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
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
posted by DR. JOJI at 12:00 AM
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