Significance level (
\r\n\t
",isbn:"978-1-80355-463-1",printIsbn:"978-1-80355-462-4",pdfIsbn:"978-1-80355-464-8",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,isSalesforceBook:!1,isNomenclature:!1,hash:"0c1bf8695b453c7d16f51eb4ec3c3ae6",bookSignature:"Dr. Redmond R. Shamshiri and Dr. Sanaz Shafian",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11343.jpg",keywords:"Digital Farming, Wireless Sensors, Internet-of-Things, Digital Twin, Cloud Computing, Big Data Analysis, Data Labeling, Data Sharing, Agriculture 4.0, Precision Technology, E-agriculture, Automated Farms",numberOfDownloads:38,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 10th 2021",dateEndSecondStepPublish:"November 18th 2021",dateEndThirdStepPublish:"January 17th 2022",dateEndFourthStepPublish:"April 7th 2022",dateEndFifthStepPublish:"June 6th 2022",dateConfirmationOfParticipation:null,remainingDaysToSecondStep:"6 months",secondStepPassed:!0,areRegistrationsClosed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:"Dr. Shamshiri is a Member of the International Society of Precision Agriculture and a Member of the American Society of Agricultural and Biological Engineering. He is a scientist at the Leibniz-Institut für Agrartechnik und Bioökonomie working toward digitization of agriculture for food security.",coeditorOneBiosketch:"Sanaz is an Assistant Professor of Smart Farming at Virginia Tech University. Prior to this, she was an assistant professor at the University of Idaho. Her expertise lies in using advanced technologies and methodologies for economically and environmentally sustainable crops and trees monitoring and management. She integrates satellite/drone images and AI to develop methodologies for environmental monitoring, crop modeling, and water, and nutrient conservation.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"203413",title:"Dr.",name:"Redmond R.",middleName:null,surname:"Shamshiri",slug:"redmond-r.-shamshiri",fullName:"Redmond R. Shamshiri",profilePictureURL:"https://mts.intechopen.com/storage/users/203413/images/system/203413.png",biography:"Dr. Redmond R. Shamshiri holds a Ph.D. in agricultural automation with a focus on control systems and dynamics. He is a scientist at the Leibniz-Institut für Agrartechnik und Bioökonomie working toward digitization of agriculture for food security. His main research fields include simulation and modeling for closed-field plant production systems, LPWAN sensors, wireless control, and autonomous navigation. His work has appeared in over 100 publications, including peer-reviewed journal papers, book chapters, and conference proceedings. He is a member of the Adaptive AgroTech Consultancy Network and serves as a section editor and reviewer for various high-ranking journals in the field of smart farming.",institutionString:"Leibniz Institute of Agricultural Engineering and Bio-economy",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"7",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Leibniz Institute for Agricultural Engineering Potsdam-Bornim",institutionURL:null,country:{name:"Germany"}}}],coeditorOne:{id:"429704",title:"Dr.",name:"Sanaz",middleName:null,surname:"Shafian",slug:"sanaz-shafian",fullName:"Sanaz Shafian",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y00003CPbhJQAT/Profile_Picture_1629955207151",biography:"Sanaz is an Assistant Professor of Smart Farming at Virginia Tech University. Prior to this she was assistant professor at University of Idaho. Her expertise lies in remote sensing research, with a focus on using advanced technologies and methodologies for economically and environmentally sustainable crops and trees monitoring and management. She integrates satellite/drone images and AI to develop methodologies for environmental monitoring, crop modeling and water and nutrient conservation and she has published widely on these topics. She has been involved in several USDA projects. With University of Idaho, she led an educational and outreach project to initiate Precision Agriculture certificate. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"68077",title:"Analytical Study of Environmental Impacts and Their Effects on Groundwater Hydrology",doi:"10.5772/intechopen.88002",slug:"analytical-study-of-environmental-impacts-and-their-effects-on-groundwater-hydrology",body:'\nFor thousands of years, man has survived living in arid regions of the world solely by skillfully managing that vital but scarce resource called water [1]. Out of the two, the surface water and the groundwater, the groundwater has always been more important for survival due to its intrinsic quality of natural preservation. Groundwater is a vital source of fresh water for domestic, agricultural, and industrial use. Currently contribution of groundwater is almost 34% of the total annual water supply. Water consumption is increasing day by day due to continuous development of the economy, industrialization, and changes in life patterns, which cumulatively results in shortage of usable water.
\nTo meet the increasing water demands, reliance on groundwater has been rapidly increasing, especially in the arid and semiarid regions leading to water exhaustion and overconsumption of groundwater, causing ecological problems such as decreased water levels, water pollution, seawater intrusion, and deterioration of water quality. The recharge of groundwater occurs both naturally and artificially. The natural recharge occurs through the process of infiltration where water percolates from the surface to the bed of the aquifer. But due to rapid development and stupendous growth of population in the recent past, the areas for natural infiltration have been lessening day by day; hence the scope for natural recharge of the groundwater is also declining [2].
\nThe combination of decreasing water availability and increasing water demand can lead to drastic water shortages. Groundwater exploration involves knowledge of hydrological properties of various geological materials such as porosity, permeability, storage coefficient, transmissivity, and specific yield or in other words holding and discharge capabilities of geological materials.
\nIn the nature, water resources and water demand are unevenly distributed both spatially and temporally. It is these uneven distributions that make the groundwater hydrology more complex and dynamic in its nature and form. Ironing out of the variations and equitable juxtaposition of haves and have-nots in both demand and resource is the ultimate goal of all hydrological knowledge.
\nThese variations in the groundwater levels are with respect to physical location and space. Physical properties including type of soil, groundwater depth, porosity of vadose zone, rainfall patterns, and hydrogeology tend to vary the groundwater recharge spatially. Fluctuations in the groundwater levels are generally greater in the areas of low drainage density than those in regions of moderate to high drainage density. The factors like weathering intensity, presence of fractures, and drainage density control the quantity of groundwater. In such regions groundwater flow and quantity are not controlled by highly weathered dykes in shallow unconfined aquifers. The phenomena like fracturing, weathering, and faulting increase the permeability of rocks and the recharge which controls the fluctuations in groundwater levels. For the fluctuations in groundwater levels in terrains of hard rocks, several studies have been carried out. Fractured and weathered rocks carry the groundwater under unconfined conditions, and the major source for groundwater recharge is rainfall. Due to downward seepage of rainfall, the unconfined aquifers are recharged in the unsaturated zone [3].
\nVariations in the phreatic levels, chemical concentration levels, biological concentration levels, and fluid properties of the groundwater may be described with respect to time as seasonal variations and secular variations.
\nSuch variations are periodic. The changes in the water level due to some seasonal happenings such as rainfall, storms, and irrigation pumping are referred to as seasonal variations. Water-level fluctuation in summer and winter is also considered under the same type. The lowest variations in water levels occur in winter season, while the highest occur during late spring. At the end of the irrigation season in an irrigated area, the lowest variations in water levels normally occur where frozen ground is not a factor. \nFigure 1\n shows the variations in the water levels for frozen ground areas in winter are periodic [4].
\nSeasonal variations [
Such variations are nonperiodic and show the change in the water level over several years, which cover the dry and wet seasons and the related groundwater fluctuations. Long-term fluctuations in water levels are produced when rainfall is above or below the mean, during alternating a series of dry and wet years. \nFigure 2\n shows the long records of groundwater levels and rainfall and illustrates that rainfall is not an accurate indicator of variations in groundwater levels [4].
\nSecular variations [
Groundwater, as the world’s most vital natural resource for the reliable provision of potable water supply, is affected by urbanization. Due to rapid urbanization and increasing industrial activities, the need for fresh water has increased in the past few decades. Almost 50% of the world population lives in urban areas, and the proportion is expected to increase in the coming decades. Urbanization brings many benefits such as increased job and education opportunities, cultural activity, and economic diversification. However, unplanned urban growth is also leading to challenges such as the overexploitation of water resources. Furthermore, land-use changes and anthropogenic activities such as surface sealing due to streets and buildings, flood control, forest management, and irrigation modify the infiltration and movement of water. The authors [5] have shown that due to urbanization, built-up area increased by 271%, water bodies decreased by 46%, and bare land decreased by 129% in the study area. These modifications linked with urbanization often lead to groundwater resource deterioration [6].
\nThere are many conditions which interrupt the subsurface water balance, and as a result groundwater levels are lowered. A few of such conditions are listed below:
Groundwater recharge is reduced by paving the surface areas and building the storm sewers. When the surface area is paved, it stops the surface water entry into the ground, and as a result the groundwater recharge is reduced. Also when storm sewers are built, they store the amount of surface water, stop the water entry into the ground, and result in reduction of recharge.
Pumping wells increase the groundwater discharge which results in lowering of groundwater table.
Collection of wastewater in sanitary sewers also decreases the groundwater recharge.
Huge reduction in groundwater recharge occurred nowadays due to excess plastic wastage.
Groundwater is our major source of water. Due to climate change, rapid urbanization, industrial activities, and intensive agricultural practices have put a tremendous pressure on groundwater. Groundwater depletion occurs when the pumping rates are excessively higher than the rate of replenishment.
\nThe extreme use of groundwater resources can have serious concerns, such as uplifting and seismic activities, ecological environment deterioration, land subsidence, vegetation degradation, livelihoods for rural poor, and food security implications. In view of the shrinking groundwater resources, it is important to develop effective techniques and methods to study the trend of groundwater storage (increase/decrease) and its recharge-discharge relationship, which can support the mitigating measures of overpumping shallow groundwater to ensure the sustainable utilization of groundwater resources [7].
\nFluctuations in groundwater due to meteorological phenomena are caused by atmospheric pressure, rainfall, wind, and frost. As stated by [8], aquifers are inherently very resilient to atmospheric variations above ground, but climate adversely alters the aquifer’s groundwater recharge, thus introducing uncertainties in spatial pattern definitions.
\nVariations in atmospheric pressure produce fluctuations in wells penetrating confined aquifers. There is an inverse relationship between atmospheric pressure and water levels. It means that increase in atmospheric pressure will decrease the water levels and vice versa. If the changes in the atmospheric pressure are expressed in terms of a column of water, then the ratio between changes in water levels and pressure is known as barometric efficiency of an aquifer. This efficiency is expressed by the following equation:
\nwhere B = barometric efficiency of an aquifer, γ = specific weight of water [981 N/m3 or 62.4 lb/ft3], ∆h = change in piezo-metric levels, and ∆pa = change in atmospheric pressure.
\nDiscussions related to the effect of atmospheric pressure on confined and unconfined aquifers assume that no delay occurs in the balance of pressure between the aquifer and well. But in reality, the time required for movement of a finite volume of water between the surrounding aquifers and well delays the transmission of atmospheric pressure change between the aquifer and well. This delay in time depends on the properties of aquifer (i.e., storability and transmissivity) and conditions of existing boreholes (i.e., well skin effects and well bore storage). Due to imbalance of pressure between an aquifer and a well, at the instance of pressure change, previous investigators have observed that these temporary imbalances in the pressure can be treated as individual step changes in pressure applied at the well [9]. Due to travel time for percolation and surface and subsurface losses, rainfall is not considered as an accurate indicator for groundwater recharge. The travel time for vertical percolation may vary from a few minutes for permeable formations with shallow water tables to several years for low permeable formations with deep water tables. The regions that lie between semi-humid and semiarid zones with seasonal climatic conditions observe zero recharge in the groundwater due to rainfall [4].
\nIn arid and semiarid regions, due to heavy rainfalls, groundwater recharge tends to occur unlike those regions which are a combination of constant rate and periodic behavior. Physical properties including type of soil, groundwater depth, porosity of vadose zone, rainfall patterns, and hydrogeology tend to vary the groundwater recharge spatially [10].
\nWind blowing over the top of wells generates minor fluctuations in water levels. It works on the principle of vacuum pump. When wind is blowing over the top of a well casing, the air pressure within the well lowers down suddenly due to which the water level rises quickly. Once the wind passes, the air pressure within the well rises and water level falls [4].
\nIt has been observed in the regions of extreme frost that shallow water tables are reduced during the winter season and increased in early spring. These fluctuations are observed due to the presence of frost layer above the water table. Due to capillary action and transfer of vapors to the frost layer, water moves upward from water table during winter. Thermal gradient and the fact that at 0°C vapor pressure over liquid water is greater than that over ice play an important role in the migration of vapors. When mean air temperature reaches 0°C in early spring, the frost layer begins thawing from the bottom due to which meltwater percolates down in the water table [4].
\nGroundwater is an important source of fresh water with high quality for coastal communities worldwide. These sources of fresh groundwater in the coastal communities are highly affected by intrusion of seawater caused by excessive groundwater extraction and rises in sea levels. Globally increasing population will lead to rising demands of fresh water in the coming decades and will result in a decline of groundwater sources gradually. Coastal flooding will also be increased due to rise in sea levels, which may lead to seawater intrusion and coastal erosion, and as a result it will affect the biodiversity and losses of wetland [11].
\nIn response to the tides, sinusoidal fluctuations of groundwater levels occur in the coastal aquifers which are in contact with the ocean. If a simple harmonic motion varies the sea levels, a pattern of sinusoidal waves is propagated inland from the submarine outcrop of the aquifer. The time lag of given maximum increases, and inland amplitude of waves decreases with respect to distance [4].
\nIn coastal regions, tidal forces acting on an adjacent groundwater are a common feature and can be important pore water phenomena in tidal and saturated zones. Near the top of the water table, the entry of saltwater and variations in the concentration of solutes can be increased due to tidal forces in shallow unconfined aquifers. Comparative studies between tidal and water-level variations show that increase in the height of tide will increase the corresponding water levels [12].
\nFluctuations produced by the attraction of sun and moon on the crust of the earth are a result of earth tides. The following observations are analyzed based on well record:
Fluctuations occur twice in a daily cycle due to moon about 50 min later each day.
Retardation of cycle on average daily bases matches with that of moon’s transit closely.
At the lower and upper peaks, the moon’s transits and the troughs of water levels on daily bases are coincided.
Periods of full and new moon coincide with the periods of large regular fluctuations, while the periods of the first and third quarters of moon coincide with periods of small irregular fluctuations [4].
Forces of sun and moon which produce tides act in the same direction at the time of new and full moon, causing ocean tides to be greater than the average range. But at the time of the first and third quarter of moon, the forces of sun and moon which produce tides act perpendicular to each other, causing ocean tides to be smaller than the average range. At the time of coincidence of the moon’s transit with time of low water, the tidal attraction will be maximum; therefore, the load on the aquifer is reduced which allows the aquifer to expand slightly [4].
\nHistory reveals that there are varieties of effects of earthquakes on groundwater. Fluctuations like sudden rises and falls of water levels in wells, variations in spring discharges, formation of new springs, and venting of mud and water out of the ground are observed due to earthquake shocks. Such fluctuations produced due to earthquake shocks are known as
Seismic waves generated by earthquakes affect the groundwater in two major ways. One is that oscillations are produced in the groundwater levels, and second is that permanent changes occur in the groundwater levels. As groundwater remains in contact with the surface water, some variations in surface water flows are also observed. Half to one year long time variations in water level have been observed due to the response of earthquakes at a great distance from the monitoring locations [13].
\nResponse of groundwater to earthquakes is somehow complex and can be observed by different processes on varying time scales. The impact of earthquake on the groundwater is considered in three parts: before, during, and after an earthquake event. Before an earthquake, in the area of a fault zone, there will be an increase or decrease in pore pressure due to poroelastic deformation caused by variations in stresses. Increase in pore pressure will occur in compressional regime, while decrease in pore pressure will occur in extensional regime. In a confined aquifer of high permeability or in an unconfined aquifer, the variations in pore pressure will be dissipated quickly, and no significant changes in surface water flow or groundwater will be observed. Ground deformation resulted from the passage of seismic waves during an earthquake event will change the pore pressure in an aquifer. These changes occur at different frequencies, and excess pore pressure is not allowed through groundwater flow.
\nThe processes involved between an earthquake and groundwater are shaking of ground, stresses in the crust, mobilization of fines, microfractures, liquefaction, storability release, pore pressure, change in porosity, and change in permeability. Summary of relationships between earthquakes and groundwater processes is described in \nFigure 3\n.
\nRelationship between earthquake and groundwater processes.
Groundwater resources are not managed properly in different parts of the world. For the proper management of groundwater resources, simple and effective rules and regulation must be adopted. The governing regulations may be based on knowledge and practical experiences of the local region supported by scientific and field information. The groundwater management strategies are recommended to be planned such that:
Groundwater withdrawal will be adjusted as per forecasted supply and demand requirements of the future.
The renewable character of potential aquifers must be considered with optimum aquifer pump rates, well locations, and relative priority of each sub-aquifer unit within the integrated management system of the entire aquifer field.
Water quality, effect of urbanization, intensive agricultural practices, economy, social impact, and local administrative strategies should also be considered.
Recommended groundwater management practices need to scientifically determine different hydrogeological parameters such as porosity, specific yield, and hydraulic conductivity for actual water volume calculations. It is preferable to obtain estimated parameter by field techniques like the aquifer tests and their proper interpretations.
For strategic planning of groundwater reservoirs that may be replenished, the groundwater quality is significant not only for management but also for controlling the excessive exploitation possibilities. Naturally existing groundwater does not have homogenous but heterogeneous properties within the same storage. Generally, the bottom layers are saline, and, therefore, during pumping operations, the up-coning must be avoided.
Private well owners must be convinced to allow for groundwater strategic planning by avoiding haphazard and unnecessary exploitations.
Implementation of artificial recharge system in order to compensate the present deficit. Increasing groundwater recharge could counteract the projected effects of climate changes on the groundwater system.
Construction of new management system helps in monitoring the groundwater system in terms of quantity and quality.
The importance of statistical modeling and forecasting of time series data, etc., cannot be overemphasized. The benefits ranges from easy interpretability arising from visualization of results to the removal of the mysticism factor for the layman. The word ‘forecasting’ has to do with predicting the future based on data from the past and present. This is regularly done by the analysis of trends.
A routine example might be the estimation of temperature trends for some specified future date. Compared to forecasting, prediction can be seen as a term which is more general.
Forecasting methods have been applied in different areas ranging from climatology, finance, foreign exchange, etc. This has been applied in different regions of the world for better prediction and simulation. The key distinction in Information and Communication Technology (ICT) is the fact that with this technology, we can make predictions and simulations from previously obtained data. This is true and can be applied for every area while paying attention to the rules that govern them.
In this study we will be applying some statistical methods which can be adopted for the forecasting of climatic (weather) parameters in different regions of the world.
It is important to note that the predictability of the atmosphere is not perfect, this brings into context the fact that although statistical methods are necessary, results obtained are not totally accurate which is why room for errors (uncertainties) are given, albeit, a trend can be observed [1]. Statistical methods have been applied in the study of different regions for example, Daniel S. Wilks in [1] buttressed on the use of these methods on the analyses of different regions that do not necessarily have the same climatic condition. This brings into context the fact that laws are true irrespective of the region, i.e. neglecting all other factors that have little contribution to weather, the same methods can be applied in different regions to yield accurate results.
Analysis of trends can be useful in depicting and predicting the changing patterns and erraticism of some climatic parameters. This analysis gives a proper knowledge about the changing conditions of the climate and its effects, by the evaluation of meteorological parameters.
A data scientist using any tool or software for modeling and forecasting is particularly interested in the progression of these parameters (meteorological) as a function of time(t)
A very popular software for any data scientist that is willing to understand the nitty-gritty of weather forecasting is Python Programming. This paper will explain in detail the setup processes for this to help the layman get started. A dataset of temperature trend in Calabar, Nigeria will be used at the end of this chapter to test the processes explained for better visualization.
The applicability of results from forecasting cannot be underestimated because this is great information for people that depend on weather conditions like farmers, surfers, and event planners, etc. The accurate prediction of atmospheric parameters can go a long way in positively affecting the financials of the informed, as money can be saved by avoiding unnecessary cost during trying times [3]. Natural disasters like Tsunami can be predicted with the correlation of meteorological parameters, harnessing information as explained previously and then incorporating this information through machine learning into the design of forecasting systems.
We delve deeper into a review of statistical methods like the M-K test and its different variations, the Angstrom-Prescott model for the estimation of solar radiation, linear regression techniques, with a deep look into multiple linear regression which will be applied in predicting refractivity after obtaining the coefficients of the variables. Results will be obtained and explained.
With the shift going on in the world of technology, the implementation of some time series forecasting methods will be explained as well as their python implementation techniques. We often use forecasting models on time series data for the estimation of future trends of meteorological parameters.
One of the most important and widely applied test for trends involving time series is the Mann-Kendall trend test. It is mostly used for environmental and hydrological data. The test is non parametric and does not necessitate the data conforming to a particular distribution, similarly, the sensitivity of the test due to an inhomogeneous series resulting to abrupt breaks is very low [4]. The null hypothesis
The Mann-Kendall test statistic
where;
In the case where
To find the variance of
From the equation, the number of data values is represented by
We now use the results from
A decreasing trend can be discerned from results of Eq. (5) when the value of
Significance level ( | Required n |
---|---|
0.1 (10%) | ≥ 4 |
0.05 (5%) | ≥ 5 |
0.01 (1%) | ≥ 6 |
0.001 (10%) | ≥ 7 |
Significance level (
The significance of an increasing or decreasing trend is observed when the p-value of the series is lower than the significance level
The classification of this probability/significance level is important because results can be confused to be entirely true. We need to understand that the significance level of say 0.05, means that there is a 5% probability that a mistake will be made while rejecting the null hypothesis
The two easiest ways to forecast time series data by observation are the simple regression and the moving average, they both depend on historical data. The former demands mere observation of the previous trend and drawing up an extrapolation from there; this can be somewhat less accurate. The moving average has been used for forecasting meteorological data like rainfall (See reference [6]). Analyzing with regression has to do with the relationship one variable which is dependent has with one or more independent variables. We use them to check for models showing the strength of relationship between the variables and any possible future relationships [1].
This regression variation is based on the assumption that the two variables (dependent and independent variable) show a linear relationship between the intercept and the slope, similarly, there is no residual error in this regression and the value is constant across all observations.
The regression is depicted by a straight line describing the Eq. (6) above (Figure 1).
Schematic illustration of simple linear regression. The regression line,
This model is similar to that of simple linear regression, but the only exception is that it has multiple independent variables, unlike that of simple linear regression which has just the one. This can be represented by Eq. (7);
One thing to note about multiple linear regression is that the independent variables must not be collinear, i.e., they do not have to have a high correlation coefficient between each other, else there will be difficulty in assessing the relationship between the dependent and independent variables.
We also need to take note that before multiple linear regression is performed on range of data values, a linear relationship must exist between each independent variable and the dependent variable. The amount of residual error must be almost constant at each point in the model. The multiple linear regression will be applied to study and predict refractivity trend in Calabar, Nigeria. This was done with the ‘statsmodel’ package in python programming and results have been displayed in section 2.5.
A perfect meteorological equation that this regression technique can be applied to is the refractivity equation recommended by the International Telecommunication Union (ITU) shown in Eq. (8);
Eq. (8) shows the relationship between refractivity (dependent variable) and meteorological parameters (ambient temperature, atmospheric pressure, and vapor pressure) which are all independent variables.
This has been applied in [7] modeling the meteorological parameters for the accurate determination of refractivity. These meteorological parameters (Ambient Temperature, Atmospheric Pressure and Relative Humidity) have been obtained from the Nigeria meteorological Agency (NiMet), Calabar.
Results have been presented in section 2.5. From Eq. (8), we obtain the atmospheric vapor pressure
The linear regression technique can be applied to find the relationships between an independent variable and the dependent variable. We can see the explanation of this from Eq. (6).
One major example of the benefits of linear regression is the estimation of the Angstrom-Prescott coefficients of the Angstrom-Prescott model for a particular region as this relates to solar radiation. The Angstrom-Prescott model is given by [8];
where the monthly average daily extraterrestrial radiation is given by
This shows that if we have the variables ‘
For better understanding, the extraterrestrial radiation
Here,
The monthly mean length of the day (in hours) can be obtained from [9].
The above equations can be applied to estimate the coefficients using linear regression. By this we can use these coefficients to predict solar radiation for a given region.
We know that the declination angle ranges from
Yearly variation of declination angle
Klein in 1977 [10] recommended average days of the various months and corresponding angle of declination as in Table 2.
Month | Date | Day of the year (d) | declination angle ( |
---|---|---|---|
January | 17 | 17 | −20.9 |
February | 16 | 47 | −13 |
March | 16 | 75 | −2.4 |
April | 15 | 105 | 9.4 |
May | 15 | 135 | 18.8 |
June | 11 | 162 | 23.1 |
July | 17 | 198 | 21.2 |
August | 16 | 228 | 13.5 |
September | 15 | 258 | 2.2 |
October | 15 | 288 | 9.6 |
November | 14 | 318 | −18.9 |
December | 10 | 344 | −23 |
Recommended average days for various months and their corresponding declination angles [10].
Applying calculus in environmental science is important in predicting a lot of things. It can be applied to understand the impacts of parameters on the variations of other parameters that they relate to. It is important to know that calculus is the ‘mathematical study continuous change’ so this can be applied in climatology to discern the impacts of some parameters on the “continuous change” of others [11, 12, 13].
Writing the refractivity equation in terms of relative humidity
Similarly, obtaining refractivity in terms of the saturated vapor pressure
Now applying partial differentials to the equations for refractivity; Eqs. (8), (16), and (17), we obtain partial differentials relating each parameter to refractivity;
From monthly Temperature, Humidity and Atmospheric pressure data obtained for 2005–2018 from the archives of the Nigerian meteorological agency (NiMet) Calabar, the atmospheric vapor pressure and the saturated vapor pressure can be obtained by applying these parameters in Eqs. (9) and (10) (Figure 3).
Map of study area showing Calabar as a coastal area (left) and the exact location of the Nigerian meteorological agency (NiMet) where the data was obtained (right).
With the python software installed, the next step will be installing an IDE (integrated development environment). The easiest IDE to use is the Jupyter Notebook. This IDE displays results as you code.
We will walk you through the processes for analyzing data by using the data for Calabar in the south of Nigeria, collected from the archives of the Nigeria meteorological agency (NiMet). Research has been done in this area in climatology [14, 15, 16, 17, 18], but with the application of python and the Mann-Kendall test can give more meaning to time series data.
We need to install the python package for the Mann-Kendall test called ‘
Numpy
Scipy
For handling and cleaning data we need the ‘
We want to analyze maximum ambient temperature data for 20 years in Calabar.
In the Jupyter notebook, the first step will be to import the respective packages. We must also note that for our examples in the Appendices, we stored the excel file containing the data used for the analysis in the same folder as the python file for easy reference.
Before we perform the Mann-Kendall test, we need to import the excel file titled ‘
We now perform the seasonal M-K test for the dry season variation, we import the excel file titled ‘
For the wet season variation, the excel file titled ‘
We can now perform the seasonal Mann-Kendall test on the wet season data.
There are other variations of the Mann-Kendall test along with their python implementation [19]. These can be used depending on the data obtained and the aim of the test.
Hamed and Rao Modified MK Test (
Yue and Wang Modified MK Test (
Modified MK test using Pre-Whitening method (
Modified MK test using Trend Free Pre-Whitening method (
Multivariate MK Test (
Regional MK Test (
Correlated Multivariate MK Test (
Correlated Seasonal MK Test (
Partial MK Test (
Theil-Sen’s Slope Estimator (
Seasonal Theil-Sen’s Slope Estimator (
For the annual variation in Figure 4, results show that there is a trend in the series as the p-value is less than the significance level (0.05). The positive Z value (observed from
Mann-Kendall trend of maximum ambient temperature.
For the dry season variation observed in Figure 5, results show that there is a trend in the series. The positive Z value of the dry season trend observed from
Seasonal trend of maximum ambient temperature for dry and wet season.
For the wet season variation observed also in Figure 5, results show that there is a trend in the series. The positive Z value from
These results are in agreement with Agbo et al. [2] for the same region.
To understand the relationship between refractivity and all parameters relating to it, we adopt Eq. (18) by substituting obtained and calculated data.
From the data obtained at the Nigerian Meteorological Agency (NiMet) Calabar, and adopting Eq. (9) and (10) we obtain the total annual values for the meteorological parameters as;
Results from the gradients of the differential equations in Eq. (19) show that the vapor pressure and saturated vapor pressure contributes more to the variation of refractivity. The relative humidity similarly has a high gradient; this can be physically explained by relating the water vapor content of the atmosphere to the variation of refractivity.
Correlation matrix of atmospheric parameters and refractivity.
The correlation plot of refractivity and all other meteorological parameters is shown in Figure 6. Results agree with that of the differential equations in Eq. (19). As seen in Eq. (19), the correlation plot showed that the atmospheric vapor pressure and relative humidity had high positive relationships with refractivity. The saturated vapor pressure however has a low correlation coefficient compared to the high gradient in Eq. (19); this can be interpreted thus; that the variation of the saturated vapor pressure has a relatively high contribution to the variation of refractivity, but the saturated vapor pressure does not have a similar trend to that of refractivity.
Multiple linear regression has been applied to relate refractivity with obtained meteorological parameters. The goal is to obtain an equation that relates refractivity to meteorological parameters through Multiple Linear Regression (MLG). Using Eq. (8) to calculate refractivity, we show results in Table 3. As part of the conditions for carrying out multiple linear regression, we have to test for collinearity between the independent variables. We see from the correlation matrix in Figure 6 that the independent variables are not collinear, hence this satisfies the criteria for carrying out MLG.
Year | Pressure | Temperature | Humidity | Refractivity (N) |
---|---|---|---|---|
2005 | 1005.15 | 300.23 | 87.15 | 388.88 |
2006 | 1005.38 | 300.17 | 85.38 | 385.73 |
2007 | 1005.50 | 300.10 | 84.84 | 384.74 |
2008 | 1005.44 | 300.21 | 86.00 | 387.11 |
2009 | 1005.83 | 300.29 | 83.36 | 383.75 |
2010 | 1005.46 | 300.71 | 83.26 | 385.62 |
2011 | 1005.80 | 300.12 | 87.49 | 388.83 |
2012 | 1005.75 | 300.44 | 87.97 | 391.57 |
2013 | 1005.74 | 300.03 | 87.07 | 387.69 |
2014 | 1005.92 | 299.79 | 85.15 | 383.38 |
2015 | 1006.55 | 300.03 | 85.68 | 385.83 |
2016 | 1006.97 | 300.70 | 85.69 | 389.73 |
2017 | 1007.09 | 300.58 | 86.33 | 389.90 |
2018 | 1007.02 | 300.52 | 84.58 | 386.84 |
Data of obtained meteorological parameters and refractivity.
From our analysis we obtain the coefficients (slopes) of the variables (meteorological parameters) and the intercept from Table 4 to form the equation below;
1617.97 | 51.05 | −31.69 | 2.30 × 10−11 | −1731.72 | −1504.23 | |
0.17 | 0.05 | 3.25 | 8.75 × 10−03 | 0.05 | 0.28 | |
5.68 | 0.13 | 44.90 | 7.22 × 10−13 | 5.39 | 5.96 | |
1.53 | 0.02 | 68.62 | 1.05 × 10−14 | 1.48 | 1.58 |
Output of the multiple linear regression showing the coefficients (C) of each parameter and their standard error (
The above equation can be used to accurately predict the variation of refractivity, given the values of the meteorological parameters. Table 4 shows these results obtained from the multiple linear regression. The values for the predicted refractivity (Predicted N) was gotten from Eq. (20) by substituting the values of the meteorological parameters. This equation is more straight forward that the equation recommended by ITU as all the variables and coefficients are all linear with respect to refractivity.
Figure 7 shows the trend of refractivity calculated from Eq. (8) with that of predicted refractivity, calculated from Eq. (20). The residual error seen from Table 5 shows relatively constant values (in agreement with our MLG conditions), and a small deviation from the original values of refractivity.
Comparison plot of annual refractivity and predicted refractivity.
Year | N | Predicted N | Residuals |
---|---|---|---|
2005 | 388.88 | 388.87 | 0.005 |
2006 | 385.73 | 385.85 | −0.121 |
2007 | 384.74 | 384.69 | 0.056 |
2008 | 387.11 | 387.09 | 0.025 |
2009 | 383.75 | 383.54 | 0.204 |
2010 | 385.62 | 385.72 | −0.109 |
2011 | 388.83 | 388.89 | −0.060 |
2012 | 391.57 | 391.45 | 0.124 |
2013 | 387.69 | 387.74 | −0.048 |
2014 | 383.38 | 383.45 | −0.074 |
2015 | 385.83 | 385.74 | 0.091 |
2016 | 389.73 | 389.65 | 0.076 |
2017 | 389.90 | 389.97 | −0.072 |
2018 | 386.84 | 386.93 | −0.095 |
Residual output derived from the results of the coefficients, showing the predicted refractivity values compared to the refractivity values to give the residuals.
From Table 4 probability values (p-values) of the parameters are all less than the significance level (5% = 0.05; 95% confidence level), this shows that the variation agrees with the alternative hypothesis and shows a trend relating the independent variables to the dependent variables.
Results from Figure 7 show the minimal error between the predicted refractivity and the calculated refractivity. Table 5 shows the values for both as well as the residual error between them. This shows that the error is small and thus, Eq. (20) can be adopted for the prediction of refractivity for the study area. This equation can be modified and refractivity N can be gotten in terms of other parameters like the saturated vapor pressure and the atmospheric vapor pressure.
There are myriads of ways in which weather can be forecasted and this arises from the understanding of basic meteorological parameters and how they behave in the atmosphere; and also from the understanding of the role of statistics in climate research [21]. Research in this area has been reviewed to give a better understanding of the different techniques for analyzing trends; which include, Linear Regression (Multiple and Simple), the Mann-Kendall trend test [22, 23] (to test for trends in a time series variation), the Angstrom-Prescott model for estimating solar radiation as well as the python implementation of some various techniques.
The multiple linear regression technique was applied to model an equation to accurately predict the trend for refractivity in the study location, the simple linear regression technique has been explained as well as accurate methods for its application in the predicting/estimation of the Angstrom-Prescott coefficients. These coefficients can be gotten for specific regions and can be accurately applied to predict solar radiation in that region.
Results from the multiple linear regression gave an accurate model for the prediction of refractivity in the region after the residual error between the calculated refractivity and predicted refractivity was minimal.
The Mann-Kendall original and seasonal test has been applied to analyze the maximum temperature in Calabar, Nigeria for the annual and seasonal (dry and wet season) variation respectively, and results show that the annual, dry season and wet season had increasing variations (after having positive Kendall Z-values of 2.52, 3.23, 4.04 respectively) and they were all increasing significantly at 5% (0.05) level of significance after their p-values were all less than 0.05 agreeing with Agbo and Ekpo [23].
The relationship between refractivity and other meteorological parameters relating to it was discerned using partial differential equations giving the gradient of each with refractivity; this was compared with results from the correlation matrix to show that the water vapor contents of the atmosphere contributes significantly to the variation of refractivity.
The author will like to acknowledge the Nigerian Meteorological Agency (NiMet) Calabar for providing the necessary data for applying in this study.
The author will also like to express his thanks and appreciation to the editor, whose comments greatly improved the chapter.
The author declares no conflict of interest.
This will import the above installed packages into the workspace.
The excel file titled ‘
We can now perform the Mann-Kendall test
The excel file titled ‘
We can now perform the Mann-Kendall test
The excel file titled ‘
We can now perform the Mann-Kendall test
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