HYDROGEOLOGY - STATISTICAL APPROACH

Hydrogeology is a science, which deals with the origin, distribution and properties of water on the earth including that in then atmosphere in the form of water vapor. The hydro geologic phenomenon is highly erratic, complex and random in nature and hence they can be interpreted only in a probabilistic sense (i.e. statistical analysis)

Basic Requirements

Statistical analysis deals with the computation of sampled data. Where as in Hydrology, sampled data are experimental data, which measured through the experimental and historical data, which are collected from natural phenomenon.

Objectives

The basic objectives are,

§ Interpretation of observation
§ Extraction of maximum information from hydrological data
§ Presentation of hydrologic information in condensed form

Statistical Methods

Probability

It is the ratio of number of “ favorable” cases to the total number of equally likely cases.

Number of Favorable cases
P (A) = ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾
Total number of equally likely cases

A probability is number which ranges from zero (event which cannot occur) to One (event which can occur)

Return Period

Return period is represented by the following formula

R= 1- (1-1/T) n


R called risk that will occur at least once in successive years

MEASURES OF CENTRAL TENDENCY

Mean

It is familiar to most persons by name average. It can be classified into three types

§ Arithmetic mean
§ Geometric mean
§ Harmonic Mean

Median

It is defined as the middle value or the arithmetic mean of two middle values of the observed data.

Mode

Mode is discrete variables as the value occurring most frequently, while in continuous variable it is the peak of the probability density.

Skewness

The third moment of the observed data is called as skewness coefficient is defined as the ratio of the third central moment to the cube of standard deviation

Kurtosis

Kurtosis is the degree of measure of flatness or peaked ness in the region about the mode of a frequency curve.

Time Series Analysis

A time series is defined as a collection of magnitude belonging to different time-periods of some variable or composite of variables (fig 5.1). It portrays the variation of a variable through time. If we find that a certain underlying and persistent tend of a series has continued foe decades it will not be a wise decision to ignore the possibility that it will continue in the future. The belief that past behaviour of a series may continue into the future is the basis for statistical forecasting. It further classified into two groups.

Stationary

In this time series the mean, variance and moment of marginal probability distribution are completely unaffected by a shift in the time origin.

Non-stationary

In this case, the different segment of time series are dissimilar in one or more aspects.


The original data plotted may be a highly irregular. The trend of this curve is smoothed using 3 years or 5 years running averages. If either of these does not fit, then we resort to 7 years running averages.

Analysis Of Secular Trend

Trend is characteristic of any time series over a period of time. It may be upward or downward depending upon the set of observed data. It is very much useful in the analysis of water level data.






















Fig 5.1 Time series analysis and secular trend analysis


First degree curve
Second degree curve
Third degree curve
Exponential curve
Reciprocal
Modified exponential curve
Geometry curve
Logistic curve



Regression Analysis

Regression analysis is a study of functional relationship between the variables in order to provide a prediction or fore casting. Further this analysis, we can calculate the correlation coefficient, which is the degree of association of correlation that exists between the two variables. The greater value of r2 the better is the fit and the more useful the regression equations for prediction

Y= a +bx

Correlation Analysis

The degree of relationship between the variables under consideration is measured through the correlation analysis. Correlation would be called non-linear when the amount of change in one variable does not bear a constant ratio to the amount of change in the other variable

GROUND WATER HYDRAULICS

GROUND WATER HYDRAULICS

Ground water hydraulics refers to movement of ground water into and out of geological formation (aquifer). Aquifer properties and fluid properties control the movement of water. The Darcy’s law is the principle of all type of ground water hydraulics

DARCY’S LAW

Law: The specific discharge (v) through the cylindrical porous media is directly proportional to head loss and inversely proportional to the length of the flow path when the flow is laminar in nature.
ig 1: Darcy’s Law experimetns





\
and


k is constant – ve sign indicate that, hydraulic gradient decreases with increase in head.



Q= - KiA
Where
i - hydraulic gradient

Darcy law is valid for ground water flow in any direction is space. In 1956 Hubert pointed out that the constant k is not a function of porous medium but also of the fluid. The new version of Darcy’s law becomes





In above equation cd2 is function of medium where rg/m is properties of fluid alone.

\ k = cd2 and K = k rg/m
Where

k - intrinsic permeability

Validity of Darcy’s Law

Darcy’s law is valid only for linear flow. The lower and upper limits of Darcy’s law are represented by Reynold’s number (Re). Darcy’s law is valid as long as Re is between 1 and 10. In most of the ground water flow conditions it is less than one.

HYDROCHEMICAL PROVINCE OF INDIA

This has been classified on the basis of geo-chemical character and chemical composition of water influenced by Physiographic, Orographic, Geological and Climatologically conditions. Ground water occurring in sedimentary rocks of India has been divided into three major hydrogeochemical provinces namely Bicarbonates, Bicarbonate chloride and chloride

Bicarbonate Province

In this province ground water is characterized by high percentage of HCO3 ion generally exceeding 90% of the total ions. The ration of alkaline earth to Na is above 2. EC value 75 micro mho/cm.

Bicarbonate – Chloride Province

In this province HCO3- is dominant ion. The Cl- and Na, also become significant. The ration of Alkaline earth to Na+ falls below 1 and EC value reaching about 1500 micro mhos/cm.

Chloride Province

Chloride is dominant in this province and concentration of the Cl exceeds 50% of the total anions and exceeding of Na over alkaline earth Metal ions. EC value exceeds 1500 micro mho/cm.

AQUIFERS AND THEIR PROPERTIES

1. AAquifers are saturated geological formations which yield sufficient quantities of water to wells, springs, or seepages.
   
   In general there are 3 types of aquifer system
   
   1. Unconfined aquifer: An unconfined aquifer is one in which a water table varies in undulating form and in slope, depending areas of recharge and discharge. It is also known as a water table aquifer. Water in a well penetrating in unconfined aquifer is at atmospheric pressure and does not rise above the water table.
   
   2. Confined aquifer: A confined aquifer is bounded above and below by an aquiclude. In a confined aquifer the pressure of the water is usually higher than that of the atmosphere
   
   3.Leaky aquifer: A leaky aquifer also known, as a semi-confined aquifer is an aquifer whose upper and lower boundaries are aquitard or one boundary is an aquitard and other is aquiclude. Water is free to move through the aquitard either upward or downward. If a leaky aquifer is in hydrogeological equilibrium, the water level in a well tapping it may coincide with the water table.
   
   Aquifers are generally aerially extensive and may be overlain or underlain by a confining bed, which may be defined as a relatively impermeable material stratigraphically adjacent to one or more aquifer. Clearly there are various types of confining beds. The following types are well established
   
   Aquiclude : A saturated but relatively impermeable material that does not yield appreciates quantities of water to well. Clay is example
   Aquifuge : A relatively impermeably formation neither containing nor transmitting water; solid granite belongs in this category
   Aquitard : A saturated but poorly permeable stratum that impedes ground water movement and does not yield water freely to wells but that may transmit appreciable water to of from adjacent aquifer. Example is sandy clay.

Aquifer properties

Porosity

It defined as the ratio of open pore space to the bulk volume.

h = Vp / Vb
Where,
h = porosity
vp = volume of pore space
Vb = Bulk volume

Effective porosity

It is the ratio of volume of interconnected pore space to the bulk volume. In ground water hydraulic the effective porosity is generally used.

Permeability

It is ability of aquifer to transmit the water through it. If the material having more porosity, will have the higher permeability

Void ratio

It is ratio of value of void to the volume of mineral grains

Specific storage

The specific storage of a saturated confined aquifer is the volume of water that a unit value of aquifer release from storage under a unit declines in hydraulic head. The dimension of specific storage is per liter

Hydraulic Conductivity (K)

It is defined as the volume of water that will pass through a porous medium in unit hydraulic gradient through a unit area measured at right to the duration of flow. Dimension Liter per day

Storativity or storage coefficient (S)

It is the volume of water realised from storage per unit surface area of the aquifer per unit decline in component of hydraulic head moment to that surface. It is dimensionless quantity

Specific yield

It is the volume of water through an unconfined aquifer releases from storage per unit area of aquifer per unit decline of the water table. This expressed in percentage

Transmissivity

Transmissivity is the product of the hydraulic conductivity (k) and saturated thickness of the aquifer (D). Dimension is m2/day

Hydraulic Diffusivity

This is the ratio of Transmissivity to storage of saturated aquifer. Dimension is m2/day.

Hydraulic Conductance

It is the reciprocal of the leakage or leakage coefficient. It often expressed in days

C= D¢/K¢

Leakage factor (L)

It is a measure of spatial distribution of the leakage through an aquitard into a leaky aquifer and vice versa. It dimension is meter

v

HARD ROCK HYDROGEOLOGY

The “Hard rock” involves the crystalline volcanic & carbonate rocks along with the Pre-Cambrian rocks, occupying nearly 22, 27, 2000 km2 out of the total landmass of 32, 57,200 sq.km.

Unweathered & Weathered Crystalline Rocks

The storage capacity of weathered or un-weathered hard rocks is restricted to the interconnected system of fractures, joints & fissures. Tensile joints have storage capacity & hydraulic conductivity as compare to tensile fractures. Extensive thickness of saturated weathered zone has more productive aquifer system. Exploration shows that fractured withered zones water yielding within a depth of 100m to 150m.The hydraulic conductivity of the rock mass is a function of fracture spacing / frequency, fracture aperture & fracture conductivity. i.e.

K= ge3/12V.S

Where
e - fracture aperture
v - kinematic porosity, and
S – fracture spacing

The total porosity in fracture medium qt is

q t = qk + q d + q r
Where,

qk - Effective flow porosity
qd - Differentiation porosity
qr - Residual porosity.

PDTA of such rocks show that initially stored water in fracture system released then pressure within the fracture is reduced.

Volcanic Rocks

In India volcanic rocks extrusion is mostly confined as a Deccan traps of central India covering 51,0000 km2 & are hydro geologically unique. The lower massive & upper vesicular horizons make a one trap flow & based on their thickness the Deccan traps are classified as


1. Upper trap 450m
2. Middle trap 1200m
3. Lower trap 150m

The weathered portion as a recharge area, fractured traps, vesicular flows & intertrappeans controls the hydrogeology of Deccan Traps. The ground water occurs under both water table & confined conditions. A hydraulic continuity does exist between the consecutive massive & vesicular units. The weathered and jointed zones in the massive units act as leaking aquitard. Issuance of springs along the slopes of hill & on high grounds due to impervious nature of red boles, flow contacts etc. is a common feature of deccan traps. Secondary porosity because of weathering, brecciation, shrinkage cracks, joints & fracture causes effective permeability with high values of transmissivity. The aquifer mostly an isotropic & heterogeneous and water is mostly bicarbonate-chloride type.

Carbonate Rocks

These are the rocks having 50% of carbonate minerals by weight like limestone, dolomite etc. They have less primary porosity while the secondary porosity due to sink holes, karstification are the major controlling factor over the hydrogeology of carbonate rocks. Chemical composition of solute, temperature variation, climate & solubility strength is the major factors governing the development of secondary porosity.

High Mg calcite ® Aragonite ® Low Mg calcite ® dolomite
¾¾¾¾¾¾¾¾¾¾¾¾ Solubility decreases.¾¾¾¾¾¾¾¾¾¾¾®

Karstic Aquifers

Karstic aquifers are three end members type and they are, a) Porous (granular) b) fissure (fracture) c) conduit (cavernous). Like other aquifers they are further classified as confined, un-confined, leaky & semi-confined.

Summary

Ground water occurrences in hard rock are very much controlled by secondary porosity & permeability, which is ultimately developed by fracture & joints. The concept of fractured aquifers with double porosity system should consider before going for exploration in hard rock terrain.

ISLAND HYDROGEOLOGY

The islands of India are broadly classified into

Oceanic Island

These are originated within ocean by volcanic activity or tectonic or due to the activity of microorganism. E.g. Lakshadwep group of Islands.

Deltaic Island

These are formed at the confluence of river mouth. e.g Sunderban in Bay of Bengal.

Continental Island

These are part of Main Island but later separated from main land. e.g. Diu group of islands

Origin of Island

Volcanic eruption from oceanic ridge or sea beds results oceanic islands and submergence of these with gradual growth of corals around them results atolls and ultimately coral islands. They are generally formed in tropical climate. An atoll is characterized by ring like structure consisting of barrier reef system totally or partially by central lagoon.

The Coral Reef

The coral reefs are the largest animal mode structure in the world. The coral reef can be divided as:

Fringing reef : Grow along coastal region and connected to
shore.
Barrier reef : Grow along coastal region but are farther from
shore.
Atoll : Atolls are large rings of corals that exist under
sea volcanic cones.


The coral reef is composed of calcareous and material derived from atoll and has very high % of CaCo3 (87%). The beach rock consists of moderately well cemented calc arenites. The beach sediments of lagoon consist of various types of coral materials of fine sand to cobble size.

The volcanic island comes in contact with shore by both marine and fresh water environments. It is proved that digenesis process occurs more rapidly in fresh water phreatic environment and it results in dissolution and/or precipitation of carbonate minerals forming well cemented litho units than those of under vadose or marine environment. The end product is low magnesian calcite and caliches. The accumulation of CaCo3 decreases porosity and permeability of the profile.

Water needs is met in various way, as there is tremendous scarcity of water. People have adjusted their life style for bathing and washing and they generally use common ponds for this. Rainwater is the main source for fresh water. In these regions rainfall intensity is 1.5 to 3.5 and 80 to 200 days are rainy.

Although overall geology of an atoll is interesting, its significance is limited to few meters from mean sea level. In oceanic island fresh ground water occurs as a lens floating over saline water. The hydro dynamic balance of fresh and saline water determines the shape and movement of interface and may be controlled by some of the following factors:

1. Water table fluctuation due to diurnal tides
2. Seasonal fluctuation of water table due to recharge or draft
3. Dispersion
4. Molecular diffusion

Due to the above controlling factors there is an alternate up and down movement of the interface. If the fresh ground water flux is high the transition zone will be thin.

In small island due to high permeability almost all the rain falling onto the ground seeps below and a part about 7.15%of the rain fall is intercepted and evaporated before reaching the ground. After rainfall water table rises temporarily and within 2-3 days readjusted and water level stabilise and there is as much as only 5% outflow into the sea.

For water balance the following formula is used. The recharge to ground water lens = rain fall – interception – evapotranspiration.

Ground water utilisation = Evapotranspiration + mixing + pumping + outflow

For water balance study monthly water budgeting or weekly water budgeting gives appropriate value of recharge. The main consumer of ground water is coconut plant because one coconut tree consumes 40 lpd and density of coconut trees is 25 000 – 35000 sq km. But draft through plant is slow, steady and spread uniformly.

Control of saline Water up Coning

Well should be just few cm below mean water table & spread out all over the fresh water lens. Pumping should proceed in slow, steady rate and should be spread in wide area. Pumping site should located preferably in less permeable aquifer.

Ground Water Pollution

Disposal of pollutant in Small Island is a problem since water table is shallow. Special care should be taken for ground water contamination. The spacing between latrine and well should be at least 15m. But due to high density of population remedial measure is not easy implement. In such area precautions should be taken before using ground water.