Rain Drop Research Articles

Proposal and design a comprehensive framework to provide water and energy from rain and precipitation

In this paper a new renewable energy source was proposed based on rain power. Rain energy was not used as an energy source up to now; so, in this research its applicability was investigated as a green large scale power source. Hence, three innovative mechanisms were presented to harvest the energy of rain. Firstly, the kinetic energy of rain drops was converted to electricity using piezoelectric harvesters designed and named as Pizo-panel collectors. Secondly, potential energy of collected rainwater was enhanced by utilizing designed towers and converted to electricity using a water turbine. Thirdly, collected water was used in osmotic power units to generate electricity from the salinity gradient of that rain water and brine. The results show that generated power in the presented power plant named as rain power plant, was considerable and can be used for diversifying of energy basket. In addition to power generation, collected water in the rain power plant can be used for supplying urban and agricultural need for water. The presented power source not only does not have destructive impacts on the environment, but also helps the soil to prevent it from splash and crusting erosion. The results showed that total global annual rain energy potential amount was estimated to be 3.44×108 GWh which is comparable with global potential of solar energy. Also, the results showed that for rainy areas with an annual rainfall of 200 cm, 2.59 kWh/m2 could be produced, which is equal to 51.7 MWh for an area of 200,000 m2.

Enhancing Agricultural Practices Through IoT-Based Smart Farming Technologies: A Case Study on Banana Crop Yield Optimization

Aims: Smart farming and precision agriculture have emerged as transformative paradigms in modern agricultural practices, leveraging technological innovations to enhance productivity, sustainability, and efficiency in food production. This paper provides a comprehensive review of the concepts and technologies related to smart farming. The work proposed implements a sensor assisted IoT based model to enhance the overall yield of banana crop, by monitoring the current conditions existing at the site and predicting the alterations to achieve optimal conditions for conducive and healthy growth, further early identification and prediction of infection causing pathogens to have also been embedded in the model. Model designed has been tested on the farm field of banana crop located in the premises of Amity University Lucknow Campus equipped with moisture and humidity sensors (DHT11), NPK soil nutrient sensor, PIR motion sensor (HC-SR501), pH Sensor (pH -450), rain drop sensor along with camera installed drone for infection identification. Data from sensors and drone camera were monitored at regular intervals for future predictions about health and productivity estimate of the crop.

Dependence of rain attenuation on rain rate and drop size distribution for Ka-band satellite communication over India

The Raindrop size distribution (DSD) is the most effective parameter to calculate rain-induced attenuation, which can be severe at Ka-band and higher frequencies. The authors have investigated the impact of rain rate and DSD on rain-induced specific attenuation over a tropical location Kolkata, India. DSD data from disdrometer has been used to calculate the specific rain attenuation with the help of Mie scattering theorem. Low to medium drop diameters (up to 3 mm) are the largest contributors to the various classes of rain rate and attenuation. Double peaks of drop sizes are significant for medium rain rate. The contribution of smaller drop diameters decrease, whereas the contribution of higher drop diameters increase with increasing rain attenuation. At lower rain attenuation, (up to 1.5 dB), complementary cumulative distribution function (CCDF) shows higher value for stratiform rain, with respect to convective rain. The higher attenuation occurrences are mostly observed during 12–18 Indian standard time (IST), i.e., in the afternoon. The results will be helpful for Ka-band (GSAT-14) and higher frequency satellite communication channel modeling over India.

Highly electronegative borophene/PVDF composite hybrid nanofibers based triboelectric nanogenerator for self-powered sensor for human motion monitoring and energy harvesting from rain

In recent advancements in energy harvesting, triboelectric nanogenerators(TENG) have emerged as promising candidates for powering various sensors and small electronic devices autonomously. So, this work focuses on the development of a novel TENG utilizing borophene/PVDF hybrid nanofibers and Al as tribo-materials. Sono-chemically synthesized borophene and PVDF hybrid nanofibers are fabricated by electrospinning method. The formation of borophene/PVDF hybrid nanofibers is confirmed by different physiochemical characterization like Transmission Electron microscopy (TEM), X-Ray diffractometer (XRD), and Raman spectroscopy. The as-fabricated TENG is used as mechanical energy harvester to generate open circuit voltage (Voc) of 102.5 V and short circuit current (Isc) of 0.80 μA. Furthermore, the power density of the as-fabricated TENG is 0.08 W/m2 at an external resistance load of 200 MΩ. For practical applications, TENG is used to power small electronics like LED, watch, and calculator. Further, borophene/PVDF hybrid nanofibers is used to fabricate single electrode based TENG (SE-TENG) to harvest energy from the rain drops, which generates Voc of 13 V and Isc of 0.10 μA. Integrating energy harvesting from different medium represents a significant advancement, as it provides higher output power density. This approach holds great promise for enhancing energy conversion efficiency of TENG technology and for exploring its applications in healthcare and consumer electronics.

Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach

While there are multiple methods to ventilate protective clothing, there is still room for improvement. In our research, we are using ventilation elements that are positioned at the ventilation holes in the air space between the body and clothing. These ventilation elements allow air to flow freely while preventing sun radiation, rain drops, and insects from directly accessing the body. Therefore, the shape of the ventilation element is crucial. This led us to study the shape optimization of ventilation elements through the utilization of metamodels and numerical approaches. In order to accomplish the objective, it is crucial to thoroughly evaluate and choose suitable criteria for the optimization process. We know from prior research that the toroidal cut-out shape element provides better results. In a previous study, we optimized the shape of this element based on the minimum pressure difference as a criterion. In this study, we are using different criteria for the shape optimization of ventilation elements to determine which are most effective. This study involves a metamodeling strategy that utilizes local and global approximations with different order polynomials, as well as Kriging approximations, for the purpose of optimizing the geometry of ventilation elements. The goal was achieved by a sequential process. (1) Planning the position of control points of Non-Uniform Rational B-Splines (NURBS) in order to generate elements with a smooth shape. (2) Constructing geometric CAD models based on the design of experiments. (3) Compute detailed model solutions using SolidWorks Flow Simulation. (4) Developing metamodels for responses using computer experiments. (5) Optimization of element shape using metamodels. The procedure is repeated for six criteria, and subsequently, the results are compared to determine the most efficient criteria for optimizing the design of the ventilation element.

HYGIENE HIVE MONITOR

In modern days, we desire a healthy and hygiene-friendly environment for our society. We see multiple dustbins with an overflow of waste in urban areas. This situation is created pathogens, which spread diseases in our society. Its affect clean India mission. So, we designed the system aimed at improve the effectiveness and sustainability of waste collection and disposal processes. In this setup, once the dustbin reaches its maximum capacity, a notification containing its live location is dispatched to the corporation. The detection of the dustbin's capacity is facilitated by employing an ultrasonic sensor. Then level of garbage is displayed by LCD and the level is sent to the corporation. This helps the timely collection of garbage. As the rain is fell into the trash can; the stink was affecting our society. The rain drop sensor detects the rain drops; trashcan will be automatically close. This helps to reduce the stench and improves healthy environment. If suppose, after sending the live location notification, the dustbin does not cleaned by workers then the notification sent to the higher authority. Then if the dustbin is empty or less than capacity of 80, message is sent to the corporation (Cleaned). It is helping the higher official, whether the workers are working properly or not. We used an efficient and cheap component to make this project economical. It can be easily understood by the workers. It reduces the overflow of garbage. A system is used to improve our nation. Concluding that the system helping us to save the time, energy, cost, and fuel. Improve the concept of less human and speedup process. Key Words: Ultrasonic sensor, raindrop sensor, IR sensor, IoT, Dustbin

Seasonal dependence of characteristics of rain drop size distribution over two different climatic zones of India

Seasonal dependence of characteristics of rain drop size distribution over two different climatic zones of India

Diurnal Variation of Rain Drop Size Distribution over the Western Ghats of India

Diurnal Variation of Rain Drop Size Distribution over the Western Ghats of India

Prevalence of Skin Cancer in Chronic Arsenicosis in Chittagong Medical College Hospital, Bangladesh

A descriptive study was done in the Department of Dermatology and Venereology; Chittagong Medical College Hospital, Chittagong, during the period of July 2004 to June 2008, to find out the prevalence of skin cancer among various skin manifestations of chronic arsenicosis. All suspected patients of chronic arsenicosis coming from endemic zones of Bangladesh were the study population. A total number of 234 patients of chronic arsenicosis were included in this study. The patients were diagnosed by physical examination and by estimation of arsenic level of scalp hair. The majority of the patients came from Noakhali, Chitagong, Feni, Laxmipur, Comilla and Chandpur districts. The mean age of the patients was 27.80 years ± 10.22 SD (Range: 12-70 years). About 70% patients were around 30 years of age. The male & female ratio was 1.9: 1. Most of them came from average socio-economic status. About 28.6 % patients were students, while about 25% patients were daily labour. 94 % patients used tube well as drinking water source. 12.8o patients had family history of chronic arsenicosis and about 19% patients took alternative medicines (homeopathic /kobirajee) for treatment of the same or other illness. The cent percent patients presented with hypo and hipermelanosis (rain drop pigmentation), while 90,6 % patients were with hyperkeratosis in palms and soles. The measurement of arsenic in scalp hair was done. The mean arsenic level of scalp hair was found to be 2.63 1.39 SD (range: 2.0 - 17.6 mg/kg). Skin biopsy for histopathology was done for suspected patients and skin lesions of 21.4% patients were detected as arsenical keratosis. Among the total patients, 6 (six) patients were found to develop skin cancers (2.6 %). Among them, 3 patients developed Squamous Cell Carcinoma (SCC), 1 patient developed Basal Cell Carcinoma (BCC), while Bowen's disease and Melanoma was found in I patient each. Regarding treatment response, about 48% patients showed good response with topical ........

Further development and testing of a rainfall test rig

Changes made recently by The Ministry of Health New Zealand, to the internal noise design requirements for Preschools, has required that the design of the roof reduces rainfall noise to Ministry of Education, Design Quality Learning Spaces Acoustics (DQLS) Version 3.0, for rainfall noise. Previously Canterbury Acoustic Testing Services (CATS) had developed a rainfall noise test rig, in accordance with ISO 10140-1: 2016 [3] and ISO 10140-5:2010/Amd 1:2014 and carried out testing on a series of warm roof/ceiling constructions. Preschools tend to use cold roof systems where the thermal insulation sits on the ceiling, rather than in a warm roof, where the insulation is part of the roof structure. So there has been no tested performance data for rainfall noise acoustic design purpose, using a cold roof construction. As part of the testing program, there was a need to recommission the rig, to verify rain drop size and rainfall rate. A testing program was established, to include the base roof structure (roofing iron only) to a full buildup of roof and ceiling, to get a better understanding of how each component in the system contributes to the control of the rainfall noise.

Comprehensive properties of non-penetrating and penetrating deep convection precipitation in summer over the Tibetan Plateau derived from GPM observations

The spatial-temporal distribution, drop size distribution and their associated thermal structure as well as the tropopause anomalies of non-penetrating and penetrating deep convection precipitation in summer of 2014–2021 over the Tibetan Plateau are explored using GPM observations, ERA5 reanalysis data and topographic data in this study. The result shows that frequencies and intensities of non-penetrating deep convection precipitation are generally larger than those of penetrating deep convection precipitation. The storm tops of non-penetrating and penetrating deep convection are approximately 15–16 km and 18–19 km respectively, whereas the corresponding lapse rate tropopause heights for both types of deep convection are similar (about 17.4 km). The radar reflectivity decreases with height and the maximum appears near the surface. Latent heat release of non-penetrating deep convection is largely confined in the lower troposphere, while latent heating of penetrating deep convection is higher. Moreover, rain drop concentration of non-penetrating deep convection distributes uniformly (5–15 km) and particle size is large (2.0–2.5 mm) near the surface. In contrast, penetrating deep convection particles concentrate below 10 km and near the storm top (19–20 km), with small size (1.0–1.5 mm). Furthermore, there are evident differences in thermal structure during non-penetrating and penetrating deep convection process over the Tibetan Plateau. Notably, slight net warming anomaly occurs above tropopause during penetrating deep convection due to subsidence from divergent flow. Moistening anomaly is more significant below 11 km following non-penetrating deep convection. However, slight dehydration appears near the tropopause after penetrating deep convection. Descending tropopause and increasing CAPE before penetrating deep convection are more significant and conducive to penetrating. These results suggest macro-micro features of non-penetrating and penetrating deep convection and interaction between two types of deep convection and thermal structure over the Tibetan Plateau.

Development and Characterisation of a New Hibiscus rosa-sinensis L. Cultivar (‘Krishna's Radiance’) from India

A new significant cultivar Hibiscus rosa-sinensis L. cv. ‘Krishna's Radiance’ has been developed from the cross pollination of H. rosa-sinensis L. cv. ‘Houdini’ (Female pod parent) and Hibiscus rosa-sinensis L. cv. ‘HVH Rain Drop’ (Male pollen parent). The new cultivar characterised by upright, fast growing shrubs with bluish-purple flowers. It can be recognised from parents by its large, creamy-white eye zone and allied to male parent (HVH Rain Drop) by its bluish colour flower but it can be separated by large single regular flower, clockwise arrangement of petals and creamy-white large eye zone whereas male parent has small single cartwheel flower, anticlockwise arrangement of petals and small whitish-pink eye zone.

Perancangan Prototipe Rain Drop Sensor Berbasis Arduino Uno

In Indonesia, the climate is mostly hot and humid, and most of the rainfall occurs. As a result, people are less aware of how much rain occurs inside rooms, homes, and offices. We need a warning to explain the problem so that we can take the necessary action when it rains. By creating Arduino-based rain sensors and implementing the fourth industrial revolution in everyday life, the study aims to raise awareness of rain unknowingly. The initial method is the implementation of the Raindrop Sensor based arduino which is an Arduino standard board based on the ATmega328P microcontroller. The Rain Drop Sensor Module works when it rains, when the electric vibration buzzer rains into sound vibration, then the buzzer will provide sound information. The research results of the sensor value of more than 500 with the green light indicator lighting the Buzzer does not emit noise then the conditions are not rainy or can be meant the weather is medium bright, then the sensor value is less than 500 by the indicator Buzzer on then emits the sound and the red lighting indicator color lighting, then indicates the rain condition.

Characterization of Rain Attenuation in 80–200 GHz From Experimental Drop Size Distributions

The use of frequencies well into the EHF band (30-300 GHz) is a key element in 5G and beyond technologies. Rain attenuation is the major impairment affecting terrestrial radio links in this band. In the absence of enough experimental measurements, rain attenuation can be estimated by using physical models of radiowave scattering in rain drops combined with information about the rain Drop Size Distributions (DSD). In this work, the characterization of rain attenuation in the 80-200 GHz frequency range is carried out from a large database of twelve years of experimental DSD gathered in Madrid, Spain. Rain attenuation is estimated for each collected minute of rain using two approaches: a first one based on the assumption of raindrops as spherical and the application of the Mie theory, and a second one that uses a non-spherical raindrop model and electromagnetic simulations and is consequently more realistic. The main results show that the currently used ITU-R model generally underestimates rain specific attenuation; the influence of polarization becomes smaller and negligible as frequency approaches 200 GHz; and rain specific attenuation significantly varies due to the spread of the DSD. Moreover, a model for this variability of rain attenuation is also proposed.

A study of rain drop size distributions and associated rain microphysical processes over a subtropical station in the Northeast India

A study of rain Drop Size Distributions (DSDs) and associated microphysical processes is carried out during the premonsoon and monsoon seasons at Kohima (25.67° N, 94.08° E) in the Patkai hill range of the Northeast India. The study is carried out with the help of Micro Rain Radar (24.1 GHz). The rainfall is classified in three categories namely, Bright Band (BB), No Bright Band Low rain rate (R) i.e. 0.10 mm h−1< R ≤ 10 mm h−1 (NBBL) and No Bright Band High rain rate i.e. 10 mm h−1 <R ≤ 20 mm h−1 (NBBH). During the premonsoon and monsoon, for R ≤ 20 mm h−1, rainfall occurrence time constitute around 96% and 98% respectively, whereas rainfall accumulation constitute around 51%. and 72% respectively. The BB height is found to be lower during the premonsoon (∼2.2 km from surface level) compared to monsoon (∼3.6 km from surface level) season. The observational results suggest that, during the premonsoon as well monsoon seasons, BB rain is predominantly associated with collision–coalescence–breakup process with varying proportion, whereas NBBL and NBBH rain are predominantly associated with collision–coalescence process with varying proportion. In each season, collision-coalescence process is most dominant for NBBH type of rain. Seasonally, collision-coalescence process is found to be stronger during the premonsoon season. For the falling rain drops, there is a transition in the microphysical process from number controlled (collision-coalescence-breakup) to size-controlled (collision-coalescence) process with varying proportion. For each season, for R ≤ 10 mm h−1, larger rain drops are found for BB type of rain compared to NBBL rain. Overall, relatively larger raindrops are found to be associated with NBBH rain. Seasonally, larger drops are found during the premonsoon compared to the monsoon season. The rain DSDs and associated microphysical processes during the premonsoon are found to be associated with stronger convection compared to the monsoon season.

Perovskite quantum dot-based tandem triboelectric-solar cell for boosting the efficiency and rain energy harvesting

Silicon (Si) solar cell efficiently convert solar energy into electricity under the sun illumination, but its inherent intermittent power generation due to diurnal and seasonal cycle has usually allowed for the requirement for alternative power sources. Owing to the abundance, diversity and availability, rain drop energy is one of the most promising green energy sources. Hence, hybrid energy harvesting could be a promising strategy of achieving preferential hybrid performances without sacrificing the advantages in individual devices. Herein, we proposed a hybrid solar and rain energy harvesting device featuring the integration of triboelectric nanogenerator (TENG) top-cell and a crystalline Si solar cell bottom-cell by laminating perovskite quantum dots-embedded polydimethylsiloxane composite film (PQDP) onto the Si solar cell, which endows enhanced electrical output performances under rainy days. To overcome the limitation of low external quantum efficiency (EQE) in the ultraviolet region of the Si solar cell, the PCE of the hybrid solar cell is significantly enhanced from 18.47% of bare Si solar cell to 20.16% owing to the anti-reflection effect of PQDP film and the down-conversion property of CsPbBr3 QDs doped with Ce3+ ions. Meanwhile, this hybrid solar cell presents excellent durability after continuous measurement over 7 days. This tandem hybrid solar cell provides a promising strategy to simultaneously scavenging the solar and rain energy and boosting the power conversion efficiency by introducing the perovskite QDs without affecting the efficiency of bare Si solar cell.

The capture of airborne particulates by rain

Rain cleans pollution out of the atmosphere, as droplets collide with airborne particles during free fall. Such particle–droplet collisions have been presumed to be capture events, but the details of such collisions lack thorough investigation. We show that rain droplets and pollution particles interact through multiple collision behaviours, including captures on the droplet surface, cavity-forming droplet entries and ricochets. Rain drop diameter and free fall velocity, in addition to pollution particle density, size, wettability and droplet impact location, determine which capture or escape behaviour occurs. Our findings reveal that rain does not capture all airborne pollutants equally even upon collision, and certain pollutants prove more difficult to remove from the air than others. Consequently, we must account for both rain and pollution characteristics to understand pollution capture mechanisms and pollution fluxes in the environment.

Assessment of Soil Erosion Hazards in Kambiti Subcatchment, Murang’a County, Kenya

Erosion is a global problem that destroys soil and adversely affects ecosystem productivity. Soil erosion generally involves many processes but the major activities involve particles being transported and deposited to another location. With an increasing population, soil erosion, water availability, energy production, and biodiversity loss are some of the most pressing environmental problems around the world. Erosion is a hazard associated with agriculture in tropical and semi-arid areas. Kambiti sub catchment is part of the upper Tana catchment. The upper Tana catchment includes 25% of Kenya gazette forest. A large area of land has been degraded, resulting in a drastic reduction in surface water availability during the dry season and poor-quality water during the wet season caused by high silt levels. The main objective of the study is to assess erosion hazards using RUSLE model in Kambiti sub catchment area, Murang’a County. The specific objectives of the study were to determine the effect of rainfall erosivity and soil erodibility factor in Kambiti Sub catchment area in Murang’a County, to determine effect of slope factor to soil loss in Kambiti Sub-catchment area in Murang’a County, to determine the effect of crop protection and management factor in Kambiti Sub catchment area in Murang’a County to soil loss and to determine the strategies for management of soil and water in Kambiti Sub catchment area in Murang’a County. Data was collected from the catchment and analyzed using arc Geographical Information System to obtain the specific parameters in the revised universal soil loss equation model. Interpolation method was used to determine the mean annual precipitation. The k factor is a function of soil texture. Shape file for geological structure for Kenya was obtained from Kenya Agriculture and livestock Research Organisation and analyzed by use of arc GIS to obtain soil erodibility factor. The slope factor was analyzed using digital elevation model from arc view. Digital elevation model was gotten from STRM download. The C factor was derived from Landsat imagery from sentinel of 30metres by 30 metres. It was further analysed by unsupervised classification from Arc GIS. The sentinel clip of Kambiti sub-catchment was joined with ground trothing observations. The results were useful in estimation of soil loss therefore profiling the areas prone to soil loss. Study findings indicated rain drop impact and runoff were primarily responsible for causing erosion in Kambiti sub catchment. Anthropogenic factors played an important role in amplifying the severity of the damage, such as persistent vegetative degradation and destruction of soil structure due to organic matter depletion and routine shallow tillage. In recent years, erosion control has been hampered by the occurrence of gaps in knowledge regarding the integrated nature of erosion processes, leading to land damage caused by rill and inter-rill erosion going unaddressed. Poor people and those lacking capital to invest in reclaiming land are the main causes of abandoning degraded land. Through strategic awareness campaigns and education, soil erosion will be assessed and the knowledge gap will be closed. Participation of farmers in land use decisions is inevitable as it ensures that people who utilize land resources are recognized as equal partners in identifying problems and designing solutions. It was also recommended that Identification and operationalization of alternative off-farm income.&#x0D;

Development of Cellulose-Reinforced Polyurethane Coatings: A Novel Eco-Friendly Approach for Wind Turbine Blade Protection

Wind energy is considered a clean energy source and is predicted to be one of the primary sources of electricity. However, leading-edge erosion of wind turbine blades due to impacts from rain drops, solid particles, hailstones, bird fouling, ice, etc., is a major concern for the wind energy sector that reduces annual energy production. Therefore, leading-edge protection of turbine blades has been an important topic of research and development in the last 20 years. Further, there are critical issues related to the amount of waste produced, including glass fiber, carbon fiber, and various harmful volatile organic compounds in turbine fabrication and their end-of-life phases. Hence, it is vital to use eco-friendly, solvent-free materials and to extend blade life to make wind energy a perfect clean energy source. In this study, cellulose microparticles (CMP) and cellulose microfibers (CMF) have been used as fillers to reinforce water-based polyurethane (PU) coatings developed on glass fiber reinforced polymer (GFRP) substrates by a simple spray method for the first time. Field emission scanning electron microscopy images show the agglomerated particles of CMP and fiber-like morphology of CMF. Fourier transform infrared spectra of CMP, CMF, and related coatings exhibit associated C–H, C=O, and N–H absorption bands of cellulose and polyurethane. Thermal gravimetric analysis shows that CMP is stable up to 285 °C, whereas CMF degradation is observed at 243 °C. X-ray photoelectron spectroscopy of C 1s and O 1s core levels of CMP, CMF and related coatings show C–C/C–H, C–O, C–OH, and O–C=O bonds associated with cellulose structure. The solid particle erosion resistance properties of the coatings have been evaluated with different concentrations of CMP and CMF at impact angles of 30° and 90°, and all of the coatings are observed to outperform the PU and bare GFRP substrates. Three-dimensional (3D) profiles of erosion scans confirm the shape of erosion scars, and 2D profiles have been used to calculate volume loss due to erosion. CMP-reinforced PU coating with 5 wt.% filler concentration and CMF-reinforced PU coating with 2 wt.% concentration are found to be the best-performing coatings against solid particle erosion. Nanoindentation studies have been performed to establish a relation between H3/E2 and the average erosion rate of the coatings.

Impact of integration time steps of rain drop size distribution on their double-moment normalization: a case study in northern Benin

This study analyzed the sensitivity of the double-moment normalization of rain drop size distributions (DSDs) to their integration time steps. Six DSD datasets measured at different integration time steps were modeled by the double-moment normalization method. Six couples of reference moments are used for the normalization. Three DSD models (gamma, generalized gamma and lognormal) are used for modeling. Statistical criteria are used to assess the estimation of the moments of the DSDs made by the models. As results, the analysis highlighted the dependence of the shape function parameters on the DSD integration time step. It is also noted that the three DSD models are well adapted to the data used. Nevertheless, the generalized gamma model is recommended because of the independence of the moment estimation errors with respect to the integration time step, which is not the case for the other models.