Normalized Mean Bias Error Research Articles

A minute-resolution downscaling algorithm for high-resolution global irradiance time series

Numerous studies have demonstrated the significant impact of the resolution of solar irradiation data on the outcomes of hourly production models. Accurate integration of photovoltaic (PV) systems sometimes demands a high-resolution global horizontal irradiance (GHI) time series to capture the rapid fluctuations in PV power output induced by swift irradiance changes. Most of the available databases provide data at hourly resolution, leading to a lack of accuracy in PV simulations. Those existing hourly averages of global horizontal irradiance in open sources fail to represent this volatility adequately, especially when PV systems are coupled with fast ramp rate technologies. In the present work, an easy-to-use algorithm is implemented to synthesize high-resolution GHI time series from hourly averaged and clear sky irradiance datasets. By employing Linear interpolation, a technique that helps to achieve the desired time resolution and afterward computing critical factors, the algorithm identifies periods characterized by short-term weather phenomena, thus creating a high-resolution time series that accurately represents these dynamics. Avoiding the probabilistic components and machine learning techniques conserves computational power and reduces calculation time, but this comes at the cost of reduced fidelity in reproducing the results. Improving accuracy in PV simulations is not always directly related to reproducing real phenomena, but enhancing the amount of information contained in the data is sufficient. This study’s approach enhances user-friendliness and facilitates seamless integration into existing energy modeling frameworks, aiming for representation with sub-hourly time steps. The algorithm’s effectiveness is demonstrated by applying the model to hourly averaged data to revert them to a one-minute time step, and finally comparing the synthetically produced one-minute GHI data to the original measured data. The comparative analysis between synthesized and measured data demonstrated a strong agreement, with normalized mean bias error (MBE) values ranging between 1.8% and 9.6% and normalized root mean square error (NRMSE) values between 2.7% and 16.1%, depending on weather conditions. Additionally, the coefficient of determination (R2) consistently remained above 0.64. Successful algorithm validation makes our algorithm suitable for use in meteorological datasets and locations, with similar climatic characteristics.

Heat transfer characteristics of vertical condensers under unsteady boundary conditions: Dynamic modeling, experiment validation, and parametric analysis

A dynamic model has been developed to predict the coupled heat transfer characteristics of vertical condensers under varying boundary conditions. The model predictions closely matched the experimental data, with normalized mean bias error and root mean square error metrics below 3%. It was observed that variations in the inlet temperature of the secondary-side coolant did not immediately affect the outlet coolant temperature, exhibiting a noticeable lag phase before gradually adjusting to new conditions. Even after the inlet coolant stabilized, the outlet coolant temperature continued to rise until reaching a steady state after a defined period. The dynamic changes in the condensate film thickness and local heat flux density were categorized into three stages: lag, transitional, and steady. These stages showed differing response and transition times across various locations of the condenser. The bottom of the condenser pipeline demonstrated the shortest response time for condensate film thickness variation but the longest transition time. Additionally, the study investigated the influence of geometric parameters on the dynamic response characteristics of condensers. It was found that longer condenser tubes, lower wall thermal diffusivity, and thicker condensing walls resulted in extended transition times for condensate mass flow at the condenser bottom.

Dynamic modelling and optimal operation of the photovoltaic/thermal

This paper aims to introduce a dynamic model for a photovoltaic/thermal system, highlighting an approach and synthesis of existing dynamic models to depict the full photovoltaic/thermal system. The model was validated using data from an experimental setup at the Institute of Energy Technology, Faculty of Energy Technology, University of Maribor, under different weather conditions. The model's accuracy was assessed through normalized Root Mean Square Error, normalized Mean Bias Error, Correlation Coefficient, and the coefficient of determination error metrics, focusing on the temperature and electrical output power of the photovoltaic/thermal modules, as well as the temperature of the thermal energy storage tank. Furthermore, the paper also focuses on the optimal operation of the photovoltaic/thermal system under different mass flow rates of the working medium.

Compressive strength prediction of nano-modified concrete: A comparative study of advanced machine learning techniques

This study aims to develop predictive models for accurately forecasting the uniaxial compressive strength of concrete enhanced with nanomaterials. Various machine learning algorithms were employed, including the backpropagation neural network (BPNN), random forest (RF), extreme gradient boosting (XGB), and a hybrid ensemble stacking method (HEStack). A comprehensive dataset containing 94 data points for nano-modified concrete was collected, with eight input parameters: water-to-cement ratio, carbon nanotubes, nano-silica, nano-clay, nano-aluminum, cement, coarse aggregates, and fine aggregates. To evaluate the performance of these models, tenfold cross-validation and a case study prediction were conducted. It has been shown that the HEStack model is the most effective approach for precisely predicting the properties of nano-modified concrete. During cross-validation, the HEStack method was found to have superior predictive accuracy and resilience against overfitting compared to the stand-alone models. This underscores the potential of the HEStack algorithm in enhancing model performance. In the case study, the predicted results were assessed using metrics such as the coefficient of determination (R2), mean absolute percentage error (MAPE), root mean square error (RMSE), the ratio of RMSE to the standard deviation of observations (RSR), and the normalized mean bias error (NMBE). The HEStack model achieved the lowest MAPE of 2.84%, RMSE of 1.6495, RSR of 0.0874, and absolute NMBE of 0.0064. In addition, it attained a remarkable R2 value of 0.9924, surpassing the R2 scores of 0.9356 (BPNN), 0.9706 (RF), and 0.9884 (XGB), indicating its exceptional generalization capability.

Evaluating the applicability of a machine learning methodology to improve TMY weather file generation for different Canadian climate zones

Typical meteorological year (TMY) weather files are used in building energy simulations to represent typical weather conditions for a location. The conventional approach to generating TMY weather files uses a set of universal weighting factors determined based on expert judgment. These universal weighting factors can overlook the distinct weather patterns between different locations and their influence on energy performance. A previous study used machine learning to generate location-specific weighting factors with respect to building energy performance. The objectives of this paper are: (1) To assess the applicability of the previous study across varying Canadian climates; (2) To investigate the feasibility of using standardized climate zone-based weighting factors to reduce the computational time associated with extracting location-based weighting factors while still considering local climate conditions to facilitate wider adoption of the proposed methodology. The investigation is conducted for a medium office building for 18 locations across six Canadian climate zones and generates two weather files, TMYSTATION and TMYCZ, for each location. The TMYSTATION weather files are generated using location-based weighting factors for each location whereas the TMYCZ weather files are generated using climate zone-based weighting factors for each location. The coefficient of variation of the root mean square error (CVRMSE) and normalized mean bias error (NMBE) are used to compare the performance of the proposed weather files with conventional weather files using the energy demands obtained through building simulation. The TMYSTATION and TMYCZ weather files outperform the conventional weather files in predicting the long-term energy performance of buildings. Although the TMYSTATION files marginally outperform the TMYCZ weather files in representing the long-term weather data, the convenience of standardized climate zone-based weighting factors allows the approach to be widely deployed.

Investigating the Impact of Data Normalization Methods on Predicting Electricity Consumption in a Building Using different Artificial Neural Network Models.

The study investigates the impact of data normalization on the prediction of electricity consumption in buildings using four multilayer Artificial Neural Networks (ANN) algorithms: Long Short-Term Memory Networks (LSTM), Levenberg-Marquardt Back-propagation (LMBP), Recurrent Neural Networks (RNN), and General Regression Neural Network (GRNN). Four data normalization approaches, Min-Max Scaling, Mean, Z-score, and Gaussian function were assessed on experimental datasets. The LSTM algorithm, when combined with Min-Max normalization, showed the most favorable predictive capabilities, with a low Coefficient of Variation of the Root Mean Square Error (CVRMSE) of 10.3 and Normalized Mean Bias Error (NMBE) of 0.6. The remaining three normalization approaches showed satisfactory concordance with empirical data, but with slight disparities in precision. The LMBP model, when using Z-score normalization, had favorable performance in forecasting electricity consumption, but the discrepancies across the models were not significant. The Recurrent Neural Network (RNN) model, when used with Gaussian normalization, exhibited the most favorable performance, with the lowest Coefficient of Variation of Root Mean Square Error (CVRMSE) at 11.8 and Normalized Mean Biased Error (NMBE) at 0.6. The Generalized Regression Neural Network (GRNN) model, trained on unprocessed data, exhibited superior performance, with the lowest Coefficient of Variation of Root Mean Square Error (CVRMSE) at 19.2 and NMBE at 1.0. In conclusion, the study highlights the significant influence of data normalization on the predictive capabilities of various ANN models, suggesting that careful use of data normalization techniques can significantly improve the accuracy of electricity consumption forecasting in buildings.

Calibration of simulation model to analyze hospital building energy performance

This research paper addresses the calibration of an energy simulation model for a naturally ventilated hospital building located in Mangalore, Karnataka, India, in a warm, humid climatic zone. The study aims to enhance the accuracy of energy consumption calculations through a calibration process by developing the energy model of a reference hospital building using EnergyPlus software. The required architectural design data, construction details, occupancy and schedule data and services are collected through documents, energy audits and documentation, measured drawings, and semi-structured interviews. Calibration parameters are systematically identified and adjusted through an iterative process. The monthly electricity bill is used to validate the simulation model. The simulation model reached during the validation process has an excellent Coefficient of Variation-Root Mean Squared Error of 4.24% and a Normalized Mean Bias Error of −4.42%, both of which meet the ASHRAE-approved accuracy standards. The paper also discusses the challenges and emphasizes the need for a nuanced approach to modeling healthcare facilities. Notwithstanding the challenges faced, the study offers insightful information about how to calibrate simulation models for hospital energy usage with the significant influence of scheduling for artificial lighting and equipment usage. By pioneering a manual calibration approach tailored to hospital simulation models in the warm humid climate of India, this paper offers a novel and practical solution to address the challenges of energy performance analysis in resource-constrained environments. The calibrated simulation model presented in this study is a valuable tool for assessing and improving the energy performance of naturally ventilated healthcare facilities. By creating alternative space layouts, the research findings aim to foster the development of hospital infrastructure that is both ecologically friendly and energy-efficient in a specific climatic context. This research is assured to make a substantial contribution to the advancement of sustainable hospital design in warm-humid climates, with implications for both academia and industry.

Comparative study and validation of a new analytical method for hydraulic modelling of bidirectional low temperature networks

Bidirectional Low Temperature Networks (BLTNs) are an innovative technology of district heating and cooling systems. Because of their intrinsic feature of supplying simultaneous heating and cooling either directly from an energy source/sink or through distributed heat pumps and chillers, circulation pumps installed at each building extract water from the network and a distinct pressure cone is subsequently created. Variations in the amount (and direction) of the extracted water call for accurate hydraulic design and analysis to ensure safe and adequate network operation. This paper proposes a new analytical solution method for fast hydraulic modelling of BLTNs. The analytical method was compared against three numerical solution methods and validated using different current and future operating scenarios of a real-world bidirectional network. In all modelled cases, the calculated mass flows and pressure drops using the new analytical method yielded very small Normalised Mean Bias Error (NMBE) and Coefficient of Variation of the Root Mean Square Error (CV(RMSE)), suggesting excellent agreement between the analytical and numerical solution methods. The new analytical method offers better performance over its numerical counterparts due to its explicit nature, ease of implementation, and quick modelling time.

In-situ virtual heat flow meter model for monitoring heat flux of existing building envelope

In the building sector, remodeling of existing buildings that have low energy efficiency is a required strategy to achieve carbon neutrality. To establish a cost-effective remodeling strategy for existing buildings, accurate measurement of the thermal insulation performance of existing building envelopes is necessary. In general, to evaluate the insulation performance of a building envelope, the U-value is calculated based on the heat flux measured using a heat flow meter, which is an expensive physical sensor. This study developed an in-situ virtual heat flow meter (vHFM) model that can replace existing heat flow meter sensors. The in-situ vHFM model satisfied ASHRAE Guideline 14 with an R2 of 0.989, coefficient of variation root mean square error of 15.24%, and normalized mean bias error of −0.06% compared to the data measured using a traditional sensor. In addition, the validation through two case studies demonstrated that the field applicability of the in-situ vHFM model was very high.

Identifying and ranking of CMIP6-global climate models for projected changes in temperature over Indian subcontinent

Selecting the best region-specific climate models is a precursor information for quantifying the climate change impact studies on hydraulic/hydrological projects and extreme heat events. A crucial step in lowering GCMs simulation-related uncertainty is identifying skilled GCMs based on their ranking. This research performed a critical assessment of 30 general circulation models (GCMs) from CMIP6 (IPCC’s sixth assessment report) for maximum and minimum temperature over Indian subcontinent. The daily temperature data from 1965 to 2014 were considered to quantify maximum and minimum temperatures using a gridded spatial resolution of 1°. The Nash–Sutcliffe efficiency (NSE), correlation coefficient (CC), Perkins skill score (PSS), normalized root mean square error (NRMSE), and absolute normalized mean bias error (ANMBE) were employed as performance indicators for two different scenarios, S1 and S2. The entropy approach was used to allocate weights to each performance indicator for relative ranking. Individual ranking at each grid was achieved using a multicriteria decision-making technique, VIKOR. The combined ranking was accomplished by integrating group decision-making, average ranking perspective, and cumulative percentage coverage of India. The outcome reveals that for S1 and S2, NRMSE and NSE are the most significant indicators, respectively whereas CC is the least significant indicator in both cases. This study identifies ensemble of KIOST-ESM, MRI-ESM2-0, MIROC6, NESM3, and CanESM5 for maximum temperature and E3SM-1-0, NESM3, CanESM5, GFDL-CM4, INM-CM5-0, and CMCC-ESM2 for minimum temperature.

Development and performance evaluation of intelligent algorithm for optimal control of a hybrid heat pump system during the cooling season

The purpose of this study is to develop a control method for a hybrid heat pump system based on an artificial neural network (ANN) to reduce energy use and create a more comfortable thermal environment. The proposed optimal control method uses an ANN-based predictive model to predict the heat storage tank and indoor temperature during the cooling period and controls the flow rate of the circulation pump on the heat source and load side of the system. The performance of the predictive model for the heat storage tank temperature (R2 = 0.9988; coefficient of variation of the root mean square error [CV(RMSE)] = 1.06 %; normalized mean bias error [NMBE] = 0.16 %; and mean absolute error [MAE] = 0.09℃) and the indoor temperature (R2 = 0.9893; CV(RMSE) = 1.66 %; NMBE = 0.16 %; and MAE = 0.15℃) was excellent. The temperature control of the heat storage tank using the optimal algorithm exhibited an improvement of 18.39 % for the CV(RMSE), 3.10 % for the NMBE, and 1.31 °C for MAE compared with rule-based. For the indoor temperature, the optimal algorithm improved the CV(RMSE) by 1.30 %, NMBE by 0.42 %, and MAE by 0.29℃ compared to rule-based. The energy use was reduced by 52.85 % for the entire system using the optimal control method compared with the existing control strategy under similar outdoor conditions. Using the proposed control method, it is thus possible to improve thermal comfort and reduce carbon emissions in the building sector by improving the control and energy performance of hybrid heat pump systems.

Variable refrigerant flow heat pump model with estimated parameters and emulated controller based on manufacturer data

A new physics-based and modular variable refrigerant flow (VRF) heat pump model aimed toward multi-year simulations is presented. The model allows the simulation of any number of indoor units (IU), outdoor units (OU) and compressors. A parameter-estimation procedure and a control strategy both using available manufacturer data is proposed. The model is validated against data collected from a VRF system that services the first floor of the former ASHRAE Headquarters Building in Atlanta (USA), comprised of 22 IU, 2 OU, and 8 compressors. Results show that the model accurately predicts the total energy consumption over a two-month cooling period, with a relative error, normalized mean bias error, and coefficient of variation of the root mean square error of 1%, 1.6%, and 16.7%, respectively.

A two-stage optimization method for improving the load flexibility of existing district energy systems

Decarbonization of district energy systems is essential for China to meet its carbon neutrality goal by 2060. Most existing district energy systems are missing historical load data and have incomplete information, resulting in a lack of data support for the low-carbon transition. Moreover, demand-side load flexibility has not been fully exploited in the planning stage. In this paper, we developed a two-stage computational approach to optimize district loads. We first established an integrated Python framework, incorporating the TEASER simulation tool and AixLib model library, to efficiently calculate baseline loads through the bottom-up modeling and simulation of district buildings. Then, a price-based integrated demand response strategy was introduced. A mixed-integer nonlinear programming model was formulated to optimize the energy pricing strategy with the objective of minimum load fluctuations. Finally, a case study was employed to illustrate the feasibility of the calculation method, showing a normalized mean bias error of 7.17%. The results further demonstrated that the strategy could reduce the peak electric and heat loads by 3.55% and 9.57%, and increase load rates by 3.85% and 9.48%, respectively. The strategy could assist district energy service providers to optimize equipment capacity configuration and enhance the low-carbon planning potential of energy systems from the demand-side.

Evaluation of the global solar irradiation from the artificial neural network technique

In this study, many experiments were carried out to assess the influence of the some input parameters on performance of the multilayer perceptron techniques, which is architectures one of the artificial neural network (ANN). To estimate the daily global solar irradiation (GSI) on horizontal surface, we have developed eight models by using four weather input parameters collected from a radiometric station installed at Ghardaia site (southern of Algeria), such as sunshine duration, daily mean temperature, daily relative humidity, and Solar declination. In order to select the best configuration among the chooses combinations which provides a good accuracy, three statistical formulas (or statistical indicators) have been evaluated, such as the normalized root mean square errors, (nRMSE), normalized mean bias error (nMBE, and coefficient of determination R²). We noted that the ANN model provides best performance compared to the developed empirical models. results of the nMBE, nRMSE, and R² are about 0.048%, 4.422%, and 98.00%, for ANN and 0.0772%, 5.5381%, and 97.22% for the quadratic model. Moreover, it was proved that the sunshine duration is important parameter, for predicting the GSI.

Enhanced Operation of Ice Storage System for Peak Load Management in Shopping Malls across Diverse Climate Zones

There exists a notable research gap concerning the application of ice storage systems in shopping mall settings at the urban scale. The characteristics of large pedestrian flow, high energy consumption, and high peak loads in shopping malls make their advantages in energy conservation. This study researches sustainable cooling solutions by undertaking an economic analysis of the ice storage systems within shopping malls across 11 distinct cities, each system operating under varied electricity pricing frameworks. The methodology begins with creating baseline mall models using AutoBPS and refining them with OpenStudio. Before starting to adjust the model, measured data were used to verify the accuracy of the baseline model, the coefficient of variation of the root mean square error (CVRMSE) and normalized mean bias error (NMBE) metrics were calculated for the model energy consumption, with CVRMSE values of 8.6% and NMBE values of 1.57% for the electricity consumption, while the metrics for the gas consumption were 12.9% and 1.24%, respectively. The study extends its inquiry to encompass comprehensive economic evaluations based on the unique electricity pricing of each city. This rigorous assessment discerns the relationship between capacity, operational strategies, and economic performance. Particularly striking are the so-called peak-shaving and valley-filling effects verified in regions characterized by lower latitudes and substantial cooling loads. The interaction between ice storage capacity and operational schedules significantly influences both economic viability and cooling efficiency. Based on the temporal dynamics of time-of-use (TOU) power pricing, a finely calibrated operational schedule for the ice storage system is proposed. This operational strategy entails charging during periods of reduced electricity pricing to undertake cooling loads during peak electricity pricing intervals, culminating in substantial reductions in electricity charges of buildings. Moreover, the strategic reallocation of energy, characterized by a reduced chiller capacity and a corresponding elevation in ice storage system capacity, augments cooling efficiency and diminishes cooling-related electricity expenses. This study offers valuable insights for optimizing and deploying ice storage systems in diverse climatic regions, particularly for shopping malls. As a guiding reference, this paper provides stakeholders with a framework to reasonably apply and adjust ice storage systems, ushering in an era of energy-efficient and environmentally conscious cooling solutions tailored to shopping mall environments.

Global and direct solar irradiance estimation using deep learning and selected spectral satellite images

To fully exploit the spectral information of modern geostationary satellites, this work proposes a deep learning framework using convolutional neural networks (CNNs) and attention mechanism for 5-min ground-level global horizontal irradiance (GHI) and direct normal irradiance (DNI) estimations. The inputs are spectral satellite images with the target ground station in the center, and the labels are irradiance measurements normalized by their clear-sky estimations. The use of CNNs and attention mechanism aims to better extract the spatial information for estimating ground-level solar irradiance. To improve the modeling efficiency, only a subset of spectral bands is selected based on correlation analysis, which has comparable performance with the usage of all satellite bands. The results show that the proposed method produces GHI estimation with a normalized root mean squared error (nRMSE) of 20.57% and a normalized mean bias error (nMBE) of −2.04%, and the DNI estimation has an nRMSE of 23.63% and the nMBE is 0.36%. Compared with the national solar radiation database (NSRDB), GHI and DNI estimations of the proposed method has the nRMSE reduction of 5.15% and 13.77%, respectively. Meanwhile, the proposed models generally yield better GHI and DNI estimations under different intervals of clear-sky index than NSRDB. The combination of deep learning and remote sensing shows potential in better extracting the cloud information via multispectral satellite images, which can better support solar resource assessment, especially for cloudy conditions.

Assessment of a New Solar Radiation Nowcasting Method Based on FY-4A Satellite Imagery, the McClear Model and SHapley Additive exPlanations (SHAP)

The global warming effect has been accelerating rapidly and poses a threat to human survival and health. The top priority to solve this problem is to provide reliable renewable energy. To achieve this goal, it is important to provide fast and accurate solar radiation predictions based on limited observation data. In this study, a fast and accurate solar radiation nowcasting method is proposed by combining FY-4A satellite data and the McClear clear sky model under the condition of only radiation observation. The results show that the random forest (RF) performed better than the support vector regression (SVR) model and the reference model (Clim-Pers), with the smallest normalized root mean square error (nRMSE) values (between 13.90% and 33.80%), smallest normalized mean absolute error (nMAE) values (between 7.50% and 24.77%), smallest normalized mean bias error (nMBE) values (between −1.17% and 0.7%) and highest R2 values (between 0.76 and 0.95) under different time horizons. In addition, it can be summarized that remote sensing data can significantly improve the radiation forecasting performance and can effectively guarantee the stability of radiation predictions when the time horizon exceeds 60 min. Furthermore, to obtain the optimal operation efficiency, the prediction results were interpreted by introducing the latest SHapley Additive exPlanation (SHAP) method. From the interpretation results, we selected the three key channels of an FY-4A and then made the model lightweight. Compared with the original input model, the new one predicted the results more rapidly. For instance, the lightweight parameter input model needed only 0.3084 s (compared to 0.5591 s for full parameter input) per single data point on average for the 10 min global solar radiation forecast in Yuzhong. Meanwhile, the prediction effect also remained stable and reliable. Overall, the new method showed its advantages in radiation prediction under the condition that only solar radiation observations were available. This is very important for radiation prediction in cities with scarce meteorological observation, and it can provide a reference for the location planning of photovoltaic power stations.

Comparison of Models to Evaluate Daily Available Energy with Photovoltaic Array at Sirinka, Ethiopia

Abstract: Background: Energy utilization in Ethiopia is mainly based on traditional biomass, which causes indoor air pollution, especially for women and children (causing acute lower respiratory infection) living in rural areas. Objective: This research was conducted to assess the performance of six empirical models for estimation of daily global solar radiation (DGSR) at Sirinka sites to evaluate daily available energy with photovoltaic (PV) array and energy available to the load (energy demand) and battery (energy-storage device). Materials and Methods: In this study, sunshine hours, minimum and maximum temperatures were obtained from Kombolcha Meteorological Agency. Ms-Excel 2010 was employed as a descriptive statistics tool and MATLAB 2013a was used as software to plot the analyzed data. Results: According to the statistical performance evaluation metrics, such as normalized mean bias error (NMBE) and normalized root mean square error (NRMSE), Angstrom Prescott model (AP), Louche model (LO) and Hargreaves model (H) performed best in order. The smallest daily mean power delivered to PV and the daily mean energy available to the load (energy demand) and battery (energy-storage device) were 288.11 W/m2 and 248.92 W/m2 sequenced and the largest mean power delivered to the PV and the mean energy available to the load and battery were 851.57 W/m2 and 735.76 W/m2 in order on April-10 for the study period of 2014–2018. Conclusion The result of this work showed high solar energy potential and therefore, rural electrification using PV system is possible in the study area and can reduce health problems due to indoor pollution in the future. Keywords: Daily global solar radiation, Empirical Model, environmentally friendly, Renewable Energy, Solar Power, Sunshine, Temperature, Photovoltaic.

Evaluation of CMIP6 Models Skill in Representing Annual Extreme Precipitation over Northern and Southern Nigeria

In this study, we evaluate the performance of 13 climate models from phase 6 of the Coupled Model Intercomparison Project (CMIP6) in simulating seven (7) extreme precipitation indices over Northern and southern Nigeria. The considered extreme indices designated in this study were, Total precipitation (PRCPTOT), maximum consecutive wet days (CWD), Heavy precipitation days (R10mm), Very heavy precipitation days (R20mm), Max-5 days Precipitation (RX5day), Extremely wet days (R99pTOT) and Very wet days (R95pTOT). The performance of these 13 climate models are assesed by comparing the model simulation to the observed dataset from the Global Precipitation Climatology Project (GPCP). The performance of CMIP6 models in capturing extreme precipitation characteristics is revealed through some selected multiple descriptive statistics: the normalized mean bias error, RMSE, NRMSE, and Taylor diagram. The descriptive statistics conclusively revealed the satisfactory performance of Cmip6 models in simulation of most extreme events over the north and southern region of Nigeria, as the selected 13 climate models showed a high statistical correlation of (~0.8) when compared with the observed GPCP data except for maximum consecutive wet days (CWD). Overall, majority of CMIP6 models were able to accurately represented only six (6) of the extreme indices, and a significant majority of CMIP6 models failed in simulating maximum consecutive wet days (CWD) in both northern and southern Nigeria.

A transferable turbidity estimation method for estimating clear-sky solar irradiance

A transferable turbidity estimation method is proposed for estimating the turbidity and clear-sky solar irradiance. Instead of using on-site irradiance measurements (i.e., the local model), a transferable model is developed involving stations with sufficient information, and then applied at locations with limited data availability. Compared with the local method, the transferable model yields results with slightly higher discrepancies regrading normalized root mean squared error (nRMSE, 2.80% vs 2.75%). When compared with the Ineichen–Perez (PVLIB) model, the nRMSE of clear-sky global horizontal irradiance (GHIcs) estimation is reduced from 4.99% to 2.44%, and the normalized mean bias error (nMBE) is improved from -3.37% to 0.57%. The GHIcs estimation is comparable with physical models (i.e., McClear and REST2), where the McClear produces a nRMSE of 3.32% and the nMBE is 2.10%, while the REST2 generates results with an nRMSE of 2.55% and an nMBE of 1.30%. We further compare aforementioned models for day-ahead GHIcs forecasts using a day persistent way. GHIcs forecast from the transferable method has slightly lower discrepancies of nRMSE and nMBE than the physical models. Considering the complexity of physical models, the transferable turbidity estimation method with comparable performance demonstrates valuable potential for solar resourcing and forecasting applications.