Estimate of Reference Evapotranspiration Through Continuous Probability Modelling

Uliana, Eduardo Morgan; Silva, Demétrius D. da; Silva, José G. F. da; Fraga, Micael de Souza; Lisboa, Luana

doi:10.1590/1809-4430-eng.agric.v37n2p257-267/2017

“…In terms of the marginal structure, our results are consistent with other global-scale studies in literature (besides the ones previously mentioned in Section 2.2) on nearly Gaussian temperature [89], wind speed transition of extreme tail from Rayleigh to Weibull and Pareto-type [70,[170][171][172], sea level pressure [173], streamflow heavy tail [157,174], precipitation Pareto-type tail [3,74,149,[175][176][177][178][179][180][181][182], evaporation [183,184], and nearly Gaussian turbulent processes [185].…”

Section: Discussionsupporting

confidence: 90%

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

Dimitriadis

¹

,

Koutsoyiannis

²

,

Iliopoulou

³

et al. 2021

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To seek stochastic analogies in key processes related to the hydrological cycle, an extended collection of several billions of records from hundred thousands of worldwide stations is used in this work. The examined processes are the near-surface hourly temperature, dew point, relative humidity, sea level pressure, and atmospheric wind speed, as well as the hourly/daily streamflow and precipitation. Through the use of robust stochastic metrics such as the K-moments and a second-order climacogram (i.e., variance of the averaged process vs. scale), it is found that several stochastic similarities exist in both the marginal structure, in terms of the first four moments, and in the second-order dependence structure. Stochastic similarities are also detected among the examined processes, forming a specific hierarchy among their marginal and dependence structures, similar to the one in the hydrological cycle. Finally, similarities are also traced to the isotropic and nearly Gaussian turbulence, as analyzed through extensive lab recordings of grid turbulence and of turbulent buoyant jet along the axis, which resembles the turbulent shear and buoyant regime that dominates and drives the hydrological-cycle processes in the boundary layer. The results are found to be consistent with other studies in literature such as solar radiation, ocean waves, and evaporation, and they can be also justified by the principle of maximum entropy. Therefore, they allow for the development of a universal stochastic view of the hydrological-cycle under the Hurst–Kolmogorov dynamics, with marginal structures extending from nearly Gaussian to Pareto-type tail behavior, and with dependence structures exhibiting roughness (fractal) behavior at small scales, long-term persistence at large scales, and a transient behavior at intermediate scales.

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“…Khanmo-hammadi [31] fitted annual reference evapotranspiration data to Lognormal, generalized logistic, and Pearson III distributions and realized that Pearson III was the most appropriate. Uliana et al [32] fitted evapotranspiration to Gamma distribution, which is a type of Pearson III distribution. Msowoya et al [33] fitted the evapotranspiration data to the generalized logistic distribution.…”

Section: Reference Evapotranspirationmentioning

confidence: 99%

“…Thus, it can be assumed that yðt, VÞ is a function of time t in years only, that is yðt, VÞ = yðtÞ. Under this assumption, we have ∂y m ðt, VÞ/∂t = dy m ðtÞ/dt so that the model in Equation [32] can be expressed as…”

Section: Maize Yield Modeling and Predictionmentioning

confidence: 99%

Trivariate Stochastic Weather Model for Predicting Maize Yield

Chidzalo¹,

Ngare

²

,

Mung’atu³

2022

Journal of Applied Mathematics

5

0

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Maize yield prediction in the sub-Saharan region is imperative for mitigation of risks emanating from crop loss due to changes in climate. Temperature, rainfall amount, and reference evapotranspiration are major climatic factors affecting maize yield. They are not only interdependent but also have significantly changed due to climate change, which causes nonlinearity and nonstationarity in weather data. Hence, there exists a need for a stochastic process for predicting maize yield with higher precision. To solve the problem, this paper constructs a joint stochastic process that acquires joints effects of the three weather processes from joint a probability density function (pdf) constructed using copulas that maintain interdependence. Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R 2 = 0.8389 and M A P E = 4.31 % under a deep learning framework. Its aggregated values predict maize yield with R 2 up to 0.9765 and M A P E = 1.94 % under common machine learning algorithms. Comparatively, the R 2 is 0.8829% and M A P E = 4.18 % , under the maize yield SDE. Thus, the joint stochastic process can be used to predict maize yield with higher precision.

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“…The most influential factor for climate change and the water cycle is evapotranspiration, as it is the only linkage between the water balance and the surface energy balance of the land (Wang et al, 2014). Some well-known authors worldwide suggested that knowledge about best fit statistical probability model in site ease is a correct hydrological prediction in the dimensioning drainage and irrigation planning (Fernandes, Wolff & Folegatti, 2019;Nam & Choi, 2014;Uliana et al, 2017;Yoo, Choi & Jang, 2008).…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of statistical probability distribution and non-parametric trend analysis for reference evapotranspiration

Gul

¹

,

Ren

²

,

Xiong

³

et al. 2021

PeerJ

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Accurate estimates of reference evapotranspiration are critical for water-resource management strategies such as irrigation scheduling and operation. Therefore, knowledge of events such as spatial and temporal reference evapotranspiration (ETo) and their related principle of statistical probability theory plays a vital role in amplifying sustainable irrigation planning. Spatiotemporal statistical probability distribution and its associated trends have not yet has explored in Pakistan. In this study, we have two objectives: (1) to determine the most appropriate statistical probability distribution that better describes ETo on mean monthly and seasons wise estimates for the design of irrigation system in Khyber Pakhtunkhwa, and (2) to check the trends in ETo on a monthly, seasonal, and annual basis. To check the ETo trends, we used the modified version of the Mann-Kendall and Sen Slope. We used Bayesian Kriging for spatial interpolation and propose a practical approach to the design and study of statistical probability distributions for the irrigation system and water supplies management. Also, the scheme preeminent explains ETo, on a monthly and seasonal basis. The statistical distribution that showed the best fit ETo result occupying 58.33% and 25% performance for the design of irrigation scheme in the entire study region on the monthly level was Johnson SB and Generalized Pareto, respectively. However, according to the Anderson-Darling (AD) and Kolmogorov–Smirnov (KS) goodness of fit measure, seasonal ETo estimates were preferably suited to the Burr, Johnson SB & Generalized Extreme Value. More research work must be conduct to assess the significance of this study to other fields. In conclusion, these findings might be helpful for water resource management and policymaker in future operations.

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Estimate of Reference Evapotranspiration Through Continuous Probability Modelling

Cited by 6 publications

References 6 publications

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

Trivariate Stochastic Weather Model for Predicting Maize Yield

Design and analysis of statistical probability distribution and non-parametric trend analysis for reference evapotranspiration

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