Relevant bibliographies by topics / Rain and rainfall Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Rain and rainfall Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Rain and rainfall Mathematical models"

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Guideli, Leandro Canezin, André Lucas dos Reis Cuenca, Milena Arruda Silva, and Larissa de Brum Passini. "Road crashes and field rainfall data: mathematical modeling for the Brazilian mountainous highway BR-376/PR." TRANSPORTES 29, no. 4 (December 2, 2021): 2498. http://dx.doi.org/10.14295/transportes.v29i4.2498.

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Recent studies analyze the influence of rainfall on traffic crashes, indicating that precipitation intensity is an important factor, for modeling crashes occurrence. This research presents a relationship between daily-basis traffic crashes and precipitation, from 2014 to 2018, in a rural mountainous Brazilian Highway (BR-376/PR), where field rain gauges were used to obtain precipitation data. Data modeling considered a Negative Binomial regression for precipitation influence in crash frequency. Separate regression models were estimated to account for the rainfall effect in different seasons, and for different vehicle types. All models analyzed presented a positive relationship between daily rainfall intensity and daily crashes number. This can indicate that generally rainfall presence is a hazardous factor. Different critical seasons for rainfall influence were also highlighted, alerting for the possible necessity of distinct road safety policies concerning seasonality. Finally, for the vehicle type analysis, typically, rainfall seemed to have a greater effect in lighter vehicles. Moreover, results are useful for traffic control, in order to increase safety conditions.
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Rauch, W., N. Thurner, and P. Harremoës. "Required accuracy of rainfall data for integrated urban drainage modeling." Water Science and Technology 37, no. 11 (June 1, 1998): 81–89. http://dx.doi.org/10.2166/wst.1998.0441.

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It is standard practice in integrated urban water management to apply mathematical models of the total drainage system for calculating the frequency of occurrence of critical states in the receiving water body. The model input for such computations are long term time-series of rainfall data. However, it is inevitable that those rainfall data measurements deviate from reality. This is a result of inaccuracy of the measurement devices, errors in data transmission, local meteorological effects, etc. In this work we investigate the effect of such uncertainty in the rainfall data on the return period of the occurrence of oxygen depletion in the river due to the drainage of storm water. The errors in the rain data measurements are simulated by means of both stochastic and deterministic models. A comparison of the results obtained from the erroneous data series against the reference data reveals the small effect of random deviation in rain measurements. Only a constant and significant offset of the measured data (greater 20%) has an equally significant effect on the modeling result.
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Yakovleva, Valentina, Aleksey Zelinskiy, Roman Parovik, Grigorii Yakovlev, and Aleksey Kobzev. "Model for Reconstruction of γ-Background during Liquid Atmospheric Precipitation." Mathematics 9, no. 14 (July 11, 2021): 1636. http://dx.doi.org/10.3390/math9141636.

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With regard to reconstructing the gamma background dose rate, existing models are either empirical with limited applicability or have many unknown input parameters, which complicates their application in practice. Due to this, there is a need to search for a new approach and build a convenient, easily applicable and universal model. The paper proposes a mathematical model for reconstructing the temporal evolution of the ambient equivalent γ-radiation dose rate during rain episodes, depending on the density of radon flux from the soil surface, as well as the duration and intensity of rain. The efficiency of the model is confirmed by the high coefficient of determination (R2 = 0.81–0.99) between the measured and reconstructed ambient equivalent dose rate during periods of rain, the simulation of which was performed using Wolfram Mathematica. An algorithm was developed for restoring the dynamics of the ambient equivalent γ-radiation dose rate during rainfall. Based on the results obtained, assumptions were made where the washout of radionuclides originates. The influence of the radionuclides ratio on the increase in the total γ-radiation dose rate was investigated.
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Cowpertwait, Paul, Valerie Isham, and Christian Onof. "Point process models of rainfall: developments for fine-scale structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (July 18, 2007): 2569–87. http://dx.doi.org/10.1098/rspa.2007.1889.

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A conceptual stochastic model of rainfall is proposed in which storm origins occur in a Poisson process, where each storm has a random lifetime during which rain cell origins occur in a secondary Poisson process. In addition, each cell has a random lifetime during which instantaneous random depths (or ‘pulses’) of rain occur in a further Poisson process. A key motivation behind the model formulation is to account for the variability in rainfall data over small (e.g. 5 min) and larger time intervals. Time-series properties are derived to enable the model to be fitted to aggregated rain gauge data. These properties include moments up to third order, the probability that an interval is dry, and the autocovariance function. To allow for distinct storm types (e.g. convective and stratiform), several processes may be superposed. Using the derived properties, a model consisting of two storm types is fitted to 60 years of 5 min rainfall data taken from a site near Wellington, New Zealand, using sample estimates taken at 5 min, 1 hour, 6 hours and daily levels of aggregation. The model is found to fit moments of the depth distribution up to third order very well at these time scales. Using the fitted model, 5 min series are simulated, and annual maxima are extracted and compared with equivalent values taken from the historical record. A good fit in the extremes is found at both 1 and 24 hour levels of aggregation, although at the 5 min level there is some underestimation of the historical values. Proportions of time intervals with depths below various low thresholds are extracted from the simulated and historical series and compared. A tendency for underestimation of the historical values is evident at some time scales, with a close fit being obtained as the threshold is increased.
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Ramesh, Nadarajah I., Gayatri Rode, and Christian Onof. "A Cox Process with State-Dependent Exponential Pulses to Model Rainfall." Water Resources Management 36, no. 1 (November 29, 2021): 297–313. http://dx.doi.org/10.1007/s11269-021-03028-6.

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AbstractA point process model based on a class of Cox processes is developed to analyse precipitation data at a point location. The model is constructed using state-dependent exponential pulses that are governed by an unobserved underlying Markov chain. The mathematical formulation of the model where both the arrival rate of the rain cells and the initial pulse depth are determined by the Markov chain is presented. Second-order properties of the rainfall depth process are derived and utilised in model assessment. A method of moment estimation is employed in model fitting. The proposed model is used to analyse 69 years of sub-hourly rainfall data from Germany and 15 years of English rainfall data. The results of the analysis using variants of the proposed model with fixed pulse lifetime and variable pulse duration are presented. The performance of the proposed model, in reproducing second-moment characteristics of the rainfall, is compared with that of two stochastic models where one has exponential pulses and the other has rectangular pulses. The proposed model is found to capture most of the empirical rainfall properties well and outperform the two alternative models considered in our analysis.
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Parsons, Scott A., and Robert A. Congdon. "Plant litter decomposition and nutrient cycling in north Queensland tropical rain-forest communities of differing successional status." Journal of Tropical Ecology 24, no. 3 (May 2008): 317–27. http://dx.doi.org/10.1017/s0266467408004963.

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Abstract:Soil processes are essential in enabling forest regeneration in disturbed landscapes. Little is known about whether litterfall from dominating pioneer species in secondary rain forest is functionally equivalent to that of mixed rain-forest litter in terms of contribution to soil processes. This study used the litterbag technique to quantify the decomposition and nutrient dynamics of leaf litter characteristic of three wet tropical forest communities in the Paluma Range National Park, Queensland, Australia over 511 d. These were: undisturbed primary rain forest (mixed rain-forest species), selectively logged secondary rain forest (pioneer Alphitonia petriei) and tall open eucalypt forest (Eucalyptus grandis). Mass loss, total N, total P, K, Ca and Mg dynamics of the decaying leaves were determined, and different mathematical models were used to explain the mass loss data. Rainfall and temperature data were also collected from each site. The leaves of A. petriei and E. grandis both decomposed significantly slower in situ than the mixed rain-forest species (39%, 38% and 29% ash-free dry mass remaining respectively). Nitrogen and phosphorus were immobilized, with 182% N and 134% P remaining in E. grandis, 127% N and 132% P remaining in A. petriei and 168% N and 121% P remaining in the mixed rain-forest species. The initial lignin:P ratio and initial lignin:N ratio exerted significant controls on decomposition rates. The exceptionally slow decomposition of the pioneer species is likely to limit soil processes at disturbed tropical rain-forest sites in Australia.
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Ke, Shitang, Wenlin Yu, and Yaojun Ge. "Wind Load Characteristics and Action Mechanism on Internal and External Surfaces of Super-Large Cooling Towers under Wind-Rain Combined Effects." Mathematical Problems in Engineering 2018 (July 8, 2018): 1–22. http://dx.doi.org/10.1155/2018/2921709.

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By focusing on wind-rain two-way coupling algorithm, simulation iterations of wind field and raindrops in the world highest cooling tower (210m) in northwest China were carried out using continuous phase and discrete phase models based on CFD numerical simulation. Firstly, influence laws of 9 wind velocity-rainfall intensity combinations on wind-induced rainfall, raindrop additional force, and equivalent pressure coefficient on internal and external surface of the tower body were discussed. On this basis, speed flow line, turbulence energy strength, raindrop running speed, and track on the tower body in the wind-rain coupling field were disclosed. Finally, qualitative and quantitative contrastive analyses on wind pressure, rain pressure, and equivalent pressure coefficient on internal and external surfaces of the tower body were conducted under different working conditions. Thus, the most unfavorable wind-rain combination was identified. Calculation formulas of equivalent internal and external pressure coefficients of super-large cooling towers were fitted from nonlinear least square method. Research results demonstrate that the 3D effect of equivalent internal and external pressure coefficients with considerations to wind-rain two-way coupling is more prominent. Particularly, there is strong transition on the windward region of the external surface and leeside region at bottom of internal surface. The quantity of caught raindrops on the structural surface is negatively related to wind velocity but is positively related to rainfall intensity. Rain load and rainfall coefficients on the external surface are significantly higher than those on the internal surface. Equivalent internal pressure coefficient has a sharp reduction on the leeside region under different working conditions. Besides, equivalent internal pressure coefficient of different meridians decreases with the increase of height. The maximum and minimum are -0.574 and -0.282, respectively. The proposed equivalent internal and external pressure coefficients of super-large cooling tower can predict wind load under extreme climate conditions accurately.
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Sansom, John, and Peter Thomson. "Fitting hidden semi-Markov models to breakpoint rainfall data." Journal of Applied Probability 38, A (2001): 142–57. http://dx.doi.org/10.1239/jap/1085496598.

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The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.
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Klamerus-Iwan, Anna, and Maciej Sporysz. "Laboratory determination of potential interception of young deciduous trees during low-intense precipitation." Folia Forestalia Polonica 56, no. 1 (March 1, 2014): 3–8. http://dx.doi.org/10.2478/ffp-2014-0001.

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Abstract The research issue focuses on potential interception, which is the maximum amount of water that can be stored on plant surface. Tests under controlled conditions remain the best way to enhance knowledge on interception determinants in forest communities. Such tests can provide data for identification of mathematical models based on ecological criteria. The study presented in this paper concerned tree interception under simulated rain in a range from 2 to 11 mm/h. To perform the experiment a set of sprinklers was designed and built. The study included two deciduous species: beech (Fagus sylvatica L.) and oak (Quercus robur L.). Descriptive characteristic and nonlinear estimation were suggested for the obtained data. Interdependence of potential interception, the intensity of rain and the size of raindrops were described using exponential equation. The intensity and drop size of simulated rainfall significantly influence the obtained values of potential interception. Data analysis shows a decrease of interception value with an increase of intensity of simulated rainfall for both analysed species. Every run of the experiment that differed in the intensity and size of raindrops reached an individual level of potential interception and time needed to realize it. The formation of ability of plants to intercept water depends both on the dynamics and the time of spraying.
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Wang, Zhenlong, Yingying Xu, Guoqiang Dong, Haishen Lv, Yue Fan, and Yining Wang. "Methods for calculating phreatic evaporation on bare grounds on rainy and dry days." Hydrology Research 51, no. 6 (July 7, 2020): 1221–37. http://dx.doi.org/10.2166/nh.2020.017.

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Abstract In order to depict the impact of rainfall on phreatic evaporation, this study analyzes phreatic evaporation and the phreatic evaporation coefficient between surface evaporation and soil depth in Shajiang black soil and Fluyo-aquic soil. We have improved the existing commonly used mathematical framework, established two rainless day phreatic evaporation calculation models, and then calculated the calculation model of the phreatic evaporation reduction on rainy days. Finally, rainy day evaporation calculation models on two soils were proposed. The results show that the evaporation coefficient is affected by both depth and the evaporation ability of the surface water. The evaporation reduction of Shajiang black soil increased with depth and the increasing trend gradually slowed down until it approached zero. The evaporation reduction of the Fluyo-aquic soil phreatic decreased first and then increased with depth, reaching a minimum at 0.4 m. The reduction of phreatic evaporation in both soils decreased with the increase in rainfall level and decreased with the increase in rainfall duration showing ‘inverted S-type’. In summary, the phreatic evaporation composite calculation models on rainy days and rainless days have good fitting and prediction results, which can improve the accuracy of phreatic evaporation calculations.
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Dissertations / Theses on the topic "Rain and rainfall Mathematical models"

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To, Chun-hung, and 杜振雄. "Stochastic model of daily rainfall." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31976098.

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de, Roulhac Darde Gregoire 1956. "APPLICATION OF COMPUTER GRAPHICS IN THE SELECTION OF RAINFALL FREQUENCY MODELS FOR ENVIRONMENTAL ENGINEERING." Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276407.

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Enright, Peter 1962. "Simulation of rainfall excess on flat rural watersheds in Quebec." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61952.

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Goodrich, David Charles. "Basin Scale and Runoff Model Complexity." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1990. http://hdl.handle.net/10150/614028.

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Distributed Rainfall-Runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel -dominated flow response. The methodology is tested on four subcatchments in the USDA -ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall -runoff data was used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semiarid environment such as Walnut Gulch. In this semiarid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.
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Sorooshian, Soroosh, and Vijai Kumar Gupta. "Improving the Reliability of Compartmental Models: Case of Conceptual Hydrologic Rainfall-Runoff Models." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1986. http://hdl.handle.net/10150/614011.

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Hendrickson, Jene Diane, and Soroosh Sorooshian. "CALIBRATION OF RAINFALL-RUNOFF MODELS USING GRADIENT-BASED ALGORITHMS AND ANALYTIC DERIVATIVES." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1987. http://hdl.handle.net/10150/614186.

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In the past, derivative-based optimization algorithms have not frequently been used to calibrate conceptual rainfall -riff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently- developed technique of analytically computing derivatives of a CRR model to a complex, widely -used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative -based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton- Raphsoz) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the Newton-Raphsoi algorithm was thought to be due to discontinuities and a rough texture of the response surface.
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Luckemeier, Richard Ewald 1948. "A rainfall-runoff model for an urban watershed in Tucson, Arizona." Thesis, The University of Arizona, 1989. http://hdl.handle.net/10150/277165.

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The U.S. Geological Survey and the City of Tucson, Arizona, have been collecting rainfall and runoff data on several watersheds in the Tucson area for several years. Among the purposes of this project is to use the data to test rainfall-runoff models in an effort to find one to successfully simulate flood flows in Tucson. One such model, the Distributed Routing Rainfall-Runoff Model (DR3M), was tested using data collected on Rob Wash in Tucson. It was found DR3M performs about as well as it does in other parts of the United States, although it tends to underestimate flood flows for large storms and overestimate flows for smaller storms. Unique features with regard to the hydrology of urban Tucson require special attention when using DR3M; these features are associated with the nature of dry washes and summer rainfall in Tucson. Experience indicates DR3M is not truly a deterministic model.
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Lau, Wai-hin, and 劉偉憲. "Stochastic analysis of monthly rainfall in Hong Kong." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31210387.

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Harrold, Timothy Ives Civil &amp Environmental Engineering Faculty of Engineering UNSW. "Stochastic generation of daily rainfall for catchment water management studies." Awarded by:University of New South Wales. School of Civil and Environmental Engineering, 2002. http://handle.unsw.edu.au/1959.4/18640.

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This thesis presents an approach for generating long synthetic sequences of single-site daily rainfall which can incorporate low-frequency features such as drought, while still accurately representing the day-to-day variations in rainfall. The approach is implemented in a two-stage process. The first stage is to generate the entire sequence of rainfall occurrence (i.e. whether each day is dry or wet). The second stage is to generate the rainfall amount on all wet days in the sequence. The models used in both stages are nonparametric (they make minimal general assumptions rather than specific assumptions about the distributional and dependence characteristics of the variables involved), and ensure an appropriate representation of the seasonal variations in rainfall. A key aspect in formulation of the models is selection of the predictor variables used to represent the historical features of the rainfall record. Methods for selection of the predictors are presented here. The approach is applied to daily rainfall from Sydney and Melbourne. The models that are developed use daily-level, seasonal-level, annual-level, and multi-year predictors for rainfall occurrence, and daily-level and annual-level predictors for rainfall amount. The resulting generated sequences provide a better representation of the variability associated with droughts and sustained wet periods than was previously possible. These sequences will be useful in catchment water management studies as a tool for exploring the potential response of catchments to possible future rainfall.
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Kapangaziwiri, Evison. "Revised parameter estimation methods for the Pitman monthly rainfall-runoff model." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1006172.

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In recent years, increased demands have been placed on hydrologists to find the most effective methods of making predictions of hydrologic variables in ungauged basins. A huge part of the southern African region is ungauged and, in gauged basins, the extent to which observed flows represent natural flows is unknown, given unquantified upstream activities. The need to exploit water resources for social and economic development, considered in the light of water scarcity forecasts for the region, makes the reliable quantification of water resources a priority. Contemporary approaches to the problem of hydrological prediction in ungauged basins in the region have relied heavily on calibration against a limited gauged streamflow database and somewhat subjective parameter regionalizations using areas of assumed hydrological similarity. The reliance of these approaches on limited historical records, often of dubious quality, introduces uncertainty in water resources decisions. Thus, it is necessary to develop methods of estimating model parameters that are less reliant on calibration. This thesis addresses the question of whether physical basin properties and the role they play in runoff generation processes can be used directly in the estimation of parameter values of the Pitman monthly rainfall-runoff model. A physically-based approach to estimating the soil moisture accounting and runoff parameters of a conceptual, monthly time-step rainfall-runoff model is proposed. The study investigates the physical meaning of the model parameters, establishes linkages between parameter values and basin physical properties and develops relationships and equations for estimating the parameters taking into account the spatial and temporal scales used in typical model applications. The estimationmethods are then tested in selected gauged basins in southern Africa and the results of model simulations evaluated against historical observed flows. The results of 71 basins chosen from the southern African region suggest that it is possible to directly estimate hydrologically relevant parameters for the Pitman model from physical basin attributes. For South Africa, the statistical and visual fit of the simulations using the revised parameters were at least as good as the current regional sets, albeit the parameter sets being different. In the other countries where no regionalized parameter sets currently exist, simulations were equally good. The availability, within the southern African region, of the appropriate physical basin data and the disparities in the spatial scales and the levels of detail of the data currently available were identified as potential sources of uncertainty. GIS and remote sensing technologies and a widespread use of this revised approach are expected to facilitate access to these data.
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Books on the topic "Rain and rainfall Mathematical models"

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Beven, K. J. Rainfall-runoff modelling: The primer. 2nd ed. Hoboken: Wiley, 2011.

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Bell, Thomas L. Statistical problems in rainfall measurements from space. Toronto: University of Toronto, Dept. of Statistics, 1989.

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Miller, Lisa D. Statistical analyses of hydrologic system components and simulation of Edwards Aquifer water-level response to rainfall using transfer-function models, San Antonio region, Texas. Reston, Va: U.S. Geological Survey, 2006.

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Haase, Günther. A physical initialization algorithm for non-hydrostatic weather prediction models using radar derived rain rates. St. Augustin [Germany]: Asgard Verlag, 2002.

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Srikanthan, R. Stochastic generation of rainfall and evaporation data. Canberra: Australian Govt. Pub. Service, 1985.

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Rientjes, Thomas Henricus Maria. Inverse modelling of the rainfall-runoff relation: A multi objective model calibration approach. Delft: Delft University Press, 2004.

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Tattelman, Paul. Model vertical profiles of extreme rainfall rate, liquid water content, and drop-size distribution. Hanscom AFB, MA: Atmospheric Sciences Division, Air Force Geophysics Laboratory, 1985.

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Nakama, Lenore Y. Use of a rainfall-runoff model for simulating effects of forest management on streamflow in the east fork Lobster Creek Basin, Oregon. Portland, Or: U.S. Geological Survey, 1993.

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Dinicola, R. S. Validation of a numerical modeling method for simulating rainfall-runoff relations for headwater basins in western King and Snohomish counties, Washington. Reston, Va: U.S. Dept. of the Interior, U.S. Geological Survey, 2001.

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C, Risley John. Use of a precipitation-runoff model for simulating effects of forest management on streamflow in 11 small drainage basins, Oregon coast range. Portland, Or: U.S. Dept. of the Interior, U.S. Geological Survey, 1994.

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Book chapters on the topic "Rain and rainfall Mathematical models"

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Sille, Roohi, Bhumika Sharma, Tanupriya Choudhury, Teoh Teik Toe, and Jung-Sup Um. "Survey on DL Methods for Flood Prediction in Smart Cities." In Handbook of Research on Data-Driven Mathematical Modeling in Smart Cities, 377–95. IGI Global, 2023. http://dx.doi.org/10.4018/978-1-6684-6408-3.ch020.

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The government has focused to maintain the needs of the populace's health and hygienic standards; numerous initiatives are involved, such as flood forecasting, water management, and sewage management. To prevent damage throughout the city, flood prediction must be done early on. “Smart” refers to artificial intelligence or machine learning methods, either directly or indirectly. To comprehend the general pattern and depth of the rainfall and to forecast the occurrence of floods, artificial intelligence techniques like deep learning are applied. To extract key properties for forecasting heavy rains and floods, many deep learning approaches, including CNN and deep belief networks, are applied. As a result, there is less harm done to both city infrastructure and human life. The study done on flood forecasting utilizing AI, ML, and deep learning techniques will be covered in this chapter. This review research will provide a thorough analysis based on the many types of deep learning models, the input datatypes for forecasting, the model effectiveness, real-time application, etc.
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Nirmala, M. "Computational Rainfall Forecasting Models." In Recent Advances in Mathematical Research and Computer Science Vol. 8, 35–44. Book Publisher International (a part of SCIENCEDOMAIN International), 2022. http://dx.doi.org/10.9734/bpi/ramrcs/v8/2411c.

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Moreno, A., E. Soria, J. García, J. D. Martín, and R. Magdalena. "Neural Models for Rainfall Forecasting." In Soft Computing Methods for Practical Environment Solutions, 353–69. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-61520-893-7.ch021.

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This chapter is focused on obtaining an optimal forecast of one month lagged rainfall in Spain. It is assessed by analyzing 22 years of both satellite observations of vegetation activity (e.g. NDVI) and climatic data (precipitation, temperature). The specific influence of non-spatial climatic indices such as NAO and SOI is also addressed. The approaches considered for rainfall forecasting include classical Auto-Regressive Moving-Average with Exogenous Inputs (ARMAX) models and Artificial Neural Networks (ANN), the so-called Multilayer Perceptron (MLP), in particular. The use of neural models is proven to be an adequate mathematical prediction tool in this problem due the non-linearity of the problem. These models enable us to predict, with one month foresight, the general rainfall dynamics, with average errors of 44 mm (RMSE) in a test series of 4 years with a rainfall standard deviation equal to 73 mm. Also, the sensitivity analysis in the neural network models reveals that observations in the status of the vegetation cover in previous months have a predictive power greater than other considered variables. Linear models yield average results of 55 mm (RMSE) although they need a large number of error terms (12) to obtain acceptable models. Nevertheless, they provide means for assessing the seasonal influence of the precipitation regime with the aid of linear dummy regression parameters, thereby offering an immediate interpretation (e.g. coherent maps) of the causality between vegetation cover and rainfall.
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Rosenzweig, Cynthia, and Daniel Hillel. "Regional Activities in a Global Framework: Developing and Developed Countries." In Climate Variability and the Global Harvest. Oxford University Press, 2008. http://dx.doi.org/10.1093/oso/9780195137637.003.0012.

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Regional studies and activities related to the El Niño–Southern Oscillation (ENSO) and other oscillations, seasonal climate prediction, and agricultural impacts are in progress around the world (figure 7.1). Here we describe some regional impacts and programs in place that are entraining climate information into decision making. Elements of these activities include the definition of the agricultural or other targeted systems; exploration of the social, political, and cultural contexts; examination of the temporal and spatial patterns of physical and biological impacts related to ENSO; analysis of economic effects; development and testing of seasonal climate forecasts and their delivery; investigation of crop management and other adaptations leading to implementation of dynamic risk-management strategies; and the development and evaluation of programs. In northern Peru, El Niño events bring torrential rains and floods that damage crops by eroding slopes, silting valleys, and oversaturating soils. The precipitation regime of Chile is likely to be intensified as well when El Niño events occur (Meza et al., 2003). Downscaled seasonal climate forecasts and crop growth models have been used to evaluate the impact of ENSO and management responses on crops in the Andean highlands of Peru (Baigorria, 2007); and Meza (2007) combined stochastic modeling of meteorological variables, a simple soil crop algorithm, and a mathematical programming model to assess the value of ENSO information for irrigation in the Maipo River Basin, Chile. Central America, being a narrow strip of land tightly squeezed between the Atlantic and Pacific oceans, is particularly influenced by major global climate variability systems, especially the El Nino–Southern Oscillation and the Arctic Oscillation (AO; M. Campos and P. Ramirez, personal communication, 2007; Rosenzweig et al., 2007). El Niño events are associated with dry summers on the Pacific coast and wet summers on the Caribbean coast, while the opposite pattern is associated with La Niña. A decrease in winter rainfall on the Caribbean coast since the late 1970s has been linked to changes in the Arctic Oscillation. Events with important economic and social consequences affected Central America in 1926, 1945–56, 1956–57, 1965, 1972–73, 1982–83, 1992–94, and 1997–98 (Ramirez, 2005).
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Polyak, Ilya. "Second Moments of Rain." In Computational Statistics in Climatology. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195099997.003.0010.

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The first part of this chapter presents a description of the GATE rain rate data (Polyak and North, 1995), its two-dimensional spectral and correlation characteristics, and multivariate models. Such descriptions have made it possible to show the concentration of significant power along the frequency axis in the spatial-temporal spectra; to detect a diurnal cycle (a range of variation of which is about 3.4 to 5.4 mm/hr); to study the anisotropy (as the result of the distinction between the north-south and east-west transport of rain) of spatial rain rate fields; to evaluate the scales of the distinction between second-moment estimates associated with ground and satellite samples; to determine the appropriate spatial and temporal scales of the simple linear stochastic models fitted to averaged rain rate fields; and to evaluate the mean advection velocity of the rain rate fluctuations. The second part of this chapter (adapted from Polyak et al., 1994) is mainly devoted to the diffusion of rainfall (from PRE-STORM experiment) by associating the multivariate autoregressive model parameters and the diffusion equation coefficients. This analysis led to the use of rain data to estimate rain advection velocity as well as other coefficients of the diffusion equation of the corresponding field. The results obtained can be used in the ground truth problem for TRMM (Tropical Rainfall Measuring Mission) satellite observations, for comparison with corresponding estimates of other sources of data (TOGA-COARE, or simulated by physical, models), for generating multiple rain samples of any size, and in some other areas of rain data analysis and modeling. For many years, the GATE data base has served as the richest and most accurate source of rain observations. Dozens of articles presenting the results of the GATE rain rate data analysis and modeling have been published, and more continue to be released. Recently, a new, valuable set of rain data was produced as a result of the TOGA-COARE experiment. In a few years, it will be possible to obtain satellite (TRMM) rain information, and a rain statistical description will be needed in the analysis of the observations obtained on an irregular spatial and temporal grid.
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"SOME STOCHASTIC MODELS OF RAINFALL WITH PARTICULAR REFERENCE TO HYDROLOGICAL APPLICATIONS." In Mathematical Statistics Theory and Applications, 605–10. De Gruyter, 1987. http://dx.doi.org/10.1515/9783112319086-091.

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Hudnurkar, Shilpa, Vidur Sood, Vedansh Mishra, Manobhav Mehta, Akash Upadhyay, Shilpa Gite, and Neela Rayavarapu. "Multivariate Time Series Forecasting of Rainfall Using Machine Learning." In Artificial Intelligence of Things for Weather Forecasting and Climatic Behavioral Analysis, 87–106. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-3981-4.ch007.

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Predicting rainfall is essential for assessing the impact of climatic and hydrological changes over a specific region, predicting natural disasters or day-to-day life. It is one of the most prominent, complex, and essential weather forecasting and meteorology tasks. In this chapter, long short-term memory network (LSTM), artificial neural network (ANN), and 1-dimensional convolutional neural network LSTM (1D CNN-LSTM) models are explored for predicting rainfall at multiple lead times. The daily weather parameter data of over 15 years is collected for a station in Maharashtra. Rainfall data is classified into three classes: no-rain, light rain, and moderate-to-heavy rain. The principal component analysis (PCA) helped to reduce the input feature dimension. The performance of all the networks are compared in terms of accuracy and F1 score. It is observed that LSTM predicts rainfall with consistent accuracy of 82% for 1 to 6 days lead time while the performance of 1D CNN-LSTM and ANN are comparable to LSTM.
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Jayswal, Ekta N., and Purvi M. Pandya. "Fractional-Order Model to Visualize the Effect of Plastic Pollution on Rain." In Mathematical Models of Infectious Diseases and Social Issues, 178–95. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3741-1.ch008.

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In this era, one of the biggest issues faced by humans is due to plastic pollution as it dwells in environment and depletes the ecosystem. This affects the climate and disturbs the chain of rain, which is the common source of obtaining water body. Also, this resulting pollution causes the toxicity in rain. Accordingly, the mathematical model is framed by considering fractional order derivative. Pollution free and endemic equilibrium points are worked out for integer order system of non-linear differential equations. Local stability of equilibrium points brings attention on dynamical behavior of model with sufficient condition. With the help of basic reproduction number, bifurcation is analyzed, which shows the chaotic nature of this model. Providing Caputo derivative of fractional order, a numerical simulation has been done by taking different values of order for the system.
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Hartomo, Kristoko Dwi, Sri Yulianto Joko Prasetyo, Muchamad Taufiq Anwar, and Hindriyanto Dwi Purnomo. "Rainfall Prediction Model Using Exponential Smoothing Seasonal Planting Index (ESSPI) For Determination of Crop Planting Pattern." In Computational Intelligence in the Internet of Things, 234–55. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7955-7.ch010.

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The traditional crop farmers rely heavily on rain pattern to decide the time for planting crops. The emerging climate change has caused a shift in the rain pattern and consequently affected the crop yield. Therefore, providing a good rainfall prediction models would enable us to recommend best planting pattern (when to plant) in order to give maximum yield. The recent and widely used rainfall prediction model for determining the cropping patterns using exponential smoothing method recommended by the Food and Agriculture Organization (FAO) suffered from short-term forecasting inconsistencies and inaccuracies for long-term forecasting. In this study, the authors developed a new rainfall prediction model which applied exponential smoothing onto seasonal planting index as the basis for determining planting pattern. The results show that the model gives better accuracy than the original exponential smoothing model.
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Prottasha, Nusrat Jahan, Md Jashim Uddin, Md Kowsher, Rokeya Khatun Shorna, Niaz Al Murshed, and Boktiar Ahmed Bappy. "Development of Multiple Combined Regression Methods for Rainfall Measurement." In SCRS CONFERENCE PROCEEDINGS ON INTELLIGENT SYSTEMS. Soft Computing Research Society, 2021. http://dx.doi.org/10.52458/978-93-91842-08-6-7.

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Rainfall forecast is imperative as overwhelming precipitation can lead to numerous catastrophes. The prediction makes a difference for individuals to require preventive measures. In addition, the expectation ought to be precise. Most of the nations in the world is an agricultural nation and most of the economy of any nation depends upon agriculture. Rain plays an imperative part in agribusiness so the early expectation of rainfall plays a vital part within the economy of any agricultural. Overwhelming precipitation may well be a major disadvantage. It’s a cause for natural disasters like floods and drought that unit of measurement experienced by people over the world each year. Rainfall forecast has been one of the foremost challenging issues around the world in the final year. There are so many techniques that have been invented for predicting rainfall but most of them are classification, clustering techniques. Predicting the quantity of rain prediction is crucial for countries' people. In our paperwork, we have proposed some regression analysis techniques which can be utilized for predicting the quantity of rainfall (The amount of rainfall recorded for the day in mm) based on some historical weather conditions dataset. we have applied 10 supervised regressors (Machine Learning Model) and some preprocessing methodology to the dataset. We have also analyzed the result and compared them using various statistical parameters among these trained models to find the bestperformed model. Using this model for predicting the quantity of rainfall in some different places. Finally, the Random Forest regressor has predicted the best r2 score of 0.869904217, and the mean absolute error is 0.194459262, mean squared error is 0.126358647 and the root mean squared error is 0.355469615.
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Conference papers on the topic "Rain and rainfall Mathematical models"

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Olurotimi, E. O., and J. S. Ojo. "Testing rainfall rate models for rain attenuation prediction purposes in tropical climate." In 2014 XXXIth URSI General Assembly and Scientific Symposium (URSI GASS). IEEE, 2014. http://dx.doi.org/10.1109/ursigass.2014.6929688.

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Hopkins, C., and Y. Yu. "PREDICTION OF RAIN NOISE IN BUILDINGS USING EMPIRICAL MODELS FOR ARTIFICIAL AND NATURAL RAINFALL." In ACOUSTICS 2020. Institute of Acoustics, 2020. http://dx.doi.org/10.25144/13331.

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Hopkins, C., and Y. Yu. "PREDICTION OF RAIN NOISE IN BUILDINGS USING EMPIRICAL MODELS FOR ARTIFICIAL AND NATURAL RAINFALL." In ACOUSTICS 2020. Institute of Acoustics, 2020. http://dx.doi.org/10.25144/13331.

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Hanisah, Suhaimi, and Jamaludin Suhaila. "Generalized linear models (GLMs) approach in modeling rainfall data over Johor area." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887723.

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Karthika, D., and K. Karthikeyan. "Analysis of Mathematical Models for Rainfall Prediction Using Seasonal Rainfall Data: A Case Study for Tamil Nadu, India." In 2022 First International Conference on Electrical, Electronics, Information and Communication Technologies (ICEEICT). IEEE, 2022. http://dx.doi.org/10.1109/iceeict53079.2022.9768602.

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Suhaimi, Nor Hanisah, and Shariffah Suhaila. "Generalized additive models (GAMs) approach in modeling rainfall data over Johor area." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954626.

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Vinayak S Shedekar, Larry C Brown, Maryjane Heckel, Kevin W King, Norman R Fausey, and R Daren Harmel. "Measurement Errors in Tipping Bucket Rain Gauges under Different Rainfall Intensities and their implication to Hydrologic Models." In 2009 Reno, Nevada, June 21 - June 24, 2009. St. Joseph, MI: American Society of Agricultural and Biological Engineers, 2009. http://dx.doi.org/10.13031/2013.27308.

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Suryana, J., S. Utoro, K. Tanaka, K. Igarashi, and M. Iida. "Study of Prediction Models Compared with the Measurement Results of Rainfall Rate and Ku-band Rain Attenuation at Indonesian Tropical Cities." In 2005 5th International Conference on Information Communications and Signal Processing. IEEE, 2005. http://dx.doi.org/10.1109/icics.2005.1689325.

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Silva, Anderson, Thiago Moeda, and Fabio Porto. "Analysis and Visualization of Extreme Weather Events in the City of Rio de Janeiro." In Simpósio Brasileiro de Banco de Dados. Sociedade Brasileira de Computação - SBC, 2022. http://dx.doi.org/10.5753/sbbd_estendido.2022.21866.

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Extreme weather events regularly occur in different locations, causing immense social, environmental and economic impact and damage. Especially in the city of Rio de Janeiro, understanding extreme events related to heavy rains is a fundamental component for the correct prediction of new phenomena, ideally resulting in models capable of predicting when, how and where they will occur. The current work proposes the analysis of rain data collected from rainfall stations positioned in the city of Rio de Janeiro, with the objective of developing a spatial representation that can be used to predict heavy rains from climate models.
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Gahlot, Aishwerya, Ritu Eshcol, Richard Kreeger, and Lakshmi Sankar. "Numerical Simulations of the Adverse Effects of Rain on Airfoil and Rotor Aerodynamic Characteristics." In Vertical Flight Society 78th Annual Forum & Technology Display. The Vertical Flight Society, 2022. http://dx.doi.org/10.4050/f-0078-2022-17476.

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There is a significant interest in improving the performance of rotors under adverse operating conditions. However, there is a very limited understanding of the performance implications on 2D airfoils and rotor blades under adverse effects of rainfall. Furthermore, the fundamental physical phenomena causing the loss in performance are not clearly understood. In this study, low fidelity models are first developed to rapidly estimate the water layer formation on 2D airfoils and assess the resulting impact on lift and drag characteristics. The low fidelity simulations are also useful to obtain quick estimates of water layer thickness as a function of liquid water content and droplet diameter. Subsequently, computational fluid dynamics studies for 2D airfoils and a small-scale rotor in hover are done to obtain more accurate estimates of the effects of rain on airfoil performance and match test data where available. Higher-fidelity parametric studies for various airfoils were conducted by varying angles of attack, the liquid water content in the rain droplets, and the droplet diameters to capture trends in performance degradation. The resulting trends match the trends from the test data reasonably well. The higher fidelity airfoil loads are subsequently used within a classical combined blade element-momentum model (BEM) to assess the loss of performance attributable to rain for a small-scale rotor.
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Reports on the topic "Rain and rainfall Mathematical models"

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Agassi, Menahem, Michael J. Singer, Eyal Ben-Dor, Naftaly Goldshleger, Donald Rundquist, Dan Blumberg, and Yoram Benyamini. Developing Remote Sensing Based-Techniques for the Evaluation of Soil Infiltration Rate and Surface Roughness. United States Department of Agriculture, November 2001. http://dx.doi.org/10.32747/2001.7586479.bard.

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The objective of this one-year project was to show whether a significant correlation can be established between the decreasing infiltration rate of the soil, during simulated rainstorm, and a following increase in the reflectance of the crusting soil. The project was supposed to be conducted under laboratory conditions, using at least three types of soils from each country. The general goal of this work was to develop a method for measuring the soil infiltration rate in-situ, solely from the reflectance readings, using a spectrometer. Loss of rain and irrigation water from cultivated fields is a matter of great concern, especially in arid, semi-arid regions, e.g. much of Israel and vast area in US, where water is a limiting factor for crop production. A major reason for runoff of rain and overhead irrigation water is the structural crust that is generated over a bare soils surface during rainfall or overhead irrigation events and reduces its infiltration rate (IR), considerably. IR data is essential for predicting the amount of percolating rainwater and runoff. Available information on in situ infiltration rate and crust strength is necessary for the farmers to consider: when it is necessary to cultivate for breaking the soil crust, crust strength and seedlings emergence, precision farming, etc. To date, soil IR is measured in the laboratory and in small-scale field plots, using rainfall simulators. This method is tedious and consumes considerable resources. Therefore, an available, non-destructive-in situ methods for soil IR and soil crusting levels evaluations, are essential for the verification of infiltration and runoff models and the evaluation of the amount of available water in the soil. In this research, soil samples from the US and Israel were subjected to simulated rainstorms of increasing levels of cumulative energies, during which IR (crusting levels) were measured. The soils from the US were studied simultaneously in the US and in Israel in order to compare the effect of the methodology on the results. The soil surface reflectance was remotely measured, using laboratory and portable spectrometers in the VIS-NIR and SWIR spectral region (0.4-2.5mm). A correlation coefficient spectra in which the wavelength, consisting of the higher correlation, was selected to hold the highest linear correlation between the spectroscopy and the infiltration rate. There does not appear to be a single wavelength that will be best for all soils. The results with the six soils in both countries indeed showed that there is a significant correlation between the infiltration rate of crusted soils and their reflectance values. Regarding the wavelength with the highest correlation for each soil, it is likely that either a combined analysis with more then one wavelength or several "best" wavelengths will be found that will provide useful data on soil surface condition and infiltration rate. The product of this work will serve as a model for predicting infiltration rate and crusting levels solely from the reflectance readings. Developing the aforementioned methodologies will allow increased utilization of rain and irrigation water, reduced runoff, floods and soil erosion hazards, reduced seedlings emergence problems and increased plants stand and yields.
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