Week 3 Lecture.pdf

WEEK 3 PRECIPITATION Part 2 of 2 WEEK 3 PRECIPITATION ADEQUACY OF RAINGAUGE STATIONS ESTIMATION OF MISSING RAINFALL DATA CONVERSION OF POINT RAINFALL TO AREAL RAINFALL PRESENTATION OF RAINFALL DATA CONSISTENCY OF RAINFALL DATA  ADEQUACY OF...

WEEK 3 PRECIPITATION Part 2 of 2 WEEK 3 PRECIPITATION ADEQUACY OF RAINGAUGE STATIONS ESTIMATION OF MISSING RAINFALL DATA CONVERSION OF POINT RAINFALL TO AREAL RAINFALL PRESENTATION OF RAINFALL DATA CONSISTENCY OF RAINFALL DATA  ADEQUACY OF RAINGAUGE STATIONS where: N = optimal number of stations ε = allowable degree of error in the estimation of mean rainfall, usually taken as 10% Cv = coefficient of variation of rainfall values at the existing m stations EXAMPLE A catchment has six raingauge stations. In a year, the annual rainfall recorded by the gauges are as follows: For a 10% error in the estimation of the mean rainfall, calculate the optimum number of stations in the catchment.  NORMAL RAINFALL Average value of rainfall at a particular date, month or year over a specified 30-year period, which are recomputed every decade. ESTIMATION OF MISSING DATA SIMPLE ARITHMETIC. NORMAL RATIO METHOD INVERSE DISTANCE WEIGHTING.  Given: Annual Precipitation Values (P1, P2, P3,..., Pm) Normal Precipitation Values (N1, N2, N3,..., Nm and Nx) Find: Annual Precipitation at Station X, Px SIMPLE ARITHMETIC NORMAL RATIO PROCEDURE METHOD If Normal Annual Precipitation at other If Normal Annual Precipitations vary stations are within 10% of the Normal considerably Annual Precipitation at station X EXAMPLE The normal annual rainfall at stations A, B, C, and D in a basin are 80.97, 67.59, 76.28 and 92.01 cm respectively. In the year 1975, the station D was inoperative and the stations A, B and C recorded annual precipitations of 91.11, 72.23 and 79.89 cm respectively. Estimate the rainfall at station D in that year.  Given: Precipitation Values at Gauged Sites(P1, P2. P3,..., Pm) Distance from the Ungauged Site to the each Gauged Site (d1, d2, d3,..., dm) Find: Precipitation at Ungauged Site X, Px INVERSE DISTANCE WEIGHTING METHOD EXAMPLE Precipitation data are unavailable at a proposed development area in a watershed. However, precipitation data at four stations surrounding the development are complete and reliable. The available data are given in the following table. Calculate precipitation P in the area in inches / hour. CONVERSION OF POINT RAINFALL TO AREAL RAINFALL Hydrological analysis requires knowledge of the rainfall over an area, such as over a catchment. ARITHMETICAL MEAN. THIESSEN-POLYGON. ISOHYETAL METHOD.  ARITHMETICAL MEAN METHOD Can be used if rainfall at various stations show little variation Given: Annual Precipitation Values (P1, P2. P3,..., Pm) _ Find: Mean Precipitation of the Area, P In practice, this method is rarely used.  THEISSEN POLYGON METHOD rainfall recorded at each station is given a weightage on the basis of an area closest to the station. Steps: 1. Draw lines joining adjacent gauges 2. Draw perpendicular bisectors to the lines created in step 1 3. Extend the lines created in step 2 in both directions to form representative areas for the gauges 4. Compute the representative area for each gauge 5. Compute the areal average using the formula: is the where weightage factor  THEISSEN POLYGON METHOD Steps: 1. Draw lines joining adjacent gauges 2. Draw perpendicular bisectors to the lines created in step 1 3. Extend the lines created in step 2 in both directions to form representative areas for the gauges 4. Compute the representative area for each gauge 5. Compute the areal average using the formula: THEISSEN POLYGON METHOD  ISOHYETAL METHOD ISOHYET - a line joining points of equal rainfall magnitude this method estimates the mean precipitation across an area by drawing lines of equal precipitation. Steps: 1. Construct isohyets (rainfall contours) 2. Compute area between each pair of isohyets (Ai) 3. Compute the average precipitation for each pair of adjacent isohyets (Pi) 4. Compute areal average using the formula: or use the direct formula EXAMPLE In a catchment area, approximated by a circle of diameter 100 km, four rainfall stations are situated inside the catchment and one station is outside in its neigh-bourhood. The coordinates of the centre of the catchment and of the five stations are given below. Also given are the annual precipitation recorded by the five stations in 1980. Determine the average annual precipitation by the Thiessen-mean method. EXAMPLE EXAMPLE The isohyets due to storm in a catchment are shown in the figure below, and the area of the catchment bounded by isohyets were tabulated as below: Estimate the mean precipitation due to the storm. PRESENTATION OF RAINFALL DATA MASS CURVE OF RAINFALL. HYETOGRAPH. MOVING AVERAGE.  MASS CURVE OF RAINFALL plot of accumulated rainfall against time, plotted in chronological order records from float type and weighing bucket type gauges are of this form  HYETOGRAPHS plot of intensity of rainfall against the time interval derived from the mass curve and is usually represented as a bar chart  MOVING AVERAGE a technique of smoothening out the high frequency fluctuations of a time series and to enable the trend, if any, to be noticed.  TEST FOR CONSISTENCY OF RECORD inconsistencies relevant to the recording of rain gauge due to significant changes may arise in the rainfall data of a station that could be felt from the time the significant change took place COMMON CAUSES OF INCONSISTENCY OF RECORDS shifting of a raingauge station to a new location the neighborhood of the station undergoing a marked change change in ecosystem due to calamities occurrence of observational records checking for inconsistency could be done by double-mass curve technique  DOUBLE-MASS CURVE TECHNIQUE based on the principle that when each recorded data comes from the same parent population, they should be consistent. Steps: 1. Sort the data in descending order, starting from the latest year. 2. Calculate the cumulative precipitation for both precipitation of a specific station X (i.e. ΣPx) and the average of the group of base stations (i.e. ΣPav) 3. Plot the values of ΣPx against ΣPav 4. Check for the break in the slope. this indicates a change in precipitation regime of station X 5. Precipitation values at station X beyond the period of change of regime is corrected using the relation: