Home Technology Spatial mixture modeling for analyzing a rainfall pattern: A case study in Ireland
Article Open Access

Spatial mixture modeling for analyzing a rainfall pattern: A case study in Ireland

  • Amjad Hussein EMAIL logo and Safaa K. Kadhem
Published/Copyright: March 22, 2022
Download Article (PDF)
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Open Engineering
From the journal Open Engineering Volume 12 Issue 1

Abstract

This study investigates the spatial heterogeneity in the maximum monthly rainfall amounts reported by stations in Ireland from January 2018 to December 2020. The heterogeneity is modeled by the Bayesian normal mixture model with different ranks. The selection of the best model or the degree of heterogeneity is implemented using four criteria which are the modified Akaike information criterion, the modified Bayesian information criterion, the deviance information criterion, and the widely applicable information criterion. The estimation and model selection process is implemented using the Gibbs sampling. The results show that the maximum monthly rainfall amounts are accommodated in two and three components. The goodness of fit for the selected models is checked using the graphical plots including the probability density function and cumulative distribution function. This article also contributes via the spatial determination of return level or rainfall amounts at risk with different return periods using the prediction intervals constructed from the posterior predictive distribution.

Keywords: rainfall amounts; Bayesian mixture modeling; cumulative distribution; prediction interval; posterior predictive distribution

1 Introduction

Rainwater, also called precipitation, is a natural feature of the earth’s weather system. Air currents in the atmosphere bring evaporated water from the ocean and the earth’s surface into the sky. The evaporated liquid condenses in the cold air, forming moisture-filled rain clouds [1]. Rain water’s most well-known and most important effect is providing water to drink. According to the United States Geological Survey, rainwater seeps into the ground in a process called infiltration. Some of the water seeps deep beneath the top layers of soil where it fills up the space between subsurface rocks and becomes groundwater, also called the water table. Less than 2% of the earth’s water is groundwater, but it provides 30% of our freshwater. Without rain water’s continued replenishment of the water table, potable water would become scarcer than it already is in ref. [2]. Furthermore, many researchers demonstrated the impact of heavy rainfall on floods [3,4,5]. Therefore, the analysis of precipitation quantities on a certain area aims to give an overall visualization or prior information to evaluate the risk of some natural disasters such as droughts, floods, landslides, and so in ref. [6].

Many researchers have used different analysis methods to analyze the rainfall trend. Meneghini et al. [7] used different statistical methods such as the area-time integral (ATI) method to estimate the average rainfall over a large space. Arvind et al. [8] used different analysis methods on the Annual and Monthly rainfall for Musiri Region; they concluded that Gumbel distribution is the best type. Panda and Sahu [9] used the Mann–Kendall test as a statistical method and Sen’s slope estimator to examine and analyze the seasonal rainfall over the state of Odisha in India. Their results showed a relatively maximum amount of rainfall in monsoonal months. Nyatuame et al. [10] used linear regression analysis as a statistical method for annual and monthly rainfall. They stated an insignificant increasing trend in annual mean rainfall data among the Volta Region and a significant trend in mean monthly rainfall. Asfaw et al. [11] inspected the change of rainfall and temperature in north-central Ethiopia using gridded monthly precipitation data. The Mann–Kendall was used to detect the time series trend. Praveen et al. [12] analyzed and forecasted rainfall changed in India. They used Pettitt and Mann–Kendall tests as analysis methods. However, this group of studies did not take into account the variation in data.

This study assumes that the maximum rainfall quantities follow the normal distribution assuming that rains are distributed equally throughout Ireland. However, this assumption is invalid due to variation or fluctuation in rainfall amounts, leading to a phenomenon called the heterogeneity of the data. Identifying spatial heterogeneity of rainfall can give a valuable indicator for the analytical studies and government planning to detect the factors linked to various causes to the low or height in the rain falling. For this reason, the statistical modeling method called the mixture model with a finite number of components was proposed to accommodate the heterogeneity in data. The task of finite mixture models is to capture unobserved heterogeneity in the population by assuming that the population consists of K homogeneous subgroups [13]. However, identifying the number of homogeneous subgroups K or the rank of model forms is more challenging. Several criteria have been addressed in the literature to determine the model’s rank under both the frequentist and the Bayesian settings. As in this article, the Bayesian framework focused on estimating the model parameters, four well-known model selection criteria derived under the Bayesian principle. These criteria are the modified Akaike information criterion (AIC) [14], the modified Bayesian information criterion (BIC) [15], the deviance information criterion (DIC) [16], and the widely applicable information criterion (WAIC) [17]. An approach was followed to fit a set of candidate models to the data and select the best one. In other words, in this research, the assumption that the number of the model components is fixed and unknown and the best model is determined by one of our four proposed criteria via fitting several candidate mixture models with different components. Despite that, another approach called the reversible jump Markov chain Monte Carlo sampling [18] can be applied to select the appropriate number of components. However, this latter approach has drawbacks when the Markov chain moves between mixture models with different classes [13].

This article also determines the spatial return level or rainfall amounts at risk with different return periods using the prediction intervals constructed from the posterior predictive distribution. This latter can be considered as a newly developed alternative approach to the confidence intervals adopted by several kinds of literature to identify the rainfall amounts at risk [4,6].

This article is classified as follows. Section 2 introduces the article’s methodology, including the model’s construction, estimation, and election. Section 3 includes a description of the data under study. The results and discussion are shown in Section 4. Finally, Section 5 summarizes the important conclusions of this article.

2 Methodology

This section introduced the building of the model and estimation of the model parameters under the Bayesian principle. After that, the best model to fit the maximum was selected. Each station’s monthly rainfall quantity is reported under study using model selection criteria such as AIC, BIC, DIC, and WAIC. In addition, the goodness of fit was also checked.

2.1 Model construction and Bayesian analysis

Let us assume that the study region is divided into m stations, and let y i represent the maximum monthly rainfall quantity reported by ith station, i = 1 , 2 , … , n . To take into account the heterogeneity in the data of rainfall quantities, those data follow a mixture of univariate Gaussian distribution:

(1) Pr ( y ∣ k , w , μ , σ 2 ) = ∑ j = 1 k w j N j ( y ∣ μ j , σ j 2 ) ,

where k is the number of components of the model (that can be viewed as levels of monthly rainfall quantity), w = ( w 1 , w 2 , … , w k ) is the vector of probabilities associated with the components of the model, with ∑ j = 1 k w j = 1 and w j ≥ 0 , and N ( y i ∣ . ) represent the mixed Gaussian probability density function (PDF) which is defined as

(2) N j ( y ∣ μ j , σ j 2 ) = 1 2 π σ j 2 exp − 1 2 σ j 2 ( y − μ j ) 2 ,

where μ j and σ j 2 are the mean and variance of j th mixture of the Gaussian distribution, respectively. The mixture models can be analytically easier by including latent variables in their formation as this latter makes it more useful for the purpose of interpretation and numerical computations. For a mixture with a certain number of components, the model can be described by inserting n independent discrete variables, z 1 , z 2 , … , z n , with the multinomial distribution Pr ( z i = j ∣ μ , σ 2 , w , K ) = w j , for j = 1 , 2 , … , K . Given z = ( z 1 , z 2 , … , z n ) , equation (1) can be written as

(3) Pr ( y , z ∣ μ , σ 2 , w , K ) = ∏ i = 1 n ∏ j = 1 K { w j N j ( y i ∣ μ j , σ j 2 ) } z i j ,

which is called the complete-data likelihood function. The role of latent variable, z i , is to assign the observation y i to one of the mixture components. By taking the logarithm for equation (3), we obtain:

(4) ℓ ( μ , σ 2 , w ∣ y , z ) = log ∏ i = 1 n ∏ j = 1 K { w j N j ( y i ∣ μ j , σ j 2 ) } z i j , = ∑ i = 1 n ∑ j = 1 K [ log w z i j N j ( y i ∣ μ z i j , σ z i j 2 ) ] .

The log-likelihood function in equation (4) can be approximated over the posterior distribution. For example, given ( ℓ ( 0 ) , ℓ ( 1 ) , … , ℓ ( M ) ) computed over a full Monte Carlo Markov chain (MCMC) run, obtaining the estimated log-likelihood by post-processing the posterior outcome:

(5) ℓ ˆ ( μ , σ 2 , w ∣ y , z ) = 1 M ∑ m = 1 M ∑ i = 1 n ∑ j = 1 K [ log w z i j ( m ) ( m ) N ( y i ∣ μ z i j ( m ) ( m ) , σ z i j ( m ) 2 ( m ) ) ] .

To complete the Bayesian analysis for the model, we have to define the prior and posterior distributions for all the model parameters. For this purpose, Algorithm 1, given by ref. [19], is used to implement the sampling process using one of the MCMC approaches that is called Gibbs sampler.

Algorithm 1: Gibbs sampler for K -component normal mixture model
1. Initialization: Choose w j ( 0 ) , μ j ( 0 ) and σ j 2 ( 0 ) , j = 1 , 2 , … , K .
2 Iteration: for m = 1 , 2 , … , M
(a) Generate z t ( m ) ; t = 1 , … , T from ( j = 1 , 2 , … , K )
Pr ( z t ( m ) = j ) = ∝ w j ( m − 1 ) σ j ( m − 1 ) exp − ( y t − μ j ( m − 1 ) ) 2 2 ( σ j 2 ) ( m − 1 ) ,
and compute: n k ( m ) = ∑ l = 1 n I z l ( m ) = j and s j y ( m ) = ∑ l = 1 n I z l ( m ) = j y l .
(b) Update w j ( m ) from Dir ( δ 1 + n 1 ( m ) , δ 2 + n 2 ( m ) , … , δ K + n K ( m ) ) ,  for j = 1 , 2 , … , K
(c) Generate μ j ( m ) ; j = 1 , 2 , … , K  from N η j ζ j + s j y ( m ) ζ j + ( n j ) ( m ) , σ j 2 ( m − 1 ) ζ j + ( n j ) ( m ) ,
and compute: s j ν ( m ) = ∑ t = 1 n I z l ( m ) = j ( y t − μ j ( m ) ) 2 .
(d) Generate σ j 2 ( m ) ; j = 1 , 2 , … , K from
InvGamma ( a j + 0.5 ( n j ( m ) + 1 ) , b j + 0.5 ζ j ( μ j ( m ) − η j ) 2 + 0.5 ( s j ν ( m ) ) ).

where η j , ζ j , a j , b j , and δ j are known hyper-parameters, j = 1 , 2 , … , K , and they are commonly given non-informative hyper-priors or flat values [20]. For instance, the inverse Gamma with parameters a = 0.001 and b = 0.001 and thus a mean of a / b = 1 and a variance of a / b 2 = 1,000 can give diffuse values of this form. The prior of the mean parameter can be assigned flat values from a Normal distribution with a shape parameter, η = 0 , and a scale parameter, ζ = 0.001 , which has a large variance equal to 1,000. The weight parameter, π , is given a Dirichlet prior with non-informative value, δ j = 1 , j = 1 , 2 , … , K .

2.2 Model selection criteria

These first three sections introduce four criteria for choosing the number of components in Gaussian mixture models in Bayesian settings. In the last section, a graphitic display method to evaluate the goodness of fitness of the model is shown.

2.2.1 Akaike information and Bayesian information criteria

Two well-known criteria modified were introduced under the Bayesian principle, which are the AIC and BIC proposed by Kadhem et al. [21]. These criteria depend on the deviance and penality term. From equation (5), the deviance can be defined as twice the negative log likelihood:

(6) D ( μ , σ 2 , w ) = − 2 { ℓ ˆ ( μ , σ 2 , w ∣ y , z ) } ,

where the deviance above is approximated over MCMC samples as explained in equation (5). The penality term is computed based on the free parameters of the model as: h = 3 K − 1 [22]. The AIC and BIC take the deviance as a measure of model fit and penalizes it for the number of parameters in the model. Then, AIC and BIC are given as follows:

(7) AIC = D ( μ , σ 2 , w ) + 2 h , BIC = D ( μ , σ 2 , w ) + h log ( n ) ,

where n is the sample size.

2.2.2 DIC

Another criterion proposed in this article is the DIC. Eight versions of this criterion were introduced by Celeux et al. [23]. They recommended the version that is based on the complete-data likelihood. In this article, we apply this version which is given by:

(8) DIC = − 4 E μ , σ 2 , w , z [ log Pr ( y , z ∣ μ , σ 2 , w , K ) ] + 2 E z [ log Pr ( y , z ∣ μ ˆ ( z ) , σ 2 ˆ ( z ) , w ˆ ( z ) ) ] ,

with its effect number of parameters, p DIC , defined as follows:

(9) p DIC = − 2 E μ , σ 2 , w , z [ log Pr ( y , z ∣ μ , σ 2 , w , K ) ] + 2 E z [ log Pr ( y , z ∣ μ ˆ ( z ) , σ 2 ˆ ( z ) , w ˆ ( z ) ) ] ,

where μ ˆ ( z ) , σ ˆ 2 ( z ) , and w ˆ ( z ) are the complete-data posterior modes of the parameters μ , σ 2 , and w , respectively, which are computed for each samples from the posterior p ( z ∣ y , μ , σ 2 , w ) .

2.2.3 WAIC

The last criterion proposed in this article is the WAIC. This criterion is fully Bayesian and it is computed based on the so-called integrated pointwise predictive density (ilppd). For a Gaussian mixture distribution, the ilppd can be defined as follows:

(10) ilppd y = log ∏ i = 1 n Gaussian post ( y i ) , = ∑ i = 1 n log E { μ , σ 2 , w , z } [ Gaussian ( y i ∣ μ , σ 2 , w , z ) ∣ y ] , = 1 M ∑ m = 1 M ∑ i = 1 n log Gaussian ( y i ∣ μ z i ( m ) ( m ) , σ z i ( m ) 2 ( m ) , w z i ( m ) ( m ) ) ,

where μ z i t ( m ) ( m ) , σ z i ( m ) 2 ( m ) , and w z i ( m ) ( m ) represent the m th sample drawn in Gibbs sampler. To complete the definition of the WAIC, Gelman et al. [20] proposed adding a correction term or the so-called effect number of parameters p WAIC , to avoid the bias. This number is based on computing the variance of individual terms in the ilppd, which is defined as follows:

(11) p WAIC = ∑ i = 1 n V { μ , σ 2 , w , z } [ log Gaussian ( y i ∣ μ , σ 2 , w , z ) ∣ y ] , = ∑ m = 1 M ∑ i = 1 n V { μ , σ 2 , w , z } [ log Gaussian × ( y i ∣ μ z i ( m ) ( m ) , σ z i ( m ) 2 ( m ) , w z i ( m ) ( m ) ) ] .

The WAIC then is constructed as follows:

(12) WAIC = − 2 ilppd ^ Y + 2 p WAIC .

2.2.4 Graphical display method

In this research, the cumulative distribution function (CDF) is used as one of the graphical display methods to reinforce the correct model chosen by the model selection criteria above. The CDF plot is implemented to visualize the fitness of model distributions where it is monotonically increasing between the limits from 0 to 1. The CDF of a Gaussian mixture with K components can be given as

(13) F ( x ) = w 1 F 1 ( x ) + w 2 F 2 ( x ) + … + w K F K ( x ) .

2.3 Analysis of rainfall amounts at risk

In this section, the so-called prediction intervals that are being constructed from the posterior predictive distribution were introduced [20] to analyze the extreme amounts of rainfall. The predicted values can be used as a goodness of fit approach to prediction accuracy of a statistical model. The limits of prediction interval can be constructed by the lower prediction limit, LPI ( y ∗ ), and upper prediction limit, UPI ( y ∗ ), where y ∗ represent the predicted data. In such cases, the interval [LPI ( y ∗ ), UPI ( y ∗ )] is termed as the prediction interval and has a prediction coefficient of (1 − p)100%. By introducing the prediction interval, the range that T-year rainfall takes can be theoretically estimated and also becomes possible to estimate the swing of T-year probability hydrological quantities in flood control measures for a T-year probability scale. This makes it possible to interpret the record-breaking heavy rainfall mentioned above as a phenomenon within the prediction interval. In other words, the prediction interval can be a tool to evaluate the return period of heavy rainfall.

In this research, the prediction interval is constructed as follows. Given the estimation of the model parameters sampling through an MCMC, ( w j ( m ) , μ j ( m ) , σ j 2 ( m ) ; m = 1 , 2 , … , M ) and observed infections data, y = ( y 1 , y 2 , … , y n ) , for each region i at the time t , the PPD for predicted infections, y i ∗ ; i = 1 , 2 , … , n of the normal mixture model can be defined as

(14) Pr ( y i ∗ ∣ y ) = ∫ μ ∫ σ 2 ∫ z Normal ( y i t ∗ ∣ μ , σ 2 , w , z ) × Normal post ( μ , σ 2 , w , z ∣ y ) d z d μ d σ 2 ,

where Normal post ( μ , σ 2 , w , z ∣ y ) represents the joint complete posterior distribution. Given samples of the relative risk parameter, λ j t ( m ) , and latent variables, z ( m ) , drawn from an MCMC run, the predictive data of a Poisson mixture model can be approximated as

(15) y i ∗ ( m ) ∼ Normal ( μ z i j t ( m ) ( m ) , σ z i j ( m ) 2 ( m ) ) ; i = 1 , 2 , … , n ; j = 1 , 2 , … , K .

Hence, the prediction interval can be formulated as follows:

(16) y i + h ∗ ± c σ h ˆ ,

where σ h ˆ is an estimate of the standard deviation of the h -step forecast distribution and c is the multiplier that includes a range of coverage probabilities assuming a normal forecast distribution.

Given that the return period can be calculated as follows. Let us assume that X is the variable that equals to or greater than an incident of magnitude x T occurring once in T years. In a given year, the probability of occurrence of incident X , Pr ( X ≥ x ) , is expressed as:

(17) Pr ( X ≥ x ) = 1 T ,

(18) T = 1 1 − Pr ( X ≥ x ) .

Wilks [6] pointed out that the amounts of maximum monthly rainfall with the 50-year or 100-year return periods cannot be directly calculated from the data set used here, but have to be extrapolated from the 98th and 99th percentiles of the fitted distribution, respectively, i.e., [ 1 − 0.9 8 − year ] − 1 = 50 years and [ 1 − 0.9 9 − year ] − 1 = 100 years. On this basis, we can compute the return periods based on the prediction intervals.

3 Data description

Ireland is an island in North western Europe in the North Atlantic Ocean with 84,421 km 2 (land; 98.2%, water; 1.8%). The coordinates are 5 3 ∘ 20.65 ′ N 6 ∘ 16.06 ′ W . It lies on the European continental shelf, part of the Eurasian Plate. Low lowlands and low mountainous beaches characterize it. Corran Tuathail, at 1,041 m above sea level, is the highest summit. The western coast has a rough shoreline with many islands, peninsulas, headlands, and bays. The Shannon River is Ireland’s longest river, flowing south from County Cavan in Ulster to the Atlantic Ocean. Along Ireland’s rivers, there are several big lakes, the greatest of which being Lough Neagh: 392 km 2 . More than 134,600 ha (19.5% of the total area) were devoted to growing crops; 6 and 1.5% of the agricultural area were used to grow cereals, and root and green crops, respectively. Over half of the agricultural production is exported. The income was increased from 314 £ million in 1972 to 1920 £ million in 1995 and 1.1 £ billion in 2001. Ireland’s climate is mild, moist, and changeable, with abundant rainfall and a lack of temperature extremes. Ireland’s climate is defined as a temperate oceanic climate. In general, Iceland has warm summers and pleasant winters, as compared to, say, Newfoundland, which is significantly warmer at the same latitude and located downwind of the Atlantic Ocean. It is also hotter than marine climates around the same latitude, such as the Pacific Northwest, due to the heat released by the Atlantic overturning circulation, which includes the North Atlantic Current and Gulf Stream. In comparison, Dublin is 9 ∘ warmer in the winter than St. John’s, Newfoundland, and 4 ∘ warmer than Seattle, Washington [23]. Ireland’s climate is not vulnerable to extreme weather phenomena, such as tornadoes, and storms are uncommon. Throughout the winter, the North Atlantic Current keeps the Irish coast clear of ice. Ireland, on the other hand, is vulnerable to storms heading eastward from the North Atlantic. The prevailing wind is from the southwest, and it breaks on the west coast’s steep mountains. As a result, off the west coast of County Kerry, Valentia Island receives nearly twice as much rain as Dublin, on the east coast (1,400 vs 762) mm, demonstrating the importance of rainfall in Western Ireland. The coldest months are January and February, with average daily air temperatures ranging from four to 7 ∘ C . July and August are the hottest months, with average daily air temperatures of 14 to 1 6 ∘ C . In July and August, daily maximum temperatures range from 17 to 1 8 ∘ along the coast to 19 to 2 0 ∘ inland. May and June are the months with the highest sunshine, with an average of 5–7 h per day. Extreme weather occurrences do occur, notwithstanding their rarity in comparison to other European countries. Atlantic depressions can bring gusts of up to 160 km/h to Western coastal regions in December, January, and February. Thunderstorms are common during the summer months, especially in late July and early August. This article investigates the rainfall pattern via analyzing the monthly maximum rainfall quantities reported by the stations on Island. The data on the rainfall are obtained from Met’ Eireann, Ireland’s National Meteorological Service, via web site (https://www.met.ie/climate/available-data/monthly-data#top) as shown in Table 1. The maximum values of rainfall amounts for all stations are presented from January 2018 to December 2020, as shown in Figure 1.

Table 1

Geographic characteristics of the stations under study

No. Stations Latitude (N) Longitude (E) Elevation (m)
1 Ballyhaise 52.69 − 8.918 15
2 Shannon Airport 51.847 − 8.486 155
3 Cork Airport 51.793 − 8.244 40
4 Roches Point 51.576 − 9.428 21
5 Sherkin Island 52.164 − 8.264 46
6 Moore Park 54.494 − 8.243 33
7 Finner Camp 55.372 − 7.339 20
8 Malin Head 53.248 − 6.241 71
9 Dublin Airport 53.364 − 6.35 48
10 Phoenix Park 53.289 − 8.786 40
11 Athenry 53.326 − 9.901 21
12 Mace Head 53.306 − 6.439 91
13 Casement 51.948 − 10.241 24
14 Valentia Observatory 54.051 − 7.31 78
15 Belmullet 54.228 − 10.007 9
16 Claremorris 53.711 − 8.993 68
17 Knock Airport 53.906 − 8.817 201
18 Dunsany 53.516 − 6.66 83
19 Newport Furnace 53.922 − 9.572 22
20 Gurteen 53.053 − 8.009 75
21 Markree Castle 54.175 − 8.456 34
22 Mullingar 53.537 − 7.362 101
23 Johnstown Castle 52.298 − 6.497 62
24 Oak Park 52.861 − 6.915 62
25 Mount Dillon 53.727 − 7.981 39
Figure 1 The maximum values of rainfall amounts for all stations over period from January 2018 to December 2020.
Figure 1

The maximum values of rainfall amounts for all stations over period from January 2018 to December 2020.

4 Results and discussion

For every station, the aim is to select the best normal mixture fitted to the monthly maximum rainfall amounts for return periods of 50 and 100 years expressed with prediction interval periods derived from a posterior predictive distribution. Table 2 shows the results of model selection, where the maximum rainfall amounts reported by the stations follow models either with two or three components as produced by the proposed criteria. Note that model with K = 1 (standard normal distribution) is not selected by all model selection criteria suggesting that the data suffer from the heterogeneity. The model estimation results for the models selected by the criteria are shown in Table 3, where the estimated weights, means, and variances represent the estimated parameters of the models selected by our proposed criteria. In addition, we provide the CDF and PDF plots for the model selection, in Figures 2 and 3, respectively, which appear as adequate goodness of fit. It can be noted from Table 2 that most of the rainfall data reported by stations (18 stations) are modeled by models with K = 2 , except seven stations such as Dublin Airport, Phoenix Park, Athenry, Mace Head, Newport Furnace, Mullingar, and Johnstown Castle are modeled by mixture model with K = 3 .

Table 2

Results of the best model selected by all or most selection criteria for every station

No. of components Best model
No. Stations 1 2 3 4 5 6 (Selection %)
1 Ballyhaise — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
2 Shannon Airport — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
3 Cork Airport — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
4 Roches Point — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
5 Sherkin Island — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
6 Moore Park — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
7 Finner Camp — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
8 Malin Head — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
9 Dublin Airport — AIC BIC, DIC, WAIC — — — K = 3 (75%)
10 Phoenix Park — AIC BIC, DIC, WAIC — — — K = 3 (75%)
11 Athenry — AIC BIC, DIC, WAIC — — — K = 3 (75%)
12 Mace Head — AIC BIC, DIC, WAIC — — — K = 3 (75%)
13 Casement — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
14 Valentia Observatory — AIC, BIC, DIC WAIC — — — K = 2 (75%)
15 Belmullet — AIC, BIC, DIC WAIC — — — K = 2 (75%)
16 Claremorris — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
17 Knock Airport — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
18 Dunsany — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
19 Newport Furnace — AIC BIC, DIC, WAIC — — — K = 3 (75%)
20 Gurteen — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
21 Markree Castle — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
22 Mullingar — AIC BIC, DIC, WAIC — — — K = 3 (75%)
23 Johnstown Castle — AIC BIC, DIC, WAIC — — — K = 3 (75%)
24 Oak Park — AIC, BIC, DIC WAIC — — — K = 2 (75%)
25 Mount Dillon — AIC, BIC, DIC, WAIC — — — — K = 2 (100%)
Table 3

Results of the best model selected by the model selection criteria

Weights Means Variances
Station w 1 w 2 w 3 μ 1 μ 2 μ 3 σ 1 2 σ 2 2 σ 3 2
Ballyhaise 0.54 0.45 — 61.81 121.91 — 21.76 41.31 —
Shannon Airport 0.78 0.21 — 70.90 170.42 — 29.79 39.32 —
Cork Airport 0.71 0.28 — 82.57 177.62 — 33.55 17.44 —
Roches Point 0.55 0.44 — 60.97 133.86 — 23.21 35.791 —
Sherkin Island 0.55 0.44 — 68.29 141.36 — 26.44 33.82 —
Moore Park 0.56 0.43 — 57.26 134.74 — 20.07 26.65 —
Finner Camp 0.63 0.36 — 78.24 164.70 — 27.02 43.46 —
Malin Head 0.51 0.48 — 73.48 126.48 — 26.05 39.82 —
Dublin Airport 0.49 0.41 0.09 34.51 84.73 140.68 15.49 11.53 23.37
Phoenix Park 0.47 0.44 0.08 33.27 80.30 139.25 15.74 12.67 14.69
Athenry 0.62 0.32 0.05 76.90 148.94 272.88 22.99 24.85 24.48
Mace Head 0.31 0.19 0.49 46.24 160.97 97.68 16.11 10.36 16.74
Casement 0.36 0.63 — 30.60 84.88 — 12.52 29.65 —
Valentia Observatory 0.57 0.42 — 101.25 216.01 — 37.68 30.20 —
Belmullet 0.24 0.75 — 47.43 133.60 — 16.93 42.71 —
Claremorris 0.75 0.24 — 98.21 182.56 — 39.09 54.85 —
Knock Airport 0.64 0.35 — 103.33 186.36 — 36.37 39.62 —
Dunsany 0.79 0.20 — 58.02 139.22 — 25.10 17.04 —
Newport Furnace 0.264 0.43 0.30 152.88 244.76 73.52 14.69 44.09 25.04
Gurteen 0.61 0.38 — 61.67 106.88 — 26.86 48.08 —
Markree Castle 0.83 0.16 — 89.19 202.55 — 30.27 24.39 —
Mullingar 0.47 0.29 0.24 47.01 134.91 86.86 15.53 28.73 11.59
Johnstown Castle 0.36 0.42 0.22 41.83 100.52 166.24 15.48 18.02 19.36
Oak Park 0.56 0.44 — 44.25 108.62 — 20.91 29.38 —
Mount Dillon 0.68 0.32 — 76.63 132.65 — 27.12 52.12 —
Figure 2 The CDF plots for the model selected by the proposed model selection criteria for each station.
Figure 2

The CDF plots for the model selected by the proposed model selection criteria for each station.

Figure 3 The best-fitting model for each station.
Figure 3

The best-fitting model for each station.

For the results of determination of the return periods, Figures 2 and 3 show the estimation of risk levels for a certain incident, with including a plot of the actual maximum monthly rainfall amounts in red color (as threshold), which are represented by the heights of rainfall levels of 50 and 100 year return periods with 95% prediction intervals. It can see from Figure 4 that there is a stable in rainfall amounts over 50 years return period (all values of mid-point of prediction intervals under the actual data), but there is a notable increase in the rainfall amounts at the risk over 100 years return period as shown in Figure 5. More specifically, the stations: Cork Airport (215 mm), Roches Point (214 mm), Sherkin Island (214 mm), Morre Park (213 mm), Malin Head (214 mm), Dublin Airport (209 mm), Phoenix Park (210 mm), Mace Head (212 mm), Casement (210 mm), Dunsany (210 mm), Mullingar (214 mm), Johnstown Castle (212 mm) and Oak Park (215 mm), show high rainfall amounts on the long term.

Figure 4 The maximum monthly rainfall amounts (measured in millimeter (mm)) for each station vs the predicted values represented by 95% prediction intervals for return period 50 years.
Figure 4

The maximum monthly rainfall amounts (measured in millimeter (mm)) for each station vs the predicted values represented by 95% prediction intervals for return period 50 years.

Figure 5 The maximum monthly rainfall amounts (measured in millimeter (mm)) for each station vs the predicted values represented by 95% prediction intervals for return period 100 years.
Figure 5

The maximum monthly rainfall amounts (measured in millimeter (mm)) for each station vs the predicted values represented by 95% prediction intervals for return period 100 years.

5 Conclusion

In this study, we used a finite mixture of Gaussian distributions to model the heterogeneity in monthly rainfall quantities in Ireland based on databases taken from 25 stations. Several tools were used to assess the Bayesian normal mixture models fitted to the data under study. The model selection criteria such as AIC, BIC, DIC, and WAIC were used to select the best model fit to the data. In addition, we used graphical approaches such as the CDF and PDF to assess both the selected models. Most of the data reported by stations were modeled under a normal mixture model with two components, while the rest stations were modeled with only three components. We conclude that data that have been modeled by two components are more homogeneous than those modeled by three components. This article also shows the computation of return periods, for 50 and 100 years, for each station using the prediction intervals deriving from the posterior predictive distribution of the models selected by the model selection criteria. The diagnostic of high rainfall rates in the long term can help the related systems to put the plans that save lives and possessions. The advantage of the methodology used in this article is to reveal the heterogeneity in data by modeling it over several homogeneous groups. On the other hand, the disadvantage of this methodology is that it could not taken into account the hidden trend in increasing and decreasing in the maximum rates of rainfall. This latter can be modeled by so-called the hidden Markov mixture model which represents our future interest to study this phenomenon.

tel: +96-47807921448

Acknowledgement

The authors would like to thank the engineering and science colleges as well as all anonymous reviewers in advance for their constructive comments.

  1. Conflict of interest: Authors state no conflict of interest.

References

[1] Brutsaert W. Evaporation into the atmosphere: theory, history and applications. Vol. 1. Amsterdam: Springer Science and Business Media; 2013. Search in Google Scholar

[2] Fletcher TD, Andrieu H, Hamel P. Understanding, management and modeling of urban hydrology and its consequences for receiving waters: a state of the art. Adv Water Res. 2013;51:261–79. 10.1016/j.advwatres.2012.09.001Search in Google Scholar

[3] Rojas R, Feyen L, Bianchi A, Dosio A. Assessment of future flood hazard in Europe using a large ensemble of bias-corrected regional climate simulations. J Geophys Res Atmospheres. 2012;117(D17):1–22.10.1029/2012JD017461Search in Google Scholar

[4] Alfieri L, Burek P, Feyen L, Forzieri G. Global warming increases the frequency of river floods in Europe. Hydrol Earth Sys Sci. 2015;19(5):2247–60. 10.5194/hess-19-2247-2015Search in Google Scholar

[5] Tabari H. Climate change impact on flood and extreme precipitation increases with water availability. Scientific Reports. 2020;10(1):1–10. 10.1038/s41598-020-70816-2Search in Google Scholar

[6] Wilks DS. Comparison of three-?parameter probability distributions for representing annual extreme and partial duration precipitation series. Water Resour Res. 1993;29(10):3543–9. 10.1029/93WR01710Search in Google Scholar

[7] Meneghini R, Jones JA, Iguchi T, Okamoto K, Kwiatkowski J. Statistical methods of estimating average rainfall over large space-timescales using data from the TRMM precipitation radar. J Appl Meteorol. 2001;40(3):568–85. 10.1175/1520-0450(2001)040<0568:SMOEAR>2.0.CO;2Search in Google Scholar

[8] Arvind G, Kumar PA, Karthi SG, Suribabu CR. Statistical analysis of 30 years rainfall data: a case study. IOP Confer Ser Earth Environ Sci. 2017;80(1):012067. 10.1088/1755-1315/80/1/012067Search in Google Scholar

[9] Panda A, Sahu N. Trend analysis of seasonal rainfall and temperature pattern in Kalahandi, Bolangir and Koraput districts of Odisha, India. Atmospheric Sci Lett. 2019;20(10):e932. 10.1002/asl.932Search in Google Scholar

[10] Nyatuame M, Owusu-Gyimah V, Ampiaw F. Statistical analysis of rainfall trend for Volta Region in Ghana. Int J Atmospheric Sci. 2014;2014:1–11.10.1155/2014/203245Search in Google Scholar

[11] Asfaw A, Simane B, Hassen A, Bantider A. Variability and time series trend analysis of rainfall and temperature in northcentral Ethiopia: a case study in Woleka sub-basin. Weather Climate Extremes. 2018;19:29–41. 10.1016/j.wace.2017.12.002Search in Google Scholar

[12] Praveen B, Talukdar S, Mahato S, Mondal J, Sharma P, Islam ARMT, et al., Analyzing trend and forecasting of rainfall changes in India using non-parametrical and machine learning approaches. Scientific Reports. 2020;10(1):1–21. 10.1038/s41598-020-67228-7Search in Google Scholar

[13] Fruhwirth-Schnatter S, Celeux G, Robert CP. Handbook of mixture analysis. Boca Raton, FL: CRC Press, 2019. 10.1201/9780429055911Search in Google Scholar

[14] Parzen E, Tanabe K, Kitagawa G. Selected papers of Hirotugu Akaike. USA: Springer Science and Business Media; 2012. Search in Google Scholar

[15] Schwarz G. Estimating the dimension of a model. Annals Statistics. 1978;6(2):461–4. 10.1214/aos/1176344136Search in Google Scholar

[16] Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc B (Statist Methodol). 2002;64(4):583–639. 10.1111/1467-9868.00353Search in Google Scholar

[17] Watanabe S. A widely applicable Bayesian information criterion. J Mach Learn Res. 2013;14(Mar):867–97. Search in Google Scholar

[18] Green PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika. 1995;82(4):711–32. 10.1093/biomet/82.4.711Search in Google Scholar

[19] Marin JM, Robert CP. Bayesian essentials with R. New York: Springer; 2014. 10.1007/978-1-4614-8687-9Search in Google Scholar

[20] Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. Boca Raton, FL: CRC Press; 2013. 10.1201/b16018Search in Google Scholar

[21] Kadhem SK, Hewson P, Kaimi I. Using hidden Markov models to model spatial dependence in a network. Aust N Z J Stat. 2018;60(4):423–46. 10.1111/anzs.12250Search in Google Scholar

[22] Celeux G, Forbes F, Robert CP, Titterington DM. Deviance information criteria for missing data models. Bayesian Anal. 2006;1(4):651–73. 10.1214/06-BA122Search in Google Scholar

[23] Leahy PG, Foley AM. Wind generation output during cold weather-driven electricity demand peaks in Ireland. Energy 2012;39(1):48–53. 10.1016/j.energy.2011.07.013Search in Google Scholar
Received: 2021-08-23
Revised: 2021-10-11
Accepted: 2021-10-23
Published Online: 2022-03-22

© 2022 Amjad Hussein and Safaa K. Kadhem, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Performance of a horizontal well in a bounded anisotropic reservoir: Part I: Mathematical analysis
  3. Key competences for Transport 4.0 – Educators’ and Practitioners’ opinions
  4. COVID-19 lockdown impact on CERN seismic station ambient noise levels
  5. Constraint evaluation and effects on selected fracture parameters for single-edge notched beam under four-point bending
  6. Minimizing form errors in additive manufacturing with part build orientation: An optimization method for continuous solution spaces
  7. The method of selecting adaptive devices for the needs of drivers with disabilities
  8. Control logic algorithm to create gaps for mixed traffic: A comprehensive evaluation
  9. Numerical prediction of cavitation phenomena on marine vessel: Effect of the water environment profile on the propulsion performance
  10. Boundary element analysis of rotating functionally graded anisotropic fiber-reinforced magneto-thermoelastic composites
  11. Effect of heat-treatment processes and high temperature variation of acid-chloride media on the corrosion resistance of B265 (Ti–6Al–4V) titanium alloy in acid-chloride solution
  12. Influence of selected physical parameters on vibroinsulation of base-exited vibratory conveyors
  13. System and eco-material design based on slow-release ferrate(vi) combined with ultrasound for ballast water treatment
  14. Experimental investigations on transmission of whole body vibration to the wheelchair user's body
  15. Determination of accident scenarios via freely available accident databases
  16. Elastic–plastic analysis of the plane strain under combined thermal and pressure loads with a new technique in the finite element method
  17. Design and development of the application monitoring the use of server resources for server maintenance
  18. The LBC-3 lightweight encryption algorithm
  19. Impact of the COVID-19 pandemic on road traffic accident forecasting in Poland and Slovakia
  20. Development and implementation of disaster recovery plan in stock exchange industry in Indonesia
  21. Pre-determination of prediction of yield-line pattern of slabs using Voronoi diagrams
  22. Urban air mobility and flying cars: Overview, examples, prospects, drawbacks, and solutions
  23. Stadiums based on curvilinear geometry: Approximation of the ellipsoid offset surface
  24. Driftwood blocking sensitivity on sluice gate flow
  25. Solar PV power forecasting at Yarmouk University using machine learning techniques
  26. 3D FE modeling of cable-stayed bridge according to ICE code
  27. Review Articles
  28. Partial discharge calibrator of a cavity inside high-voltage insulator
  29. Health issues using 5G frequencies from an engineering perspective: Current review
  30. Modern structures of military logistic bridges
  31. Retraction
  32. Retraction note: COVID-19 lockdown impact on CERN seismic station ambient noise levels
  33. Special Issue: Trends in Logistics and Production for the 21st Century - Part II
  34. Solving transportation externalities, economic approaches, and their risks
  35. Demand forecast for parking spaces and parking areas in Olomouc
  36. Rescue of persons in traffic accidents on roads
  37. Special Issue: ICRTEEC - 2021 - Part II
  38. Switching transient analysis for low voltage distribution cable
  39. Frequency amelioration of an interconnected microgrid system
  40. Wireless power transfer topology analysis for inkjet-printed coil
  41. Analysis and control strategy of standalone PV system with various reference frames
  42. Special Issue: AESMT
  43. Study of emitted gases from incinerator of Al-Sadr hospital in Najaf city
  44. Experimentally investigating comparison between the behavior of fibrous concrete slabs with steel stiffeners and reinforced concrete slabs under dynamic–static loads
  45. ANN-based model to predict groundwater salinity: A case study of West Najaf–Kerbala region
  46. Future short-term estimation of flowrate of the Euphrates river catchment located in Al-Najaf Governorate, Iraq through using weather data and statistical downscaling model
  47. Utilization of ANN technique to estimate the discharge coefficient for trapezoidal weir-gate
  48. Experimental study to enhance the productivity of single-slope single-basin solar still
  49. An empirical formula development to predict suspended sediment load for Khour Al-Zubair port, South of Iraq
  50. A model for variation with time of flexiblepavement temperature
  51. Analytical and numerical investigation of free vibration for stepped beam with different materials
  52. Identifying the reasons for the prolongation of school construction projects in Najaf
  53. Spatial mixture modeling for analyzing a rainfall pattern: A case study in Ireland
  54. Flow parameters effect on water hammer stability in hydraulic system by using state-space method
  55. Experimental study of the behaviour and failure modes of tapered castellated steel beams
  56. Water hammer phenomenon in pumping stations: A stability investigation based on root locus
  57. Mechanical properties and freeze-thaw resistance of lightweight aggregate concrete using artificial clay aggregate
  58. Compatibility between delay functions and highway capacity manual on Iraqi highways
  59. The effect of expanded polystyrene beads (EPS) on the physical and mechanical properties of aerated concrete
  60. The effect of cutoff angle on the head pressure underneath dams constructed on soils having rectangular void
  61. An experimental study on vibration isolation by open and in-filled trenches
  62. Designing a 3D virtual test platform for evaluating prosthetic knee joint performance during the walking cycle
  63. Special Issue: AESMT-2 - Part I
  64. Optimization process of resistance spot welding for high-strength low-alloy steel using Taguchi method
  65. Cyclic performance of moment connections with reduced beam sections using different cut-flange profiles
  66. Time overruns in the construction projects in Iraq: Case study on investigating and analyzing the root causes
  67. Contribution of lift-to-drag ratio on power coefficient of HAWT blade for different cross-sections
  68. Geotechnical correlations of soil properties in Hilla City – Iraq
  69. Improve the performance of solar thermal collectors by varying the concentration and nanoparticles diameter of silicon dioxide
  70. Enhancement of evaporative cooling system in a green-house by geothermal energy
  71. Destructive and nondestructive tests formulation for concrete containing polyolefin fibers
  72. Quantify distribution of topsoil erodibility factor for watersheds that feed the Al-Shewicha trough – Iraq using GIS
  73. Seamless geospatial data methodology for topographic map: A case study on Baghdad
  74. Mechanical properties investigation of composite FGM fabricated from Al/Zn
  75. Causes of change orders in the cycle of construction project: A case study in Al-Najaf province
  76. Optimum hydraulic investigation of pipe aqueduct by MATLAB software and Newton–Raphson method
  77. Numerical analysis of high-strength reinforcing steel with conventional strength in reinforced concrete beams under monotonic loading
  78. Deriving rainfall intensity–duration–frequency (IDF) curves and testing the best distribution using EasyFit software 5.5 for Kut city, Iraq
  79. Designing of a dual-functional XOR block in QCA technology
  80. Producing low-cost self-consolidation concrete using sustainable material
  81. Performance of the anaerobic baffled reactor for primary treatment of rural domestic wastewater in Iraq
  82. Enhancement isolation antenna to multi-port for wireless communication
  83. A comparative study of different coagulants used in treatment of turbid water
  84. Field tests of grouted ground anchors in the sandy soil of Najaf, Iraq
  85. New methodology to reduce power by using smart street lighting system
  86. Optimization of the synergistic effect of micro silica and fly ash on the behavior of concrete using response surface method
  87. Ergodic capacity of correlated multiple-input–multiple-output channel with impact of transmitter impairments
  88. Numerical studies of the simultaneous development of forced convective laminar flow with heat transfer inside a microtube at a uniform temperature
  89. Enhancement of heat transfer from solar thermal collector using nanofluid
  90. Improvement of permeable asphalt pavement by adding crumb rubber waste
  91. Study the effect of adding zirconia particles to nickel–phosphorus electroless coatings as product innovation on stainless steel substrate
  92. Waste aggregate concrete properties using waste tiles as coarse aggregate and modified with PC superplasticizer
  93. CuO–Cu/water hybrid nonofluid potentials in impingement jet
  94. Satellite vibration effects on communication quality of OISN system
  95. Special Issue: Annual Engineering and Vocational Education Conference - Part III
  96. Mechanical and thermal properties of recycled high-density polyethylene/bamboo with different fiber loadings
  97. Special Issue: Advanced Energy Storage
  98. Cu-foil modification for anode-free lithium-ion battery from electronic cable waste
  99. Review of various sulfide electrolyte types for solid-state lithium-ion batteries
  100. Optimization type of filler on electrochemical and thermal properties of gel polymer electrolytes membranes for safety lithium-ion batteries
  101. Pr-doped BiFeO3 thin films growth on quartz using chemical solution deposition
  102. An environmentally friendly hydrometallurgy process for the recovery and reuse of metals from spent lithium-ion batteries, using organic acid
  103. Production of nickel-rich LiNi0.89Co0.08Al0.03O2 cathode material for high capacity NCA/graphite secondary battery fabrication
  104. Special Issue: Sustainable Materials Production and Processes
  105. Corrosion polarization and passivation behavior of selected stainless steel alloys and Ti6Al4V titanium in elevated temperature acid-chloride electrolytes
  106. Special Issue: Modern Scientific Problems in Civil Engineering - Part II
  107. The modelling of railway subgrade strengthening foundation on weak soils
  108. Special Issue: Automation in Finland 2021 - Part II
  109. Manufacturing operations as services by robots with skills
  110. Foundations and case studies on the scalable intelligence in AIoT domains
  111. Safety risk sources of autonomous mobile machines
  112. Special Issue: 49th KKBN - Part I
  113. Residual magnetic field as a source of information about steel wire rope technical condition
  114. Monitoring the boundary of an adhesive coating to a steel substrate with an ultrasonic Rayleigh wave
  115. Detection of early stage of ductile and fatigue damage presented in Inconel 718 alloy using instrumented indentation technique
  116. Identification and characterization of the grinding burns by eddy current method
  117. Special Issue: ICIMECE 2020 - Part II
  118. Selection of MR damper model suitable for SMC applied to semi-active suspension system by using similarity measures
https://doi.org/10.1515/eng-2022-0024
Keywords for this article
rainfall amounts; Bayesian mixture modeling; cumulative distribution; prediction interval; posterior predictive distribution
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Performance of a horizontal well in a bounded anisotropic reservoir: Part I: Mathematical analysis
  3. Key competences for Transport 4.0 – Educators’ and Practitioners’ opinions
  4. COVID-19 lockdown impact on CERN seismic station ambient noise levels
  5. Constraint evaluation and effects on selected fracture parameters for single-edge notched beam under four-point bending
  6. Minimizing form errors in additive manufacturing with part build orientation: An optimization method for continuous solution spaces
  7. The method of selecting adaptive devices for the needs of drivers with disabilities
  8. Control logic algorithm to create gaps for mixed traffic: A comprehensive evaluation
  9. Numerical prediction of cavitation phenomena on marine vessel: Effect of the water environment profile on the propulsion performance
  10. Boundary element analysis of rotating functionally graded anisotropic fiber-reinforced magneto-thermoelastic composites
  11. Effect of heat-treatment processes and high temperature variation of acid-chloride media on the corrosion resistance of B265 (Ti–6Al–4V) titanium alloy in acid-chloride solution
  12. Influence of selected physical parameters on vibroinsulation of base-exited vibratory conveyors
  13. System and eco-material design based on slow-release ferrate(vi) combined with ultrasound for ballast water treatment
  14. Experimental investigations on transmission of whole body vibration to the wheelchair user's body
  15. Determination of accident scenarios via freely available accident databases
  16. Elastic–plastic analysis of the plane strain under combined thermal and pressure loads with a new technique in the finite element method
  17. Design and development of the application monitoring the use of server resources for server maintenance
  18. The LBC-3 lightweight encryption algorithm
  19. Impact of the COVID-19 pandemic on road traffic accident forecasting in Poland and Slovakia
  20. Development and implementation of disaster recovery plan in stock exchange industry in Indonesia
  21. Pre-determination of prediction of yield-line pattern of slabs using Voronoi diagrams
  22. Urban air mobility and flying cars: Overview, examples, prospects, drawbacks, and solutions
  23. Stadiums based on curvilinear geometry: Approximation of the ellipsoid offset surface
  24. Driftwood blocking sensitivity on sluice gate flow
  25. Solar PV power forecasting at Yarmouk University using machine learning techniques
  26. 3D FE modeling of cable-stayed bridge according to ICE code
  27. Review Articles
  28. Partial discharge calibrator of a cavity inside high-voltage insulator
  29. Health issues using 5G frequencies from an engineering perspective: Current review
  30. Modern structures of military logistic bridges
  31. Retraction
  32. Retraction note: COVID-19 lockdown impact on CERN seismic station ambient noise levels
  33. Special Issue: Trends in Logistics and Production for the 21st Century - Part II
  34. Solving transportation externalities, economic approaches, and their risks
  35. Demand forecast for parking spaces and parking areas in Olomouc
  36. Rescue of persons in traffic accidents on roads
  37. Special Issue: ICRTEEC - 2021 - Part II
  38. Switching transient analysis for low voltage distribution cable
  39. Frequency amelioration of an interconnected microgrid system
  40. Wireless power transfer topology analysis for inkjet-printed coil
  41. Analysis and control strategy of standalone PV system with various reference frames
  42. Special Issue: AESMT
  43. Study of emitted gases from incinerator of Al-Sadr hospital in Najaf city
  44. Experimentally investigating comparison between the behavior of fibrous concrete slabs with steel stiffeners and reinforced concrete slabs under dynamic–static loads
  45. ANN-based model to predict groundwater salinity: A case study of West Najaf–Kerbala region
  46. Future short-term estimation of flowrate of the Euphrates river catchment located in Al-Najaf Governorate, Iraq through using weather data and statistical downscaling model
  47. Utilization of ANN technique to estimate the discharge coefficient for trapezoidal weir-gate
  48. Experimental study to enhance the productivity of single-slope single-basin solar still
  49. An empirical formula development to predict suspended sediment load for Khour Al-Zubair port, South of Iraq
  50. A model for variation with time of flexiblepavement temperature
  51. Analytical and numerical investigation of free vibration for stepped beam with different materials
  52. Identifying the reasons for the prolongation of school construction projects in Najaf
  53. Spatial mixture modeling for analyzing a rainfall pattern: A case study in Ireland
  54. Flow parameters effect on water hammer stability in hydraulic system by using state-space method
  55. Experimental study of the behaviour and failure modes of tapered castellated steel beams
  56. Water hammer phenomenon in pumping stations: A stability investigation based on root locus
  57. Mechanical properties and freeze-thaw resistance of lightweight aggregate concrete using artificial clay aggregate
  58. Compatibility between delay functions and highway capacity manual on Iraqi highways
  59. The effect of expanded polystyrene beads (EPS) on the physical and mechanical properties of aerated concrete
  60. The effect of cutoff angle on the head pressure underneath dams constructed on soils having rectangular void
  61. An experimental study on vibration isolation by open and in-filled trenches
  62. Designing a 3D virtual test platform for evaluating prosthetic knee joint performance during the walking cycle
  63. Special Issue: AESMT-2 - Part I
  64. Optimization process of resistance spot welding for high-strength low-alloy steel using Taguchi method
  65. Cyclic performance of moment connections with reduced beam sections using different cut-flange profiles
  66. Time overruns in the construction projects in Iraq: Case study on investigating and analyzing the root causes
  67. Contribution of lift-to-drag ratio on power coefficient of HAWT blade for different cross-sections
  68. Geotechnical correlations of soil properties in Hilla City – Iraq
  69. Improve the performance of solar thermal collectors by varying the concentration and nanoparticles diameter of silicon dioxide
  70. Enhancement of evaporative cooling system in a green-house by geothermal energy
  71. Destructive and nondestructive tests formulation for concrete containing polyolefin fibers
  72. Quantify distribution of topsoil erodibility factor for watersheds that feed the Al-Shewicha trough – Iraq using GIS
  73. Seamless geospatial data methodology for topographic map: A case study on Baghdad
  74. Mechanical properties investigation of composite FGM fabricated from Al/Zn
  75. Causes of change orders in the cycle of construction project: A case study in Al-Najaf province
  76. Optimum hydraulic investigation of pipe aqueduct by MATLAB software and Newton–Raphson method
  77. Numerical analysis of high-strength reinforcing steel with conventional strength in reinforced concrete beams under monotonic loading
  78. Deriving rainfall intensity–duration–frequency (IDF) curves and testing the best distribution using EasyFit software 5.5 for Kut city, Iraq
  79. Designing of a dual-functional XOR block in QCA technology
  80. Producing low-cost self-consolidation concrete using sustainable material
  81. Performance of the anaerobic baffled reactor for primary treatment of rural domestic wastewater in Iraq
  82. Enhancement isolation antenna to multi-port for wireless communication
  83. A comparative study of different coagulants used in treatment of turbid water
  84. Field tests of grouted ground anchors in the sandy soil of Najaf, Iraq
  85. New methodology to reduce power by using smart street lighting system
  86. Optimization of the synergistic effect of micro silica and fly ash on the behavior of concrete using response surface method
  87. Ergodic capacity of correlated multiple-input–multiple-output channel with impact of transmitter impairments
  88. Numerical studies of the simultaneous development of forced convective laminar flow with heat transfer inside a microtube at a uniform temperature
  89. Enhancement of heat transfer from solar thermal collector using nanofluid
  90. Improvement of permeable asphalt pavement by adding crumb rubber waste
  91. Study the effect of adding zirconia particles to nickel–phosphorus electroless coatings as product innovation on stainless steel substrate
  92. Waste aggregate concrete properties using waste tiles as coarse aggregate and modified with PC superplasticizer
  93. CuO–Cu/water hybrid nonofluid potentials in impingement jet
  94. Satellite vibration effects on communication quality of OISN system
  95. Special Issue: Annual Engineering and Vocational Education Conference - Part III
  96. Mechanical and thermal properties of recycled high-density polyethylene/bamboo with different fiber loadings
  97. Special Issue: Advanced Energy Storage
  98. Cu-foil modification for anode-free lithium-ion battery from electronic cable waste
  99. Review of various sulfide electrolyte types for solid-state lithium-ion batteries
  100. Optimization type of filler on electrochemical and thermal properties of gel polymer electrolytes membranes for safety lithium-ion batteries
  101. Pr-doped BiFeO3 thin films growth on quartz using chemical solution deposition
  102. An environmentally friendly hydrometallurgy process for the recovery and reuse of metals from spent lithium-ion batteries, using organic acid
  103. Production of nickel-rich LiNi0.89Co0.08Al0.03O2 cathode material for high capacity NCA/graphite secondary battery fabrication
  104. Special Issue: Sustainable Materials Production and Processes
  105. Corrosion polarization and passivation behavior of selected stainless steel alloys and Ti6Al4V titanium in elevated temperature acid-chloride electrolytes
  106. Special Issue: Modern Scientific Problems in Civil Engineering - Part II
  107. The modelling of railway subgrade strengthening foundation on weak soils
  108. Special Issue: Automation in Finland 2021 - Part II
  109. Manufacturing operations as services by robots with skills
  110. Foundations and case studies on the scalable intelligence in AIoT domains
  111. Safety risk sources of autonomous mobile machines
  112. Special Issue: 49th KKBN - Part I
  113. Residual magnetic field as a source of information about steel wire rope technical condition
  114. Monitoring the boundary of an adhesive coating to a steel substrate with an ultrasonic Rayleigh wave
  115. Detection of early stage of ductile and fatigue damage presented in Inconel 718 alloy using instrumented indentation technique
  116. Identification and characterization of the grinding burns by eddy current method
  117. Special Issue: ICIMECE 2020 - Part II
  118. Selection of MR damper model suitable for SMC applied to semi-active suspension system by using similarity measures
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Winner of the OpenAthens UX Award 2026
Winner of the OpenAthens UX Award 2026
Have an idea on how to improve our website?
Please write us.
© 2026 De Gruyter Brill
Downloaded on 7.3.2026 from https://www.degruyterbrill.com/document/doi/10.1515/eng-2022-0024/html
Scroll to top button