using L-moments, which was confirmed as a more reliable method through this study. Maps for the design drought rainfalls for the classified five homogeneous regions following the various consecutive durations were accomplished by the method of inverse distance weight and Arc-View, which is one of GIS techniques.

Rainfall frequency analyses for four cities namely Benin City, Port Harcourt, Calabar and Uyo in Nigeria's Niger Delta area were carried out utilizing daily rainfall data from the yearly maxima series for 48 years (1965 – 2012) at each location. The study's goal was to identify the probability distribution model that fit the data the best and applicable to each location from among six candidate probability distribution models namely: Pearson Type III (PIII), log Normal (LN), log Pearson Type III, Generalized Extreme value (GEV), Extreme value type I (EVI), and Generalized Pareto (GPA). The method of moments (MOM) was used to estimate the distributions' parameters applying the outcomes of seven goodness of fit tests, the most optimal fit distribution model was chosen for each site namely Root Mean Squared Error (RMSE), Relative Root Mean Square Error (RRMSE), Maximum Absolute Derivation Index (MADI), Chi–Square etc. The best distribution model at each location was utilized to predict rainfall of desired return periods. Based on our findings, PIII for Benin City, GEV for Port Harcourt, GEV for Calabar and EVI and LN for Uyo are the distribution models that suit the data the best., The Best Fit Probability Distribution Model predicted rainfall return values (RT) at 200 years return period ranging from192.92mm at Uyo, 185mm at Port Harcourt; 218mm for Benin City; and 245 mm at Calabar.. The study's findings are helpful in the planning, designing, and maintaining of hydraulic structures for preventing flood damage and mitigating floods at the locations

The choice of optimum probability distribution model that would accurately simulate flood discharges at a particular location or region has remained a challenging problem to water resources engineers. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the quantile - probability relationship for planning, design and management of water resources systems, risk assessment in flood plains and flood insurance. This paper presents the evaluation of five probability distributions models: Gumbel (EV1), 2-parameter lognormal (LN2), log pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of five hydrological stations in the lower Niger River Basin in Nigeria. The choice of optimum probability distribution model was made on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR), and probability plot correlation coefficient (PPCC). The results show that GEV is the optimum distribution in 3 stations, and LP3 in 2 stations. On the overall GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. Furthermore, GEV simulated discharges were in closest agreement with the observed flood discharges. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

The error and bias of supplementing a short, arid climate, rainfall record with regional vs. global frequency analysis

The LQ-moment proposed by Mudholkar, et al. (1998) is used for regional flood frequency analysis of the North-Bank region of the river Brahmaputra, India. Five probability distributions are used for the LQmoment: generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA), lognormal (LN3) and Pearson Type III (PE3). The same regional frequency analysis procedure proposed by Hosking (1990) for the L-moment is used for the LQ-moment. Based on the LQ-moment ratio diagram and |Zidist| -statistic criteria, the PE3 distribution is identified as the robust distribution for the study area. For estimation of floods of various return periods for both gauged and ungauged catchments of the study area, regional flood frequency relationships are developed using the LQ-moment based PE3 distribution.

Regional Rainfall Frequency Analysis for the Luanhe Basin – by Using L-moments and Cluster Techniques

ABSTRACTThe normalized difference vegetation index (NDVI) is a commonly used index for monitoring crop growth status. Previous studies have shown that the leaf area index (LAI) estimation based on NDVI is limited by saturation that occurs under conditions of relatively dense canopies (LAI > 2 m2 m–2). To reduce the saturation effect, we suggested new spectral indices through the spectral indices approach. The results suggested that the two-band normalized difference spectral index (NDSI = ((ρ940 – ρ730) /(ρ940 + ρ730))) resulted from the two-band spectral indices approach and the three-band modified normalized difference spectral index (mNDSI = ((ρ940 – 0.8 × ρ950) – ρ730) /((ρ940 – 0.8 × ρ950) + ρ730)) resulted from the three-band spectral indices approach, and they were able to mitigate saturation and improve the LAI prediction with a determination coefficient (R2) of 0.77 and 0.78, respectively. In the validation based on data from independent experiments, these new indices exhibited an accuracy with relative root mean square error (RRMSE) lower than 23.38% and bias higher than –0.40. These accuracies were significantly higher than those obtained with some existing indices with good performance in LAI estimation, such as the enhanced vegetation index (EVI) (RRMSE = 30.19%, bias = –0.34) and the modified triangular vegetation index 2 (MTVI2) (RRMSE = 29.30%, bias = –0.28), and the indices with the ability to mitigate the saturation, such as the wide dynamic range vegetation index (WDRVI) (RRMSE = 31.37%, bias = –0.54), the red-edge wide dynamic range vegetation index (red-edge WDRVI) (RRMSE = 26.34%, bias = –0.54), and the normalized difference red-edge index (NDRE) (RRMSE = 28.41%, bias = –0.56). Additionally, these new indices were more sensitive under moderate to high LAI conditions (between 2 and 8 m2 m–2). Between these two new developed spectral indices, there was no significant difference in the accuracy and sensitivity assessments. Considering the index structure and convenience in application, we demonstrated that the two-band spectral index NDSI((ρ940 – ρ730) /(ρ940 + ρ730)) is efficient in mitigating saturation and has considerable potential for estimating the LAI of canopies throughout the entire growing season of wheat (Triticum aestivum L.), whereas the three-band spectral index contributes lesser in the saturation mitigation provided the red-edge band has been contained.

An approach based on regional frequency analysis using L moments and LH moments are revisited in this study. Subsequently, an alternative regional frequency analysis using the partial L moments (PL moments) method is employed, and a new relationship for homogeneity analysis is developed. The results were then compared with those obtained using the method of L moments and LH moments of order two. The Selangor catchment, consisting of 37 sites and located on the west coast of Peninsular Malaysia, is chosen as a case study. PL moments for the generalized extreme value (GEV), generalized logistic (GLO), and generalized Pareto distributions were derived and used to develop the regional frequency analysis procedure. PL moment ratio diagram and Z test were employed in determining the best-fit distribution. Comparison between the three approaches showed that GLO and GEV distributions were identified as the suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation used for performance evaluation shows that the method of PL moments would outperform L and LH moments methods for estimation of large return period events.

Abstract. This paper examines various geometric shapes to determine the most suitable one for calculating tree crown area in field measurements. The study was conducted in an Eldarica pine plantation forest, which was digitally mapped using RGB images captured by a Phantom 4 Pro drone. Tree crowns were manually digitized (MD) from these images to serve as reference data. Field measurements, including the large and small crown diameters, were collected to evaluate crown areas derived from different geometric shapes. The geometric shapes considered were: Oval with Both Diameters (OBD), Circle with Small Diameter (CSD), Circle with Large Diameter (CLD), and Circle with Mean Diameters (CMD). Three analyses were performed to assess the results: correlation analysis (R2), relative root mean square error (RRMSE), and shape analysis, which included overestimation (OverID) and underestimation (UnderID) indices. The results revealed that the choice of geometric shape significantly impacts the accuracy of crown area calculations. The OBD model based on the outer boundary diameter yielded the best results with RRMSE = 0.29, R2 = 0.84, OverID = 0.18, and UnderID = 0.23, followed closely by the CMD method. In contrast, the CSD and CLD models performed less effectively, with RRMSE = 0.52, R2 = 0.42, OverID = 0.11, UnderID = 0.35 (CSD), and RRMSE = 0.59, R2 = 0.37, OverID = 0.46, UnderID = 0.22 (CLD). These differences in performance are likely due to the inclusion of empty spaces within the crown area in some models. However, the findings of this study are not universally applicable to all tree crown area calculations. The geometric shape used for crown area estimation must align with the structural characteristics of the forest and the specific geometry of the tree species under consideration.

Information related to distributions of rainfall amounts are of great importance for designs of water-related structures. One of the concerns of hydrologists and engineers is the probability distribution for modeling of regional data. In this study, a novel approach to regional frequency analysis using L-moments is revisited. Subsequently, an alternative regional frequency analysis using the TL-moments method is employed. The results from both methods were then compared. The analysis was based on daily annual maximum rainfall data from 40 stations in Selangor Malaysia. TL-moments for the generalized extreme value (GEV) and generalized logistic (GLO) distributions were derived and used to develop the regional frequency analysis procedure. TL-moment ratio diagram and Z-test were employed in determining the best-fit distribution. Comparison between the two approaches showed that the L-moments and TL-moments produced equivalent results. GLO and GEV distributions were identified as the most suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation was used for performance evaluation, and it showed that the method of TL-moments was more efficient for lower quantile estimation compared with the L-moments.

Determination of the extent of peak rainfall for different return periods is an essential ingredient for the accurate design of hydraulic structures such as drains, dams and culverts as well as detection of flood risk areas. The focus of this study is to analyze annual maximum daily rainfall series in some selected sites within the coastal region of Nigeria using three parameter probability distribution models, namely, Generalized Logistics (GLO), Generalized Extreme Value (GEV) and Generalized Pareto (GPA) with the view of identifying the best fit probability distribution model per station that can be employed to estimate the rainfall magnitude for selected return periods. Specific time series analysis test, namely, detection of outlier and homogeneity test were performed to certify that the data utilized are adequate and suitable. Descriptive statistics such as sample mean, variance, standard deviation, kurtosis, skewness, and coefficient of variation were computed using basic statistical equations. The probability weighted moment parameters (b0, b1, b2 and b3), L-moment values (λ1, λ2, λ3 and λ4) and ratios (τ2, τ 3 and τ4) including the distribution parameters, namely, shape (k), scale (α) and location (ξ) parameters were computed based on L-moments procedures. To select the best-fit probability distribution model per station, carefully chosen goodness-of-fit statistics, namely, root mean square error, relative root mean square error, maximum absolute deviation index, maximum absolute error and probability plot correlation coefficient were employed since they can adequately assess the fitted distribution at a site. Results obtained indicate that the GLO is the best fit distribution for analyzing annual maximum daily rainfall series from Warri and Calabar while GPA for Port Harcourt and Uyo.

Abstract. A dual-lidar system comprising two WindCube v2.1 Doppler lidars – one oriented horizontally at a 45° angle relative to the other – was deployed to estimate atmospheric turbulence using the variance method. This approach derives second-order velocity statistics directly from line-of-sight (LOS) velocity variances, enabling the reconstruction of the three-dimensional velocity variance components without retrieving instantaneous wind vectors. Its performance is evaluated against the traditional method commonly used in the wind energy sector, which reconstructs instantaneous velocity components from single-lidar LOS measurements prior to computing turbulence statistics. Both methods are assessed at a single measurement height using a 30 d collocated dataset, with sonic anemometer measurements as reference and classification by atmospheric stability. The analysis focuses on turbulence intensity (TI), and performance is quantified using the mean relative bias error (MRBE) and relative root mean square error (RRMSE), following Det Norske Veritas (DNV) load-validation acceptance criteria (MRBE within ±5 % and RRMSE ≤ 15 %). Results show that the variance method demonstrates improved agreement with the reference measurements across nearly all wind-speed bins. For along-wind TI, MRBE values range between 0 % and −5 %, with RRMSE remaining below 15 % over the full wind-speed range, fully satisfying the DNV criteria. For cross-wind TI, the MRBE criterion is met, while the RRMSE threshold is exceeded. In contrast, the traditional method meets both DNV criteria for along-wind TI only at wind speeds above approximately 7 m s−1 and fails to satisfy either criterion for cross-wind TI across the investigated range. Overall, the results demonstrate that the variance method provides more robust and DNV-compliant TI estimates than the traditional reconstruction approach, particularly for along-wind turbulence relevant to wind turbine load validation.

Soil pH is a key factor that controls soil nutrient availability, soil microbial activities, and crop growth and development. However, studies on the soil pH variations of cultivated lands in different horizons at the regional scale remain limited. In this work, 348 soil samples were collected from three soil horizons (A, B, and C) at 120 sites over the hilly region of Chongqing, southwestern China. Six topographic indicators, four climate parameters, and parent material were considered. Classification and regression trees (CARTs) were applied to investigate the relationships between soil pH and the variables in the A, B, and C horizons. Model performances were evaluated by root mean square error (RMSE), relative root mean square error (RRMSE), and coefficient of determination (R2). Results showed that soil pH increased obviously from the A to C horizons. Soil pH was predicted well by the forcing factors with the CART models in all horizons. RMSE, RRMSE, and R2 varied between 0.37 and 0.435, between 5.93 and 7.23%, and between 0.71 and 0.80, respectively. The relative importance of the studied variables to soil pH differed with the horizons. Annual temperature range (ATR), terrain wetness index (TWI), and Melton ruggedness number were critical factors that controlled soil pH variability in the A horizon. Parent material, precipitation of warmest quarter (PWQ), ATR, and TWI were important variables in the B horizon. Parent material, PWQ, ATR, and precipitation were key factors in the C horizon. The results are expected to provide valuable information for designing appropriate measurements for agricultural practices and preventing soil acidification.

Unsaturated zone N fate and transport were evaluated at four sites to identify the predominant pathways of N cycling: an almond [Prunus dulcis (Mill.) D.A. Webb] orchard and cornfield (Zea mays L.) in the lower Merced River study basin, California; and corn-soybean [Glycine max (L.) Merr.] rotations in study basins at Maple Creek, Nebraska, and at Morgan Creek, Maryland. We used inverse modeling with a new version of the Root Zone Water Quality Model (RZWQM2) to estimate soil hydraulic and nitrogen transformation parameters throughout the unsaturated zone; previous versions were limited to 3-m depth and relied on manual calibration. The overall goal of the modeling was to derive unsaturated zone N mass balances for the four sites. RZWQM2 showed promise for deeper simulation profiles. Relative root mean square error (RRMSE) values for predicted and observed nitrate concentrations in lysimeters were 0.40 and 0.52 for California (6.5 m depth) and Nebraska (10 m), respectively, and index of agreement (d) values were 0.60 and 0.71 (d varies between 0 and 1, with higher values indicating better agreement). For the shallow simulation profile (1 m) in Maryland, RRMSE and d for nitrate were 0.22 and 0.86, respectively. Except for Nebraska, predictions of average nitrate concentration at the bottom of the simulation profile agreed reasonably well with measured concentrations in monitoring wells. The largest additions of N were predicted to come from inorganic fertilizer (153-195 kg N ha(-1) yr(-1) in California) and N fixation (99 and 131 kg N ha(-1) yr(-1) in Maryland and Nebraska, respectively). Predicted N losses occurred primarily through plant uptake (144-237 kg N ha(-1) yr(-1)) and deep seepage out of the profile (56-102 kg N ha(-1) yr(-1)). Large reservoirs of organic N (up to 17,500 kg N ha(-1) m(-1) at Nebraska) were predicted to reside in the unsaturated zone, which has implications for potential future transfer of nitrate to groundwater.

Soil water content (SWC) is an important factor restricting crop growth and yield in cropland ecosystems. The observation and simulation of soil moisture contribute greatly to improving water-use efficiency and crop yield. This study was conducted at the Shandong Yucheng Agro-ecosystem National Observation and Research Station in the North China Plain. The study period was across the winter wheat (Triticum aestivum L.) growth stages from 2017 to 2019. A cosmic-ray neutron probe was used to monitor the continuous daily SWC. Furthermore, the crop leaf area index (LAI), yield, and aboveground biomass of winter wheat were determined. The root zone quality model 2 (RZWQM2) was used to simulate and validate the SWC, crop LAI, yield, and aboveground biomass. The results showed that the simulation errors of SWC were minute across the wheat growth stages and mature stages in 2017–2019. The root mean square error (RMSE) and relative root mean square error (RRMSE) of the SWC simulation at the jointing stage of winter wheat were 0.0296 and 0.1605 in 2017–2018, and 0.0265 and 0.1480 in 2018–2019, respectively. During the rain-affected days, the RMSE (0.0253) and RRMSE (0.0980) for 2017–2018 were significantly lower than those of 2018–2019 (0.0301 and 0.1458, respectively), indicating that rain events decreased the model accuracy in the dry years compared to the wet years. The simulated LAIs were significantly higher than the measured values. The simulated yield value of winter wheat was 5.61% lower and 3.92% higher than the measured yield in 2017–2018 and in 2018–2019, respectively. The simulated value of aboveground biomass was significantly (45.48%) lower than the measured value in 2017–2018. This study showed that, compared with the dry and cold wheat growth period of 2018–2019, the higher precipitation and temperature in 2017–2018 led to a poorer simulation of SWC and crop-growth components. This study indicated that annual abnormal rainfall and temperature had a significant influence on the simulation of SWC and wheat growth, especially under intensive climate-change stress conditions.